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Reiner Anderl, Peter Binde
Simulations with NX
Reiner Anderl Peter Binde
Simulations with NX Kinematics, FEA, CFD, EM and Data Management. With numerous examples of NX 9
The authors: Prof. Dr.-Ing. Reiner Anderl, Technische Universität Darmstadt Peter Binde, Dr. Binde Ingenieure, Design & Engineering GmbH, Wiesbaden Translated by the authors with the help of Dimitri Albert, Jan Helge Bøhn, Martin Geyer and Andreas Rauschnabel
Distributed in North and South America by Hanser Publications 6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA Fax: (513) 527-8801 Phone: (513) 527-8977 www.hanserpublications.com Distributed in all other countries by Carl Hanser Verlag Postfach 86 04 20, 81631 Munich, Germany Fax: +49 (89) 98 48 09 www.hanser-fachbuch.de The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cataloging-in-Publication Data is on file with the Library of Congress. Bibliografische Information der deutschen Bibliothek: Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar. All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, with out permission in writing from the publisher. © Carl Hanser Verlag, Munich 2014 Copy editing: Jürgen Dubau, Jan Helge Bøhn Production Management: Andrea Reffke Coverconcept: Marc Müller-Bremer, www.rebranding.de, Munich Coverdesign: Stephan Rönigk Typeset, printed and bound by Kösel, Krugzell Printed in Germany ISBN 978-1-56990-479-4 E-Book ISBN 978-1-56990-480-0
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1 Learning Tasks, Learning Objectives, and Important Prerequisites for Working with the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Work Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Working with the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Motion-Simulation (Multibody Dynamics) . . . . . . . . . . . . . . . . 2.1
11
Introduction and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Classifications of MBD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Learning Tasks on Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Steering Gear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Top-down Development of the Steering Lever Kinematics . . . . . . . . . . . . . . 2.2.3 Collision Check on Overall Model of the Steering System . . . . . . . . . . . . . . Learning Tasks on Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Drop Test on Vehicle Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Learning Tasks on Co-Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Balancing a Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11 12 14 14 15 15 33 50 59 59 68 68
3 Design-Simulation FEM (Nastran) . . . . . . . . . . . . . . . . . . . . . . . . .
79
2.2
2.3 2.4
3.1
Introduction and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.1.1 Linear Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.1.2 Nonlinear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.1.3 Influence of the Mesh Fineness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.1.4 Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.1.5 Eigenfrequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.1.6 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.1.7 Linear Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
VI
Contents
3.2
Learning Tasks on Design Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.2.1 Notch Stress at the Steering Lever (Sol101) . . . . . . . . . . . . . . . . . . . . . . . . 91 3.2.2 Temperature Field in a Rocket (Sol153) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4 Advanced Simulation (FEM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
149
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.1.1 4.1.2 4.1.3 4.1.4
Sol 101: Linear Static and Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sol 103: Natural Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sol 106: Nonlinear Static . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sol 601/701: Advanced Nonlinear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Learning Tasks on Linear Analysis and Contact (Sol 101/103) . . . . . 4.2.1 Stiffness of the Vehicle Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Size and Calculation of a Coil Spring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Natural Frequencies of the Vehicle Frame . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Clamping Seat Analysis on the Wing Lever with Contact . . . . . . . . . . . . . . . 4.3 Learning Tasks Basic Non-Linear Analysis (Sol 106) . . . . . . . . . . . . . . . 4.3.1 Analysis of the Leaf Spring with Large Deformation . . . . . . . . . . . . . . . . . . . 4.3.2 Plastic Deformation of the Brake Pedal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Learning Tasks Advanced Nonlinear (Sol 601) . . . . . . . . . . . . . . . . . . . . 4.4.1 Snap Hook with Contact and Large Deformation . . . . . . . . . . . . . . . . . . . . . .
151 151 152 152 154 154 185 199 207 229 229 239 249 249
5 Advanced Simulation (CFD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
271
5.1 5.2
Principle of Numerical Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Learning Tasks (NX-Flow) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 5.2.1 Flow Behavior and Lift Forces at a Wing Profile . . . . . . . . . . . . . . . . . . . . . . 273
6 Advanced Simulation (EM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1
6.2
Principles of Electromagnetic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Electromagnetic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Material Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.4 Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.5 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.6 Electrokinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.7 Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.8 Magnetostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.9 Magnetodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.10 Full Wave (High Frequency) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Installation and Licensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
297 298 299 300 302 303 306 306 306 307 307 307 308
Contents VII
6.3
Learning Tasks (EM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 6.3.1 Coil with Core, Axisymmetric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 6.3.2 Coil with Core, 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 6.3.3 Electric Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
7 Management of Analysis and Simulation Data . . . . . . . . . . . 7.1
351
Introduction and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 CAD/CAE Integration Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Solutions with Teamcenter for Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Learning Tasks on Teamcenter for Simulation . . . . . . . . . . . . . . . . . . . . 7.2.1 Carrying out an NX CAE Analysis in Teamcenter . . . . . . . . . . . . . . . . . . . . . 7.2.2 Which CAD Model Belongs to which FEM Model? . . . . . . . . . . . . . . . . . . . . 7.2.3 Creating Revisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
351 351 352 354 355 362 365
8 Manual Analysis of a FEM Example . . . . . . . . . . . . . . . . . . . . . . . .
371
8.1 Task Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 8.2 Idealization and Choice of a Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 8.3 Analytical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 8.4 Space Discretization for FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 8.5 Setting up and Solving the FEA System of Equations . . . . . . . . . . . . . . 374 8.6 Analytical Solution Compared with Solution from FEA . . . . . . . . . . . . . 376
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index
379
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Preface
Virtual product development has gained significant importance in particular through the integration of 3D solid based modeling, analysis and simulation. Supported by the rapid enhancement of modern information and communication technology application integrated virtual product development has become an essential contribution in higher engineering education, continuing education as well as in industrial advanced and on-the-job training. Since 2003 Technische Universität Darmstadt has been selected and approved as PACE university and has become a part of the international PACE network. PACE stands for Partners for the Advancement of Collaborative Engineering Education and is a sponsoring program initiated by General Motors Corp. (in Germany Adam Opel GmbH). PACE is driven by General Motors Corp., Autodesk, HP (Hewlett Packard), Siemens, Oracle, and further well acknowledged companies of the virtual product development branch (www. pacepartners.org). Donations and sponsoring through the PACE partner companies has facilitated the preparation and the publishing of this book. This publication has been developed based on cooperation between Dr. Binde Ingenieure – Design & Engineering GmbH (www.drbinde.de) and the Division of Computer Integrated Design within the department of Mechanical Engineering of Technische Universität Darmstadt (www.dik.maschinenbau.tu-darmstadt.de). We thank very much Mr. Haiko Klause for his support to chapter 7 and Mr. Andreas Rauschnabel for his contribution to the Motion and FEM examples for Version 9 of the CAD system NXTM. Furthermore we are grateful for the support of Carl Hanser Verlag, mainly Mrs. Julia Stepp. A very special thank you is dedicated to Prof. Dr. Jan Helge BØhn who supported us through his excellent cross-reading. Last but not least we thank all readers who encouraged us to prepare this book also in English. We wish all readers and users a successful application of the selected examples and hopefully a beneficial knowledge acquisition usable for both, the successful graduation and the successful knowledge application during the industrial career. August 2014 Prof. Dr.-Ing. Reiner Anderl Dr.-Ing. Peter Binde
1
Introduction
Engineering science has seen significant changes take place during the past two decades. These changes have been driven by a powerful development of information and communication technologies and their introduction into both the product development process and the products themselves. In essence, it has enabled computer integrated virtual product development, complete with integrated 3D modeling, analysis, simulation, and optimization. The primary goal of virtual product development is the efficient development of innovative product solutions that satisfy the customers’ needs. Consequently, the integration of computer-based methods into the digital workflow of the product development process has become critical to the success of virtual product development. Engineering, designing, and detailing are all essential tasks for the development of innovative product solutions, as is the ability to accurately predict the product’s behavior subject to the multitude of potential use cases and operating conditions. Fortunately, with the continuous improvement of information and communication technologies, and with the subsequent improvements in integration of computer aided design, analysis, simulation, and optimization, it has become increasingly easier to complete these essential product development tasks. Information and communication technologies (ICT) are increasingly influencing the product development process, especially as the process becomes increasingly virtualized. This influence results from: Rapid information acquisition from sources worldwide; Availability of new computer-based methods for product development and design – such as for product modeling (e. g., parametric, feature based, and knowledge-driven CAD); analysis, simulation and optimization (e. g., finite element analysis (FEA), multibody simulation (MBS), and computational fluid dynamics (CFD)); rapid validation and verification (e. g., digital mock-up (DMU)); rapid prototyping (e. g., virtually by using virtual and augmented reality, or physically by using generative manufacturing machines); and processing product data in successive process chains (so called CAX processes); and Mapping of the organizational and workflow structures within product data management (PDM) systems, with the aim to provide easy, intuitive, and immediate access to development status, progress, and results.
Impact of information and communication technologies on product development
4 1 Introduction
The concept of virtual product development has clearly been shaped by the deep penetration of ICT into the product development process, to provide seamless flows of product data. Virtual product development can be systematically achieved over an escalating set of levels (see next figure). These levels consist of: 3D CAD; Digital mock-ups; Virtual prototyping; Virtual product simulation; and Virtual factory.
Virtuality
Virtual Product Development FunctionalDigital Mockup
3D-CAD 3D CAD
Digital Mockup
+ Geometry + Assembling+ Assemblyinformation structure + Features + Parametrics
Virtual Factory
Virtual Prototype/ Virtual Product + Functional information + Material + (Software Logics)
Integration of Information
Levels of virtual product development
+ Production + Controlling + Logistics + Finances + Marketing...
Product Data Management 3D CAD is the fundamental basis.
3D CAD is the fundamental basis for describing product geometry; usually modeled as solid geometry. These digital product descriptions involve single-part modeling as well as assembly modeling, and generally describe a product structure. This modeling is typically parametric and feature-based.
DMU
Digital mock-ups (DMU) provide a visual representation of the product structure, including the part and assembly geometries. These geometries are typically approximated using triangles. When the part and assembly models are represented as solids, and complemented by material data, then mass properties, such as mass and center of gravity, can be estimated. Digital mock-ups enable virtual prototyping for simulating assembly and dis assembly processes, and for investigating collision detection.
The most important simulation methods are FEA, MBS and CFD.
Virtual prototypes – often referred to as digital prototypes – include material and physical properties in addition to part geometries and product structures. These prototypes can therefore be used to simulate the functional and physical behavior of a product while
1.1 Learning Tasks, Learning Objectives, and Important Prerequisites for Working with the Book 5
isualizing its behavior. The functional and physical modeling within a virtual prototype v tends to be application and discipline specific. Typical applications include stress analysis using finite element analysis (FEA) based on the finite element method (FEM), multi-body simulation/dynamics (MBS/MBD), or fluid dynamic simulation using computational fluid dynamics (CFD). Simulations may also integrate thermal analysis, electromagnetic analysis (EM), or kinematic analysis, or their combinations, usually based on FEA, to more fully investigate and understand the product behavior. The term virtual product refers to the aggregation of a product’s physical properties together with its logical dependencies to produce a comprehensive, interoperable product model. The term virtual factory refers to the digital representation of a factory, including its physical properties and manufacturing processes. The objective is to facilitate simulation, analysis, and optimization of factory operations, including material flows, logistics, and order processing. Product data resulting from the application of the various modeling, analysis, simulation and optimization software systems is stored as files in the product data management (PDM) system, enhanced by meta-data representing organizational and workflow information such as release status, effectivity, identification, classification, and version numbers. The increasing use of 3D CAD in industry leads to an increasing need to integrate numerical analysis, simulation, and optimization methods and tools. With this integration, product data, once it is described or generated, can then be used and reused in successive processes to avoid manual reentry errors, and to identify errors and mistakes early. This in turn enhances product quality and increases the efficiency of the virtual product development process and successive physical product realization.
The PDM system manages all product data generated through virtual product development.
■■1.1 Learning Tasks, Learning Objectives, and Important Prerequisites for Working with the Book Based on the objective to use 3D CAD data for analysis, simulation and optimization, the question of how 3D CAD data can be further used follows. For this purpose representative example scenarios for the procedures of the finite element method, the multi-body simulation, fluid dynamics and the electromagnetic simulation have been developed in this book, by which the integration of modeling, analysis and simulation will be presented. The here outlined scenarios are based on the 3D CAD system NX9 and its integral analysis and simulation modules. To facilitate understanding the methodology and to shorten the training period, a single contiguous assembly was chosen for most learning tasks of this book. This is the CAD model of the legendary Opel RAK2 that was created in student projects as a 3D CAD solid
The training content is taught on the basis of methodology examples.
6 1 Introduction
model in the past at the Department of Computer Integrated Design (DiK, TU Darmstadt), for which to take this opportunity, any party shall be gratefully acknowledged.
The CAD model of the Opel RAK2 forms the basis for learning tasks: The figure shows some sample images
A colored version of this figure is available at www.drbinde.de/index.php/en/203
In 1928, Fritz von Opel, grandson of Adam Opel, built the rocket driven cars RAK1 and RAK2 for testing purposes. With RAK2 he reached a speed record of 238 km/h on the AVUS, the Berlin high speed track, on 23/05/1928. The RAK2 was powered by 24 solid-
1.2 Work Environments 7
fuel rockets, which were filled with 120 kg of fuel. This attempt to establish the rocket engine was followed by further attempts by road, rail and air. All CAD and analysis data used or created in the learning tasks are stored in an archive file, that can be downloaded via the Internet (see following link) and should be used to reproduce the examples.
Prerequisites for working with the book
The following Internet link must be used to download the archive file. This file contains all CAD models, analysis and result files. Furthermore, the installation files for the electromagnetic solver are included in this file. The size is 188 MB. download link: www.drbinde.de/index.php/en/203 The training content is taught using practical examples. Functions of the NX system are therefore not explained isolated, but always in connection with an example. Since this is similar to learning from real-world projects, this method is efficient, memorable and modern didactic. The chapters are structured in a way that follows the didactic concept of continuous learning progress, but also build on the fundamentals of working with 3D CAD, in particular the system NX9. Therefore, knowledge of the construction of 3D parametric models and assemblies as well as general technical understanding is required, as it is usually taught in technical vocational education. The learning objective is to convey to the student designer or analysis engineer the knowledge that he or she needs to solve simple tasks using the finite element method, multibody simulation, and flow simulation within NX itself, and to develop an understanding of these technologies in general. However one must not expect that complex practical problems can immediately be solved using the intermediate level of knowledge presented in this book. This would be an excessively high claim that would be placed on the book. Instead, a novice develops into an expert by working through as many as possible practical tasks and thereby collects valuable experience. His experience thus results from successfully developed projects. This book, with its learning examples, provides important basic experiences and thus forms the basis for a systematic expandable wealth of experience.
■■1.2 Work Environments Engineering simulation problems can be subdivided into four classes: rigid bodies, elastic bodies, fluids, and electrical/magnetic bodies. Rigid body systems are simulated using Multibody Dynamics programs (MBD); elastic and also electric/magnetic bodies are simulated using the Finite Element Method (FEM); and flow tasks are simulated using Computational Fluid Dynamics (CFD).
Objective is to build a fundamental wealth of experience.
8 1 Introduction
Technical simulation can be roughly divided into four parts.
Technical Simula on Rigid Bodies Rigid Body Mechanics MBD (Mul body Dynamics)
The CAD system NX provides three modules for technical simulation.
Elas c Bodies Fluids Structural Mechanics Fluid Mechanics FEM CFD (Finite Element (Computa onal Method) Fluid Dynamics)
Electric Bodies Electromagne cs (EM) FEM (Finite Element Method)
Within the NX system there are several modules for engineering simulation. The three most important ones used in this book are (in addition to some others that are not covered here): Motion Simulation for kinematic and dynamic motion simulations with MBD; Design-Simulation FEM for simple structural, thermal, and eigenfrequency analysis; and Advanced Simulation for complex simulation tasks: This module is intended for engineers that focus on analysis. Additional simulation capabilities include modeling and simulation of complex assembly structures and the choice of various solvers for addressing particular physical phenomena. The problem domains that can be addressed include structural mechanics, thermodynamics, fluid mechanics, and electromagnetism (EM). The working environments for these modules have a common interface, and default to only include those features that are useful in the selected context. This book looks in detail at these working environments. Possibilities and limitations will be illustrated by examples.
■■1.3 Working with the Book Structure of the book
The book is organized into chapters as follows: Motion Simulation, Design Simulation, Advanced Simulation (FEM), Advanced Simulation (CFD), Advanced Simulation (EM), and manual analysis of an FEM example.
The joint forces are calculated in Motion Simulation.
First, we will explore motion simulation (Chapter 2) because this class of analysis is common in engineering design and is usually carried out first. The joint forces that are determined here are often used in subsequent strength analysis using FEM.
1.3 Working with the Book 9
The chapters can be largely worked through independently. That means, those who do not care for motion simulation, can skip that chapter. The one exception is that those interested in FEM and “Advanced Simulation (FEM)” (Chapter 4), should first read “Design Simulation FEM (Nastran)” (Chapter 3) to attain the necessary prerequisites. At the beginning of each chapter an introduction to the principles of each topic is given. For the analysis newcomer these statements might sound very theoretical and difficult. But this should not discourage you to begin with the learning tasks on this subject, on which the focus lies. Explanations in the learning tasks usually build on the principles of the introductions, clarify and expand them. A hurried reader therefore can skip these introductions, and go straight to the learning tasks.
A hurried reader can also directly start with the examples.
The download files belonging to this book (www.drbinde.de/index.php/ en/203) contain the RAK2 folder. This includes all outlined learning tasks to the areas motion, structural, thermal, and flow simulation. A second folder named EM contains installation files and examples for electromagnetics. There are also solution files in the download file available so that any result can be looked up in it. For working through the book this entire file should be unpacked and copied to a directory on the hard disk of the computer. The learning tasks of a chapter can best be worked through in the order given, because all learning content builds on each other. In Motion and Design Simulation, as well as EM, each first learning task is a basic example. All important principles and foundations are taught here, which are necessary to understand and build the following learning tasks.
In each case the first example is of fundamental nature.
When describing the learning tasks, there is a distinction between background explanations and steps to be carried out (mouse clicks in NX). Steps to be carried out are always marked with the pin icon:
Pin icons indicate steps to be performed.
ÍÍHere a step to be carried out is described. Very hurried readers can therefore skip the background explanations (hopefully, they understand intuitively quite a bit) and jump straight from one pin icon to the next. To work through the learning tasks, a computer with NX installation must be available. The examples were calculated by NX9, but should also work in other NX versions e. g. NX8.5 or 10. With a normal installation of NX9, all required modules for simulation, especially the NX Nastran solver, are automatically installed. It is, other than with previous NX versions, no longer required to define specific environment variables for the simulation manually. Only for electromagnetic simulation (Chapter 6) the installation of some additional files is required. But this is explained at the beginning of the chapter. In addition, the computer hardware should preferably be well equipped. We would like to give the following recommendations: Processor: The highest possible clock frequency is essential for all simulation problems.
NX installation and computer performance
10 1 Introduction
Multi-Processor: For FEM analyses and some thermal analysis, the use of multiple processors is supported. Memory: FEA, thermal and fluid flow analysis need a lot of memory. There is a simple rule: the more, the better. To work through the examples in this book, we recommend at least 4 GB of main memory. Hard drive: Again, There should be enough free disk space available. For the examples in this book we recommend at least 2 GB. 32-/64-Bit Operating System: For medium to large analysis models 64-bit architecture must be selected, since much more memory can be addressed here. The EM installation will only run on 64-bit systems. For more information on these topics, we recommend reading the documents [nxn_paral] for parallel-processing and [nxn_num] for efficient memory usage with NX/Nastran. Presetting the motion solver
For motion analysis there are two solvers available: Adams and RecurDyn. The learning tasks of this book were carried out with the RecurDyn solver, but can also be run with Adams. Well, our introduction is now complete. We wish you fun and success in learning!
Bibliography [nxn_num] NX Nastran Numerical Methods User’s Guide. Online-Documentation to NX Nastran [nxn_paral] NX Nastran Parallel Processing User’s Guide. Online-Documentation to NX Nastran
2
Motion-Simulation (Multibody Dynamics)
In Section 2.1, first the theory, limitations, special effects, and rules of this discipline are represented. This is followed by kinematic learning tasks, which first start with a basic example (Section 2.2.1). In the second learning task, principle sketches and kinematics are used to support the early design phase (Section 2.2.2). In the third task, collisions and assembling of various sub-kinematics are treated (Section 2.2.3). The fourth learning task deals with dynamic problems and the simulation of contact (Section 2.3.1) and the final task deals with the coupling of NX-Motion with MATLAB® Simulink® for the so-called co-simulation (Section 2.4.1).
Content of the chapter
■■2.1 Introduction and Theory Motion simulation offers the designer the ability to control the movements of his or her otherwise statically constructed machine. This allows that a better understanding of the machine can be obtained and it can be checked whether the movement of the components leads to collisions. It also can be checked if the machine can carry out the desired movement, or even reach certain positions. Often one of the tasks is to adjust the geometrical dimensions suitable. The use of parametric CAD is often an important way to create variants.
Use cases and benefits of motion simulation in practice
But also and especially in the early stage of the design process when only first rough draft designs are available, the use of kinematic analysis is very useful. Using the motion simulation application, principle sketches or simple curves can be moved and their dimensions can be optimized. Thus, the sketches of the early design phase become movementbased control sketches. In the further design process, the kinematic models can be used over and over again to check the latest state of the mechanism. As soon as mass properties are assigned to the CAD geometry, motion analysis can be extended to dynamic analysis. In this case bearing forces, velocities and accelerations can be determined. Therefore motion analyses are often preparations for subsequent FEM analyses because the FEM use bearing forces as boundary conditions. Based on the re-
Mass properties of the components expand the area into the dynamics.
12 2 Motion-Simulation (Multibody Dynamics)
sults (forces and translations) it is possible to choose springs, dampers, additional masses, vibration absorbers, bearings (load capacity) etc. from supplier catalogs. Users of motion simulation should have experience in modeling parts and assemblies with the NX system. This is necessary because the examples in this chapter do not only use finished assemblies, but partly also make changes in the construction methodology necessary. However, no further previous experience is required. Subdivision of technical simulation in four fields
Motion simulation covers the part of the mechanics that deals with rigid bodies. Usually there is a plurality of rigid bodies that are connected to each other by joints. Such problems appear, for example, in chassis of automobiles. The software for the analysis of such tasks is denoted by the term MBD program. MBD means Multibody Dynamics. Technical Simula on Rigid Bodies Rigid Body Mechanics MBD (Mul body Dynamics)
Elas c Bodies Fluids Structural Mechanics Fluid Mechanics FEM CFD (Finite Element (Computa onal Method) Fluid Dynamics)
Electric Bodies Electromagne cs (EM) FEM (Finite Element Method)
Within the CAD model, the user defines moving rigid bodies (links), joints, drivers, and possibly external forces or constraints. Even springs and dampers may be involved. Process steps in the MBD analysis
Creation of geometry
Definition of links
Definition of joints and drivers
Solving the solution
Post processing of results
Links are usually defined using CAD geometry (components and assemblies). In addition, the CAD system, with its powerful capabilities, can also be used to define, for example, cams or other control elements.
2.1.1 Simulation Methods Additional literature
It is difficult to generalize how MBD methods work because the different solvers, including RecurDyn and ADAMS, work quite differently. For a detailed description on ADAMS, see [adams1]; and for a detailed description on RecurDyn, see [RecurDyn1]. Internally, the moving bodies, joints and drivers are converted into a mathematical system of differential equations, which is then solved to determine the desired quantities. This includes the displacements, velocities, and accelerations of the moving bodies and joints, as well as the reaction forces at the joints. Each component that is defined as moving body has to be cut free, and six dynamic equations (describing forces and accelerations) and six kinematic equations (describing positions and velocities) in the translational and rotational directions are established. These equations thus form a system of equations describing the motion.
2.1 Introduction and Theory 13
The number of unknowns in the system of equations can be reduced by adding constraints. Each joint that restricts the possibility of movement of two bodies may be expressed in the form of additional equations in the system of equations. For example, a revolute joint between two moving bodies leads to a reduction of five unknowns in the system of equations because only one rotational degree of freedom remains where once there were six. A differential system of equations is set up.
m2
m1 g
Motion drivers, which define the displacement, the velocity or the acceleration, also reduce the degrees of freedom (DOF). A rotational driver, for example, with an enforced speed of 360 deg/sec, reduces the number of DOF by one. On the other hand, forces and torques, appearing on the motion model, neither bring additional unknowns into the system nor reduce the count of DOF.
Drivers and constraints reduce the number of unknowns.
That way, the count of the DOF is reduced either to zero (in which case the system of equations can be solved directly) or to a number greater than zero. In the second case, the system can be solved by adding initial conditions and integrating the equations over the time. In the case of zero degrees of freedom, we have a kinematic system; otherwise we have a dynamic system to be solved. It also should be noted that the resulting system of equations is either linear or nonlinear, depending on the correlations in the system that the various types of joints introduce. While simple types of joints such as revolute, slider, or spherical joints behave linearly, complex joints such as the point on curve connections require nonlinear equations. Linear equation solvers – as they are usually used for FEM – are therefore not used for solving MBD systems. For MBD rather such solvers with ability to reduce the order are used. After solving the system of equations, the following variables are available for post-processing: translational velocity rotational velocity
Some kinds of joints cause nonlinearity in the system of equations.
14 2 Motion-Simulation (Multibody Dynamics)
coordinates of center of gravity orientation angles applied, external Forces Forces in joints and constraints
2.1.2 Restrictions Restrictions of MBD systems and demarcation to FEM
A very basic property and restriction of MBD is given by the rigidity of the considered body. A link can be moved in space, but cannot be deformed. For MBD, real bodies are reduced to their mass and inertia properties and their geometrical dimensions, while their deformation properties are neglected. This is the fundamental difference from the structural mechanics, which uses FEM to consider flexible bodies, including their deformations and stresses. The disadvantage of linear FEM compared to MBD is that no movements and only small deformations can be simulated. The assumption of rigidity in the motion links in MBD therefore has the advantage of simplifying the analysis and reducing the computational effort, thus enabling even complex motions of large assemblies to be analyzed.
Clearance, tolerance and flexible bodies can be modeled in MBD only with great effort.
In reality, however, there are some effects that are difficult to model using MBD. These include clearance, tolerance, and flexibility. Because such effects are often not taken into account in the MBD model, in some cases it may appear, for instance, that a clamping situation has occurred, when in reality there is a slight clearance in the joints or there is some flexibility in the body to ensure motion without any problems. Clearances can be considered in MBD as well, but then the corresponding parts must be considered dynamic and the contacts with restoring forces must be modeled. If so, the system will have open degrees of freedom, which will make the problem significantly more difficult to solve.
2.1.3 Classifications of MBD Classification of dynamics
For a classification of motion simulation we refer to the classification of mechanics as it is, for example, described in [HaugerSchnellGross]. Accordingly, the mechanics may be divided into kinematics and dynamics. The kinematics is the science of the temporal and spatial movement, without regarding forces as a cause or effect of the movement. The dynamics, however, deals with the interaction of forces and movements. It is divided into the statics and kinetics. The statics deals with the forces at stationary bodies (e. g., a truss in equilibrium), while the kinetics examines actual movements under the effect of forces.
2.2 Learning Tasks on Kinematics 15
Classification of MBD Simulations
Technical Simulaon Rigid Bodies Rigid Body Mechanics MBD (Mulbody Dynamics)
Elasc Bodies Fluids Structural Mechanics Fluid Mechanics FEM CFD (Finite Element (Computaonal Method) Fluid Dynamics)
Kinemacs Degrees of freedom = 0
Electric Bodies Electromagnecs (EM) FEM (Finite Element Method)
Dynamics Forces and moons
Stacs Forces without moons
Kinecs Degrees of freedom > 0
All these phenomena can be analyzed with NX Motion, with the restriction of rigid bodies in the MBD. Furthermore, starting with version NX 7.5, it has also been possible to take into account single flexible bodies in the MBD. These bodies must be prepared in advance using FEM, which means that the stiffness matrix must be determined (in reduced form) and included as Flexible Body in the MBD system.
Flexible bodies are a special case.
Kinematic systems are characterized by the fact that all degrees of freedom of a moving body are determined. This determination may be made either by joints or by driver rules. Such systems are predictable to a certain extent, and can also be referred to as motiondriven systems (tied movement).
Determined and undetermined degrees of freedom.
Kinetic systems are available if one or more degrees of freedom are undetermined. The motion then results from external forces (untied movement). For example, the force of gravity can lead to a swinging movement of a lever with rotational DOF. Kinetic systems are therefore also known as power-driven systems.
■■2.2 Learning Tasks on Kinematics 2.2.1 Steering Gear This basic example will explain the most important issues that are necessary for a simple motion analysis using the NX system. The example will take the user through the process of generating links (the motion bodies in NX) and basic joints, and uses the articulation function as the driver since it is well suited for purely kinematic motion simulations. In addition, the function for dynamic analysis will be used as a method for detecting indefinite degrees of freedom.
16 2 Motion-Simulation (Multibody Dynamics)
This kinematic model is here first created as a single mechanism. In a later example, this mechanism will be modularly assembled with other mechanisms to form a larger motion model. This basic example should be performed by everyone who wants to work with NX Motion.
2.2.1.1 Task The aim is to control the design.
A designer has redesigned the levers for the steering gear. Now he or she has to check if collisions occur. Therefore, a kinematic model must be created that allows the rotational movement of the steering wheel, and (associated with it) of the pitman arm. In this task, the steering gear of the RAK2 and its steering wheel and pitman arm are used. The steering gear is accommodated in a housing and connects the steering wheel with the pitman arm. For this task, the simulation should only be used for visual control, however, the examination of minimum distances to other components, the study of the resulting reaction forces in the joints and collision checks would be possible in further analyses. In the following section some principles are explained at first. Thereafter, the solution steps for this task are presented. Very urgent readers can skip the next section and move straight to the creation of the model (see Section 2.2.1.4).
2.2.1.2 Overview of the Functions In the kinematics application (Motion Simulation) the kinematic or kinetic model is established and the simulation is performed and evaluated. The following figure shows the Motion toolbar that appears after changing to the module. The toolbar contains all the main features of the Motion module that are used. Usually, this toolbar is along the left edge of the NX window.
2.2 Learning Tasks on Kinematics 17
Overview and brief explanation of the main functions for NX Motion Simulation
The following is an overview of the main functions of the Motion module, which already refer to the later use. Very hurried readers can skip this section and proceed immediately to the creation of the model (Section 2.2.1.4).
The function Environment allows the basic setting of the system for kinematic or kinetic properties (herein called Dynamics). For our task, we will adjust “Dynamics”, although it is actually a kinematic model. The reason for this approach is, that the user has more possibilities, which contribute to a better understanding and error identification. In addition, advanced solution options can be selected in the Environment function, for example the option of Co-Simulation to use control engineering elements with MATLAB Simulink, the Motor Driver option for accessing electric motor libraries or the option of Flexible Body Dynamics. The option Component-based Simulation is suited for assemblies, because it activates the filter for assembly components when generating moving bodies.
In addition to the links, the user defines joints, which specify how the connected links can be moved. In this context the function Driver is also used, which is necessary to drive the joints. If the Joint function is opened, you can find a lot of different joint types as a selection. These are the most important joints:
The Solution function must be activated by the user to specify the type of solution that is desired. The options include the Normal Run, the Articulation, and others.
The main elements for the definition of the motion model are the moving bodies (links). With this function the user defines which geometry or component should be a part of the moving system.
In addition to the links, joints are defined by the user, which describe the possible movement of the links to each other or to the environment. In this context, the Driver function also is used to define a constant or time depending driver on a DOF of the joint. If the Joint function is selected, a lot of different joint types are listed. These are the most important joint types:
18 2 Motion-Simulation (Multibody Dynamics)
The revolute joint only allows a rotation.
The slider allows a translational displacement between two parts or one part and the environment.
The cylindrical joint allows the rotational and translational displacement along one axis.
The screw forces a rotation if a part is displaced in translational direction.
The spherical joint allows all rotational movements.
The planar joint allows the frictionless sliding of two parts in a plane.
The joint primitives
Sensors etc.
The universal joint allows tilting movements between two parts, however, a rotation around the main axis is transmitted to the other part. Depending on the angular position of the axes it can cause uneven rotational speeds as in real universal joints. This non-uniformity can be avoided by use of the constant velocity joint described below.
The fixed joint eliminates all degrees of freedom so that there is no displacement between a part and the environment, or between two parts.
In addition to the conventional joints, which are based on the model of realistic joints, there are some joint primitives that offer more precise control of the DOF of the connected links. So it is possible to fix every single degree of freedom with the help of joint primitives. Here you can find some of the useful joint primitives:
Constant Velocity: This joint works very similar to the universal joint described earlier. But unlike the universal joint, the rotational velocity is constant on both sides and even angles with over 90° are possible too.
Inline fixes two translational DOF, so that the both links could be moved on one axis to each other (similar to Point on Curve).
Parallel: A joint that keeps two faces, lines or axes in parallel. Two rotational DOF are fixed.
The Orientation primitive fixes all rotational DOF between two links but it allows the translation in all three directions.
Further functions are: Smart Point: A general CAD point that is associative to the geometry it was assigned
to.
Marker: A marker that is used to request results such as the velocities and accelerations on certain positions of the link.
Sensor: Enables the user to record motion results such as displacements, velocities, and accelerations relative to other results or markers.
2.2 Learning Tasks on Kinematics 19
Further functions of the Motion Simulation toolbar:
The function Master Model Dimension could be used to alter the CAD parameters of the underlying CAD model in a motion model. The special thing about this feature is that the changes only affect the motion model, and the underlying CAD model itself is not changed. Therefore this function can be used for “what-if” studies.
The Function Manager is used to define more complex functions, such as a driver whose control that is time- or motion-dependent. Simpler functions, however, are usually available directly in the appropriate motion features. Therefore in such a case, the function manager is not needed.
The Flexible Link function allows calculated flexible links, which previously had been calculated with FEM, instead of solely using rigid bodies.
Another group of special joint are couplers and gears. The user can choose between the following options:
Gear: Defines the relative motion of two revolute joints or a revolute and a cylindrical joint with a defined ratio.
Rack and Pinion: Defines the relative motion of a revolute and a slider joint with a defined ratio.
Cable: Defines the ratio of the relative translational motion of two slider joints.
2–3 Joint Coupler: Defines the relative motion between 2 or 3 revolute, slider and cylindrical joints.
The next group of special joint types summarizes the connections:
Spring: Flexible element that is defined between two joints, or a joint and the environment or on an existing joint with stiffness value, preload and damping coefficient.
Damper: Damper element defined like a spring, but with a damping coefficient. This results in a velocity-dependent force between the respective links.
Bushing: A cylindrical combination of spring and damper (stiffness and damping coefficient in all directions)
The 3D Contact and the 2D Contact are special contact functions because they allow the impact on each other and the lifting of each other. Strictly speaking, these contact definitions are no joints, but force objects that respond by restoring forces in the event of contact. In this case, friction and contact damping can play a role too and can be replicated using assigned parameters. While the 3D Contact is applied to the whole solid, the 2D Contact is a simplification that may be used in the case of planar curves. These two contacts should be used with caution due to their complexity. If possible, the following constraints should be used instead.
Now a group follows, in which the constraints are summarized. These include:
Point on Curve forces a point on a link to move along a desired curve.
Couplers
The elements for connections are collected in a group.
Various types of constraints
20 2 Motion-Simulation (Multibody Dynamics)
Springs, Dampers and Forces
Curve on Curve: Two curves are forced to slide tangentially on each other. Both curves have to be coplanar. With this function most of the cam disc tasks are solved. Point on Surface: A point on a link is forced to slide on a selected surface.
Additional motion features in the toolbar belonging to the group of loads. These include:
Force
Torque, which are available as vector or scalar approach.
Some advanced features are only available after appropriate adjustment of the settings in the environment dialog. These include:
PMDC-Motor: defines the electrical parameters of a motor, such as voltage, resistance, and inductance Signal Chart: provides an input signal to the PMDC motor Plant Input: defines the control variables that are read from the optional Matlab Simulink control and which are provided to the MBD model, for example as a driver. Plant Output: measured value, which is fed to the Matlab Simulink loop.
For running the analysis, first a solution has to be created and then the following function is started:
Solve
Now the solution can be solved, and the results are available after the solving process has finished. The penultimate function group provides functions for geometric analysis. This includes the following functions:
Assistance for post- processing
Interference checks the model for collision and could create intersection solids
Measure for measuring distances and angles
Trace for recording the geometry during the movement
The last function group provides five methods for post-processing:
Animation displays the calculated movements of the model
Graphing for the graphical evaluation of motion results
Populate Spreadsheet for editing, re-using, and saving of motions using a spreadsheet as input
Create Sequence saves a motion animation in an assembly sequence so that the motion sequence is also available in the master assembly
Load Transfer for transferring reaction forces from the kinematics analysis in the FEM application
2.2 Learning Tasks on Kinematics 21
2.2.1.3 Overview of the Solution Steps To solve this exercise, a Motion Simulation file must first be created in the NX system. Then the geometry that should be movable in the motion system has to be defined with the Link function. The creation of two revolute joints, one gear, and a driver on the steering wheel follows. The time-dependent Normal Run is used to find accidentally indefinite degrees of freedom, and the Articulation function is used to manually move the actuator on the steering wheel.
The steps of the exercise
2.2.1.4 Creating the Motion Simulation File According to the master model concept, all elements that are used for motion analysis (links, joints, drivers), are stored in a separate file (i. e., the kinematic sim-file; see the following figure). This kinematic file is connected to an assembly file via an assembly reference, which means that the kinematic file is a quasi-assembly comprised of the assembly part to be analyzed as a single component. In addition to these assembly references, other associative connections are similarly added to reflect the associative relationships between the joint and link objects defined in the kinematics file with the geometry objects describing these components (curved arrows in the figure). This way, the NX Motion application is fully integrated into the master model concept, similar to how, for instance, the NX Drafting application is.
Reference of Assembly structure (associative)
Part1 (…)
Kinematics (Joints, Links) Reference of MBD Objects (associative)
Assembly
Part2 steering wheel
Part3 (…)
With the help of the master model concept, the entire product is digitally mapped. Internal references between geometry and MBDjoints are created.
Part4 (pitman arm)
This motion structure is automatically created when the user creates a simulation as shown here: ÍÍLoad the assembly from which you want to create a simulation in the NX system. For our exercise, the assembly file ls_lenkgetriebe.prt. The files are located in the RAK2 directory of the DVD. ÍÍNext, start the Motion application. The Motion Navigator appears as the first tab in the resource bar. This navigator supports the work with the Motion application by representing all the features and providing opportunities for their manipulation.
Here the exercise begins.
22 2 Motion-Simulation (Multibody Dynamics)
The navigator shows that a motion file named motion_1 already exists. This is the already finished solution of this problem. Since you will create an own solution, you should delete this file. ÍÍDelete the existing simulation motion_1 by opening and executing the Delete function from the context menu of the simulation. Now the Motion Navigator only shows the master node, i. e., the module that you have opened. ÍÍCreate a first simulation by clicking on this master node, and invoke the function New Simulation in its context menu. ÍÍConfirm the following menu Environment by selecting OK. We will come back to it later on. The navigator shows the structure of the model, and allows the manipulation of its features.
After activating this function, the system creates a simulation file that is associated with the master model via the assembly structure. In addition, the function Motion Joint Wizard is activated automatically, which tries to create links and joints according to the existing assemblies Mating Conditions/Constraints.
The Motion Joint Wizard implements the Mating Conditions/Constraints into motion joints.
The Motion Joint Wizard function analyzes each set of constraints with respect to the degrees of freedom that exist between the affected assembly components. If there is only an indeterminate rotational degree of freedom, then a Revolute is generated. If there is an indeterminate translational degree of freedom, then a Slider is generated. An assembly constraint that links, for example, one point to another, is translated by the Motion Joint Wizard into a Spherical joint. An assembly constraint that defines all degrees of freedom between two parts, is translated into a fixed joint. In a similar manner, a few more joints can be generated automatically. Advantages and dis advantages of Motion Joint Wizard.
The Motion Joint Wizard can therefore automatically create the motion model, or parts of it, when the assembly on which the motion should be based on, has been constructed in such a way that the mating already describes the potential movements of the parts. This approach can be quite useful, though the following disadvantages must be considered: The joints automatically generated by the Motion Joint Wizard are not associative to the geometry. That means that in case of changes on the master model, the joints must be adjusted manually. A manual creation of the associativity of the joints is subsequently possible. Only the assembly constraints of the top-level assembly are analyzed and converted. Constraints from the subassemblies are not considered.
2.2 Learning Tasks on Kinematics 23
Assembly constraints are often used for parts that are irrelevant in terms of the motion model, such as small bolts, nuts and washers. In the case of automatic translation by the Motion Joint Wizard all these parts are made into links. The motion model is then considerably more complex than it needs to be. One remedy for this problem is to disable single conditions in the Motion Joint Wizard. For these reasons, the Motion Joint Wizard should not to be used for the solution of our problem:
We are not using the Motion Joint Wizard.
ÍÍCancel the Motion Joint Wizard with the CANCEL function. The Motion Navigator should now shows a structure as shown in the following figure.
A characteristic of the Motion Navigator is that the motion model is represented under the master model. This is done for reasons of clarity, because the motion features that are generated are displayed in the navigator below the motion model. In addition, several motion models can be clearly displayed side by side in this way if desired. The NX system has thus automatically created a new file that is associated with the master model according to the master model concept, and the Assembly Navigator can now be used to represent or to work with the new structure. The picture to the right of the Motion Navigator shows the Assembly Navigator that represents the motion model, now as the top-level assembly.
The motion model is a quasi-assembly of the master model.
You should be cognizant of the operating system directories in which the new master file has been stored, which you can confirm by using the Windows Explorer. The following illustration shows on the left side the master file ls_lenkgetriebe.prt, which can be located in any folder of the operating system. Once a motion model is created, the NX system creates a subfolder with the name of the master model. All the data that is needed for motion simulation is thus stored in this new subfolder. In our case, we see that the folder now includes motion_1.sim, which is the file for the motion model. The resulting files of the simulation are stored in a folder.
During the following simulation several additional files are created, which are then stored in this folder as well.
24 2 Motion-Simulation (Multibody Dynamics)
2.2.1.5 Selection of the Environment As a next step, the environment for the motion model should be adjusted. This is done using the Environment function. There are the two alternatives, kinematics and dynamics, which correspond to the classes of mechanics that were described at the beginning of this chapter. The following should be observed for the use of these two classes in the NX Motion application.
Kinematics The decisive factor is whether indeterminate degrees of freedom have to be processed.
The key characteristic of kinematic analysis is that all the degrees of freedom for the entire system are determined. In this context, each link can have three translational and three rotational degrees of freedom. Hence, if a kinematic simulation is to be performed, the user must ensure that none of the links can move freely. Instead, all movements must be determined by joints or drivers.
Over-determined and redundant degrees of freedom.
Of course, no conflicts may arise from joints or drives in the movement possibilities. Overdeterminations that do not lead to conflicts are called redundant degrees of freedom. These are allowed, but not recommended, because even the smallest inaccuracies can lead to conflict situations. Such very small inaccuracies can occur, even when working really carefully, due to numerical rounding errors during computations. Experience has therefore shown that large kinematic models will effectively only work correctly if they are constructed without redundancy. Smaller models, however, will usually run with limited redundancy without any problem. The advantage of the kinematic environment is that no mass properties are required for the links. The disadvantage is that the user is forced to create a motion system with exactly zero degrees of freedom. Until such is created, it is not possible to perform a test run.
Dynamics Dynamics also allows the simulation of undetermined degrees of freedom.
Dynamic analysis is characterized by the possibility of undetermined degrees of freedom and free movement opportunities. Such movements are obtained by including the mass and inertia properties of the links as well as the external forces such as the gravitational acceleration in the analysis. A dynamic analysis will calculate results even if undetermined degrees of freedom are available, while a kinematic analysis will stop in such a case. This is an advantage for dynamic analysis during the model-building phase when the joints have not yet all been defined. To do this, the mass properties for each link must be assigned and verified. For these reasons, the dynamic environment should be chosen for the solution to our problem, even though no indeterminate degrees of freedom are desired. We use this method only to simplify the development of the motion model, so that we can temporarily test the model without having fully determined degrees of freedom. Once the model is complete, we can then easily switch back to the kinematic environment.
Description of the Advanced Solution Options.
In addition, Advanced Solution Options can be selected in the environment settings. These include the Motor Driver, which defines an electric motor based on its electrical parameters and for which a signal diagram can be submitted; the Co-Simulation, which allows one
2.2 Learning Tasks on Kinematics 25
to couple controls that have been defined using Matlab Simulink to the NX-motion model; and Flexible Body Dynamics, with which it is possible to work not solely with rigid moving bodies, but to also make them partially flexible. For this, however, a prior FEM analysis of the corresponding parts is required. Furthermore, you can choose whether a Component-based simulation shall be used or not. This is useful if assemblies shall be simulated. With this option, the link selection filter is preset to components. However, this can always be changed manually.
2.2.1.6 Definition of the Links Now the Links will be created. ÍÍSelect the Link
function.
First, a link should be defined to describe the steering wheel, and then a second one to describe the pitman arm. The menu for the definition of a link.
The first selection step concerns the selection of the geometry that should be part of the link. If you have not already selected the setting to filter for components in the environment, it should be set now. This will make it easy to change the geometry of the assembly components later, without the danger of the links in the motion model losing their references.
Both components of the assembly, as well as the solids, simple curves, and points, can be moved.
ÍÍNow select in the graphics window the assembly components that belong to the steering wheel; that is, all the parts that move together with the steering wheel. There are 19 components that belong to the sub-assembly ls_ubg_spindel. You can use the Assembly Navigator to select these components. Once you have selected the components, the mass properties of the link can be defined as shown in the following selection steps. However, this is not necessary in this case because the system can automatically calculate the mass properties based on the geometry and the assigned material respectively the density. Because these properties are not of interest in this exercise, we will use the automatic mass analysis instead. Therefore, keep the Automatic setting under the Mass Properties option. ÍÍIn the field “Name” you fill in an appropriate name, such as “steering wheel”.
Mass properties are determined automatically for solid bodies.
26 2 Motion-Simulation (Multibody Dynamics)
Do not include any spaces or special characters in the name of motion objects. ÍÍWith a click on OK or APPLY, the link will be created and displayed in the Motion Navigator under the Links group. ÍÍNow, in the same way, create the next link. Add the three components ls_lenkstockhebel, ls_segment, and ls_lenkgetriebewelle, and then name the link “Lenkstockhebel” (pitman arm).
At this point, all the necessary links have been defined, Next, we will define the joints.
2.2.1.7 Definition of Revolute Joints Now we will define a rotatable bearing between the link steering wheel and the fixed environment. Other joints can be defined similarly. Proceed as follows: ÍÍSelect the Joint For the definition of revolute joints the selection should be done on arcs. Then the point and axis of rotation can be determined automatically.
function. You will see the menu shown below.
At the top of the menu, the type of the desired joint can be selected. The default is the Revolute joint, which is a joint that has only one rotational degree of freedom. Since this is the desired joint, we will proceed with the selection steps. With the first selection step the first link which shall be connected, that is the steering wheel, is specified. In principle, the steering wheel can now be selected in any manner in the graphics window, but it is advisable to take into account the following aspects for the selection: It is recommended to select a geometry from which the system can derive the desired joint center and the axis of rotation. This is possible, for example with a circle: In this case, the circle center becomes the center of rotation and the circle normal becomes the rotational axis. But also a straight edge or curve is possible: In this case the next control point becomes the center of rotation and the direction of the edge or corner the axis of rotation. It is also advisable to select a geometry that in the further design history is subjected to as few as possible changes. Because if the selected geometry is subjected to changes, it is not sure if the joint remains associative to the geometry and is updated automatically. For example, if an edge is selected, which is rounded later, the joint loses its associativity to the geometry.
2.2 Learning Tasks on Kinematics 27
The best way is to select on circular edges. Then the center point and direction can be used automatically.
ÍÍTherefore, select a circular edge on the steering wheel which is not subjected to significant changes. In the second step, the origin and orientation of the joint should be selected. In the case of the pivot joint this is the center and the axis of rotation. Because these two pieces of information have been given in the first selection step, this question does not need to be answered.
A joint can often be generated with just two mouse clicks.
In the third selection step the second link, which should be connected, can be selected. If there is nothing selected, the system assumes that the joint connects the first link to the fixed environment. Because this is desired here, no selection is made in the third step. ÍÍAccept with OK to create the revolute joint. In the graphics window and in the Motion Navigator the joint is now displayed. A joint which is connected to the fixed environment can be identified by its symbol.
If the symbol of the joint is displayed very small, the size specification can be increased under Icon Scale in the default settings (MAIN MENU > PREFERENCES > MOTION) for motion simulation.
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ÍÍIn the same way you can create a revolute joint which connects the pitman arm with the fixed environment (as you can see in the following figure) Now you have created a first mechanism with two moving bodies that are connected to the environment, each with a revolute joint. But the task is not yet solved. In the interest of better understanding, some test runs are carried out in the following. The pitman arm is also attached with a revolute to the environment.
2.2.1.8 Detection of Undetermined Degrees of Freedom Due to the missing driver and the absence of a coupling gear, the previously completed mechanism is still underdetermined. The number of the undefined degrees of freedom can be determined either by plausibility checking, or by examining the Information window shown in the next figure. ÍÍFrom the context menu of the motion model in the Motion Navigator, select the function Information, Motion Connections. The information window that then appears lists the number of undetermined degrees of freedom in the mechanism (Degrees of Freedom). For complex mechanisms, the identification of undetermined degrees of freedom can be difficult. The function Information, Motion Connections helps.
In this case, there are two degrees of freedom because both the steering wheel and the pitman arm can still freely rotate about their respective axes.
2.2 Learning Tasks on Kinematics 29
2.2.1.9 Test Run with Two Undetermined Degrees of Freedom In cases of more complex mechanisms, it is often difficult to identify the undetermined degrees of freedom of a mechanism only from plausibility considerations. One useful approach in such cases is to perform a test run with, in our case the two open degrees of freedom, to develop a better understanding of the mechanism. ÍÍSelect the Solution
In a dynamic run usually undetermined degrees of freedom can easily be recognized.
function. Now the dialog appears to define the solution.
In this dialog, you are prompted to select the Solution Type. You have the following options: Normal Run, Articulation, and Spreadsheet Run. We accept the default type Normal Run to perform an analysis that takes into account time and gravity. Furthermore, the simulation Time and the number of Steps can be specified here. Additionally, you can choose Analysis Type to specify a Kinematic / Dynamic Analysis or a Static Equilibrium Analysis. In addition, the direction and the magnitude of the gravitational acceleration can be set. In our case we want to customize it as follows: ÍÍIn the dialog, set the Gravity vector to -ZC and verify the direction of the resulting arrow. The direction of the gravity is important for undetermined degrees of freedom.
This direction of gravity does not correspond to reality, but this way the pitman arm should fall definitely into oscillation, which is what we want to check in the following. ÍÍFor our example, leave all other settings as default, and select OK. After that, the solution is created. ÍÍAfter the creation of the solution, select the Solve function. The analysis should be completed quickly. ÍÍNow you can start the Animation function. The menu to control the animation of the movements will appear. ÍÍUse the function Play to view the results of one second of simulation time.
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The Animation dialog is used to review the simulated movements of the mechanism.
It should be recognizable that the lever performs approximately one full oscillation. The simulation makes it easy to see that there still exists an indeterminate degree of freedom. The second undetermined degree of freedom cannot be discovered in this way, because due to symmetry, there is no reason for the steering wheel to move. ÍÍCancel the Animation function with CLOSE.
2.2.1.10 Definition of a Kinematic Driver In the next step, a driver is defined on the steering wheel. Such a driver can be used both for the Normal Run simulation method and for the Articulation method. With Normal Run it is time-dependent, while with Articulation it is performed after manual specification. A driver works like an additional constraint.
Drivers are defined either directly in the joints or by the Driver function. It should be noted that not all joints can have drivers defined. Only the Revolute, the Slider, the Cylindrical, and the Point on Curve can have drivers defined. If other joints are to be driven, then this must be realized through the use of appropriate joint combinations. In the Revolute joint the driver works as a rotational driver; in the Slider joint the driver works as a sliding driver; and in the Cylindrical joint the driver may be a combination of a revolute and a slider driver. The following shows how a revolute joint can be provided with a drive. ÍÍSelect the Edit option in the context menu for the revolute joint on the steering wheel, and then select the Driver tab. The definition dialog of the revolute joint appears. From here, all the properties of this joint can be changed. In the menu item Driver, the parameters describing the different driver types in the list can be set.
2.2 Learning Tasks on Kinematics 31
Several types of drivers are possible for example the constant type.
The Constant driver performs a time-constant motion or acceleration with the solution type Normal Run . It can be specified an Initial Displacement, an Initial Velocity and an Acceleration. The Harmonic driver defines a harmonic oscillation.
The Harmonic driver performs a harmonic oscillation during a Normal Run . The oscillation Amplitude, the oscillation Frequency, a Phase Angle, and an initial Displacement can be specified. The Function driver can be used to define more complex motion functions with the help of the Function Manager . The last driver is the Articulation. This driver corresponds to fixing the degree of freedom in the solution type Normal Run , however, with the addition in the solution type Articulation , that the driver may also be operated manually. All types of drivers can be used in the solution type Articulation. The modified values are simply reset and remain irrelevant. For the visual control in our example, the Articulation function should be used, which therefore means that we can use any of the four driver types.
The type Function allows the access to advanced functions. The Articulation is a special driver. It can be virtually moved by remote control.
ÍÍIn order to make good use of simple test runs for both Articulation and Normal Run, you should use, for instance, the Constant driver with an Initial Velocity of 360 [deg/ sec], as shown in the previous figures. ÍÍAfter defining the driver, close the dialog box with OK. Using these settings for the driver, and a simulation time of one second, our simulation should complete exactly one full rotation.
2.2.1.11 Creation of a Gear The gear pair connects the two rotational joints and defines the relative rotational motions for the two joints.
Two revolute joints could be coupled by a gear.
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ÍÍCreate the gear by using the Gear function. ÍÍThe first selection step asks you to select the first revolute joint, such as the joint of the steering wheel. You can select the joint in the graphics window or in the Motion Navigator. After this selection the second selection step in the dialog box is activated automatically. ÍÍNow select the second revolute joint, which is the joint of the pitman arm. ÍÍFor Ratio enter the desired gear reduction or ratio. For our example enter a value of 0.25. ÍÍAccept with OK. The joint will be created. Unfortunately the joint Gear has the following limitation: It can only be created if the two joints (revolute or cylindrical) have the same base. The base of a joint is the link, which has been selected as the second body during the generation of the joint. In case of our example, this is the environment.
2.2.1.12 Visual Control through the Use of Articulation After complete generation of the motion model it could be moved manually with the Articulation function. ÍÍTo do this, create a new solution and select the Articulation option as Solution Type. After that accept your input with OK. ÍÍNow select the Solve function. The dialog shown in the following figure appears. The Articulation function is well suited for the control of movement sequences.
Thereby, it can be moved forwards and backwards step by step.
ÍÍTo move the single driver of the model manually, first activate the check box for the joint J001. ÍÍThen enter the desired Step Size, for example 1 degree.
2.2 Learning Tasks on Kinematics 33
ÍÍWith the buttons and , the driver could be moved forward and backward step by step. ÍÍWith Number of Steps you can specify a number of steps that are executed at every mouse click on or . ÍÍUsing this function, the visual control of the mechanism which is desired in this task can now be performed. ÍÍExit the articulation function with CLOSE. ÍÍSave the file. ÍÍLeave the motion simulation by execute the function Make Work on the master node ls_lenkgetriebe in the Motion Navigator and then switch to the Modeling application. This completes the first learning task for motion simulation.
2.2.2 Top-down Development of the Steering Lever Kinematics In this example it is shown how kinematics simulations can be used effectively in the early design phase. Background is the usual design methodology in the early phase, in which a designer does not yet have a detailed idea of the finished product. Rather, he tries to approximate the first very rough drafts to find possible designs, for which the motion of the planned machine plays an important role. In most cases, simple curves, 2D sketches or coarse solids are used, which can be manipulated easily. Only when appropriate geometrical parameters were found, the detailed design begins. This includes the structuring of the geometry objects in assembly components or the definition of sub-assemblies. This type of construction is known as a top-down design, because the product is developed from the top downwards. In this example, you learn about design methodology, which is used in early design phases. However, the main focus is on the use of motion simulations in the context of principle sketches and the optimization of geometric parameters. It is also shown how the simulation results are displayed as a graph.
2.2.2.1 Task The aim is the construction of the steering levers which means the left and the right steering arm and the tie rod. The following figure already shows the result of the task. With a parallelogram like geometry of the steering lever it should be achieved, that the wheels are wrapped unevenly whilst driving through a curve, which helps to improve the driving dynamics. To check the correct movement in this example the different angular position of the wheels should be displayed in a graph.
An example of the support of early design phases through motion simulation.
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Based on principle lines a mechanism should be developed.
2.2.2.2 Overview of the Solution Steps Before we will start we would like to give an overview of the solution steps first. After the required subassembly of the RAK2 is loaded in NX, you will delete or hide the existing components of the steering lever mechanism. Then you will create a basic sketch in the context of the assembly, which serves as a rough geometry for the components to be developed. The motion model, and a motion graph shall be created. The control of motions is important.
Based on this schematic sketch you will create a motion model that represents the required movement of the mechanism. According to your preference, you can also add the existing wheel geometry to your motion model for visual control. Next, a graph is recorded, which represents the angles of the two wheels when the steering wheel is turned. The difference of the wheel angles is controlled. If desired some changes to the parameters of the schematic sketch can be made and a re-inspection of the wheel angle can be solved. After the geometric variables are appropriately adjusted, you will create assembly components from the principle sketch curves. To maintain associativity to the principle curves, the WAVE Geometry Linker is used. Finally, a new motion control is created including the solids.
2.2.2.3 Preparation The exercise starts here.
ÍÍStart with loading the assembly vr_lenkung in NX and have a closer look at the Assembly Navigator. ÍÍMake the Part lenkhebelmechanik the active part (Make Work Part). The final solution of the learning task consists of the components of the subassembly lenkhebelmechanik. Here are in addition to some small parts the left and right steering lever vr_lenkhebel_li, vr_lenkhebel_re as well as the tie rod vr_spurstange. You will also find the finished principal sketch lenkhebelmechanik_prinzip. First, the existing solution should be deleted: ÍÍDelete all components of the assembly lenkhebelmechanik, by selecting the components in the Assembly Navigator and select the DELETE function in the context menu.
2.2 Learning Tasks on Kinematics 35
The parts are not deleted by this, they are only removed from the assembly structure of the lenkhebelmechanik. ÍÍSave the part lenkhebelmechanik. If you need the original file lenkhebelmechanik later, create a new copy of the downloaded model.
2.2.2.4 Creation of a Schematic Sketch of the Steering Levers Now create a new part and therein the new schematic sketch: ÍÍIf not already done: Make the part lenkhebelmechanik active (Make Work Part) (not the displayed part). In the following, we will create a new part using the top-down method: ÍÍTo do this, use the Create New function in the Assemblies toolbar to create a new component. ÍÍIn the window that appears, enter the name lenkhebelmechanik_prinzip2.prt for the part which should be created. ÍÍIn the following dialog box Create New Component accept all default settings with OK.
The use of the top-down method.
The result in the Assembly Navigator should look as shown in the figure below.
The next step is to create a schematic sketch in the new created part. Proceed as shown in the steps below which are illustrated in the figures. The principle geometry for the steering system can be created by a parametric sketch or by non-parametric curves.
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ÍÍSet the new created part lenkhebelmechanik_prinzip2.prt active (Make Work Part). ÍÍAlign the WCS at the marked hole according to the previous figure (MENU> FORMAT> WCS> ORIENT), so that a sketch can be created in this plane. Make sure that the selection filter is set to Entire Assembly. ÍÍChange to the Modeling application. ÍÍCreate a Sketch of four lines with MENU> INSERT according to the picture. For the first line start in the origin of the sketch. The angle of 65 degrees and the distance of 200 mm can be adjusted arbitrarily. Later, according to the results of the kinematic analysis, some changes should be performed here. Use for the left and right lever the Sketch Constraint “Equal Length”. Then, the angle of the two has to be the same. ÍÍFinish Sketch . ÍÍSave the file lenkhebelmechanik_prinzip2. You have now successfully created the schematic sketch of the steering levers. In the next solution step, the motion model is created.
2.2.2.5 Creation of the Motion Simulation File Prior to the creation of a motion-simulation file, the question has to be answered, which master model should be used for creating the motion model. There are several ways which have advantages and disadvantages: In large assemblies, a meaningful structure for the motion files should be chosen.
If the kinematics is created by the new part lenkhebelmechanik_prinzip2, we have the advantage that a very simple file structure is created, but there is also the disadvantage that in the motion model only the sketch curves can be used. So, for example, it would be impossible to let the wheels move along, because they are not visible in the file lenkhebelmechanik_prinzip2. If a level above is assumed, in our case the part lenkhebelmechanik, the structure is somewhat more complex, but the steering lever components which should be created later can be moved with the sketch, because they can be seen from here. Another level above, based on the sub-assembly vr_lenkung, even the wheels could be moved in the model. The top assembly OPEL_Rak2 finally would even allow that parts of the frame could be included, for example for the purpose of collision control. The general problem is that a motion model can access only those components, which can be seen from the assembly level. A workaround for this is provided by a function that allows you to assume a motion model of a sub-assembly in higher-level assemblies. The use of this option should be explained in a later exercise. The challenge is to find a useful compromise. For our example, we want to use the assembly lenkhebelmechanik, because all steering lever parts should be included later. Proceed as follows: ÍÍMake the part lenkhebelmechanik active and displayed by using Make Displayed Part in the context menu of the Assembly Navigator. ÍÍStart the Motion Simulation application and delete the file motion_1 that already exists in the Motion Navigator. This motion model no longer works, because it refers to the previously deleted component files.
2.2 Learning Tasks on Kinematics 37
ÍÍNow create a New Simulation using the context menu of the master node in the Motion Navigator. The name motion_1 is assigned automatically. Accept the default settings of the dialogue. ÍÍThe Motion Joint Wizard appears. Close the window with CANCEL.
The creation of the simulation file.
The figure shows the Motion Navigator after the new motion file (motion_1) was created. Now Links, Joints and Drivers can be defined for the motion model.
2.2.2.6 Definition of the Links by Sketch Curves If links should be generated based on curves, it is a difference whether the kinematic or dynamic environment was selected. The default is usually the dynamics environment. In this case, the system requires that all links have mass properties. If only curves exist as moving objects, the system cannot automatically calculate mass properties. Therefore, the user is forced to specify these properties, even if he does not know them yet. If the kinematic environment is selected, mass properties are not necessarily required. The creation of Links based on curves is more user-friendly. However, the kinematic environment forces the user to define a fully constraint mechanism, which makes the creation of the motion model more complex, because no dynamic test runs are possible. For our exercise the dynamic environment setting should be maintained. For the definition of the links dummy-values can be used for the required mass properties. Proceed as follows: ÍÍSelect the function for the definition of Links . ÍÍSelect the corresponding geometry in the first selection step (Link Objects). Start with the two curves which represent the right steering lever (see the figure below).
If curves should be moved instead of solids, the properties mass and inertia are required.
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A link needs the specification of the center of gravity, the mass and the inertia properties.
The system recognizes that the mass properties could not be calculated automatically. Therefore, the menu displays the option User Defined. The mass properties have to be defined as follows:
Dummy properties can also be set, e. g. “1”. Optionally, an initial velocity could be assigned.
ÍÍOpen the Mass and Inertia dialog box. ÍÍFor the definition of the Center of Mass select any point on one of the two lines. ÍÍFor the CSYS of Inertia you define any coordinate system for the orientation of the inertial properties, for example the absolute coordinate system. ÍÍFor the values of mass and inertia you can simply define dummy properties such as a mass of 1 kg and inertia values of 1 corresponding to the previous figure. Now you have made all the necessary specifications. Further options of the dialogue refer to an optional initial velocity of the link which is not needed here. ÍÍWith OK the link will be created. It is recommended to enter a meaningful name before the link is created (Hebel_re). ÍÍNow you create links in the same way for the left lever and for the tie rod. The result should look like in the figure above. Next, the joints can be generated.
2.2.2.7 Creation of Revolute Joints Generating joints by schematic sketch curves is usually more complex than the use of solids, because the definition of the axes of rotation must be carried out explicitly. For solids at joint locations there often exist form features such as holes, which make an explicit specification of the direction unnecessary. This was the case in the previous example.
2.2 Learning Tasks on Kinematics 39
Subsequently four revolute joints are created for the bearing of the two levers to the environment and for the connection of the tie rod to the two levers. We begin with the joint of the right lever to the environment. ÍÍActivate the Joint function to create the revolute joints. ÍÍSelect Revolute for the joint type. ÍÍSelect the right lever for the Action definition roughly at the location where the joint should have his center of rotation. With this selection, you have defined the first link that should be connected by the joint and the point at which the joint should be located. In the next step the Origin and the Orientation of the joint can be defined. The origin has been assigned already in the first step, therefore, it can be changed to the direction definition, which has automatically not been determined correctly. The direction of rotation of the revolute joint is defined by the Z-direction of the displayed coordinate system. ÍÍIn the dialog box, navigate to the selection step of the vector definition for the orientation and change it to the global Y-direction.
Using curves for the creation of links, the system can usually not automatically determine the direction of rotation. Therefore, this must be defined manually.
A red coordinate system for the orientation of the joint appears. This is the local joint coordinate system. The Z-direction of this system is the direction of rotation of the joint. With the next selection step Base the second link could be specified which is connected to the first. In the case of a connection with the fixed environment, as desired here, this step is skipped. ÍÍTherefore, just select OK. The joint will be created then. The dialog box for creating joints: A joint connects two bodies (Action and Base). An origin and an orientation are required.
ÍÍYou now create the revolute joint between the left lever and the fixed environment in an appropriate way (in this case there is nothing new to be considered). ÍÍA little different is the generation of the two joints between the left and right lever and the tie rod, because the joints are not fixed to the environment, but to another link. For
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both joints the connected Link has to be selected for the Base as the last selection step. That means, that if the lever is selected for the Action, the tie rod must be selected for the Base. ÍÍCreate the two joints between the tie rod and the two levers in the same way. The vector direction is always the Y-direction. At Base, Select Link the respectively other body will be selected. ÍÍSave the file. The result should look like the figure above. The display size of the joints has been enlarged in the figure. This can be done under the Preferences settings for Motion. With this last step the generation of the joints is completed and a test run can be performed.
2.2.2.8 Test Run with one Undetermined Degree of Freedom The dynamic test run with an undetermined degree of freedom helps to understand the mechanism and its behavior.
Because the mechanism does not have a kinematic driver yet, there is an undetermined motion possibility for the entire system. The number of undetermined degrees of freedom can also be obtained via the function Information, Motion Connections from the context menu of the motion model, as it has been shown in the previous example.
The dynamic analysis is performed as a plausibility check. The curves oscillate back and forth.
The direction of gravity should be set in a suitable way before a dynamic test run. The negative x-direction, for example, would be good. A solution is generated here, which calculates a time of three seconds.
ÍÍCreate a Solution of the type Normal Run, and select a Time of, for example, three seconds, and a number of Steps of 200. Change the direction of the Gravity to the positive x-direction. ÍÍWith OK the solution will be created and is ready to be solved (Solve). ÍÍAn information window occurs that indicates the number of redundant constraints. This will be discussed in more detail in the next section. Therefore, the window can be ignored first. ÍÍNow, the Animation can be started. ÍÍTo run the motion, use the Play function.
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The result is a pendulum-like oscillation. A snapshot of it is shown in the above figure on the right. The previous mechanism therefore results in a slightly damped1 oscillation, which also seems plausible. After this successful plausibility test the creation of the mechanism could be continued, but first we want to insert a section about redundant degrees of freedom.
2.2.2.9 The Meaning of Redundant Degrees of Freedom The information window that appears during the previously performed test run, points the user to redundant constraints. This can be understood as a warning.
Degrees of freedom with redundant determination are redundancies which do not lead necessarily to conflicts.
A redundant degree of freedom means that a degree of freedom of the system is over-determined, but this over-determination does not result in a conflict yet. Indeed, the mechanism runs, but small changes in the geometry or the axes of rotation could lead to a conflict situation. In our case, there are three such redundancies according to the information window. The occurrence of these redundancies is relatively difficult to understand. One method is the following: At each link and each joint a small translation or rotation in all six possible directions is theoretically applied. If the mechanism gets into a conflict situation, then there is an over-determination of the according degree of freedom. In our case, the following three redundancies are present:
How to imagine redundant degrees of freedom.
If any of the axes of rotation is tilted around the global X-axis, it results in a conflict, if any of the axes of rotation is tilted around the Z-axis, too, and if one of the two points which are connected to the environment is translated in Y-direction, it also results in a conflict situation.
Smallest geometric changes can cause a redundant degree of freedom leading to a conflict.
1 The RecurDyn solver has a numerical damping preset and active. The ADAMS solver does not use such a damping by default. These settings can be checked and changed in the Solver parameters of the Solution element.
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To understand the meaning of redundant degrees of freedom, it should be remembered again that a motion simulation model is a rigid body model, in which the moving bodies are not elastic like in reality. In reality, small inaccuracies (for example, thermal expansion) are tolerated – on the one hand by clearance in the joints and on the other hand by the resilience of the parts. The two effects “clearance” and “elasticity/flexibility” are not included in the MBS simulation. Therefore, in a redundant defined motion model, even smallest inaccuracies, as they also occur in the construction of a CAD model, already lead to conflict situations. It is therefore recommended to accept such redundant degrees of freedom only for very simple motion models. More complex motion models should be possibly built without redundancies, so that they work reliably. Complex mechanisms should be possibly set up without redundancies.
In order to build the motion model free of redundancies, appropriate joint types must be found by which the degrees of freedom are not over-determined. What types of joints are suitable for this purpose, must result from plausibility considerations. One solution for example would be the following: If any of the four Revolute joints is replaced by a Spherical joint , the first two conflict situations shown before can no longer occur. If additionally any revolute joint is replaced by a Cylindrical joint , the third conflict situation will be resolved.
The used joints may not always correspond to reality, because in the motion model no tolerance and no flexible parts are initially possible.
This joint configuration does not suit the way how the mechanism is constructed in reality, but this difference has no influence on the consideration of the kinematics. This approach is typical for creating motion models with multi-body-dynamic programs in which clearance and elasticity are not considered. Of course, clearance and elasticity can be simulated, but therefore more complex methods are required. For example, reference may be made here to the function of 3D Contact, with which clearance can be modeled in the motion model, and the finite element method that can calculate the flexible bodies. Therefore, in the following, the described joints will be replaced in order to obtain a model which is free of redundancy.
2.2.2.10 Integration of a Spherical Joint We create alternative joints.
A spherical joint needs less information compared with a revolute joint because no information about the axis of rotation is required. That is why an existing revolute could be directly changed into a spherical joint. Proceed as follows: ÍÍSelect the node of the joint which should be modified in the Motion Navigator (see figure below).
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ÍÍSelect the EDIT function from the context menu. The definition dialogue of the joint appears. ÍÍSet the joint type to Spherical and accept with OK. Alternatively, instead of this change, a new spherical joint can be created. The direction of orientation can be assumed arbitrarily, because in a spherical joint it plays no role.
A spherical joint may act like a revolute joint, which has “clearance”.
2.2.2.11 Integration of a Cylindrical Joint A rotary-sliding-joint or a Cylindrical joint requires the same information as a revolute joint. Therefore, an existing revolute joint can be converted directly into a cylindrical joint. Proceed as follows: ÍÍSelect the EDIT function in the context menu of the joint which shall be transformed (see figure below). The joint types could be easily changed subsequently.
ÍÍFrom the dialog, select the joint type Cylindrical
and accept with OK.
Alternatively a new cylindrical joint could be created corresponding to the revolute joint. After these two joints have been replaced, a new dynamic test run can optionally show that there are now no redundant degrees of freedom anymore. Despite the problem with the redundant degrees of freedom, it should be kept in mind that there should not be free degrees of freedom (no “loose screws”), too. Therefore, this should also be verified with the previously described method. The term “Degrees of Freedom: 1” indicates that currently there is an existing undetermined degree of freedom, which is reflected in the free pendulum motion. This will be removed in the next section.
2.2.2.12 Definition of a Kinematic Driver With the definition of a kinematic driver the last undetermined degree of freedom is eliminated from the mechanism, and the system becomes a pure kinematic system. Proceed as follows: ÍÍEdit the revolute joint from the right steering lever for which you want to define the driver (see the following figure). ÍÍIn the generation dialog box, select in the Driver tab the type Constant and set the desired driver parameters. ÍÍAccept with OK.
An undetermined degree of freedom still exists.
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On revolute joints a translational driver could be enforced.
Therefore, the driver parameters may be set arbitrarily, because for the pure movement investigation, the articulation function is to be used, which allows manual operation of the drivers. With the motion model build up this way, both the articulation and the animation can be performed.
2.2.2.13 Performance of an Articulation With the following articulation the motion of interest shall be displayed once. Based on this motion a graph shall be created in the next section. Proceed as follows: The animation shows the calculated motion.
We let the mechanism move in both directions.
ÍÍCreate a new Solution and change the type to articulation. Accept with OK. ÍÍStart the articulation by selecting the Solve function. ÍÍActivate the box of the joint driver and insert a Step Size of, for example, 1 degree and a Number of Steps of 30. Depending on the dimensions in the sketch, calculating a rotational displacement of 30 degrees can also lead to clamping situations. This is indicated by the Solver Lockup window. In such a case, you should calculate the solution again and define a smaller displacement, for example only 25 degrees. ÍÍSelect the function Step Forward once to rotate the driver 30 degrees in one direction, then twice Step Backward , to move it to 60 degrees in the other direction, and once again to come back to the starting position. ÍÍWith CLOSE the motion is finished.
Here we have 30 steps run.
The defined motion is used in the next section for the creation of graphs.
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2.2.2.14 Graphing the Wheel Angle Motion In the previous section, a motion was defined in terms of the articulation function. Now this is to be evaluated graphically. It is important to ensure that when executing the articulation indeed only that motion is done, which shall be analyzed later. In the background, the NX system writes a results file in which the performed motion is described. This results file is now evaluated with the NX Graphing function. The resulting file has the extension “rad” and can be found in the directory in which the Motion Simulation file is located. To create a graph with respect to the wheel angle movement, proceed as follows (see also figure below): ÍÍSelect the function Graphing . ÍÍIn the upper part of the appearing menu, all joints are displayed. Here you select the first of the two revolute joints whose way is to be recorded, in our case the joint J001 (the drive link).
selection of the recording joint or link selection of the recording value
selection of the component translational (X, Y, Z) rotational (RX, RY, RZ) or magnitude
Relative: Coordinates of joint Absolute: Coordinates of model list of all curves which should be plotted add curve (+) or remove curve (-) from the graph
At Request select the result type. Possible choices are Displacement/Rotation, Velocity, Acceleration and Force/Moment. ÍÍTherefore, for the desired angle of rotation in this case, select Displacement.
The graph to be created always evaluates the last performed motion.
Displacement, velocity, acceleration or force/ moment in each joint are evaluated. The information may be given in absolute or in moving coordinate system.
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At Component select the desired component of the previously specified request. Available are translational values, rotational values and the respective magnitudes. This definition refers to the indication at Reference Frame which can use either Relative or Absolute. In the relative case the definition belongs to the moving joint coordinate system, in the absolute case to the absolute coordinate system of the part. ÍÍFor our example, select the relative coordinate system and the component “RZ”. Thus, the rotation of the revolute joint to the local axis of rotation is displayed. ÍÍSelect the plus sign (Add one Curve) to add the so-specified graph to the list of output graphs. ÍÍIn order to record the second revolute joint in the same way, you choose J002 in the upper area joint, use the same settings and add this definition with Plus also to the list. ÍÍFinally, select OK, and click once in the graphics window so that the graph is represented. The result is shown in the figure below. In the graph, the movement course over time for the articulation function is shown. Each moving step here corresponds to one second. It can be seen that the first end position is reached at step 30. Furthermore it can be recognized that the two wheel angles have different sizes. In the following we will measure the difference of the angles in the first end position. The wheel angles move unevenly. This is a consequence of the parallelogram in the steering levers.
To read values from the graph, the function Probing Mode from the toolbar XY graph can be used. This toolbar has several more interesting functions that are mostly self-explanatory. To evaluate the graph a set of utility functions are available.
The function allows to traverse the graph with the mouse. In the upper right area the graph values are displayed in a small window. In our example for the first steering angle
2.2 Learning Tasks on Kinematics 47
you read 27° for the right and 20.58° for the left lever. The angle difference is thus 6.42°. These numbers may vary, depending on the dimensions of the basic sketch. ÍÍWith the function Return to Model
you leave the graph representation.
Changes to the geometry of the basic sketch can now be done as desired and checked again using the difference in angle.
2.2.2.15 Creation of Assembly Components out of Sketch Curves As soon as the geometric variables are set in an acceptable way using the basic sketch, you can proceed with the top-down design of assembly components. This problem is more related to design methodology than to motion simulation, therefore, only short explanations shall be made here. The aim is to create assembly components, whose geometry and position depend on the principle geometry of the sketch. In addition, the components to be created shall be moved in Motion Simulation.
After the kinematics is properly adjusted, components can be created using the topdown method.
The dependence of geometry and position can be reached via Wave Geometry Linker. The movement in the motion simulation may be accomplished by simply adding new geometry to existing Links. We start with the generation of empty components, add the sketch geometry with the Wave linker in the new components and then build detailed geometry objects of the levers depending on the newly inserted linked curves. Proceed as follows:
If associativity is desired the WAVE-GeometryLinker has to be used.
ÍÍSave the file motion_1. ÍÍLeave the Motion Simulation environment by selecting the master part in the simulation navigator and in the context menu the Make Work option. ÍÍStart the Modeling application. The part lenkhebelmechanik is the active and displayed part now. ÍÍUse the Create New function from the Assemblies toolbar and enter the file name for the first component, for example vr_lenkhebel_re2.prt. Now click OK. ÍÍIn the next window just accept with OK without any selection. ÍÍPerform the same procedure from the last two steps for the next two components. Name them vr_lenkhebel_li2.prt and vr_spurstange2.prt. ÍÍSave the file lenkhebelmechanik. The new assembly structure
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The result in the Assembly Navigator should look like displayed in the previous figure. In the following WAVE Geometry Links are created. Proceed as follows: ÍÍMake the part vr_lenkhebel_re2 the active part. ÍÍOpen the WAVE Geometry Linker with MAIN MENU > INSERT > ASSOCIATIVE COPY. ÍÍSet the type to Composite Curve. Now, select the two curves which should belong to the right lever as shown in the following figure. Accept with OK. ÍÍRepeat the last three steps for the left lever and the tie rod. Select the geometry for each. Creation of associative geometry objects within the assembly
After these steps have been performed, the work can continue in each of the three components. The idea is that the overall geometry of the part is generated as a function of the linked sketch curve. Very different methods can be used for the construction of the geo metry. We will describe a very simple modelling strategy below. In addition, we are modeling only one of the parts as an example: the tie rod. The other parts can be modeled at will. Proceed as follows: ÍÍMake the component vr_spurstange2 the active part. Use the Fit function of the View toolbar to make the curve visible. ÍÍOpen the Tube function, select the curve and enter 20 mm for the outer diameter and 0 for the inner diameter. Accept with OK. Within each component, the respective part geometry is modeled. The basic feature is the associative curve from the kinematics.
At discretion further features can be created now, for example for a higher level of detail of the joints on both sides as shown in the previous figure on the right. The parts can be arbitrarily detailed. However, basic geometric dimensions are determined by the control sketch.
ÍÍAfter finishing the 3D-modelling of the part, change to the lenkhebelmechanik by using the Display Parent command from the Assembly Navigator. ÍÍThe geometry objects for the further components (vr_lenkhebel_li2 and vr_spurstange2) can be created in the same way.
2.2 Learning Tasks on Kinematics 49
The principle is always the same: The coarse geometry of the basic sketch contains the basic dimensions and positions. From these curves, the component parts are designed and detailed dependently. If necessary, you can look up in the already constructed parts vr_hebel_re.prt, vr_hebel_li.prt and vr_spurstange.prt which design methodology could be used. However, for the methodology of our learning task a very simple design is enough, as it was shown at the tie rod.
ÍÍMake the part lenkhebelmechanik the active part and save the file after creating all geometry objects in the components. In the next step the new created geometry should be included in the motion model, so it follows the movements to check the model for collisions.
2.2.2.16 Adding the New Components to the Motion Model If new geometry objects should be moved together with existing links, we have to work on the links. Proceed as follows: ÍÍIn the assembly make the part lenkhebelmechanik the displayed part and the active part. In this part the motion model is located. ÍÍChange to the Motion Simulation application and open the already created motion model motion_1 in the Motion Navigator. ÍÍPerhaps the solid bodies are invisible. In this case select in View the function Show and Hide and select the plus button for All. ÍÍEdit the Link Spurstange by right-clicking it in the Motion Navigator and selecting the EDIT function in the context menu. ÍÍChange the Selection Filter to COMPONENT and select the new created geometry. ÍÍChange the Mass Properties Option from User Defined to Automatic. ÍÍAccept with OK. ÍÍPerform these steps for the other two parts.
The new geometries do not move with the existing links initially in the kinematics.
Any new geometry objects can be assigned to existing bodies.
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After performing these steps the animation or articulation function can be run again. The newly created geometry now moves with the principle curves. In addition further changes can be made to the principle sketch. The component geometry is updated accordingly. To leave the Motion Modell proceed as follows: ÍÍSave the file. ÍÍDouble click the part lenkhebelmechanik in the Simulation Navigator. ÍÍChange to the Modelling application. ÍÍSave the assembly and close all parts. With this the subtask is finished.
2.2.3 Collision Check on Overall Model of the Steering System This task shows how already created motion models that belong to subassemblies are assembled to a motion model in an upper assembly and how they are reused. This is an important method in the development of complex assemblies, because it allows to work with a modular method to build motion models. In addition, this example shows even more types of joints and the method for checking the model for collisions. Single kinematic models are assembled to an overall system.
If you have worked through the prior two exercises you can use your own motion models. Otherwise, you can use the already finished models from the download.
2.2.3.1 Task The designers now have already created assemblies and motion models of the steering gear and the steering arm kinematics. Therefore, now the overall steering system should be analyzed.
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The finished sub kinematics should be used whenever possible and not be recreated. The overall system has to be tested for collisions between the levers during the turning of the steering wheel. To make matters worse, the deflection of the wheels has to be taken into account. The deflection movement of the wheels is another difficultly manageable movement of the system. Therefore, tests must also be made here. It would also possibly make sense, to check the size of the wheel housing the wheel movements. If it comes to collisions, the penetrating bodies must be recorded. This is done so that the designer gets an indication of the possible improvement of the affected parts.
2.2.3.2 Creation of the Motion File ÍÍOpen the vr_lenkung assembly in NX. ÍÍStart the Motion-Simulation application. ÍÍDelete the already existing motion files in the Simulation Navigator. ÍÍCreate a new motion file. Accept the default settings (e. g. Dynamics). ÍÍCANCEL the occurring Motion Joint Wizard.
2.2.3.3 Import of the Motion Subassemblies In large assemblies, subkinematics can be created at first. Later, these subsystems are assembled to the overall system. The import of a motion model from a subassembly is described below.
2.2.3.3.1 Preparations ÍÍUse the Rename function from the context menu of the model motion_1 in the Motion Navigator and rename the new motion model Lenkungssystem, for example. The original name cannot be used because this will lead to naming conflicts with the imported motion models that possibly use the same names. When importing Motion submodels you should pay attention that all geometry objects that belong to the links are loaded. This also means that these geometry objects are not excluded by Reference Sets. ÍÍTherefore, check if the part lenkhebelmechanik_prinzip is set to the Reference Set Entire Part before you start with the next steps. Use the Assembly Navigator for this. The sketch curves have to be visible after changing the Reference Set.
2.2.3.3.2 Performing the Imports ÍÍSelect the Import, Mechanism function from the context menu of the Motion Navigator.
Check for collision and simulation of the deflection
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ÍÍIn the next window select the Import From Subassembly button. A kinematic model is imported.
A dialog appears in which you select the subassembly whose motion model you want to import. The easiest way to select this subassembly is the selection in the Assembly Navigator. We start with ls_lenkgetriebe: ÍÍSelect the subassembly ls_lenkgetriebe in the Assembly Navigator. In the dialog box existing motion models of the selected assembly are displayed, as shown in the figure below.
For the selection of the subassembly the Assembly Navigator can be used.
ÍÍSelect the model motion_1 and accept with OK. ÍÍConfirm the reoccurring menu Mechanism Import with OK. An information message appears confirming that all motion features were successfully imported. Now the import of the second motion model follows. ÍÍSelect the FILE > IMPORT > MECHANISM > IMPORT FROM SUBASSEMBLY function again and select the lenkhebelmechanik assembly from the Assembly Navigator and from that the Motion Model motion_1. If there is a conflict between identical names, for example at the joints, the system automatically assigns new names. In our case the joint names J001 and J002 are already taken by the steering gear, and the corresponding joints in the lenkhebelmechanik get the names J001_01, J002_01 allocated. This is also documented in an information window. The result in the Motion Navigator should look like shown in the following figure.
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imported sub kinematics: steering gear
In the navigator the sub kinematics are displayed as groups.
the driver should stay in this joint imported sub kinematics: steering arm mechanism
remove the driver for this joint
The two submechanisms are arranged in groups. However, they can be manipulated without restriction (as before).
2.2.3.3.3 Post-Processing Finally, you should delete the driver in the joint of the lenkhebelmechanik (joint J001_01 in the figure above). Instead, the steering rod is used for transmitting the movement from the steering wheel driver. Otherwise there would be a deadlock in the system.
A few things have to be adjusted.
ÍÍEdit the revolute joint (J001_01 in the figure above), whose driver should be deactivated. Change the option Driver to None. ÍÍAccept with OK. You should also add the right wheel to the link of the right and the left wheel to the link of the left steering lever. Proceed as follows: ÍÍEdit the link of the right lever. ÍÍSet the Selection Filter on Component and select the parts which belong to the right wheel. This can either be done by a rectangle gesture for multi-selection or the parts can be selected via the Assemblies Navigator. ÍÍAccept with OK. ÍÍAdd the parts of the left wheel to the Link of the left lever in the same way. ÍÍSave the file.
Some assembly components are added to the links subsequently.
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After this last step the import of the models is finished. As desired, a dynamic test run in order to improve the understanding of the undetermined degrees of freedom of the whole system can be performed as far as created.
2.2.3.4 Adding the Steering Rod The steering rod connects the two kinematic modules.
The steering rod performs a complex motion in space.
The steering rod has to be constraint so that they can perform movements in space, without causing conflict situations (see also the figure below). A possible type of constraint for such cases is composed of a turnstile on one end and a spherical joint on the other side. The turnstile consists of an auxiliary body, which connects the adjacent two parts with two revolute joints. These joint types are already provided in the CAD model, as the following figure shows. pitman arm
steering rod spherical joint
steering arm right
connecting body with two revolute joints
The following describes how this combination of joints is created in the motion model.
2.2.3.5 Creation of the Turnstile with an Auxiliary Body ÍÍFirst create a Link for the part of the steering rod (the mass properties are set to Automatic). ÍÍCreate an additional link for the part of the auxiliary body. ÍÍThen create a first Revolute Joint that connects the auxiliary body to the pitman arm, and a second Revolute that connects it to the steering rod according to the figure below. According to the figure below, the two revolute joints are oriented rectangular, thus forming a turnstile. The auxiliary body connects the steering rod with the pitman arm.
pitman arm
revolute joint
steering rod revolute joint connecting body
If desired, a further dynamical test run could be performed.
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2.2.3.6 Creation of a Spherical Joint Prior to the generation of the spherical joint between steering rod and right steering lever (see figure below), the link of the right steering lever should be prepared in such a way that two other components belong to it:
The spherical joint connects the steering rod on the front side.
ÍÍEdit the link of the right steering lever and add the components ls_lenkstangengelenk and ls_lenkstangenkugelkopf. ÍÍFor the spherical joint, it is important that the correct point of rotation is defined. Therefore, you should set the Reference Set of Part ls_lenkstangen-kugelkopf on Entire Part because basic sketches are visible then, and with those the center of the sphere can be properly associated. Create the spherical joint as follows: ÍÍSelect the Spherical joint and select the center of the sphere as the first link (static wireframe), which is shown in the following picture. This point belongs to the component steering bar ball head (lenkstangenkugelkopf) and therefore to the link Hebel_re you have now selected as the first link. Because the correct center of the sphere was already defined in the first selection step, the selection of the Origin can now be omitted, and just one (arbitrary) orientation has to be selected. ÍÍSelect any edge or face to specify the Orientation. ÍÍThe next selection step is to define the second connecting link, the steering rod, as Base. Select again any edge or face. ÍÍAccept with OK and the spherical joint will be created. ÍÍSave the file. An extra point defines the exact position of the rotation point of the spherical joint.
2.2.3.7 Articulation of the Overall System The current state of the mechanism has no more undetermined degrees of freedom. This should be checked with the function that was described in the basic example (Information, Motion Connections in the context menu of the simulation file). The mechanism has its driver on the steering wheel that is part of the imported model.
Test the current state of the overall system
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ÍÍTherefore a Solution of the type Articulation can be created. ÍÍThe articulation is started by selecting the Solve function. ÍÍThe steering wheel can be rotated in any way, and the whole steering mechanism should follow this movements.
2.2.3.8 Add Mechanism for Spring Deflection A simplified representation of the deflection
In addition to the previously created mechanism of the steering system, the effect of spring deflection at the wheel shall be considered. We only want to look at a simplified deflection at which both wheels deflect simultaneously. The result is a mechanism in which two different drivers exist, one for compression, and one for the steering movement. With that mechanism, for example, the required space for the wheel cases can be checked. With a little more effort a separate controllable deflection of the two wheels could easily be implemented, which would be of course more realistic. We leave the realization of this to the motivated reader as a “voluntary exercise.” The desired deflection of the wheels in the motion model is realized as shown in the figure below. Therefore, the right and left steering levers are no longer connected to the fixed environment but to the cross member. First, a Link has to be created for the cross member. The cross member is then connected to the fixed environment by a Slider. This Slider is ultimately the driven joint. With this, the cross member can be moved via the articulation function. Of course, the steering wheel can be moved at the same time, too.
This model allows only the deflection of both wheels at the same time.
2.2.3.8.1 Creation of a Slider at the Cross Member For the creation of the slider at the cross member proceed as follows: ÍÍFirst the component vr_quertraeger_gerade is defined as a Link . ÍÍThen you select the function to create a Joint of the type Slider . ÍÍIn the first selection step choose the geometry of the cross member at an edge which points in the sliding direction of the joint, if possible. Thereafter, the joint coordinate system appears and points with its Z-axis in the chosen direction.
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ÍÍA second link does not need to be selected because the joint should be connected to the environment. ÍÍEnter a meaningful name like “Einfedern” (deflection), for example. ÍÍChange to the Driver tab and select the Constant or Articulation option. No values have to be entered. ÍÍAccept with OK to create the joint.
Steps for the creation of the Slider which performs the deflection movement.
As described above, it does not matter which driver type is selected and which parameters have been entered if using the articulation function.
2.2.3.8.2 Edit the Revolute Joints at the Steering Levers The two revolute joints at the steering levers connect the levers to the fixed environment because we have defined them like this before. Now this joints should be edited in a way, that they connect the levers to the new created link of the cross member. Joints are associative objects. So all properties could be edited or re-referenced at a later time.
Proceed as follows (see previous figure): ÍÍEdit the revolute joint which connects the right steering lever to the environment. The dialog appears in which you can do any change of the properties. ÍÍActivate the selection of the Base. Note that a zero is entered so far. You had previously selected nothing here and thus chosen the fixed environment. ÍÍSelect the new created cross member. ÍÍAccept with OK. The Revolute is updated with all changed settings. ÍÍProceed with the revolute joint at the left steering lever in the same way. ÍÍSave the file.
The environment is replaced by a second Link.
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2.2.3.9 Go through the Motion during Deflection and Steering ÍÍNow, since two manually variable drivers are present, it is useful to name the drivers (or their joints) according to their function, such as “Einfedern” (deflection) and “Lenken” (steering). The articulation function is well suited to control the movements with several drivers.
With the current mechanism, the movements for steering and deflection may be combined or controlled individually. For example, first a 30 mm deflection could be applied and then the steering will be performed in the deflected state. ÍÍTest the motion of the steering with the articulation function. It can be checked visually, if collisions occur and which deflection leads to a collision between the two parts steering rod and tie rod. A further collision control is discussed in the next section.
2.2.3.10 Collision Check To perform a collision check between steering rod and tie rod during the deflection, you can proceed as follows: The penetration test is prepared.
ÍÍSelect the function Interference . ÍÍSelect for the First Set the steering rod and for the Second Set the tie Rod. ÍÍAccept with OK to create the penetration test. The feature appears in the Motion Navigator and can be manipulated from there.
The penetration test can be used.
ÍÍAfter creating the Interference feature the collision check can be performed by selecting the Solve function. With this, the articulation is started. You can perform the collision check the same way also with the animation function. ÍÍBefore you perform the motion in the articulation select the More button. The advanced options of the menu are opened in the dialog now. Activate the check box of the Interference under the Packaging Options. ÍÍIf you want to calculate the point of collision exactly and want the simulation to stop after the occurrence then you have to additionally activate the check box Stop on Event. ÍÍNow run the articulation for the desired displacement and rotation of the joints. As soon as a collision between the two solid bodies occurs a stop message appears and the
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motion stops immediately. After accepting the message, the exact position of the drivers during the collision can be read. The articulation function determines and displays exactly in which position the interference occurs.
ÍÍClose all parts. With this last step the Motion Simulation exercise of the steering system is completed.
■■2.3 Learning Tasks on Dynamics 2.3.1 Drop Test on Vehicle Wheel This learning task explains how to deal with tasks that have to do with free movements. This could involve, for example, free-fall, inertial effects or similar problems. There are thus indeterminate degrees of freedom, and the movement arises due to forces. Experience has shown that such problems are much more difficult to use in practice than is the case with the previously-considered kinematic systems. We therefore wish to clarify the principles on a very simple model.
Characteristic of dynamics is that there are indefinite degrees of freedom and that movement results from external forces.
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motion track
initial position
end position Geometry of environment Lifting off or hitting contacts often plays a role in dynamic tasks.
Additionally to dynamics, also complex contacts play a role in this example which definitely differ from the previously used purely kinematic joints. Hitting or lifting off parts of the contacts under consideration is possible. Thus, opportunities arise for the analysis of impact tests, friction effects, clearance or tolerances.
2.3.1.1 Task In this learning object, a simulation shall be created, which shows how a wheel of RAK2 is released from a certain height and accelerates through gravity. It bumps against several stairs and finally remains lying on a plane. Finally, the movement has to be tracked and recorded, which describes the wheel during the fall.
2.3.1.2 Preparations First some preparations must be made. These things are basically already known from the previous examples:
The steps to be performed for the learning task
ÍÍLoad the file vr_rechts that contains the right front wheel of RAK2 and associated parts of the brake from the RAK2 directory. ÍÍSwitch into the application Motion-Simulation and create a simulation file in the motion navigator. Accept the default option Dynamics. ÍÍThen the Motion Joint Wizard appears – cancel this wizard. ÍÍCheck to see in Environment whether the setting Dynamic is active, so that the analysis of indeterminate degrees of freedom is possible. ÍÍAlso make sure that the direction of gravity points into positive y-direction: Change the default settings for motion (Preferences, Motion) at Gravitational Constant. Next, the surrounding geometry must be imported. You can also create your own environment geometry if you wish. If you want to create it yourself, turn into application modelling and feel free creating your own geometry. If you prefer using the prepared geometry, which exists in part umgebung1.prt, proceed as follows:
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ÍÍSwitch into the application Modelling . ÍÍSelect function FILE > IMPORT > PART . . . ÍÍIn the next menu, confirm all settings with OK. Now, the dialog for file selection appears. ÍÍHere you select the file umgebung1.prt in the RAK2 directory and confirm with OK. ÍÍIn the next menu you confirm the position (0, 0, 0). Then cancel the menu. ÍÍFill the screen. ÍÍSwitch back to application Motion.
A geometry will be imported.
Now the imported geometry can be viewed.
2.3.1.3 Assignment of Mass Properties Prior to generating links in the next section, the assignment of mass properties for this dynamic analysis shall be performed. This is done by material properties, which are given to volumes or sheet bodies. Together with geometric characteristics which are already available from CAD geometry, the NX system is capable to calculate accurate mass properties, i. e. mass, center of gravity and inertial properties. In the following, these properties are applied to the bodies in the simulation file. Thus any other possibly existing material or density information of a body is overwritten. If a body does not have material or density, then by default the density of steel is active. It is also possible and quite meaningful to assign the material information not only in the simulation file, but already in the CAD master part. This has the advantage that information is available in each assembly and each simulation file into which this master part is installed.
The NX system calculates mass properties for each moving body via assigned density.
If material information includes not only the density, but also, for example, the Young’s modulus and Poisson’s ratio, this method even has the advantage that different applications such as finite element analysis and multi-body simulation can be supported simultaneously. The functionality in NX allows the selection of stored materials from a library as well as the definition of new material properties. To assign a user-defined material with the density properties of rubber to the tire in the simulation file, proceed as follows: ÍÍSelect from main menu at Tools, Material Properties the function Assign Materials . ÍÍSelect from the graphics window the tire geometry. ÍÍNow select (at the bottom of the window) the function Create Material . ÍÍIn the next field Name, enter a material name, such as Rubber, and for Mass Density the value 1.3e-006 kg/mm3. ÍÍConfirm with OK to create the material. On the next window, click APPLY to assign the material to the selected tire body.
The NX system has a library of standard materials. Own libraries can be created.
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To assign the properties of steel (from the library) for the remaining parts, proceed as follows: ÍÍSelect the remaining geometry objects and after you have set the search criteria to metal, select the material Steel from the library list. ÍÍConfirm with OK. If no material is assigned NX assumes steel density.
The second step of assigning steel is not necessary because of the general preference for steel. The materials database of NX can be customized and provided with additional materials. Also very useful is the opportunity to create your own private libraries. Functions of this can be found in NX at TOOLS > MATERIAL LIBRARY MANAGER. The format used for material data in NX is a standardized XML format that is compatible with many other software programs.
2.3.1.4 Definition of Links The definition of links is easy if they are solid bodies to which material properties have already been assigned. In principle, only one link for the wheel would be required in this example. The environment geometry does not move, so there is no need for creating a link for this. However, each MBD mechanism needs at least one link that is connected to the fixed ground via a joint to be calculated. Because the wheel will float freely in space and therefore will get no joint, there would be no joint-fixing to the ground at all. For this reason the environment geometry will be defined as a link and connected by a fixed joint to the fixed ground. Alternatively, at any other location a joint could be added to the ground. Proceed as follows for the definition of the moving body in the wheel: ÍÍSwitch into the application Motion. ÍÍSelect the function for generating motion bodies (Link) . ÍÍSet a selection filter to Component and select, easiest in the assembly navigator, the component vr_rechts. ÍÍMake sure that the option for mass properties is set to Automatic. ÍÍConfirm with OK. The link is now generated. Consider that the creation of this link may take some time to complete, because the geo metry is complex and therefore the mass properties analysis is correspondingly complex. A link may already be made associated with ground at the creation process.
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ÍÍNow create the Link for the ambient geometry. ÍÍSet the selection filter this time on Solid Body and select the environment geometry. ÍÍTo immediately fix this link to ground, activate Fix the Link in the menu. Alternatively, you can also create a joint of the type Fixed afterwards that connects the environment geometry with the ground. ÍÍConfirm with OK. The link is now generated. Now both moving bodies are generated and there exists a joint to the fixed ground. You can now perform a dynamic test run if desired, in which the wheel would fall through the environment geometry, because still no contact element has been defined. This contact element will be discussed and constructed in the following two sections.
2.3.1.5 Operation of 3D Contacts Using the feature 3D Contact , the collision behavior of two solid bodies is modeled. This contact can take place either between two moving bodies or between one moving and one stationary environment body. The settings on the contact differ depending on whether the RecurDyn or Adams solver is used. However, the basic operation is the same for both. Our explanations are used in a way that the findings can be used for both solvers. Furthermore, we restrict our explanations to the default contact type Solid, which is the recommended one. The other two types Facetted and Fitted are useful only for compatibility purposes with older NX models. If 3D contacts are included in the motion model, the system has to divide the movement into many small steps. There will be performed even subdivisions pwhich go beyond the user specified number of steps. Therefore, there will be considerably higher computation times in the presence of 3D contacts.
The movement is divided into small steps.
In contact analysis, there will be small penetrations, because moving bodies are assumed to be not flexible.
During each step all involved surface pairs must be examined with respect to their contact behavior. If a contact surface pair penetrates, the system immediately calculates contact restoring forces and additional forces that are responsible for friction and damping behavior. In the next computation step these forces ensure that the involved bodies are prevented from further penetration and that realistic frictional effects arise.
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The contact restoring forces are calculated with a non-linear relationship.
The basic equation for analysis of contact restoring forces F is: F = K · xe In this equation K is stiffness, x penetration and e is the force exponent for nonlinear contact stiffness. The stiffness and force exponent values can be changed by the user, but there are default settings for these parameters, which can be used in many cases. To give more realistic results, these parameters must be adjusted, for example, by measurements during experiments. Additionally to contact restoring forces, in order to describe contact behavior even more realistic, friction and damping forces can occur, which will be described in the following section.
2.3.1.6 Operation of Friction on 3D Contact Friction is calculated according to the Coulomb model. Frictional forces are determined from pressing forces between two components, and a user-definable coefficient of friction μ. This coefficient of friction results from a coefficient of static friction and one for sliding friction. In addition to friction coefficients, two speeds must be specified: Stiction Velocity and Friction Velocity, which are applied by the system as follows (see figure below). Friction is calculated according to Coulomb’s law.
The smaller velocity must be Stiction Velocity. This indicates up to what speed the coefficient of static friction should apply. The greater velocity must be the Friction Velocity. This indicates the speed at which the coefficient of sliding friction is applied. Between these two speeds there remains a speed range in which the coefficient of friction is linearly transferred from static friction to sliding friction.
The two velocities should not be chosen too close to each other, since otherwise, due to very abruptly applied forces, the convergence behavior of the internal analysis may be disturbed. For all these friction parameters there are presets, which can be used in many cases.
2.3.1.7 Operation of Damping on 3D Contact Damping properties reduce velocities at movements. When using the Adams Solver, damping can be defined by the user by specifying a Force Model. In the RecurDyn solver only the model Impact is possible. We will explain this below.
2.3 Learning Tasks on Dynamics 65
For the consideration of damping, there exist two different models.
With the model Impact a value for Material Damping and a Penetration Depth are specified. The damping value is not immediately fully applied at penetration, but is gently rising, so that it grows to its full value only at the predetermined depth. This method prevents any suddenly applied loads from disturbing convergence behavior of the internal analysis. Furthermore, the contact stiffness is defined in this menu.
2.3.1.8 Solver Settings for Contacts and Accuracy Among the default settings for kinematics (PREFERENCES > MOTION), there are some parameters that can affect the analysis of 3D or 2D contacts. These settings have strong effects on performance in calculating contacts, but they are also of interest for all other motion analyses. The following settings and recommendations apply to the RecurDyn solver, however, they are very similar to those of Adams. These preferences control the numerical solution of the RecurDyn solver.
Maximum Step Size: This value controls the step increment in the numerical solution of differential equations performed by the solver. The default value of 0.01 forces the solver not to allow major steps. If error messages like “Solver Lock-Up” occur when calculating the model, this may be the result of suddenly occurring forces which can occur in contacts, for example. In this case it is recommended to reduce the Maximum Step Size parameter (e. g. by one power), so that smaller increments are done, but of course this leads to higher computation times. Error Tolerance: This tolerance value, which controls the accuracy of the computed displacements, can be scaled down in order to get more accurate solutions, again an increase in computation time must be taken into account.
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2.3.1.9 Creating 3D Contact Each contact increases the processing time noticeably.
3D contact is defined between two solid bodies. In case you want to calculate a contact at several solid bodies, correspondingly several 3D contact elements must be inserted in the model. Remember that each additional 3D contact increases the analysis time significantly. It should also be noted that contact elements between complex geometry objects also lead to considerable computational delays because the number of contact checks is much larger then. By the way, an efficient method to use contacts is to use only bodies with spherical or planar surfaces as contact bodies, because the contact tests are simpler. If necessary, bodies with complex geometry can be divided into several simpler bodies which are respectively connected to each other by fixed joints.
The 3D contact is defined between two solids.
In our example two points of contact shall be considered: on the one hand between tire and environment geometry and on the other hand between the brake body and the environment geometry. For sake of simplicity, all default settings of the system shall be accepted here. This will also demonstrate that default settings are useful in many cases. Follow these steps for the generation of first 3D-contacts: ÍÍCall the function 3D Contact . ÍÍSelect the solid body of the tire. ÍÍSelect the solid geometry of the environment. ÍÍConfirm with OK. The contact element is then produced. You will find the contact element in the motion navigator below group Connectors. Here you can manipulate the element if necessary. ÍÍIn a corresponding way, you create a contact between the brake body (vr_radtraeger_ rechts) and the ambient geometry.
2.3.1.10 Solving and Animation of Results The solving of the simulation can take considerably longer with contacts.
ÍÍNow create a Solution , if you have not already done so. Select Normal Run and a realistic simulation time, such as five seconds, and a step number of 300, for example. ÍÍSelect a y-direction for the direction of gravity. ÍÍConfirm with OK. ÍÍSolve the solution. Consider that the computation may consume a few minutes, depending on the configuration of hardware. ÍÍNow you can perform the Animation
.
2.3.1.11 Generating a Trace of Movement A trace is useful for representation of the path without animation.
In order to produce a trace of the wheel during the movement, it is useful to record a point in the wheel center, for example. However, in a similar manner it would be also possible to record an entire solid or any other geometry. In the following we want to create a point in the center of the wheel, which is associated with the motion link of the wheel, so
2.3 Learning Tasks on Dynamics 67
that it moves with the wheel. Then, the point is defined as a trace object and is recorded in the animation. To proceed with this method, follow these steps: ÍÍCreate an ordinary point approximately in the center of the wheel using the function of the main menu INSERT > DATUM/POINT > POINT . . . . Now add the new point to the motion link of the wheel: ÍÍRMB select the Link in the motion navigator and select EDIT from the context menu. ÍÍIn the appearing dialog box select the point. Possibly it is helpful to set the selection filter to Point. Sometimes it helps to hide the geometry of the wheel. ÍÍConfirm with OK. The point now is added. ÍÍSelect the function Trace under the function group Analysis. ÍÍNow select the newly created point and confirm the menu with OK. One point for the record is created, activated in the animation and displayed in the navigator.
A trace object is inserted into the motion navigator. A new analysis is not required. ÍÍCall the animation function to perform a movement. ÍÍIn the options of the animation menu you find the switch in the Packaging Options to activate the trace object. Switch it on. ÍÍNow use the function Play to start the motion. At each motion step the point is logged once, and therefore yields the desired track. Upon request you can yet perform modifications, for example, to the coefficients of friction of the contact, and check the changed wheel movement (see figure below).
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In the figure, the movement track on the left is obtained without friction and on the right with friction.
Thus, we conclude this dynamic learning task.
■■2.4 Learning Tasks on Co-Simulation The co-simulation allows calculating complex geometry models from the NX system associated with complex control systems from the MATLAB Simulink system. This is very promising, since both software systems are powerful in their respective fields, and we thus have the opportunity for the simulation of complex mechatronic systems. Matlab Simulink is also required.
The solution of the following learning task is performed using NX and Matlab Simulink. Therefore, it is necessary for the execution of the example that in addition to NX you have also MATLAB Simulink Mathworks installed and licensed.
2.4.1 Balancing a Pendulum In this learning task an upside-down pendulum shall be balanced. In MATLAB Simulink, a P-controller is defined for this purpose. This gets the deviation angle of the pendulum from vertical as measured input quantity. A proportional controller (P-controller) handles this measure (with a gain factor) and the output is used in NX Motion as the manipulated variable (force).
2.4 Learning Tasks on Co-Simulation 69
The pendulum always wants to fall over. A controlled force on the slider prevents this.
Due to the force the base slides under the center of gravity of the pendulum. The pendulum then falls in the opposite direction. The force pushes the base back under the center of gravity of the pendulum, etc. This corresponds to the behavior of a P-controller. In other controller types also higher-quality regulations can be implemented (e. g. PIDcontroller).
2.4.1.1 Task The pendulum shown in the figure above shall be analyzed. The movement that occurs when a P-controller is applied on it is to be determined. Given is the CAD assembly of the pendulum and the Simulink file P_Regler.mdl, in which a simple P-controller is defined. We want to demonstrate the solution with this simple P-controller.
2.4.1.2 Customize Customer Defaults In the Customer Defaults , the executable program matlab.exe must be specified (see following figure). This is not the case by default. ÍÍCheck the settings in the Customer Defaults and enter optionally the correct path.
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The program matlab.exe must be specified as installed on the computer.
2.4.1.3 Start the Application for Co-Simulation The co-simulation is possible since the NX6. It is activated as follows.
Perform the following steps to generate the co-simulation (see figure above): ÍÍOpen the pendulum assembly Bgr_Pendel.prt from the directory Co-Simulation. ÍÍStart the application (Motion). ÍÍCreate a new Simulation in the simulation navigator. ÍÍSelect the setting Dynamics and Co-Simulation in the Environment menu according to the figure. Click OK. ÍÍCancel the appearing Motion Joint Wizard. ÍÍSelect the function Solution . ÍÍAccording to the figure, set the settings Analysis Type to Control/Dynamics, Time to 5 sec, Steps to 500 and the Direction of Gravity to −Y. ÍÍThe Matlab file for the controller must already exist. It is specified here. Using the file browser, select the P_Regler.mdl file at the very bottom in the Template Simulink Model File. Click OK.
2.4 Learning Tasks on Co-Simulation 71
2.4.1.4 Generating the Links and Joints We use very simple joints: a slider and a revolute, both without driver.
ÍÍCreate a Link for the base. Accept default settings for automatic mass analysis. ÍÍCreate a Link for the pendulum in the same way. ÍÍNow create a Slider Joint from the base to environment and a Revolute Joint from the pendulum to the base; both initially without driver.
2.4.1.5 Create Markers and Sensors First, the markers at the base and the pendulum must be created. From this, a sensor is produced by means of which the measured quantity, i. e. the angle, can be taken up. The sign of the measured variable must be observed. Proceed as follows for the marker on the base: ÍÍSelect the function Marker . ÍÍSelect the base at one of the circular edges of its pin. Thus, the associated body is defined as well as the orientation point of the new marker. ÍÍIn Specify CSYS select a circular edge of the pin. Thus, the orientation of the marker is determined. ÍÍConfirm with OK. The marker named A001 is now generated. The coordinate system for this marker is displayed as in the figure below. The X-direction points horizontally to the right.
The sensor measures the pendulum angle and provides the control with this information.
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The first two markers are defined, then the sensor, which refers to it. Here, the first marker is created.
Similarly, you create the marker on the pendulum: ÍÍSelect the function Marker . ÍÍSelect the pendulum at its circular edge-center. ÍÍIn Specify CSYS select for example the method to define a coordinate system via three points, and create it rotated with the pendulum, according to the figure.
2.4 Learning Tasks on Co-Simulation 73
Between these two markers, a sensor can now be generated which during the analysis always measures the angle between the two parts. Proceed as follows:
Now the second marker is set.
ÍÍSelect the function Sensor . ÍÍAs Type select Displacement. ÍÍSelect RZ as the Component and for Reference Frame the option Relative. ÍÍIn Measurement select the first marker and in Relative the second one. ÍÍConfirm with OK. The sensor is now generated. The sensor measures displacement/rotation between the Z-axis of the two marker coordinate systems.
2.4.1.6 Generate Measured Output Quantity for Simulink First, we generate the measured output quantity, which will provide information about the current angle for Simulink. ÍÍSelect the function Plant Output . ÍÍSet the type to Sensor and select the sensor. ÍÍConfirm with OK. The measured output quantity is created. ÍÍThe name of the measured output quantity element just created is Pou001.
The sensor is the measured output variable.
2.4.1.7 Generate Measured Input Quantity and Associate with Force Now we create the function for the measured input quantity: ÍÍSelect the function Plant Input . ÍÍAccept the suggested name Pin001 for this element and press OK to confirm.
The measured input quantity initially has nothing more than a name.
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Now create a force in the sliding direction of the slider joint and link this with the just created measured input quantity element Pin001: ÍÍSelect the function Scalar Force . A dialog appears. ÍÍIn the dialog for Action select the sliding body and in Origin any point on it. At this point the force will act. ÍÍDefine a second point in the dialog for Base. These two points define the force direction. Through the force symbol, you can afterwards easily see whether the direction is correct. The force on the base is generated and defined as a function. As function for the force we choose the measured input quantity from Simulink.
ÍÍIn Type select the option Function. ÍÍSelect the green arrow to the right and therein the option Function Manager. ÍÍIn the function manager function F001_Math is displayed in the list. Select this and confirm several times with OK. ÍÍThe measured input quantity is generated with the force.
2.4.1.8 Solve Co-Simulation Solving is done in two steps. First, the control system is integrated.
ÍÍSelect the function Solve . ÍÍSet the setting Host Program to option NX Motion and setting Submit to Control System Integration. ÍÍConfirm with OK. The file of the controller is opened in MATLAB Simulink. The Motion Plant also appears (see figure below). ÍÍPlace the appearing Motion Plant via drag and drop into the controller circuit diagram.
2.4 Learning Tasks on Co-Simulation 75
ÍÍSelect the function SAVE in MATLAB Simulink and exit the program. ÍÍIn NX select the function Solve. ÍÍAt SUBMIT select this time the option EXECUTE (RUN), and then click OK.
Then the analysis itself is performed.
Now the co-simulation is calculated.
2.4.1.9 Post-Processing for P-Controller For the post-processing run the animation or produce a graph, e.g. with sensor angle over time, as shown in the figure below. As a result, the pendulum moves oscillating back and forth. The drive ensures that it will not fall off.
The proportional controller indeed keeps the pendulum above, but it remains in a state of vibration all the time that is not subsiding.
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2.4.1.10 Results with PD-Controller
With PD-controller, the result would be more quiet.
If a proportional-differential controller (PD) is used instead of the simple P-controller, the angular velocity of the pendulum is used as additional measured output quantity for Simulink. The result of the angular motion in this case would look like the figure in section 2.4.1.10. The PD-controller suppresses the vibrations, keeping the pendulum almost exactly vertical. However, the base moves as a result of force because the pendulum is not held exactly vertical.
2.4.1.11 Results with PID-Controller When a proportional-integral-differential controller (PID) is used, the pendulum remains even closer to vertical, and transverse movements of the base are much smaller.
2.4 Learning Tasks on Co-Simulation 77
After settling, almost no movement would be seen with the PID-controller.
Bibliography [adams1]
Overview of ADAMS/SOLVER. Online-Documentation for NX
[HaugerSchnellGross] Hauger, W./Schnell, W./Gross, D.: Technische Mechanik 3: Kinetik. 12th Edition. Springer Verlag, Berlin/Heidelberg/New York 2012 [RecurDyn1]
Using RecurDyn. Online-Documentation for NX
3
Design-Simulation FEM (Nastran)
With the NX module Design-Simulation the designer can analyze components and assemblies that have been designed in 3D in structural mechanics. He can gain knowledge about the properties of his product in early design phases, which could otherwise only be found with a prototype. Also plenty of time remains for the correction of errors before the construction of prototypes starts.
Application scenarios and usage of Design Simulation in practice.
With Design-Simulation static structural analyses, analysis of eigenfrequencies, buckling and thermal transfer analyses can be performed. Characteristic for the NX tool DesignSimulation is that, for example, no special abstractions are made by shell or beam meshes. Instead, working directly with existing 3D geometry of the CAD model and automatic tetrahedral mesh is typical for Design Simulation. Only small design features are removed. The analyses are always in the range of linear FEM, so they are relatively easy to perform and interpret. With such types of analysis, on the one hand the design engineer gets a better understanding of his design, for example through the force flow in one component. Very easy A-B comparisons are possible, in which new designs are compared with previous ones. Of course, component deformations and stresses can be estimated. On the other hand, stress and deformation results can be calculated with higher accuracy requirements, as needed for strength verification. For this, the manual control of the mesh and thorough inspection of the boundary conditions are required, which requires some experience for the user. The detailed, manual control of the mesh is not the destination in Design-Simulation. If you aim for this goal, you should use the module Advanced-Simulation.
Simple FEM analyses help in A-B comparisons and improve the general understanding.
In many cases, boundary conditions for FEM analyses can be found through movement analyses, which are carried out with massive bodies before. These include, for example, acceleration and reaction forces, which result from dynamic motion analysis.
FEM analyses are often preceded by multibody dynamics simulations.
Because the generated file formats of Design Simulation are compatible with Advanced Simulation, started tasks can be continued in the advanced module. This could be the case if it turns out that nonlinear effects such as uplift or impingement contacts, plastic material behavior or large deformations have to be considered. Users of Design Simulation should be familiar in modeling of components and assemblies with the NX system. Although the examples in this book are based on finished assemblies, simple geometry elements have occasionally to be created or manipulated. We are also generally working in the assembly context. In addition, mechanical basics should be
80 3 Design-Simulation FEM (Nastran)
known with respect to stresses, deformations and evaluation of these quantities, i. e. parts of the strength of materials, as these topics are only touched in the book. Further experience is not necessary. The contents of this chapter.
In section 3.1 the basic theory, limits, special effects, and rules of linear FEM are presented. This is followed by learning tasks for linear FEM, which start off with a basic example for statics (see section 3.2.1). This example should be worked through by all FEM interested readers, because the discussed principles are important for all further learning tasks. The second learning task deals with a simple heat transfer analysis (see section 3.2.2).
■■3.1 Introduction and Theory With Design Simulation mechanical tasks in structural mechanics can be solved. The bodies under consideration are of an elastic nature and can therefore deform. Subdivision of engineering simulation: possibilities with NX Design Simulation.
Technical Simulaon Rigid Bodies Rigid Body Mechanics MBD (Mulbody Dynamics)
Linear Stacs staonary small displacement no contacts linear material
Elasc Bodies Structural Mechanics FEM (Finite Element Method)
Natural Frequencies no excitaon no damping
Fluids Fluid Mechanics CFD (Computaonal Fluid Dynamics)
Electric Bodies Electromagnecs (EM) FEM (Finite Element Method)
Thermal Transfer staonary heat conducon convecon
Linear Buckling instability buckling
This area is called Structural Mechanics and is usually calculated with FEM programs (finite element method). Instead of elastic bodies the term structures is generally used. Also the possible analysis of stationary temperature fields in Design Simulation belongs to this class. Within Structural Mechanics with Design Simulation tasks of linear statics, eigenfrequencies, thermal transfer, and linear buckling can be solved. In the following sections the four types are explained in more detail. Because linear statics analyses are among the most important tasks in CAD integrated finite element analysis, this will be explained in detail.
3.1 Introduction and Theory 81
The finite element method is explained in a clear way. This explanation should be sufficient for usefully working with a FEM software and in particular understanding the limits of the FEM. If you want to go further into this you will find a small example on bars in Chapter 8 that can be worked through with FEM manually (that is, without software support). This example also explains topics such as the importance of the shape functions and the stiffness matrix.
Chapter 8, “Manual Analysis of a FEM Example”, provides more background understanding.
For anyone who is looking for more background knowledge, we recommend the reading of
References
[RiegHackenschmidt] for a very clear introduction – with insights into the software algorithms of a small FEM program [Schäfer] for an inclusive representation of the popular numerical methods in mechanical engineering [Bathe] as a basis for work, whose methods are used in most software programs [Komzsik] as a work that was and is implemented in particular in the development of the Nastran solver
3.1.1 Linear Statics Indicator of statics is that components or assemblies are constrained and loaded with forces, pressures, moments, enforced displacements or temperature loads. Calculated deformations, strains, and stresses are always stationary and hence time-independent. Linear means that cause and effect are always proportional to each other. Causes are, for example, the applied forces, effects are the calculated deformations and stresses. This means, if a linear analysis is performed, doubling the forces exactly leads to doubling of the deformations and stresses. Linear statics can also be characterized by the fact that there are no changes of the boundary conditions and in the stiffness of the component during the analysis. What this means is explained in more detail in subsequent explanations in this section. In the case of linear statics the superposition principle can also be applied. The results of different load cases can therefore be overlapped. The procedure for the analysis of linear static tasks with a FEM program is usually as follows: After creating 3D geometry in the CAD system, the next step is idealization, i.e. the removal of irrelevant form elements, the generation of symmetry cuts or the subdivision of areas for subsequent boundary conditions. In the next step the meshing of the geometry with finite elements and the assignment of material properties will be done. However, the assignment of material properties can also take place at the geometry. Further steps concern the definition of the constraints and loads. Now the model is built up and can be solved. Finally, the results are evaluated, and if applicable, the model is changed and re-analyzed.
Indicator of linear statics.
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Process of the FEM.
Op miza on Construct geometry
Meshing, assign material
Idealize geometry
Constraints, loads
Solve
Evaluate results
Within the program the finite elements are processed with the constraints to form a stiffness model of the body. This is possible, because the individual stiffness properties of a finite element are theoretically known. A most simple element which is suitable for the conception is a spring element, which is described by a single stiffness value k. The equation k · u = F is used to calculate the unknown displacement u from the stiffness k and the nodal force F.
k ku=F
Principle of linear FEM.
u F
Individual stiffnesses of finite elements can be assembled to the overall stiffness of the component using appropriate algorithms. In this case, the displacements of the nodes of the finite elements provide the sought degrees of freedom, u1, u2, . . . The stiffness is therefore shown in form of a matrix, the stiffness matrix.
Overall sffness matrix k1 ... ... ...
... ... k2 ... ... k3 ... ...
... ... ... ...
Displacements
Forces
u1 u2 u3 ...
F1 F2 F3 ...
*
=
Structure with finite elements F
Real constraints are translated into nodal degrees of freedom.
Constraints are always defined at the nodes of finite elements. Real boundary conditions have to be translated into degrees of freedom of the nodes by the user. A fixed constraint on a surface, for example, holds all degrees of freedom for the nodes of the surface. A sliding boundary condition on the other hand keeps the nodes only fixed in the direction perpendicular to the surface.
Loads are distributed to the nodes.
Such as the constraints, also the real loads have to be translated into nodal loads of finite elements. For example, a surface load of 50 N is split in many separate forces at the participating nodes of the surface, together resulting in 50 N. Accordingly, a gravity load or centrifugal force will be divided into individual forces, so that each node of the whole component receives a portion of it. The results are a stiffness matrix, a force vector with the nodal forces, and a vector of the unknown nodal displacements. These three components form a linear system of equations which can be solved, and therefore the displacement and deformation values at each node are obtained and used as primary variables of the linear FEM.
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If the displacements of the component are known, the present stresses can be concluded through the intermediate step of strains. Strain is defined as the change in length divided by the original length and can therefore be determined from the displacement values at each point. From the strain, the stress is calculated with help of a material law. In the linear FEM Hooke’s law is always used, which provides a linear relationship between strain and stress. In this way, the stresses at each element can be determined. The linear FEM uses Hooke’s law.
σ E-Modul Young’s σ = E ε modulus ε A main characteristic of the linear FEM is that the stiffness of the structure is determined on the basis of the undeformed geometry and is unchangeably fixed in the stiffness matrix. The linear method has the advantage of simplicity and speed and can thus achieve suitable results in many cases. Linear analysis inevitably leads to a result, but nonlinear analysis not necessarily because it can get unstable. The result must be determined iteratively and can diverge. In the meantime, however, there are non-linear analysis methods that work very stable and because of this the calculator only needs to take much less aspects into account to stabilize the iteration process.
Nonlinear analysis is much more sophisticated.
3.1.2 Nonlinear Effects The linear FEM appears to have clear limits. These are the limits to non-linear tasks that should not be neglected or misunderstood. These limits are based on two important properties of linear analysis which the user must know: The results for linear analysis are always scalable, i. e., a doubling of forces always leads to the doubling of strain and stress. The directions of the displacements are always retained. Each point thus deforms in the direction in which it was deforming in the first moment.
Two properties of the linear FEM.
The user of a FEM program has then to decide if a linear analysis is suitable for his real task. If reality cannot be described approximately linear, a non-linear analysis method needs to be used or errors that are hard to estimate need to be taken into account. The most important technical limitations of the linear FEM can be divided into three classes: non-linear contact, non-linear material and large deformation. These three effects are described in the following sections.
There are three major categories of non- linearities.
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3.1.2.1 Contact Non-Linearity If a contact or impingement occurs during the deformation of a component, the linear property is violated, because doubling the force no longer leads to a doubling of the deformation distance. If the boundary conditions change during deformation, there is non-linear behavior. This happens with contacts.
This can also be explained as: With contact non-linearities, different deformations typically result in different boundary conditions. Consequently, the stiffness of the real component changes very abruptly during deformation. The linear FEM cannot account for this, because it is always the rigidity of the original geometry is that is used. This limitation of the linear FEM in many tasks with assemblies leads to considerable difficulties. Although contact analyses are difficult because of their non-linearity, they are fully supported in the NX software. Even in the simpler Design-Simulation tool contacts with limitations are calculable. The function for this is called Surface to Surface Contact. In the further tools of Advanced Simulation, extensive contact tools, depending on the solution method, are available.
3.1.2.2 Non-Linear Material If the stresses are not proportionally increasing with the strains, the material behavior is non-linear. This occurs, for example, with steel if the stresses reach into the plastic region. The linear FEM can only calculate linear elastic stresses. In most cases, this is sufficient, because plastic deformations are usually undesirable and can be detected in the linear FEM, when the stresses are beyond the elastic limit of the material. If Hooke’s law does not apply, there is a material non-linearity.
However, there are materials, such as some plastics, which in particular in the elastic region show non-linear stress-strain behavior. Such materials can only be calculated in Advanced Simulation.
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3.1.2.3 Large Displacements or Non-Linear Geometry If the deformed component has a different stiffness, non-linear, large deformations are present.
If the deformation of the component is so large that the stiffness matrix and the deformation vector in the deformed position significantly vary from the quantities of the undeformed model, it is spoken of large deformations. The linear FEM, which indeed works with the quantities of the undeformed model, will then be erroneous. This can also be explained as follows: The directions of deformation in the linear analysis remain as in the first moment of deformation. The example of a bending beam shows that this is widely correct for small deformations. However, if the deformation is larger, in reality a more and more curved deformation at the point of force application would occur. This arc would only be calculated as a line in the linear analysis.
3.1.3 Influence of the Mesh Fineness In addition to non-linear effects, loads and clamping conditions, especially the mesh fineness has a significant influence on the accuracy of the results of a FE analysis. For a given FE mesh, the spacing of the determined result to the exact one generally is unknown. Some program systems therefore offer the opportunity to make the mesh twice as fine at the touch of a button. If it is determined by a renewed analysis, that there are only minor changes to the previous analysis, the first result can be regarded as a quasi-sufficient approximation. Another possibility is to use a higher order shape function for the elements. In the figure below the convergence curve is shown which is obtained when a mesh is gradually refined. In this case, the exact stress result from an analytical analysis is known.
The mesh fineness affects the result significantly.
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The examination of convergence helps in assessing the accuracy.
Stress, theoretically
A colored version of this figure is available at www.drbinde.de/index.php/en/203
There are two rules regarding the mesh fineness and stress results: Two important rules.
Rule 1: With finer meshes, stress spikes are finer resolved. Therefore, the FE stress results increase with smaller element sizes. Rule 2: The stress values asymptotically approach the exact result. This effect is named convergence. Therefore, a common method for verifying the accuracy of a finite element analysis is to compare the differences of the calculated stress values, which result from different-fine meshes from FE analysis. A small difference indicates accurate results. Other verification methods are common, e. g. the comparison of the averaged and unaveraged stress results. We will talk about this later (see section 3.2.1.32). Such a verification of stress results is carried out in our first FEM-learning task.
3.1.4 Singularities Singularities are disturbances of the force flow in the FE model. This does not happen in reality. Therefore, it distorts the results.
In connection with the accuracy and the convergence behavior of FE analysis, the effects of singular spots must be observed. Singular spots are places where the real flow of force is not correctly mapped in the FE model. Often these sites occur at radii or notches that were omitted for simplicity in the CAD and FE model. If such a notch is loaded with tensile stress, the power flow is disturbed. This manifests itself in FE analyses through unrealistic stress results at this spot (see figure below).
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315
192
188
At a singularity, stresses increase without limits.
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A colored version of this figure is available at www.drbinde.de/index.php/en/203
In reality there is no such problem. The best locksmith would not be able to get any perfect sharp corners into the workpiece. There is always a – if ever so small – radius. In addition, localized stress peaks would immediately be reduced by microscopic plastic deformations. Then a hypothetical, perfectly sharp corner would immediately be a small radius. We are talking about something that does not exist in reality, but only for simplified models of reality, the CAD and FEM model. In such a case the stress results rise on and on with finer meshes and convergence cannot be achieved at this point. Another important case of disruption in the force flow are constraints that are not realistically defined. Again, no convergence can be achieved and it is spoken of singularities. Such singular spots can usually not be avoided in practice. The user should therefore know which influence emanates from them and how they can be judged. The rule is: At a singular point no stress statements can be made, at all other points this is possible.
Fixtures and load applications often lead to disturbances of the force flow.
3.1.5 Eigenfrequencies Dynamically loaded systems are studied with eigenfrequency analyses. They give the user the possibility to get an idea of the expected vibrational behavior.
c
m
The starting point is the undamped oscillation differential equation for free oscillations. The parameter M describes the mass properties, the parameter K represents the stiffness characteristics, and u is the displacement/deformation:
Mü + Ku = 0.
The single-mass oscillator is a plausible example of a free oscillation.
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With the displacement approach
u i = ϕi sin (ωi ⋅ t ) the equation of motion can be formulated as an eigenvalue problem:
(K − ω M)φ = 0 2 i
The eigenfrequencies are calculated with this method.
i
Therefore we are looking for the solutions φi, that satisfy the oscillation differential equation through a common time law sin(ωt). Nontrivial solutions are obtained if:
(
)
det K − ωi2 M = 0 The solution of this eigenvalue problem gives n eigenvectors φi, which are determined up to a constant factor, and the corresponding natural angular frequency ωi. The variable n is the number of degrees of freedom. In resolving the following formula, the example of the single-mass oscillator from the previous figure with the stiffness c and the mass m
c − ω 2m = 0 leads to a natural angular frequency of:
ω=
c m
The natural angular frequency ω is linked to the frequency f through ω = 2πf. So, the results of eigenfrequency analyses are the frequencies at which a structure swings freely without influence from the outside after it is excitated shortly, for example a sounding wine glass or a tuning fork. A sounding glass or a tuning fork are examples of free oscillations. Conclusions for modeling.
In addition, the shape of the resulting oscillation is obtained. Since the excitation is not taken into account, the amplitude of the vibration cannot be calculated. By the way, conclusions for the design can immediately be drawn from the last equation above: It is often difficult to change the eigenfrequency of a component, because as soon as material is removed somewhere, usually also the stiffness is reduced. The natural frequency then hardly changes because, according to the equation, the stiffness and the mass are related in a ratio. The challenge here is making changes to the stiffness without changing the mass or vice versa. This is achieved, for example, with additional local mass points. In the learning tasks for Advanced Simulation (FEM), such a modal analysis is included (see section 4.2.3).
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3.1.6 Heat Transfer With heat transfer problems, the distribution of the scalar temperature T in a body has to be determined. From the temperature gradient in the heat flow results the transfer of heat energy from the warmer to the colder place. This quantity is responsible for the “heat accumulation” and therefore also of interest for the designer.
Calculating the temperature distribution in a component
The descriptive differential equation is derived from an equation for the description of the heat conduction effect, the energy equation and some assumptions for simplification [Schäfer]. As material equation for the heat flux vector and the effect of heat conduction, the Fourier’s law for isotropic materials is used:
hi = −κ
∂T ∂xi
Thus, the heat flow h is proportional to the temperature gradient. The proportionality factor is the thermal conductivityκ. In Design-Simulation a stationary heat transfer is assumed. In Advanced Simulation, even more complex temperature problems can be solved. Taking into account the energy conservation equation, assuming a constant specific heat capacity cp , neglecting the work that is done by pressure and friction forces and with q as the heat source or sink, the descriptive differential equation is obtained:
ρq +
∂ ∂xi
Design Simulation, as opposed to Advanced Simulation, can only take simple thermal effects into account.
∂T κ =0 ∂xi
Common boundary conditions are: Input of the temperature T Input of the heat flux h The heat flux is assumed to be proportional to the local heat transfer. This constraint is used to describe the convective heat transfer. The α parameter is the heat transfer coefficient:
k
∂T ni = α (Ts − T ) ∂xi
After solving the differential equation using FEM, the temperatures and heat flows at all points are determined and are available for post-processing. Such a thermal analysis is included in the learning tasks for Design Simulation (see section 3.2.2).
Boundary conditions for simple thermal analysis.
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3.1.7 Linear Buckling Using linear buckling analysis, bending and buckling loads and the corresponding buckling shapes are determined. A buckling load is the critical load at which a structure becomes unstable. A buckling shape is the associated form. Buckling is the cause of the failure of components under pressure load. Such an analysis does not make sense under tensile load. If a structure that is subjected to pressure would only be calculated in linear statics, you would get a false impression of the strength. Only a buckling analysis indicates whether this structure fails or not. The risk of buckling exists with pressureloaded components.
In a linear statics analysis, it is assumed that there is a structure in stable equilibrium. With increasing load, the deformation is proportionally rising. If the load is removed, the structure returns to the original shape. When a structure becomes unstable, the deformation of the structure is increasing without the load increasing any further. The load at which this effect occurs is called the critical buckling load.
An example of a buckling task
If one calculates an unstable pressure condition with a linear statics analysis, the instability is not visible, and the results lead to false conclusions. The occurrence of instability can only be checked by a previous buckling analysis. A linear buckling analysis finds the load conditions that make a structure unstable. This is done based on an eigenvalue analysis. Therefore the Nastran solution method 105 is used.
■■3.2 Learning Tasks on Design Simulation The following learning tasks are not only useful for users of Design Simulation but also for all who are interested in FEM and want to actually work with the Advanced Simulation. Since the two modules are mutually compatible, simpler tasks can be carried out in each of both tools, and the methodology is the same (including the mouse clicks).
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3.2.1 Notch Stress at the Steering Lever (Sol101) This learning task shows the essential steps of a FE analysis with the NX system. In particular, the qualitative assessment is treated, e. g. the question of how well and how accurate the results are. This first example is of basic character and should therefore be worked through by all readers who are looking for an introduction to FEM analysis with the NX system. This also applies to users who will later work with the more advanced package Advanced Simulation.
The steering lever of the RAK2 is analyzed.
To evaluate the accuracy of the results, values are used in this first theoretical analysis, that arise from the DIN. This procedure for review is of course only possible with selected tasks, such as notch stresses of simple geometries under exactly defined external loads. Usually, the theoretical result is unknown in practice, otherwise the FEM analysis would be unnecessary. For beginners in FEM, this comparison between theory/FEM is intended for gaining experience regarding the expected accuracy of subsequent FE analyses.
For the evaluation of the accuracy theoretically exact results are used.
In many cases these experiences can be applied to other analysis cases that can certainly have complex geometries. Very often, for example, castings have to be analyzed under static load. The dangerous stresses usually appear in the fillets. With the knowledge gained from this learning task it can be estimated how the mesh needs to look here, so that the errors of the FE results, for example, are less than 10 %.
Many other tasks can be performed in a similar way.
In this example important sources for errors are also pointed out, which may occur in linear static FE analysis which the FE users should be able to estimate and understand. This also ties the learning task to the theoretical principles presented above, illustrating them with an example from practice.
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3.2.1.1 Task Formulation The joint force could result from a MBD analysis.
In this learning task, the steering lever of the front wheel of the RAK2 is analyzed (see figure above), which is stressed with a bending load from the handlebar. Especially dangerous would be, for example, a situation in which the wheel cannot move (e. g., it is at the curb) and the steering wheel would be turned. In particular at a step, the axis is at risk from the notch effect. Therefore, the stresses here have to be calculated specifically. The tensile force of the steering rod in this example is assumed with 150N. It would also be possible to derive this joint force from a previous motion analysis.
3.2.1.2 Load and Prepare CAD Assembly
ÍÍLoad the assembly Opel_Rak2.prt and get a general overview of the overall system and the structure of the sub-assemblies. The steering lever, which is of interest, is located in the assembly structure at the following position: OPEL_Rak2 → vr_lenkung → lenkhebelmechanik → vr_lenkhebel_re. For large assemblies, a suitable sub-assembly should be chosen for the FEM analysis.
You could set the component vr_lenkhebel_re as displayed part or from the beginning only load this component and then start the FE analysis. However, in this case, you would have no access to neighboring parts, such as the bearing. You may also need those neighboring parts in the analysis, e. g. to take over their positions for boundary conditions.
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Therefore, the surest way is to carry out the analysis on top of the assembly, which, however, results in that the entire assembly always needs to be kept in the computer memory. Be sure to make a sensible compromise and set a subassembly as displayed part, which on the one hand includes all possibly required neighboring components and on the other hand is as small as possible. In our example, no neighboring parts are likely to be needed. ÍÍTherefore now set the component vr_lenkhebel_re.prt as displayed part. ÍÍIf you like, you can now close the remaining parts of the assembly. In this way you unburden the memory of your computer.
3.2.1.3 Starting FE Application and Creating File Structure ÍÍMake sure that the Assembly mode is active. ÍÍTo start the application, select FILE > ALL APPLICATIONS > DESIGN SIMULATION or choose Design in the Application Ribbon tab in the Simulation group. Users of Advanced Simulation choose the application Advanced Simulation .
In this way, the application FEM is started.
These are preferences that can simply be used in many cases.
ÍÍIn Design Simulation the menu New FEM and Simulation automatically appears, prompting you to create a new simulation. ÍÍIn Advanced Simulation, it does not appear automatically. Instead, choose the function New FEM and Simulation in the Simulation Navigator from the context menu of the master model.
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Especially for FEM analysis, the NX system creates a special file structure of three additional files. Before the setup of the computational model is continued, we will give some explanations regarding this data management.
3.2.1.3.1 File Structure for Design- and Advanced Simulation The following statement about the file structure is the same for both Design Simulation and Advanced Simulation modules. Simulation data is always kept in three separate but interrelated associated files. It involves the simulation file, the FEM file and the optional idealized file. Added to this is the master file containing the original component. The files are identified via the extension. For FEM simulations a file structure is created that is compatible with Advanced Simulation.
If simulation files for this master model already exist, the system renames the files to be created with a new index. Sim1 then changes to sim2, for example. This file already exists: The master file is the basis.
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The vr_lenkhebel_re.prt file contains the master part. Here the unmodified part geometry is maintained. The master part is never changed, all geometry simplifications are added to the idealized part. In the Advanced Simulation application, the master part is optional. The following files will be created: The file vr_lenkhebel_re_fem1_i.prt contains the idealized part. The master part is connected with the idealized part through an assembly structure. In the idealized part geometry abstractions of the CAD model can be made. The master part must be promoted or wave-linked into the idealized part in order to make changes to the idealized part. The idealized file is optional. The FEM file vr_lenkhebel_re_fem1.fem contains the FEM mesh, i.e. nodes, elements, physical properties and possibly material properties. All geometries in FEM file (CAE geometry) are of a special kind, these are faceted or tessellated polygon geometries of the original body. FE meshes and other geometry simplifications are always only made on polygon geometry. This brings advantages in terms of performance. The FEM file is associated with the idealized part. Several FEM files can be connected to the same idealized part. The simulation file vr_lenkhebel_re_sim1.sim contains all other data generated for the simulation, such as loads, boundary conditions, solutions, solution steps and more. Several simulation files can be connected to the same FEM file.
The idealized file is for geometry preparations.
The FEM file is for meshing.
The simulation file contains all the boundary conditions.
Now we switch back to the current menu New FEM and Simulation: The settings Analysis Type and Solver determine the solver environment and thus the available elements and boundary conditions. The relevant adjustment of the solution method is performed in the next section. ÍÍAll settings are as shown in the previous figure. Confirm with OK. The system now generates an idealized part, a FEM file and a simulation file. This process takes a while – especially when complex geometries or assemblies are used, because the creation of the polygon geometry is complex. The simulation file is initially active and prompts you to choose a solution method, as explained in the next section.
3.2.1.4 Selection of Solution Method The following Solution menu appears, which includes basic settings for the planned simulation. The available solver in the application Design Simulation is NX Nastran Design, containing only those FEM functionalities that can be used effectively in the design and construction surrounding area. The solver, which is used in the Advanced Simulation environment for structural analysis, is NX/Nastran, while interfaces/integrations to other solvers are also available. These functionalities can be selected at Analysis Type and Solution Type. In structural analysis, there is: the linear statics, that is the analysis of stresses and deformations due to constraints and loads,
The solution method is chosen at the beginning.
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the vibration modes and the linear buckling analysis. A solution for linear statics is created.
In the thermal analysis type, there are no further subdivisions. This is the linear analysis of stationary temperature fields. Convection properties, predetermined temperatures or heat flows can be specified. The balanced temperature field and the resulting heat flow will be calculated. ÍÍIn the case of our example, confirm the default settings, i. e. linear statics, with OK. ÍÍNow save the simulation file. The associative file structure is set up in a way when saving a particular file type, the respective underlying files will be saved, too. If all files are saved, it makes sense to click SAVE in the simulation file.
3.2.1.5 Handling of the Simulation Navigator The simulation navigator will appear at the top of the palette bar. It provides options for creating, editing and deleting simulations and to switch between them. In addition, there are further functions for generating FE features. The easiest way to find out the possibilities is to look at the context menu of the respective nodes. Following the key features of each context menu are explained. A navigator illustrates the structure of the features and files.
The four top-level nodes in the navigator represent the file structure previously described. At the master node of the idealized part only the function Make Displayed Part is available. If you want to work on the master geometry, switch into the master via this function. If you want to work on the geometry idealization or meshing, you switch into the corresponding part. After the changes are done, go back into the top simulation file. On the FEM file we have the opportunity to directly generate meshes and connections (the FEM file automatically changes to Work Part). Switching between the four files is facilitated through the Simulation File View, which is available below in the navigator. This is shown in the figure below.
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Each node has a context menu with its features. At the bottom of the navigator, the file structure can be shown again. (Simulation File View)
3.2.1.5.1 Navigation in the File Structure The Simulation File View is used for easy overview and provides access to the other files. By double clicking on one of the nodes, it is set as the displayed part.
3.2.1.5.2 Nodes of the Simulation File The top node shows the simulation file. Here are the options for creating a new solution (New Solution), for importing a solution (Import Results), for generating a solution process (New Solution Process), i.e. an adaptive solution (Adaptivity), for fatigue solution (Durability) or for a parameter optimization (Optimization). Very useful is the function for generating a new solution (New Solution). It allows you to manage several solutions in one simulation file, that have been carried out for example with the same geometry or meshing, but with different loads, boundary conditions, and solution methods. For example, a component can be calculated statically at first and then thermally. Of course, this can also be achieved with the aid of two simulation files.
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At the simulation node a new solution can be inserted, for example.
3.2.1.5.3 Polygon Geometry Node Geometries are represented through polygon bodies. These can be switched on and hidden.
This node does not have a context menu. It is only used for viewing and showing and hiding the polygonal geometries, i. e. the geometries that are available for meshing. In our example case, there is only one such polygon body because the simulation was started from a single item. In case of an assembly, many geometries can be created here. The generation of these polygon bodies can take quite a long time, so not every body should be converted to a polygon body within an assembly. This is achieved by selecting only the desired bodies in the previously described New FEM and Simulation menu.
3.2.1.5.4 “Simulation Object Container” Node Special simulation objects are grouped together separately.
This node contains specific simulation objects such as non-linear contacts (Surf to Surf Contact) or special boundary conditions for thermal or fluid flow analysis. Which simulation objects are available depends on the capabilities of the active solver. The solver used in the application Design Simulation includes the two functions Surface to Surface Contact and Surface to Surface Gluing. The contact function refers to the non-linear contact, which allows the deformation during impact, and the gluing function allows the fixed connection of two bodies at a surface.
3.2.1.5.5 “Load Container” and “Constraint Container” Nodes Load and constraint containers hold all necessary boundary conditions together.
Furthermore, there is one Container node for Loads and one for Constraints. According to these two nodes, there are context menu functions available, which allow the creation of new loads or new constraints. These containers nodes can be understand as a quasi-reservoir in which any number of different loads and boundary conditions are first generated and stored. Which of the loads and boundary conditions are really used for analysis is set in the respective Solution, which is described below.
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3.2.1.5.6 Solution Node A simulation file can have more than one solution node.
The node Solution contains the functions EDIT . . . and EDIT SOLVER PARAMETERS . . . in which changes to some of the properties of the solution or the solver can be made. Furthermore there are the functions for renaming (RENAME), deleting (DELETE) and cloning (CLONE) a solution. Cloning is used for doubling a solution to then generate a solution variant by modifying it. There is also the ability to produce new load steps (NEW SUBCASE) and to manage existing load steps (SUBCASE MANAGER). Load steps or load cases can be understood as load situations, which are calculated with the same geometry and meshing, the same boundary conditions and the same solution method, but with different loads. Such load cases can be combined with each other in linear FE analysis, for example, a load case for torsional loading can be combined with another for transverse loading. Often, it saves the repeated analysis of a FE model when the desired load case can be achieved through a combination of existing ones. There is also a function for disabling (MAKE INACTIVE) the solution available. With MODEL SETUP CHECK at the Solution node gross errors of the FE model can be found, for example, if the material was not specified. This check is performed automatically by default prior to the analysis. In MECHANICAL LOAD SUMMARY, an overview of the mechanical loads, i. e. all forces and moments, can be displayed in an information window.
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The SOLVE function performs the FEM analysis. Finally with the SETUP REPORT function, an automatic report can be created, that describes all previously defined features. Loads and boundary conditions can be added by drag and drop.
The node Constraints below the Solution includes the boundary conditions actually used for this solution. According to this, the node Loads contains the used loads. Loads and boundary conditions may be either right here or initially “in stock” created in the container node and then dragged and dropped into the nodes of the respective solution.
3.2.1.6 Overview of Solution Steps Further steps.
After you have created the file structure of the simulation, especially basic information is already defined. The system knows that a static structural analysis shall be performed with the solver NX Nastran Design. The further steps required relate to: Preparation and simplification of geometry Meshing Specification of material properties Definition of loads and boundary conditions Performing the analysis The processing order of these four points is initially arbitrary, only the geometry preparation should be done first. In the following, we will address the individual solution steps.
3.2.1.7 Preparation of Geometry Mostly CAD models have to be simplified for FEM simulations.
A preparation of CAD geometry for the analysis model is reasonable and necessary in most cases because design and computation unfortunately usually have different requirements for the geometry. In our case, the CAD model is available as it is often created in design phase. Here, for example, the fillets have been omitted, in which now stresses should be calculated. At first we will explain the general needs of the analysis, which are requested from the CAD model. Some of these requirements already occur in our example and are then processed. A series of special functions of the NX system are used and shown.
3.2.1.7.1 Requirements for CAD Geometry For the following reasons CAD geometries are specially prepared for the FEM analysis:
Mostly the geometry is coarsened.
Hiding neighboring components: To limit the effort in FE analyses, usually only the part of interest in a design is cut out from its surroundings. At the cut faces, the corresponding FE boundary conditions are set later. This method is allowed if the applied FE boundary conditions can reproduce the omitted surroundings exactly or at least approximately. Coarsening of geometry: Geometry elements that seem to have no effect on the desired result would lead to much more finite elements and should be removed. For this purpose usually small features, i.e. chamfers, fillets and holes are removed. Sometimes, however, this can also lead to dangerous stresses which are not noticed because for ex-
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ample a fillet was removed. More will be explained in the next section. In the NX system, the Idealize Geometry function helps in coarsening. In our example, a portion of the steering knuckle shall be coarsened and removed. Refinements of geometry: At the places of interest and critical points, the model should be represented as realistically as possible. These include, for example, welding seams, notches and such geometries in which local stress or strain results shall be determined. In many cases, the CAD models are, for simplicity reasons, not modeled realistically in such places, e. g. small fillets in cast parts are omitted. It is important to always find a sensible compromise here, because on one hand a detailed CAD model drives up the number of FE elements and on the other hand a rough CAD model does not allow local statements. Ideal is a model that is detailed at the critical points and coarse in the remaining areas. Unfortunately, from the beginning, you often do not know where the critical points are. One possibility is to start with a coarse model to identify the critical points in a first analysis and then to detail these areas in a second analysis. In our example, the notch in which the stress shall be determined requires more detailed modeling. Usage of symmetric characteristics: If the geometry and loading of the component that shall be analyzed are symmetrical, this should be utilized to save FE elements. In case of mirror symmetry, the CAD model needs to be cut at the plane of symmetry, in the case of axial symmetry, it must be cut in such a way that a half-section is formed. At the intersections, appropriate boundary conditions must be set, which ensure that only symmetric deformations are possible. Surface subdivisions for FE boundary conditions: FE boundary conditions are usually associatively linked with the topological elements of the CAD model (solids, surfaces, edges, or vertices). For example, a gravity load is combined with a solid body and a pressure load is applied to a surface. Because the surfaces of the CAD model, often do not match the desired regions of the boundary conditions, the surfaces of the CAD models must be divided at these sites. Only then the targeted FE boundary conditions can be attached. In Design Simulation there is the Divide Face function, in Advanced Simulation the Split Face function can be used in addition, which operates on the polygon geometry. Merging CAD surfaces: If the CAD geometry consists of many small or sharp surfaces, FE meshers usually have difficulties in creating high-quality meshes. It is often the case that absolutely no useful mesh can be created. The reason is that initially all vertices and edges of the CAD model are fitted with nodes in the meshing process. Then closely spaced points and edges cause difficulties. In such cases, a merging of problematic surface areas to surface compounds is required. In Advanced Simulation there is the very useful function Merge Face , which operates on the polygon geometry.
In some cases, a refinement of the CAD geometry is required.
For later boundary conditions surface subdivisions are made.
Surface areas with many unnecessary edges interfere with the meshing.
3.2.1.7.2 Requirements for Geometry Changes in FE Environment A direct modification of the geometry in the simulation files is not easily possible because the simulation files work like assemblies. The master geometry can indeed be seen from here, but cannot be changed. For changes in the geometry, there are various methods:
The geometry preparation should not change the master model.
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The easiest way to change the geometry of a finite element analysis is the direct modification of the master geometry. This can be done with operations such as suppression of form elements, trimming, filleting, or the functions of Synchronous Modeling. Disadvantage of this method is that usually the master geometry is needed for other downstream processes, such as drawing creation. Therefore, a modification of the master geometry is contrary to the master model concept and should be avoided whenever possible. An associative copy of the master model is thus useful.
So a separation of the geometry for the analysis model from the master geometry is required. Such a separation may be performed by generating a copy of the master and all of the desired geometric modifications are made to the copy. In the optimal case, the copy and all modifications would be associative to the original geometry in the master model. Then, the analysis model and possibly the drawing and all other derivatives can be automatically updated when changes are made to the master model. The NX system offers two functions that meet the mentioned requirements: These are the Wave Geometry Linker and the function Promote . Both functions create associative copies of any solid or sheet bodies and can be used for the separation of the master model from the analysis model. When creating a wave link, a second body is created, which is exactly at the position of the master part. Therefore, it is useful to hide the master part after the wave link creation to avoid confusion. The Promote function does not generate a second body, so the master part does not need to be hidden. The advantages of the Wave Geometry Linker compared to the Promote function lie in the usage within assemblies. Here the procedure is that the geometries that are relevant for the analysis “are waved” and then just the whole assembly is hidden. This means that only the required geometries can be seen and edited. A further advantage lies in the editing of wave links. Thus, the underlying body can be changed easily. For these reasons, our learning tasks are exclusively worked through with the Wave Geometry Linker.
The Wave Geometry Linker generates an associative copy of the master model. This method is recommended.
In the Part Navigator a Linked Body is displayed.
3.2.1.7.3 Generating a Wave Geometry Link of the Component ÍÍSwitch the idealized part via the simulation navigator to be the displayed, because CAD geometry preparations have to be made in this part. ÍÍNow create a copy by selecting the Wave Geometry Linker , set the type to Body and select the geometry of the steering lever. ÍÍConfirm with OK. ÍÍNow hide the master part in the assembly navigator so you do not see the body doubled.
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In order to make the Wave link visible, you can also open the Part Navigator feature is visible and can, for example, be renamed or deleted.
. Here the
Now the lever can be changed without problems, and changes do not affect the master model. However, changes to the master model are reversely passed to the analysis model.
3.2.1.7.4 Symmetry Cut at Lever A utilization of mirror symmetry is always possible if both the geometry and the loads are equally symmetric. In our case, the steering lever mirror symmetry exists at the central plane, so we will utilize this. For the use of the mirror symmetry, only half of the symmetrical geometry is considered. It is also important to note that in such a case, only half of the load must be applied. Symmetry has not to be utilized, but it is recommended because FE elements and thus computation time and data volume can be saved in this way. However, the benefits of symmetry usually require a bit more complicated boundary conditions, and therefore errors can easier sneak in with inexperienced users. On the other hand, there are also cases in which appropriate boundary conditions are only possible through the use of symmetry. However, at such a simple geometry, as with our lever, you could successfully work even without the use of symmetry. Nevertheless, we want to perform the methodology for symmetry use for education purposes:
Symmetry simplifies the analysis.
To continue working with one half of the geometry, a cut of the lever is required. In the idealized part a Linked Body of the lever already exists and will be a prerequisite that the lever in the idealized part can be cut. However, the required CAD function for this, Trim Body , is not available under the functions of geometry preparation. In such a case, you may easily change into the design application of NX, which makes all functions for CAD design available.
If desired, the full functionality of the design application of the NX-system is accessible.
ÍÍTherefore, start the application Modeling in the idealized part. ÍÍCreate a Datum Plane in the mid of the lever. ÍÍUse the Trim function to trim the lever at the reference plane. A Datum Plane, which is already present in the master model, cannot be used for trimming (it would need to be “waved”). A new datum plane has to be generated in the idealized part. Here, mirror symmetry is used.
Symmetry plane
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3.2.1.7.5 Free Punch of the Relevant Geometry Parts For the FE analysis the model should be simplified as much as possible.
In FE analysis already in the preparation of the geometry consideration must be given to the applied boundary conditions. The part of interest of geometry should be considered isolated as far as possible. As a rule, geometry parts should always be truncated if it is possible to set a corresponding FE boundary condition instead of the trimmed geometry. As simple boundary conditions, there are loads, i.e. forces, pressures, moments, temperature expansions, and on the other side constraints such as fixed or movable in any direction constraints. Boundary conditions are explained in more detail later.
The relevant properties may not be changed.
A first free punch of irrelevant parts has already taken place through the selection of the single item from the assembly. The effect of the adjacent parts must later be simulated by FE boundary conditions. The figure below shows four different ways in which trims of the geometry in conjunction with FE boundary conditions would be possible.
Various possibilities for the simplification of the geometry.
pivotable bearing
Fixed constraint
pivotable bearing
Fixed constraint
Fixed constraint
Bending moment Fixed constraint
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The first variant contains no trims. Only at the borders to the neighboring parts conditions are applied. These are the tensile force of 150 N, which is transmitted from the handlebar, the pivotable bearing at the connection to the cross-member and the fixed constraint at the engagement point of the second lever arm. At the constraint of the second lever arm a piece can easily be cut off, as shown in the second variant. Thus, while the deformation of the entire part will change, this action has no influence on the stress at the notch of interest. The third variant shows an even further simplification. The second lever is completely removed here and also the in reality pivotable bearing is represented by a simple clamping. Since the notch of interest is far enough away, this should have no influence on the stress. Therefore, this variant is also possible. The last variant replaces the tensile force with its lever arm through a corresponding bending moment. Indeed such a simplification takes into account the bending moment generated by the force, but not the transverse force stress. This is generally acceptable with long beams, since the moment effect is substantially greater than the transverse force stress. All four variants require a symmetry boundary condition at the symmetry cut face. All four variants would be possible and would approximately deliver the same results in the notch. For didactic reasons we choose the second variant, in which the interesting boundary condition of a pivotable bearing as well as a part of the second lever arm are also considered.
We choose the second variant.
In order to perform the body cut, proceed for example as follows: ÍÍIn application modeling create a Sketch on the previously established symmetry plane of the lever. ÍÍDraw a rectangle for cutting the lever. The dimensions are not particularly relevant. ÍÍExit the sketch . ÍÍExtrude the rectangle in depth, and in the extrusion function select the option Subtract to subtract the extruded body from the lever.
3.2.1.7.6 Detailing in the Notch Region Since exact stresses in the region of the notch shall be determined, it must be ensured that the geometry reflects the reality as accurately as possible. In particular it has to be ensured that the force flux of the real component is simulated in the FE model. In many cases shoulder edges, as in this example, are in the CAD modeled without radius for simplicity reasons. But in FE models sharp edges result in errors in force flux. This leads to analysis of incorrect notch stresses. In our example, those notch stresses shall be calculated, hence the correct necessary radius has to be inserted. This radius shall be assumed with 2 mm for our example. ÍÍNow within the modeling application, add a 2 mm Edge Blend
to the edge.
These are the CAD methods.
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If stresses shall be determined in a notch, the geometry needs to be modeled accurately.
Radius 2mm
Edge
At the second lever, that we also consider partly for didactic reasons, the same shaft shoulder exists and therefore there is the same problem. But we do not want to add an edge blend to this second shaft shoulder, because we firstly do not care about the stress and secondly, we want to see how such a disturbance affects the force flow.
3.2.1.7.7 Coarsening the Geometry In our case, the geometry is already quite simple, a further coarsening is therefore hardly necessary. Complex geometries such as castings or welded constructions normally have to be coarsened extensively. In our example, only a small chamfer shall be removed at the end of the long lever arm. To do this, use a simple useful feature that is specially designed for the removal of individual surfaces in FE analysis. Chamfers and fillets are removed. The NX system has many options for simplification of CAD models for FEA.
ÍÍStart the application Design Simulation . ÍÍUse the function Defeature Geometry , select the face of the chamfer, and confirm this. As an alternative to this function, the Delete Face function in the toolbar Synchronous Modeling can also be used in the modeling environment, which offers significantly more options. The chamfer is now removed. Such operations work on the basis of pure geometry and not on the basis of geometric features, i. e. they can also be applied to models that do not have a feature history. This is a great advantage. For testing you can switch through the simulation navigator into the master model to see that the geometry preparations have no effect here. Afterwards, we proceed with our work in the FEM file: ÍÍNow set the FEM file as displayed part via simulation navigator. The model you see now has not yet been updated, so you still see the full lever. A look at the Polygon Geometry folder shows you that now two polygon bodies are present: one for the (“linked”) simplified lever and one for the original. ÍÍThe polygon model of the original lever should be hidden in the simulation navigator, so turn off the red tick at the corresponding node. ÍÍIt is now recommended to save the prepared model .
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3.2.1.8 General Information on Meshing Apart from the correct choice of boundary conditions, the proper preparation of the mesh is the most important but also most difficult task of the FEM user. The reason for this is that meshing and boundary conditions highly influence the results (stresses and strains). This is demonstrated by this learning task, but also on all other tasks, when tests with different meshing or boundary conditions are taken. The newcomer will be amazed how strong results may differ, in which the inputs only differ slightly.
The meshing highly influences the result.
The most important points that need to be considered when meshing with volume elements are:
Important aspects regarding the meshing of volumetric parts.
The fineness of the mesh The form of the elements the occurrence of singularities For the treatment of these points, you learn the required methodology in our learning task. Finding a suitable meshing mostly depends on the component under consideration or even on the form element at which the results are needed. Often empirical values that arise when repeatedly analyzing similar components are taken into account. Then very precise rules can be given, according to which the meshing needs to be created in order to obtain accurate results. Therefore, designers and engineers that repeatedly develop similar components have an advantage. In disadvantage, however, are the ones who always analyze different components, because new experience always has to be gained through the new models. The sensitivity of the results in particular depends on which evaluation of the FE results is needed. The pure FE analysis initially only returns deformations and reaction forces. All other quantities derive from them. Based on the formulas which are shown in the following figure, the relationships which affect the accuracy and required meshing can be explained:
Which type of result is asked?
For Eigenfrequency analysis, the simple formula for the single mass oscillator can be used as explanation. The meshing only slightly affects the results because the stiffness k (represented by the meshing) is under the root. Changes (i. e. including errors) of k therefore have less impact on the result. This effect can be shown quickly with a simple FEM example. Therefore the resulting natural frequency at various mesh sizes must be computed. It turns out that the result hardly varies. Therefore, a coarse grid is already sufficient for the analysis of natural frequencies.
Eigenfrequencies
ω = k /m
Displacements
F = k ⋅u Sensivity
Stresses
Durability
σ =ε ⋅E ε = ∆l l
Life = load k
Principle formulas show: stress analysis requires better and finer meshes than deformation analysis.
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An explanation that deformations can be calculated easily.
For Displacement analysis, the stiffness k is in a linear context with the result (F: reaction force or u: Displacement). Therefore, errors in the meshing have a stronger effect. Nevertheless, it is still not a dramatic effect to expect if inaccuracies in meshing are present. The model can therefore also be meshed roughly. Stress analysis requires that the deformations are translated into strains first. Because strains are calculated locally, even small errors of the elements are clearly taken into account for the stress analysis. For example at coarse meshed notches, the deformation values are fine, but the strain values in particular depend on each finite element in the notch. Therefore, stress analysis requires fine meshing in particular at the locations of interest. If even the Lifetime shall be calculated, the mesh quality dramatically impinges the result. Lifetime statements should therefore only be made with great caution.
3.2.1.9 Creating a Standard Mesh For the first rough tests a mesh “by pressing a button” is sufficient.
A standard meshing means a meshing that is generated “by pressing a button” without having to worry about details. From such a meshing no great accuracy of the results can be expected, it is used for rapid qualitative viewing. Often this kind is used in order to check if the boundary conditions behave as expected. If only deformations shall be calculated, such coarse meshing is sufficient in many cases, because in deformation analysis the meshing is much less demanding than in stress analysis. Proceed as follows: ÍÍThrough the Simulation Navigator switch into the FEM part. Now the functions for meshing are active. They were previously hidden. ÍÍFor the preparation of this coarse mesh select the function 3D Tetrahedral Mesh . ÍÍSelect the volumetric body to be meshed and use the Automatic element size (yellow flash) for the automatic suggestion of a suitable element size. Based on the size of the component and other geometric features, the system now calculates a suggestion for the overall element size, i. e. the approximate size of the generated finite elements. For creating a coarse mesh, we always recommend to accept the suggested value here.
Elements with middle nodes should always be used.
ÍÍConfirm with OK. The mesh is being created. The preset element type is CTETRA(10), i. e., tetrahedral elements having a central node on each edge are generated. This preset is strongly recommended for static analysis and you should not change anything here. Among the other menu items, there are still some other settings that are reasonably preset, therefore nothing should be changed here at first. The previous figure shows the coarse mesh, which has been created in this manner. It is typical that the automatic mesh has generated a single layer of elements over the requested radius.
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Here a “push-button” network is created. This is recommended for the first attempt.
3.2.1.10 Defining Material Properties Material properties can be defined in the master part, but also be defined in the idealized part, or in the FEM file. Once defined material properties are inherited from the bottom part to the part above, as long as they are not overwritten at another point of the structure. So it is possible to assign a material, for example in the master part, and override this in the FEM file. This corresponds to a “what-if” study. It is often advisable to assign the material properties in the master part, because they can be accessed by all of the following applications, such as motion simulation or advanced simulation.
It is useful to assign material properties already in the master part. These can then be used in subsequent processes such as FEM.
Material properties can be defined either manually or selected from the library. To select material properties from the library and assign them to the body in the FEM file – i. e. all potential material definitions from the master part will be overwritten – proceed as follows (also see figure below): ÍÍStay in the FEM file. ÍÍChoose the function Assign Material . ÍÍSelect the steering lever geometry in the graphics window. ÍÍChoose the right material, in this case Steel, from the list. ÍÍConfirm with OK.
We assign a material Steel from the library.
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Alternatively, separate material can be defined and created through the input of the crucial values Young’s modulus and Poisson’s ratio. There may be a plurality of other material parameters defined. In certain cases they play a role for the analysis, e. g. the density is needed when centrifugal force or weight shall be included in the analysis; according to this, the coefficient of thermal expansion is only needed when temperature loads are pre sent. Many material parameters that appear here are only needed in very special cases. The list of standard materials, which is included with the NX installation.
As shown here, you could define a material.
If you want to manually define a material, select the function Create Material at the bottom of the material properties menu. A dialog for entering material properties will appear. For our example, the properties of common steel could be used. The following values should be specified for steel:
Essential characteristics for FEM are the Young’s modulus and Poisson’s ratio.
For Mass Density: 7,85e-6[kg/mm3]. For Young’s Modulus: 2,1e5 [N/mm2]. The Poisson’s Ratio: 0,33. After that the material can be created with APPLY. For the assignment, select the newly created material at the top of the list, then select the body in the graphics window and press OK. In the status bar the following text appears: “Material was successfully created/changed.”
You can check which material is assigned to a body.
For verifying assigned material properties of a body, select the body in the function ssign Materials A . Then the information of the assigned material will appear in the status bar. Alternatively, the material of the body can be verified with the function Infor-
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mation, Object or through the information panel of the mesh (RMB at the mesh, Infor mation). NX will initially check if the component already has a material definition from the master model. If no material definition exists, an error message is displayed when the Nastran solver is called.
3.2.1.11 Creating the Load Loads and boundary conditions are objects that belong to the simulation file. Therefore, the corresponding SIM file has to be set as displayed part. ÍÍSet the simulation file as the displayed part. Instead of a real tensile force through the steering gear, you create a force at the affected area. The assumed load of 150N is also reduced by half due to the half model (symmetry). A detailed modeling of the force application is not necessary for the force boundary condition as it is far away from the region of interest. It only needs to be ensured that the lever arm and the direction and magnitude of the force are identified correctly. Therefore a simple force type can be selected from the function group. An overview of other load types is given in the next section.
Loads and constraints are generated in the simulation file.
ÍÍYou will find the function for the generation of a simple force in the function group for loads , with the symbol Force . Activate this function. ÍÍIn the menu that appears select as Type the first option Magnitude and Direction. ÍÍIn the first selection step, according to the following figure, select the area for the force application. ÍÍNow enter a value of 75 N. ÍÍTo define the direction, select the appropriate direction arrow. Under certain circumstances, the direction needs to be reversed (Reverse Direction). You can also select an edge, pointing in this direction. ÍÍConfirm with OK. The force is generated at the location and in the direction of the steering lever.
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The force is an associative object.
The force appears as an icon in the graphics window and as a feature in the simulation navigator. The force generated is uniformly distributed to the selected area through the NX system. First, the force is linked to the CAD surface, later it will be automatically linked with the respective FE nodes that are connected to the surface and passed to the solver. This geometry-based concept applies to all kinds of boundary conditions and even for additional information such as the material. All this information will be associated with the geometry and automatically passed to the corresponding FE nodes and elements only at the end of preprocessing, when calling the solver. Advantage of this method is that you can edit each of these generated features without having any other feature affected. For example, a mesh can be deleted and created without constraints being lost.
3.2.1.12 Overview of other Types of Loads In this section an overview of the other available load types of the applications Design and Advanced Simulation will be given. The most important load type is the simple force.
All load types at a glance.
All load types at a glance.
Force: A force is uniformly distributed across a face, edge or point. The direction can be specified in a number of ways: using an indication of direction, normal to the surface, using the directional arrows or on the basis of the coordinate system. Using the field method, the force can also be (as well as most other types of loads) distributed unevenly.
Bearing: This feature is defined on a cylindrical surface and produces a force distribution that approximately corresponds to a bearing load (e. g. a shaft in a hole or bearing seat). The force distribution is then parabolic or sinusoidal. So the force increases and decreases again.
Torque: Forces that form a torque are created on a cylindrical surface. The rotational axis of torque is always the center axis of the cylindrical surface.
Pressure: With this function, pressure loads can be produced on areas, for example for pressure loads on hydraulic vessels.
Hydrostatic pressure: This pressure increases linearly. Thus, for example, a load can be described that increases pressure to the wall surfaces with increasing depth.
Centrifugal Pressure: Here a pressure is applied to a rotating body, which increases or decreases depending on the radius of the body.
Gravity: This is an acceleration force which is applied to the entire meshed body. If such a load is used, it is of course of great importance that every meshed part has the correct mass density assigned. The software calculates the mass for each finite element and distributes it to the associated nodes. The default value is the magnitude of the gravitational acceleration i. e., in this case just the own weight of each body results.
Rotation: Centrifugal forces are created when a body is rotating about an axis. This feature is expecting the indication of the axis of rotation and the angular velocity or
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acceleration. This leads to a computed force for each node in a meshed component. Again, the correct specification of the mass density is required.
Temperature Load: With this function, temperatures can be applied to bodies, and their resulting thermal expansions are then included in the FE analysis. The affected finite elements are, according to the material specification Thermal Expansion Coefficient, expanded or shrunk. In addition, there is another way to specify temperatures: temperatures can be added to the Solution Step as a Pre-Load. Such temperatures have to be calculated by a previous temperature analysis.
3.2.1.13 Generating the Fixed Constraint A fixed constraint in volume-meshed parts (tetrahedral or hexahedral) means that all three translational degrees of freedom are held. Thus, in an area each movement is impossible. At a straight edge on the other hand, rotation about its own axis would still be possible, at a point, all three rotational degrees of freedom would still be free.
Constraints always refer to the corresponding nodes.
ÍÍFor our example, select the Fixed Constraint in the function group Constraints . ÍÍSelect the desired face as shown in the figure below. ÍÍConfirm with OK. The constraint will now be displayed in the simulation navigator and as an icon at the geometry. A fixed constraint at an area prevents any movement.
3.2.1.14 Creating the Pivotable Constraint A pivotable constraint is realized within the program by using a cylindrical coordinate system which is positioned in the axis of rotation. The face to be constrained is then held in the radial direction and set free in the tangential direction. For small deformations, this method corresponds to the real rotation. In NX, there are the following functions to realize this: Pinned Constraint : With this constraint, the axial direction is additionally held. Cylindrical Constraint : Here, all three degrees of freedom can be specified separately by the user.
With a pivotable bearing, the software internally uses cylindrical coordinates.
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Because we want to preserve the axial displacement ability, we will use the cylindrical condition for this example. ÍÍSelect the function Cylindrical Constraint in the function group Constraint Type . ÍÍSelect the inner cylindrical surface, because we want to set the pivotable bearing here. ÍÍAccording to the following figure (left), set the radial direction of Radial Growth to Fixed, the Axial Rotation to Free and the Axial Growth also to Free. ÍÍConfirm with OK. Left: Each degree of freedom in the cylindrical coordinate system can be set. The inner surface is now constrained pivotable. Right: The user defined constraint could alternatively be used. The results would be the same.
The boundary condition is shown in the graphics window and in the simulation navigator. As an alternative to the prefabricated boundary conditions, a User Defined Constraint can also be used. To achieve the desired effect of a pivotable bearing, a Cylindrical coordinate system would have to be selected and, in accordance with the preceding figure, a circular edge could be selected in the second selection step, for inheriting the axial direction. Now the directions of the degrees of freedom can be set in cylindrical coordinates. The radial direction DOF1 would have to be fixed, the tangential DOF2 and the axial direction DOF3 must remain free.
3.2.1.15 Creating the Condition for Mirror Symmetry A condition for mirror symmetry in volume-meshed components means that any displacement is prevented perpendicularly to the plane of symmetry. Displacements in the transverse directions must, however, be possible. ÍÍUse the function Symmetric Constraint and create a symmetry condition. ÍÍSelect the symmetry cut surface of the component. ÍÍConfirm with OK.
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At the cut surface a symmetry condition is generated.
Alternatively, such a symmetry condition can also be generated with the User Defined Constraint function, in which each degree of freedom can be manually and separately adjusted.
3.2.1.16 Resolving Conflicts of the Boundary Conditions Some geometric elements, in our case two edges (see figure below), received several boundary conditions simultaneously, which initially leads to a state of conflict. At two edges a conflict results.
The circular edge is part of both the plane of symmetry and the cylindrically constrained surface. The straight edge also belongs to the plane of symmetry and simultaneously to the fix constrained surface. In the simulation navigator such a conflict is displayed with an exclamation mark on yellow background. ÍÍIn order to resolve the conflict of the boundary conditions, click with the RMB on the affected solution and select the option Resolve Constraints. Here you can determine solutions for the individual conflicts. In the case of the steering lever, both constraints should be active. Therefore, choose the option Keep overlapping.
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The individual conflicts are resolved.
3.2.1.17 Checking the Completeness of the Constraints A static FE analysis requires that a set of constraint types is present, which constrains the FE model statically correct. This means that the model must not be under-constrained. The model may therefore not have the possibility to freely move in any direction or rotate around an axis. Static FE analysis requires that each component is fully constrained. Over-constraining is allowed.
This correct constrainment has to be achieved through boundary conditions sufficient that loads are applied, which are in equilibrium with each other.
. It is not
If such uncertainty exists, this is called rigid body motion and the system normally is not able to perform the analysis. This leads, depending on the solver used, to error messages that indicate a singular matrix. Background information for this issue can, for example, be found in [RiegHackenschmidt]. An over-determination of the system, for example through multiple fixations of one degree of freedom in various places, however, can easily be computed with FEM. This is even possible when pre-displacements are enforced. Therefore, the FEM also is an excellent tool for the analysis of over-determined systems.
3.2.1.18 Overview of Additional Constraints This section gives an overview of the remaining available constraint types of the applications Design and Advanced Simulation: All constraints at a glance.
Fixed constraint: This condition fixes all degrees of freedom, which are supported by the subsequent finite elements. It should be noted that, for the volume elements, only the three translational degrees of freedom are considered, while in shell and beam elements (available only in Advanced Simulation) all six degrees of freedom can be set and taken into account (for example the bending transfer between two beam elements).
Fixed Translation Constraint: This constraint only fixes the displacement degrees of freedom and leaves the rotational degrees of freedom free. Therefore, for volumemeshed parts, there is no difference between this one and the first condition.
Fixed Rotational Constraint: This constraint determines all rotational degrees of freedom. At solid meshes, this boundary condition is not working and therefore it is not available in the Design Simulation.
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Enforced Displacement Constraint: With this constraint, a given displacement on a surface, edge or point can be enforced. Therefore some types of biases can for example be realized.
Simply Supported Constraint: Here, the component cannot move in one direction. Thus, it corresponds to a support, but the part also cannot withdraw from the support.
Pinned Constraint: This condition may be generated on cylindrical faces. It then holds the axial motion but allows the rotation of the face.
Cylindrical Constraint: Here, cylindrical coordinates are used that relate to the s elected cylindrical surface. First of all, all degrees of freedom are fixed. However, the user is free to choose which of the three he would like to have freely movable.
Slider Constraint: In this case, only one translational displacement direction is left free. This is specified by the user.
Roller Constraint: This allows an area to rotate about an axis or to move along an axis. The axis can be defined freely.
Symmetric Constraint: At a surface which belongs to a volume meshed component, the displacement in normal direction of the surface is fixed. With volume-meshed parts this is sufficient. With shell or beam elements (Advanced Simulation), the symmetry condition is more complex.
Anti-Symmetric Constraint: In some cases, there is a symmetric component with loads also being symmetrical, but in reverse with respect to the plane of symmetry. In such a case an anti-symmetric condition would be useful.
Automatic Coupling: Automatically couples the nodes of an independent side to a dependent side. This constraint can be used for example for rotational symmetry.
Manual Coupling: Provides either the possibility for coupling of degrees of freedom or the generation of multi-point constraints between the selected nodes.
User Defined Constraint: This condition allows to separately adjust all six degrees of freedom (in Design Simulation only the three translational DOFs). The adjustment can be fixed, made free or set to an enforced displacement.
The most important constraint is the user defined constraint.
Now all the information for the FEM model has been added and a first FE analysis can be performed next.
3.2.1.19 Calculating Results After the model is built up, i. e., material, loads, boundary conditions and meshing have been generated, the analysis job can be passed to the solver. To do this, follow these steps: ÍÍThrough the simulation navigator, set the simulation part as the displayed part. Now the functions associated to solving are available.
The analysis model is passed to the solver.
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ÍÍSelect the node Solution 1 in the simulation navigator and select the function Solve in the context menu. ÍÍClick OK in the following window. The Job Monitor shows the end of the analysis.
Possibly, depending on the settings in the customer defaults, one more question appears that suggests the iterative solver for this analysis. You can accept or decline it. The iterative solver is faster than the direct one, when a well-conditioned numerical system is present. This is the case when a pure tetrahedral mesh is present, which is what we have here in our example. Therefore, the iterative solver can as well be used here. A small window with the Job-Monitor displays the run. The end of the analysis is displayed with “Completed”. The results can be seen in the simulation navigator as the icon Results (shown in color when results are available). Double-clicking it opens the Results and starts the post-processor.
3.2.1.20 Overview of the Post-Processor In the post-processor, the results are displayed.
Before the results of this job are explained, this section shall provide an overview of the functions of the post-processor. ÍÍAfter the analysis job is finished, perform a double-click on Results and thus open the post-processor. You can also directly go to the Post-Processing Navigator for displaying and evaluating the results. The post-processor can on the one hand be controlled via the Toolbars of the Results tab, on the other hand through the simulation navigator. The toolbars offer the following main functions:
Setting the options for representation, types of results, the color scale and the labels
Defining the display options of each result Identifying results in specific areas
Creating labels
Animating a result
Setting up layouts with multiple result windows
Exit of the post-processor and return to the model
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Using the simulation navigator (see figure below), the type of result to be displayed is set. For this purpose, the node Solution 1 is opened in the Navigator. Here, all available results can be found, like essentially Displacement, Stress, Strain and Reaction Force. Below the node with the result type, its individual components or combinations of components can be found. Thus, for example, the directional displacements X, Y and Z and the Magnitude of the three components can be found in the result type Displacement. The result type Stress – Element Nodal contains the three stresses in the X-, Y- and Z-direction (XX, YY and ZZ) and the shear stresses in the corresponding planes and directions (XY, YZ and ZX). These are the first pure result components of the FE analysis. In addition, the important combinations Max Principal, Min Principal, Max Shear, and in most cases the initially considered equivalent stress of Von Mises are available
The different results can be switched by setting the corresponding node active through double-clicking it. Alternatively, with the function Edit Post View or POST-PROCESSING NAVIGATOR > POST VIEW > EDIT you can also switch between the results.
The most important result types.
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The post-processing navigator provides access to the different results. Displacements, Strains and Stresses Below the nodes Displacement and Stress, the respective components are found.
3.2.1.21 Evaluation of Displacement Results ÍÍTo display the deformation results, double click the Displacement – Nodal in the simulation navigator. The deformation should be checked first.
By default the Magnitude displacement is displayed in this case. Your result should look similar to the figure below.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
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First, for each FE analysis it should be determined on the basis of the deformation representation, whether the result is reasonable and the boundary conditions behave as expected. The animation of the deformation could be helpful to understand the simulation.
ÍÍTo evaluate the plausibility in many cases it is meaningful to have a look at the animated results. Therefore you should use the Animation function. The animation of a result simulates the rise of all loads step by step from zero to the maximum value. This helps to get a better understanding of the characteristics of the loads. The plausibility of the deformation result is given, because the determined deflection of the lever appears as expected. Now, the magnitude value of the deformation is also read and checked for plausibility: Maximum displacement occurs in the red region. The maximum value is about 5.5 mm, which seems quite plausible for a component with a total size of about 470 mm. ÍÍStop the Animation
.
Now the assessment follows if the deformation can still be counted to the “small” displacements in terms of the linear theory or if they could not be handled with the linear method.
The linear approach requires “small” displacements.
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ÍÍFor this, the deformation has to be displayed without exaggeration or understatement, just as it has actually been calculated. You can reach this by selecting the Edit Post View function and in the Display tab the Result function next to Deformation. The dialog shown below will appear.
In the dialog you can see that the scaling method for the display of deformation is set to 10 % of the model size by default. So it does not matter if the deformation is large or small because the displayed deformation only depends on the size of the model and the distribution of the displacements. With this scaling the deformation of the solved geometry is displayed considerably which is suitable for qualitative evaluation in most cases. Deformations are usually displayed in a scaled way. We reset them to “Absolute”.
ÍÍIn order to display the real deformation, namely the 5.5 mm, change from % Modell to Absolute, and set the value “1” for Scale. Accept with OK. ÍÍYou can also activate the check box Show Undeformed Model so that the undeformed geometry is also displayed for comparison. The result should now look like the following figure.
The non-scaled representation of the deformation shows that in our case small deformations occur.
A colored version of this figure is available at www.drbinde.de/index.php/en/203 We only work with small displacements in this example.
The decision about small and large deformations or the validity of the linear theory should be taken according to the following point of view: Therefore consider the newly arisen and the original geometry. The key question is: Does the component with the new geometry has a significantly different stiffness compared to the component with the original geometry? If you had modeled the new geometry and with this geometry per-
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formed the same FE analysis, would the calculated deformations differ from the 5.5 mm of the original result? The answer is: The deformation from the old to the new geometry is so small that both geometries have approximately the same stiffness properties. Therefore, the requirement of “small displacements” is in our case given without any problems.
3.2.1.22 Examination of Provisional Stress Results The stresses are derived from the deformations in FE analysis. For this, strains are derived from the nodal displacements first and therefrom, the stress values are determined by the utilization of the stress-strain relationship of the material. First, the six components of the stress tensor results from this. To assess the strength of the geometry usually an equivalent stress hypothesis is used, by means of that these six components can be reduced to one single reference stress. This equivalent stress can then be compared with material properties, such as the yield point. The selection of an appropriate equivalent stress hypothesis generally has to do with the material properties, which are relevant to the fracture. A simple rule applies: For ductile materials such as steel the shear and tensile stresses have influence on the fracture. Therefore, the equivalent stress hypothesis is applied according to von Mises here, which is also known under the name of maximum distortion energy hypothesis. For brittle materials such as cast iron, the shear stresses are less relevant, only the tensile stresses counts. Therefore the maximum principal stress or the minimum principal stress is used in this case as equivalent stress.
For ductile materials the von Mises stress and for brittle materials the principal stresses are used for the evaluation.
Because we have selected steel in this example, we want to use the von Mises stress. Please note, that the von Mises stress does not indicate whether it is tension or compression stress. Only large or small stress is shown. For later comparison with theoretically exact calculated stress values we want to read the maximum principal stress. Further background information for strength-related topics you can find in [FKM] and [RoloffMatek].
References
ÍÍTo display the stresses select Stress – Element Nodal in the post-processing navigator. By default, the von Mises stress is now displayed. This is the most common way for the display of stress results. The result should look similar to the figure below. Keep in mind that with the values presented herein and those you calculate – in particular the stress values – differences of about 50 % can occur as long as we have such a coarse mesh in the fillet of interest. As displacement results are quite accurate even with coarse meshes, meshes for stress results have to meet higher requirements. To provide an understanding of this is also one of the objectives in this basic example.
The differences in results can be high for coarse meshes.
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von Mises stresses in the region of interest: The quality of results is plausible but the meshing is too coarse.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
In order to evaluate the notch stress value, now the color scale can be used. However, you should not simply read off the maximum value, which occurs in the scale, since this value can also occur at another point of the model, which may not be of interest. ÍÍMake use of the Identify function for reading a targeted value, e. g. on a surface. ÍÍThe function is preset for manual selection of individual nodes. In this case, it is better to switch the Pick filter from Single to Feature Edge or Feature Face and read all of the nodal results on an edge or surface of the fillet at the same time. In the output window of the Identify function, among other things, the maximum value of all the nodes of the surface will be displayed. Now evaluate the stress values and write them down. On the tensioned side of the fillet, we get a von Mises notch stress value of approximately 233 N/mm2, and a main stress value that should be around 285 N/mm2. These are the so-called “unaveraged nodal stresses”.
3.2.1.23 Averaged and Unaveraged Nodal Stresses Stresses are first calculated with FEM in about the middle of each finite element. These are the so-called integration or Gauss points. These stresses are referred as “elemental” stresses and can be displayed in NX. More important than the elemental stresses are the “nodal stresses”, which are determined through the stresses of the integration points being extrapolated to the nodes of each element. These nodal stresses are therefore almost always higher than the elemental stresses. Remember that a node usually belongs to several elements. Therefore, a node also has different nodal stresses, depending from which element it is queried. If now simply the average is formed with these different stress values of a node, we speak of so-called “averaged nodal stresses”. The function Set Result switches between these various stress plots in NX. For this purpose the option Nodal Combination has to be changed to Average (see figure above). The unaveraged maximum valuesof the stresses are almost always higher than the averaged ones and, considering coarse meshes, can also lie above the theoretical value.
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The unaveraged stresses are higher. Here you can switch between the two types.
If the stress values in our example are again evaluated with averaged results, a value of about 184N/mm2 for the von Mises notch stress and a principal stress value of about 216N/mm2 arise. Keep in mind that both the averaged as well as the unaveraged values can only have a very preliminary nature due to error influences. Such influences of errors, that have to be considered in all FE analyses, will be discussed in the following.
3.2.1.24 Comparison of FE Results with Theoretical Results Our basic example of the steering lever has now been calculated with FEM, wherein no efforts to achieve a particular accuracy have been made. Before improving the accuracy, the theoretically exact result for such a load case should first be determined, so that it can serve as a comparison. The determination of the theoretically exact result in this case is possible, since a DIN standard is available, which fits for this geometry in approximately the applied load case. It is the DIN 743-2, with the help of which the maximum principal stress of notched, stepped shafts loaded with bending moments can theoretically be calculated exactly. More of these standards can be found in the table book [RoloffMatekTab]. It should be noted that this standard comes from pure bending moment load but in our case, a combination load of bending moment and shear force occurs. For long beams, the transverse force percentage can be neglected because in relation to the bending stress it is negligibly small. For our example, the assumption of a long beam is justified. In the FE analysis the exact load case is calculated, consisting of bending and low shear force effects, which in a precise analysis tend to cause slightly higher stress values as they are obtained from the standard.
DIN 743-2 for the analytical analysis of notch stresses.
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The notch stress σmaxK results from the product of the nominal stress of the unnotched shaft σn and a notch factor ασ, which results from the formula of the geometric dimensions of the shaft step and notch radius. In this case, the notch stresses can be calculated exactly from the DIN 743-2.
Analysis of the notch factor.
σ max K = σ n ⋅ ασ σn =
Mb π ⋅ d 3 / 32
ασ = 1 +
1 r r 0, 62 ⋅ + 11, 6 ⋅ t d
2
3
r r d ⋅ 1 + 2 ⋅ + 0, 2 ⋅ ⋅ d t D
The bending moment Mb is obtained from the effective lever arm of 359.5 mm and the bending force of 150 N to 53925 Nmm. With D = 25 mm, d = 15 mm, t = 5 mm and r = 2 mm, the nominal stress σn = 162.7 N/mm2 and the notch factor ασ = 1.723 are then obtained. Thus we obtain a theoretical tensile stress of 280 N/mm2 in the notch. The error in the first analysis is about 30 %.
The result of the first FEM analysis gave us a value of 285N/mm2 for the non-averaged and 216N/mm2 for the average tensile stress (Maximum Principal). The relative error with respect to the theoretical value is therefore approximately 2 % (non-averaged stress) and about 23 % (average stress). These results demonstrate, now as the first experience, that in FE analyses such errors can be expected, if no special efforts are made in meshing (the good approximation of the unaveraged results should not be overstated, adjustments to the elements will even here cause significant changes in the result). As will be shown below, these errors result solely from the meshing. The boundary conditions or loads in this case do not cause any errors in the calculated notch stress, because they have been applied without errors here.
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3.2.1.25 Assessment of FE mesh quality The quality of the stress results of FE analysis crucially depends on the quality of the meshing that is used. On the one hand the selected item type is decisive, on the other hand the size and shape of the respective elements is very important. As an element type we have chosen ten-node tetrahedral elements (Tet10) , what is the correct and easiest way in most cases. Four-node tetrahedrons lead to a much lower accuracy and are only needed in special cases, such as contact analysis, in which middle node elements are not suitable. Hexahedral elements are even better than Tet10 elements considering accuracy, but they have the disadvantage that they can only be generated automatically for very simple geometries.
Tetrahedral elements with middle nodes provide much more accurate results than those without middle nodes.
Therefore, in the majority of cases of volumetric components of complex shape, the Tet10 element will be used. In the following, we will therefore only speak of this element type. In the application Design Simulation this element type is (besides Tet4) the only available. In later learning tasks, other types of elements can be treated as long as they are functional.
3.2.1.25.1 Visual Inspection In many cases, visual inspection of the FE mesh is already sufficient to judge the quality. In particular, in areas where the stress (or strain, but not displacement) is of interest, the following four criteria should be checked. The critical areas of the mesh should be inspected visually.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
Location of the stresses: Caution is advised if locations where you would expect tension do not show any special stresses in the FE analysis. Two reasons in particular can lead to this effect: As we will discuss later in this example, elements with higher shape usually show smaller stresses than those with lower shape. Therefore, it may occur, that a location that actually carries considerable stresses, is only roughly meshed and therefore the stress results are hardly noticeable. So always check whether such areas occur in
Criteria for the visual inspection.
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An element should not have a stress gradient that is too high.
your result. In our example, this is not the case. The notch area shows the expected stress concentration. In addition, it also happens that small geometry details were not generated in the CAD model or have also been “simplified away” even though they are highly stressed. Of course, in such a case, no special stresses can be displayed here. Stress Figure: Large stress gradients have to be mapped with several element layers, because each element may only represent a relatively simple stress curve. This criterion is usually the most important. In our example, the area of stress concentration is only covered with one element layer. This is likely to have significant inaccuracies. Element shape: There should be no highly distorted elements at locations of interest. In the optimal case, the elements have the shape of an equilateral and equiangular tetrahedron. Sharp elements in the critical region lead to inaccurate results. In the case of our example, the element shapes in the radius are perfectly acceptable. Geometry Mapping: At locations of interest, the real component geometry should be mapped as accurately as possible by the elements. Too coarse elements often cannot ensure this. In our example, only one element layer covers the requested radius, so the edge is not displayed as a circle, but merely as a straight line. This results in a significant loss of accuracy.
3.2.1.25.2 Inspection by Automatically Checking the Element Shapes Inspection using the NX system.
An automatic check of element shapes, alternatively to visual inspection, helps to quickly gain an overview of the elements with the worst shape. This is useful in many cases, because some solvers, such as NX/Nastran, set very high demands on the element shape. If only a single element does not meet a critical criterion of quality, then the solver stops the job. If you use the automatic check, you should perform a visual check of the meshing anyway, because in addition to the element shape, other criteria, e.g. the element size, are important. ÍÍThe automatic test is performed in the FEM part. So you should set this part as displayed. ÍÍIn the simulation navigator, choose the node of the 3D mesh and in its context menu the option Check, Element Shapes, or select the function Element Quality from the group Checks and Information in the toolbar and perform the quality check. The result should be similar to the following figure.
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In this examination there are no failed elements.
Number Failed should be at zero, i. e., all elements have passed the pre-set criteria. Such a mesh should be easily processed by most solvers and especially by Nastran and bring good results.
3.2.1.25.3 Inspection by Comparison of the Averaged and Unaveraged Stresses From the difference of unaveraged to averaged stress results, also the quality of the mesh and the accuracy of the results can be concluded.
This is also a popular type of inspection.
In our case, the values of tensile stress are (maximum principal stress) between 2 % (unaveraged) and 23 % (averaged) below the theoretical value. Despite the good approximation of the unaveraged results, it can be seen that the results are still very far apart in comparison. When the mesh is refined, the two values approximate the theoretical value and therefore each other. Thus, if only a small difference between the values is present, then an accurate result can be assumed.
3.2.1.26 Possibilities for Improving the FE Mesh A refinement of the finite elements usually automatically leads to an improvement of the mesh quality, because all described criteria for visual inspection are fostered. In the following, four methods that can be used for refining, are described. The fourth method is then used for this example.
3.2.1.26.1 Reduction of the Overall Element Size In the simplest case, a global reduction of the element size can be performed in order to obtain better results.
A refinement of the elements leads to a more precise result.
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Since this method affects the whole component, this leads to a considerable increase in the number of elements and nodes. Depending on how powerful the used hardware is and how large or complex the model to be calculated is, this way is quite purposeful. However, with the number of elements the size of the files that are needed for processing also increases. It follows a more or less strong deceleration of all interactive actions of the computer, for example open, close, zoom, rotate, etc. It is even more unpleasant when nonlinear analysis has to be performed with the model, because the analysis then gets an iterative nature, which leads to a multiple of the computing time.
3.2.1.26.2 Local Refinement of Fillets In order to refine the mesh directly at a fillet, there is a simple function in the menu of the mesher of design simulation. For this purpose, the method of the Smart Selector needs to be changed to Fillet. In the Smart Selector options can be set, which fillets shall be considered.
Once this is done, under the Mesh Parameters, the number of elements per 90 degrees is asked. Thus, it is very easy to define how many elemental layers shall be created on a fillet, regardless of the total element size. Therefore, this can quickly lead to sharp elements depending on the setting of the overall elemental size, which again leads to less accurate results.
3.2.1.26.3 Local Refinement Using 2D Surface Meshes In stress analysis of notches, these have to be meshed finely.
The refinement of a local site, such as a chamfer or fillet, can be achieved using a 2D mesh. For this purpose, a 2D mesh with the desired fineness is produced at the site of interest. It is important that the option Export Mesh to Solver is turned off, because it is only an auxiliary mesh. Now, as usual, a 3D mesh can be generated and the nodes of the 2D mesh are applied to the 3D mesh. Future changes to the 2D mesh cause that the underlying 3D mesh needs to be rebuilt or updated. This method is, however, only available in the module Advanced Simulation and should therefore not be used for this example.
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3.2.1.26.4 Local Refinement with Mesh Control The Mesh Control offers several options for controlling local meshes. Thus, the size or the number of elements on edges, the element size in an area or specifically at fillets and cylindrical surfaces can be specified.
3.2.1.26.5 Local Refinement through Volumetric Partitioning A refinement only at the volumetric areas of interest is often desired in order to save elements on the one hand, and on the other hand to obtain accurate results down to the volumetric inside. In the case of our example, this is the area around the fillet of the step. We want to take advantage of this useful method, which is valid both for Design and Advanced Simulation. In the following, we describe the required methodology for a local mesh refinement with partitioning in an area.
3.2.1.27 Volumetric Partitioning at the Region of Interest The desired FE mesh should be fine in the region of interest and coarse in the remaining region. The transition from the fine to the coarse range should preferably be smooth.
The whole body is split.
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For preparation of the volumetric partitioning, planes are generated. Then the body is divided at the planes with the help of CAD functions.
In the case of our example, the fillet and the two adjacent regions will be refined. These are included, so that in the critical region there is no abrupt transition from coarse to fine. For this purpose, the body is divided and individually meshed. In the following, the method for dividing the body is described.
Here, the region of interest is divided.
ÍÍThe following operations have to be carried out in the idealized part. Therefore set this part as displayed. ÍÍSwitch into the modeling environment. Now you will specify the geometry at which the body shall be divided. It can either be a surface or a plane. In our case, it would make sense to use two Datum Planes, which are generated in parallel distance from the planar step area with, for example, 10 mm. ÍÍCreate two Datum Planes at the locations where the body shall be split, such as shown in the figure below. ÍÍNow choose the Split Body function. As Target select the body to be subdivided and as Tool the two planes where the cut shall be performed. Confirm with OK. ÍÍAfter that, the body is divided into three single bodies. Check the FEM file in the simulation navigator for the creation of two new polygon bodies. There should now exist four polygon bodies: the original and three pieces of the simplified one. ÍÍSwitch back to the application Design Simulation. ÍÍNavigate into the FEM file, delete the old mesh and check the polygon bodies. Make sure that only the three split pieces are visible.
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The individual bodies now have to be linked, so that the nodes of the meshes to be created are coincident at the cut faces. ÍÍSelect the function Mesh Mating Conditions and drag a window across all three bodies. ÍÍThe mesh mating Type should be set to Glue-Coincident (this is the default). Check to see this. Glue Coincident means that the nodes of the split body will be coincident and merged. The steering lever can be meshed as a single body, but with three different meshes. ÍÍConfirm with OK. The two pairs of faces are automatically detected and linked.
3.2.1.28 Meshing of the Partitioned Body Now the divided bodies shall be individually meshed. Therefore it is useful to create the finest mesh first, i.e. in the area where the fillet is located, to ensure that the nodes of the fine mesh are adopted by the more coarse meshes.
Mesh mating conditions allow the interconnection of meshes.
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The result is a locally refined mesh. In this way we obtain a significantly more accurate analysis.
ÍÍChoose the 3D Tetrahedral Mesh and in the graphics area select the polygonal body with the fillet. ÍÍSet the type to CTETRA(10) elements. ÍÍCreate a mesh using the Automatic Element Size . ÍÍCreate the meshes of the other two bodies in the same way. ÍÍNow you have to assign the material to the two newly added bodies.
3.2.1.29 Reworking of the Boundary Conditions With the subdivision of the body, the boundary conditions have become obsolete. Therefore, they either have to be deleted and recreated or controlled and reassigned. ÍÍSwitch to the simulation file. ÍÍCheck the individual constraints and the load. The symmetry constraint only applies to one surface. ÍÍBecause now two more faces have been added to the body, also assign the symmetry constraint to these two new faces.
3.2.1.30 Re-Analysis Now the subdivided and refined model is ready for the next analysis. ÍÍCalculate the results again with the function Solve The error has become much smaller.
.
After the new FE-analysis was carried out, open the results and once again evaluate the values of Maximum Principal Stress in the notch as averaged and non-averaged. This now results in a value of about 255 N/mm2 for the averaged stress and approximately 314 N/ mm2 for the non-averaged. The averaged values have thus come closer to the theoretical value, the unaveraged now lie above the theoretical value and come closer from the top with further mesh refinement. The displacement has hardly changed.
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3.2.1.31 Further Refinements until Convergence In order to provide a convergence verification, it is necessary to show that the results of a FE analysis only hardly change when the mesh is further refined. Only by proving this characteristic, the safety is given that the results obtained are close to the theoretically exact value or that the error caused by the FE analysis is small. ÍÍYou should therefore create a mesh next, for example having about four element layers over the fillet radius (this results with half of the automatic element size). ÍÍThen you should calculate your model and thereafter perform further meshing with about six element layers over the fillet radius (this is achieved with a quarter of the automatic element size).
You should verify the convergence of your task.
If the mesh of the body with the fillet is changed, it is recommended to delete the other meshes at first and then to recreate them, so the most important mesh is always built first. The coarser meshes then depend on the nodes of the fine one. ÍÍEach time calculate the stresses and write down the result.
3.2.1.32 Comparison of the Results and Assessment If the stress results of these four FE analyses are compared each in an averaged and unaveraged type with increasing mesh fineness, then the characteristic asymptotic convergence behavior (see figure below) is detected. There are the following three rules: 1. Large elements provide less accurate stresses than small ones. In a stepwise refinement, the stresses approximate the theoretical result. 2. The averaged stress results of the FEM are approaching from below to the theoretically exact result. 3. The unaveraged stress results are generally higher than the averaged ones, because of local stress peaks. Typically, they are also too small in case of coarse meshes. In refinement they overtake the theoretical result and then are approaching it again from the top.
There are three rules.
Our general recommendation regarding stress evaluation is therefore to use the unaveraged nodal stresses (that means the preset stresses), because they are relatively accurate even with coarse meshes.
Recommendations
In many cases major or minor fluctuations against the shown curve can occur, because the results indeed depend on the quality of each element’s shape that lies in the stressed notch. In addition, we also want to point out that the elements may not be refined too much; otherwise the numerical errors (rounding errors) may become more significant. This happens, for example, if the coordinates of two adjacent nodes cannot be distinguished since a computer processes only a limited number of digits. So the mesh should not be refined extremely strong.
Too much refinement should not be done.
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A successful convergence validation with the typical behavior of the stresses: The averaged stresses are approaching from below to the theoretical result. The unaveraged stresses overshoot the exact result to then approach from top.
A colored version of this figure is available at www.drbinde.de/index.php/en/203 The knowledge gained can be transferred.
With the knowledge from this example, you have now gained some very valuable experience as a new FE user, because you have seen how the accuracy of FE results depends on the type of meshing. An advantage is that the knowledge obtained here can be applied to other examples. So in future tasks you can estimate the accuracy of a finite element analysis, if you compare the type of meshing.
This example provides valuable experience.
It should be noted that the transfer of the knowledge gained here is particularly successful if it is a similar shaped element and a similar load condition. For example, if the considered task is a casting, the region where dangerous stress concentrations will occur, are likely the fillets. Components with fillets that are under tensile stress should be meshed with four element layers over the fillet radius for very accurate stress results. But rough statements, such as the identification of critical spots, are already possible with only one layer. Once again it should be noted that the pure error of the finite element method is viewed in this example. This error can thus be reduced close to zero, when proceeding in the manner shown. In practice, probably other error influences will play a larger role, and we can summarize them under the term model errors. Important examples of such errors are: Uncertainties regarding the loads: The external loads are usually very uncertain. Therefore, in many cases only rough assumptions of them can be made.
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Uncertainties regarding the bearings or constraints: The real situation can often only be reproduced approximately. Preloads of the component from the mounting or any temperature effects: These effects can be taken into account only through tolerance analysis. Uncertainties about the exact geometry: With casting radii or welds, the exact form is unknown. Therefore no accurate stresses can be obtained. When a comparative analysis/measurement fails, this may also indicate that the component does not match the drawing according to which the component has been created, or that inside the component imperfections are present (cast-blowholes). The weighing of the device and then a comparison with the weight data from the CAD system should remedy the situation. If the mass is not the same, an error is very likely. Inhomogenities of the material, e. g. through surface treatments or if the development process caused hardening: These variables can hardly be considered in the FE analysis.
Other error sources besides the meshing.
All of these uncertainties must be observed by the user in the real-life case and be included in the evaluation of the result. Therefore, in many cases the experimental testing should be included for strength evaluation. For AB comparisons under same conditions, the FE analysis is well suited.
3.2.1.33 The Effect of Singularities While the geometry of real components is always present clearly and correctly, in CAD or FE models we are dealing with replicas of the real geometry. This results in errors, for example, no blowholes are modeled in cast models. Also the roughness of real surfaces in CAD is shown as a smooth surface. During the transition from CAD to the FE model, these inaccuracies are taken over and are often intensified because many small form elements of the CAD model are undesirable in the FE model.
Singularities are disturbances of the force flow in the FE model. Here stresses must not be read.
In some cases, such simplifications of the real geometry cause the force flow in the FE model not being displayed correctly. Very often, this effect occurs for example when fillets on a real component, which are under tensile stress, are suppressed in the FE model or do not even exist. At such points, the real lines of force cannot be simulated in the FE model. This case is referred to as singularity. In the area of a singularity no correct stress or strain can be determined. The local site is undeterminable. In the FE model, in a certain distance from this point, where the lines of force are formed correctly again, this disturbance is no longer effective and the displayed values can be taken seriously again. As singular points, besides sharp notches, also load areas that load a surface area abruptly can be included. Even at such a point, the lines of force can be disturbed, because in reality, a surface load always slowly increases until it reaches its full magnitude. In addition, constraints are often singular points, where stress values cannot be evaluated. The reason is that real clamped supports always have a more or less high flexibility, which is usually represented through a fixed condition in the FE model. The rigid fixture in the FE model again leads to a disturbance of the real lines of force and therefore stresses and strains cannot be correctly evaluated in these areas.
Sharp notches, fixed constraints and load applications often lead to singularities.
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A little experiment with the FE model of the steering lever illustrates the effect of singularities. It will be shown how the stress behaves in a singular notch when the meshing is varied from coarse to finer and finer. Proceed as follows: Here we will provoke the behavior of a singularity.
ÍÍDelete the fillet that we have created in the idealized model. ÍÍAfter you have deleted the fillet, you have to update the FE model . ÍÍCheck if the boundary conditions are still connected to the correct areas. This is done in the simulation file. ÍÍYou now mesh the component coarsely at first and then, in the range of the deleted fillet, finer step by step. Calculate and determine the results the maximum stress occurring at the two faces. The result should look similar to the figure below, whereby the behavior of the two curves can deviate significantly.
At a singularity, the stress continues to rise with a finer network.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The results show that the previously studied asymptotic course cannot be seen here. Instead, the stresses continuously rise with finer meshing regardless of whether the nodal results are averaged or not. This behavior is typical for disturbances in the power flow or
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singularities. In such a case, the stresses at this point must not be evaluated because their size fluctuates arbitrarily with the meshing fineness. In practice, such singularities or similar ones occur at almost every FE model. They usually cannot be resolved or removed without considerable effort. The user must therefore recognize this effect and must not make the mistake to evaluate stress results in such disturbance areas under any circumstances. At a little distance from the singularity, however, the disturbing effect is already decayed. Therefore, at all other points stresses can be evaluated, but just not in the notch itself.
Dealing with singularities in practice.
So the basic FEM example is now completed.
3.2.2 Temperature Field in a Rocket (Sol153) The RAK2 was powered by a rocket magazine with 24 individual rockets. Such a rocket consists of a tube which is closed on one side and has a nozzle on the other side. In the tube, the fuel is stored. For its ignition, a trigger is provided, which is operated by the driver. The rocket magazine of the Opel RAK2.
In this task you will learn the implementation, possibilities and limitations of temperature field analysis in the application Design Simulation of the NX system. In addition, procedures for the treatment of axisymmetric problems frequently occuring in practice are dealt with. The treatment of mesh connections, such as connections for components, is explained in this example. In addition, it is shown how a plurality of solutions are treated in a simulation file.
What you can learn in this example.
Also for users of Advanced Simulation this example is advisable to get to know the capabilities of the NX Nastran solver in the thermal area. We also want to point out that the Nastran solver, which has its strengths in structural mechanics, is only designed for simple thermal simulations (as shown in this example). For more complex thermal simulations, perhaps coupled with the NX/flow solver, better use the NX/Thermal Solver. However, we cannot disuss the thermal solver, also known as TMG, because of the limited scope of this book.
More complex thermal tasks should be solved with the NX/Thermal Solver.
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3.2.2.1 Task Formulation Assumptions are made with the temperature field analysis in design simulation.
The real thermal situation at the rocket propulsion of the RAK2 has of course a complex nature. This is because, firstly, the occurring physical effects, e. g. combustion, are complex. Secondly, there are large uncertainties regarding the actually occurring conditions, such as temperatures and convection properties. A thermal computation with linear FEM assumptions must presuppose that allow difficult to estimate error influences. Therefore, the methodology presented here is not suitable to calculate the real rocket propulsion of the RAK2 exactly, but at best to estimate it. Rather, it should be the goal of this methodology to illustrate the possibilities and limitations of temperature field analysis in the NX system with the application of Design Simulation. The task is therefore highly simplified.
A rocket and the assumed boundary conditions.
In this task, the temperature field shall be calculated in one of the booster rockets when the following conditions prevail: At the exit surface of the nozzle, a temperature of 500 °C prevails. On all outer surfaces of the rocket tube convective heat exchange with the ambient air takes place, which has a temperature of 18°C. Between the fuel and the rocket tube an ideal heat transfer is assumed. How far is the tube’s back cooling down?
The heat transfer coefficient between the tube and the ambient air shall be 0.5e-5W/ mm2C. The tube is made of a material having a thermal conductivity of 0.052W/mm C, the fuel, however, shall only have 0.026W/mm C. We want the temperature profile in the tube. We are particularly interested in how far the tube is going to cool down in the rear area.
3.2.2.2 Loading the Parts The rocket tube to be calculated can be found in the directory of the RAK2 under the name as_rakete.prt. This part also contains the geometry of the fuel charge. Because apparently, no other components from parent modules for the proposed analysis are needed, load this part now in the NX system and continue with the next steps. ÍÍLoad the file as_rakete.prt in NX. For the FEM analysis, a separate file structure is created.
3.2.2.3 Creating the File Structure ÍÍNext, you switch to the application Design Simulation
.
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ÍÍSelect the function New FEM and Simulation in the Simulation Navigator to create the file structure. Maybe this function also automatically starts, depending on the settings in the Customer Defaults. ÍÍIn the upcoming menu New FEM and Simulation preferences for future solutions can be specified. Since you want to perform a thermal analysis, choose the analysis type Thermal. ÍÍConfirm with OK. The system asks for the solution you want to use. First, however, the symmetry properties of the task should be reflected.
3.2.2.4 Considerations for Symmetry and Solution Type In order to save elements, computing time and data volume, any existing symmetric properties should be exploited. Symmetric properties can always be exploited, when both the geometry and the boundary conditions are symmetrical in the same way. In the NX system, mirror symmetries, axial symmetries and anti-symmetries can be exploited. In case of our example, axial symmetry is situated. Axisymmetric problems can be treated in NX in two different ways: With the volume-based method, that computes a “piece of cake” of the component. With the ring-element-based method: In this method, only a section of the geometry is meshed with 2D elements. Each element enters the analysis like a ring around the symmetry axis. The ring-element-based method is reserved for users of the application Advanced Simulation. In the ring-element-based method when generating the solution, the type of analysis needs to be switched to Axisymmetric Structural or Axisymmetric Thermal, depending on whether temperatures or displacements shall be calculated.
For ring-like parts, there is the axisymmetric analysis method.
3.2.2.5 Creating a Solution With the volume-based method for symmetry use, which will be used subsequently, no special settings are required, i. e. the Thermal analysis type is used. The generation of a thermal solution for NX Design Simulation (left) and for NX Advanced Simulation (right)
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Another possibility to use the symmetry is the analysis of a “piece of cake”.
ÍÍYou therefore have to switch the analysis type to Thermal in the Solution menu. (If you have previously performed the default setting, the option is already on Thermal.) With this option, a new environment is enabled in the system, which leads to a change in the functions that are available for the user. The thermal environment can for example not handle structural boundary conditions such as fixed constraints or forces, but only temperatures, convection and heat fluxes. ÍÍConfirm with OK, whereupon the solution is generated. For the volume-based symmetry, a piece of cake of the components, as mentioned earlier, is required. Then later appropriate symmetry boundary conditions are generated at the cut surfaces. In the following, the necessary geometry preparations are explained.
3.2.2.6 Creating a Wave Geometry Link In the analysis, the two volumes of the rocket body tube and the fuel are considered. Therefore, two cuts are made through these parts, which define the “piece of cake”. In this case, there is again the requirement that the cut should not be carried out on the master geometry, but only in the analysis model. For this reason, wave geometry links for the two solids are first generated in the idealized part. For the geometry preparation an associative copy is required.
Proceed as follows: ÍÍFirst of all, set the idealized part as displayed part. ÍÍThen select the function WAVE Geometry Link and set the type to Body. ÍÍSelect the body of the rocket tube as well as the fuel and confirm with OK. ÍÍYou may check in the part navigator to see whether really both bodies are included in the wave link. The master part geometries and the generated wave links are now displayed over each other and later mistakenly the wrong body could be selected, e. g. in geometry simplifications. Therefore, it is useful and important to hide the master part geometries. This can be done in the assembly navigator: ÍÍIn the assembly navigator, turn off the whole red checks of the components, so only the linked bodies are displayed.
3.2.2.7 Creating the Symmetry Cuts ÍÍIn order to generate the symmetry cuts, switch to the application Modeling , because the required functions are not available in the FEM application. ÍÍCreate two Datum Planes through the symmetry axis of the parts, which are at an angle of 30° to each other. The size of the piece of cake angle is arbitrary. We recommend a small piece of cake, because fewer elements are needed then, but later on this leads to a smaller angle for the tip-elements. Therefore an angle between 15° and 45° for the cake segment is recommended.
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Symmetry cuts can be generated in the modeling environment.
ÍÍTrim the two solids at the two planes with the function Trim Body . ÍÍNow that the geometry preparations are completed, switch back to the application Design-Simulation .
3.2.2.8 Creating and Assigning Material Properties For the thermal analysis only the thermal conductivity is required as material parameter. So two different materials with the characteristic values are produced and allocated to the respective bodies. To do this, follow these steps: ÍÍSet the FEM file as displayed part. In the FEM file, you will notice, that the symmetry cuts of the idealized part are no longer visible. The reason for this is that all parts were created as polygon bodies, in other words for both the original parts of the master file as well as for the linked and prepared parts of the idealized file, polygon geometry is created. Now, all these bodies are coincident. However, since we only want to work with the linked, prepared bodies, the master geo metries should be hidden. ÍÍIn the simulation navigator, in the Polygon Geometry folder, switch off the necessary red checks, so that only the bodies of the prepared geometry remain visible. ÍÍUse the function Assign Material and therein select Create Material . ÍÍIn the name field, enter the name of the first material, for example “Pipe Material”. ÍÍIn the Thermal Conductivity field, enter the thermal conductivity of the tube of 0.052W/ mm C. Make sure that the correct unit is set. In order to define the material for the thermal analysis, this specification is sufficient from the side of the FEM, however, the NX system requires a density specified at each material. ÍÍWithout specifying the density of the material, it cannot be created, so please enter, for example, the value 7.5e-6 kg/mm3 in the Mass Density field. ÍÍConfirm with OK, and the material will be generated. ÍÍNow in the graphics area, select the cut pipe geometry and confirm with APPLY to assign the material you just created to the geometry. ÍÍProceed in a corresponding way for the definition of the second material. Name it for example “Fuel”. ÍÍEnter the value 0.026W/mm C for the Thermal Conductivity and 7.5 e-6 kg/mm3 as Mass Density. ÍÍConfirm with APPLY so that the second material is also generated. ÍÍAssign the material to the second body in the above-mentioned way.
The polygon bodies need to be hidden.
For this analysis, the specification of thermal conductivity is required.
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3.2.2.9 Creation of Mesh Connections The function Mesh Mating Condition could be used to define a fixed connection between two different meshes for a structural analysis. The two meshes are coupled at their contact surfaces with respect to the displacements, as it has already been done in the previous example. The heat transfer between two different components is considered.
In a similar way the function Mesh Mating Condition could be used in the thermal analysis to couple two meshes with respect to their temperature values. The result of such a coupling is therefore an ideal temperature transfer from one body to another. This is required in our task. For the creation proceed as follows: ÍÍMake the FEM file the displayed part, if this is not already the case. ÍÍSelect the function Mesh Mating Condition .
The mesh mating conditions are displayed in the simulation navigator.
All adjacent surfaces that are present in the model should be connected. Therefore, the automated method can be used for the generation. ÍÍSet the Type to Automatic Creation . This is the default. ÍÍFor safety reasons, choose the Preview function to check if all five pairs of surfaces have been found. ÍÍThe Mesh Mating Type has to be set to the option Glue Coincident because hereby identical nodes are created at the contact points. This is also the default. ÍÍConfirm with OK. Now the five conditions are created. They are displayed in the simulation navigator.
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3.2.2.10 Create the Mesh A coarse mesh is sufficient for meshing, because temperature field analysis (quite similar to the deformation analysis) is uncritical with respect to the element size. Due to the thinwall geometry of the pipe, it should be ensured that at least two element layers are formed over the thickness in order to maintain an acceptable accuracy. Follow these steps to create the mesh with two layers on the pipe:
The mesh can be coarse.
ÍÍSelect the function 3D Tetrahedral Mesh . ÍÍSelect the body of the pipe and choose the function for automatically determining a suitable element size . ÍÍDivide this value i. e. by 3. With a “/ 3” written behind the default value an element size with two layers should be arisen. ÍÍConfirm with OK. ÍÍCreate the second mesh for the fuel in the same way. We need at least two layers in the wall of the tube.
Alternatively a coarser element size with the option Minimum Two Elements Through Thickness is possible, but make sure that no highly distorted elements are generated.
3.2.2.11 Generate Temperature Boundary Condition ÍÍNow switch to the simulation file. ÍÍCreate the temperature boundary condition by calling the function thermal constraints below constraints group and select the surface that will be applied with the constant temperature (see figure below).
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At this location the temperature is pre determined.
ÍÍEnter a temperature of 500 and make sure that the unit is set to “C”. ÍÍConfirm with OK to generate the boundary condition.
3.2.2.12 Generate the Convection Boundary Condition ÍÍCreate the convection boundary condition with the function Convection and select all the faces on which the rocket geometry is in contact to outer air, except the surface with the temperature condition.
The outer surfaces receive a convection boundary condition.
ÍÍEnter a convection coefficient of 0.5e-5 in the unit W/mm2 C and a ambient temperature of 18 in the unit “C”. ÍÍConfirm with OK to generate the boundary condition.
3.2.2.13 The Thermal Symmetry Boundary Condition The symmetry condition is designed to have the property that no heat is exchanged through the cut surfaces of the “piece of cake”. Perfect insulation should prevail on the cut surfaces. This type of condition is achieved when no FE boundary condition is given here. So these areas need to receive no conditions.
3.2.2.14 Calculate and Display the Results ÍÍAfter the model has been created so far, it can be solved with the Solve function. ÍÍAfter the analysis process switch to the result presentation with the Results function.
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The temperature profile in the rocket is the result.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The temperature distribution is the first result displayed. In the area at the rocket outlet where the temperature is specified the temperature of 500 degrees should be accurately displayed, and at the rear of the rocket, the temperature should be decreased to about 100 degrees. Other results like the temperature gradient or the heat flux can be displayed in the simulation navigator when appropriate. The heat flux shows the locations at which the heat flow is accumulated.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The learning task is completed for thermal simulation.
Bibliography [Bathe] Bathe, H. J.: Finite-Elemente-Methoden. 2nd Edition. Springer Verlag, Berlin/Heidelberg/New York/Tokyo 2006 [FKM] Forschungskuratorium Maschinenbau e.V. (FKM): Rechnerischer Festigkeitsnachweis für Maschinenbauteile aus Stahl, Eisenguss- und Aluminiumwerkstoffen (FKM-Richtlinie). 6th extended Edition. VDMA Verlag 2012 [Komzsik] Komzsik, L. What every Engineer should know about Computational Techniques of Finite Element Analysis, 2nd Edition. CRC Press, London/ New York 2009
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[RiegHackenschmidt] Rieg F./Hackenschmidt R.: Finite Elemente Analyse für Ingenieure. Eine leicht verständliche Einführung. 3rd Edition. Carl Hanser Verlag, München 2009 [RoloffMatek] Muhs D./Wittel H./Jannasch D./Voßiek J.: Roloff/Matek Maschinenelemente. Normung, Berechnung, Gestaltung. 21th Edition. Springer Vie weg, Wiesbaden 2013 [RoloffMatekTab] Muhs D./Wittel H./Jannasch D./Voßiek J.: Roloff/Matek Maschinen elemente. Tabellen. 18th Edition. Vieweg+Teubner Verlag, Wiesbaden 2007 [Schäfer] Schäfer, M.: Numerik im Maschinenbau. Springer Verlag, Berlin/Heidelberg/New York 1999
4
Advanced Simulation (FEM)
The module NX Advanced Simulation allows analysis engineers or interested design engineers in the FEM field the simulation of complex mechanical effects. On the one hand, the predictable physical phenomena go far beyond linear FEM. For example, classical nonlinearities like contact, non-linear material and large deformation can be calculated here, as well as special areas such as crash, metal forming or laminate analysis. On the other hand, it is possible to analyze more complex geometry than in module Design Simulation because many functions exist for geometry preparation, mesh control and coupling of meshes. This chapter describes the part of the Advanced Simulation module that works with FEM. We deal with the CFD portion comprising flow and complex thermal problems in Chapter 5. The conclusion is Chapter 6 dealing with electromagnetic simulation.
Application scenarios and benefits for the NX Advanced Simulation module in practice.
Users of Advanced Simulation (FEM) should be familiar using 3D design of components and simple assemblies in the NX system. In addition, basic knowledge should exist in the field of linear FEM, just as it is taught in Chapter 3 for module Design Simulation. Working through Chapter 3 (at least the review of the first example) is recommended because the CAE file structure and many basic functions are the same as in Advanced Simulation. These basics are therefore not repeated in this chapter. However, further assumptions on prior knowledge do not exist. In Section 4.1 Nastran solution methods are described which are used in later examples. You will learn how they work, what they can deliver, and what their limits are.
Content of the chapter.
In Section 4.2 to 4.4 learning tasks follow dealing with the topics linear, basic non-linear and advanced non-linear analysis. All learning tasks are derived from the context of the RAK2 rocket vehicle. In the learning tasks for linear analysis complex meshes are discussed first. In the first example (Section 4.2.1) there are shell elements used, in the second example (Section 4.2.2) beam elements and in the third example (Section 4.2.3) mass points. The fourth example (Section 4.2.4) finally shows the contact feature, strictly speaking this should belong to the non-linear part. However, since this simplified contact function (Sol 101) is associated with the solution method for linear statics, it will be displayed and used in this context.
Content of learning tasks.
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Learning tasks to basic non-linear analysis describe non-linear effects “large deformations” (section 4.3.1) and “non-linear material behavior” (Section 4.3.2) by using NX/Nastran solution method Sol 106. Finally, NX/Nastran’s solution method Sol 601 is explained in the context of an advanced non-linear analysis of a snap hook that is analyzed, taking into account contact and large deformation effects (Section 4.4.1).
■■4.1 Introduction Mechanical problems can – as mentioned several times – be structured in four fields: rigid bodies, elastic bodies, fluids and electrical bodies. Rigid body mechanics is calculated by using MBD programs (multi-body dynamics). This is made possible by using the module Motion Simulation in NX. Elastic bodies or structural mechanics is calculated by FEM/FEA (Finite Element Method/Finite Element Analysis) and fluid mechanics by using CFD (Computational Fluid Dynamics). Electrical bodies or Electromechanics are calculated with FEM. Simulation disciplines: FEM, CFD, Thermal, EM and coupled systems
Advanced Simulation offers the ability to use the methods FEM and CFD. In this chapter, the FEM part is considered, the CFD part follows in Chapter 5. We want to point out that with Advanced Simulation even complex thermodynamic problems can be solved. For this the separate solver NX/Thermal (formerly TMG) is available. This discipline is not covered in this book because of its complexity. In addition, the electromagnetic field analysis (EM) is available as another discipline with help of the new solver “MAGNETICS”. This topic is considered in detail in Chapter 6. In addition, some of these analyses can be coupled in order to analyze connected physical phenomena.
Four main divisions of engineering simulation
Technical Simula on Rigid Bodies Rigid Body Mechanics MBD (Mul body Dynamics)
Elas c Bodies Fluids Structural Mechanics Fluid Mechanics FEM CFD (Finite Element (Computa onal Method) Fluid Dynamics)
Electric Bodies Electromagne cs (EM) FEM (Finite Element Method)
In structural mechanics, a variety of mechanical tasks is solved by using linear and nonlinear FEM. The NX/Nastran system divides these tasks into classes that can be addressed with a particular solution method. For example, the solution number 101 is the method for linear statics. Selecting one of these solution methods is the first thing the user has to do. It should be noted that each solution method in the NX system is associated with own licenses.
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Of course, the chosen solution method significantly influences the further construction of the computational model. Therefore, those solution methods are presented, that are used later in the learning tasks. The presented solution methods only represent a selection of the comprehensive possible solutions, which are available in NX/Nastran. With time, more and more NX/Nastran solutions are integrated into the user interface of the NX system and can be applied easier. In this book, however, just fundamental solution methods are presented, which are already integrated in the NX system and are intended for direct use. For example, we do not cover the numerous Nastran solution methods for dynamic analysis, i. e. the solution numbers 107 to 112, the built-in NX Response Analysis and also not the subject of Super Elements.
Solution methods of NX Nastran.
Those Nastran solution methods that are not already integrated into the NX user interface can also be used by NX users, but this requires that the solver input file, which is passed to the NX Nastran system must be manually edited. For this purpose the detailed Nastran commands must be entered. For an introduction to this topic, see for example [nxn_user]. Finally, NX/Nastran provides the opportunity to develop own solution methodswith its programming language DMAP (Direct Matrix Abstraction Programming). A documentation can be found in [nxn_dmap].
4.1.1 Sol 101: Linear Static and Contact The Solution 101 treats linear statics as well as the simpler NX module Design Simulation. A special feature is that despite the linear nature of the basic solution method 101, the function for calculating contact is included, although this actually requires a nonlinear solution. So if the contact feature is used, in fact a non-linear algorithm is used for the computation. The reason for this characteristic is that contacts are required extremely common in static analyses, so it has been decided that this important feature should be available in any structural analysis. This contact functionality of solution 101 will be treated in the learning task “Clamping Seat Analysis of the Wing Lever”.
4.1.2 Sol 103: Natural Frequencies The solution 103 performs the analysis of natural frequencies, and that is also possible in module Design Simulation. The only difference is that the Advanced Simulation uses complex meshes and additional element types. Moreover targeted mass points may be created, which are especially useful for affecting natural frequencies. This solution method is used in the example “Natural Frequencies of the Vehicle Frame”.
The most commonly used solution method.
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4.1.3 Sol 106: Nonlinear Static Smaller non-linear effects can be calculated with the solution 106.
Smaller non-linear effects can be analyzed using solution 106. Here the effects of large deformation and plastic material can be calculated. However, contact is also possible. For this, the so-called gap elements are used which are less comfortable in use. The method for non-linear material behavior is limited due to the used algorithms. The use is no longer recommended, if maximum strain becomes greater than about 4 %. More complex nonlinear effects can be performed in the continuing solution 601 or 701. The non-linear solution procedure is based on the fact that the loads are applied iteratively increasing. Each iteration complies doing a linear FE analysis. After an iteration, new node positions and directions of boundary condition will be the load and displacement vector and are inserted in the stiffness matrix. Thus nonlinear behavior is modeled. For example, in this way stiffness changes are included in the analysis as they occur in large deformation, non-linear material. A detailed description of the methods used is available in [nxn_nonlinear106_1] and [nxn_nonlinear106_2]. The solution 106 is illustrated in two learning tasks. In the task of the leaf spring there are large deformations and in the task of the brake pedal there is non-linear material taken into account.
4.1.4 Sol 601/701: Advanced Nonlinear The solution method 601 is based on technology of the FEM system ADINA.
The solution methods 601 and 701 are based on the integration of the well-established FEM solver technology of the ADINA system in NX Nastran and are focused on non-linear problems. The non-linearities large deformation, material non-linearity and contact are simultaneously calculated. In addition, time-varying loads and boundary conditions are possible. The solution methods 601/701 can therefore solve static and dynamic tasks. 601 is an implicit and 701 an explicit FEM formulation. The 601 is divided into two parts: 601.106 performs non-linear analysis with no consideration of dynamic effects, and 601.129 (as well as 701) takes into account dynamics of motion. The non-linear solution method is based on iteratively increasing loads or movable constraints, so that stiffness modifications or geometrical changes can be updated that occur during the deformation. During each iteration, equilibrium conditions are set up between external and internal forces or energies and tested with respect to convergence. With time dependent analysis that loads iterations additionally time increments must be performed. This also takes into account inertial forces, velocities and accelerations. In addition to a fixed specification of time step size, different methods for automatic time step control are available (ATS – Auto Time Stepping). This way it is ensured that the time step size is set in the best possible way. This means that in time-critical areas, such as a contact, small time steps will be performed while during non-critical ranges time steps are coarse. There is also a set of features for influencing convergence behavior that can be used if necessary. These include:
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Stiffness stabilization, Limit maximum displacement, Line Search, Low Speed Dynamics, Auto Time Stepping (ATS), Total Load Application (TLA, TLA-S), Contact Damping, Contact Surface Extension, Control Initial Penetrations, Contact Compliance and Suppression of Contact Oscillations.
Auxiliary functions or features for the nonlinear solution process.
More information on the solution method 601/701 can be found in [nxn_ad-vnonlinear] or in appropriate training documents [Binde4]. NX Nastran solution method 601 is shown in this book in a learning task that analyzes a snap hook. For this purpose, a time-dependent travel path is defined, and contact and large deformations will be considered. Forming simulation of a sheet metal: The metal sheet is plastically formed by two L-shaped tools.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
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Below we give some illustrations of non-linear simulations taken from [Binde4]. The four images represent a strip of sheet metal that is plastically deformed. For this simulation, a solution of type Sol 601, 106 is performed in which the non-linear effects plasticity (nonlinear material), large deformations and contact are calculated. The path of the tool is divided into two parts. The first way does a vertical and the second a horizontal movement. The following figure shows a simulation of impacting a ball (such as a golf ball or hailstone) to a curved metal surface (such as a car roof). The ball will fall down from a height of one meter and cause permanent plastic deformations on the sheet. For this simulation, the solution Sol 601,129 or 701 is used, in which, besides contact, large deformations, plasticity, and dynamic effects are all shown. At 0.45 seconds the ball is just before impact, at 0.46 seconds the contact is established and at 0.47 seconds the ball bounces back. An impact simulation with plastic deformation, that also takes the dynamic influence into account.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
■■4.2 Learning Tasks on Linear Analysis and Contact (Sol 101/103) 4.2.1 Stiffness of the Vehicle Frame An important use case for linear FEM analysis is stiffness analysis. Thus, for example, new car bodies are studied extensively for their stiffness and optimized for different applications (torsion, bending, self-weight). In this learning task the metal frame of the RAK2 is to be analyzed regarding its stiffness against bending. This corresponds approximately to the load by the weight of the vehicle. Shell elements and mesh connections are among the learning effects of this example. The technique of Assembly FEMs is shown.
You will learn how to deal with shell elements which should be used often in the case of thin-walled geometries (sheet metal, thin plastic skeleton). In addition, important techniques are described, for example constraints to define rotatable situations. In the second part of the learning task that you can perform independently from the first, you will learn how an assembly FEM model is built that uses already finished piece-part meshes. Based on this very comfortable technology the riveted frame parts are then analyzed in conjunction.
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The frame of the RAK2 consists of longitudinal and transverse beams.
You will also learn techniques that will help shell components to be connected together (rivets, spot welds). Ultimately, the complete vehicle could be analyzed in combination in this way. The real load situation of the frame contains a whole series of related attached parts, which have a more or less strong influence. On the one hand all four wheels need to be mentioned, which are mounted by means of leaf springs to the frame, and on the other hand, the gravity forces of the driver and of the rocket engine and the wing are of major importance. Furthermore, the load on the frame also critically sdependent on the way of driving. Cornering, acceleration and braking as well as driving on different surfaces are load cases that would be considered. Within the framework of methodology instructions in this book the complex loads and constraints of such a framework, as well as driving conditions, are shown highly simplified to keep the number of solution steps manageable that the user needs to perform. Extensions can be of course carried out by the user.
4.2.1.1 Task Part 1 The frame of the RAK2 consists of several sheet metal parts that are riveted together. Essentially the two longitudinal beams are stressed by bending through static loading from the weight of the vehicle and the driver. For judging the stiffnesss of one of the longitudinal beams, it has to be analyzed for bending in this example, loaded by half of the total weight.
3000N
A longitudinal beam under load.
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For this purpose the longitudinal beam shall be supported rotatable at the beginning and at the end and loaded at its center by a force of 3000 N.
4.2.1.2 Prior Considerations to the Assembly Structure We start with an analysis of the single parts.
In this task, we will only consider and calculate the longitudinal beam. Later, we will then include the remaining parts for the full frame in the analysis. This corresponds to typical procedures in progressive design and development processes, because at the beginning no complete product has been engineered, only parts of it. Nevertheless, the already designed parts shall be calculated. Therefore, we will first perform a part analysis of the right longitudinal beam here. Later, the FEM mesh from this item will be further used in the assembly analysis together with the other parts/meshes. ÍÍOpen the file rh_laengstraeger_re.prt from the RAK2 directory in NX.
4.2.1.3 Considerations for Meshing Thin parts should be meshed with shell elements.
The geometry of the longitudinal beam is characterized by thin walls which are welded together. Meshing with tetrahedral elements, as described in the fundamental example before, is principally possible, but it would require that a sufficient number of elements were arranged over the wall thickness of the sheet metal parts, so that sufficient accuracy could be achieved. Because of the large size and the thin walls of the part so many elements would be required in a tetrahedral mesh that probably the computer capacity would be exceeded. Even for deformation analysis that requires less quality meshes, a tetrahedron mesh of this component would not be suitable. Much more useful is the choice of shell elements in the case of such thin-walled components. With shell elements only the midsurface area of a thin-walled part is meshed. Those elements have 2D geometry and process the thickness of the component by their internal stiffness description. At each node of a shell element the translational and rotational degrees of freedom are available. Thus, the bending behavior can be transmitted from one element to the next. An additional advantage is, that shell elements can process moment loads directly. In this way, thin-walled parts can be calculated very efficiently.
Shell elements process translational and rotational degrees of freedom at nodes. The rotational degrees of freedom are required to allow bending to be transferred.
thin walled dünnwandiger Körper body shell element (Quad8) nodal degrees of freedom trans rot
Mittelfläche midsurface
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Shell elements are somewhat more difficult to handle than tetrahedral elements. On the one hand, the reason for this is the preparation of more complex geometry, because a midsurface is to be extracted. On the other hand, the presentation and evaluation of results are more demanding. Stress and strain results of shells are calculated over the thickness at the three locations outside, inside and center: In the post-processor it must therefore be tracked carefully, which of the three results is displayed. It is easy to get confused. It is also conceivable to mesh the frame with beam elements. However, this would simplify the real geometry very much.
4.2.1.4 Create the File Structure for Shell Element Simulation Before the file structure is created with the idealized part, the FEM and simulation part, we should consider geometry requirements for subsequent meshing. By default, the NX system generates polygon geometries for all bodies, which are included and visible in the CAD master file. But in the case of our task, the solid-volume of the body of the longitudinal beam is not required, instead a corresponding midsurface, which we will derive using a special function in the idealized file in the next steps. Therefore, we want to suppress any automatic creation of polygon geometries in the subsequent creation of the file structure. After the midsurface has been created, we want to perform their subsequent conversion into a polygon geometry.
For shell elements, one works a little differently.
Proceed as follows: ÍÍSwitch to the application Advanced Simulation . ÍÍCreate a simulation in the simulation navigator (New FEM and Simulation). ÍÍIn the following menu (see figure above), select the option None in Bodies to use. ÍÍIn the next menu Create Solution you set, as already explained in the basic example, the options for your solver and the linear static analysis method. These things should normally be preset in such a way, that you only need to confirm with OK. We again choose the solver NX Nastran. However, the choice of the solver has no particular relevance for this example since this task is linear statics, which is supported by all structural solvers very similar.
The midsurfaces are added to the polygon models later on.
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Now, various geometry preparations must be performed on the longitudinal beam. The most important preparation relates to the creation of the midsurface for the later shell meshing. Moreover, small form elements must be removed and markings must be created for later boundary conditions.
4.2.1.5 Generating Markers for Subsequent Boundary Conditions After the file structure is created, you are in the simulation file. ÍÍNow switch via the simulation navigator into the idealized part because subsequently preparations of the CAD geometry shall be performed. ÍÍIf the message Idealized Part Warning appears, confirm with OK. Let us first mark two positions for subsequent boundary conditions before irrelevant form elements are removed. These are points on both ends of the longitudinal beam, where later rotary bearings are to be installed (see figure below). The CAD model has a cylindrical bolt and a hole there, which fit into a corresponding sleeve and a pin of the adjacent parts. At these pins respective dot marks are generated at the center of the circle, which are later used for boundary conditions. At these two marks boundary conditions will be defined later.
Such markings can be done by simple points. For the analysis it is irrelevant whether these are associative or non-associative points. You can, therefore, easily use the methods known from the design to create the two points. ÍÍGenerate a Wave-Link for the body of the longitudinal beam. ÍÍThen hide the underlying assembly (this is only the part rh_laengstraeger_re) using the assembly navigator. Only the linked body remains visible. ÍÍChange the application to modeling . ÍÍNow create the two markers. Use for example, the following function: MAIN MENU > INSERT > DATUM/POINT > POINT. According to the previous figure, select the respective circular edge to form a point in the center of the circle. Make sure that not two points areaccidentally generated at the same position.
4.2.1.6 Removal of Non-Relevant Form Elements Next, those geometries that are irrelevant for the stiffness of the beam shall be removed. This geometry simplification has also the purpose that the component geometry for subsequent automatic midsurface creation will be improved. This work is also done in the idealized part.
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The figure below shows three regions to be simplified.
delete
delete
delete For the removal of these areas, either the feature Idealize Geometry group of the geometry preparations or alternatively Delete Face group of the Synchronous Modeling can be used.
The longitudinal beam contains some form elements which disturb the creation and meshing of the midsurface.
from the function from the function
We want to point out that the synchronous modeling capabilities are very diverse and powerful. In addition to the function to delete faces there still exists a number of other useful functions. Since the synchronous modeling functions are very useful in particular for the preparation of FEM models, we will work with some of these functions in our example. Synchronous Modeling is very well suited for model preparation.
These simplification functions operate independently of the feature structure of the CAD model, so they have the advantage that they can also work with non-parametric or poorly parameterized geometries. Prior to the application of such a function a Promote or Wave Link must be created, which is already done in our case. In these simplification operations only those surfaces are selected which are to be removed from the CAD model. After removal of those surfaces the CAD body will be first no longer closed. This may not stay in such way. Therefore, the function attempts closing the body back on by modifying neighboring areas of the removed faces. The neighboring areas are either extended or shortened corresponding to their natural shape. If the body can be closed in this manner, the function completes successfully. Otherwise, an error message appears. Proceed as follows: ÍÍSelect the function Delete Face
from the toolbar Synchronous Modeling.
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This area is to be removed for the simulation.
ÍÍNow select the faces which are to be removed (see the previous two figures). You can either select only the faces of one region, or all three areas simultaneously. In case of complex geometry simplifications specifying smaller areas is recommended because it may help the function to perform successfully. Another useful feature is the use of very ingenious selection filter in NX. ÍÍAfter confirming with OK, the operation is performed. Finally, the area at the front end of the longitudinal beam is to be simplified by cutting the sleeve that is welded to the sheet metal. This area disturbs the creation of the mid surface. Therefore, it gets truncated (rght: the truncated body).
This clipping can take place in various ways. We propose the following universal method (see figure above): ÍÍCreate a sketch
with a rectangle on a surface of the longitudinal beam.
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ÍÍExtrude this rectangle. In the extrusion function select the mode Subtract and choose the longitudinal beam as the target body. The result is a simplified geometry of the longitudinal beam. Out of this a midsurface can now be easily created.
4.2.1.7 Creating the Midsurface The midsurface can be created in various ways. Note that the user has the full functionality of the CAD application within the NX system to generate or to manipulate midsurfaces , additionally to the special midsurface feature shown here. In many cases, thin-walled parts are CAD designed by first modeling the midsurface, and then thickening in both directions. Some components are not designed as a volume, but as a pure surface model. In these cases, the midsurface is already available and can be used for the FE analysis immediately. The midsurface feature, which is available in NX, can work completely automatic in many cases, in other cases only portions are generated automatically. They need to be reworked manually. Knowledge of the functions of the free-form area are of advantage.
Depending on the generation method, the midsurface is created already during the CAD design phase.
The midsurface feature from the NX system provides three different methods for the procedure that will be explained in the following: The NX system has three different methods for midsurface generation.
Face Pair : This method searches in the model according to face pairs whose areas face each other. For each pair of faces found an own midsurface is generated. The generated surfaces are automatically extended or trimmed so far that they adjoin to each other. The user must later sew the resulting individual surfaces into a sheet-body. The function works well for geometries that are characterized by such pairings of faces. It can therefore also process ribbed geometry. As a special feature, the thickness of the body can be automatically processed and passed on to the subsequent shell mesh. Offset : This method is not suitable for ribbed geometry, but only for single sheets or thin walls. The function searches for the outside surface of sheets by examining their smoothness. Normally each face of the sheet body should be smooth to its neighbor. Only at sharp cut edges this will not be the case. Therefore, the function can automatically identify one entire side of a sheet. The function then creates an offset surface with half the thickness. Again, the thickness of the body can be automatically processed and passed on to the subsequent shell mesh. User Defined : This method allows the user to declare any previously existing surface as midsurface and to pass any thickness information to it.
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The method Face Pair is well suited for sheets which abut against each other.
In our example we use the method Face Pair, since the present body is not smooth or rounded on the outside and therefore the offset method would not work. Due to its robustness, the method Offset is recommended for rounded sheet metal parts.
The individual surfaces should be sewn.
The individual midsurfaces should now be sewn so that a single sheet is created. Sewing of individual surfaces is not absolutely necessary since individual areas can be also meshed each for itself. However, it should be ensured that the nodes are merged between those individual surfaces. By using the described sew operation we avoid this step with all the associated uncertainties.
ÍÍSwitch to the application Advanced Simulation. ÍÍSwitch to the function Midsurface by Face Pairs from the function group Model Preparation and select the body. ÍÍNext, activate the switch Automatically Create Face Pairs in the midsurface dialog and change the setting Strategy to the option Progressive. Thus, the system will search for surface pairs and generate all midsurfaces of the longitudinal beam. ÍÍTo see the midsurface after creation, you should hide the solid body. This can either be done manually using the feature Show/Hide or directly in the midsurface dialog by activating the switch Hide Solid Body. ÍÍConfirm with OK, so the midsurfaces are created.
ÍÍTo do this, select the function Sew from the function group of model preparations. ÍÍFirst select one of the faces, and then drag a window over all other faces. ÍÍAfter confirming with OK, the sew operation is performed. Faces that are not sewed or stitched will be meshed worse.
When sewing, make sure that single faces will be connected at all adjacent edges. A nonconnected edge can be recognized just after sewing because the newly created surface boundaries are displayed temporarily. If two edges to be sewn have a distance which is greater than the tolerance specified in the sew dialog, such tolerance must be increased or the distance must be corrected. A very powerful alternative for sewing is the feature Stitch Edge, which can be found in the FEM file.
4.2.1.8 Subdividing the Surface for Load Application The position of the load shall take place in this example in the middle of the beam, which is a rough approximation of the real situation. For this purpose, a point load could be generated at a node of the FE model. However, point loads are usually unrealistic. The real load would always be distributed over an area. In addition, point loads lead to singularities. Therefore, the force shall be applied to a circular area. First, a circuit must be drawn on the side face and then a face subdivision is performed with the circuit. Proceed as follows: ÍÍTurn into the design environment . ÍÍCreate a sketch and draw a circle on the side surface of the midsurface – such as shown in the following figure.
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A sketch characterizes the range in which the force is applied.
ÍÍThen switch back to the FEM environment . ÍÍSelect the function Divide Face from the function group of model preparations. ÍÍSelect the surface of the carrier. ÍÍSwitch to the next selection step. ÍÍThen select the newly created circuit. ÍÍAfter confirming with OK the surface subdivision is created.
A face subdivision for subsequent load application.
Thus, the work in the idealized file is completed.
4.2.1.9 Add Polygon Geometry for the Midsurface In this section, the meshing of the sheet is to be performed with shell elements. Meshings must be performed in the FEM file. ÍÍTherefore, first turn in the FEM simulation file via the navigator. You will realize that the newly created sheet cannot be found in the FEM file. The reason for this is that we had set the option Bodies to Use to None when we generated the FEM file. Therefore, the FEM file will now be manipulated and the new midsurface sheet is added subsequently so that a polygon geometry is created from it. To do this, follow these steps: ÍÍIn the simulation navigator, open the context menu of the node of the FEM part (RMB on rh_laengstraeger_re_fem1.fem). ÍÍChoose the function EDIT . . . The dialog Edit FEM appears, which can be seen in the figure below. ÍÍActivate the option Edit Bodies to Use. ÍÍSet the option to Select. Now you have the possibility to add or remove geometry from the idealized part. ÍÍSelect the geometry of the newly created midsurface body.
The new midsurface must manually be added to the polygon model.
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In addition the two points for the later boundary conditions should also be taken into the FEM model. ÍÍAdditionally activate in Geometry Options the setting Points. Confirm with OK and save the part. In this menu the midsurface is subsequently added to the polygon geometry. Also, points out of the CAD design are made visible in the FEM file.
The polygon geometry is now updated, the two points are added and should be visible now. In the following, the meshes can be created.
4.2.1.10 2D-Meshing the Midsurface The meshing occurs, as explained earlier, with shell elements. ÍÍSelect from function group for meshing the function 2D Mesh . ÍÍSelect the sheet body. Make sure that you select not just a single face, but the whole polygon body. Thin-walled parts such as sheets are meshed with 2D shell elements.
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ÍÍIn the 2D mesh dialog, you enter in the options for the type CQUAD4 or the symbol for quadrilaterals without mid-side nodes. ÍÍSelect the function for automatically determining a suitable element size , which always makes a proposal for a coarse mesh. ÍÍTo achieve better networking, use half the value proposal. Enter “/2” after the default value. ÍÍLast, confirm with OK. The mesh is now created. The element type used here, that is quadrilateral without mid-side nodes, achieves a relatively good accuracy. Indeed, in static linear analysis elements with mid-side nodes are more accurate than those without. But there is also another rule: quadrilateral elements are more accurate than triangles. The best element is therefore the CQUAD8. However, these 2D mid-side nodes elements often cannot be generated immediately with sufficient quality in cases of more complex geometries. Manual rework or setting additional solver parameters may be required. Therefore, we have decided on the universal quad4. This element type is found in FEM analysis practice most frequently.
4.2.1.11 Specify the Wall Thickness Wall thickness of the thin-walled body is associated with 2D elements. Thus the stiffness behavior of the real 3D structure can be simulated by 2D elements. ÍÍUse RMB on the 2D mesh collector. Select the EDIT option. ÍÍHere you select the button Modify Selected . ÍÍIn the next window at Default Thickness you enter the value for the material thickness. In our case, the thickness is 4 mm. ÍÍConfirm twice with OK to exit the dialogs.
4.2.1.12 Connect the Mesh to the Bearing Points The peculiarity of the bearing condition, how it will be done in this example, is that it will be made to our self-defined points. This has the advantage that boundary conditions can be defined later very well with respect to their degrees of freedom. The task now is to connect the points with the actual body. Thus, each of the two bearing points must be connected to the longitudinal beam. The connection is executed in a rigid manner, that is, any movement of the point is directly transmitted to the respective part of the longitudinal beam. This way the allowed degrees of freedom at the points will be transmitted to the corresponding part of the longitudinal beam. Formally speaking, a mathematical coupling of the respective nodal degrees of freedom of the FE system is generated, which is equivalent to an absolutely rigid coupling of the two areas. Such a coupling is achieved with so-called coupling elements. These can be found under the function 1D Connection in the NX system.
The wall thickness is provided in the mesh collector or in the physical properties.
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Such types of connections are very often required.
The procedure for rigidly connecting points with meshed faces is used in FE analysis in many cases. Proceed as follows (see also figure above): ÍÍChoose function 1D Connection Each node of the edges is rigidly connected to the point.
.
At Type you can specify whether there is a Point-to-Edge or Point-to-Face connection. At the back of the geometry we want to create a Point-to-Face connection and at the front a Pointto-Edge connection (see figure above). Let’s start with the front part. ÍÍSet the Type option to Point-to-Edge. ÍÍIn the lower option field, select the option RBE2 as connecting element. RBE2 means Rigid Body Element Type 2 and defines a rigid coupling. ÍÍNow select as Source the front point of that should be connected to the beam. ÍÍThen select as Target the three edges of the longitudinal beam to be associated with the point. ÍÍConfirm with OK. Then, the mesh connection is created. It looks like a spider. Therefore, such meshes are referred to as “spiders”. ÍÍIn a corresponding way, you proceed at the rear side of the longitudinal beam. Select the option Point-to-Face and select the appropriate face.
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When you change the 2D mesh of the body or delete and recreate them, then the 1D connections automatically adapt to the new nodes. ÍÍSave the file.
4.2.1.13 Material Properties You do not need to give material properties in this case because the properties have already been assigned to the body in the master part of the CAD assembly and therefore will automatically be transferred to the mesh. This approach is recommended because it saves work and provides security. Moreover, all CAD assemblies in which the longitudinal beam is installed have access to the material properties. If you use this method for all components, then you can, for example, immediately determine the mass of the whole assembly.
Material properties are taken from the CAD master.
If a “what if” study should be performed with a different material, so the different material could now be passed to the mesh in the FEM file. In this way the original material would be overwritten for that mesh.
4.2.1.14 Generating the Load Next, the load is to be applied. ÍÍBecause loads and boundary conditions are in the simulation file, switch via the simulation navigator to the simulation file. ÍÍSelect from the loads group the Force . ÍÍSelect the newly subdivided circular area. ÍÍEnter a size of 3000 N. ÍÍUse the direction method Y. ÍÍConfirm with OK.
The load corresponds to the load from its own weight and a factor for the acceleration.
4.2.1.15 Generating the Mountings The bearings in this example will be applied to those points which are previously connected by RBE2 to the geometry of the frame. The definition of constraint conditions on points that are connected by RBE2 to geometry is a procedure that is very often used in finite element tasks. One the one hand, this allows a large flexibility in the definition of the position of the mounting, because the position is specified by this external point. On the other hand, advantages are obtained because degrees of freedom on points can be specified more flexible than on edges or faces. In particular, rotational degrees of freedom can work very flexible on points, as shown in the following. The constraint conditions are to be performed such that both bearing points permit rotation about the transverse axis of the vehicle. In addition one of the two points will represent the movable bearing and therefore allow shifts in the longitudinal direction.
Both bearings will allow rotating.
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Therefore, you now generate boundary conditions with the settings that are shown in the figure below: ÍÍSelect the User Defined Constraint in the function group Constraint Type ÍÍSet the filterin the selection bar to Point. ÍÍSelect the respective point and enter the degrees of freedom in such a way as the figure below shows. The degrees of freedom of the bearings are set as shown in the figure.
ÍÍConfirm with OK. ÍÍRepeat this for front and rear storage, according to the previous figure. ÍÍSave the file. So the desired constraint conditions are generated, and the model can be solved.
4.2.1.16 Calculate and Evaluate Solutions ÍÍAfter the FE model is finished, you can calculate the solutions with the function Solve . ÍÍAfter completion of the solution change to the post-processor to analyze the deformation results. First, the deformation results are displayed and checked for plausibility. The bearings allow the desired rotation, therefore a plausible picture is obtained. The deformation of the longitudinal beam is plausible. A colored version of this figure is available at www.drbinde.de/index.php/en/203
After the deformations appear plausible, stresses shall be displayed. As equivalent stress we will evaluate the von Mises stress due to the ductile properties of steel. ÍÍSwitch in the post-processing navigator on the stresses, i. e. Stress, Element-Nodal. With the function Set Result
you can select, which type of stress is to be displayed.
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Here you can specify on which side of the shell stresses are to be displayed.
Shell Top: With this option, the stresses at the top of the thin body will be displayed. The next section shows how you can identify the top side of shell elements. Shell Bottom: These are the stresses on the bottom of the thin-walled body. Shell Minimum: This method displays the smallest value of the three possibilities outside, inside or middle. This only makes sense to see compressive stresses which have negative sign. Shell Maximum: This method displays the largest value of the three possibilities outside, inside or middle. This is the safest method to find the largest value. Shell Average/Middle: This means that the stresses are shown that were calculated in the middle of the thin-walled fiber component. If there is only bending load these stresses will be zero. Shell Top and Bottom: This option is recommended. It shows either top or bottom stresses, depending on the view you look on the geometry. Shell Bending: Allows that only the bending portion and not the membrane component of the stress is displayed. To identify the top or bottom of a shell mesh, you must exit the post-processor Checks and Information you will find the function 2D Element Normals.
When displaying stresses on shell elements we must distinguish between the top side, the bottom side and the central fiber.
. At This way you can find out the top side of shell elements.
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After calling this function and selecting the desired mesh, arrows are shown, pointing towards the top of the elements. This is the side on which the results relate to top. ÍÍTo be on the safe side, we now want to display those stresses, which is the largest in any case. Therefore, we set the function Set Result to Maximum. The most stressed region should look similar to the following figure. Evaluation of accuracy of the results.
It can be found that in our FE model in the area of high stresses no disturbances of forceflux appears. Therefore, no stress singularities are present and therefore the stress results can be evaluated as sensible. The mesh seems already to be sufficiently fine, so the result should be essentially converge out. To be safe, a second analysis should always be performed with a refined or coarser grid. Only if it can be shown that the result changes barely, the convergence proof is furnished.
The highest stresses arise in a transition area of the cross section.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
4.2.1.17 Verification Based on Simple Beam Theory To gain confidence in FEM analysis and safeguard themselves, the beginner should regularly perform rough recalculations. But even experts often do these rough recalculations in order to exclude gross errors, to test new types of elements or to check new versions of the software. Here the simple beam theory in quite many cases helps, because many tasks can be more or less simplistic seen as a beam. By the way, you will find a very comprehensive verification Manual for NX / Nastran in [nxn_verif], which compares many FEM examples with theoretical solutions. Also, the correctness of the solver is demonstrated. With the simple beam theory rough recalculations should be performed.
3 kN 2075 mm reaction force in bearing: 1500 N
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B = 69 mm
t = 4 mm
It cannot be expected, of course, that the results of beam theory coincide exactly with FEM results. Rather, the discrepancies can be explained. It creates a lot of confidence when it is shown that the methods of classical mechanics with FEM analysis match. The cross-section of our beam in the undisturbed area.
H = 100 mm
xmax
Such a beam analysis “by hand” should be kept as simple as possible. Therefore, for simplification we assume a beam with a constant cross section, while the real beam changes its cross-section. We decide for the cross section of the essential part of the carrier and pretend as if this section remains constant. So the geometric values of the longitudinal beam are now be measured out from the CAD model. They result as shown in the figure above. The theoretical stress value resulting from the beam theory is calculated from the bending moment Mb and the moment of resistance W by σmax = Mb / W as it results from the classical formulas of mechanics, for example, can be found in [SchnellGrossHauger]. The moment of resistance of a C-section is calculated according to [Dubbel] as follows from the geometry of the cross section: B
BH 3 – bh3 12
W=
BH 3 – bh3 6H
H
h
I=
b
This results in W = 1532106,67 mm4.
The theoretical stress results from the bending moment divided by the moment of resistance.
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If we now calculate the bending moment Mb for our example from the reaction force at one of the two bearings, multiplied by the lever arm, which results from the half length of the beam, we obtain Mb = 3112500 Nmm. With these two calculated values we obtain a value of 101,6 N/mm2 for the theoretical beam stress. For our FEM comparison value, we select the von Mises stress (or maximum principal stress) and find the values on the outside in the center of the beam, as it corresponds to our beam-comparison method. The discovered values vary between 45 and 150 N/mm2. So they vary significantly around the theoretical value.
A colored version of this figure is available at www.drbinde.de/index.php/en/203 In the order of magnitude, the hand analysis and the FEM results agree. The differences are explainable: FEM results are more detailed and accurate than classical machine elements-formulas.
From the order of magnitude the two analyses – FEM and beam theory – agree. Granted, less scattering would be desirable, but the rough estimate is satisfactory. It is apparent that our FEM longitudinal beam is not a “pure” beam. At the same time it becomes clear that results from FEM analysis are much more detailed than those of classical mechanics. The FEM stresses are calculated locally at each point and can be evaluated, while the beam theory only provides a general stress value. This is also the reason that in FEM analyzes stresses are often calculated larger than in classical machine elements-formulas. With FEM, the small details of the geometry are calculated – of course only if they are included in the mesh, while the classical formulas often overlook this. In addition, certain mechanical effects are neglected in the classical formulas often. In the case of the beam theory, this is e. g. the effect of transverse force on bending stress. It is assumed that the beam is long, and therefore the bending influence is much more important than the transverse force. In FEM analysis, this is automatically calculated. This is also a reason for slightly larger stresses in the FEM result. Thus the result of our FEM analysis has been made credible. Thus, also results at locations which are not so easy to calculate by hand, be considered as credible values. ÍÍClose all files in NX. The sub-task is completed now.
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4.2.1.18 Task Part 2 You can also perform this task section independently of part 1. Once the task of the right longitudinal beam was successfully analyzed as a single component in the first task part, we now want to calculate the total frame assembly with all its cross-beams and rivet joints. With this overall assembly analysis, we expect more realistic results, because each omitted portion has an uncertain influence. Of course, the vehicle stiffness can only be determined from a consideration of the overall system. The results of both analyses will be compared. From this example you learn techniques for assembly FEM models and methods for connecting the FE mesh. In particular, interconnection techniques for rivets are shown. However, in a very similar manner welds, screws or similar connections can also be established. Now the frame is to be analyzed as FEM assembly. From this a more complex FEM model will be built.
We assume that the other items in the overall framework, i.e. the transverse beam parts and the left longitudinal beam, have already been analyzed as individual parts. So this would be, for example, done by other engineers in the company in the course of development. In order to simplify the amount of work for you as a user, the FEM models of these parts are available in the zip archive. The methodology for their set up does not contain any new learning content. Therefore, these models need not be built up themselves, but can be easily accessed. Below we will explain the available options in setting up assembly FEM models.
4.2.1.19 Possibilities for Assembly FEMs FEM models for assemblies can be constructed in two different ways. On the one hand the FEM meshes of all parts can be created and stored together in a single FEM file. On the other hand, the FEM meshes of the items can be kept in separate files. In the latter case we speak of Assembly FEM (short: AFEM), in the first case of conventional design of FEM assemblies. The two methods are compared in the figure below. The assembly FEM method has the distinct advantage that the meshes of the individual parts can be further used in subsequent analyses of assemblies. Thus, the method supports the natural course of bottom-up developments: Firstly, items are designed and calculated, then the items are put together in assemblies and analyzed in conjunction.
Advantages and dis advantages of the two methods.
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However, the Assembly FEM method also has a disadvantage compared to the conventional method. In some cases you may want to align or merge FEM nodes at contact areas of two adjacent parts, e. g. because these are to be interconnected or because a further contact analysis should run which gives the best accuracy when nodes are aligned. Such an alignment of nodes in two adjacent components is much easier to achieve if the two meshes are in the same file. So this speaks for the conventional method. Left the conventional, right the AFEM method for setting up assembly FEM models.
SIM
SIM
FEM
AFEM
id
BG
T1
T2
T3
FEM1
FEM2
FEM3
id1
id2
id3
T1
T2
T3
For our example task, both methods could be employed. We want to follow the path of AFEM, because the typical course of development is supported thus that we have already started with the first task part. The item meshes (and possibly also their analysis) are therefore already available. Now only their meshes need to be used. You will see that this is very easy and comfortable.
4.2.1.20 Set up of an Assembly FEM Starting point for building an assembly FEM is the CAD assembly, which contains important information. In particular, the positioning of the items and the number of installed items are included in the CAD assembly. This information can now be used for the AFEM, i.e. which meshes should be inserted and how they are oriented in space, can easily be derived from the CAD assembly. Proceed as follows:
The steps in building an assembly FEM.
ÍÍOpen the file rh_rahmen.prt. ÍÍStart the application Advanced Simulation. ÍÍFrom the context menu of the simulation navigator, select New Assembly FEM. ÍÍIn the following window, enter a file name and folder for the new AFEM file. In this case use rh_rahmen_assyfem1.afm as name. Confirm with OK ÍÍIn the following window New Assembly FEM all settings are correct. Confirm with OK.
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With this setting, following the information about the existing assembly components and their positioning can be easily derived from the specified assembly file rh_rahmen.prt. Once this is done, the simulation navigator displays the CAD assembly and all its components under the AFEM file. All components have now the status Ignored because we have not yet specified which components shall be included in the analysis of the components and which of the parts already have FEM meshes (see figure below). The next task is to assign FEM meshes of those components that should be included in the assembly analysis. To do this, follow these steps: ÍÍIn the simulation navigator select the first component for which there is an FEM mesh, which you want to assign. Start, for example, with rh_laengstraeger_re.prt. ÍÍSelect in the context menu of this node the option Map Existing. ÍÍIn the next menu choose OPEN and then select the FEM file of the associated mesh rh_laengstraeger_re_fem1.fem.
The original CAD assembly rh_rahmen is used as a “pattern”.
The desired component meshes are assigned.
At this point you can choose whether you want to use the mesh files of the longitudinal beam you created yourself or the original from the zip archive. Multiple uses of meshes are thus easily possible.
ÍÍConfirm any further questions with OK. Then the FEM mesh of the component is inserted into the AFEM. ÍÍNow in the same way you assign the FEM mesh of the component rh_laengstraeger_li. You need not create it yourself because it is already in the zip archive and ready to use. ÍÍFinally, you also organize the meshes of the component rh_ubg_quertraeger. Note that this component is installed four times. Therefore, you assign this component four times.
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It is appreciated that the mesh of the cross beam has been truly created only once, but inserted by the assembly technology four times and positioned in different places. All these information was derived from the CAD assembly. Not all components of the CAD assembly shall be included in the FEM analysis. Only those that are important for stability shall be mapped.
We do not want to include the remaining parts that are installed in the assembly in this analysis – on the one hand, because no FEM meshes exist for them, on the other hand, because we assume that these parts do not exert any significant influence on the stiffness behavior. Next is the connection of the individual meshes by FEM rivet models. These fasteners are consequently generated in the newly created assembly FEM file. So we continue to work in this file.
4.2.1.21 Generating Models of Rivet Joints The combination of two sheet metal parts with rivets can be simulated in FEM.
Real rivet joints have very complex properties and therefore cannot be analyzed in our example. We will instead produce a model for rivet joints, which reflects the effects of real rivets on adjacent components. In the analysis, we must not ask for detailed results in the local area of a rivet, because for this the model will be too coarse. But some distance away, it can be expected that the results are reasonable. For this example, the rivets will be modeled in such a way that the circular edge of the first sheet is joined to the circular edge of the second sheet. The two circular edges correspond approximately to the bearing surfaces of the rivet. This is a quite common type of FEM modeling of such connections. The proposed rivet-model here has a distinctive feature. The connection will indeed couple the circles tightly together, but rotations around the axis of the rivet shall be freely possible – in the same way as real rivets still allow rotation. While this special property has little influence on the result in this example, however, the method can be used effec-
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tively for other cases, when it comes to obtain a rotational degree of freedom between two parts (e. g. screws, bolts . . .).
The rivet model is composed by a combination of coupling elements that are created in a similar manner as previously the connection of the longitudinal beam to its constraint points (spiders). On the transverse beam meshes, which you have inserted, these rivet models are ready. Here you can, as in the following figure, already take a look at.
A “spider” of coupling elements forms the model for a riveted joint.
On the cross beam rivets are already done.
Please consider that the subsequent working section has to be performed on each rivet, i. e. 32 times, to complete the whole frame. If you find this is too time-consuming and you only want to see the effect, you should just remove some of the cross beam meshes from the AFEM. At least one of the cross beams should of course remain. In that case you would have to create only eight rivets. If you want to simplify even more, you generate only one or two rivets on each side. You can also generate only one or two rivets, but then continue to use the finished AFEM model of the zip archive.
There are 32 rivets!
A rivet on our frame in the CAD model consists of two or three circular edges (depending on number of sheets). We will now in each case generate spiders from the edges to the respective centers, and then generate point-to-point connections between the respective center points.
What a rivet consists of.
Alternatively to the method described here with the function 1D Connection you can also use the slightly faster feature Bolt Connection. Here you can directly select two circular edges, and produce the spider automatically between them. But we do not want to use this, because in our example, some spiders are already in place and only need to be supplemented. For this the function of 1D Connection is better suited.
How can you simplify the work.
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Go for the generation of a rivet model as follows:
Just three mouse clicks generate a “spider”.
ÍÍDecide for one of the positions and zoom in this position tight. Turn the display option appropriately to the static wireframe mode. ÍÍHide all 2D meshes (in the navigator turn off the red hooks at 2D Collectors). ÍÍSelect the function 1D-Connection . ÍÍChoose the type Point-to-Edge and RBE2. ÍÍSelect as Source the center point of the first edge and the edge itself as Target Confirm with APPLY. ÍÍDo this in the same way for the second (and possibly third) edge. Consider this: Three mouse clicks should be sufficient to create such a “spider”: Click one goes on the circle edge, so that the center point is selected. Click two also goes to the circle edge, so that the edge itself is selected. The third click is the APPLY button. It is best to first create all the spiders in this way. Granted, for all 32 rivets you must have a little patience. But you will see that this three-click method is very fast. (We are experienced “clickers” and have done this job in about four minutes.) ÍÍFinally, connect the two points of two spiders by using the function 1D-Connection again, but now the type Point-to-Point. As Source you select the first point and the second as Target. (This takes a trained “clicker” another five minutes.) You have now created rivet connections by initially having all degrees of freedom rigidly coupled together. Thus, this model is similar to the behavior of a spot weld. However, since a real rivet allows rotations, this property could now be realized in our FEM model of the rivet. If you wish, enter those 1D meshes, which connect two centers, and insert the special property that it allows rotations around an axis. You can do this as follows: ÍÍOptional: Select in the simulation navigator the corresponding 1D mesh, where the rotation is to be allowed. Multiple selection possible. ÍÍOptional: Select with RMB the option Edit Mesh Associated Data. The menu appears as shown in the figure above.
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In this menu, all degrees of freedom of the coupling element are set to On, so it is initially a completely rigid connection. ÍÍOptional: Depending on how the absolute coordinate system is aligned set the desired degree of rotational freedom to Off. In our example, this is the degree of freedom for Y-rotation, i. e. the DOF5. ÍÍOptional: Confirm with OK to apply the settings are applied. ÍÍOptional: Use the same procedure for each desired rivet.
The rotational degree of freedom of the 1D coupling element is set undetermined.
4.2.1.22 Merging Duplicate Nodes When establishing such FEM assemblies such as our vehicle frame, it often happens that duplicate nodes exist. This can occur, for example, when generating RBE2 elements: Generating one RBE2 arises two new nodes. At the junction of the neighboring element however there is already a node. These two nodes are therefore now very close to each other, they have virtually the same coordinates, but they are not connected. Such a state must be recognized by the software. In most cases the software will automatically unite or merge such two nodes. But if this merging does not automatically work and the analysis is performed, something may come out as shown in the figure below. But it can also happen that the analysis gives no result at all, possibly because underdetermined bearings appear and this will create a situation that cannot be calculated with the linear static FEM. It may look like this when duplicated nodes exist: The parts are not connected.
Therefore, we now want to exploit a function that performs tests for closely located nodes and that can merge them if necessary. ÍÍChoose from Checks and Information the function Duplicate Nodes. ÍÍMake all meshes visible again and drag a window over all. ÍÍChoose List Nodes in the dialog. The tolerance by default is set to 0.001 mm. So all nodes will be found that are closer together than 0.001 mm.
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One double node was found, which must be merged.
After a while the NX status line reports: “number of candidates for duplicate nodes . . .” This means that unwanted nodes were found. Furthermore, the found nodes should also highlight in the graphic. (Sometimes they can be difficult to see, so please search a little.) After these unwanted nodes have now been discovered, they just have to be merged. ÍÍIf duplicate nodes were found in your model, choose the function Merge Nodes in the dialog. The duplicate nodes are now merged. A corresponding message appears in the status line.
4.2.1.23 Resolving Numbering Conflicts The numbers of nodes and elements must be unique.
Would the FEM analysis now be performed, an error message would be received indicating that numbering conflicts exist. The reason is, for example, that the node with the number one occurs more than once in the overall model. Each item that is included in the assembly was meshed alone, while the node and element numbers each time have been counted starting from one. Therefore the conflict arises because duplicate numbers are not permitted. This conflict can be resolved easily by adding new numbers for the nodes and elements and assigning them within the AFEM file. For this purpose, the so-called Assembly Label Manager will be used. So follow these steps: ÍÍFrom the simulation navigator RMB on the node of the AFEM file and select the function Assembly Label Manager.
In the AFEM file numbers are reassigned according to rules.
The dialog opens. There is a whole range of options provided to control the new numbers. In the simplest case, you want to ensure that the conflicts are automatically resolved, i. e., the numbers are simply incremented new. ÍÍIn this dialog select the function with the yellow flash: Automatically Resolve ÍÍConfirm with OK. ÍÍSave the file.
.
4.2.1.24 Generating a Simulation File The Sim file is created manually here.
The AFEM-file now works in the same manner as previously the simple FEM file. But there still belongs a simulation file to it. The simulation file for this AFEM was not generated automatically, it must be created manually now.
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ÍÍIf you have not performed the previous steps by yourself, you now open the AFEM model of the zip archive: rh_rahmen_assyfem1.afm. Otherwise you continue working with your self-created model. ÍÍFrom the simulation navigator RMB on the node of the AFEM file and choose the function New Simulation. ÍÍSpecify a file name and folder for the new simulation file. For example, enter rh_rahmen_assyfem1_sim1.sim. ÍÍConfirm with OK and confirm also the defaults in the following menu New Simulation with OK. ÍÍThere follows the solution dialog to select the Nastran solution type. Confirm the settings for a linear static analysis with 101 OK. Now loads and boundary conditions can be defined again. We want to achieve, for example, a corresponding load situation as in problem part 1. ÍÍCreate the same constraint conditions as in problem part 1 now again. Specify this condition, but this time on both longitudinal beams. ÍÍDefine the same forces as in the previous analysis now on both carriers, i. e. 3000 N on the right and 3000 N on the left.
We want to create such loads and constraints that correspond to the component analysis.
4.2.1.25 Finding an Error in the Model Structure and Resolve ÍÍPerform the function Solve . ÍÍDuring the automatic model check an error message (probably) will appear. The message “Failed to Write and Solve, see info window for details” is supplemented with a more detailed explanation in the NX information window, as shown in the figure below.
A NX error message appears associated with recommendations for the solution of the problem.
The NX system has detected an error in the model construction. To understand the error, following relationship should be known: Rigid elements (RBE2), which we use here, connect two nodes by a fixed coupling. Such elements therefore have one dependent and one independent node. The Nastran solver sets those respective degrees of freedom to equal within the stiffness matrix. It produces so-called “Multipoint Constraints” or MPCs. Now there is a simple rule saying that one degree of freedom may be dependent on one and not on several other degrees of freedom. Therefore, there may be no redundancies here. The definition of independent and dependent node is automatically done when generating the rigid element: the first click defines the independent and the second the dependent node. In our model, however, there is due to the composite rivet element designs a whole series of rigid elements. Also, we have not respected in the generation which node should dependent on which. It would also be very difficult for the user, if he had to take this into account. Rather, we want to use a function that automatically resolves redundancies in
We activate the para meter AUTOMPC.
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the MPCs or rigid links. This function is already suggested in the error statement in the NX information window: it is called AUTOMPC and must be passed as parameters to the Nastran solver. To do this, follow these steps: ÍÍSelect the function EDIT in the context menu of Solution 1 in the simulation navigator. ÍÍIn the following menu, go to the Parameters tab. You acknowledge from the setting None that no additional parameters are passed to the solver. ÍÍSelect the function Create Modeling Object to generate a new parameter list. ÍÍYou will see a large list of all possible NX Nastran parameters (in alphabetical order). Unfold at A-B you will find the parameter AUTOMPC. Here a list of parameters is generated, which also will be written into the Nastran input file.
ÍÍSet this to YES and turn on the switch next to it, so that this parameter is also written into the Nastran input file. ÍÍConfirm with OK several times to exit all menus again. Now you have created an additional parameter list and activated an entry for AUTOMPC = Yes. This parameter is written into the Nastran input file. You can verify this after solving by opening the *. dat file with a text editor and search for AUTOMPC.
4.2.1.26 Solving the Solution ÍÍNow run again the Solve
.
The computational job should now be performed successfully. However, it may take a while, because this model is not quite as small. ÍÍWait until the end of the Nastran job. ÍÍGo to the Post-Processing Navigator , open the result and analyze it as desired. The von Mises stresses calculated on the frame.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
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4.2.1.27 Comparing two different Results Results are available now for this second analysis. We want to make a small preparation in the post-processor that provides that results of the first simulation can be viewed for comparison. For this preparation, proceed as follows:
For an A-B comparison, the old result will first be imported.
ÍÍChange to the Post-Processing Navigator . ÍÍSelect the function Import Results in the context menu of the node Imported Results. ÍÍNow select the Browse function and select the result file of our component analysis, that is the file rh_laengstraeger_re_sim1-solution_1.op2. ÍÍConfirm twice with OK. In the navigator, a reference to the first simulation is added. The results of this first analysis can now be displayed as desired. To make a comparison of the two results, proceed as follows: ÍÍSwitch to a layout with two views, for example, by means of the function Upper and Lower .
The results of the A-B comparison are faced.
The screen is divided into two areas. If you had previously shown a result, this can now be seen in one of the windows. The other window shows the model from the pre-processing. In the top view we want to represent the stress results of the component analysis and in the lower view the stress results of the assembly analysis. For this purpose the following is to be done: ÍÍSelect the function Plot in the context menu of the imported result on the node Stress – Element nodal. Then click with the mouse in the upper view. The stress result will be shown here. ÍÍYou do the same with the stress result from the assembly analysis. Here you select the bottom view. The two results are now displayed in both views. The geometry can be rotated and moved in the two separate views. ÍÍOf course, the views should be identically orientated. You can do this by use of the function View Synchronize . Select the two views and confirm in the menu Viewport . If you now make a move, then both views align with each other. In the navigator, views and results are presented quite clearly. Under Viewports it can be seen that there exist two result views. The symbols here clearly demonstrate which is the upper and which is the lower view. On each of these views or PostViews a RMB context menu can be used for changes, e.g. the legend. You can also manipulate simultaneously multiple views by marking the desired PostViews and then using the function Edit Post View or others. By this way, you can now add the following changes for both views: ÍÍSelect on the navigator both views. ÍÍChoose the function Edit Post View
.
Here the views are synchronized.
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The picture shows the view of the navigator when multiple analysis results are included.
ÍÍIn register Edges and Faces, select at Edges, the option Feature. Now any edges of the finite elements are not shown anymore. ÍÍNow select the function Set Result and there set Shell to the option Maximum. Now the results of the outside and inside are displayed so that the maximum always appears. The result should now look something like the figure below. It can be clearly seen that in the assembly analysis the transverse beams perform stress reducing on the frame. This influence results probably because of the strong torsional twisting of the longitudinal beam, which was seen in the first simulation, is suppressed in the assembly analysis because of the other components. A convergence test for the accuracy of the results would still be useful.
The stress results shown in the figure below are to be considered with caution for two reasons. On one side there is no convergence test done in accordance with the basic example. Therefore, the specified stress values are still difficult to estimate. A convergence proof is not to be further investigated in this learning task for reasons of size and character of principle of the example. On the other hand there are quite large uncertainties regarding the rivet geometry, because here the real geometry has been significantly simplified. For these reasons, the absolute numerical values of the stresses at these locations should not be evaluated, only a comparison of the two simulations is permitted.
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The additional cross beam has a slightly stress reducing effect.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The deformation results, however, are barely affected by these mentioned influences and can therefore be used with greater reliability. Deformations are global quantities of interest, therefore small perturbations, such as those coming from the rivet models, have no considerable influence on their result. They only depend on the constraint conditions and the loading. This statement can be generalized: Deformation results for FE analyses are usually easy to identify because we are interested in their globally behavior. Stress results are mostly evaluated in geometrical small details, so they are much more sensitive.
Deformations are easier to calculate than stresses.
With this, learning task is completed.
4.2.2 Size and Calculation of a Coil Spring The RAK2 has drum brakes on all four wheels. When braking each two brake shoes are pushed apart by a cam so that the brake linings drag with the rotating outer drum. When the brake is released afterwards, it must be ensured that the brake shoes are brought back from the pressing position. For this purpose, the restoring spring is designed to be adjusted in this learning task. A coil spring can be sized and calculated well with FEM. The parametric functions of the CAD system can be used effectively.
Ideally, the spring to be sized is designed parametrically in such way in the CAD system, that all maybe appropriate geometric variables can be changed as parameters (expres-
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sions). In the FEM analysis all elements are then likewise generated as associative features, resulting in a fully parametric FE model. Any desired modification of a geometry parameter leads to a simple updating of the model to new results. A manual optimization of the geometry sizes can be carried out very efficiently with this method, as shown in this learning task. Another learning effect of this example relates to pretensioned bearings.
In this learning task, you will learn details about the use of parametric and associative elements in order to proceed in the manner described. In addition, you learn how to use beam elements and the analysis of reaction forces. You also learn how forced displacements are applied as boundary conditions on a finite element model.
4.2.2.1 Task Starting from a parametric CAD model in this learning task a spring design is to be performed. The spring shall be just relaxed or nearly force-free when installed. The task is to specify the wire diameter in such a way that, for a way to work of 4 mm, the maximum principal stress in the spring of 500 N/mm2 is not exceeded and that the clamping force is at the same time during deformation of 4 mm not smaller than 30 N. From the manufacture of spring wire there are diameters available in size increments of 0.1 mm. We want the wire dia meter of the coil spring.
4.2.2.2 Overview of the Solution Steps In the first step, the current spring geometry is analyzed. There will be applied a displacement of 4 mm, and reaction force and appearing tensile stress are determined. If the result does not meet the requirements, another wire diameter is selected, and the model is reanalyzed. This is repeated until a wire diameter is found which meets the requirements.
4.2.2.3 Structure of the Parametric CAD Model Basis for the construction of a suitable associative-parametric FE model is the parameterization of the underlying CAD geometry of the spring. Springs are often built up in the system by the NX helix feature that forms a curve shaped according a spring. The parameters radius, pitch and number of gears can be parametrically varied. The CAD model is constructed parametrically.
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To shape the beginning and the end of the spring, sketches are added, which can be arbitrarily shaped. Possibly, the transition of the helix to such a sketch can be designed by a bridge curve. Finally, the curve is thickened with the Cable function to a pipe or circular profile. The figure above represents the feature structure of the spring model, as it is already created and ready to use as part-file bs_rueckholfeder.prt available in RAK2 directory.
4.2.2.4 Considerations for Meshing Strategy In principle, a mesh of the solid spring with tetrahedral elements would be possible. However, in this case, a relatively large amount of tetrahedral elements would be required to mesh the body with an appropriate fineness, because of the thin and elongated geometry characteristics. Such a spring corresponds geometrically to a beam. Therefore, in this example, the use of beams elements will be shown. Alternatively, however, a tetrahedral mesh of the spring would be possible. Absolutely essential will be the beam mesh only at complex beam-like geometry, e. g. at machine portals, which are screwed together or welded beam carriers. An example of such a task is shown in the figure below. In this case, a suitable meshing with tetrahedral elements would be barely possible. A combined shell/beam meshing would however be quite simple and efficient. Machine frames are other examples of appropriate use of beam elements.
Beam elements have a one-dimensional geometric shape and connect two points in space. Visually there is only one line represented, but the properties of a beam are analyzed software internally, i. e., it can transmit tension, compression, bending and torsional forces in all three spatial directions. Each node of a beam element can therefore accommodate displacements, rotations, forces and moments, as shown in the figure below.
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A beam element transfers tension, compression, bending and torsion. The nodes must therefore also process rotational degrees of freedom.
The stiffness characteristics of the beam are processed by a cross-sectional profile which can be defined in various ways by the user. Of course, also materials must be assigned. The requirement is that each beam has a constant cross-section. If the cross section changes, different beam elements could be coupled together. In the case of our task there is a constant circular cross-section, which is loaded by tension and torsion. For these reasons, the use of beam elements for the solution of this problem is useful. For the generation of the beam elements, the center line of the spring wire is needed. Therefore, care must be taken in the following that the appropriate spline curves are transferred to the FEM part.
4.2.2.5 Considerations for Boundary Conditions The enforced deformation is a special boundary condition.
Instead of the real installation situation of the spring in the brake boundary conditions must be generated at the two points where the environment has been removed in the FE model. At one of the sides the boundary conditions intend to provide a constraint that corresponds to mounting the hook, on the other side there will be a constraint which applies a prescribed displacement of 4 mm, according to the task.
4.2.2.6 Generating the File Structure and Solution Method ÍÍOpen the part bs_rueckholfeder.prt in NX. ÍÍSwitch to the application Advanced-Simulation. ÍÍCreate a new simulation file structure in the simulation navigator with New FEM and Simulation. ÍÍIn the appearing menu New FEM and Simulation select Geometry Options and activate the button Sketch Curves, as shown in the figure below. The usual steps in the model set up.
These settings ensure that the center curves of the spring are inserted into the FEM part. By default no curves or points from the CAD model are transferred to the simulation, because this is usually not desired. ÍÍConfirm twice with OK. The file structure is created.
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Next, the menu Create Solution is displayed. ÍÍBecause this task is a static analysis of deformations, stresses and reaction forces, accept the default settings in this menu for solution 101 and confirm with OK. The system now creates the simulation files and displays them in the simulation navigator. If curves or points from the CAD will be needed during the simulation, this must be turned on here.
4.2.2.7 Preparations for Boundary Conditions ÍÍSubsequent work addresses the meshing. Therefore, now make the FEM file to the displayed part. First we create a so-called Mesh Point in each place where boundary conditions are to be set later at points . This preparation is always required when boundary conditions or loads are to be produced on points. It is important that the mesh point is assigned exactly to that geometry, which is subsequently meshed. This can be done incorrectly very quickly if the desired point is adjacent to multiple geometric objects, as is the case in our example. If you assign the mesh point to a geometry that will be not meshed, error messages will appear when solving and those messages are hard to understand. In our example, the boundary condition is to be applied at the end of the straight line of the spring. So here a mesh point must be generated, and this long straight line must necessarily be assigned and not the semicircle! A mesh point forces the mesher to put a node here.
For the generation of the grid point, proceed as follows: ÍÍIn the simulation navigator hide the polygon body of the spring. ÍÍSelect in the main menu bar the function INSERT > MODEL PREPARATION > MESH POINT . . . . ÍÍActivate the point method for end point .
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ÍÍSelect the straight line on the corresponding side and confirm with APPLY. ÍÍGenerate an additional mesh point on the other side of the spring.
4.2.2.8 Meshing with Beam Elements In NX beam elements belong to 1D meshes and are close beside the other types of onedimensional elements, namely the rod elements, the coupling elements and spring elements. Beam elements belong to the group of 1D meshes.
In the following list, we explain the main characteristics of the five major types of 1D elements. These elements are found under the function 1D Mesh . Different types of 1D meshes.
Beam : These are classical beam elements that can transfer the usual properties tension, compression, bending and torsion. The cross-sectional profile and material must be assigned to this element type. As special feature this element can also have conical cross-sectional profiles (this is the difference between CBEAM and CBAR). Therefore, a transition from one cross-sectional profile to another is possible. Rod : These are rod elements, i. e., they transmit tension and pressure, but no bending, and no twist. Content area and material has to be assigned to the elements. The software determines the necessary stiffness values of the element from these properties. Rigid Body Element : These elements are coupling elements, which represent fixed connections without flexibility. It is possible to set these elements in such a way that only certain degrees of freedom are transferred. General Spring : General spring/damper elements, which allow the definition of spring and damping properties in all spatial directions.
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One-dimensional spring : These elements allow the definition of translational or torsion-spring properties in one spatial direction. According to the figure below, our model consists of five individual curves: two straight lines, two bridge curves and the large helix. For the 1D mesh of the curves proceed as follows:
Steps for generating a beam mesh.
ÍÍSelect the function 1D-Mesh . ÍÍSet the type to CBEAM . ÍÍIn the menu set Mesh Density by to the option Size. ÍÍIn the field for Element Size enter for example 0.5, which corresponds to a sufficient element fineness on the windings. In some cases, when working with more than one mesh, it happens that a node of a mesh is very close to another node of another mesh (see also the learning task “stiffness of the vehicle frame”, Section 4.2.1). Such a situation results in no connection at this point. This can hardly be recognized visually. Therefore, the FE system provides a way to find such “double” nodes and merges them if necessary. With the following option such nodes are merged already in production.
The nodes of different bodies sometimes do not automatically merge.
ÍÍActivate Merge Nodes to merge nodes of the various curves that lie tightly together. ÍÍSelect the first curve to be meshed. Note that depending on the selection position, i.e. whether more at the beginning or at the end of the respective curve, arrows will be displayed (see figure below). These arrows are important because they point into the X-direction of the guided coordinate systems of the beam elements. Make sure that at each piece of curve the arrows point in the same direction. If there is a change in the direction of the arrow, so the guided coordinate system would undesirable change the direction. The direction of the arrows is not critical, as long as all curves have the same. A further indication of directions for Y or Z is still required for the complete definition of this coordinate system. These directions may be defined later in the properties of the 1D meshes. In our case this is not necessary because it is a circular cross section.
Arrow directions need to be considered.
Arrows indicate the X-direction of the guided coordinate system for the beam cross-section.
ÍÍNow select the other four curves at the beginning or at the end of the curve, just as you did with the first curve to obtain a uniform direction. ÍÍConfirm with OK. The mesh will be created.
4.2.2.9 Assigning Material The material is produced in the usual way in the material dialogue or taken from the library. Only the assignment is done in other ways. So far, the material was always associated with the underlying geometry that has passed it on to the appropriate mesh. In the
For beam elements, material is directly assigned to the physical property of the mesh.
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actual example case, however, the material must be directly assigned to the mesh, because it is not possible to assign material to curves. Proceed as follows: ÍÍThe FEM file is still the displayed part. ÍÍSelect 1D Collector in the simulation navigator and with RMB the EDIT function in the context menu of the beam collector. ÍÍIn the mesh collector window, next to Beam Property, select the function MODIFY SELECTED . ÍÍIn the next menu PBEAM, select Choose Material. ÍÍNow you can select the required material (Steel) from the list and click OK several times to exit from the dialogs.
4.2.2.10 Creating and Assigning a Beam Cross-Section After beam elements have been selected for the mesh the cross-section must still be defined and assigned to the 1D mesh whose stiffness characteristics are to be used. Much like the material, the cross-section will be associated with the mesh, namely in the properties dialog of the PBEAM. The intended cross- section of the beam elements is defined. A library for cross- sections is available.
ÍÍEdit the mesh collector as before and switch to the menu PBEAM. ÍÍSelect the function Show Section Manager . ÍÍIn the next window, select the Beam Section Manager and then the function Create Section . Here, the desired beam section is created. The options available for it are explained briefly in the following. The standard cross- sections are explained.
Available for simple definitions of standard cross sections there is a library of 20 commonly used cross-sectional geometries, such as the thin-walled rectangular profile. These default profiles must be defined only by its overall dimensions. For this purpose there are menu fields further down to specify the desired dimensions for height, width, wall thickness, etc. Notice also the symbols next to the y-z coordinate directions that assign coordinate systems to each element. This coordinate system plays an important role, for example at an L-profile, because of course the stiffness depends on it. In the case of our example, however, this is of no concern since the circular cross-section used in all directions has the same properties.
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The type User Defined Properties allows the definition of arbitrary cross-sectional profiles by manually specifying the area-relevant variables, i. e. area and area moments of inertia. Moreover, four positions of points are queried afterwards on which stress results are to be calculated. According to the first option there is to pay attention on the YZ coordinate directions. The type General Geometry allows the definition of the cross-sectional profile with the aid of a sketch. After selecting this option, a choice appears below in the menu listing all sketches appearing in the underlying CAD model. Once a sketch has been selected, each line contained in the sketch must be associated with a wall thickness. In this way results the definition of thin-walled structures and their properties are used in the analysis. According to the first option again the YZ coordinate directions have to be observed. The type Face of Solid allows the selection of a face of a solid, for example a sectional area of a CAD beam that you wish to calculate. Using this face, the system automatically calculates the area and all inertial properties and uses them for analysis. Pay attention to the indicated y-z coordinate directions for future assignments.
There are convenient options for the definition of cross-sectional profiles.
The following is the cross-sectional profile generated for our example: ÍÍSelect the option Rod . ÍÍEnter the only required dimension, the radius of 0.75 mm. The x-y coordinate directions, in the case of circular sections, are not relevant, because the orientation of the circuit is not significant.
The cross-section is assigned to the 1D mesh.
ÍÍClick OK to confirm, and then the cross section is generated. Then click CLOSE. You are now back in PBEAM menu. ÍÍThe assignment of the profile just created is done in PBEAM menu under Fore Section by selecting the newly created cross-section ROD1 from the list. ÍÍClick twice on OK. This completes the creation and assignment of the cross section. The cross-section is displayed visually to check.
The associated cross-section should be checked visually according to the previous figure. ÍÍSave the file. However, if the orientation of the cross section plays a role in another case, i.e. if we, for example, have an L-profile, so the Y-direction of the element coordinates systems has yet to be defined. This would be done in the menu Mesh Associated Data of the 1D mesh.
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4.2.2.11 Generating the Constraints The mounting of the hook corresponds roughly to a ball bearing, that would mean, translational degrees of freedom would be fixed, rotationals remained free. However, in the case of this spring the spring wire contacts the wall. Therefore, the rotation is impeded at least in one direction. Therefore, also a fixation of the rotational degrees of freedom should be made as FE boundary condition. This rotatory fixation should also be made, because otherwise there would be an unrealistic bending of the spring, due to the points of the boundary conditions not being located exactly on the neutral axis. The fixed constraint on one side of the spring.
For the generation of this fixed constraint proceed as follows: ÍÍFirst, switch into the simulation file via the simulation navigator. ÍÍWhere appropriate, hide the polygon geometry of the spring body and also the 1D mesh. ÍÍSelect from the group Constraints the function Fixed Constraint . ÍÍSelect the Mesh Point on either side of the spring and confirm with OK. Alternatively, you can use the User Defined Constraint all to Fix.
and set the degrees of freedom
4.2.2.12 Generating the Enforced Displacement On the other side of the spring a displacement is to be determined. Proceed as follows: We need 4 mm enforced displacement for the spring.
ÍÍIn the group Constraints , select the function Enforced Displacement ÍÍSelect the Mesh Point on the corresponding side of the spring. ÍÍEnter the degrees of freedom as shown in the figure below.
Constraint.
Except for the translation in Z-direction (DOF3) all degrees of freedom are fixed again, i. e., they are set to 0 mm. The desired displacement into Z-direction can be achieved by specifying the amount of “4” on the degree of freedom DOF3. ÍÍConfirm with OK for the boundary condition to be generated.
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In this way, a forced deformation is defined.
Since a drawn condition has been defined by specifying these two constraints, the specification of loads is not required. The FE analysis will determine the deformation and stress state due to the clamping and the prescribed displacement conditions. Moreover, reaction forces that are required to maintain the given condition are determined in the finite element analysis, too.
4.2.2.13 Calculate Solutions After building up the analysis model it can now be solved. ÍÍSelect Solve and confirm in the next menu by pressing OK. ÍÍThe job should run only a few seconds, since the number of nodes and elements is very low. ÍÍIf the job monitor indicates the end of the job, switch to the post-processor for analyzing the results.
Solving is very fast, if only beam elements are included.
4.2.2.14 Determine Reaction Force Reaction forces are calculated at the nodes of the fixed constraints of the FE model. In principle, reaction forces are indeed calculated on all nodes, but only at the constraints they have a non-zero value. In our example, the fixed constraints consist each of only one node, so the total reaction forces appear on these two nodes. For example, if an area would be constrained, which included multiple nodes, the reaction force would result from the sum of the reaction forces of all associated nodes. In such cases the function Identify can be used which allows determining the sum of results on areas.
The method for the evaluation of reaction forces
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ÍÍTo display reaction force, select in the navigator the result type Reaction Force – Nodal. ÍÍBelow this node, the X-, Y-and Z-directions of the reaction force and the Magnitude can be selected. Here you can switch to the Z-direction, because this corresponds to the direction of deformation of the spring. The reaction force can be represented via the navigator. It should always be considered only one direction.
ÍÍReading the values of the two nodes can be performed either on the basis of the color scale or the function Identify . ÍÍAccording to the figure below, a reaction force in the Z-direction of approximately 73 N was determined.
One of the nodes has a positive, the other negative reaction force, so that in total the equilibrium of forces is satisfied. The stiffness R of this spring is obtained with: R= The results agree with reference formulas.
F s
to 18.3 N/mm. From engineering handbooks, such as [RoloffMatek], the stiffness or rate of a coil spring, can be calculated with R=
G⋅d4 8 ⋅ n ⋅ D3
to 18.8 N/mm. Here are: G = 80000 N/mm2 (shear modulus), d = 1.5 mm (wire diameter), n = ca. 21.5 (number of windings),
D = 5 mm (winding diameter)
4.2.2.15 Determining the Maximum Tensile Stress For beam elements theoretical stresses are calculated at four socalled Stress Recovery Points.
Similar to shell elements, the stress results for beam elements are calculated on the outer side, inner side and the center. The analysis of the stresses also occurs at characteristic points. These are the so-called Stress Recovery Points.
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The exact position of the four points for calculated stresses at the beam can be viewed here.
Here are four positions at the outermost edge of the cross-sectional profile of the beam, which are by default of interest to the stress evaluation. These points are indicated by C, D, E and F and are shown in the figure above. ÍÍIn order to display the maximum tension, according to the task, in the spring wire, open Stress – Element Nodal in the simulation navigator and activate the subnode Max Principal. In your own definition of a cross-sectional profile these positions can be specified by the user, whereas with the selection of the default profiles the location of the Stress Recovery Points is given. To find the locations of those points in the menu 1D Element Section the created cross-section must be selected and the function View Section Properties must be executed. This function opens a text window in which the coordinates of the points are indicated next to the inertia properties. The coordinates relate to the guided beam coordinate system (see figure above). A nice method to look at the stress distribution resulting from the cross section the function Beam Cross-Section View can also be used. Only the node must be selected where you want to know the stress, for example, the node having maximum stress. From the
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four calculated points the rest of the values is interpolated, and there can be constructed a complete image of stress distribution. Again, it is possible to display the maximum value. It can also be set via Set Result , which stress is to be displayed in the section. To represent always the largest of the four points A, B, C or D in any case, set the following: The safest course is to present the largest of the four calculated stress points.
ÍÍSelect the function Set Result
and switch in Beam to the option Maximum.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
Now you can see that the maximum value of the stress occurs in the area of the bridge curves. ÍÍFrom the color bar or using the Identify 548 N/mm2. ÍÍLeave the post-processor .
function, you can read a value of about
4.2.2.16 Conclusions for the Design The design must be modified. The parametric CAD system helps.
According to the task, the maximum occurring tensile stress in the spring should not exceed the value of 500 N/mm2, while the spring force shall not fall below the threshold of 30 N at a displacement of 4 mm. With the current design of the spring, the second requirement is satisfied, but not the first because the tension is a little too high. So we need to change the design. It can be difficult to predict whether the spring wire must be thinner or thicker to reduce the stress. Therefore, this should be simply tried. The next test to be performed will therefore use a wire that is 0.2 mm thinner.
4.2.2.17 Design Change and Re-Analysis To change the thickness of the circular cross-sectional profile to the new value, proceed as follows: ÍÍSwitch to the FEM file. ÍÍSwitch to the function 1D-Element-Section . ÍÍSelect the newly generated cross-section ROD1. ÍÍStart the function Edit Section . ÍÍEnter the new value 0.65 mm in the Radius field, confirm with OK and CLOSE.
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ÍÍSwitch back to the simulation file. ÍÍThen the job is restarted with the function Solve and the new results are detected in the post-processor. It turns out that now a reaction force of 42 N and a maximum principal stress of about 476 N/mm2 is calculated. These values correspond to our requirements. Therefore, the construction of this example can be carried out with a wire diameter of 1.3 mm.
The modified design now meets the requirements.
ÍÍSave the files and close them. Thus, the task is finished.
4.2.3 Natural Frequencies of the Vehicle Frame The vehicle frame has already been analyzed in a previous example, even under a static load. Now, its natural frequencies shall be determined. We expect that the frame will perform vibrations especially in the vertical direction, i.e. up and down. Additionally to vertical oscillations probably also other vibration modes are possible, but those vertical vibrations are of particular importance for the driving characteristics of RAK2 because any uneven road surface while driving may lead to excitation of these vibrations.
The vehicle frame may start to vibrate while driving.
This learning task teaches you the possibilities and limits which must be observed with natural frequency analysis in the NX system. You will also learn how to deal with additionally inserted point masses.
4.2.3.1 Task In this example a model is to be formed, that on the one hand is very easy to create and on the other hand can reflect the real situation approximately. Similarly as in the static analysis we argue here that the main stiffness is embodied in the vertical direction by the longitudinal support. Therefore, the natural frequency of the overall frame will be estimated only on the basis of the natural frequency of one longitudinal beam. However, if you would like to consider a slightly larger FE model, you can easily use the entire model of the frame for this learning task as a starting point, which is known already from the previous tasks.
300Kg
The constraint situation of the longitudinal beam is to be performed according to the methods of static analysis. That means it is rotatably supported at the beginning and at the end. This roughly corresponds to the real situation.
One longitudinal beam is already sufficient for the vibration analysis.
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A loading by forces, such as in the static case, is not needed for this analysis because in natural frequency analysis, only stiffness and mass play a role. The weight of the driver and other components, which in the static case was assumed with 3000 N will now be realized by selectively applying mass. Therefore, for this analysis a mass of 300 kg shall be applied in the middle of the longitudinal beam.
4.2.3.2 Cloning a Similar Model A former analysis model is copied and then modified.
To accomplish this task, the model does not need to be created from scratch, because it is similar to the existing static analysis of the longitudinal beam respectively the vehicle frame. The static analysis involves already the mid-surface model of the longitudinal beam, the simplifications of the geometry and the bearings. Therefore, this simulation can be cloned, only a few things need to be changed afterwards yet. To do this, follow these steps: ÍÍOpen in NX the simulation file rh_laengstraeger_re_sim1.sim that was used for the stiffness analysis of the longitudinal beam. To open a simulation file, set in the FILE > OPEN dialog the file type to Simulation Files (*.sim), as shown in the figure below.
The NX system automatically switches to the simulation application. In the simulation navigator, you realize that only the simulation file and the FEM file are loaded automatically. The idealized file and the master model were not loaded. ÍÍTo perform cloning a fully opened file structure is required. To fully open the files, you switch to, according to the figure below, the function Load on the idealized part.
Before the cloning operation is processed, it must be decided which files of the structure will stay and which should be cloned. The following considerations have to be taken: We now have two analyses on the same master model. Organizing the data is done in accordance with the Master Model Concept.
The master model shall not be changed. The idealized model includes mid-surface and markers. This shall also remain. The FEM model has to be changed a little because the point mass must be added as a special finite element. Therefore, this file needs to be cloned. Due to the assembly structure also the simulation file must be then cloned because it is arranged above the FEM file.
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ÍÍTherefore, the FEM file will now be made the displayed part and the FILE > SAVE AS . . . function is run. ÍÍThe system now asks for a new name for the FEM file. Enter here for example rh_laengstraeger_re_fem2.fem. It is advisable that the file name of the FE analyses retains its main part and only the number will be incremented. ÍÍAfter confirming with OK, the system prompts for a new name for the simulation file. Specify, for example rh_laengstraeger_re_sim2.sim. ÍÍThe next question of the system “Do you want the Save As to continue?” is confirmed with YES. The cloning process is then performed. After this cloning process you are already working in the new file structure. The old files are automatically closed.
4.2.3.3 Generating a Point Mass on the Frame ÍÍThe following steps apply to meshing. So you make the FEM file the displayed part. Instead of the static force of 3000 N now a point mass at the same place must be added with a weight of 300 kg. The force was added to a small circular area. Therefore, for the sake of simplicity, this circular area shall be used for the mass point, too. However, since a point is required, we can generate another 1D-Connection (“Spider”) from the circular edge to its center point. Proceed as follows: ÍÍCreate the connection from the circular edge to its mid point by choosing the function 1D-Connection at the function group for meshing. ÍÍIn the 1D-Connection menu set the type to Point-to-Edge and the element type to RBE2. ÍÍSelect the center of the circle on which formerly the force has applied, and then its edge. ÍÍConfirm with OK. The connection is now created. Finally, you create the point mass as follows: ÍÍSelect the function 0D-Mesh from the group of meshes. ÍÍSelect the center of the circle and set the type to CONM2. ÍÍThen select the function Edit Mesh Associated Data and enter for mass 300 kg. ÍÍConfirm twice with OK.
The total weight of the vehicle is set by a point mass.
The point mass is attached via a “Spider” to the circular area.
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In the NX system mass points are 0D-Meshes.
In the graphics window, a CM symbol is displayed and in the simulation navigator the new element also appears. ÍÍSave the file.
4.2.3.4 Inserting a Solution for Natural Frequencies ÍÍThe following work relates boundary conditions and solutions. Therefore, you now make the simulation file to the displayed part. A simulation may well contain two solutions: one for static and one for frequencies.
Initially the cloned simulation file contains still the old solution for static analysis. This solution method cannot be changed afterwards, rather a new solution must be generated. ÍÍDelete the old Solution 1 in the simulation navigator. Optionally, you can also delete the old force of 3000 N, which was used for the static analysis. However, the force does not bother, because it will not be inserted into the natural frequency solution. It simply remains in the load container. ÍÍNow add a new solution by using the function New Solution gator.
in the simulation navi-
In the appearing menu Solution, again the solver, the type of analysis and the Solution Type must now be set, according to the following figure. ÍÍFor modal analysis, set the solution type to SOL 103 Real Eigenvalues. (In older versions of NX: SEMODES 103). The name SEMODES incidentally means Super Elements Modal, i. e., hereby it is also possible to integrate parts of large models into so-called super elements. Super elements allow integrating stiffness properties of entire FEM models, e. g. the wing on an aircraft, into single super elements and maybe even reducing its complexity. In subsequent analysis, these super elements can then be calculated very quickly.
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Nastran Solution Type 103 calculates natural frequencies.
ÍÍFurthermore, it should be set in a way that the lowermost five frequencies are calculated. This is done in register Case Control. ÍÍEdit the settings in Lanczos Data and enter 5 for the Number of Desired Modes. This means that the five lowest natural frequencies of the beam will be found. In many cases, only the lowest natural frequency is of interest, as this is often most critical. Keep in mind that a higher number here also leads to a significantly higher computational time. If you give no setting in this menu, the first ten frequencies are calculated by default. ÍÍConfirm twice with OK and the solution is generated.
4.2.3.5 Assigning Boundary Conditions to the New Solution Since we copied our simulation file from the former file, the old boundary conditions still do exist in the file. You can see them in the constraint container. When creating new solutions existing boundary conditions are not automatically added, but the opportunity arises to select which boundary conditions are to be applied in this solution. This is particularly useful if several solutions are available in a simulation file, because in such cases, certain boundary conditions can be applied in the first, while others are used in the second solution. In our case, the new solution still contains no boundary conditions. You can check this by checking the constraints that are associated with the new solution. It should not be forgotten, assigning them, because otherwise the natural frequency analysis would be performed without constraints. ÍÍAssign the existing boundary conditions to the new solution by dragging the appropriate nodes in the simulation navigator from the group constraint container with the mouse into the group constraints of the new solution.
Different solutions can have different boundary conditions.
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The navigator provides the structure of the analysis model. Loads and boundary conditions can be moved by drag and drop from the containers into the solutions.
The simulation navigator should now look as shown in the figure above.
4.2.3.6 Calculating and Evaluating Vibration Modes and Frequencies ÍÍStart the analysis with the function Solve and confirm with OK. ÍÍAfter the solution is complete, start the post-processor . In this natural frequency analysis, the first five frequencies of the component were calculated. These five results are now displayed in the simulation navigator, as shown in the following figure. Mode 1 means that it is the lowest natural frequency found. The number behind it is the frequency in units of hertz. The result node shows the calculated natural frequencies for all modes.
ÍÍNow activate the displacement results of the first mode, which occurs at a frequency of 1.3 Hz (open the plus symbol).
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The easiest way to understand the result is seeing it animated. Proceed as follows: ÍÍSelect the function Animation . ÍÍTurn in the following menu Style to Modal. ÍÍEnter at Number of Frames for example 30. ÍÍActivate the option Full Cycle. ÍÍStart the animation with .
For vibration results, the settings of the animation should be changed.
For Mode 1 there should be a vibration mode seen that deforms the longitudinal beam sideways, as shown in the following figure on the left. Since we are interested only in vibrations in the vertical direction, this lateral mode shape must not be considered in more detail. In addition, the lateral movement will not likely occur in the real situation, because the frame is significantly stiffer in the lateral direction due to the influence of cross beams. Therefore, the next higher natural frequency will now be analyzed. ÍÍSo you activate in the simulation navigator Mode 2 and watch again the animated deformation results. Animated natural frequency results allow the wave forms to be understood.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The animation shows that this is a form of vibration in the vertical direction. This is a vibration mode that could occur in reality, because the neglected cross beams and the second longitudinal beam would not substantially impede this wave form. The Mode 2 corresponding natural frequency of about 2.7 Hz can thus be used for a rough estimation of the natural vibration of the vehicle frame.
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4.2.3.7 Evaluation of Other Result Quantities The modal or natural frequency analysis shows, in addition to the natural frequency and shape additional results, deformations and stresses. These results need to be taken with caution, as explained in the following. The basis of the explanations is the fact that the following quantities are not processed in the natural frequency analysis, but play a significant role in reality: The modal analysis does not account for excitation and damping.
Excitations through which vibrations are caused are not included in the modal analysis. In reality, movements or forces are imposed on one or more positions of the component. This movement would have to be defined in its temporal and spatial course and included in the FE analysis, so that the result could be interpreted accordingly. However, the natural frequency analysis does not take this into account but merely the free vibration is considered. Damping of material also is not included in the modal analysis. Damping causes loss of energy during oscillation. Without any damping the amplitude of vibration at resonance would be infinitely high.
Therefore the size of the vibration deflection cannot be stated.
The amplitude of vibration that will occur in reality therefore depends on excitation and damping. Stress or strain in the part that occurs during the oscillation, in turn, are dependent on the size of the vibration amplitude that arises. However, because the excitation and damping are not processed, almost no statement can be made about amplitude and stresses. The only statements that are possible in this case, ground in assumptions made by the system about the size of the amplitude. With such an arbitrarily assumed amplitude, the stresses that would occur with this amplitude, can be inferred. For the user this means that the indicated stresses can merely be evaluated qualitatively, i. e., he can detect, where the locations for large respectively small stresses would occur in the vibrational case, the numerical value itself has no meaning. However, this information can be of quite great interest for the design. ÍÍTo illustrate this qualitative stress, therefore, open the subtree of Mode 2 in the simulation navigator. ÍÍHere you can find all other results. If you want to be on the safe side for the shell elements, so if you want to see the greatest value of the outside, inside or center of the sheet, then select the node Stress – Element Nodal and in Set Result set the shell option to Maximum.
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In modal analysis, the stress profile can be specified only qualitatively.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The result should look as shown in the figure above. In this case, it is recommended to switch off the legend, so that the arbitrary numerical values are not visible. ÍÍSave the files and close them. Thus this learning task is completed.
4.2.4 Clamping Seat Analysis on the Wing Lever with Contact For clamped connections (also press fits or similar) there exist analytical formulas in engineering handbooks [RoloffMatek]. However, these machine elements are usually CAD modeled by designers and integrated with in components and assemblies.
Analytical formulas no longer help.
This leads to complex geometry being used – with the result that analytical design formulas from the engineering manuals provide only very limited meaningful results. Therefore, analysis of clamped connections and similar elements have become an important application for FEA. The methodology for this will be explained in this learning task. Clamping seats, clamping elements or press fits are usually calculated in FEA with nonlinear contact.
Flügel Wing
wing handle mit Flügelhebel with press Klemmsitz fit
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The focus of this learning task is the use of the non-linear contact, which is required in such applications, but also in many others. Thus, in this learning task, the need, the operation, the adjustment parameters, and finally the application of contact in a typical example will be shown. The methodology presented here can be applied to other contact examples in a very similar way.
4.2.4.1 Task To achieve the required transferable torque, a screw force of 2500 N is to be reached on the clamping lever of the wing seat. The question is whether at this load, the permissible surface pressure in the contact area or the allowable stress in the rest of the geometry will exceed. Therefore, a stress analysis is to be performed, on the basis of which occurring surface pressures and stresses can be estimated.
4.2.4.2 Need for Non-Linear Contact and Alternatives Non-linear contact is always necessary if in reality during deformation impact, lifting, sliding or rubbing surfaces between bodies occurs and if these effects must be modeled in detail in the simulation. Contact analyses lead to significantly higher computation times.
So the non-linear contact is often important for assemblies analyses. Theoretically, nonlinear contact could be calculated between all parts of an assembly, because it could well be that somewhere a touch occurs. But this should be avoided, because contact analysis leads to clearly higher computational times, and because even further difficulties may occur, as shown in this example. Therefore, it is very important that the FE analyst thinks ahead and decides sensible, where to apply non-linear contact analysis and where maybe it is sufficient to use simplified types of connection. Frequently, it is even sufficient to generate fixed connections between components. Such fixed component connections are simply linear in nature, i. e., they are defined a priori, and the parts always remain in conjunction even during the deformation. NX functions for such types of solid compounds are:
Overview of linear functions for connections.
Surface to Surface Gluing for the flat connection of two bodies.
Edge to Surface Gluing for connecting of example shell elements to volume elements. Edge to Edge Gluing for connecting at two edges.
Mesh Mating Condition for the alignment or merging of nodes of two bodies at an
area.
1D-Connection with RBE2-elements (for example, a point with an area over rigid coupling elements)
Such cases have already been covered in previous examples. The functions which are available in the NX system for non-linear contact in the Nastran solution 101 for this are:
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Surface to Surface Contact for sheet-like contact situations.
Edge-to-Edge Contact
Summary table of nonlinear functions for contacts.
1D-Connection with CGAP-elements, which can be defined, for example, from one edge to another edge.
The press fit is an example in which two parts slide or rub on each other. Perhaps there would even be an initial gap between the contact surfaces, or perhaps there will, due to the load, arise a gap somewhere. A simple fixed connection at the contact surface, such as the functions Glue or Mesh-Mating-Condition allow, is not effective, when stresses at the contact surface shall be determined with good accuracy, because with the gluing all transverse movements of the parts to each other are suppressed, which are possible in reality. The simple bonding of the parts would therefore lead to unrealistic transverse stresses. For this reason, the non-linear contact in the case of the clamping seat useful.
transverse movement at contact face
With a clamping the two parts deform. The contact forces between the parts change during deformation. In addition, the surfaces slide on each other.
A possible alternative to the non-linear contact could be the function Surface to Surface Gluing if it is adjusted such that it possesses in the tangential direction – i. e. the sliding direction – a small and in the normal direction a large stiffness. Adjusted this way it corresponds to a sliding connection. This is possible because in this function, a separate stiffness definition of the two directions is possible.
The glue function, in some cases, can replace the non-linear contact.
bolt load 2500 N
4.2.4.3 Operation of Nonlinear Contact In the linear FE analysis stiffness and boundary conditions are determined only once from the component and added to the stiffness matrix and the load and displacement vector. In contrast, in the analysis with non-linear contact, it is checked again and again during the deformation, whether penetration of contact surface pairs happens. If there is such a penetration, opposing forces must be formed, which counteract the penetration. To realize this, it is necessary that the external loads are applied in small steps and examined after each step, whether there appear penetrations in the potential contact area. Such penetrations can easily be found by checking geometric positions of corresponding nodes. Each of these load steps is realized by a linear finite element analysis, which proceeds much like usual. The only difference is that the load steps do not come from the relaxed body, but always include the preload of the previously already loaded body.
The contact leads to iterations.
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In the outer iteration (status loop) external forces are applied piecewise.
F
F F
outer iteration (status loop)
F
F
F
F
F
inner iteration (force loop)
As long as no penetrations occur, the load is simply increased until the desired full load reaches at the end or until it comes to a penetration of nodes. The progressively increasing load and finding of contact nodes is called outer iteration or status loop. When it comes to the first node penetration, an algorithm starts that we call the inner iteration or force loop. This algorithm ensures that the nodes are pushed back so that they adjacent flat and realistically to each other at the end. In the second iteration (force loop) contact restoring forces are applied.
The retraction of the inner nodes in the iteration is obtained by restoring forces that are applied to the corresponding nodes. So there are following linear FE analyses performed in which now additionally these restoring forces are inserted. The restoring forces can be estimated only roughly by the software using the current penetration of a node and multiplying it by a given stiffness value. With such estimated restoring forces there will surely not immediately be achieved, that the contact nodes remain lying exactly on a surface. The restoring forces are assumed rather too large or too small. Therefore, restoring forces are recalculated based on the resulting node overlap and applied in the next linear FE analysis. Now, the overlap should have become smaller. This inner iteration is repeated until a convergence criterion has been reached.
After the contact restoring forces have been found correct, the next piece of external force can be applied.
After the inner iteration has converged, in the outer iteration, the next piece of load is applied, and the inner iteration begins again. So the non-linear contact is a doubly nested iteration of each case linear FE analyses. Therefore, considerably larger computation times will arise. Non-linear contacts should therefore be used only when it is absolutely necessary.
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4.2.4.4 Loading the Assembly and Creating the File Structure ÍÍTo begin the task, you now load the assembly fl_bg_fluegeleinheit.prt from the RAK2 directory. This assembly contains the two parts fl_fluegeltr_klemmhebel and fl_fluegel-traeger. These are the clamping lever and the tube on which the clamp is to be realized. ÍÍNow switch to the application Advanced Simulation. ÍÍCreate in the simulation navigator the structure for the simulation. Please note that not all bodies must be transformed into polygonal geometries, but only the geometry of the clamping lever and the tube. Moreover, these two bodies are supposed to be changed significantly in the idealized file. That’s why it makes sense to initially create no polygon body at all and make this selection at a later date.
ÍÍSet the option Bodies to Use to None.
4.2.4.5 Contact Specific Parameters in the Solution After creating the file structure you will be prompted to define the solution. In the previous examples it was mostly confirmed here with OK and so the defaults were accepted. Also in the case of this example, the default settings can be accepted, too, but let’s first explain some important settings for the control of the contact algorithm.
At first, a body is not yet included in the analysis.
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The default parameters should be changed only if problems appear.
In some cases, upon contact analyses, it is advisable to make changes to these parameters to reach acceptable results. We refer to the explanation on the contact algorithm of NX Nastran. Settings for other solver types must be found in the online help. Below, we explain the meaning and give recommendations to some important contact parameters. These explanations are partially taken from the document NX Nastran User’s Guide [nxn_user], which belongs to the online help of NX Nastran. Some of the explanations are enriched by own experience of the authors. The following figure shows the global contact parameters in which the declared parameters will be passed to the NX system menu. You can find this in the menu Solution in the Case Control register in Create Object Modeling.
The global contact parameters menu and the default values.
Stiffness values and recommendations for contact.
Penalty Normal Direction, PENN: This value controls the stiffness in the normal direction when the contact surfaces run into overlap. Larger values lead generally to faster convergence and smaller maintaining overlap. However, too large values also mean that no convergence can be achieved. The default is a value of 10. This is not displayed, but internally stored by the software. If a value is entered, the default value is overridden for the analysis. There are following recommendations: Stiffness values between 1000 and 10000 are suitable in most cases. Stiffness values between 10 and 100 are suitable when the contact surfaces are identical but nodes do not match. Smaller values can smooth out irregularities of not matching meshes. If contact stresses are to be determined, we get the best results when matching meshes exist on both sides of the contact.
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Very small stiffness values, that is, values less than one, lead to very slow convergence and are not recommended. Penalty Tangential Direction, PENT: This value controls the convergence of the frictional forces when the friction is not zero. The value should generally be 10 to 100 times smaller than the Penalty Normal Direction. Contact Force Tolerance, CTOL: This is the limit for the contact-convergence tolerance (Eucid Norm). Once the contact convergence tolerance is less than this limit, the contact algorithm has converged. Max Iterations Force Loop, MAXF: Here, the maximum number of iterations for the inner or force loop iteration can be set. Max Iterations Status Loop, MAXS: Specifying the maximum number of iterations for the outer or status loop iteration. Percentage of Active Contact Elements, NCHG: Hereby it can be achieved that contact analysis terminates, although not all contact elements have converged or become inactive. This makes sense in cases when coarser accuracy is acceptable or when it is recognized from the convergence history that the last contact elements converge very slowly or not at all. Such a behavior would indicate so-called contact-oscillations, i. e., the contact elements oscillate back and forth between the closed and open state. If this parameter is set such as 0.01, this means that 1% of the contact elements do not need to converge. Shell Thickness Offset, SHLTHK: The contact feature in NX Nastran can be used both for shells as well as the solid elements. This value is only relevant for shells and manages the control of the shell thickness in the contact area. If the option Include is used, the system assumes that the shell elements are at the center of the body, that is, the thickness t is assumed on both sides by t/2. However, if the shell elements represent the outer surface of the body, enter the option Exclude, then the thickness is ignored. Contact Status, RESET: If multiple load cases are calculated, with the default option Start from Previous it is achieved that for the analysis of subsequent load case, the final contact condition of the previous load case is utilized. This often makes sense to speed up contact computation. Initial Penetration/Gap, INIPENE: Unfortunately, there are often tiny initial penetrations of individual nodes of the contact surfaces. These are almost not visible at the FEM mesh, but result in unrealistic stress peaks on the contact surfaces. This parameter controls how such situations should be handled. The default setting Calculate from Geometry does not change anything at the given geometry. The option Ignore Penetration/Use gaps removes artificially penetration at positions where initial penetrations exist, therefore puts these areas exactly adjacent to one another. The third option Set to Zero sets all contact surface areas exactly to zero distance. This third option is very effective. In many practical contact tasks it has been found that good results could be achieved just by using this option. In the case of our example, all defaults can be accepted. ÍÍTherefore, confirm with OK, and the solution will be generated.
Termination criteria for contact
If the contact has to stop sooner . . .
Invisible initial penetrations are often guilty of “dotted” stress results.
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4.2.4.6 Part 1: Rough Analysis with Tetrahedrons In this first part of the task we want to come to a conclusion in a rapid manner. We just want to perform the most essential work. For that we accept a certain loss of precision. In the second part of the task we then pull out all the stops for a high-quality contact analysis.
4.2.4.7 Geometry Simplifications for Symmetry A mirror symmetry exists if on the left of a symmetry plane exactly the same deformation happens as on the right. In our task we have this condition twice. The following figure shows those two planes of symmetry and the already cut model, so as it should be after the operations in this section. The model is simplified. Symmetry is used twice.
In most cases the symmetry is exploited in FEM tasks in order to save computing time and memory. Finally, it makes no sense to produce duplicate results if we already know that left of the plane the same result will come out as right. Symmetry should be exploited in any case, especially if it is anticipated that the analysis will take longer. At a contact task this is definitely the case. To get to the double cut model presented, the following steps are to perform: ÍÍTurn into the idealized file and create two wave links, one for the pipe and one for the clamp lever. ÍÍHide in the assembly navigator the entire assembly fl_bg_fluegeleinheit. The two wavelinked parts remain visible. ÍÍTurn into the modeling application, create two Datum Planes at the corresponding planes of symmetry, and trim the two bodies at these planes. ÍÍIf you wish, you can also – as shown in the figure above right – trim a part of the lever, because this area has little impact on our results. ÍÍAlso, the pipe can be truncated a piece, so that only the part of interest is left. ÍÍSwitch back to the application Simulation.
4.2.4.8 Add Polygon Geometries Subsequently ÍÍChange to the FEM file. The polygon bodies are not yet there or need to be replaced again.
You notice that there is no single polygon body in the FEM file. This is how it should be, because when generating the FEM file at Bodies to Use we have set the option to No. Now there is geometry ready prepared in the idealized file, so polygon geometry for meshing
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shall be generated. To perform the subsequent generation of the polygon geometry, proceed as follows: ÍÍSelect from the simulation navigator on the uppermost node RMB and EDIT. ÍÍActivate the switch Edit Bodies to Use. Now the idealized file is temporarily shown in the graph window. ÍÍSwitch the option Bodies to Use to SELECT. ÍÍSelect the two simplified bodies tube and clamping lever. ÍÍConfirm with OK. Now the two wave-linked and simplified geometries are shown in the FEM file and can be used.
4.2.4.9 Material Properties Both the pipe and the clamping lever should be made of common steel. ÍÍSelect the function Assign Materials. ÍÍSearch the library to find the material Steel. ÍÍSelect the two bodies. ÍÍConfirm with OK.
4.2.4.10 Meshing with Tetrahedrons For a rough contact analysis a simple tetrahedral mesh is generated with refinement to half or one quarter of the value proposal. Proceed as follows: ÍÍSelect the function 3D Tetrahedral Mesh. ÍÍLeave the element type to the default CTETRA10. ÍÍSelect the clamping lever. ÍÍSelect the yellow flash for the proposal of element size. ÍÍDivide this default value by two. ÍÍConfirm with OK. ÍÍPerform the same steps again with the shaft. Use here the default element size value divided by four.
A rough analysis should always be performed first.
This is a standard mesh: Tet10 elements and half or one quarter of the proposal value for the element size.
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The result should look as shown in the figure above. As you see, the nodes at the contact point do not coincide. Although this mesh and contact analysis can be performed, but the accuracy of results in the contact area is limited.
4.2.4.11 Symmetry and Further Boundary Conditions ÍÍSwitch to the simulation file. The condition of symmetry is: No deformation perpendicular to the symmetry plane.
An appropriate boundary condition must now be applied to all cut surfaces of symmetry. There are two ways to choose from: First, the function Symmetric Constraint and secondly the general function User Defined Constraint could be used. When using symmetric constraint condition you need not to worry about the directions. You should only avoid combining all planes of symmetry into a single condition. Rather, put always those faces together that belong to the same section – i. e., that face in the same direction. When using the user-defined function, note that for symmetry conditions on volume elements this degree of freedom perpendicular to the cutting surface must always be fixed and all others must be free. We want to use the symmetric constraint condition here: ÍÍSelect the Symmetric Constraint and select all faces that belong to the first symmetry-section. These are three faces. ÍÍConfirm with OK. ÍÍCreate the same condition again on the three faces that belong to the second symmetry section.
These constraints prevent the movement of the clamping lever, but not that of the sleeve.
In the navigator on the solution node it can be seen that there are conflicts with the boundary conditions. The reason is that at some edges both symmetry conditions act. The system displays this conflict situation (see figure below) and the user should now intervene and define, how to proceed on these edges. There are several possibilities: The first (Apply – Symmetric (1)) or the second (Apply – Symmetric (2)) condition may be active or the degrees of freedom can be specified individually (Specify Values). ÍÍAfter the two symmetry conditions have been created, switch to the navigator choose on the solution node with RMB the function Resolve Constraints.
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ÍÍIn the following dialog, use RMB on the displayed conflict and select the function Specify Values. Set the X and Y translations, i. e. DOF1 and DOF2, to fix and the Z translation to free. ÍÍClick APPLY and CLOSE. The conflicts are solved now.
Moreover, movements in the Z-direction must be prevented. This is required even if under the given loads no movement in the Z-direction would occur. Static FEM analysis will always require that statically determined supports of the parts is given. Over-determined bearings are indeed allowed, but not under-determined. ÍÍAccording to the figure above, you create a User Defined Constraint on the small sectional area, which fixes the Z-direction. ÍÍNow we have created yet another overlap conflict in the solution. Solve this example by assigning the symmetry condition. With this constraint set the clamping lever is mounted statically determined. The tube, however, still has a possibility of movement in the Z-direction. Preventing this will be our focus in the next section.
4.2.4.12 Add Soft Springs for Static Determination The requirement for static determination leads in particular in contact analysis in many cases to difficulties. The problem is the fact that in reality contacts contribute to determination, but in FE analysis, non-linear contacts act only in form of forces on the parts. However, the static determination must be achieved by merely boundary conditions in the FE system, therefore, the contact forces do not count. If we check in our task each part to its constraint situation, we note that the pipe is still undetermined in Z-direction. Now we have a typical problem: On the one hand, the tube needs a constraint in Z-direction, on the other hand, this constraint would distort the re-
The constraints may be over-determined, but not under-determined.
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sult, because the position of the tube in the Z-direction will be determined by the contact forces. This problem is typical in contact analysis. One possible solution is to support the tube with soft springs in the missing Z-direction. With such a soft spring the tube can adjust its position almost free. Nevertheless, there is statically determined support and the FE analysis can be performed. Soft springs are a way to reach bearings without applying hard constraints.
Follow the steps for creating such a soft spring bearing as follows: ÍÍFirst, make the FEM file to the displayed part. ÍÍGenerate a 0D-Mesh of type CBUSH (Grounded) on an edge of the tube. It does not matter which edge you use. ÍÍIn the navigator there is a mesh collector for the 0D Mesh. Edit this and modify the contained Physical. Enter a small value for the stiffness in the Z-direction, for example, 0.01 N/mm. The spring elements CBUSH (Grounded) used here have the property that they are automatically connected to the earth. This means that no further constraint in the SIM file is necessary.
4.2.4.13 Definition of the Contact Area The following is about the definition of contact areas, i. e. surface pairs, where during deformation will be examined for penetration and, where appropriate restoring forces will be applied. In addition, also the coefficient of friction is given here, to be in this area of contact. Go to the definition as follows: ÍÍMake the simulation file to the displayed file. ÍÍSelect the function Surface to Surface Contact in the functional group Simulation Object Type.
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The contact is a nonlinear function in the otherwise limited to linear static Nastran solution 101.
The contact requires the definition of a pair of surfaces. The first of the two partners we call Source Region, the second Target Region. If meshes are of different element size on both sides of the contact, the following rule applies: The first side (Source Region) shall be the one with the smaller mesh size. The background is that the contact check is always performed starting from the first side. Using the nodes of the first side there are normal projections performed to the surfaces of the second side. So when the first side is meshed by smaller elements, the contact analysis can be performed with greater accuracy. side 1 (source), fine
side 2 (target), coarse
In our example, the contact surface on the tube is meshed finer and should therefore be the starting area. So follow these steps: ÍÍSelect at Type the Manual option. ÍÍSelect the function Create Region in Source Region. ÍÍSelect the cylindrical contact face on the tube. ÍÍLeave all settings in the menu Region at default and click OK. ÍÍSelect at the Target Region the corresponding contact face on the clamping lever.
In case of different mesh sizes there is to pay attention to the order of selection: The first is to be the finer one.
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Now you have created a surface pair for the contact. Some further adjustments are still possible back in the main menu of the contact, which are sometimes very useful. These include: The contact parameters at a glance.
If press fits have oversize . . .
For shell elements, there are particularities.
Coefficient of Static Friction: Here the coefficient of friction is given, which is responsible for ensuring that shear forces are transmitted from one body to another. These forces are calculated according to Coulomb’s friction law using the pressure force. Min./Max. Search Distance: The contact algorithm will search for contact only in a range between these two limits. For the default setting zero and one, this means that analysis of the contact is performed only where the contact faces have smaller distance than 1 mm. The setting Offset that is available in the Region menu can be used to artificially move the contact surface a little. This corresponds approximately to an additional layer of material in the contact region. This could represent, for example, a layer of paint to be considered for the contact that is not specifically FE modeled. Even so, an initial penetration of the contact surfaces could be modeled this way, for example, as it is required in the analysis of press fits with interference. Surface: This setting from the Region menu is only relevant if shell elements are in the contact area and moreover if the shell elements are defined as Source region. If this is the case, the contact checks are normally executed into top side direction of the shell elements. However, if this is the wrong side, there can be switched over to the bottom side using this option. Finally, there are the settings in Linear Overrides (BCTPARM). Here some of the global contact settings can be overridden. This is useful if multiple contacts are in the model and different settings shall be used. ÍÍConfirm with OK, so the contact function is generated.
4.2.4.14 Generation of the Bolt Load The last thing missing is the bolt load of 2500 N. According to the figure below, this can, for example, be applied to the supporting face of the screw head. Keep in mind that the applied bolt load in the FEM model is only half due to symmetry. ÍÍAccording to the figure, create a force of 1250 N in the positive y-direction on the supporting face of the screw head. ÍÍSave the files. The bolt load acts on the support surface of the screw head.
Screws can be modeled in many different ways in FEM. We have selected a very simple method here.
This type of bolt load does not consider the bolt load increase or decrease that may occur due to operating force. If this is required, the screw must be generated via 1D BEAM element that receives the diameter of the screw, or by volume elements with the realistic
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geometry dimensions of the screw. The bolt load must then be defined with the function Bolt Pre-Load .
4.2.4.15 Request Output of Contact Pressure In contact analysis thus contact forces are calculated along the way. These can be utilized to calculate the surface pressure in the contact. Incidentally, there is another interesting quantity which can be calculated with contact analysis, namely the gap size of the contact. If these additional results shall be displayed in the post-processor, this must be requested in the so-called output requests. To do this, follow these steps: ÍÍFrom the simulation navigator using RMB on node Solution 1, select the EDIT function. ÍÍGo to the register Case Control. ÍÍSelect at Output Requests the function EDIT. ÍÍIn the following menu, go to the register Contact Result. ÍÍActivate the switch Enable BCRESULT Request. ÍÍSelect at Separation Distance the option SEPDIS. ÍÍConfirm twice with OK.
Additional results which are indeed calculated, but normally not output can be requested.
4.2.4.16 Solve Solutions and Evaluate Results The solutions are calculated in a conventional manner, whereby, due to the non-linearity, higher computation time (about two to five minutes, depending on the hardware) are expected. ÍÍRun the function Solve. ÍÍChange after the completion of the solution into the post-processor. ÍÍFor the contact pressure, set the result to Contact Pressure – Nodal. In case that no results are calculated you should look for error messages in the f06 file (FATAL). Here the solution progress is documented. After successful solution the deformation should be initially displayed and checked for plausibility.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The result for the contact pressure shows the expected pattern. Due to the unaligned nodes on the two sides of the contact the pattern is slightly non-uniform. But it certainly allows the use of values. When peaks are excluded at the very border, maximum values of about 35 N/mm2 yield. ÍÍSet the result to von Mises stresses.
The result of contact pressure with tetra hedral meshes trembles a little. This can be improved through better meshings in the second part of this task.
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The von Mises stresses.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
The pattern shown in the figure above displays stress results. In the area of contact, the von Mises stress is similar to the result of the contact pressure previously shown. This has to be like that, because pressure and stress is the same thing. The contact pressure is just a more detailed analysis of stress in the contact area. For this sample problem it means that the surface pressure is far below the permissible values and the tightening force is therefore acceptable.
4.2.4.17 Part 2: Alternative Meshing with Hex-Tet Transition The previous analysis with pure tetrahedral meshes of part 1 of this task has worked reasonably simple. Therefore, there is not much to suggest now to create even a more complex mesh. Nevertheless, in this second part an alternative meshing will be shown, which leads to more accurate and more uniform results in the contact area. Especially if fairly accurate results are desired in the contact region, there are two requirements for the meshing: 1. Hexahedral elements without middle node should be used. 2. The nodes of the two contact surfaces should be aligned with each other. To meet the requirements for a very high quality mesh, some preparations need to be done.
If we want to fulfill these two requirements, we have some work to do. Elements without mid nodes are either eight node hexahedrons (Hex8) or four node tetrahedra (Tet4). Tet4 elements should be avoided if possible, because of their significant inaccuracy. Therefore, only the eight node hexahedron elements come into question, which are often used because of their high uniformity and good accuracy. With good accuracy, we mean here that even in cases of coarse meshes accurate results appear. The Tet4 elements are of course accurately, but only at very, very fine meshes. However, hexahedral elements have the characteristic that they can be created just on extrusion capable geometry. To use hexahedrons, the model needs to be decomposed into parts such that each part is extrudable for itself. However, this method would be feasible for our model, but in general much more complex than the simple tetrahedron meshing. A good way is to work with transitions. We can therefore mesh only the area of contact with hexahedra, then go to tetrahedron and use pyramidal elements in the transition area for the correct coupling of the two element types. This method is often very suitable, because it is very flexible, and so we use this route.
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So we want to apply the following strategy for meshing: On the tube and the clamping lever we split the geometry such that extrudable parts are created in the relevant area of contact. At the partition boundaries we create so-called Mesh Mating Conditions, which ensure that co-aligned and merged nodes arise. At the contact surfaces, we also create mesh mating conditions, however, we choose an option here that ensures although the nodes from both sides will be aligned they will not merge. The extrudable parts are meshed with Hex8. The remaining parts are meshed with Tet10 and in the transition region of Hex to Tet we create pyramidal elements.
Important geometry is meshed with Hex, others with Tet elements.
Following the operation steps in the NX system are shown. We start cloning the existing file structure: ÍÍSave the simulation file and switch to the idealized file. ÍÍSelect the function FILE > SAVE AS . . . ÍÍEnter the new file name fl_bg_fluegel-einheit_fem2_i.prt. ÍÍThere immediately follows the question about the new FEM file. Enter the name fl_bg_ fluegeleinheit_fem2.fem and for the simulation file name fl_bg_fluegeleinheit_sim2.sim. ÍÍConfirm the question “Do you want the Save As to continue?” with YES.
The steps in NX.
You are now in the new idealized file in which we now want to perform the body partitions.
4.2.4.18 Generating Body Partitions for HEX Meshing Let’s start with the pipe. Here we need a partition that separates the contact area from the remaining parts. For this purpose a plane, as shown in the figure below, is used. ÍÍCreate a Datum Plane as shown in the figure below. ÍÍSelect the function Split Body and select the pipe. ÍÍChoose in the dialog at Tool Option the option Face or Plane and select the plane you just created. ÍÍActivate in the menu at Simulation Settings the button Create Mesh Mating Condition. With this option, the Mesh Mating Condition is generated automatically, which provides for aligned and merged nodes. Alternatively, you can manually create it in the FEM file afterwards. However, it is very useful if this information is already specified in this Partition function, because the software will always automatically ensure the correct Mesh Mating Conditions. Also it has been found that meshing works more robust if this condition is activated.
Body partitions are often necessary as a preparation.
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Body partitions help to obtain extrudable bodies.
ÍÍClick OK to confirm, after which the partition is created. Next follows a partition of the clamping lever so that it is capable of extrusion in the contact area. To achieve this, we want to make a circular partitioning. ÍÍCreate a sketch with a 54-mm diameter circle on the clamp lever surface as shown in the figure below. Extrusion capable does not necessarily mean cuboid. The partitioning shown in the figure is also possible.
ÍÍSelect the function Split Body and select the clamping lever. ÍÍSelect from the function at Tool Option the option Extrude and select at Section the circle you just created. ÍÍAt Direction select, for example, again the circle. ÍÍTurn on the option Create Mesh Mating Condition again. ÍÍClick OK to confirm, and then the partitioning is produced. Now two additional bodies are formed. If you switch to the FEM file, you will notice that the two new bodies are absent because they were not selected as polygon bodies. You should therefore add these new bodies yet:
The new polygonal bodies need to be added in the FEM file.
ÍÍSwitch to the FEM file. ÍÍPerform the function Update . ÍÍFirst, delete the two old tetrahedron networks. The 0D-Mesh with the spring elements may persist. ÍÍFrom the simulation navigator on the top node use RMB and choose EDIT. ÍÍActivate the button Edit Bodies to Use.
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ÍÍSelect at Bodies to Use the option SELECT. ÍÍSelect the two newly acquired bodies. ÍÍConfirm with OK. Make sure that two Mesh Mating Conditions have been added in the simulation navigator under the group Collection Collector. Check whether these two conditions are created. In case they are not created, they must manually be produced, much like in the following section.
4.2.4.19 Forcing a Matching Mesh in the Contact Area ÍÍChoose the function Mesh Mating Condition . ÍÍIn the menu Mesh Mating Type switch to the option Free Coincident ÍÍDrag a window in the graphics area over the entire model. ÍÍConfirm with OK.
.
The software scans all selected faces according to those that abut each other. There will be found three pairs, but two of them are the ones who already have their join condition and will therefore not be taken into account. So the only remaining pair of surfaces is our desired contact surface pair. Here the new condition is generated.
Matching nodes yield superior accuracy in contact analysis.
Leave the Face Search Option at the default value “All Pairs”. In this case also faces will be connected which are not exactly the same, but which overlap, as in our case. In some cases it is not possible to generate matching surfaces. This happens for example when the surfaces have a significant distance from each other. In such cases Mesh Mating Conditions cannot be produced in this manner. You should control the successful generation in simulation navigator. You can detect the type by indicating the icons. The symbol of the Mesh Mating Condition in the navigator indicates the type.
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If you want to select specifically where links will be generated, the type Manual Creation can be selected. In this case, each of the two surfaces to be joined must be selected. The faces can glue together or only have aligned nodes.
By default the function creates the link type Glue Coincident . This type provides aligned nodes that are also merged and this is correct to connect the pre-divided bodies. But in the contact area we want to have another option, namely Free Coincident . Although the Free Coincident option would align the nodes, it would not merge them. So this option behaves just as we want it for contact analysis. The tube consists of two bodies each being extrudable. With the subdivision we have achieved that identical faces exist in the contact area on both sides and that the bodies are both extrudable. Identical faces area prerequisite for later creation of identical nodes by using the function Mesh Mating Condition.
Matching meshes also require matching faces.
Two small areas have been forgotten by the way, as shown in the figure above. Actually, we would also need to make volume subdivisions, so that the contact area is really separate from the remaining. However, volume subdivisions are not absolutely necessary. Face subdivisions are sufficient because they will not disturb the extrusion capability of the body in this case. Those face subdivisions have been automatically generated by the way of the Mesh Mating Condition. This function is in fact clever: you know that only identical faces can also have identical nodes. So they created this identical faces if necessary even by corresponding face divisions.
4.2.4.20 Meshing with Hexahedral Elements When these preparations were carried out, the hexa meshing becomes quite easy. Proceed as follows: ÍÍSelect the function 3D Swept Mesh and set the type to the option Until Target. ÍÍSelect at Select Source Face according to the figure below the marked “1” source surface and at Select Target Face the corresponding target face. It makes sense to start meshing with the most important bodies. The others must then tie in these meshes.
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For each case we give start and destination for the HEX solid meshing. There are various ways and sequences.
ÍÍSelect the default option CHEXA8 for elements without mid nodes. ÍÍFor the size of the source element, for example half of the suggested value, given from the yellow flash, would be useful. ÍÍLeave all other options at their defaults and click OK. ÍÍIn the same way you mesh the other two bodies. ÍÍPlay a little with the element size, so that a uniform mesh results. It may help to switch Attempt free Mapped Meshing. The two hexahedral meshes are created and should look similar to the figure below. For the exact analysis of contact pressures linear elements should be used.
4.2.4.21 Meshing with Pyramid Transition and Tetrahedral Elements ÍÍSelect the function 3D Tetrahedral Mesh and select the clamping lever body. ÍÍNow an additional option Transition with Pyramid Elements appears in the menu. Turn on this option. ÍÍUse the default Tet10 element type. ÍÍFor the element size you choose half of the suggested value you get from the yellow flash function. ÍÍClick OK to confirm, then the mesh is generated. If you look closely, that is, hide the polygon bodies and other meshes, you can see the pyramid elements in the transition region.
This type of meshing is very high quality, because all degrees of freedom of the different elements are coupled correctly.
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Linear hexahedral elements and quadratic tetrahedrons inter connected via pyramid elements. Hex in the important area, tets in less important area – this is a good mesh!
This method of meshing with pyramids for the Hex-Tet transition and aligned nodes in the contact area allows for very high accuracy for contact analysis.
4.2.4.22 Further Steps to the Result These last steps are not new.
ÍÍCreate the new spring elements, or check whether these still exist. ÍÍApply material properties to all parts. ÍÍSwitch to the simulation file.
Here associativities will be restored.
You will find that some of the boundary conditions have lost their assignment to geometry. This is shown by the symbol of the red circle with diagonal line (see figure above). You can decide if you delete these conditions and re-create them again or if you “bring it to
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life” by assigning them the new geometry. It works by editing the respective function and reclicking on the respective face, edge or point. ÍÍCorrect the boundary conditions, the force and the contact, or delete the functions, and then recreate them. ÍÍSolve the solution. ÍÍAfter NX Nastran has ended, go to the post processor and display the von Mises stress and the contact pressure. Left is the simple tetrahedron mesh, right the high quality mesh. Top is the contact pressure, bottom the von Mises stress. The uniformity of the contact pressure is better for the high-quality mesh. Otherwise results are very similar. A colored version of this figure is available at www.drbinde.de/index.php/en/203
With regard to the numerical values, the two analyses are not very different, only the uniformity is more convincing at the enhanced mesh. So this learning task is completed.
■■4.3 Learning Tasks Basic Non-Linear Analysis (Sol 106) 4.3.1 Analysis of the Leaf Spring with Large Deformation Leaf springs are often used for simple suspension in commercial vehicles. For the purposes of calculating and simulation leaf springs are considered as classic examples of non-linear geometry. In this example, you learn how to deal with tasks involving large deformations and nonlinear geometry behavior. The example of the leaf spring makes clear what differences arise when effects of large deformation in the analysis are taken into account.
4.3.1.1 Task The suspension of RAK2 is realized by leaf springs at each wheel. The one side of each leaf spring is coupled via a rotation point to the frame and the other side by an additional swing arm. This swing arm has to compensate for the possibly occurring transverse movements of the leaf spring during spring compression.
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The wheels of the RAK2 were spring mounted with leaf springs.
In this task it is to be determined what value these transverse motions will be during compression. The maximum force is thereby applied by the wheel on the leaf spring and it amounts to 20 KN.
4.3.1.2 Need for Geometric Nonlinear Analysis Given the here assumed force, the leaf spring geometry is significantly deformed, as will be found in the analysis. The assumption of “small deformations”, as it is required in the linear FE analysis, may no longer be valid. Therefore, in this analysis the differences arising between linear and non-linear FE analysis shall be examined taking into account effects of large deformation. To illustrate the effects of small and large deformation, the following schematic illustration of the leaf spring task should be considered. The displacement of the left point of the bearing is analyzed. As long as the deformation of the leaf spring is small, the point will move only to the left. However, in a large deformation, due to the changed geometrical conditions, a shift to the right arises. The leaf spring is a classic example of non-linear geometry behavior.
A linear FE analysis will always take the stiffness into account and use that results from small deformations. Therefore, when the point at a minimally small force such as 1 N, moves, for example, 1 mm to the left, the stiffness of the body is known. The stiffness is not changed in the linear analysis, i.e., if the force is 1000 N now, the analysis will result in a displacement of exactly 1000 mm. The move direction is also preserved.
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4.3.1.3 Operation of the Geometrically Nonlinear Analysis The error impact from large deformations thus results from the changing of the stiffness of the component during the deformation. If the stiffness is calculated only once, much computational effort can be saved, but changed geometrical conditions are not included in the analysis. Only through repeated updatings of the stiffness matrix during deformation, the actual behavior will be modeled correctly. Such repeated updatings of stiffness properties are achieved in the FEM system by external loads being divided into, for example, ten steps. Then only one-tenth of the full load is applied in the first step, and the changed coordinates of all nodes will result.
The stiffness matrix is updated several times during the deformation.
With these changed node coordinates, the stiffness matrix of the part is recalculated and the next analysis with the second tenth of the full force is performed using the new stiffness matrix. Note that the new calculated stresses of the first load step are applied as pre-stresses into the second load step. This way the varying stiffness is taken into account.
4.3.1.4 Overview of the Solution Steps In the following solution steps, a linear finite element analysis model is first constructed and solved. To pursue the non-linear solution strategy, it is only necessary to change the type of solution, which is possible with little effort. However, the computing time for the analysis of the second solution will increase significantly, but this is barely noticeable in this small model. The FE model is to be built up using shell elements, because the leaf spring is a geometry with constant thickness. The leaf spring, which consists of individual layers of sheet metal, is considered here for simplicity, as one contiguous body. So we neglect that the sheet metal layers can slide off each other. This would be the case if the sheet layers would be bonded to each other, welded or riveted. If slipping of the sheet metal layers shall be taken into account, so in addition, the method of non-linear contact must be inserted. This would be rather an appropriate task for the NX/Nastran solution method 601, which provides advanced nonlinear methods.
Linear analysis will be compared with non- linear analysis.
4.3.1.5 Preparation and Creation of the Solution for Linear Statics First, the necessary components or assemblies are loaded into the NX system. The geometry of one leaf spring is contained in the file hr_blattfeder, but the geometry of one clamp is also required, because here the force applied to the leaf spring is marked. An assembly which includes both parts is the file hr_ubg_schelle. ÍÍOpen the file hr_ubg_schelle.prt into the NX system. ÍÍThen turn into the application Advanced-Simulation and generate the file structure in the simulation navigator. ÍÍWhen asked for the bodies to be used, select the option None. We must consider that shell elements are to be used and therefore no body from the original geometry has to be converted into a polygon geometry. Rather, a mid-surface
We want to use shell elements.
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needs to be generated and will then be used. Therefore, we first use the None option and later replace the selection against the mid-surface. ÍÍAll other default settings can be accepted with OK. ÍÍIn the subsequent question about the solution, confirm the default settings for linear statics, i. e., the solution 101. Later in the non-linear solution we need to change the solution type. There is no need to assign material properties, because they have already been defined in the master geometry of the leaf spring.
4.3.1.6 Generating a Midsurface and Adding it to the Polygon Geometry ÍÍFirst, change into the idealized part. Before the mid-surface is generated, the individual sheet metal layers must be joined into one body. For the union, in turn, it is necessary that the various bodies are wave-linked. The steps for the generation of the mid-surface.
ÍÍTherefore, first create four wave links of the four sheet metal layers. ÍÍHide the assembly hr_ubg_schelle using the assembly navigator. ÍÍSwitch to the modeling application, and unite the four sheet metal layers into a single body. ÍÍBack in the simulation application, select the function Midsurface by Face Pairs and select the united body. ÍÍSet the option Strategy to Manual. ÍÍSelect at Select Side 1 Face one planar side surface and at Select Side 2 Face the second planar surface. ÍÍThen select the switch Create Face Pair and click OK.
The leaf spring is idealized by a midsurface.
ÍÍTo add the mid-surface to the polygon geometry, switch to the FEM file. ÍÍIn the simulation navigator use RMB on the top node and select the EDIT function. ÍÍActivate the button Edit Bodies to use in the following menu. ÍÍIn Bodies to Use select the option SELECT. ÍÍSelect the newly created mid-surface. ÍÍSelect in addition the clamping sheet (see figure above). This is later used to define the location of force application. For that, you need to briefly unhide it using the assembly navigator. ÍÍConfirm with OK.
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Now the mid-surface and the clamping sheet are taken over into the polygon geometry and can be further processed and meshed.
4.3.1.7 Edge Subdivisions on the Polygon Geometry In order to realize the transmission of force into the generated mid-surface, the lower edge of the mid-surface, as shown in the figure below, must be divided. An edge must be divided for the later application of force.
The function of dividing edges operates in a similar way as the function for face subdividing, whereby it does not operate on the basis of CAD but rather polygon geometry. Because those geometry preparations on polygon geometry have significant advantages in performance over those on CAD, there is a whole series of functions available for geo metry preparations on polygon geometry. There is also an additional function for face subdivisions. That means, face subdivisions may be performed on both CAD and polygon geometry. Next, those functions for editing polygon geometry will be explained:
Auto Heal: You specify a tolerance for small features. All geometry features with dimensions smaller than the tolerance will be ignored during meshing. In addition, specifically for fillets it can be indicated by the option Process Fillets whether they are to be ignored in meshing.
Split Edge: This feature allows subdivisions of edges as it is necessary in our example for the application of force.
Split Face: Herewith faces can be divided. The function Subdivide Face that is available in the idealized file works quite similar. The decisive difference of these two functions is that the function in the FEM file works on the basis of the polygon model.
Important functions for manipulating the polygon model at a glance.
Merge Edge: This function allows the joining of two adjacent edges.
Merge Face: The function is used for combining two faces of a sheet. The edge between the two individual faces disappears. This feature is important as preparation, if geometry is to be meshed, whose faces are composed of many individual pieces (patchwork). The meshing can thus be effectively improved.
Stitch Edge: This powerful feature allows edges to adapt to each other that have small distances, as it often occurs with imported geometry from external CAD systems. A special feature is also that more than two edges can be joined together, as for example in the case of T-joints to be meshed with 2D elements.
Unstitch Edge: This function disconnects edges again, which were prior combined with the Stitch Edge function.
Merge Face and Stitch Edge are two particularly useful features.
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Important functions for manipulating the polygon model at a glance.
Collapse Edge: With this function, small edges of the polygon model are combined to form points. All subsequent edges or faces will fit in accordance with the changed new edge. This is very effective to simplify small edges.
Face Repair: Using this function, a polygonal surface can be re-created if it is damaged.
Reset: This function clears all previous polygon edits. It can be selected on faces or on whole bodies.
Circular Imprint: With this function, circular area subdivisions can be created around points or circular edges. This can be used to quickly create face divisions for example for screws or similar conditions.
ÍÍIn order to divide the edge for the subsequent load application for our example task, select the function Split Edge. ÍÍSelect the edge approximately at those two points to which the clamping sheet adjoins. For this, use the type Location on Edge. ÍÍCreate in this manner two edge subdivisions. ÍÍNow hide the clamping sheet polygon body.
4.3.1.8 Meshing for Analysis with Nonlinear Geometry In the subsequent analysis, including large deformations, linear elements must be used, i.e. elements without mid nodes. If quadratic elements are used, the non-linear effect in solution 106 is not taken into account. This restriction does not apply in the Advanced Non-linear solution, i. e. the solution 601. ÍÍThe meshing of the mid surface is to be performed with a 2D mesh. ÍÍTherefore, select the element type CQUAD4 and for the element size, for example, three. The result is a mesh with two element layers in the thinnest area. This mesh fineness should be achieved at least. In solution 106 elements without mid nodes are needed.
Quad4
ÍÍEdit the resulting mesh collector ThinShell(1). ÍÍAssign the thickness of 90 mm to its physical properties at Default Thickness.
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4.3.1.9 Generating the Boundary Conditions On both sides of the leaf spring, in which the bearings are arranged, create the usual supporting structures (spiders), as shown in the figure below. Both sides are rotatably supported. Moreover, one side can translate.
ÍÍCreate the 1D Connecting Point-to-Edge with type RBE2 each from the center of the circle to the shown edge. ÍÍTo create the boundary conditions, switch to the simulation file. ÍÍFor the rotatable support you create a User Defined Constraint which is set according to the previous figure to the right so that there only remains free rotation about the desired axis of rotation, i. e. DOF4. ÍÍOn the second side there is a boundary condition needed that allows rotation and displacement. For this, the corresponding degrees of freedom of the User Defined Constraints are set according to the previous figure.
4.3.1.10 Creation of Loads for Two Load Cases
In order to draw a comparison between small and large deformations, one small and one large load is applied to the leaf spring. To achieve separate analysis of these two loads each will be solved with its own solution. The additional solutions will be created later. All loads under consideration can be stored initially in the Load Container, as shown in the figure above. Later, the loads are then assigned to the corresponding solutions. The two loads are generated on the previously sectioned edge of the mid surface. Proceed as follows: ÍÍCall the function Force and select the previously divided edge of the mid surface. ÍÍSelect Y for the direction and enter a value of 500 N. ÍÍName the small force, for example Force_small. ÍÍCreate in the same way a force with the amount of 20,000 N and the name Force_large.
We use a load case for large and one for small force. The load cases are calculated successively.
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4.3.1.11 Creation of a Second Solution for Linear Statics We want to compare several solutions with each other.
A solution for linear statics has already been created when producing the file structure. All loads and boundary conditions that are available have been incorporated in this solution. It should be noted that any force or constraint occurs twice in the simulation navigator: once in the container and once under the solution. The first solution will be changed so that it contains only the small force. You will therefore now remove the large force from the solution, while the large force is not deleted from the Load Container. This has the advantage that the large force can be applied in another solution.
Proceed as follows: ÍÍSelect the large force at solution Solution 1. ÍÍUse the RMB function Remove. Now, each solution contains its own load.
The force disappears from the solution, but remains in the Load Container. ÍÍIn order to distinguish this solution later by another, rename the solution element with a meaningful name, such as S_Lin_F_small. Furthermore, we need a second solution, which is similar to the first. ÍÍTherefore, we use the function Clone in the context menu of the solution element and thus receive an identical copy of the first solution that you manipulate as follows: ÍÍRemove the small force and add the large force. The removal works as described above. Adding can be done by dragging the element Force_large from the container and dropping into the new solution. So you pull it in the new solution element into the group Loads at Subcase. ÍÍFinally assign an appropriate name to the new solution, for example S_Lin_F_large. It is possible now to solve the two solutions. In practice, one would go this route now, i. e., one would always perform the linear before any non-linear analysis and check whether everything (except for the non-linearity) is plausible.
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For simplicity we want to go a way in which first all necessary elements of the solutions are created and then all will be calculated together.
4.3.1.12 Generation of Solutions for Nonlinear Statics Now follows the creation of two solutions corresponding to the previously already created, where the non-linear solution method must be chosen. ÍÍTo insert a new solution in the simulation, use the function Solution bar.
from the tool-
It appears the familiar menu of the Solution. ÍÍTo activate the consideration of non-linear geometry, select the Nastran solution type SOL 106 Nonlinear Statics - Global Constraints (in earlier versions of NX it was called NLSTATIC 106). ÍÍSelect the Parameters tab and select Large Displacements according to the following figure.
Nastran Sol 106 is the “small” non-linear solution of Nastran.
ÍÍConfirm with OK. The new solution element is now added. The new solution does not yet contain constraints and no loads. ÍÍTherefore, drag both constraints from the Constraint-Container into the group Constraints of the new solution. ÍÍNow drag the small force from the Load Container into the group Loads of the new solution. ÍÍRename the new solution with a meaningful name, such as S_NL_F_small. Finally, we need the second non-linear solution in which the large force is inserted. ÍÍClone the newly created non-linear solution.
The solution method for simple nonlinear statics has the designation 106.
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ÍÍRemove the small force and drag the large force into it. ÍÍName this solution S_NL_F_large. So now there are four solution elements, which are solved in the following section. ÍÍSave the file.
4.3.1.13 Automatic Processing of All Solutions Several solutions can be processed in batch.
Each solution can be solved with the function Solve, but also all solutions can be sequentially processed automatically. This is useful in the case of our example. ÍÍUse the function Solve all Solutions in the RMB context menu of the simulation node.
All four solutions are solved one after the other.
Now NX Nastran is called four times one after the other. Depending on the system performance, the analysis may take some time. The end of the computations is indicated by a corresponding message.
4.3.1.14 Contrast and Evaluate Results After all four solutions were calculated, the results shall be compared. According to our task, the displacements of the supporting point that is connected to the swing arm are of interest. Therefore, the results of the displacement in Z-direction will be considered and compared.
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With the large force the results of the linear and non-linear analysis differ significantly from each other.
It yields the results listed below for the four different solutions: S_Lin_F_small (small force/displacement, linear analysis): 1,13 mm S_NL_F_small (small force/displacement, non-linear analysis): 1,07 mm S_Lin_F_large (large force/displacement, linear analysis): 45 mm S_NL_F_large (large force/displacement, non-linear analysis): 9,3 mm The results show that the difference between the linear and non-linear analysis for small deformation is small. For large deformations, however, there is a considerable difference. The large force (20,000 N) is exactly 40 times the small force (500 N). Therefore, in the linear analysis, the computed displacement at large force (45.26 mm) is very precisely 40 times the deformation at small force (1,132 mm). Only the repeated updating of the stiffness in non-linear analysis can take the non-linear effect correctly into account. Therefore, here the more realistic, much smaller deformation (9.3 mm) is calculated. So, this learning task is completed.
4.3.2 Plastic Deformation of the Brake Pedal Brake pedals of vehicles must always be analyzed for their strength behavior at maximum pedal pressure. It must be found which permanent damage will be caused from maximum load. Therefore, here, an analysis is performed under a static pressure on the pedal. Here also plastic material behavior shall be considered. In addition, pressurized parts must usually also be examined for buckling. This aspect is neglected in this learning task, however. With buckling analysis possible instabilities of geometry are found, that cannot be found in the static analysis. In practice, such studies are usually covered by tests. The object of the analysis is to minimize the number of tests.
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Brake pedals must bear heavy loads, which can lead to material flow.
This example shows how non-linear plastic material properties can be considered in static finite element analysis using the RAK2 brake pedal. The solution method employed for this purpose is the Nastran solution 106, which was already used in the example of large deformation of the leaf spring. As an alternative to the solution 106 plastic material behavior can also be calculated with solution 601, which opens up even further possibilities in non-linear region. We want to point out that prior to such a non-linear analysis, a linear analysis should always be performed, in which the plausibility of the results is checked (except for the missing non-linearity). Thereafter, the non-linearity should be inserted.
4.3.2.1 Task The brake pedal should be analyzed under the load at kick down. At full braking power, it is assumed that, including a safety margin, a force of 4000 N operates on the pedal. If it comes to plastic deformation, the deformed shape after releasing the pedal force and the remaining residual stress state of the pedal shall be determined. Given are the material properties of the steel with the non-linear stress-strain curve. The non-linear stressstrain curve is considered in the analysis.
σ [N/mm2]
ε
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4.3.2.2 Models for Plasticity In plastic deformation, loading processes along the non-linear stress-strain curve, while release proceeds only elastic. Here a number of effects play a role, which are described within the program through appropriate analysis models. The models for plasticity can be adapted.
In principle, all these computation models can be changed and adapted, but when using the NX user interface there are always presets applied and passed to NX Nastran, which are useful in many cases. If changes are required, this can be done in material properties at Stress-Strain Related Properties. Following some important effects and terms are explained with respect to plasticity: Yield Stress: The yield stress is typically measured as the stress value which causes minimum permanent deformation. In NX this specification can be found in the Strength registers. Yield Function Criterion YF: In uniaxial tension, there is a unique stress value from which plastic flow occurs. In multiaxial stress states, however, stress components exist in the different directions. In this case a criterion is required, indicating the combination of stress components at which first plastic flow occurs. This criterion is called the yield criterion. It describes in the coordinate system of the three principal stresses a surface – the yield surface – beyond which plastic material flow is assumed. In NX Nastran, there are four different flow criteria: von Mises, Tresca, Mohr-Coulomb and Drucker-Prager. The von Mises criterion is usually used in plastic analysis of ductile materials. This criterion is applied by default by NX. If another criterion is to be used, this can be defined in material properties at Stress-Strain Related Properties. σ2
σ2
σ1
σ3
Yield Surface (3D)
σ1
Yield Surface (2D)
The yield surface describes the space within which elastic material behavior is assumed.
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The hardening rule indicates how the flow surface is modified when the yield surface is exceeded.
σ2
σ2 1
2
1
σ1
0 3
2
yield surface new yield surface
isotropic hardening
3
σ1
0 new yield surface yield surface
kinematic hardening
Yield Surface: The yield surface in the stress space describes (σ1-σ2-σ3) the range within which no plastic flow occurs. For the von Mises yield criterion the yield surface corresponds just to a cylinder. Hardening Rule HR: If material is plastically deformed, it usually hardens. Here, the yield surface changes. Isotropic hardening occurs when the yield surface expands and kinematic hardening when it shifts. The NX system uses the isotropic hardening method by default. If another criterion shall be used, this can be defined in material properties at Stress-Strain Related Properties.
4.3.2.3 Preparations and Generating the Solution ÍÍOpen the part bs_bremspedal.prt in NX from the directory of RAK2 and switch to Advanced Simulation. ÍÍUse the simulation navigator to create the file structure with the idealized part, the FEM part and the simulation file. NX Nastran solution 106 takes into account nonlinear material behavior.
ÍÍWhen asked about the solution method, you switch to the Nastran solution type SOL 106 Nonlinear Statics – Global Constraints (in previous versions of NX also called NLSTATIC 106) ÍÍAll other settings can be retained. Click OK to confirm, and then the file structure with the solution method is created.
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4.3.2.4 Simplifying Geometry ÍÍFor the following geometry simplifications, go to the idealized part. ÍÍFirst, create a wave link of the brake pedal geometry (step 0 in the figure below) and hide the part bs_bremspedal in the assembly navigator. ÍÍIn the next operation the treadle board is removed (step 1 in the subsequent figure). For this purpose use the function Delete Face from modeling application and select all faces that belong to the treadle board. Further we assume a symmetry about the center plane, although strictly seen, this is incorrect for the one-sided bearing. ÍÍCreate a datum plane in modeling application and trim the geometry accordingly (step 2 in the figure below). ÍÍNext, you remove the flange for securing the cables, because we are not interested in results here. For this, create another plane and trim operation. At the same time simplify the cylinder for the rotatable support (step 3 in the figure below).
Functions of group Synchronous Modeling are very suitable for geometry preparations.
Finally, the CAD model for the analysis is prepared.
ÍÍIn the last step, you extend the cylinder for the rotatable mounting again using the function Move Face by about 20 mm. This way, you get a simple geometry for the area of constraints at which the results also do not interest (step 4 in the figure). Thus, the operations for geometry preparation are completed. ÍÍSave the file, switch back to the application Advanced Simulation and change to the FEM file for subsequent meshing. ÍÍIf the simplified body does not appear in the FEM file, also add this to the polygon bodies.
4.3.2.5 Meshing for Plastic Analysis To obtain accurate stress results first a convergence proof of the required mesh fineness would be necessary. Especially when using four-noded elements a high fineness of meshes is required for precise statements. But in this example no special emphasis will be placed on high accuracy. Rather, qualitative statements shall be made. Therefore, we content ourselves with a somewhat refined standard mesh, which contains about two element layers through the thickness of the material. Proceed as follows:
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ÍÍMake the FEM file to the displayed part. ÍÍSelect the function 3D-Tetrahedral Mesh. ÍÍSelect the geometry and select from the menu CTETRA10. The mesh should have at least two layers upon the thickness.
Tet4
ÍÍEnter an appropriate value in Overall Element Size, which produces a two-layer mesh. You get a basis for an appropriate value by clicking on the button for the proposal of element size and share the suggested value by two, three or four. For example, you can use a value of 3.33 mm. ÍÍClick OK to confirm, then the mesh is created.
4.3.2.6 Defining Plastic Material Properties The plastic material properties are defined in the material editor. They include elastic modulus, Poisson’s ratio, yield strength and stress-strain curve. We want to create a new material for this. Proceed as follows:
The Yield Strength of the material must be specified.
ÍÍCall the function MAIN MENU > TOOLS > MATERIALS > MANAGE MATERIALS. ÍÍHere you select the function Create Material . The dialog for creating a new material appears. ÍÍEnter any name. ÍÍEnter for Young’s Modulus the value 210 000 N/mm2 and for Poisson Ratio 0.3. ÍÍIn the register Strength enter at Yield Strength 160 N/mm2. ÍÍFinally, the definition of the stress-strain curve follows with non-linear material behavior. This is entered at Stress-Strain Related Properties. Before this the dialogue must be expanded with More.
ÍÍSet the selection to Field and select the Table Constructor in Specify Field. ÍÍFrom the Table Constructor you choose the option Strain for Independent.
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ÍÍEnter value pairs corresponding to the figure below in the window that appears now. When entering a value pair the two numbers for strain and stress are separated by a space and terminated by RETURN. ÍÍClick OK twice and then click CLOSE. Each pair of values defines one point on the stress-strain curve. For our example, it is sufficient when you just add the curve up to 10 % strain, i. e. so up to the row ID 12 with the value 0.1044. The non-linear stressstrain curve is defined via a table and can be displayed as a graph.
The points of the stress-strain curve must satisfy the following conditions: N/mm2.
All stress values must be specified in the unit The first pair of values must be zero – zero. The stress value of the second pair of values must match the yield stress previously set. The second pair of values must reflect the modulus of elasticity. In the case of our example, therefore the following must be: 160 N/mm2 / 0,0007619 = 2,1e5 N/mm2.
These conditions must be met when entering the non-linear material.
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ÍÍAfter you have defined the properties for the material, you assign it to the geometry of the brake pedal. ÍÍSave the file. Thus, non-linear material properties are created and active. If stresses above the yield point will appear in the subsequent analysis with solution 106, plastic flow of the material will be calculated.
4.3.2.7 Defining Boundary Conditions There are four boundary conditions required to describe the loading condition of the brake pedal (see figure below). Proceed as follows: ÍÍFirst, change into the simulation file. ÍÍDefine a force with − 2000 N on the face of the treadle board, pointing perpendicular to the face, by selecting the type Normal in the force function. The model of the brake pedal is provided with these boundary conditions.
ÍÍYou also define a Pinned Constraint on the cylindrical face of the bearing. This function allows merely rotation. ÍÍIn order to eliminate the last degree of freedom (turning around the cylinder), define a constraint on the opposite side of the pedal force that restricts only the motion in X-direction. This corresponds to opposing forces through the brake cable. ÍÍFinally, define the symmetry condition at the interface. ÍÍIt turns out again a conflict in the boundary conditions. Resolve this by permitting only the symmetry condition.
4.3.2.8 Define Load Steps for Loading and Unloading Each load step that occurs in the solution is processed in sequence. In NX Nastran solution 106, each stress distribution resulting from a load step is starting point for the subsequent step. Thus, a first step can be defined for loading and a second for the discharge in the following. The first load step contains all constraint conditions and the intended load. In contrast, the second step contains only the constraints and no load anymore, because it automatically receives pre-stress of the first step. The first load step should already have been created automatically.
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ÍÍTo generate the second load step, choose the function New Subcase in the RMB menu of the solution and confirm the dialog with OK. The result is an initially empty load step. The loading and unloading is defined by two load steps. The second load step is preloaded with the results of the first.
The chosen solution SOL 106 with the addition Global Constraints uses all constraints globally, i. e. in all existing load cases. This characteristic can also be recognized from the presentation in the simulation navigator, because there is only one constraint group in the solution. Therefore, we don’t need to assign the constraints to the second load case anymore. The loads are already correct, because in the new second load case, there is no load included. The result in the simulation navigator should look like the figure above.
4.3.2.9 Calculate Solutions and Evaluate Results ÍÍAfter the model has been set up so far, the Solve function can be performed to compute the solution. The computation can use significantly more time as it would be the case in a linear analysis because of non-linearity and the two last steps. ÍÍAfter the completion of the solve process, switch to the post-processor. At the results node in the simulation navigator, you will now find the two load steps. Among the load steps, you find the results for Displacement and Stress. Below the results node the two load steps are shown.
As result, for the first load step there are displacements of about 1.7 mm and stresses of about 161 N/mm2, thus a stress that is in the range of the material’s yield strength. The second load step shows the status after discharge. The analysis has found permanent displacement of about 0.02 mm and residual stresses of about 50 N/mm2.
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The stress state and deformation before and after the discharge is shown.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
An analysis with linear material behavior should be made always prior to such with a non-linear behavior. (This can now very quickly be made up by inserting a new solution 101 and adding of the boundary conditions). Here, slightly smaller displacements of 1.69 mm and significantly higher stresses with about 200 N/mm2 arises. Thus, elastic material shows higher stresses, while for plastic already local yielding occurs. Due to slight yielding, in turn, higher displacements result for plastic material. It should be pointed out that a mesh refinement is required and to support the findings convergence (mesh independence) needs to be proved. ÍÍSave the file and close it. With this, this learning task is completed.
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■■4.4 Learning Tasks Advanced Nonlinear (Sol 601) 4.4.1 Snap Hook with Contact and Large Deformation Snap hooks are popular types of closures for plastic components that are assembled manually. In the design you want to know, for example, how much force is required to assemble such a closure. Moreover, the material in the process must not be too highly stressed. On the model of the RAK2 such a link can be found at the battery box. Snap hooks are popular types of closures for plastic components.
On this task, the basic handling of the NX Nastran solution method 601 will be described which is available for complex non-linear effects based on a plastic snap closure. A timedependent travel path will be defined, which controls the mounting operation of the cover. In this way it is possible to determine the force which is required for the assembly process. In addition, non-linear effects of large deformations and contacts are used. Recommendations are made, how to deal with complex non-linear effects in NX.
The Nastran solution method 601 is intended for complex non-linear analyses.
We want to point out that before any non-linear analysis, simple linear analysis of the problem should always be performed. If several types of non-linearity occur simultaneously (e. g. plastic material and contact), non-linear effects should first be tested individually. In our learning task, we are in violation of this rule, thus we work directly with non-linearities because the limited scope of the book forces us to.
First, in order to develop a “feel”, there always should be analyzed linear.
4.4.1.1 Task The battery box of RAK2 is mounted with plastic snap closures as shown in the figure above. Here the cover at all four sides has one hook that latches into a corresponding opening of the housing. Given are material properties of the plastic material and the geometry. It is to be analyzed, which stresses the snap hook is exposed to when the installation is done in small steps.
The battery box is to be mounted.
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4.4.1.2 Preparation and Creation of the Solution ÍÍLoad the assembly as_bg_batterie that contains the housing, cover and some other parts. ÍÍThen switch to the application Advanced Simulation and generate the file structure for the new FEM and simulation using the simulation navigator. ÍÍWhen asked for the bodies to be used select the option Select Bodies and select the geometry of the cover and the housing.
ÍÍNow the menu Solution will appear. Here you select for solution type ADVNL 601, 106. The solution method 601 can be set versatile.
First, all settings remain at their default. ÍÍConfirm all settings with OK.
4.4.1.3 Change Start Position in the Idealized Part The starting position should be the opened battery box.
During the simulation the cover shall switch from the open state into the closed. However, the cover is constructed in the closed state. And this closed position in the master CAD assembly should not be changed, because this is required for users who for example look at a 2D drawing of the assembly. The CAD assembly is the master model to be used for all subsequent applications such as analysis, preparation of drawings or fabrication support. If different positions of parts to each other are needed for our simulation, repositioning must be performed in the idealized file.
The position of the cover shall be moved for the analysis.
The original assembly position of the cover therefore must be overridden in the idealized file. In the view of the idealized file there will be another position than from the view of the real assembly. Proceed as follows to achieve this: ÍÍFirst, make the idealized file the displayed part. ÍÍSwitch into the application Modeling and make sure the application Assemblies is enabled. Now you have access to assembly capabilities of NX. ÍÍNow open the assembly navigator and select the cover as_bat_deckel. ÍÍUsing RMB, select the function to override the position Overwrite Position and then the function Move .
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Now the cover can be moved to the desired position, as shown in the figure below. The snap hook should ideally be positioned just before the point of contact. For this, you can also use the dimensions of the figure below. ÍÍApply for Z the value from the picture below, i. e. −16.25, and press ENTER. The cover is now repositioned for the FEM analysis.
ÍÍConfirm with OK. The repositioning, solely for purposes of simulation, is now done successfully. If you want, you can now change back into the application Advanced Simulation and check the old position, by making the master part in the simulation navigator the displayed part. Then go back into the idealized file. The new position is now active again.
4.4.1.4 Simplification and Partition of Geometry The geometry of the cover and the housing should then be idealized, hence the number of finite elements can be kept low on the one hand, while on the other hand, the remaining geometry is not substantially different from the stiffness properties of the original geometry. Therefore, the symmetry property should be exploited. The requirement for a small number of finite elements is even more urgent, the more it comes to non-linear effects that must be taken into account because growth of computing time by non-linearities is tremendously. You will see that even this task significantly needs more processing time than all linear tasks so far. It is therefore necessary to find a sensible compromise. In addition, it would be advantageous if the idealized geometry could be meshed by hexahedral elements instead of tetrahedral, because with these elements greater uniformity and better accuracy can be achieved. Meshing with hexahedral is always possible when a solid is extrudable, i. e., if it has a surface which can be filled with squares drawn through the whole body. In this way, hexahedral or brick elements are created. The geometry of our example could for example be simplified and partitioned in the manner shown in the figure below. The stiffness of the original geometry would remain largely intact, and the ability for HEX solid meshing would exist for both parts.
Especially for non-linear analyses, elements should be “saved”.
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The battery box and snap hook are simplified for the FEM analysis. A few CAD operations are performed.
ÍÍCreate wave links and perform geometry operations in the idealized file to obtain a corresponding geometry. ÍÍSave the file.
4.4.1.5 Mesh Mating Conditions Mesh mating conditions of type Glue Coincident ensure that partitioned areas of the body will be meshed with aligned nodes. It is recommended to turn on the Create Mesh Mating Conditions option already in the idealized file when creating the partitions with the split body function. In that case, these conditions would be automatically generated now in the FEM file. The partitioned geometry shall have identical and merged nodes at the boundaries.
Otherwise, proceed as follows: ÍÍChange to the FEM file. ÍÍCall the function Mesh Mating Condition . ÍÍEnsure that the option Glue Coincident is active. ÍÍDrag in the graphics area a window over all parts and confirm with OK. The Mesh Mating Conditions are now created on all four partitions.
4.4.1.6 HEX Solid Meshing of the Housing This time stresses in the contact area itself are not of particularly interest for us. The geometry might therefore be only roughly meshed here. However, experience has shown that difficulties with sharp edge contact surfaces may arise, as they appear, for example, if fillets are meshed very coarsely. Therefore, the fillet at which contact will first occur and slide, should be meshed refined. This way contact surfaces should become as smooth as possible. The fillet at which the first contact occurs should be meshed fine.
ÍÍCreate a Mesh Control of type Number on Edge on the fillet edge in the contact area and apply a number of four elements there.
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ÍÍFor the subsequent meshing call the function 3D Swept Mesh , set the type to Until Target and select for the Source and Target the two surfaces shown.
ÍÍSelect Hex8 elements and element size as the default value that you will receive with the yellow flash. Click OK to confirm, then the mesh is generated. The mesh should look like the figure below. The hexahedral mesh is very even. The contact area mesh is refined.
4.4.1.7 HEX Solid Meshing of the Snap Hook The body for which stress results are of substantially interest is the snap hook. Furthermore, here stresses in the bending area especially interesting. Therefore, a finer mesh must be generated here. In the remaining area of the snap hook the mesh can be coarser. Now our suggestion, how the snap hooks should be meshed, but certainly there are other reasonable ways. Just check it out once. This area will get five element layers across the thickness.
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ÍÍFor meshing the bending region of the snap hook, call the function 3D Swept Mesh set the type to Multibody Infer Target and select the face as shown above.
,
Using the option Multibody Infer Target you need to select only a starting face. The other option additionally requires a target area selection. But this second option has another advantage: It can pass the mesh through several bodies when they are connected by Mesh Mating Conditions. ÍÍAs element type, select Hex8 and as element size e. g. choose half of the suggested value. ÍÍAt Use Layer enter the desired 5. Now click on OK. This method allows you to mesh fine across the thickness and however coarser in depth. ÍÍNext, you will create, according to the following figure, again a mesh control having five elements on the fillet edge in order to also fine mesh that risky area.
ÍÍIn order for the refined mesh to gradually transition to rough again, create now, according to the figure below, on the four edges additional mesh controls. This time you use the type Biasing on Edge, which makes it possible to define such transitions. Set the options as shown in the figure below. With several mesh controls on edges it is defined how the mesh should behave here.
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ÍÍNow, the remaining parts can be meshed. Use element sizes, as shown in the figure below. A successful HEX solid meshing of the snap hook.
4.4.1.8 Add Preparation for Reaction Forces As result we want to calculate the force, which is used to assemble the snap hook. This force, which will arise as reaction force in the displacement constraint condition, can be represented at any time step and displayed as graph. For simple reading of this force, we now want to create a point-face connection on the surface of the later displacement condition: ÍÍSelect the function 1D Connection.
ÍÍSet the element to RBE2 and the type to Point to Face. ÍÍUse the function Point Dialog to define this point at the coordinate (x: 35, y: 10, z: − 18.5) and select the face corresponding to the previous figure. ÍÍClick OK to confirm, and the connection will be created.
4.4.1.9 Material Properties for Plastics The material of the two bodies should be glass fiber reinforced polypropylene. This material can be found as Polypropylenes-GF in the material library of NX at category Plastics.
Later we want to give the enforced motion to this point.
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Alternatively, you can define the material manually. The following properties are required: Modulus of elasticity: 3000 N/mm2 Poisson’s ratio: 0.4 ÍÍAssign the material Polypropylen GF to the bodies. This library’s material is a simple linear description of the material. Recommendations for the analysis of plastic materials.
If plastic materials are calculated linearized, the resulting error must be estimated.
For dealing with plastics in FEM analysis, we make the following recommendations, which can be found more detailled in [Alber-Laukant] and [RiegHackenschmidt]: Indeed plastic components show in principle a non-linear stress-strain behavior. However, there is almost always a linear region of the material properties. Even over this area, the analysis with constant modulus of elasticity and Poisson’s ratio can be made until the error caused thereby in the application can no longer be tolerated. The procedure for analysis of plastics should therefore go as follows: On the basis of resulting stresses of a first rough analysis with linear material properties it will be decided, if the stresses are still in linear or already in non-linear region. Only in the second case it is contemplated whether the error is tolerated or analysis is performed with non-linear curve.
stress
resulting error
linear approximation non-linear material behaviour
strain When the non-linear stress-strain curve shall be calculated . . .
Such a material non-linearity can be added easily in the Nastran solution 601. The material would have to be defined in the way it was the case in the example with the plastic brake pedal. Only the setting Type of Non-Linearity should be set to NLELAST. This abbreviation stands for non-linear elastic, meaning that the behavior is elastic, i.e. reversible. Therefore, if an unloading of material occurs, it follows the same curve again back down. Thus, there will be no permanent deformation. This model is often used in plastics, when it is required to calculate non-linear.
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4.4.1.10 Define Contact ÍÍFor the contact surface definitions and other boundary conditions you make the simulation file the displayed part. For contact definition there is the recommendation to first select the finer meshed surface area. This way it will be included in the Source region. The coarser meshed area should be selected secondly and assigned to the group of the Target region. The contact algorithm will ensure that nodes of the first region may not penetrate faces of the second region.
The two sides of contact should not be chosen arbitrarily.
In our example, it cannot be answered clearly which side is finer, since we are changing the mesh sizes of contact partners. If in doubt, also a computationally more elaborate twosided contact could be chosen, which can be activated at the contact parameters.
ÍÍCall the function Surface to Surface Contact . ÍÍHere you select the type Manual. ÍÍSelect for the Source Region the fillet face of the housing and the lower planar surface, since here is the mesh finer first. ÍÍSelect for the Target Region – in accordance with the previous image – the three tangential faces of the snap hook, which can come into contact. ÍÍEnter 0,1 for Coefficient of static Friction.
Upon contact, the finer meshed side should be selected first. With specification of contact friction the analysis becomes more complex.
All other menu settings you let as initially preset. ÍÍClick OK to confirm, after which the contact element is generated.
4.4.1.11 General Information about Solution ADVNLIN In solution 601 all boundary conditions should be applied time-dependent. The time will then run through gradually, on the basis of given time steps. Indeed in the case of solution 601.106 no dynamic effects are taken into account. That means it does not matter if we use one or ten seconds as the period of simulation. However, if you use the solution 601.129 or even 701, dynamic effects are calculated from time steps and defined movements. Then the simulated period must be selected necessarily realistic. In most applications of solution 601, it is even recommended to define forces or enforced displacements time-dependent, because this way smooth transitions can be achieved
The analysis is performed in many small steps.
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from one time step to the next, which in turn improve the convergence behavior of the solution. For this reason, time-dependent traverse paths, which move the snap hooks from its initial position to the closed position, will also be defined in this example.
4.4.1.12 Define Time Steps The smaller the time steps, the easier the solution converges.
Since in our chosen solution 601.106 no dynamics are taken into account, the size the time period is not an important indication. Only boundary conditions must be adjusted accordingly, because they are defined time-dependent. But the number or the size of time steps are important variables, because the smaller time steps are, the easier each step can converge.
ÍÍFrom the RMB menu of the solution, select the EDIT function, and in the following menu select the tab Case Control. ÍÍNow you choose among Time Step Intervals the function Create Time Step Intervals. ÍÍA dialog appears for the definition of time step intervals. For us it will be sufficient to define only one interval. Now select Create. You realize that the Number of Time Steps defaults to 10 and the Time Increment is 1 sec. There results a simulation period of ten seconds. Therefore the traverse path has to be defined for this period in the following. We want to use those 10 sec, but have a finer subdivision of the period, so we change this element as follows: ÍÍChange the number of steps to 50 and the increment to 0.2 sec. ÍÍClick OK to confirm and add the interval with ADD to the list. Now click CLOSE and OK.
4.4.1.13 Definition of a Time-Dependent Travel Path The installation of the snap closure is divided into time increments.
Traverse paths correspond to enforced displacement boundary conditions. This can be defined in NX either by an Enforced Displacement Constraint or by function User Defined Constraint that would also be possible. ÍÍCall the function Enforced Displacement Constraint.
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Among Type, there are various options for defining the displacement direction. It is best to use the option Components, in which all degrees of freedom can be set separately in coordinate directions. In our case, the Z-direction is critical to the forced way. All other components will be kept fixed. ÍÍSet the Type to Components and select the point, which is connected via RBE2 elements with the surface. ÍÍEnter zero in all degrees of freedom, except for the DOF3, i. e. the displacement in the Z-direction. Both the translational as well as rotational degrees of freedom have significance in this casebecause we add the constraint to a point that is coupled to a face.
For the time-dependent way at DOF3 set the selection to Field. ÍÍFor the definition of the field, it is easiest to use a table here. So you switch at Specify Field to the Table Constructor and create a field for the desired displacement. ÍÍAt Table Field first the independent variable, i. e. the time must be indicated. Therefore, choose the option Time in the box Domain at Independent.
The path is defined by a table.
The dependent variable is already defined as Length with units of mm. Now single xy pairs of values of the desired function can be specified. If there are only a few pairs of values like in our case it is advisable to enter them manually. We want to create a linear function that is 0 mm at time 0 sec and 17.5 mm at time 10 sec.
The independent variable is time, the dependent the way.
ÍÍEnter in the box below the pair of values “0 0”, followed by ENTER. ÍÍAlso enter the second value pair “10 17.5” and click ENTER. The value pairs are added to the table. If desired, the defined field can be represented as a graph.
The traverse path can be entered in the form of value pairs.
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The newly created table is assigned to the boundary condition.
ÍÍConfirm with OK and you’ll be guided to the previous menu. So you finally arrive back in the menu for defining the boundary condition. In the field for DOF3 the new, time-dependent field is now listed. ÍÍFinally confirm with OK. The time-dependent displacement constraint is now created.
4.4.1.14 Defining Further Boundary Conditions In addition to the time-varying displacement there are only a fixing of the housing and a symmetry condition necessary. ÍÍCreate a fixed constraint on the face of the housing, as shown in the figure below. ÍÍGenerate symmetry conditions on the faces belonging to the plane of symmetry. The housing is constrained fix.
There is a boundary condition conflict because on one edge two conditions exist: the symmetry condition and the RBE2 elements. If we would try to solve the model this way, an error message pointing to this conflict would appear. This conflict cannot be resolved automatically, rather we have to exclude this edge from one of the two conditions. The easiest way is as follows:
4.4 Learning Tasks Advanced Nonlinear (Sol 601) 261
ÍÍUse RMB on the symmetry condition you just created and from its context menu choose EDIT. ÍÍClick on the text Excluded. It opens another selection field. ÍÍIn this selection field, select the edge marked in the figure above that we want to exclude from this condition. Now click OK.
4.4.1.15 Activate Option for Large Displacements For this example, the solution should be performed taking into account large displacement effects. This option must be activated as follows: ÍÍUse RMB on the solution node from the simulation navigator and select the EDIT function. ÍÍSwitch to the Parameters tab and activate the switch Large Displacements.
Large displacements must be enabled when changing the stiffness.
In solution 601 the option for non-linear geometry or large displacements is activated.
4.4.1.16 Attempt to Solve without Automatic Time Stepping By default, none of the available automatic time stepping schemes is enabled. We will first attempt a solution with all the default settings, i.e. without time step method. We will try and interpret the results. The next section then follows the use of the main automatic time stepping method ATS (Auto Time Stepping). ÍÍPerform Solve . ÍÍDo not cancel the monitor solution! ÍÍYou will find that a result has been generated, in which only a few time steps have been computed. In the first steps that were apparently successful, the snap hook is simply moved a little. Then no more solutions have been calculated. To understand this and to find help, the analysis method of the non-linear solver will be described below.
4.4.1.17 Understanding Newton’s Method To understand the solution course, it needs to be explained how the non-linear solution method called Newton’s method works. The bent curve in the figure below represents a real non-linear force-displacement behavior of a model, which is caused for example by a material plasticity. It is now the task of the calculation to give a force on the model and to calculate the deformation along this curve.
Without time stepping contacts mostly cannot be calculated.
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Time steps pass through the external loads or boundary conditions specified by the user.
The Newton method uses an outer and an inner iteration loop. We call the outer loop time steps, which is marked with Δt in the figure below, and the inner loop equilibrium steps i. Let’s first look at the time steps. In this loop, the loads or other boundary conditions are passed through according to their chronological definition. Therefore, let us imagine an FEM model and a load applied on it at one time step. Thus with the finite elements the stiffness matrix K is set up and with the force F, the deformation U is calculated. Would the model behave linearly, so this would be sufficient, i. e., one would obtain correct deformations immediately. However, if non-linearities are in the game, that means contact, plasticity or non-linear geometry, we would not calculate correct deformations.
This illustration explains Newton’s method.
K t(+i −∆1t)
K t(i+)∆t
K t(+i +∆1t)
Ft + ∆t non-linear behaviour of model, e.g. due to plasticity
U(i)
U(i+1)
U(i+2)
The fact that a model behaves non-linearly is computationally identified by the fact that some convergence criteria are not satisfied. Such convergence criteria are formed from values that are also known as residuals, such as the difference between the external and internal energy in the overall model. Other such residuals are formed, for example, for contact forces that must indeed be in a plausible balance. If these residuals are large, so we are obviously far from the non-linear curve, and corrections must be made. Equilibrium steps reduce the residuals/errors.
Now equilibrium steps i come into the game for the correction of errors: The errors come from the fact that we have determined the initial stiffness of the model, whereas this stiffness has changed as a result of non-linearity. A hopefully and probably enhanced stiffness is obtained by resetting the stiffness matrix with the already deformed model and the updated contact forces and material properties. Then we already have two stiffnesses: one for the first part of the force and one for the second part. The result is thus again a deformation result. Of course, this result of the deformation is not error-free, which is reflected back to the residuals, but the errors are likely to become smaller. Are the residuals still too large, that is larger than specified limits, an additional equilibrium iteration is needed, etc. If the residuals are smaller than the limits so we can assume that a physically meaningful result is present, including the non-linearity for this time step. In this case we say that the time step Δt has converged, and the next one will be applied.
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4.4.1.18 Understanding of Solution Development based on the Solution Monitor The task now is to figure out why the analysis could not be continued. Here, the solution monitor of the Nastran analysis provides information. All time steps, equilibrium iterations and the course of the residuals are shown there. In the case of our analysis, which apparently was able to perform successfully only the first time steps, the representation of the solution monitor is shown in the figure below. The figure shows an analysis that did not converge. It has terminated at 1.4 out of 10 sec.
The left side of the figure shows the register Non-linear History of the solution monitor. On the Y-axis there is time, and on the X-axis there are equilibrium iterations shown. In our time step definition we called for 50 steps, each with 0.2 sec to be performed. Therefore, the first step at time of 0.2 sec has been done. The graph shows that this time step has converged, and that further steps up to time 1.4 seconds were performed. But the following time step has been aborted. To look up why this following time step did not converge, we look into register Load Step Convergence of the solution monitor. This figure now displays information only for the latest time step. Along the X-axis we see the number of equilibrium iterations and along the Y-axis there is the size of the examined residuals. The curves show that energy and contact residue were examined. It is typical that residuals are large at the beginning and then become smaller and smaller. When they reach the limit 1, this means that they have fallen below their respective threshold. So we wait and hope that these limits are reached. The energy residuum seems to have reached there soon, but the contact residuum not yet after 15 equilibrium iterations.
The residuals indicate problems.
A presetting allows a maximum of 15 equilibrium iterations in one time step. In case until then no convergence was reached, the analysis of this time step is aborted. So our analysis has successfully computed the first time steps. These will also be shown in the result, but no additional ones.
In our case, the contact residuum could not converge.
So in the following we need to clarify possibilities for influencing this.
4.4.1.19 Ways to Achieve a Convergent Solution In order to improve conditions to successfully carry out a complete solution, there is a number of ways. In this section, some of these options are described, but only a small in-
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sight into the extensive control parameters of solution 601 can be given. A full presentation of all settings and recommendations can be found in [nx_adv_nonlinear]. If no convergence can be achieved, there are numerous adjustments.
A list of recommended setup parameters.
Increase number of equilibrium steps: The number of equilibrium steps can be increased to improve the solution conditions. This is especially recommended if it is found that the convergence limits already have almost reached their limits using the pre-set 15 steps. The associated default setting Maximum Iterations per Time Step can be found at RMB menu of the solution (EDIT > CASE CONTROL > STRATEGY PARAMETERS > EQUILIBRIUM). Increase number of time steps: Increasing the number of time steps significantly improves conditions for finding solutions, because each step becomes smaller. However, it also results in considerably greater computation times. The corresponding parameter Number of Time Steps can be found at the Time Step Interval option in the Case Control register. If step numbers are increased, time increments should of course be reduced accordingly, so that the solution periods remain the same. Use of ATS: The use of the automatic time stepping method ATS is a highly recommended option, especially in the presence of contact. The method allows time steps that cannot converge to automatically be reduced repeatedly. On the other hand, time steps are again increased if previously problems are performed successful. In this way, time steps can be adjusted very fine at problematic areas. Nevertheless, working in the remaining areas will be done with coarse time steps for not to waste computational power. The use of ATS is described in the next section. Use of Low Speed Dynamics: This function is often very helpful. It adds dynamic inertia forces to the computational model. These forces result in stabilization of motion, thereby improving convergence. Changing convergence limits: Increasing the limits leads to easier convergence finding, but also to less accurate solutions and is therefore not recommended. Decreasing them leads for each time step to a more accurate solution, or perhaps unfortunately to none at all. Nevertheless decreasing often helps because this way inaccuracies are not even allowed that may lead to problems at subsequent time steps. Two convergence limits, which are used by default are to be found at the tab Equilibrium and are called Relative Energy Tolerance and Relative Contact Force Tolerance. Allow small contact penetration: If small penetrations of contact surfaces may be allowed, the parameter Compliance Factor (CPACTOR1) is very effective to improve conditions for solution convergence. This parameter can be found in the contact menu at Advanced Nonlinear (BCTPARA). The larger the value, the more penetration is allowed. The penetration should be checked visually in the results. Use of friction-free contact: Use of the coefficient of friction leads in many cases to worse conditions for solution convergence. In case friction is not very important, therefore, omitting the coefficient of friction and using a zero setting leads to successful solutions. In rare cases, however, the reverse may be true: By non-zero friction solution finding is favored.
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Settings that affect equilibrium iterations of Newton’s method.
In general it can be said that for non-linear computations, all physical quantities must be selected sensibly and realistically. While for linear analysis nonsensical input quantities give a result (which then of course is nonsense), in non-linear analysis unrealistic input quantities mostly lead to no solution at all. Therefore, all input magnitudes should be critically examined in terms of their closeness to reality, if the analysis does not bring converged solutions.
4.4.1.20 Solution with Automatic Time Stepping The automatic time stepping (ATS, Auto Time Stepping) is a highly recommended method for improving the solution finding. Therefore, this method is almost always turned on at practical tasks. ATS controls time step size with the aim to obtain converged solutions. In case that with the given time step size no convergence can be achieved, the program automatically reduces the time step size and tries again to bring the solution to convergence. In some cases the time step is also enlarged allowing a solution to accelerate. ATS is enabled at STRATEGY PARAMETERS> ANALYSIS CONTROL by setting the option Automatic Incrementation Scheme to ATS.
For non-linear analysis, the input parameters must be chosen realistic.
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The automatic time step method is almost always used.
Settings for the ATS scheme can be found at register ATS. In the previous figure default settings of ATS are shown which will be used in our case. However in many cases it is useful to adjust the control parameters as explained in the following. A full explanation to all control parameters can be found in [nx_qrg]. First of all the Division Factor (ATSDFAC) is of importance, which indicates how fine a time step is partitioned, if it has not led to convergence. The default 2 means that a non-converged step time is divided by 2. ATS reduces time steps. Control is defined here.
However, the time steps should not be arbitrarily small. Therefore, the finest possible subdivision is specified with the parameter Smallest Time Step Size Number (ATSSUBD). Thus, the default 10 means that the time step should not be less than one tenth of the original value.
If a time step could be calculated successfully, it must be decided how large the sub sequent time step should be. The flag Post-Convergence Time Step Size Flag (ATSNEXT) decides how to proceed in this case. There are the following possibilities: Settings for the behavior after a sub-division.
0: The setting is selected by the program, that is, 2 if contact is present, otherwise 1. 1: The last time step size, which has led to convergence, is further used. 2: The user-specified, original time step size is used. 3: A time step is determined so that the solution time matches the original solution time, which was given by the user. If a time step should be increased, the Maximum Time Step Size Factor (ATSMXDT) specifies the maximum magnification.
4.4 Learning Tasks Advanced Nonlinear (Sol 601) 267
ÍÍBecause the default settings of the ATS will be used for our example. Select only the ATS (found at: EDIT > CASE CONTROL > STRATEGY PARAMETER > ANALYSYS CONTROL > AUTOMATIC INCREMENTATION SCHEME). ÍÍNow run the solution Solve again. While solving is running the solution monitor can be reanalyzed, as shown in the figure below. At the beginning (left side of figure), it shows the same behavior as before, i. e., the first steps were successful, the step 1.4 sec was not.
Now the solution will be solved completely.
However, we now allow by the ATS, that the time step not converged is reduced to half. It can be seen that this subdivision has been sufficient. Thus convergence has been achieved. Next time steps initially run without problems. The right side of the figure shows the course of further progress. Several times ATS does its work and successfully reduces time steps. The whole analysis can be successfully completed in 10 sec. ATS allows the division of critical time steps.
4.4.1.21 Optional Interrupting the Solution for Checking Often one would like to interrupt Nastran solution 601 and have its previously calculated time steps written into the result file because you do not want to wait until the end to check the result. This can be achieved as follows: 1. Create a text file in your working directory with the name tmpadvnlin.rto. 2. Write into this file the text Stop=1. 3. Save this file. 4. Wait a while until the Nastran job stops and generates its results achieved so far. 5. Open the results in the post-processor. Even further runtime parameters can be changed in this file during the run. Look at [nx_adv_non-linear] as needed. Incidentally, also a restart function is available, that allows the analysis to continue. Details are found at [nx_adv_non-linear].
The analysis may be interrupted, e. g., if the end of the complete analysis shall not be waited for.
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4.4.1.22 Post-processing Once the ten seconds have been successfully computed, the result can be analyzed in the post-processor. ÍÍOpen the results in the post-processor. The ten steps are displayed individually. Each of the steps includes displacements, stresses, reaction forces, etc. The following figure shows an example of the 21st load step at which the snap hook already slips on the housing surface. Here now stresses and reaction forces can be read. At the last load step, the snap hook is snapped into the opening and reaches its rest position. With ATS, the solution was performed completely.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
If a movie of the motion is to be displayed, the images from each iteration are used.
ÍÍWith non-linear results, it is important that the preset exaggeration of display is turned on its real calculated value. Set the scale factor to 1 and the type to absolute. This can be found under EDIT POST VIEW > DEFORMATION RESULT. ÍÍTo make a movie of the entire traverse path, the Animation function must be set according to the following figure so that the option at Animate is set to Iterations.
ÍÍNow the function Play played as a movie.
can be started. The full path of the snap hook is now dis-
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4.4.1.23 Alternative Simplified Analysis Methods We want to conclude by pointing out that snap hooks, depending on the task, even in very simple manner, can be calculated sufficiently. In practice of plastic constructions, there is often merely the question of the occurring stress or strain at full deflection of the hook. If this forced displacement is known – e. g. it is simply assumed that the housing is rigid and the enforced displacement of the geometry can be determined – then simple linear analysis is sufficient.
Snap hooks in practice are analyzed usually simplified.
Suppose the forced displacement is 2.5 mm. The hook then gets a fixed constraint and a unit force (Fnorm) on its contact area with the size of 1 N. In a linear finite element analysis the resulting displacement of the hook under this force comes out as u1N. For example, there results a displacement of u1N = 0.1 mm. Linear scaling, i.e. simple analysis of 2.5/0.1, yields the factor for the force required (Frequ). That is, the force required is 25 N. In a second analysis (or again by upscaling the first result), the hook is calculated under this force. A linear analysis with unit force is used to find the stiffness. Thus, the force factor is derived.
A second possibility is that instead of force rather an imposed displacement is applied (as in the learning task “Design of a coil spring” in section 4.2.2), in which the contact surface is moved by exactly the required 2.5 mm. The matching force can then be read in the results as a reaction force. The analysis with Sol 601 and the two simplified analysis methods differ in the following: The simplified methods calculate the deformed state directly and sol 601 moves the full path. Also, in sol 601 the hook is slightly less deformed because of the contact that applies deformation to the housing. This learning task is now finished.
Alternatively, the required enforced displacement can be imposed directly.
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Bibliography [Alber-Laukant] Alber-Laukant B.: Struktur- und Prozesssimulation zur Bauteildimensionierung mit thermoplastischen Kunststoffen. Validierung von Werkstoffbeschreibungen für den technischen Einsatz. 1st Edition. Shaker-Verlag 2008 [Binde4] Binde, P.: NX Advanced Nonlinear FE-Analysis with NX/Nastran Solver. Training Documentation. Dr. Binde Ingenieure GmbH, Wiesbaden 2014 [Dubbel] Grote, K. H./Feldhusen, J. (Hrsg.): Dubbel. Taschenbuch für den Maschinenbau. 21st Edition. Springer Verlag, Berlin/Heidelberg/New York 2004 [nx_adv_non-linear] NX Nastran Advanced Non-linear Theory and Modeling Guide. Documentation for NX Nastran Installation [nxn_dmap] NX Nastran DMAP User’s Guide. Online documentation for NX Nastran [nxn_non-linear106_1] NX Nastran Basic Non-linear Analysis User’s Guide. Online documentation for NX Nastran [nxn_non-linear106_2] NX Nastran Handbook of Non-linear Analysis (106). Online documentation for NX Nastran [nxn_qrg] NX Nastran Quick Reference Guide. Documentation for NX Nastran Installation [nxn_user] NX Nastran User’s Guide. Online-Documentation for NX Nastran [nxn_verif] NX Nastran Verification Manual. Online documentation for NX Nastran [RiegHackenschmidt] Rieg F./Hackenschmidt R.: Finite Elemente Analyse für Ingenieure. Eine leicht verständliche Einführung. 3rd Edition. Carl Hanser Verlag, München 2009 [RoloffMatek] Muhs D./Wittel H./Jannasch D./Voßiek J.: Roloff/Matek Maschinenelemente. Normung, Berechnung, Gestaltung. 21st Edition. Springer Vie weg, Wiesbaden 2013 [SchnellGrossHauger] Schnell, W./Gross, D. Hauger, W.: Technische Mechanik 2: Elastostatik. 3rd Edition. Springer Verlag, Berlin/Heidelberg/New York 1989
5
Advanced Simulation (CFD)
With the module NX Advanced Simulation CFD tasks of fluid mechanics, complex thermal problems and coupled thermal/fluid tasks can be solved. This is possible with one solver for thermal analysis (NX Thermal) and one for fluid analysis (NX flow), that can be coupled if necessary. With these solvers, also the third type of engineering simulations in the NX system can be treated: the fluid mechanics. The module Motion-Simulation treats the rigid body mechanics, the modules Design- and Advanced Simulation FEM treat the structural mechanics. In this book, we focus on the fluid solver (NX Flow) and the methodology required for this purpose. Technical Simulation can be classified in four parts.
Technical Simula on Rigid Bodies Rigid Body Mechanics MBD (Mul body Dynamics)
Elas c Bodies Fluids Structural Mechanics Fluid Mechanics FEM CFD (Finite Element (Computa onal Method) Fluid Dynamics)
Electric Bodies Electromagne cs (EM) FEM (Finite Element Method)
Since Advanced Simulation is fully integrated into the NX system, the same tools and methods for meshing used in structural analysis are available for fluid mechanics. In the production and preparation of geometry, the known methods from the field of CAD can be used. This simplifies the application for beginners significantly. In addition, the resulting data can be stored and managed in the PDM system Teamcenter together with the design.
CFD-Analysis is integrated in the standard NX simulation environment.
It should not be denied that flow analysis and the applied solution method Computational Fluid Dynamics (CFD) are complex issues that should not be applied without basic knowledge of fluid mechanics and methods of numerical analysis. Because of the nonlinear characteristics of flow analysis, meaningful and convergent solutions result only when the input variables are chosen realistically. A comparison with experimental results has to be done in many cases in order to confirm the results.
CFD users should have prior knowledge.
In section 5.1, some principles are discussed to give a basic understanding of the theoretical backgrounds. In section 5.2 a learning example shows the methodology of fluid flow analysis on airplane wings in a flow passage.
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■■5.1 Principle of Numerical Flow Analysis For flow analysis the basic conservation equations for mass, momentum1 and energy are solved. An established numerical solution method for the three above-mentioned transport equations is the finite-volume method (FVM), which is used here. Five conserved quantities are balanced on the cells.
The principle of the finite-volume method is as follows: First, the area in which the equations shall be solved, is divided into a finite number of cells. In each of these cells, the conservation laws (transport equations) are valid. The change of a conserving quantity (i. e. energy) in a cell can therefore only happen through incoming or outgoing flow over the edge of a cell and in special cases through a source or sink.
A typical analysis mesh (C-network) for the CFD analysis of an airfoil.
If these flows are calculated (or at least a good approximation), a system of equations which describes their change over time in the cells can be set up. This system of equations is finally solved approximately using numerical methods. A wide application of CFD is possible only since the 90s.
Because of the high computational effort, wide applications of flow analysis with FVM have only become possible through the intensive use of hardware. Therefore, a practical use is possible only since the early 90s. The main advantage compared to experimental measurements, such as those in wind tunnels, results from the spatial (and transient) display of the variables pressure, velocity and temperature.
1 The momentum conservation equation is also known as Navier-Stokes equation.
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■■5.2 Learning Tasks (NX-Flow) 5.2.1 Flow Behavior and Lift Forces at a Wing Profile The wings at the RAK2 should formerly ensure that the car does not lift at higher speeds. To produce the required downforce, they have been made with a negative angle against the airstream, as it can be seen in the CAD model. Later it turned out that the positive curvature of the wing is more lifting than downforcing, and therefore a negative curvature would have been more appropriate. For the experimental investigation of such a flow around a wing, measurements are often carried out in wind tunnels. Therefore we also want to investigate the case of a wind tunnel flow in this learning task.
We will take a look at the wing in a wind tunnel. Formerly the wings should keep the RAK2 on the ground.
5.2.1.1 Exercise In order to investigate the flow around the wing, the CAD model of the RAK2 wing will be examined in the wind tunnel using the CFD method in NX Advanced Simulation. The goal is to determine the flow speed around the profile and the overall flow directions. In addition, the lift and drag which are caused by the wind shall be determined.
We want to calculate lift and drag at 100 km/h.
It should also be evaluated from the results whether the flow on the profile is attached or separating (detection of swirl and dead water regions). The wing is being inclined with a negative attack angle of 10 degrees to the incoming flow. The travel speed shall be 100 km/h.
Detection of swirl and dead water region.
5.2.1.2 Preparing the CAD model of the wind tunnel ÍÍOpen the file fl_fluegel_links.prt from the RAK2 directory in the NX-system. ÍÍMake Layer 2 visible because here the flow chamber of the wind tunnel is located (via FORMAT> LAYER SETTINGS> TURN ON LAYER 2). Your model should now look like in the following figure.
One-tenth of the real space should be enough for our investigation.
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The flow chamber of the wind tunnel could be used completely, for simulation of the whole span of the wing. The result would be the forces on one of the two wings. However, the analysis would take some time to complete, and this would hardly improve the learning effect. Therefore, we want to calculate only a minor part of the space for this learning task. Those who wish can calculate the whole room. Therefore the CAD parameter p107 would have to be changed from 150 to 1500 mm. CAD parameters help adjusting the geometry.
Edge effects due to vortex strings could also be calculated.
So we calculate the flow chamber with only about one-tenth of its original size. The forces that we compute can then later be multiplied by a factor of 10 in order to get the full flow force. Of course, this is not quite right, because the edge effect of the wing with its expected vortex strings enters the real power result not simply linear. So we neglect this effect, but you can of course perform the complete analysis as desired.
5.2.1.3 Creating the File Structure and Selection of the Solution ÍÍStart the application Advanced Simulation and create a new FEM and Simulation in the simulation navigator through the context menu of the master-node. ÍÍIn the menu new FEM and Simulation switch the option Bodies to Use to SELECT and select the flow chamber body. ÍÍAs Solver select NX THERMAL/FLOW (see figure below), which is designed for complex thermal and fluid flow analysis with the CFD method. As Analysis Type select the option Flow, this means the pure flow simulation without coupling to the thermal analysis, because in this example we are only interested in flow results. ÍÍConfirm with OK. The file structure is now created.
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For the CFD analysis, a file structure is created within the NX system. The figure on the right shows the settings of the CFD solution. The default settings can be used initially.
Now the menu Solution will appear. Here, the detailed properties of the solution process such as the turbulence model can be set. The following sections explain some important options. Changes in the time step size, the convergence criterion, the turbulence model and the result outputs are made for our example problem. ÍÍTherefore, confirm the Solution menu with OK, whereupon the solution element is created with the default settings. Some settings are changed in the following.
5.2.1.4 Time Step Size and Convergence Limit The time step that is used for the numerical solution method has a significant impact on whether a solution is found at all and how fast this happens. The default value for the time step size in the NX system is 0.5 sec. This value should normally be set carefully by the user. The meaning of the time step and convergence control will be considered because changes to these settings should usually first be made when convergence problems occur.
The time step affects the computational speed and convergence.
The time step size controls the size of a solution step in the iterative procedure of the CFD solver. The smaller the time step is, the more prone the solver is to resolve transient (time dependent) effects in the flow. Therefore, the step size must not be too small. In addition, the computation time increases with smaller time steps. With a larger time step, the analysis will be faster, and with a too large time step, the solution diverges and may even result in an incorrect simulation result. The convergence criterion provides control over when the analysis is completed. For a convergent solution, the convergence parameter must be less than the convergence criterion. The graph of the convergence parameter can be observed in the Solution Monitor while solving. This is explained in section 5.2.1.21, that also contains hints for the time step size and convergence criterion. An indication (cf. [Maya], [Binde5] and [ESCref]) for an appropriate time step size dt for stationary analysis can be obtained by the equation
The convergence criterion controls the accuracy of the solution.
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dt =
L V
where L (e. g., the length of the stream along the wing) is a characteristic length, and V is the average velocity of the fluid. A rule of thumb for the time step.
L = 1475mm V=100Km/h
Accordingly, the appropriate time step size for our example is about 0.05 sec. It can now be set (in this case the default size of 0.5 leads to the same result): ÍÍSet the simulation file as work and displayed part. ÍÍFrom the context menu of the solution element, choose Edit Solver Parameters and open the register 3D Flow Solver. ÍÍEnter the value of 0.05 sec as Time Step. Time step and convergence control in the NX system.
In addition, the convergence criterion shall also be scaled down by a factor of 1/10, so that the solution is more precise. ÍÍEnter a value of 2e-5 for Maximum Residuals. ÍÍConfirm with OK.
5.2.1.5 Selection of a Turbulence Model Technically considered flows are almost always turbulent.
Laminar filmy flow only occurs at low Reynolds numbers. Here, each particle moves in a straight line and parallel to its neighboring particles. Once the critical Reynolds number (about 2320 for pipe flow) is exceeded, the flow switches to turbulent. In this kind of flow tiny vortices exist, that lead to a strong mixing of the particles. Almost always, technically considered flows are turbulent. Laminar flows only occur in special cases. Examples are high-viscosity fluids such as in extruding operations and flows in small dimensions (microfluids, gap flows).
NX has six different predefined turbulence models.
The Turbulence Model option in the settings of the solution element controls the lence model for the analysis. The seldom-used option for purely laminar flow is None in NX. In addition to this option, which does not imply turbulence, the six lence models are: Fixed Turbulent Viscosity, Mixing Length, K-Epsilon, SST Shear
turbucalled turbuStress
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Transport, K-Omega and LES – Large Eddy Simulation. The last three models are only available with solution type Advanced Flow, which also requires an extended license. Since turbulent flow is expected in almost all technical applications, especially with larger Reynolds numbers, a turbulence model should be used, except in those cases where a simple test analysis is performed. The available models differ in terms of their accuracy and the required computational effort. The following passage provides an explanation of the six models: The model Fixed Turbulent Viscosity only provides low accuracy. With this model, an equivalent turbulent viscosity is calculated as a fixed value throughout the flow. Because this method does not account for local differences and works very coarse, it should not be used. The Mixing Length model is more accurate than the model Fixed Turbulent Viscosity and also requires more computational effort. Here, the turbulent viscosity is calculated at each node depending on the respective flow rate, density, and the so-called Mixing Length. The Mixing Length is calculated from the distance of the node to the next wall and a characteristic length. This turbulence model also no longer corresponds to the current state of the art and should therefore not be used.
The first two turbulence models are only recommended for coarse test analysis.
The turbulence models K-epsilon, K-omega, and SST are the most accurate but also computationally very expensive.
The K-Epsilon model is more accurate than the Mixing Length model but requires more computing time. The turbulent viscosity is thereby also calculated at each node. The specific kinetic Energy (K) and Dissipation rate (Epsilon) are used for the analysis of the turbulent viscosity. The model requires no additional license. Therefore, it will be used in our example. The model K-Omega is also a proven model that can be used as an alternative to K-Epsilon. It calculates the turbulent viscosity as well as the K-Epsilon at each node. The kinetic energy (K) is also calculated. Instead of the Dissipation rate used in the K-Epsilon model, a specific Dissipation rate (Omega) is calculated. The model SST Shear Stress Transport can be used as an alternative to K-Epsilon or K-Omega. It bridges the gap between the two: In proximity to the wall, it behaves like the K-Omega and inside the flow as the K-Epsilon. This model is mainly used
The models SST, K-Omega, and LES are only available with the Advanced Flow license.
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when it comes to the exact analysis of shear stresses or temperature transitions at walls. Among the available models in NX, the model LES (Large Eddy Simulation) calculates turbulences the most accurate but also with the highest computational effort. While in all other turbulence models, the Reynolds-Averaged Navier-Stokes (RANS) equations are calculated, LES does not use this simplification. Instead, the turbulence is divided in large and smaller Eddies and processed differently. The large ones are calculated in a direct method, resulting in a high mesh resolution requirement. For the small eddies additional assumptions are made. For more information about the turbulence models, see [nxflowref] and the online help. In our example we use the K-Epsilon turbulence model.
ÍÍTo activate the K-Epsilon turbulence model, choose the option EDIT. ÍÍSelect the tab Solution Details and then the option K-Epsilon in Turbulence Model from the context menu of the solution element. ÍÍConfirm with OK. It makes sense to carry out just a rough preliminary investigation of the flow first and then to use only a very simple turbulence model as the preset Mixing Length model. In our learning task we will skip this procedure.
5.2.1.6 Request Y+ Result Y + helps with precision control.
To judge by the results, whether the mesh fineness at the walls is well set, a dimensionless quantity called Y+ is used. By default, this quantity is not written into the result file. Therefore, we will select this option now: ÍÍAgain, select the EDIT function at the solution element. ÍÍOpen the Results Options tab, open the box 3D Flow and turn on in the switch Y+. When evaluating the results, we will come back to Y+ and give further recommendations.
5.2.1.7 Some Further Options of the Solution Element After time step size, convergence limit, turbulence model and Y+ are suitably set, additional options of the solution element can be considered if necessary. We explain some important settings below. The following options can be found in the context menu of the solution element at the EDIT option in the register Solution Details: Some optional features and settings.
The directory option Run Directory creates a directory, and all auxiliary files such as log files, etc., which are created during the analysis, will be stored in this directory. If gravity effects should be taken into account, the switch Buoyancy must be activated. In this case, the magnitude and direction of gravity must be specified in the tab Ambient Conditions. In single-phase and isothermal flows, only the hydrostatic pressure distribution is calculated by the buoyancy.
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With the option Solution Type switched to Steady State, a steady flow analysis will be performed. With Transient selected, a time-dependent flow analysis can be activated. Other settings for the time-dependent analysis can be found in the register Transient Setup. The initial fluid temperature, pressure, and velocity can be defined in the register Initial Conditions. In some cases, the computation can be accelerated by adjusting these variables to the real situation. Unfavorable settings in this register can cause a sharp deterioration of the conditions of the solution. Therefore, the default automatic option is recommended to be set to automatically adjust the speed and pressure in the beginning. The Register Restart allows the continuation of a previously interrupted analysis. The interruption of a solution for a later restart must be performed with the Pause function in the Solution Monitor, which appears during the computation. In this way, for example, only the first time steps can be performed and then the result can be checked. If necessary, the analysis can then be restarted from this point by enabling the Restart option and then Solving the solution until the final convergence is reached.
In this case we can solve transient.
The ability to restart can save much time.
All of these settings, however, should only be changed if necessary, as they are suitably preset in most cases, as in our example. Therefore, we want to continue with further steps of creating the simulation model.
5.2.1.8 Strategies for the Creation of the Flow Volume The finite elements (or better finite volumes) in flow analysis must, of course, mesh the fluid volume and not the wing itself. Therefore, in many cases, the first task is to create or derive this fluid volume as a CAD model. In the case of our example, we have the finished flow volume already available in the original file fl_fluegel_links.prt. We prepared this to ensure you can focus on the fluid analysis. However, this preparation is not entirely correct, because the flow volume should not be in the original file, the preparation for the simulation should be made in the idealized file. Imagine that a geometry is calculated for which the CAD file has no write permission.
The flow volume must exist as a CAD model.
The right place for the creation of the flow volume in the real case is therefore the idealized file. Here a wave link or promote feature of the wing should be created and then the flow volume can be built up upon it. In the case of our example, the flow volume has for once already been created in the original master file to relieve the user from this time consuming work. We would like to point out that the NX system with the function group Synchronous Modeling has excellent tools for the derivation of interior volumes from the CAD geometry.
5.2.1.9 Strategies for Meshing in Flow Analysis In the NX system there are two alternative possibilities for the creation of a mesh for flow volumes: Ordinary meshing in the FEM file: the meshing for the flow volume can be made in exactly the same way as in structural analysis. It can consist of tetrahedrons and hexa-
Synchronous Modeling offers excellent possibilities.
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hedrons, and grid controls or 2D networks can be used. The Mesh Mating Conditions are possible and useful to connect the meshes with each other. The fluid domain mesh is specially made for CFD analysis.
Special fluid domain meshing in the Sim File: Especially for flow volumes this is the alternative and recommended method. Exceptionally, this mesh is not generated in the FEM file, but created as a simulation object in the simulation file. The special feature of this type of meshing is the ability to easily generate element layers at walls. Especially when flow forces or temperature transitions shall be calculated, these wall layers are very helpful to achieve good result accuracy. We want to choose the second method for our example. Of course the first one would also work. Just check it out!
5.2.1.10 Generating and Visualizing a Fluid Domain Mesh The fluid domain mesh is unusual.
The fluid domain mesh is exceptionally defined in the simulation file. At this point the concept of CAE file structure is not implemented fully consistent with the idealized file, the FEM and the SIM file. Also the type of visualization of the mesh takes some time to get used to, it is in fact created only before the solve process takes place. To control the mesh, without running a full CFD analysis, we have to use an unusual way. For the definition follows these steps: ÍÍStay in the simulation file and select the function Fluid Domain among the simulation objects. ÍÍLeave the type setting on Fluid Mesh and assign the name VolumeMesh.
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ÍÍSelect the fluid volume. ÍÍFor Fluid Material you select the option Air.
Also, the material is assigned here.
It is also unusual that the material is specified at this point. ÍÍChange the element size to 70 mm (absolute). ÍÍConfirm with OK. The element size can be specified either absolute or relative. The default option is Relative. Then the option of Element Size Type is set to Relative, in element size a percentage size is specified. The preset number 0.06 means that 6 % of the size of the whole component is set as the element size. This would be a reasonable number for a very coarse mesh. The Absolute option is activated by setting the Element Size Type to Absolute. Then the desired element size is specified directly. To see the mesh, the solver has to be running.
Well, of course, we want to see how this mesh will then look like. The somewhat unusual way to visualize the fluid domain mesh is as follows: ÍÍSelect the option Solve and at Submit switch to Write Solver Input File. ÍÍConfirm with OK. Now a window appears that displays the work of the mesher. Once this window is gone, the mesh is generated. You should notice that the simulation navigator now displays results. These results include nothing more than the mesh. ÍÍTo view the mesh, go to the post-processor and open the results. The mesh is displayed and can be checked. Now a fairly coarse mesh should be shown. The various quality criteria (Aspect Ratio, Size, . . .) can be reviewed. These are now shown instead of the results in the post-processing navigator. ÍÍOnce you have inspected the mesh visually, unload the result file again (right click on Result, Unload).
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First, the fluid domain mesher generates common tetrahedrons.
5.2.1.11 Defining Boundary Layers for Meshing A special feature of the fluid domain mesh is the easy way to create wall layers and fine tune these to the requirements of the flow (boundary layer resolution). The flow results depend quite strongly on this method, especially when temperature transitions or flow forces are of interest. The special feature is the specific indication of the thickness of the wall layers.
The thickness of the first layer at the wall influences this particularly because the software uses a wall function for the flow variables in the first wall layer. This means that the realistic, highly complex and turbulent flow conditions in the boundary layer are not really calculated, but are recognized and adjusted. This matches reality relatively good because it is approximately known how flow variables behave at walls. The advantage resulting from this is that the wall film can be meshed much coarser than it would be required without the wall function. Nevertheless, there remains the question of an appropriate thickness of the first layer of the wall elements. In order to access this, the already requested Y+ result helps us.
The Y + result later helps in deciding whether the chosen thickness is good.
In the following, we first want to create some sort of wall layers and then judge based on the Y+ results, if the thickness has to be changed. ÍÍSelect the function Fluid Domain . ÍÍSet the Type to Fluid Surface Mesh and assign the name SurfaceMesh. ÍÍSelect the four faces of the wing profile. With the following function a mesh refinement on the four surfaces is activated. ÍÍActivate the option Specify Local Surface Mesh Density and enter an Element Size of 15 mm (absolute).
Here the layers are defined.
With this next function you finally get the layered mesh. ÍÍActivate the switch Create Boundary Layer Mesh. ÍÍEnter a First Layer Thickness of 3 mm, a Total Thickness of 30 mm and 5 as Number of Layers. Create this mesh again and inspect it. It should look like the figure below.
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In the figure the wall layers can be seen.
5.2.1.12 Material Properties for Flow Analysis We have already assigned the material Air. To see which properties are processed behind it, in the material editor the material can be selected and the function Inspect Material can be called. Density and dynamic viscosity are the most important material properties for fluid flow analysis.
The following material properties are needed for CFD analysis: Mass Density Thermal Conductivity Coefficient of thermal expansion (required for gravity effects) Dynamic Viscosity (corresponds to friction in the liquid) Specific Thermal Capacity at constant pressure (this quantity corresponds to the ability to store heat and has no effect on stationary problems) Gas constant (required for gases and must be zero for liquids)
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5.2.1.13 Overview of Flow Boundary Conditions We describe only selected boundary condition types.
The NX system allows the definition of different boundary conditions for the flow analysis. These are flow surfaces, fans (intake, etc.), openings and filters (porous materials), and other conditions, which are very special and should be excluded here. Before the necessary boundary conditions are applied to our specific example, the main conditions that are available in the NX system will be explained in the following overview. Only the most common options will be shown. A comprehensive presentation of all types of conditions as well as the theoretical background can be found at [ESCref11a].
5.2.1.13.1 Flow Surfaces Flow surfaces belong to the essential boundary conditions for fluid flow analysis with CFD.
Flow surfaces are defined by the function group Flow Surface in the NX system. The most important2 of the available types here is the Boundary Flow Surface representing a simple wall condition (see figure below). In our example, such a boundary condition is needed at the wing profile. This boundary condition type is important because in areas that have such a condition, additional results concerning the forces are automatically calculated by the solver. This particularly helps to determine lift, forces and moments which are transmitted from the flow to the boundary surface. In our example case, it is important to estimate the lift at the wing.
The menu for the main wall condition.
The surface roughness plays a role in the boundary condition, too.
At a flow surface, the flow velocity or the mass flow perpendicular to the wall is always set equal to zero. In this way, any flow is prevented by the wall. Furthermore, it must be determined how the speed shall run along the wall. In reality, this depends on the surface condition of the flow surface. The NX system provides these three options:
Slip Wall: boundary condition to the environment or symmetry.
With the Slip Wall function, a frictionless wall is defined. In this case, there can be no more friction definition. In this way, a boundary condition to the external environment of the analyzed flow volume is defined, for example, if the real volume actually continues. The flow along the wall may move freely but cannot pass through the wall. 2 The other types that are available here are generally focused on the definition of small interfering elements (Obstructions), such as electronic components on a circuit board. These types shall not be considered further here.
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The wall friction option Smooth – With Friction shall be set for hydraulically smooth walls. Hydraulically smooth walls are all machined (turned, milled). In this condition, the flow velocity at the wall is set to zero or to the speed of the wall if it is moving. The Rough option at the wall itself applies the same condition as the option Smooth – With Friction. Wall functions are also applied here, the switch should therefore be turned on for this. For the usage of such wall functions, the roughness of the wall and its influence will then be included in the border flow. Therefore, a roughness height must be specified in such a case. A classic application for this are rough cast surfaces.
Smooth for turned or milled surfaces.
To describe the flow behavior in the region near to the wall, special logarithmic wall functions are used that allow an already acceptable result accuracy even with relatively coarse mesh resolution. These wall functions are automatically activated when using the Mixing-Length and K-Epsilon turbulence models. Because we use the K-epsilon model, the switch Use Wall Function has no meaning in our case. The wall function will in any case be enabled. Only when using the more complex turbulence models SST, K-Omega or LES this switch is relevant. Turning the wall function off only makes sense if the behavior of the flow shall be calculated in detail in a wall region with a very fine mesh.
Usage of the logarithmic wall function.
Rough for cast surfaces.
For more information about the specifics of the wall function, Y+ and meshing in the wall region can be found in the online help under the term “Meshing for turbulence modeling”.
5.2.1.13.2 Openings, inlet and outlet An opening and an inlet are later used in our example. At an Opening, the direction and the pressure, but not the speed is specified for an exit or entrance of the flow. An example is the rear opening of the flow volume in our case. On the other hand, Inlets and Outlets can be used to predetermine speed, mass flow, or pressure at an opening, for example by a pump. The entrance surface of our example is defined as such an inlet. The NX menus for inlet and opening.
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Other important boundary conditions that can be defined are: Additional types.
Internal Fan for an internal location with predetermined velocity ratios. Recirculation Loop, i.e. locations where fluid is sucked and then discharged in the same amount in other places. In all but the opening, the velocity ratios must be set with a mode. The following modes can be specified:
Specifying the speed ratios.
The Velocity The Mass Flow The Volume Flow The Pressure Rise A Fan Curve, this means the dependence of the pressure increase from the volume flow After this general discussion of important boundary conditions for flows, the following part shows the actual creation of the conditions for our example.
5.2.1.14 Inlet Definition with Velocity Boundary Condition In-/Outlet and opening can be interchanged.
As boundary conditions for a flow through the flow volume, an inlet and an opening need to be defined. The area in front of the profile is suitable for the inlet condition, because the flow speed of 100 km/h can be specified here. The area behind the profile is defined as an opening where only the ambient pressure has to be specified. These are common boundary conditions for such a flow task, but an outlet fan and front opening could also match the requirements. On the other hand it would be unfavorable to specify two mass flows and no opening, because these two streams would have to be carefully matched to obtain a convergent solution. If this is not the case (two unequal mass flows are specified for example), we have provided a physically impossible task, which is simply confirmed by the CFD system by the lack of convergence.
100 km/h flow velocity.
Follow the steps for the definition of the inlet as follows: ÍÍIf necessary, switch to the simulation file. ÍÍSelect the Flow Boundary Condition function
among the simulation objects.
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ÍÍIn the menu that appears, select the type Inlet Flow . ÍÍNow, in accordance with the preceding figure, select the inlet area of the flow volume. ÍÍEnter a speed of 100 km/h in the menu (don’t forget the unit). Confirm with OK.
5.2.1.15 Outlet Definition After the speed has been set at the inlet face, only the pressure at the outlet opening of the flow volume has to be set. At the exit, the ambient pressure is specified. Mostly the default ambient pressure of 1 bar is used for analysis.
Proceed as follows: ÍÍSelect the function Flow Boundary Condition . ÍÍIn the menu that appears, choose the type Opening . ÍÍSelect the outlet face and confirm all default settings with OK. The default value for the pressure at the Opening is Ambient. This means that the pressure of the Ambient Conditions is used, which is already specified in the solution default settings with about 1 bar.
5.2.1.16 Boundary Condition for the Wing Profile At the wing profile, a boundary condition shall be defined, which corresponds to a smooth wall, because the deep-drawn sheet metal of the wing only has a low roughness. To do this, as explained before, a flow surface condition can be defined.
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On the plate of the wing profile, a smooth wall with friction is present. The flow “sticks” to it and therefore has no speed.
For the definition of this condition proceed as follows: ÍÍSelect the function Flow Surface. ÍÍIn the menu that appears, choose the type Boundary Flow Surface. ÍÍSelect the four faces that belong to the profile. ÍÍRename this element, for example to Profile_Walls. ÍÍConfirm all the default settings with OK. The flow surface condition is now created. With the default setting Smooth With Friction it results in the desired property for the boundary layers at the wall. In addition, the CFD solver will calculate the forces for this area and moments that arise from the pressure distribution. Using this information results in the requested lift on the wing. The switch Use Wall Function may, but need not to, be turned on because it is turned on internally. A message in the log file indicates this.
5.2.1.17 Boundary Condition for the Wind Tunnel Walls On the two walls of the wind tunnel (see figure below) we have the same flow conditions as at the previously defined wing profile. The walls are smooth and the flow particles “stick” to them, that means exactly at the wall, there is no flow speed. We want to define this condition as follows: ÍÍSelect the Flow Surface function and therein the type Boundary Flow Surface. ÍÍSelect the two faces that belong to the wind tunnel. ÍÍRename this element, for example, to Other_Walls. Confirm with OK.
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The walls of the channel will also get boundary conditions.
Please note that this condition would not be necessary, because by default this condition already applies to all areas which have not received any explicit condition. This default setting can be checked in the settings of the solution in the register 3D Flow at Friction and Convection Parameters.
By default, this condition applies to all areas which have not received any explicit condition.
5.2.1.18 Symmetry Boundary Condition at the Cut Faces On the remaining two sidewalls of our flow space where we have truncated the reality, a condition for frictionless sliding shall be specified which behaves like a truncation. Therefore the function Symmetry Plane can be used. ÍÍSelect the function Symmetry Plane . ÍÍSelect one of the two cut faces and confirm all default settings with OK. ÍÍAt the second cut face apply the same boundary condition.
A symmetry condition has the same effect as the function Slip Wall.
The symmetry condition should be generated separately for each cutting plane.
5.2.1.19 Reporting Results during the Solution Iterations During the iterations of the CFD run it shall be seen how the results of pressure and speed change. Thus, the behavior of these results can already be controlled during the run and from possible fluctuations or a quiet course, the reliability of the results can be examined. Use a function that shows pressure, speed and temperature in an area of interest for each computation step: ÍÍSelect the function Report . ÍÍSwitch to the type Track During Solve. ÍÍSelect an area of interest, e. g. the front end surface of the profile. ÍÍConfirm all settings with OK.
Such a report is very useful for the monitoring of results.
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5.2.1.20 Solving the Solution Depending on hardware, the solve process needs about 2 to 15 minutes.
After the analysis model is established completely, it can be solved. ÍÍTherefore, select the function Solve . ÍÍSwitch the option SUBMIT back to SOLVE and confirm with OK. By default, a Comprehensive Check is first performed automatically, in which gross errors in the analysis model are displayed. Subsequently, the fluid domain mesh is created and then the CFD process is started.
5.2.1.21 Observing the Solution Progress During the solving process, a solution monitor appears, which is used for the observation of the solution progress. Here, the following items are displayed: which module of the solver is currently working messages, information, warnings and errors the course of residuals for the convergence criteria The solution monitor should be controlled. It provides a lot of useful information. Through the button Graph, Convergence, a graph like the one below with the course of residuals for the convergence criteria, that is updated with each time step, is displayed.
In addition, the solution run can be canceled with the Stop button. With Pause, the solution is interrupted, so that the current results can be controlled. In this case, the continuation of the solution is possible, using the Restart function. The text content of the Solution Monitor is stored in the working directory in the log file. Through the button Graph, Convergence, a graph like the one below with the course of residuals for the convergence criteria, that is updated with each time step, is displayed.
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With the convergence graphs it can be judged whether the computation converges or diverges. For each calculated balance equation residuals arise, which are small deviations. With the course of the residuals, the solving process is controlled.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
According to the figure above, the convergence history displays the control parameters3 for each balance equation at each time step. In this case there are three parameters for the conservation of momentum and the conservation of mass. After a steep increase during the first time steps, the values should decrease. The goal is that all control parameters decrease below their convergence criterion4. If the course does not converge, the solution run should be stopped and the analysis model could be changed. It should be checked whether all input variables, such as velocity and pressure, are physically plausible. Once all control parameters fall below their convergence criterion, the solution is completed. It has then been converged.
If no convergence is reached, the model, the time step or the type of convergence control needs to be modified.
It may be useful to reduce the convergence criterion to improve the solution accuracy. With an oscillating course of the convergence parameters, it is recommended to lower the time step size. With a calm, but poorly converging course, the time step can be enlarged.
Time step recommendations to achieve a rapid solution
3 RMS residual or the maximum residual, depending on the setting of the convergence parameters in the solution parameters. 4 The convergence criterion is also preset in the solution parameters.
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The speed and pressure at the front end face of the profile are put out by the requested report during the solution steps. The quantities at the end should have a calm course. This is good for controlling the solution.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
Through the button Graph, TrackResults in the Solution Monitor, the graphs (see figure above) with the course of the requested interim results are shown and also updated with each time step. The graphs show that the velocity and the pressure at the inlet surface at the beginning of the analysis fluctuated strongly and then quickly came to rest. From this course it can be concluded that further iterations would imply little or no further change in the result. A picture with the convergence history (and accordingly for the other requested quantities) is saved as a file with the name flowcnvg.png (or equivalent). In this way it can be used later on.
5.2.1.22 Checking the Y+ result ÍÍOpen the result Y+ on +ve Side – Nodal in the post-processor. The distribution of Y+ on the surface of the profile should look like the figure below. The results on the profile surface may, for example, be read with the function Identify and Pick set to Feature Face. For the evaluation of Y+, the following rules apply: Important rules for the evaluation of the Y+ result
For best results, the Y+ value should be approximately at 30. Values between 10 and 70 are acceptable. If Y+ is too small: The First Layer Thickness of the Surface Mesh should be increased. If Y+ is too high: The First Layer Thickness of the Surface Mesh should be decreased. In our case, the Y+ value is a little too high. Therefore we want to reduce the thickness of the first element layer. These rules and recommendations for Y+ Rating are based on data supplied by the software manufacturer [Maya], on [nxflowref] and on our own experience [Binde5].
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A colored version of this figure is available at www.drbinde.de/index.php/en/203
5.2.1.23 Improvement of the Mesh Wall Distance and Reanalysis ÍÍEdit the fluid domain surface definition, that we have named SurfaceMesh. ÍÍReduce the First Layer Thickness from 3 to 2 mm. ÍÍRecalculate the model and check the Y+ result at the profile surface.
The mesh wall distance (first wall/surface layer thickness) should be reduced.
Now a maximum Y+ value of about 69 and a minimum of about 13 should be calculated. This is exactly the desired range. Therefore further results should now be evaluated.
5.2.1.24 Result of the Static and Total Pressure Distribution The static pressure is the overall or total pressure minus the dynamic component. ÍÍTo display the distribution of the static pressure, select the node Static Pressure – Element Nodal in the simulation navigator. ÍÍChange the displayed Units to Bars: SET RESULT > UNITS > BARS. The result of the static pressure distribution should look like the figure below. The pressure is always displayed as a relative value, i. e., the change relative to the ambient pressure of 1 bar is shown here. On the profile peak, at which the air impinges perpendicularly to the profile, the largest increase in pressure results. On the lower side, where the flow separates, the pressure is the lowest.
Pressure distributions are always displayed relative to the environment.
The static pressure distribution is plausible for an airfoil.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
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ÍÍFor the total pressure, select the node Total Pressure – Element Nodal in the simulation navigator. On evaluating the total pressure.
It should show an image that looks like the following figure. The total pressure is the sum of the static and the dynamic pressure. It is thus the pressure that can be measured in flow direction. As with the static pressure, the results are valued relative to the ambient pressure, i. e. a calculated pressure of zero bar corresponds exactly to the ambient pressure of about 1 bar. It is typical for the total pressure to always decrease in flow direction, which is caused by the flow losses, which always exist.
The total pressure always decreases in flow direction. Reasons therefore are the flow losses in every flow.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
5.2.1.25 Result of the Flow Forces The forces which affect the profile are resulting from integration of the calculated pressures on the surface of the profile. If boundary conditions of the type Flow Surface were applied, the solver calculates these forces automatically and writes the results into the log of the solution monitor. If the solution monitor is no longer open, the log file can also be opened with an editor. The following figure represents a section of the file fl_fluegel_ links_sim1-Solution_1.log, which can be found in the working directory of the simulation. Thus, the forces here labeled were calculated. On the profile, an integration of the pressure is automatically made. Thus, the desired force quantities result.
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Here, according to the figure above, for the Flow Surface with the name Profil_Walls, the force in the Y-direction that was calculated, is minus 25 N. Since this result was calculated for a profile piece of one-tenth of the original size, it would have to be multiplied by 10. It therefore results in a downforce of about 250 N per wing. (However, the 10 degrees rotated coordinate system is not yet included).
The calculated force quantities must be scaled to the entire width of the wing.
5.2.1.26 Display of Velocities In addition to the pressure distribution, the velocity distribution at the profile is of interest. It is at first displayed as a contour plot shown in the figure below. ÍÍChoose the result Velocity – Element-Nodal in the post-processor. ÍÍChange the unit shown to Km/h: SET RESULT > UNITS. Calculated velocities in units of km/h.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
In order to display the velocity with arrows, proceed as follows (see figure below): ÍÍChange the display to arrows: EDIT POST VIEW > COLOR DISPLAY > ARROWS. ÍÍDownsize the arrows: EDIT POST VIEW > RESULT > SIZE > 1%. The display with arrows helps for analyzing the flow directions. The velocity distribution shows the wake space, where the flow detaches from the profile.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
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The arrows indicate the direction of the calculated speed. It can be seen that the flow on the upper side is attached to the profile curvature. On the bottom, the flow immediately separates from the profile curvature right at the beginning and there is a separation region (wake space). The flow then later attaches back to the curvature of the profile. In the detached area, the speed is very low, and there is a vortex. With this examination, the learning task is completed.
Bibliography [Binde5] Binde, P.: Thermal- and Flow-Analysis with NX/Flow & Thermal. Training documentation. Dr. Binde Ingenieure GmbH, Wiesbaden 2014 [ESCref] I-DEAS ESC Electronic System Cooling. Reference Manual [Maya] Maya Heat Transfer Technologies Ltd: NX/Flow. Training documentation 2014 [nxflowref] NX Flow. Reference Manual. Documentation of installation
6
Advanced Simulation (EM)
When developing electrical engineering components by means of conventional methods, i. e. by means of rules of thumb and experience, one quickly reaches the limits due to the complexity of today’s problems. For financial reasons measuring tests are only permitted in later design phases or the prototype construction is completely dispensed in order to meet the rapid competition. Since analytical methods of electrical field theory in realistic applications with mostly complex geometry would only be applicable under impermissible simplifications, numerical methods have high potential. In combination with the CAD programs available today even very complex geometry can be treated well with numerical simulation, which makes it an indispensable tool. Scientific foundations for electromagnetic simulation have been developed primarily by Weiland [Weiland] and Bossavit [Bossavit]. With the NX Advanced Simulation Module (EM) tasks of electrostatics, electrokinetics, magnetostatics, magnetodynamics (low frequency) and high frequency (full wave) are analyzed. In this manner also the fourth type of engineering simulations can be treated in the NX system: the electromagnetics. The module Motion Simulation treats rigid body mechanics, Design and Advanced Simulation treat structural, thermal and fluid mechanics. The electromagnetic solutions are made possible by the solver MAGNETICS for NX, which is available as an add-on to the NX system starting with version 7.5. This product includes software developed by Christophe Geuzaine and Patrick Dular, Universitè de Liège. Sources for this are [getdp 2014], [Geuzaine 2001] and [Dular]. Anyone wishing to use that solver must license it from the company Dr. Binde Ingenieure GmbH (www.drbinde.de) or use the demo version for software evaluation purposes that is included in the zip-archive of this book (see section 1.3). The demo version is limited to a maximum of 1500 nodes and the examples in this book are designed in a way that they can be analyzed with this demo version. The examples in this book are limited to the topics magnetostatics and dynamics (low frequency), which are used often in practice.
All of the usual types of solutions of electro magnetics are possible.
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The Engineering Mechanics are classified into four parts.
Technical Simula on Rigid Bodies Rigid Body Mechanics MBD (Mul body Dynamics)
Elas c Bodies Fluids Structural Mechanics Fluid Mechanics FEM CFD (Finite Element (Computa onal Method) Fluid Dynamics)
Electric Bodies Electromagne cs (EM) FEM (Finite Element Method)
Electromechanical or magnetic analyses are integrated in the standard user interface of the NX system.
Since the solver MAGNETICS for NX is fully integrated into NX Advanced Simulation, the same tools and methods can be used as with structural or flow analysis.
EM users should have prior knowledge.
It should not be denied that in electromagnetics there are complex tasks that should not be solved without elementary knowledge of electrical engineering in practice. A comparison with experimental results has to be done in many cases in order to confirm the results.
In creating and preparation of geometry, the already known methods from the field of CAD are applied. This substantially simplifies the application for newcomers. In addition, the resulting data can be stored in the PDM system Teamcenter and managed together with the design data.
In section 6.1, some principles are described that provide a basic understanding of the theoretical backgrounds. In section 6.3 learning tasks follow, in which the methodology for electromagnetic analysis in 2D and 3D is shown.
■■6.1 Principles of Electromagnetic Analysis This section is based on lecture notes on “Applied & Computational Electromagnetics” from the University of Liège [Geuzaine 2013]. Maxwell’s equations are the foundation.
With electromagnetic analysis, Maxwell’s equations are solved. Depending on the application, i. e. Electrostatic or Magnetodynamics, the equations are simplified or parts are omitted. For the solution of the equations the finite element method (FEM) has been established. In the following, we provide the usual electromagnetic models, Maxwell’s equations and material relations that underlie the models. Then we explain which type of model is the right one for an application problem, and finally we show the equations that belong to the individual models.
6.1 Principles of Electromagnetic Analysis 299
6.1.1 Electromagnetic Models The following diagram shows use cases or models of interest in the electromagnetic analysis area which can arise from the Maxwell equations.
Electrosta cs Electrokine cs Maxwell Equa ons
Electrodynamics Magnetosta cs Magnetodynamics Full Wave
The six models that can be derived from the Maxwell equations differ in the way they account for the effects capacitance, ohm resistance and inductivity. Accordingly, icons for capacitor, resistor and coil can be assigned: Electrostatics: It sets static charges or electrical voltages. As a result, we obtain the electric field distribution. This corresponds to a consideration of the capacitive properties (hence the symbol of a capacitor). Electrokinetic: We consider the static distribution of electricity in conductors. The most important feature is the electrical conductivity or the ohm resistance (hence the symbol of resistance). Electrodynamics: This is a combination of electrostatics and kinetics. The distribution of the electric field and electric currents in materials (conductors and insulators) are considered. It can also lead to dynamic effects. Magnetostatics: We consider the static magnetic field, which can result from permanent magnets and stationary electric currents. As this corresponds to the effect of the inductance, we select the icon of the coil. Magnetodynamics: Result is the magnetic field and eddy currents (Eddy Currents), which results from moving magnets or time-varying currents. A suitable symbol is the coil with ohm resistance, because these two effects are considered. Full Wave (High Frequency): This includes the consideration of the full electromagnetic waves. It requires that all three effects of capacitance, resistance and inductance are taken into account. This allows vibrations and resonances to be determined, therefore the symbol of the electrical resonant circuit is suitable.
Electromagnetic applications and models
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6.1.2 Maxwell Equations Let’s look at the Maxwell equations that describe the electromagnetic effects and are the basis for the models or applications listed above. Maxwell’s equations are a set of four equations: The Maxwell-Equations are solved.
Ampere-Equation: curl h = j + ∂ t d Faraday-Equation: curl e = −∂t b Conservation of the magnetic flux density: div b = 0 Conservation of the electric flux density: div d = ρ q The formula symbols represent: h: magnetic field [A/m] e: electric field [V/m] b: magnetic flux density [T] d: electric flux density [C/m2] j: current density [A/m2] ρq: charge density [C/m3]
6.1.2.1 Ampere’s Law Ampere’s law describes the effect that each current-carrying conductor generates a magnetic field around itself which rotates according to the right-hand rule. The curl operator in the equation is often written as rot and describes this characteristic of the rotating field. The equation curl h = j is often written in integral form. This way, it is maybe easier to recognize the effect using the following illustration. Ampere’s Law: Electric current forms a magnetic field.
6.1 Principles of Electromagnetic Analysis 301
The two conductors shown in the previous figure could for example belong to a coil of an electromagnet. Ampere’s law says that on a path l surrounding the conductors the magnetic field integral equals the sum of the currents. We have incidentally omitted the term ∂ t d which is describing the so-called displacement currents and which plays a role only at high frequencies. The Ampere’s law also leads to the well-known Kirchhoff’s Current Law, which applies in electrical circuits: “The sum of the currents at a node must always be zero.” This relationship is also used later and can be described by the notation div j = 0. The so-called divergence operator div describes the occurrence of sources or sinks. The equation div j = 0 means that no sources or sinks for electrical current to a body or node exist. The current that goes in must also come out.
6.1.2.2 Faraday’s Law Faraday’s law, which is also called induction law, describes the effect that any temporal alteration of the magnetic flux leads to a rotating electric field. Written in integral form the following illustration allows recognizing the effect: Faraday’s law: By a change in the magnetic field, an electric field is generated. This is also called induction.
The integration path l could now for example, be a conductor loop or coil in an electric motor. The large arrow with Φ represents the magnetic flux and could, for example, result from a magnet of the rotor. If the magnet moves, then the flow Φ changes over time in the conductor loop, an electric field E, and thus voltage and current are produced.
6.1.2.3 Conservation of the Magnetic Flux Density This also allows to build the third Maxwell equation, the conservation of magnetic flux density div b = 0. The equation div b = 0 indicates that no sources or sinks for magnetic flux density exist. So in the magnetic flux nothing may be lost. In a horseshoe magnet i. e.,
Magnetic flux density will never be lost. That’s why magnetic field lines are closed loops in general.
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the flow advances in a circle through the horseshoe and then through the air around. This also yields the rule “Magnetic flux lines are always closed”.
6.1.3 Material Equations In addition to the Maxwell equations material equations are needed. With their help magnetic and electrical material properties are included in the analysis. We need the following three: Material properties and their relationships are included additionally to the Maxwell equations in an analysis.
Magnetic relationship: b = µ ⋅ h Dielectric relationship: d = ε ⋅ e Ohm’s law: j = σ ⋅ e The material properties contained therein and their units are: μ: magnetic permeability [H/m] ε: dielectric permeability [F/m] σ: electrical conductivity [S/m] These material properties μ, ε and σ can be constants if linear material is present. They may be functions of the electromagnetic fields, when nonlinear material is present. They can be tensors in case of anisotropic material or functions of other physical fields, very often functions of temperature.
Magnetic flux density and field strength are linked over the permeability. The permeability often is nonlinear.
Let’s look at the magnetic relationship b = µ ⋅ h which is very important because it influences each magneto-static or dynamic analysis. Accordingly, the magnetic flux density b and field strength h are associated over the magnetic permeability μ. This permeability is often written in the following form: µ = µ r ⋅ µ0 Therein μ0 is the vacuum permeability constant (4π10–7 H/m) and μr the relative magnetic permeability, which should be announced by the material manufacturer. So-called diamagnetic and paramagnetic materials have μr ≈ 1. Examples are silver, copper and aluminum. Such materials behave magnetically as air and have linear characteristics. So-called ferromagnetic materials have μr >> 1. Often the permeability is depending on the field strength, i. e. μr = μr(h). In this case we are talking about magnetically nonlinear material. Examples include steel and iron. This dependency will be shown in the form of a non-linear b-h curve (b for flux density, h for field strength) and this curve can also be applied in the simulation program (in NX we apply only the positive part of the curve). The following figure on the left side shows such a typical course.
6.1 Principles of Electromagnetic Analysis 303
flux density B
B
Satura on
field strength H
H
In the figure you see the typical dependency of the magnetic flux density on the field strength (left), which shows up in a nonlinear μr. On the right you see the course with consideration of hysteresis or magnetic losses.
The figure on the right side shows a b-h curve with consideration of hysteresis or magnetic losses. Those losses occur, for example, when the magnetic flux density in the steel sheet of an electric motor repeatedly increases and decreases, and as well if the direction of the flux changes. In such cases with each cycle a small amount of energy is lost or mutated into heat. NX Magnetics can calculate this hysteresis using the Steinmetz formula, but it requires the Steinmetz material parameters to be known and entered. As a second material equation, we have the dielectric relationship d = ε ⋅ e , which is important for electrostatic or high frequency analysis types. Similar to the magnetic relationship there is a permeability ε that associates electric flux density with electric field strength. This permeability is assumed to be constant in most applications and is therefore not critical. The third material equation is Ohm’s law j = σ ⋅ e , which is also of great importance. The electric conductivity σ is the reciprocal of electrical resistance ρ, which is often provided in material parameters, i. e. ρ = 1 / σ. The conductivity depends on temperature for many materials. As a result tasks are often more complex: a current-carrying coil for example heats up since the ohm resistance leads to losses. If temperature rises, the electrical resistance increases. In an analysis this effect should be taken into account, that is, the proper resistance for the final temperature should be used. In NX this effect can be taken into account correctly.
6.1.4 Model Selection Now it is about to determine which one of the models, i.e. Magnetostatics, Electrostatics, High Frequency . . ., is suitable and sensibly for a concrete task. Of course, this decision can already easily be done based on the descriptions of the models at the beginning of this chapter. Often however those descriptions are not sufficient to make a reliable statement. Therefore we want to constitute a scheme against which this decision can
Ohm’s law contains the electrical conductivity. This often depends on temperature.
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almost automatically be checked by specifying three characteristic quantities for the problem. Maxwell’s equations, together with the material laws, can be written in frequency domain (without sources) as follows: ∆e − iωσµ e + ω 2εµ e = 0 We want to introduce the three characteristic lengths L, δ and λ, with which a task can be evaluated. Based on of the three dimensions component size, skin depth and wave length it is decided which electromagnetic model, or what NX solution type, is utilized.
Component Size L: This stands for the geometric size of the entire model which we find in the CAD model dimensions. Skin depth δ: The skin depth is an important measure for the evaluation of eddy currents on the boundary layer region of electrical conductors. Depending on the frequency and material properties those eddy currents keep mainly in the peripheral boundary region of conductors. The approximate thickness of the layer is the skin depth. For dynamic FEM simulations this skin depth must be taken into account to ensure that in this area there are good and sufficient small finite elements. The skin depth is calculated using the following formula. It includes the eigenfrequency ω (2πf), σ and μ, the electrical conductivity and permeability μ. δ=
2 ωσµ
Wavelength λ: The wave length describes the size of the electromagnetic wave in a dynamic electromagnetics task. This wave length can be calculated using the following formula: λ=
1 2π ω with wave number k = and the speed of light c = k c εµ
Using those three characteristic lengths the previous equation ∆e − iωσµ e + ω 2εµ e = 0 can be written in a dimensionless manner: 3 2i 4π 2 − 2 + 2 e = 0 λ L δ We define the following three dimensionless parameters: 2
2
2
λ δ λ g1 = , g 2 = , g3 = , L L δ
Finally the dimensionless parameters g1, g2 and g3 allow to draw those conclusions which are necessary for the selection of an electromagnetic model: g1, g2 and g3 allow to judge about the three measures component size, skin depth and wave length in proportion.
g1 >> 1 The wave length is much larger than the part size. Therefore, vibrations and resonances of the electromagnetic waves cannot develop in the component. However, eddy currents are possible and occur in the outer layers (skin depth) on electrically conductive components. Maxwell’s equations can be considered isolated. So we present a purely electric or purely magnetic problem. You can select one of the following five models.
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g2 >> 1: Magnetostatics The skin depth is greater than the part size. The boundary layer is therefore very thick or does not exist. Boundary layer effects and thus eddy currents play only a minor role. In the magnetostatics model currents are assumed stationary, which applies in this case a good approximation. Applications are electromagnets, for example. In NX the solution type Magnetostatic is chosen. g2 1: Magnetodynamics The skin depth is smaller than the part size. Thus there is a distinct boundary layer and boundary layer effects with eddy currents play a role and must be considered. A magnetodynamic model must be selected in the time domain or frequency domain. Applications are i.e. transformers, electric motors, actuators and induction heating. In NX a solution of the type Magnetodynamic –Transient or Magnetodynamic – Frequency is selected for this purpose, depending on whether there should be analyzed in the time or frequency domain. g3 >> 1: Electrokinetics The wave length is much larger than the part size and greater than the skin depth. The frequency is so small that all dynamic effects can be neglected. It can merely be considered the steady-flow of currents as it is provided by the electrokinetic model. Applications are, for example, biological analysis in brain research. In NX a solution of the type DC Conduction Steady State is selected for this purpose. g3 ≈ 1: Electrodynamics The wave length indeed is much larger than the part size, but about as big as the skin depth. Dynamic effects in the boundary layer are therefore possible. This is taken into account by the electrodynamic model. In NX there is still no solution type for this model. g3 1: Electrostatics The wavelength is much larger than the component, but much smaller than the skin depth. Theoretically, now there are dynamic effects in the boundary layer. However, this combination can only occur through a very small electrical conductivity and magnetic permeability. Otherwise, a small wave length (high frequency) will always lead to a small skin depth. Only if the conductivity and permeability are very small, a significant skin depth may result. The electrostatic model is therefore a good approximation, because it allows no currents but an electric field. Applications are i. e. high voltage insulators, piezoelectric motors or electrical shields. In NX, a solution of type Electrostatic has to be selected. g1 1: Full Wave The wave length is less than or similar to the part size. You have to select the high-frequency model. This means that vibrations and resonances of the waves, which are distributed over the component, are possible. The decoupling of the magnetic and electric field can no longer be accepted. Applications are i.e. antennas, microwave ovens and radar systems. In NX, a solution type Full Wave has to be selected. >>
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6.1.5 Electrostatics In electrostatics from the Maxwell and material equations only those are considered in which electrical parameters are included. In addition, all time derivatives and currents are set equal to zero. Thus, the following equations arise to be solved: curl e = 0, div d = ρ q , d = ε ⋅ e
In order to solve this, a scalar potential v is introduced with e = -grad v. Assembled the scalar potential formulation for electrostatics results: div ε grad v = − ρ q
In the solution as primary result the potential v is calculated that initially has no physical meaning. But the electric field e can then be derived from e, using the potential equation by computing the gradient of v. The electric flux d with d = ε e can then be determined from the electric field.
6.1.6 Electrokinetics In the electrokinetic model all time derivatives are set to zero but currents are not zero. Again, only electrical quantities are considered. This results in the following equations to be solved: As in electrostatics, a scalar potential v is introduced with e = -grad v. This yields the scalar potential formulation for electrokinetics: div
grad v = 0
The primary result after solving the equation is the potential v. With the help of the potential equation the electric field e can be calculated from v. With the help of Ohm’s law it is possible to calculate the electric current j from e.
6.1.7 Electrodynamics The electrodynamic model has not yet been implemented in NX because it is quite rarely used. For completeness, we mention yet the associated equations: curl e = 0, curl h = j + ∂ t d , div ( j + ∂ t d ) = 0,
j = σ ⋅ e, d = ε ⋅ e
Together with e = -grad v this results in the equation to be solved: div (σ grad v + ε grad ∂ t v ) = 0
6.1 Principles of Electromagnetic Analysis 307
6.1.8 Magnetostatics The time derivatives are zero, and only those equations are considered in which magnetic quantities are included. It results in the following equations: curl h = j , div b = 0, b = µ ⋅ h
Another potential is introduced, but this time a vector potential a with b = curl a. Furthermore, for simplicity we set j = js. For currents we use therefore the externally applied source current js. If permanent magnets are taken into account, the magnetic relationship is extended to the remanence bs: b = µ ⋅ h + bs Magnetic relationship with permanent magnets
Thus the equation to be solved results, for example, in the form shown here. It should be noted that besides the form shown here others are possible and consistent. curl µ −1curl a = js
After solving the primary result a is available for further computations. With b = curl a, the magnetic flux density b can be found and through b = μh the magnetic field strength h can be calculated.
6.1.9 Magnetodynamics In the magnetodynamic model the only simplification is omitting the so-called displacement currents, i. e. the proportion ∂ t b of Ampere’s law. Thus, the following equations are solved: curl h = j , curl e = −∂ t b, div b = 0, b = µ ⋅ h + bs ,
j = σ ⋅ e + js
Now there are two different potentials introduced: a and v: b = curl a
Vector potential a of the magnetic field Scalar potential v of the electric field This gives the following equation: e = − grad v − ∂ t a
curl µ −1curl a + σ ( ∂ t a + grad v ) = js
Because of the two potentials this formulation is also called a-v formulation. In addition to this a-v formulation that is used in NX MAGNETICS others are also possible.
6.1.10 Full Wave (High Frequency) In the model for high-frequency analysis full electromagnetic waves are calculated. No simplifications of the Maxwell equations are admitted. The equations to be solved are therefore:
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curl h = j + ∂ t d , curl e = −∂ t b, b = µ ⋅ h, d = ε ⋅ e,
j = σ ⋅e
In addition to the equations there is a Silver-Müller radiation condition defined for out going waves on the border of the computational domain (infinity condition). In MAGNETICS for NX there are no potentials introduced for this solution, the equations are rather solved directly. There are two possible formulations available which result from some algebraic manipulations on the previous equations. These are: 2 curl curl e + σµ∂ t e + εµ∂ t e = 0 electric field formulation 2 curl curl h + σµ∂ t h + ε u∂ t h = 0 magnetic field formulation
■■6.2 Installation and Licensing The MAGNETICS Solver must be installed on top of an existing NX system. Updates can be downloaded from the Internet.
The solver MAGNETICS for NX is not yet included in a default installation of the NX system. To use the program, its own installation must be performed. For NX 8.5 and NX 9 the respective files are included in the zip archive (see section 1.3, “Working with the Book”. Updates and patches for the MAGNETICS installation can be downloaded via internet from www.nxmagnetics.com/support. The program may be used without commercial license as a demo or trial version software for evaluation purposes. Then it is limited to a maximum of 1500 nodes, which is sufficient for all learning examples of this book, if coarse meshes are chosen. We will now perform an example of an installation for NX9, where we assume a standard installation of the NX system, i.e. an installation, as it is produced if the NX installation is done with all the default settings on a Windows system. In such a case NX is usually installed in the folder C:\Program Files\Siemens\NX 9.0. In case of NX10.0 there would of course be “10.0” instead of “9.0” and the same applies to other NX versions. These are the steps that have to be performed: ÍÍCheck the Windows environment variables: Run in Windows START> RMB ON OMPUTER> PROPERTIES> ADVANCED SYSTEM SETTINGS > ENVIRONMENT C VARIABLES.
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ÍÍCheck if UGII_BASE_DIR points to your NX9 installation. If this is not the case, change the variable. ÍÍNext, open the following file with a text editor: C:\Program Files\Siemens\NX 9.0\UGII\ugii_env.dat ÍÍThen enter the text line, as marked in the figure below (please do not forget the dollar sign).
The variable UGII_MAGNETICS is set for use in NX. This is done in the file ugii_env.dat.
You have now defined an environment variable that can be used by NX. You have stated that a variable named UGII_MAGNETICS exists that points to the folder C:\ Program Files\ Siemens\NX 9.0\MAGNETICS. In the following the installation files are copied into this folder. If the MAGNETICS installation shall be located in another folder, change this entry in ugii_env.dat correspondingly and additionally modify the command set UGII_MAGNETICS =%UGII_BASE_DIR%\MAGNETICS in the following installation script. ÍÍSecondly, open the following file with a text editor: C:\Program Files\Siemens\NX 9.0\ UGII\menus\custom_dirs.dat ÍÍEnter the highlighted text in the figure below (please do not forget the dollar sign!).
In the file custom_dirs. dat it is entered that additional menus will appear in NX.
With this you have explained that in the NX system there are additional toolbars and menu items found under this folder. Now you can run the installation script that copies files from the installation media to the destination. The script must be started with the rights of an administrator: ÍÍIn Windows, run the command prompt as administrator: START, CMD. ÍÍNavigate to the folder of the extracted zip archive (see section 1.3) that contains the installation script. If the archive, for example, is in C:\work\SimWithNX, enter the following: cd C:\work\SimWithNX\EM\Installation\MagneticsForNX9 ÍÍRun the installation script as administrator: InstallMagneticsForNX9.bat
Now, the installation files are copied.
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The installation will now copy a number of files. You will be notified about the progress. After the script finishes the installation of MAGNETICS is ready. Now another adjustment for easy operation of the material library can be done, because there is an additional library file available for magnetic analysis. To avoid having to specify the full path to this file for each choice of materials, the following action is recommended: ÍÍStart NX. ÍÍSwitch to the Customer Defaults. ÍÍBeneath the Gateway tab, Materials/Mass enter the path to the library file: C:\Program Files\Siemens\NX 9.0\MAGNETICS\Magnetics_Materials.xml ÍÍFurther you should deactivate the switch NX Material Library: Enable that is found at the end of the dialogue (see next picture on the right-hand-side).
This ensures that, when calling a material library, you will see only the Magnetics materials. In addition, each time it is possible to manually enable the origin NX material library. Test the installation as follows: ÍÍStart NX and switch to the application Advanced Simulation. ÍÍEnable the Toolbar Magnetics. The test is successful if the toolbar exists. ÍÍSelect the function New FEM and Simulation and open the list of available solvers. The test is passed if MAGNETICS appears there.
■■6.3 Learning Tasks (EM) The learning tasks in this section show how practical problems can be solved with the solver MAGNETICS for NX. The first example is of fundamental nature. It should be worked through by all readers to see how such things as meshing, materials, boundary conditions are generated and how electromagnetic results are to be understood. The second example deals with a 3D
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geometry. Finally, the third example illustrates a simple electric motor, which again is analyzed in 2D.
6.3.1 Coil with Core, Axisymmetric The example “coil with core” is a basic example that will show you the steps to be performed in the NX system for electromagnetic analysis. In addition, it is discussed how basic results from electromagnetic analysis and the quality of results can be assessed. Here, the 2D or axisymmetric methodology is taught. In the following example, the same object is achieved with 3D methodology. Ultimately both 2D and 3D are analyzed statically and dynamically in the frequency range.
The first example serves as an introduction in order to understand the basic steps and results.
Therefore after you have performed this task, you will have already gathered a lot of useful knowledge and experience. Previous experience is not necessary. But of course it would be quite helpful if you had worked through the structural FEM analysis part in this book.
6.3.1.1 Tasks In the figure below, the CAD model is shown. It is an axisymmetric geometry with core and coil. The coil has 36 turns of copper and shall be loaded by 5 amperes. The current is to be applied either as direct (DC) or alternating (AC) current, i.e. we want a static and a dynamic analysis to perform. The magnetic fields are to be determined, i.e. the magnetic field strength and flux density, as well as the force on the core.
symmetry: flux tangent
border to environment
3D model (angular piece)
air coil, 5 A, 36 turns Core symmetry: flux normal
The analysis will now be carried out with axisymmetric method. A 3D analysis of the same geometry is of course superfluous for this purely axisymmetric example. Nevertheless, we want to use it in the next learning task in order to compare the results, and also to present basic methods for 3D analyses.
It is to be calculated both statically and dynamically in the frequency range. In the figure you see the task of the learning example (left for 2D axisymmetric, right for 3D). The 3D analysis is performed in the following example in section 6.3.2.
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6.3.1.2 2D Axisymmetric Method We start with the 2D axisymmetric analysis. Here, the geometry is set up in the X/Y plane (Y is axis of symmetry). Attention must be paid that this plane and axis are used. If the model is different in space, it needs to be reoriented. A reorientation could be done in the idealized file. In our case, the CAD model is already oriented correctly.
6.3.1.3 Create a File Structure and Solutions The procedure is initially the same as for the other solvers in NX.
ÍÍStart the NX system and open the file CoreInductor.prt. ÍÍStart the application Advanced Simulation and choose the function New FEM and Simulation. ÍÍTurn off the switch Create Idealized Part. ÍÍSelect the Solver MAGNETICS and for analysis type 2D or axisym Electromagnetics. ÍÍYou will be asked for the solution. Enter the name Static and accept the default solution type Magnetostatic. In the register Output Requests desired results are selected. There is a separation into results of type Plot and Table. Plot results are those which are output as a color representation, such as flux density. Table results are initially single number values, e.g. a total force on the core. If time steps are calculated those numerical values become tables or graphs over time.
These settings must be selected for the static solution.
ÍÍIn the output requests tab, activate the first five plot results, i. e., Magnetic Fluxdensity and Fieldstrength, Current Density, Vectorpotential and Nodal Force.
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ÍÍIn tab 2D activate Axisymmetric. ÍÍClick OK to confirm whereupon the desired solution will be created. In the other registers, the default settings are correct and can be accepted. The register 2D includes the Thickness that is only visible when the axisymmetric switch is off. Hereby for pure 2D analyses the depth of the model in the Z-direction will be specified, for example, this could be the depth of a 2D electric motor. In the register Time Steps you can define steps. In this magnetostatic analysis it means that static steps are carried out sequentially. Dynamic effects, such as eddy currents would not occur here.
Time steps are possible, but in statics there will arise no eddy currents.
In the register Initial Conditions, the Initial Time can be changed. This would for example make sense if you wanted to move a time-defined sinusoidal load in the phase. Additionally to the static solution we want to create a dynamic solution that works in the frequency domain: Make the simulation file the active part. ÍÍSelect the function New Solution. ÍÍEnter the name of the solution DynFreq. ÍÍSelect the solution type Magnetodynamic Frequency. ÍÍIn the register Output Requests activate the same switches as already for the previous solution. ÍÍFor 2D enable again Axisymmetric. ÍÍIn register Frequency Domain accept the default excitation frequency of 50 Hz.
These settings must be selected for the dynamic solution in the frequency domain.
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6.3.1.4 Meshing and Physical Properties In meshing, we can choose between triangle or quad elements. Usually, we choose the slightly higher quality quads, if the geometry is simple, and otherwise triangles. The meshing is done in the FEM file.
Analyses with the solver MAGNETICS use linear shape functions on the elements. Concepts like midnode elements known from structural analysis do not exist here. There is another fundamental difference: The degrees of freedom may be not only on the nodes of an element, but also on element edges and in 3D additionally on element faces. These are the so-called Whitney elements that are often used in high quality electromagnetic FEM codes. More details about these items can be found in [Bossavit].
The solver uses edge elements. The degrees of freedom are on node and also on element edges.
Now, we first mesh the three parts Core, Coil and Air. Each of the parts will generate his own mesh and Physical Property Table (we simply call it Physical). The physical contains all physical properties, e.g. material data. It usually arises automatically upon any new meshing and resides in the mesh collector. ÍÍChange the displayed part to the FEM file. In the navigator among Polygon Geometry, hide the three solid bodies CORE COIL and AIR. Only the sheet SHEET is now even more visible. ÍÍSelect the function 2D Mesh , select the face of the core, switch the type to quad and enter an Element Size of 1.5 mm. Accept all other default settings with OK. ÍÍAlso mesh the surface of the coil with 1.5 mm quads. ÍÍMesh the air with tri-elements and an element size of 3 mm.
In the picture on the left you see the navigator and on the right the resulting FEM mesh.
The element sizes were initially chosen rather arbitrarily so that a beautiful mesh is created. At the result, we will then assess whether the network size was reasonable. What matters is whether the results from element to element vary considerably. If this is the
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case, it should be meshed by smaller elements. It should also be checked for dynamic analyses whether there are enough elements within the skin depth. Now we assign the desired properties in the so-called Physicals in the three collectors: ÍÍDouble-click on the first collector that contains the mesh of the core. This opens the mesh collector dialog. ÍÍEnter the name of the collector Core.
Material properties and more are defined in the so-called Physicals.
This name specification is not a must, but quite reasonable for a good overview of the NX system. FE meshes are grouped in collectors. Here the Physicals are assigned. Each component gets its own Physical, even the air.
In the dialogue it can be seen that a physical of the type PlanePhysical has already been generated. This physical automatically got the name PlanePhysical1. This physical type is the standard one for 2D magnetic analyses. It can be used for all following parts. ÍÍTo check or modify properties, select EDIT . . . in the dialog. This opens the dialog PlanePhysical. ÍÍIn the PlanePhysical dialog enter the name Core again. .
This name specification is again not essential, but makes sense because the name specified here is used by the solver for the internal identification of the core. Results such as tabular outputs of force on the core will lead to meaningful labels on the axes of following graphs. Now we specify on the actual properties. We begin with the selection of materials: ÍÍIn the dialogs on physical planes, select the function Choose Material
.
This opens the dialog material list. In this bill of materials, there are a variety of functions, that you possibly already know from other simulation applications. Materials may be selected, controlled, filtered, generated or deleted. In addition, libraries can be managed.
The material can be selected from the library.
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We want to open the supplied material library that is delivered with the MAGNETICS solver to select a material for this analysis. Incidentally, such a library can also be preset by selecting it in the Customer Defaults of NX. By doing it this way, you do not need to reselect the library again and again. The installation includes a library of materials with electromagnetic properties.
ÍÍAt Libraries you disable NX Material Library. ÍÍActivate one of the two other switches Site or User MatML Library. ÍÍSpecify the path to the installation directory of the MAGNETICS solver and the file name Magnetics_Materials.xml. Now the supplied materials are displayed. ÍÍSelect the material Iron_Sample1 in the list.
The Magnetics material library opens. The columns shown can be configured such that magnetic properties are shown. They can also be sorted by column. This allows, for example, finding the material with the highest magnetic coercivity.
Let us now take a look at the optional properties of this material:
The register Magnetical shows all properties that are important for the magnetics solver.
ÍÍTo check this, select the function Inspect Material in the material list. This opens the fairly extensive material description. ÍÍChange to the register Magnetical. Here the magnetic, electrical and loss information of the material are deposited. ÍÍSelect CLOSE to close the dialog. ÍÍBack in the material list dialog, click OK to select the material Iron_Sample1 for the core. ÍÍFinally, activate the Force Results option to Compute on this Part and click OK twice to confirm.
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With this Force Results setting you state that the force analysis by virtual energy method is limited to the selected body. This setting is important because force analysis with the virtual energy method is quite complex for larger components with many elements. In order not to include unnecessarily too many elements in the analysis there is this possibility, a restriction to the specified body. Next, we want to apply correct properties to the coil: ÍÍDouble-click the mesh collector, which contains the mesh of the coil. ÍÍEnter the name Coil and select EDIT to open the dialogue of the Physical. ÍÍSelect the Material Copper from the same library as before. ÍÍYou also select in the box Conductor for Distribution the option Stranded and for Number of Turns, the value 36. Click OK twice to confirm.
The analysis of magnetic forces on a body is activated by the user in the physical if this result is required. Additionally, the force analysis must also be activated in the Output Requests of the solution.
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The settings shown in the figures are to be chosen for the coil face.
The distribution option Stranded means that the power should be distributed evenly over the coil surface. This corresponds to a coil that is wound. The indicated number of turns by the way has also important meanings: on the one hand, it affects the flooding of the coil, i. e., if later a current of 5 amperes is applied, these 5 amperes will flow 36 times through the coil, so that the flux will be 5 × 36 amperes. On the other hand, the number of turns also affects the inductive effect of a coil. So if the magnetic field varies in a dynamic analysis, e. g. in the case of an electric motor, the voltage in the coil that is produced by induction according to Faraday’s law depends on the number of turns. This voltage will be higher, the more turns it has. All these effects are taken into account in the simulation. For specifics of electrical conductors a separate box with settings is included in the Physical dialog.
In addition to the number of turns also the Fillfactor can have influence: If this is chosen to be less than 1, e. g. 0.75, this would mean that only 75 % of the cross-sectional area are filled with winding wire. This would affect the analysis as an artificial increase of the ohm’ resistance, because the current now would have less space. If in the analysis there would be conduction losses (Eddy Current Losses) requested, so now higher losses would result. Finally we give the air its property: ÍÍDouble-click the mesh collector, which contains the mesh of the air. ÍÍEnter the name Air and select EDIT to open the dialogue of the Physical. ÍÍSelect the material Air from the same library as before. Caution: It can easily happen that you select the material air from the wrong library. Namely, there exists also an air for flow simulations in the standard NX library. However, this air does not have any magnetic properties. So make sure to open the correct library.
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The settings shown in the figures are given to the air.
This completes the work in the FEM file.
6.3.1.5 Constraints and Loads As constraints, we apply two different symmetry conditions and a far-field condition to the environment according to our task. These conditions can be simultaneously used in both solutions Static and DynFreq. A current condition must be generated on the coil. This load has to be created twice: for the two solutions Static and DynFreq. We start with the constraints: ÍÍFirst, change the displayed part to the simulation file. ÍÍFor the tangential condition you create a constraint of the type Symmetry-Flux tangentially on the two edges of the Y-axis.
Boundary conditions are assigned in the simulation file.
In the figure a condition is defined, that enforces field lines to be tangential at the left edge.
The tangency condition internally sets the vector potential to zero, with the result that the magnetic field lines and the flux density vectors must be tangent here. Such a condition must always be defined at the axisymmetric axis. ÍÍAccordingly, for the normal condition you generate a constraint of type Symmetry-Flux normal to the four edges of the X-axis.
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In this figure a constraint is seen that forces the field lines to be normal on the bottom edges of the geometry.
Actually, the normal condition in the simulation causes nothing, i. e., you could omit this and would get the same result. It is the natural property of the vector potential at the outside edges of the computed region that field lines are perpendicular to the edge. The normal condition is therefore only useful for documentation purposes. Instead of the far-field condition a tangency condition can be chosen in the simplest case. At the outside edge of the computational domain, we assume that the field quantities have become very small, and a tangency condition would ensure that no magnetic flux can escape from the computational domain. Therefore, a normal condition would be completely wrong at this place, because an outgoing flux would naturally lead to a distortion of the results. Would the computational domain be large enough so that we could assume decayed fields at the outside edges, then the tangency condition would also be completely useful. But if we put the computational domain rather closely around our components, as it is the case in our geometry, we should choose a condition of the type Environment to Infinity with about three extra layers of infinite elements. In this extra layer of special elements transformations are performed to infinity, i. e., the actual distance up to infinity is calculated compressed in these elements. This is in practice a very sensible way to avoid unnecessarily large amounts of geometry that must be meshed. We produce this condition as follows: ÍÍCreate a constraint of the type Environment to Infinity on the circular edge. The environment condition automatically increases the computational domain.
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ÍÍActivate the solution Static by double-clicking because you want to work on this later. ÍÍOpen the Solver Parameters, which are found by RMB on the Static solution. Click EDIT and select Solver Parameters. ÍÍIn the register Env Condition set the Number of Circular Infinity Elements to 3. The settings shown in the figure define how the computational domain is automatically increased.
Caution: The use of these automatic infinite elements has two limitations: First, the boundary condition must be applied to a circular edge (in 3D analyses according to a spherical surface) and secondly the center of the circular edge must be located at zero. ÍÍDefine these solver parameter settings in both solutions (Static and DynFreq) and add the three constraints just created to both solutions. The simulation navigator shows the two solutions and the boundary conditions contained herein. The loads already shown will be generated in the following.
Lastly, we apply the current condition on the coil. Reminder: The coil is not solid but wound (Stranded) with 36 turns as we have defined it. Proceed as follows: ÍÍFirst activate the Static solution (double-click it so that it becomes blue). ÍÍYou can then generate a load of type Current 2D and accept the default type Static. Select the area of the coil and enter 5 A for the Electric Current. Finally, click on OK.
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The current on the coil surface is defined. 5 amperes are flowing through each winding. That means the flooding of the coil is 5 amperes x 36.
ÍÍNow activate the second solution DynFreq and create a load Current Harmonic 2D with 5 A and a phase shift of 0 degrees again on the same face.
6.3.1.6 Performing the Analysis Performing the analysis can be done quickly for these two solutions: ÍÍActivate the first solution, choose Solve . . . and click OK. ÍÍNow activate the second solution and also solve this. The computation time for this task is smaller than a second. You will be notified by a text output of the solver log file on the solution progress. Now the requested results are available in the NX post-processor. In the following, we always want to compare the results of static analysis (left) and dynamic analysis (right) in an image.
6.3.1.7 Flux Density and More Results Probably the most important result of an electromagnetic analysis is the magnetic flux density. The flux density allows, among others, to draw conclusions on the mechanical force on the body that arises at boundaries due to the magnetic field (reluctance force). The following figure shows that the distribution of flux density in statics and dynamics at 50 Hz is very different. ÍÍGo to the Post-Processing Navigator and open the two solutions. Display the result Fluxdensity__Unit_T.
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Left is the flux density for the static and right for the 50 Hz dynamic solution.
The flux density is output from MAGNETICS in the unit of Tesla. For images, the option for Color Display is best set to Banded and node combination on Average, but not at material boundaries, in the Postview settings. Of course in many cases the vector representation of the flux density is required, which is available with the Arrows option: The flux density in vector representation (left: static, right: dynamic).
Next, we’ll look at the current result. This shows both the applied currents given by us as well as possibly resulting currents by induction (eddy currents).
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The current result (left: static, right: dynamic with a recognizable induction effect on the core).
The current shown at the coil of 1.125 E6 An/m2 is exactly our specified current of 5 A, by 36 turns distributed over the area of the coil of 160 mm2. In the dynamic analysis (right) it can be seen that in the core there is an additional current density by means of induction. The skin depth is determined manually. It decides whether the element size is acceptable.
We determine the skin depth for the core. With f = 50 Hz ω = 2πf, σ = 10440000 S/m and μ = μ0 μr = 4π10-7 H/m * 295 results in the skin depth to δ ≈ 6,4 mm. In the area of skin depth there should not be too few elements (rule of thumb: five elements) to achieve a good accuracy. This is what we have achieved in our model approximately. Therefore, we are satisfied with the current mesh. Furthermore, we want to evaluate the force results. We turn on Force and select the Y component. Displaying arrows will show the results as in the figure below.
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The force result in plot representation: This can also be requested as tabular result. Then the sum of the nodes for each body is directly taken into account.
It can be seen that the forces in both cases arise almost only on the boundary edge of the core to the air. The total force can be determined by using the function Identify, selecting the mesh of the core, and the sum of all the nodes is evaluated. For the static solution, the force result is 0.08 N and for the dynamic solution 0.073 N. The axisymmetric effect, i. e. 2 Pi, is already included here. Last we want to see the vector potential, which also allows useful conclusions. Select the result Potential in the Z-direction. This result is best seen by iso curves, because this way it corresponds exactly to the magnetic field lines. The iso curves also help understanding how the magnetic flux goes: It goes along the iso curves of the potential result. The vector potential result (left: static, right: dynamic): This representation is shown when the Z-potential is represented as isolines.
The vector potential results are also interesting because they allow us to infer the magnetic flux between any two points. Because in cases of 2D magnetic field analyses using vector potential formulation, the following rule applies: The difference of the vector po-
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tential at two different points is equal to the magnetic flux passing between those two points. Once determined, the magnetic flux again can be used for the determination of magnetic inductance, which is an important parameter in electrical machines. Thus we have worked through this introductory example.
6.3.2 Coil with Core, 3D In this example, we set up a simple 3-D model. It is the geometry of the 2D axisymmetric previously analyzed model. Hence the results can be compared. The model is an angular piece with 30-degree angle. The previous 2D task (see section 6.3.1) will now be analyzed in 3D. Other 3D tasks can be solved with the presented methods in a similar manner.
We go fairly quick through the example, because it contains many things from the previous example, and concentrate on the specifics of 3D analyses.
6.3.2.1 Creating File Structure and Solutions ÍÍOpen the file CoreInductor.prt, start Advanced Simulation and select the function New FEM and Simulation. ÍÍSelect the Solver MAGNETICS and for Analysis Type set 3D Electromagnetics. When asked about the Solution Type, accept the default type Magnetostatic. ÍÍIn Output Requests activate at Plot the Magnetic Fluxdensity, Current Density and Nodal Force. Then click on OK.
6.3.2.2 Meshes and Physical Properties ÍÍSwitch to the FEM file. ÍÍUnhide the three volume polygon bodies and hide the sheet body. A continuous mesh through all the components and the air is required.
For electromagnetic analysis, it is necessary that the nodes of the finite elements coincide with each other at all borders. So we need a continuous mesh that includes both the components and the air. Gluing of meshes, as is usual in the structural analysis with NX Nastran, is not possible. This makes the meshing sometimes considerably more difficult in complex geometry. There are two methods for dealing with it: In the first method Mesh Mating Conditions are used. We want to use this method in our example. The second method works by using surface meshes (Surface Coats) that are created before the air mesh on the bodies. With such surface meshes it is usually easy to create following air meshes with use of the function Solid from Shell Mesh. The first method is more suitable for simple geometry and the second also for more complex geometry.
Two methods are possible for the air meshing. We show here only the first.
ÍÍCreate a Mesh Mating Condition: Call the function Mesh Mating Condition, drag a window over all items and confirm with OK. By default, the function creates the connection type Glue Coincident. It is searching for all interfaces of the volume bodies and providing them with such a condition. The condition ensures that in subsequent meshes the two involved meshes will have matching nodes at the interface.
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A prerequisite for this method is that the air geometry contains openings for all components. The parts were previously cut out (using a boolean subtract operation) in the CAD from the air. It should not be forgotten that this must be carried out with quite high-precision CAD and this often does not work that easy in complex geometry. Therefore, this first method is more suitable for simpler geometry. In other cases, you better make use of the method with the surface coat meshes. ÍÍMesh the core with tetrahedra elements and an element size of 3 mm and the coil with tetrahedra and an element size of 3 mm. ÍÍNow you mesh the air with tetrahedra elements and the proposed element size of 8.95 mm. The figure shows the meshed components. The simulation navigator shows the functions used in the FEM file.
Now we want to assign properties to the meshes. For most properties this is very similar to the procedure in 2D. Let’s start again with the core. Here there is no difference in practice to the 2D procedure: ÍÍDouble-click the first collector, which contains the mesh of the core. This opens the mesh collector dialog. ÍÍEnter (optional) for the name of the collector Core. Choose EDIT . This opens the dialog SolidPhysical. ÍÍEnter for the name Core in the SolidPhysical dialog. Use the function Choose Material to select the material Iron_Sample1. ÍÍIn Force Result activate Compute on this Part and click OK twice to confirm. ÍÍYou do the same for the air, but just with the material and without the setting for Force Result. Now we want to edit the coil. First, we give some properties much like previously in the 2D analysis: ÍÍEdit the collector and the Physical of the coil and enter the name Coil.
The core is treated as before in 2D.
At the coil, the procedure for the description of the winding in 3D is different from 2D.
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ÍÍAssign the material Copper. ÍÍIn the box Conductor set the option Distribution to Stranded, see Mesh Associated Data and the Number of Turns to 36. ÍÍFor Coil Section Area, enter the previously measured cross-sectional area of the coil. There are 160 mm2. This is a first difference to the 2D method. A major difference to the 2D method we have at the Stranded definition, because the directions of the current, i. e. the directions of the coil wire, still need to be specified. In the 2D model, that direction is always clear. It must simply be the Z-direction. In 3D, the direction can also extend spatially, e. g. in a circle. In NX it is possible to define this direction tangential to a curve or body edge, which allows complex current directions. Proceed as follows: ÍÍClose the dialogs by clicking twice on OK. Now edit the Mesh Associated Data of the coil mesh and define here the directions of current flow: The coil will be defined in such a way that the circular edge shown to the right is responsible for the directions of the windings. So the current can only flow in this direction. In this way, even complex coil shapes can be realized.
ÍÍOn the mesh of the coil you chose with RMB the option Edit Mesh Associated Data. ÍÍThere you set the Material Orientation Method to the option Tangent Curve. ÍÍAt Select Curve or Edge select one of the circular edges of the coil to which the current direction shall be tangent. When finished, click OK. Incidentally, this edge has a direction vector, which is defined automatically when you select it. Unfortunately, this vector is not always visualized. Using this vector, the positive current direction is determined. If the positive current direction is to be changed, this edge must be selected from the other side. These were the necessary steps in the FEM file.
6.3.2.3 Constraints and Loads ÍÍChange the displayed part to the simulation file. Now we continue with the constraints and the current load. Again, most conditions are very similar to those in the 2D method. We quickly go across the functions already known and concentrate on the specific features for 3D.
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The following figure shows the required boundary conditions and selection faces.
6 faces: flux tangent
1 face: environment
4 faces: flux normal
2 faces: SkinOfConductor
The areas shown in the figure must be provided with appropriate boundary conditions.
1 face: current 2D
Let us now turn to the conditions, which largely correspond to the 2D methodology: ÍÍFor the flux-normal condition, you create a constraint of type Symmetry-Flux normal to the four faces of the y = 0 plane. These areas correspond to the four edges of the 2D analysis. ÍÍOn the six-sectional areas of the angle piece a tangential condition needs to be generated. All six faces can be selected in a single constraint. ÍÍOn the spherical surface on the outside of the air, you create a condition Environment to Infinity. You also set in Solver Parameters the Number of Circular Infinity Elements to 3. ÍÍFor the current you generate a load Current with the type Static on Face on one of the two cut surfaces of the coil and with an amount of 5 A.
Some boundary conditions are similar to the procedure in 2D.
Now, a condition of the type Skin of Conductor must be created, which was not needed in 2D. This condition is only required for internal numerical methods – for the so-called Coulomb gauge. We hope that this condition can be generated automatically and internally in future versions of the system and is no longer expected of the user.
The Skin of Conductor condition limits the solid conductor. This condition must be applied for numerical reasons in 3D.
The condition Skin of the conductor must be defined on the entire surface of the electrically conductive geometry. The conductive geometry can be recognized by the electrical conductivity of the material, which has to be larger than zero. Exceptions to this rule are any conductors that have been defined with the Stranded option: Here no Skin of Conductor condition is applied. This rule must be observed at all times, otherwise no clear results can be calculated. In our case we have two conductors: the solid core and the coil. Because the coil is Stranded, the rule does not apply. At the core there are two areas remaining where the rule applies. ÍÍCreate a Skin of Conductor on the two surfaces shown in the previous figure. Thus the model structure is completed and it can be calculated.
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6.3.2.4 Performing the Computation and the Analysis ÍÍSelect Solve . . . The analysis takes only a few moments due to the small number of elements. ÍÍDisplay the force in the Y-direction and hide all meshes except the mesh of the core. Otherwise it is dangerous that you are querying one of the 2D meshes instead of the 3D mesh of the core. ÍÍUse the identification function to determine the sum of the forces on the core. It should be 0.008 N. If you use the output from Excel, the more accurate value 0.0076 will be calculated. The result of the force on the core differs for this rough analysis a few percent from the result of the 2D analysis.
The measured force must be multiplied by 12 if the result shall be compared with the 2D analysis, because the modeled angular piece is only one-twelfth of the overall model. Then a force of 0.09 N results. As a reminder, the 2D static analysis resulted in 0.08 N, which corresponds to a deviation of 12 %. Finer meshes would lead to a convergence of the two results. With this, the learning task is finished.
6.3.3 Electric Motor The following example of a synchronous electric motor with permanent magnets as outrunners and six pole pairs shows a simple, but realistic case of an electromagnetic motor analysis. The synchronous electric motor to be analyzed is an outrunner type: The CAD model can be found in the zip archive. The CAD surfaces are named and the air gap, as shown in the lower right figure, is divided into three parts.
run direc on 5
4
6 magnets radially nega ve
3 2
18 coils
1
6 magnets radially posi ve
airgap stator rotor
standing air empty space moving air
As special features or learning effects this task includes a rotating rotor that is moved in time steps and a 1D-circuit network for the implementation of a star circuit. In addition, a series of automatic auxiliary functions are used, with which the creation of electromagnetic FEM models will be considerably easier and faster.
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6.3.3.1 Task Typically for electric motors there is the need to analyze for the torque curve and the induced voltages of the three phases. In addition there is also interest in losses: on the one hand, these are conduction losses, which are mainly caused by the ohm resistance in copper. On the other hand, there are hysteresis losses resulting from permanent magnetic reversals, mainly in electrical sheets. Given are the speed of 1000 rev/min and the current amplitude of 6 A with 50 turns on each coil. The motor shall be driven by a star circuit. The winding scheme for the coils is provided and the depth of the motor in the Z direction is 100 mm.
Torque, induced v oltages and losses shall be analyzed.
6.3.3.2 CAD Preparations for Automation ÍÍStart the NX system and open the file ElectricMotor.prt. Our engine contains, using the 18 coils and twelve magnets, pretty much repetitive geometry. During the subsequent meshing each coil and each magnet must be individually meshed and many properties have to be applied. It is clear that too much manual work would result. Therefore, there are a number of auxiliary tools that can take over such recurring work for the MAGNETICS solver. We intend to make use of this.
The usual meshing of a motor engine would mean a lot of manual work. Therefore automations can be used.
These auxiliary tools base on the fact, that geometry in the CAD is structured by names or colors. It’s very simple: If the 18 coil faces in CAD for example are provided with names COIL01, COIL02 etc., the auxiliary tool in FEM file can search for all faces that contain the names COIL and mesh them. At present there are already such names attached to the 18 coils of the motor CAD model. The twelve magnets are already named. You can see those names in the CAD model. To use these names in subsequent tasks of the actual work, you only need to know how names are assigned in the NX system, and you will need the function for displaying those names in the graphics window. For clarification, please try this with another model: In order to give any surface a name, set the selection filter to Face and select the desired face. With the mouse on the surface you choose RMB and select Properties. In the following dialog select the General tab. Here, the name can be entered or changed. If multiple faces are selected, like all coils, you may want to add an index to the names (Add Index to Name) to ensure that a counter is appended to each name. This is very useful, for example, for the coils. When there are names assigned in the CAD system, you can automatically generate meshes, coil schema and more in the FEM file.
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First, the names are not displayed. Therefore, you must activate a switch in the Visualization Preferences in the register Names/Borders. There you set the option Show Object Names to All Views. In addition to names also colors of the faces can be exploited to use automatisms.
In addition to names also colors can be used for structuring for subsequent automatic processings. Our auxiliary tool can also be charged, for example, to mesh all white faces. In our learning example both options are used, i. e., the coils and the magnets have names. The rotating air and the stationary air, however, do not have names, but different colors.
With each analysis step the rotor is internally rotated a small angle. The air gap between stator and rotor also is remeshed internally at every analysis step.
A few words need to be said about the preparation of the air gap, which is shown enlarged on the right in the above figure. The goal is to use the so-called moving band function later, a feature that rotates the rotor finite elements internally in the solver: This feature requires that the moving and stationary parts must be separated by an air gap, as this is normally the case for each electric motor. The air gap must not be meshed in NX, because this is done by the solver MAGNETICS and updated internally with each analysis step. In the CAD model there must exist two circular edges to form the air gap: one for the stator and one for the rotor. To obtain more beautiful meshes – and more accurate results – the air gap on the CAD model is normally divided into three parts: a part of air, which moves with the rotor, a part of air, which stays with the stator, and the part that is in between them, not meshed in NX.
On the CAD model, an expression can be used for the rotor rotation. We will use this later for setting the rotor start position.
We also want to mention the CAD parameter Angle, which can be used on the motor CAD model for setting the start angle of the rotor. In the analysis, we will appreciate that the rotor does not have the optimum start position. Then we will adjust these parameters and update the FE model. Thus, the explanations for geometry preparation and the use of automation in the FEM file are complete. There were no required steps to do for you, because at the CAD model of the engine everything is already finished.
6.3.3.3 Create a File Structure and Solutions Now we can go through the steps of model construction. You will be surprised how fast it works using the auxiliary tools: The static solution is created with some default settings.
ÍÍStart the Advanced Simulation application and select the function New FEM and Simulation. ÍÍDeactivate the Create Idealized Part. ÍÍSelect the Solver MAGNETICS and for Analysis Type set 2D or axisym Electromagnetics. ÍÍYou will be asked for the solution. Enter the name Static and accept the default Solution Type Magnetostatic. ÍÍIn the register 2D set the Thickness to 100 mm. ÍÍActivate in the Output Requests at Plot: Magnetic Fluxdensity, Magnetic Field Strength, Current Density, Vector Potential and Displacement. ÍÍActivate RotorBand Torque at Table. ÍÍWhen finished, click OK.
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The displacement output is useful when rotations are performed in the analysis. Then, this result can be used for a graphical representation of this rotation. The RotorBand Torque output performs a special analysis of the torque, which is only possible when using the moving-band feature. This is done by the application of Maxwell’s stress tensor on the tape in the air gap. The method is preferred against the nodal force method due to the much higher computational speed. The nodal force/torque output uses a virtual energy method to calculate forces.
Special features of the requested results are Displacement and RotorBand Torque.
6.3.3.4 Meshes and Coil Scheme Now we can use our supporting tools for the automatic construction of the FEM model. These are the two features Auto FEM 2D and Multi Physical Edit. If we wanted to be very fast, we would need the Auto FEM 2D function only called once and would generate all the meshes and all 1D circuits for the winding diagram in one step. However, for didactic reasons, we deal with the subject in smaller steps. ÍÍChange the displayed part to the FEM file. ÍÍEnter the function Auto FEM 2D from the Magnetics toolbar.
Using the Tools Auto FEM 2D the entire meshing and coil scheme could be produced in just one step. Overview of the features of the tool Auto FEM 2D: There are three sections – Group, Network and Mesh. At the bottom of the picture the respective result is shown in the navigator. In the following the features are called one by one.
The dialog Auto FEM 2D has three sections: Group, Network and Mesh. The respective functions may be performed consecutively or together. ÍÍWe start by creating groups. The program aims to produce groups in the FEM part from all the designated faces in the CAD system, therefore, you enable Named Faces and do not specify a filter. ÍÍIn addition, the program shall produce groups for all faces without name but with color (the default colors are checked). Therefore, you also activate Colored Faces. ÍÍNote that all other switches are disabled. Click OK, and 34 groups are created in the following. In the navigator the newly created groups can be seen under the node groups. The names of the groups correspond to the name of the CAD faces. The last two groups are called StrongStone and White. They are created from colored faces and belong to the rotating (StrongStone) and the stationary (White) air.
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The 1D network is coupled with connector elements to the meshed 2D faces.
Next, the 1D network will be created. This may consist of discrete ohm resistors, inductors, capacitors or diodes. For connections to meshed 2D or 3D faces, meaning our coil, so-called connector elements must be generated. All these elements can be generated manually from point to point, for example with the standard function 1D Connection. Alternatively, the automatic method described here can be used. We start with the connector elements for the connection of the coils to the 1D network: ÍÍEnter the Auto FEM 2D feature. ÍÍDisable the two switches Named Faces and Colored Faces and ÍÍat Network activate the switch Connectors on Faces. ÍÍEnter COIL in Filter in large letters, because this way all our coil names will be found. ÍÍIn Length accept the number of 20 mm. The length is first only of visual importance. ÍÍClick OK, whereupon 18 connector elements are created onto the coils. In the navigator, the new connector elements are created and summarized in the collector AutoConnectors at 1D-Collector. Incidentally, such a connector element has two points or nodes that are formed by the names of the coil and “_A” or “_B”. Those two points are necessary because the connector element represents the two terminals of the coil. By using the names, it is possible to process these points automatically, so this is what we do next.
On the left, the connector elements are shown, with which the actual 1D network is connected to the 2D faces of the coils. On the right are the elements of the circuit network. These elements are always connected to a connector element or to the star point, either up or down. The currents can now flow through the motor as in reality. The file network.txt contains the coil scheme. This file can be imported into NX. In this way different schemes can be saved in text files easily.
Now the actual network will be created. This could be done again manually, but this is quite troublesome. It is much easier to save the definition of the coil scheme, or other electronic circuits, in text files and then import it to NX. In the following, we show the contents of the text file network.txt containing the coil scheme with star connection for this motor that we want to import. We have divided the lines of the file for lack of space in two columns. # The Starpoint:
resistor COIL12_B COIL13_B
point StarPoint 0 0 -10
resistor COIL13_A COIL18_A
# Phase U:
resistor COIL18_B COIL01_B
resistor COIL02_B COIL03_B
resistor COIL01_A Starpoint
resistor COIL03_A COIL08_A
# Phase W:
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resistor COIL08_B COIL09_B
resistor COIL04_B COIL05_B
resistor COIL09_A COIL14_A
resistor COIL05_A COIL10_A
resistor COIL14_B COIL15_B
resistor COIL10_B COIL11_B
resistor COIL15_A Starpoint
resistor COIL11_A COIL16_A
# Phase V:
resistor COIL16_B COIL17_B
resistor COIL06_B COIL07_B
resistor COIL17_A Starpoint
resistor COIL07_A COIL12_A
The definitions in the file are to be understood as follows: Each line is responsible for the creation of one network element. The first word in a line specifies the element type. Possible are resistor, inductor and capacitor. The second and the third word on the line are the names of the connector points to be connected with the network element. Another possibility is the command point, which is applied at the very beginning of our file. Thus, a node can be generated in the network, e. g. the star point. The second word is the name of the point, and then followed by the three coordinates of the spatial position. Any line that does not contain one of the commands is considered a comment line. For the import of the prepared network, proceed as follows: ÍÍEnter the feature Auto FEM 2D. ÍÍFirst deactivate all the switches. ÍÍAt Network activate the switch Import Network. ÍÍIn the file browser select the file network.txt, which is in the same directory as the CAD model. ÍÍClick OK, whereupon 18 resistor elements between the connector elements of the coils are produced. Lastly, you can generate the networks. Here again we use the auxiliary function. In this task we will create a very coarse mesh, because we do not want to exceed the limit of 1500 nodes of the software demo version. In a practical analysis of an electric motor we had to mesh much finer. The results that we produce with the coarse mesh will therefore be only qualitatively correct: ÍÍEnter the feature Auto FEM 2D. ÍÍFirst deactivate all switches. ÍÍActivate the switch Mesh Groups in Mesh. ÍÍIn Group Filter, enter nothing. This ensures that all existing groups are meshed. ÍÍAs Element Type you choose Quad. This way we can save elements most efficient. ÍÍIn Element Size enter 8 mm. This will lead to very large elements and the number of nodes will be below 1500. If you are not using the node-limited version, you should enter 1.5 mm. ÍÍClick OK, whereupon all meshes are created for the coil, magnets, stator, rotor and the two air spaces.
The 2D meshes are now created automatically.
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The following figure shows a section of the coarse grid for analysis with the node limited version on the left and the mesh with a fine resolution of 1.5 mm on the right.
The order of the meshes is determined by the alphabetical order of the names of the groups.
By the way, the order of creating the meshes is performed alphabetically according to the group names. This is quite important because the meshing sequence has a high influence: Meshes produced later must always adapt to already existing nodes at edges. The meshes first obtained thus have the greatest freedom and thus quality. In our model, we have already good names that will lead to an appropriate meshing order: first the coils (C . . .), then the magnets (M . . .), then Rotor and Stator, and finally the air (StrongStone, White) will be meshed. In other cases this may not fit so nicely. Then you may need to work with the wording: To create a mesh at the beginning, his group or face name can be given the prefix “a_”. Thus, the meshes and coil scheme or additional electrical circuits are fully assembled.
6.3.3.5 Physical Properties Physicals contain the physical characteristics of the meshes and are linked to meshes via mesh collectors. In the following, all 18 coils, all twelve magnets and the remaining meshes must be given such characteristics. Using the auxiliary tool Multi Physical Edit we can transfer characteristics of one Physical to many others. Of course, we want to use this in the following. We start with the coils: The first coil is defined manually.
ÍÍDouble-click the mesh collector of the first coil COIL01 and in the next dialog select EDIT. This opens the dialog PlanePhysical. ÍÍIn dialog PlanePhysical select material Copper from the magnetics material library. ÍÍIn Distribution set the option Stranded and in Number of Turns define 50. ÍÍClose the dialogs with twice clicking OK. ÍÍCall from the Magnetics toolbar Multi Physical Edit. This opens a dialog. ÍÍEnter the name of the master physical in the field Name of Physical, i.e. COIL01. Note the use of uppercase and lowercase letters. ÍÍEnter a portion of those physicals that shall be processed in Filter. To process all other coils, enter COIL. Finish with OK. ÍÍCheck one coil or the other. They should now have all the same properties.
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Using the function Multi Physical Edit all properties of the finished coil are passed to the others.
Next, we edit the magnets. We first want to set all twelve magnets equal, pointing with their north direction into radial direction. Then we create a material with a negative magnetic direction and assign this to the six oppositely oriented magnets: ÍÍDouble-click the mesh collector of the first magnet MAGNET_NEG1 and select EDIT. ÍÍIn the PlanePhysical dialog find and select material N30EH at 100C, a neodymium magnet from the magnetics material library. ÍÍFor Magnet CSYS select the Cylindrical option. It appears another field Magnet Orientation for the specification of a cylindrical coordinate system. ÍÍFor Magnet Orientation you choose the absolute CSYS.
A first magnet is defined manually.
The properties of the finished magnets are passed to all other magnets.
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ÍÍBelow the box Motion set the option Movability to Part can Move, because the magnets belong to the moving parts. There appear two more fields for mass properties that can be left empty, because we want to simulate not for a free but for a forced rotor movement. Then click OK twice. ÍÍSwitch to the function Multi Physical Edit, enter this time MAGNET_NEG1 for Name of Physical and MAGNET for Filter. ÍÍConfirm with OK. Now these properties are transferred to all twelve magnets. Now we create a copy of the magnetic material in which we set the Coercivity, i. e. the strength of the magnet, negative. Then we apply this new material to the six corresponding magnets. In this way, we can easily get to the desired alternating arrangement of the magnets: Because the magnets are arranged alternately, we produce a magnetic material having a negative magnetic direction.
ÍÍEdit again the Physical of the magnet MAGNET_NEG1. ÍÍFor materials you select the function Choose Material. ÍÍIn the following dialog material list set the option Local Materials. There appear Copper and our magnet material N30EH at 100C. ÍÍSelect the magnetic material and select the function to copy the selected material. ÍÍIn the next dialog, the properties of the new copied material appear which has now received the suffix “_1”. ÍÍChange to the register Magnetical and write a minus sign before the value of the former Magnetic Coercivity X. ÍÍEnable left in the row the setting Overridden Value, so that the green tick can be seen. ÍÍWith four times clicking on OK you exit the dialog.
The magnetic material has been duplicated and now the magnet strength (Coercivity) is negated.
Now you have assigned this negatively oriented magnetic material to Physical MAGNET_ NEG1. Next, you assign it to all the other physicals that need to be negative: The negated magnetic material is assigned to the corresponding magnets.
ÍÍSwitch to the function Multi Physical Edit. ÍÍEnter MAGNET_NEG1 in Name of Physical and set MAGNET_NEG for the Filter. Finish with OK. The work for which those special auxiliary tools can help is ready. There still remain the stator, the rotor, the air and the resistance of the circuits. This requires no special further knowledge:
Stator and rotor are defined.
ÍÍEdit the Physical of the rotor. Select material ElectroSheet_Sample1 from the magnetics library. Set the Movability option to Part can Move. ÍÍEdit the Physical of the stator. Select ElectroSheet_Sample1.
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ÍÍEdit the Physical StrongStone that represents the moving air. Change the name to Air_ Rotor. Select the material Air and set Movability option to Part can Move. ÍÍEdit the physical White that represents the stationary air. Change the name to Air_Stator. Select the material Air. ÍÍEdit the 1D mesh collector which is named ResistorsFromFile. Here still no Physical has been created. In the dialog chose the function Create Physical and accept the default settings in it. Then click OK twice.
Finally the two air spaces are defined.
Thus the work in the FEM file is completed.
6.3.3.6 Rotor Motion Movements of FEM meshes can be done in MAGNETICS by two alternative methods: General Motion and Moving Band. The function General Motion allows – as the name suggests – movements in a general way. The principle is that the movement is defined by the CAD parameters, parameter, for example, indicates the position of a slide in the space or the angle of a rotor. The General Motion function runs in a loop with many steps through the NX system. It respectively changes the CAD parameter by a small amount, updates the finite element meshes and boundary conditions, starts the solution, stores the results, and changes in the next step again the CAD parameter. If an electrical dynamic solution runs, then respectively the previous step of each solution step must be included to satisfy the analysis of gradients, which is done by interpolation of the old results on the new mesh. In this way, controlled by the CAD system, movements can be defined flexible. In the current software version merely translational or rotational motion types of single parts can be handled. This method has the advantage of universality. The disadvantages are first the susceptibility to update-errors and the loss of speed due to the many CAD and mesh updates. Additional uncertainty comes through the interpolation.
The General Motion function uses CAD parametrics to represent movements. This requires NX updates with each movement step, meshes and result from last step will be projected.
The moving band function also moves FE meshes for each movement step, but this is done purely in the solver, i. e., the CAD system is not involved. Here, the moving meshes and the area between the stationary and moving meshes are remeshed with each step, which also happens in the solver. The advantages are the stability and speed of the method, since everything runs in the solver. The disadvantage is that this is possible only for simple types of motion, i. e. rotation and displacement.
In this example we use the moving band operation in which the rotation is performed inside the solver.
In our example we want to use the moving band function, which is well suited for electric motors. The requirement is that all moving meshes are characterized as we already did it in the Physicals. In addition both the rotor and the stator must have a circular edge at the air gap. Before we call the moving band feature we want to define a few Expressions in the NX system to later control our movements and currents:
For the moving band function there must exist two circular edges at the air gap.
ÍÍChange the displayed part to the simulation file. ÍÍCall the function Expressions from the NX menu bar in Tools. ÍÍCreate the expressions, as shown in the figure below. Please make sure that the units shown below are used. Generate CurrentFrequency and TimeIncrement as last, because they depend on the others. Alternatively, you can run the visual basic journal Create-
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Expressions.vb that does these steps automatically. The journal is located in the folder of the CAD model. These Expressions are used later for boundary conditions, currents and other settings.
Next, the two circular edges are provided with names. The names will be referenced later in the movement function Enforced Motion 2D: Hint: The next 4 steps, e. g. the creation of Extract Physicals are not necessary included in the newest version of NX MAGNETICS. There you can simply select these two edges inside the Enforced Motion feature with the mouse. The next picture already shows the new dialog. ÍÍChoose the function Extract Physical 2D from the simulation objects. ÍÍIn the dialog set the type to On Edge and select the outer circular edge at the air gap, i.e. the edge which is part of the rotating air. ÍÍEnter the name AirGapRotorSide. (Please do not use spaces in the name.) Click on PPLY. A ÍÍCreate the same function again for the inner circular edge at the air gap. Name this AirGapStatorSide. ÍÍNow create a simulation object of the type Enforced Motion 2D. This element will define a forced movement, as it is useful in static solutions. In a dynamic solution the Dynamic Motion feature is additionally possible, which corresponds to freely movable rotors. This could simulate, for example, the starting behavior of rotors. ÍÍIn the Enforced Motion dialog switch the Technique to Moving Band. ÍÍIn the field Stator Edge Physical Name enter AirGapStatorSide and in the field Rotor Edge Physical Name enter AirGapRotorSide. ÍÍFor Step Size, enter the name of the previously generated expression RotorStep. Now click on OK.
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The definition of the moving band feature is illustrated in the following figure. On the left the dialog is shown with the names of the two circular edges and the specified step size. On the right you see once again the air gap and its edges.
Hence the rotation of the rotor is defined. Two pieces of information are still missing that need to be given in the solution: ÍÍSelect RMB on the static solution and select EDIT. ÍÍChange to the register Time Steps and set the Number of Time Steps to 90 and the Time Increment to expression TimeIncrement. Complete the steps with OK. With these settings, the rotor will perform 90 steps each with one degree of movement. The mechanical speed is 1 turn/min and the rotation is negative toward right-hand rule, i. e. clockwise.
6.3.3.7 Define Three Phase Power The definition of current conditions follows. These will be applied as three phase power between the connectors of the coils and the star point, such as is the case in reality. The current for phase U will flow between the open end of the U-winding and the star point. The same applies for phases V and W. The currents work as harmonic cosine functions with appropriate phase shifts (0, 120, and 240 degrees). In the figure below you see the star point and the three open ends of the phases. Between these points, we will define the following currents.
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The figure shows the 1D network for the coil scheme. At three points as well as at the star point the currents U, V and W are defined.
To generate the current of the U-phase between two nodes of the network, proceed as follows: ÍÍChose a load Current 2D and in the dialog set Type to Harmonic Circuit. ÍÍEnter as name U phase. ÍÍSelect in the field Primary Node the point or node that is labeled U phase in the figure. ÍÍSelect in the field Secondary Node the star point in the middle. ÍÍEnter in the box Magnitude the following expressions: Electric Current: CurrentAmplitude Frequency: CurrentFrequency Phase Shift: 0 Click on APPLY. ÍÍDefine in the same way the current for phase V. Enter the name V Phase and a Phase Shift of 120 degrees. ÍÍDefine in the same way the current for phase W with name W Phase and Phase Shift 240 degrees.
6.3.3.8 Environmental Condition At the inner and outer edges to the environment a condition is set that provides tangential field lines. We therefore assume that the field has decayed there. ÍÍGenerate a constraint condition Environment to Infinity on the outer circular edge to the surroundings and also on the inner circular edge.
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At the two edges inside and outside an ambient condition is set.
Now all entries are done and analysis can be performed.
6.3.3.9 Find Rotor Starting Position Now we can simulate the motor running and represent the produced torque and other quantities. But beforehand we want yet to find out the correct start position of the rotor for maximum load, because it would be a coincidence if this would already be the actual position which it would occupy under load. To find out, we do an analysis, in which the rotor is initially kept fixed. The magnets and coils will – even without rotor movement – generate torque on the rotor. With this torque curve we want to detect the rotational angle at which the torque has an extreme value. Using this angle, we can see how much the rotor must be pre-rotated. We have to look for the negative extreme value, because this right-handed running rotor must be driven by negative torque. It should be noted that there exist other methods to find the starting angle, too, for example, by checking phase voltages. ÍÍEdit the Enforced Joint and initially enter for Step Size the formula 0 × RotorStep. Now the rotor is artificially kept fixed. ÍÍSolve the static solution. The analysis of these 90 steps takes around one and three minutes. ÍÍAfter the solver has completed the job, select the feature Table Result to AFU Graph in the Magnetics toolbar. ÍÍIn the following file browser select the newly created file ElectricMotor_sim1-Static. Torque.txt in your working directory and confirm with OK. A new AFU-file is created, which can be represented in NX. ÍÍNow go to the NX-resource bar and open the XY feature navigator. You see at Associated AFU that the file is opened and contains an entry TorqueBand_on_Enforced_Joint (1). Double-click this entry, click in the graphics window as the target, and your graph appears.
The rotor-start position is the one in which the rotor has maximum torque.
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The figure shows the torque curve for the rotor fixed at initial and pre-rotated position. It is determined by the coarse meshes.
In the period that is shown in the graph, the rotor should rotate about 90 degrees. On the first negative peak (at 1.667 sec) it can be seen that a pre-rotation of about 10 degrees (i. e. 1.667 × pole pairs = 10.002) would cause the rotor to be started with minimum torque. So we want to set this: ÍÍChange the displayed part to the CAD master model ElectricMotor.prt. ÍÍChange the expression “p34” from zero to 10 degrees. The rotor is now moved in a clockwise direction. ÍÍSwitch to the FEM file and run the function to update the meshes. ÍÍSwitch to the SIM file, solve the solution again and check to display the graph. The rotor is now set to its starting position on the CAD model.
You notice that the rotor starts with maximum negative torque now. Thus we have a realistic starting condition for the motor running in the next section.
6.3.3.10 Calculate Torque Curve We can now bring the rotor to life and calculate the torque curve as well as other results: ÍÍEdit the Enforced Joint and adjust the Step Size back to the expression RotorStep. We want to obtain more accurate results, so we reduce the residual tolerance of the nonlinear Newton’s method by two powers, because this is rather coarse chosen on the default setting:
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ÍÍUse RMB on the static solution and chose the option Solver Parameters. Change to the Numeric tab. Set the value of Epsilon to 5e-5. ÍÍSolve the static solution and represent the torque curve. The figure shows the torque curves over 90 degrees, resulting from analysis with coarse and fine mesh.
In the above graph, the results of the coarse and finer analysis are displayed simultaneously. The coarse mesh analysis has been performed with the node-limited software version (element size 8 mm, RotorStep 1 degree, 90 steps) and the finer analysis with element size 1.5 mm, RotorStep 0.5 degrees and 180 steps. The torque curve gives a lot of information on the motor. In addition to the average torque torque-ripple is also of interest. Both can be read from the graph. ÍÍIn the XY function navigator switch to the function Information with RMB on the node TorqueBand_on_Enforced_Joint (1). Here some useful information is given. Thus you see, for example, the mean value of the graph is in the case of the coarse-analysis − 10.1 Nm (here the fine mesh-analysis shows a value of − 10.3 Nm). Those large fluctuations in the torque show the engine development specialists that the configuration of this engine is not yet optimal. More magnets and coils would improve this situation.
Coarse and fine mesh analysis differ at the averaged torque value only slightly from each other. Variations in the ripple are significantly larger.
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6.3.3.11 Represent Flux Density and Movement of the Rotor In addition to graphing tabular results you can also plot results, e. g. flux density, field strength or currents are presented. To do this, open the result in the post-processing navigator, chose any time-step and double-click on the desired result type, for example flux density. Of course it is also interesting to represent the motion of the rotor while flux density is displayed. To do this, follow these steps (see also figure below): The rotation of the rotor can be represented in the post-processor. A couple of settings are necessary.
ÍÍFirst set the result, for example, the flux density of the first time step. ÍÍThen select the function to edit the view Edit Post View. ÍÍIn the Display tab activate Deformation, disable Synchronize Color Display and Deformation, and click right next to the Results . . . button. ÍÍIn the next dialog, switch to Displacement, so that the deformation is presented on the basis of this result. Now click on OK. ÍÍBack in dialogue View Post you activate the button Synchronize Color Display and Deformation. Confirm with OK. ÍÍNow you can use the green button Next Mode/Iteration to move the rotor forward, and during this observe the behavior of flux density.
These settings are used to represent rotation of the rotor.
6.3.3.12 Determine Voltage Curve of the Phases Now the voltage induced in the coil voltages is to be determined, which is an important factor for the design of controllers. The motor shall rotate with 1000 turns per minute. We want to calculate this without external power, because the result would otherwise be affected. For this task, a dynamic analysis type must be selected and we will perform the analysis in the time domain. By the way, we can then compare how results differ from static to dynamics. Proceed as follows: The voltage characteristic in the phases is carried out automatically in the FEM analysis of a circuit network.
ÍÍCreate a new solution of type Magnetodynamic Transient and rename it MagDyn1000Umin. ÍÍEnter again for the Thickness 100 mm, for Time Steps 90 and for Time Increment the expression TimeIncrement. ÍÍActivate in the Output Requests the settings shown in the figure and click OK. ÍÍInclude any previously created simulation objects, constraints and loads of the static solution into the new solution.
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ÍÍChange the following expressions: SpeedMech = 1000 rev/min CurrentAmplitude = 0 A. Now we will define in a simple way a voltage measurement between two phases. This is done simply by inserting a further current with the magnitude 0 A between the desired two points of the 1D network. In the simulation, the resulting voltage is determined automatically on all such current conditions. The responsible output request for this is the already activated Voltage on Circuits. ÍÍFor the evaluation of a linked phase voltage, e. g. between the phases U and V, you create another current condition (Type: Static on Circuit) with 0 A between the points U and V. Call this Sensor UV Phase. ÍÍSolve the solution. These settings are required in the dynamic solution to evaluate the phase voltages.
ÍÍRead the file ElectricMotor_sim1-MagDyn1000Umin.Voltage.txt with the AFU tool. Plot the results of the three-phase voltage and the sensor as a graph.
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The figure shows the induced voltage characteristic of the three phases as well as the concatenated phase between U and V.
The voltage result shown in the figure above has been done with the fine mesh analysis. The most important result is the maximum value of the concatenated voltage of 207 V. For a rough mesh analysis a voltage of 201 V comes out.
6.3.3.13 Determine Losses Losses arising in electric machines must be controlled because they produce heat and therefore have to be dissipated in an appropriate manner. They are usually divided into conduction losses, iron losses and possibly other types. In a simulation with the MAGNETICS solver these quantities can be calculated and passed even to the NX/Thermal solver for the purpose of temperature analysis. We do not want to go this deep, but merely determine and represent losses qualitatively. The experienced user can use them to do geometry optimizations to reduce losses. Losses are divided into conduction losses (Eddy Current Losses), iron losses and other types.
Conduction losses, also called Eddy Current Losses are those arising from the current and ohm resistance. For conduction losses, no special material properties need to be known, because ohmic resistance is calculated by electric conductivity and currents are also known from the simulation. Iron losses result from magnetic reversals or hysteresis of the alternating magnetic field in iron. To compute this, there are many different approaches. In MAGNETICS the Steinmetz formula is used for this, requiring that the Steinmetz coefficients of the investigated material are known. In the material ElectroSheet_Sample1 that is used in our task such
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coefficients are given, so we can compute iron losses in the rotor and stator. Proceed as follows: ÍÍClone the solution MagDyn1000Umin and rename the new solution Losses 1000Umin. ÍÍRemove the current Sensor UV Phase from the new solution. ÍÍSet the expression CurrentAmplitude back to the value of 6 A. ÍÍSolve the solution. ÍÍRepresent the file . . . EddyCurrentLosses using the AFU tool. The file includes curves for each body that produces eddy currents, i.e. the magnets, the rotor and stator. The following figure shows an example graph for two magnets, the rotor and stator, which were determined with the fine mesh analysis. The rough mesh analysis here shows widely differing larger values, which differ by about a factor of 2. The figure shows conduction losses (Eddy Current Losses) for 90 degrees rotor rotation that arise on the magnets essentially.
Rotor and stator show almost no values. This is intended because their electrical conductivity is set to nearly zero. This is a simple trick to model the layer structure of the magnetic steel sheet. In reality, currents barely occur at these sheets because each plate is insulated from the neighbors. The magnets, however, are significantly involved in eddy current production. From the graphs it appears that each one produces about 0.5 W power dissipation. Twelve pieces make 6 W in sum. Conduction losses of the windings have to be added, which are not yet covered in the current software version. However these can be determined without FE simulation, by the length of the wire, the cross section and the Ohm resistance. ÍÍRepresent the file . . . HysteresisLosses using the AFU tools.
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The hysteresis losses are zero on the magnets because the Steinmetz coefficients are not given here. However, we expect no hysteresis losses on the magnets, because the field remains almost constant there. The figure shows iron losses arising mainly in the stator and rotor.
On the rotor, these losses are much smaller (about 3 W) than on the stator (about 40 W) because the rotor carries the magnets, and the field is less subject to changes here. Overall, the calculated losses are coarsely given as 6 W + 3 W + 40 W ≈ 50 W. These figures have been calculated with the fine mesh analysis. Using the rough mesh much larger conduction losses appear. For an analysis of losses such a rough mesh is not permitted. Of course, the losses can also be represented graphically with the plot results. With this, the learning task is completed.
Bibliography [Binde6] Binde, P.: Electromagnetic Analysis with MAGNETICS for NX. Training Documentation. Dr. Binde Ingenieure GmbH, Wiesbaden 2014 [Bossavit] Bossavit, A.: Computational Electromagnetism. Variational Formulations, Complementarity, Edge Elements. Academic Press, San Diego/London/Boston/New York/Sydney/Tokyo/Toronto 1997 [Dular] Dular, P.: Modélisation du champ magnétique et des courants induits dans des systèmes tridimensionnels non linéaires. Ph.D. thesis 152. Université de Liège, Faculty of Applied Sciences, Liège 1994 [GetDP 2014] GetDP, a general environment for the treatment of discrete problems (http:// www.geuz.org/getdp/) [Geuzaine 2001] Geuzaine, C.: High order hybrid finite element schemes for Maxwell’s equations taking thin structures and global quantities into account. Université de Liège, Liège 2001 [Geuzaine 2013] Geuzaine, C.: ELEC0041. Modeling and Design of Electromagnetic Systems. Université de Liège, Applied & Computational Electromagnetics (ACE) [Weiland] Weiland, T.: A Discretization Method for the Solution of Maxwell’s Equations for Six-Component Fields. In: International Journal of Electronics and Commu nications (AEÜ), Vol. 31, No. 3, 1977. p. 116–120
7
Management of Analysis and Simulation Data
■■7.1 Introduction and Theory The management of analysis and simulation data aims to integrate analysis and simulation results in the workflow of virtual product development. For this purpose, this information is embedded in a PDM environment. Background information can be found in the recommendation [SimPDM]. An overview of the results of the SimPDM project group provides [Anderl3].
7.1.1 CAD/CAE Integration Issues Today, most manufacturing companies face the challenge of having to develop faster and more complex products. Design and simulation play a key role for the evaluation of product development results. What is new for many engineers is that simulation is gaining an increasing importance, and for higher development efficiency its integration with 3D product modeling is a critical success factor.
To integrate CAD and CAE today is a major challenge.
This linkage problem is characterized by the following properties: Personnel separation of modeling from the analysis: Because more and more specialized know-how is needed, it necessarily results in different professional qualifications for design and for analysis. Partially a corresponding specialization is already taken in continuing education and advanced training. Engineers and designers today put up significantly different demands on software tools and find it difficult to use a common database. Many different CAE software systems: Because simulation is increasingly gaining importance and more and more physical phenomena are analyzed, more and more different software programs have been developed and are deployed. It is today therefore not uncommon if large companies use up to 100 different CAE programs. Many of these programs are very specific and sometimes used by specialized experts. The installation, maintenance and licensing of these programs is very expensive – and of course the linkage of all these programs is hardly possible.
Problems with CAD/ CAE integration
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One example is the vehicle body-analysis.
Which CAD model actually belongs to which FEM model?
PLM systems can help.
Many analysis variants: Companies that are convinced of the efficiency of simulation often carry out numerous analysis variants. For example, in the automotive industry stiffness and crash analysis of the bodies is performed in many variants – often even automated. An analysis of the body is in this case carried out with different engines, different dummies (female, male, children . . .), different seating positions (each locked position) and various load cases. This quickly leads to 1000 or more variations for a body. In fact, analysis and simulation is no longer only about the evaluation of individual parts. Lack of relationship of CAD to CAE models: The answer to the really simple question, “Which FEM model belongs to which CAD model?” becomes a challenge if, firstly, the complexity of the CAD assemblies (e. g. several thousand components), the CAD variants, the analysis disciplines and analysis load cases are large, secondly, the dynamics of the design changes increases and thirdly, an increasing number of developers is involved. Lack of process orientation: Release and change processes as well as other typical processes (e. g., maturity tracking, design review), in which design and analysis have to be involved, the processes are missing a clear identification of the stages of development as well as an automatized versioning. Inadequate data protection: In particular simulation data, which can reach enormous sizes, is today often still excluded from automatic backup data encryption. Insufficient supplier integration These challenges can be met with the functionality of PDM systems: structure and configuration management, variant and version management, workflow, and process management. However, there is a need to extend the previously specialized design data management functions for analysis and simulation data and to meet the needs of users and the heterogeneity of the system landscape [Anderl4]. Simulation Data Management enables the synchronization of the processes of different CAE domains, the change management and version control of CAE data and guarantees to work on the basis of the latest version levels. Through this increase in efficiency, a significant time saving in CAE processes is expected [Malzacher].
7.1.2 Solutions with Teamcenter for Simulation In our following discussion, we restrict ourselves to the solutions of the PLM system Teamcenter from Siemens Industry Software GmbH and its CAE expansion modules, known as Teamcenter for Simulation. So you should have basic knowledge in dealing with the Teamcenter system. There are solutions, but often significant changes to the software are required.
Teamcenter and Teamcenter for Simulation now offer solutions for some of the abovementioned problems or at least approaches to overcome them. The Teamcenter system is a very flexible product data management system (PDM), based on a database software that can be customized to individual needs and problems by configuration or application programming. This can be very expensive, of course, and is primarily used by large com-
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panies. Therefore, Teamcenter offers also a series of standard solutions that are used advantageously in many cases. For example, the connection of the NX system to Teamcenter is advanced and can be used out of the box. Fundamental to all types of simulation is the CAE data model described in the next section.
7.1.2.1 The CAE Data Model in Teamcenter for Simulation If in Teamcenter a standard CAE analysis is performed with NX, the native files (SIM, FEM and idealized) are assigned (in the dataset) to the corresponding Item Revisions (CAEAnalysis, CAEModel and CAEGeometry) as named references. These CAE Item revisions can be revisioned independently. In addition, data is automatically provided with relationships. This data model and the relations are shown simplified in the following figure [TCSim]. TC_CAE_Defining 0-n:0-1
CAEAnalysis Rev. (Sim-File)
CAEModel Rev. (FEM-File) TC_CAE_Source 0-n:0-1 TC_CAE_Target
0-n:0-n
CAD-Master Rev.
0-n:0-n
TC_CAE_Source
0-n:0-1 TC_CAE_Source
0-n:0-1
CAEGeometry Rev. (Ideal-File)
TC_CAE_Target
The CAD master can be either a single part or an assembly. The data model initially corresponds exactly to the native CAE file structure. The relations have the following meaning: TC_CAE_Defining: This relationship tracks which CAEModelRev is used by the CAEAnalysisRev, that means, which meshing is computed with a SIM file. For a CAEAnalysisRev there can be only one CAEModelRev, because there can be only one mesh for the computation. TC_CAE_Source: This relationship indicates from which item revision a model has been created, that means, which item revision was the source. It can be defined between CAEModelRev and CAEGeometryRev or between CAEGeometryRev and CAD Master revisions. In case that no idealized file is used, this relationship may also exist between CAEModelRev and CAD master. There can be only one source at a time. TC_CAE_Target: This relationship documents for which CAD-Master-Revision each CAE-Item-Revision applies (from CAEModelRev to CAD-Master-Revision, from CAEGeometryRev to CAD-Master-Revision). Several TC_CAE_Target relationships may exist parallel. An example of multiple parallel TC_CAE_Target relations is the following: The simulation for a green part shall have validity for the identical blue, yellow and red parts.
The CAE Data Model of Teamcenter for Simulation.
Three relations are mainly used.
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The relationship of CAD to CAE becomes transparent.
Using this data model, the desired relationships between CAD and CAE are now available. This answers the question: “Which CAD model belongs to which FEM model?” Also the problem of a high variety of analysis variants is addressed. Additionally, these relations allow to automate approval processes between design and analysis. Of course it is also important that these relationships can be tested and used conveniently by the user. Therefore the following learning tasks should give an overview. Finally, we would like to add that this data model is also valid for assemblies and not only limited to the NX system as a pre/post-processor and NX/Nastran as solver.
7.1.2.2 Additional Solutions Teamcenter and Teamcenter for Simulation offer additional solutions for the above mentioned problems. Due to the limited scale of the book we cannot fully discuss, but only touch these topics: In this book, we can only describe very basic solutions.
Support for the integration of foreign pre/post-processors and solvers in Teamcenter Support for the integration of foreign CAE systems through defining their own data models Automated processes, such as approval processes, as well as meshing or solving large amounts of data in a batch run Creating CAE assembly structures and automated derivation of these from existing CAD assembly structures using rules Furthermore, the software development in this area is very dynamic, and more blocks are added every year.
■■7.2 Learning Tasks on Teamcenter for Simulation In order to work through these learning tasks, it is beneficial if you already know the fundamentals of FEM analysis with NX, as they are provided in section 3.2.1 in our basic example “Notch stress at the steering lever (Sol101)”. This is not absolutely required, which means, database administrators, for example, can also make good use of these examples. In any case, however, you should have basic knowledge of working with Teamcenter.
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7.2.1 Carrying out an NX CAE Analysis in Teamcenter In this task, the steps of an ordinary structure analysis of an item in the NX system will be carried out under Teamcenter. Similarily, some of the other FEA or CFD solution types could be carried out, because they all use the same CAE file structure. Only motion analysis behaves differently.
Mini FEM task
7.2.1.1 Task Formulation A handle from the RAK2 assembly shall be analyzed with FEM in Teamcenter. The handle and its loads and constraints are shown in the following figure. In this learning task you will learn the steps to perform a FEM analysis and how to store analysis results in Teamcenter. A handle of the wing adjustment of the RAK2 serves as example. Alternatively, any other part can be used.
7.2.1.2 Importing a CAD Part in Teamcenter For our learning task, you first import a file from the RAK2 directory in Teamcenter. Alternatively, you can also use some other item. ÍÍAt first, start Teamcenter and NX. ÍÍIn NX, select the function File, Import Assembly into Teamcenter. ÍÍIn the tab Main, select the function Add Part and choose the NX CAD file to be imported. In our example, select the file fl_hebel_griff.prt. ÍÍIn the tab Load Options, choose the loading method From Directory. ÍÍIn the Main tab, start the Import with the function Execute. ÍÍNow, the question for the number of the CAD file in Teamcenter appears. You can assign any number. To make our example easy to understand, we choose a number that is easy to remember, for example, the 000100. ÍÍAfter successful importing exit the menu with CLOSE.
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After the import is complete, you can see the CAD part in the Newstuff folder.
7.2.1.3 Creation of the Teamcenter CAE Structure The CAE file structure has three files: SIM, FEM and idealized.
The Teamcenter CAE structure is preferably generated through the NX interface, because the relationships are then managed automatically. Proceed as follows:
The numbers of the three items are specified by the user.
The process for creating the SIM and FEM data and the idealized files or the associated records in Teamcenter is different from the native application of NX: First, we are asked for the FEM file, then for the idealized file and finally for the SIM file. These steps are carried out below.
ÍÍOpen the imported part in NX. ÍÍIn NX, start the application Advanced Simulation and select the function New FEM Simulation to generate a new CAE file structure.
We want to use the numbers of the data sets as follows: CAD: 000100 Idealized: 000101 FEM: 000102 SIM: 000103
7.2.1.3.1 FEM-File/CAEModelRevision The following figure shows the first dialog for the creation of the FEM file or data type CAEModelRevision. The user selects a template, in our case, the NX Nastran template, and enters an item number, revision and a name. In addition, the folder in which the item shall be placed is specified. ÍÍFor CAEModelRevision enter the number 000102, the revision A and Folder Newstuff (see figure below). Confirm with OK.
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The FEM file of data type CAEModelRevision is stored in Teamcenter. When creating a NX simulation, the CAEModelRevision is defined by the user.
This completes the creation of the FEM-File/CAEModelRevision. The next dialog will appear immediately.
7.2.1.3.2 Idealized-File/CAEGeometryRevision The following figure shows the next dialog. This is very similar to the native generation dialog. Here the idealized file is created and the settings for the solver and the type of analysis shall be defined. Also the functions Bodies to Use and Geometry Options can be found here. ÍÍFor CAEGeometryRevision enter the number 000101, the revision A and Folder Newstuff (see figure below). Confirm with OK.
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The idealized file of data type CAEGeometry Revision is stored in Teamcenter.
After the idealized file or CAEGeometryRevision is defined completely, another dialog appears.
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7.2.1.3.3 SIM-File/CAEAnalysisRevision The dialog for the SIM file or CAEAnalysisRevision is shown in the figure below. ÍÍFor CAEAnalysisRevision enter the number 000103, the revision A and Folder Newstuff (see figure below). Click OK. ÍÍConfirm the following window New Simulation with OK. The SIM file of data type CAEAnalysisRevision is stored in Teamcenter.
After this dialog is completed, the last window New Simulation appears and can be confirmed with OK. ÍÍNext, just like in the native system, the specification of the solution appears. Here just confirm the default settings of the Nastran solution 101 for linear statics. Now the ordinary steps for creating a FEM model follow. Idealizations or simplifications are not necessary here, so we skip the idealized file and begin working in the FEM file.
Lastly, the solution of the SIM file has to be specified. From here on the procedure is again identical to the native NX system.
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7.2.1.4 Steps in the FEM-File In the FEM file, the material is assigned and the mesh created. Material and meshing in the FEM file.
ÍÍSwitch into the FEM-file. ÍÍAssign the material “steel” to the body and create an automatic tetrahedral mesh, taking advantage of the element size suggested by the yellow flash. This was the minimum work that had to be done in the FEM file. The further model characteristics are created in the simulation file.
7.2.1.5 Steps in the Simulation File In the simulation file, the solving method is selected, the boundary conditions are assigned and the solution is carried out. Also the post-processing is done here. Boundary conditions are specified in the SIM file.
ÍÍSwitch to the SIM file. ÍÍWith the Pinned Constraint function , create a rotatable mounting at the four holes. ÍÍCreate a vertical Force of 100 N on the load application area. The model building and the pre-processing is now completed. The next step is to solve the solution. ÍÍChoose the function Solve and confirm with OK.
The NX Nastran solver is started out of NX.
The NX system will now create a solver input file with all information about nodes, elements, material properties, loads, and boundary conditions, which is stored in a temporary working directory on the local machine. In addition, the NX system transfers a command to the operating system. The command states that the solver, in our case the NX Nastran solver, starts and finds the input file. The exact syntax of the command can be found in the log file of NX. The solver now executes this job in exactly the same way as it would take place on a native NX system. ÍÍYou can identify the solver process most safely through the Nastran window that works in the background. Only after this window has closed itself, you should open the results. ÍÍOnce the analysis is complete, you can switch to the post-processor and check the results as desired.
This is the stress result of the mini FEM analysis with NX Teamcenter.
A colored version of this figure is available at www.drbinde.de/index.php/en/203
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Now a step follows that differs from the native method. It’s about whether and which files will be imported into Teamcenter. ÍÍNow the data shall be stored. Therefore, select the function SAVE in NX. When you run the function SAVE in the simulation file, the NX system tries to save the SIM, the FEM and the idealized file. When you are saving, the Teamcenter system searches for newly created files in the temporary working directory. All files which are found there will be displayed in a window if their extensions are registered in Teamcenter (see figure below), and it asks whether these files shall be imported into the database and assigned as references of the CAEAnalysisRevision. The following figure shows the explanation of the files displayed for a NX Nastran analysis. Here important NX Nastran files are imported into the Teamcenter database.
Which of these files will actually be imported into the database, has to be decided by each company for themselves. Of course, everything possible should be saved, but the significant amounts of data resulting from simulations need to be considered. A single analysis can easily produce several gigabytes of data. In many companies, the solver input file (*.dat) and the result file (*.op2) are stored in the database. So we also want to do this in our case: ÍÍSelect the *.dat and the *.op2 file as shown in the figure above, and choose the function Import Selected Files. ÍÍNow close all parts in NX. If any question appears after the file import, select NO. ÍÍNow in the home directory of Teamcenter check if the three new items have successfully been generated. This is how the items should look like for a FEM analysis in Teamcenter.
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Now that the native files have been successfully stored in the database, we better no longer talk of CAD, Idealized, FEM and simulation file, but rather of CADMasterRevision, CAEGeometryRevision, CAEModelRevision and CAEAnalysisRevision, because a database item is more than a native file. The database item includes the item revision and this again includes different datasets. A given dataset contains one or several more native files. Our former ideal, FEM and SIM files, are now stored in the item revisions of the database, which have been integrated as named references. This also applies to the additional files that we have just selected for import. We now want to check whether the *.dat and the *.op2 files are actually stored in the database. To perform this, follow these steps. ÍÍIn Teamcenter open the item revision of the CAEAnalysisRevision and the data contained therein. ÍÍFrom the context menu, select the function Named References. The imported files should be shown as in the figure below. The actual files are stored as named references in Teamcenter.
If you want, check the Named References listed at the other new item revisions. Now we are done with the FEM analysis in Teamcenter. The following methods are for the control of data relationships.
7.2.2 Which CAD Model Belongs to which FEM Model? Now we come to the question how to deal with the relations between the CAD and FEM data. To answer the question “Which CAD model belongs to which FEM model?”, the automatically in the background generated relations TC_CAE_Defining, TC_CAE_Source and TC_CAE_Target of the CAE data model have to be evaluated. The above stated data model is again shown briefly in the figure below.
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Reduced presentation of the CAE data model.
TC_CAE_Defining
CAEAnalysis
CAEModel TC_CAE_Source
TC_CAE_Source
TC_CAE_Target
CAD-Master
0-n:0-n
TC_CAE_Source TC_CAE_Target
CAEGeometry
Of course in this case it is trivial, because only one CAD and one FEM model are available. However, the methodology that we describe here is also valid if many CAD and CAE models are included and these themselves are built into complex assemblies. For the control of the relationship, there are several possibilities. Two important alternatives are discussed in the next sections.
7.2.2.1 Representation of Relationships in Detail The first possibility is that in the Teamcenter view, the details of an item revision are displayed. We want to see, for example, the relationships of the FEM item revision. ÍÍIn Teamcenter, open My Teamcenter. ÍÍSelect the CAEModelRevision (number 000102) and on the right side open the Details tab. ÍÍCheck if the relationships are correct.
Relationships or relations should be controlled.
Now the figure below should be displayed. This is how the relations of the ordinary Teamcenter view looks like.
It can be seen that the source relationship of 000102 points to 000101, in other words it points to the CAEGeometryRevision. That is correct, because from this CAEGeometryRevision the FEM model has been generated. Also the target relationship of 000102 points to 000100, the CAD master. As a result the mesh in 000102 represents the CAD model in 000100.
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ÍÍIn this way also check the relations of CAEAnalysisRevision 000103. There should be a CAE_Defining relationship to CAEModelRevision 000102. The ability to display the relationships in common details has the disadvantage that information can only be displayed in the direction of each relationship. Because our three relationships of interest point “top to bottom”, we can now indeed answer the question “Which CAD model belongs to my analysis?”, but we still cannot answer the question: “What analysis belongs to my CAD model?” The section below offers an answer to this question.
7.2.2.2 Displaying Relationships in the CAE Manager The CAE Manager can track relationships.
The CAE Manager is one of the additional tools that are provided by Teamcenter for Simulation. It allows detailed and varied tracking of the relationships between CAD and CAE. The crucial difference to the previous method is that relations can be evaluated in both directions. In order to use this, proceed as follows: ÍÍIn Teamcenter select the item revision of the CAD master model 000100. ÍÍIn the context menu select the function Send to, CAE-Manager. Now the Teamcenter application switches and the CAE Manager appears. Therein three tabs (as seen in the figure below) are included.
The CAE Manager provides information about CAD and CAE relations.
With these three tabs relations can be evaluated: Product: This tab is for the analysis of relations of the initial or CAD model. On the right side of the display linked data can be displayed in various ways. Model: In this tab the relationships of FEM models are displayed. Analysis: Accordingly, the relations of SIM models are analyzed here. Now we would like to find out which FEM models are part of our CAD model 000100: We find out which CAD model belongs to which FEM model.
ÍÍActivate the tab Product. ÍÍSwitch to double-sided view with the function ÍÍIn the right view activate the tab Composite.
Show/Hide the Data Panel.
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The following conclusions can be drawn from the view: The CAEModelRevision 000102 has a target relationship to our CAD model 000100. This means that this is a valid FEM model to our CAD model. The CAEGeometryRevision 000101 has a source and a target relationship to our CAD model 000100. This means, that this is an idealized model of our CAD model. Hereby the question “Which FEM model belongs to my CAD model?” is answered. ÍÍClose the application CAE Manager in Teamcenter.
7.2.3 Creating Revisions Because CAE data is stored in its own database items just like CAD data, the possibility (and even the compulsion) to revise these specifically is provided. This is a big advantage, because otherwise CAD and CAE models would have to be coupled firmly in some way, and when revising, all data would be doubled. In addition, through own database items it is also possible that CAE models can exist without a CAD model.
The three items can be revisioned separately.
An important question must be answered each time a CAD model is changed that has already been analyzed: Is the associated CAE model still valid or does it need updating? We therefore explain the procedure of creating revisions on the basis of two typical processes.
Two typical scenarios shall be exercised in the learning task.
In the first case, a computationally relevant CAD change shall be performed. Then the FEM model needs to be updated, recalculated and also revisioned. In the second case, we want to carry out a CAD change that does not affect the computation. In this case, the FEM model does not need to be changed, only its relations need to be changed.
7.2.3.1 Revising the CAD Model, Computationally Relevant In this task we perform a computationally relevant change to our CAD model and revise it. Such a change would, for example, be a change in the wall thickness, a change in material, or an additional bore hole. Proceed as follows: ÍÍOpen the previously imported CAD model 000100 (or any other that has already been calculated) in NX. ÍÍIn the modeling environment, insert an additional hole or something similar. ÍÍWith the function FILE > SAVE AS create a new revision B. ÍÍClose the file in NX. ÍÍIn Teamcenter, check whether the new revision has been created.
7.2.3.2 Checking the FEM Model for New CAD Revisions After revision B for the CAD model 000100 has been created in the last section, it is particularly important that the computation can ask the FEM model if new CAD revisions exist. You are now the analysis expert and ask the Teamcenter system this question:
Not every change is important for analysis.
366 7 Management of Analysis and Simulation Data
It is very important that it is displayed, whether new revisions exist.
ÍÍSelect the item revision of the FEM model 000102 in Teamcenter and choose the function Send to, CAE Manager from the context menu. ÍÍIn the CAE Manager, switch to the Model tab and activate the function Show/Hide the Data Panel . ÍÍIn the right view, activate the tab Composite. ÍÍSelect (left or right view) the FEM model being monitored, meaning 000102 (as shown in the figure below). ÍÍOn the main menu bar at Tools, turn on the function Check for later Revisions. The view in Teamcenter should now look as shown in the figure below. With this function, the relationships are analyzed and color-coded. The colors are defined as follows: Green indicates that no newer revisions are available. Red indicates that there are new revisions.
A decision has to be made whether the change is relevant or not.
This color coding indicates that one or more new revisions are available for the CAD model 000100. In practice, the latest revision of the CAD model should now be opened and it has to be decided, whether the change is computationally relevant or not. In our case this would be affirmed, because the inserted hole changes the strength of the geometry and therefore the analysis of the modified geometry would have to be updated and reperformed. This process is carried out in the next section. ÍÍClose the CAE Manager.
Colors show the time liness of the revisions.
7.2.3.3 Updating and Revising the FEM Model The CAD change was strength-relevant. Therefore, the analysis will be updated and re-performed.
So we have the situation that the CAD model was revisioned and the change is so important that an update of the analysis is required. Of course, then the analysis items have to be revisioned, too. To perform these steps, proceed as follows: ÍÍOpen the new revision of the CAD model 000100/B in NX. ÍÍNow open the old simulation 000103/A. Initially, only the SIM and the FEM file are loaded. But we want to fully load the model to revise it.
7.2 Learning Tasks on Teamcenter for Simulation 367
ÍÍLoad the idealized file by running the Load function in simulation navigator on the node of the idealized file. In this way, the already open new revision B of the CAD model gets “pushed underneath” the FEM model. You can see this structure in the simulation navigator. This avoids manually replacing the old CAD model with the new one. Now you just need to update and revise the FEM model. ÍÍSwitch into the idealized file. In our example, there is nothing to update, so you create a new revision B with the function FILE > SAVE AS. ÍÍSwitch into the FEM file, update the mesh with the function Update Finite Element Model and create a new revision B with the function FILE > SAVE AS. ÍÍSwitch into the simulation file, select FILE > SAVE AS and specify the revision B. ÍÍWhen asked about the files to be imported, select CANCEL. ÍÍRun the function Solve. ÍÍAfter the analysis is completed, save the file. ÍÍWhen asked about the files to be imported, select the *.dat and the *.op2 file. ÍÍClose all parts. ÍÍSend the newly created item revision of the SIM or FEM file to the CAE Manager.
Follow these steps to revise the analysis model.
Finally, back in the CAE Manager you should check the timeliness of relationships. Now they should be displayed in green. Both colors are green. This shows that all revisions are up to date.
7.2.3.4 Revising the CAD Model, Computationally Irrelevant Now a change that does not affect the analysis shall be added to the CAD model. We change the color, for example. ÍÍOpen the CAD model 000100/B and change the color of the solid to blue. ÍÍSave the part as new Revision C and close it. To check, you can send the item revision of the FEM part back to the CAE Manager. By the red marking it can be identified again, that the target relation pointing to the CAD model has new revisions.
Now only the color of the solid is changed.
368 7 Management of Analysis and Simulation Data
The first is green, the second red. Red indicates that new revisions are available.
7.2.3.5 Link old FEM Model with Modified CAD Model The old analysis is only appended to the modified model.
Now we show how to proceed in order to assign the old analysis to the only slightly modified CAD model without revising it because the revising would be a pointless effort in this case. This is obtained in Teamcenter with an additional target relationship, which we add with the function Add latest References. This operation is carried out in Teamcenter only, we do not need NX to do this. ÍÍAgain check the relations of the FEM part in the CAE Manager. The CAE Manager still looks like in the previous figure. ÍÍSelect the red marked relationship. ÍÍRun the Add latest References function from the main menu bar under Tools. This generates an additional target relationship to the last revision C. The display should now look like the figure below.
We see: The FEM model represents two CAD model revisions.
From the two target relations, we see that this analysis model represents two revisions of the CAD model 000100, namely B and C. It should also be recognized by the green color that C is the latest revision of the CAD model. Nothing has changed on the source relationship, it still points to model B, from which the analysis has been generated. A summary of the source and target relationships.
Thus, the target relations point to all CAD models, for which the analysis (i. e. the CAEModelRev and CAEGeometryRev) should have validity – in our case to the handle in blue and in original color gray (these are two separate CAD models). The source relationship points to the physical source of the computational model (i. e. the CAEModelRev and CAEGeometryRev). There can only be one source relationship per analysis model.
It may also happen that such database relationships have to be manually created and maintained.
In this way it is documented, that an analysis model is valid for two CAD models. The generation of the corresponding relationships happens in Teamcenter via the illustrated automatic method. This automatic method is only used if the new target relationship shall point to a new revision of the same model, as in our example. If there are two completely separate items and still one analysis for both shall be valid, the target relationship must be manually created and maintained.
7.2 Learning Tasks on Teamcenter for Simulation 369
Bibliography [Anderl3] Anderl R./Grau M./Malzacher J.: SIMPDM – a harmonized approach for the strategic implementation of simulation data management. NAFEMS World Congress 2009 [Anderl4] Anderl R./Malzacher J.: SimPDM – Simulationsdatenmanagement-Standard nach Maß. In: CAD CAM, No.1–2, 2009, p. 38–41 [Binde7] Binde, P.: Teamcenter for Simulation, Training documentation. Dr. Binde Inge nieure GmbH, Wiesbaden 2014 [Malzacher] Malzacher J./Tabbert P.: Simulationsdatenmanagement. Integration der Simulationsdaten in die PDM-Strategie. Engineering Process Day, Darmstadt 2008 [SimPDM] ProStep iViP Recommendation “Integration of Simulation and Computation in a PDM Environment (SimPDM)”. PSI 4, Version 2.0 2008 [TCSim] Training documentation for Teamcenter for Simulation. Siemens PLM Software
8
Manual Analysis of a FEM Example
Many newcomers to FEM wonder how this fascinating analysis method for simulating a wide variety of physical phenomena works. If you look for it in current literature you will either find very simplistic representations – such as in the FEM basic example of the book – or representations that are dominated by theoretical mathematics and require such a deep knowledge of the subject that many are overwhelmed. In order to give the technician or engineer who is interested in the application an understanding of how FEM works, we have prepared a FEM analysis in this chapter, in which every single solution step can be manually performed and understood without a computer. The basic ideas (i. e., shape functions, principle of the minimum of the energy) shall become clear by working it through. Of course, we have therefore chosen a very simple example.
A FEM analysis is carried out without using a computer program.
The basic idea of all numerical methods is that an approximation function for the unknown function is set up and this function is then adjusted to the unknown function. The special feature of the FEM is that the approximation function consists of piecewise contiguous individual functions. The first foundations of the finite element method go back to the works of Ritz [Ritz] and Galerkin [Galerkin].
■■8.1 Task Formulation The example is shown in the figure below. There is a rod-like, conical body1, which is held on one side and loaded on the other side with a force F. Sought is the displacement function u(x). From the known displacement the stress could then be calculated. For the sake of simplicity, we want to do this without stress analysis.
1 If we do not choose the body conical, but constant, we would exactly meet the analytical solution using the FEM. For didactic reasons this would not be useful.
A FEM analysis is carried out without using a computer program.
372 8 Manual Analysis of a FEM Example
■■8.2 Idealization and Choice of a Theory In idealization, assumptions and simplifications are made to carry out the analysis afterwards. For this task, the truss theory is assumed, since a dimension is large compared to the other two. Further, it is assumed that the component is at rest, small deformations are present and the stress-strain behavior is linear, so it can be described by Hooke’s law. Example task for the representation of the principle of FEM: The body is divided into two finite elements, so there are three nodes.
2L = 200mm
F=1000N
x u1
u2
u3
F1
F2
F3
El1 Kn1
El2 Kn2
Kn3
A(x)=300mm2 - x E=210000N/mm2
■■8.3 Analytical Solution The differential equation to be solved for the problem results from the conditions for: The analytical solution will be compared with the FEM results.
Statics (equilibrium condition, S: force in cutting plane normal), S ( x) = F
σ ( x) =
S ( x)
A( x)
=
1000 N 300mm 2 − x
Kinematics and ε ( x) =
∂u ∂x
Material law σ ( x) = E ⋅ε ( x)
8.4 Space Discretization for FEM 373
Merged together as: ∂u F 1 = , or ∂x E 300mm 2 − x
u ( x) =
x
F dx ∫ E 0 300mm 2 − x
Resolved to this integral calculus: dx
1
∫ ax + b = a ⋅ ln(ax + b) The corresponding solutions at the three locations of interest2 are found3 for the unknown function [Bronstein]: 1 ( ln ( 300 − x ) − ln ( 300 ) ) 210 u1 = u ( x = 0 ) = 0 mm u2 = u ( x = 100 ) = 0, 001930786 mm u3 = u ( x = 200 ) = 0, 005231487 mm u ( x) =
Results at three points from the analytical solution.
■■8.4 Space Discretization for FEM For the analysis with the FEM, the body has to be separated into two elements. Out of this, three nodes arise. At each node, the displacement and the force are identified. Elements, nodes, displacements and forces in the following are labeled as shown in the figure above. For each element a shape function is chosen which still has unknown coefficients. With these coefficients, each of the shape functions can be adjusted so that it approximates the real solution. We choose the following linear shape functions for the elements 1 and 2: uEL1 = aEL1 x + bEL1 uEL 2 = aEL 2 x + bEL 2
Next, the shape functions have to be represented as functions of the unknown nodal quantities. For the designated nodal quantities u1, u2 and u3 are incorporated. The following conditions are available: u ( x = 0 ) = u1 , u ( x = L ) = u2 , u ( x = 2 L ) = u3
For the shape functions depending on the nodal quantities results:
2 These locations are later the node locations at which FEA solutions will be calculated. 3 Because of the simple geometry in this case an analytic solution for the differential equation can easily be found.
A linear shape function means that we assume that the desired solution result behaves linear.
374 8 Manual Analysis of a FEM Example
These are still the same shape functions as before, they now only depend on the sought nodal displacements.
u2 − u1 x + u1 L u −u = 3 2 x + 2u2 − u3 L
uEL1 = uEL 2
With these terms, the displacement pattern in the two elements is set up on the unknown nodal displacement magnitudes.
■■8.5 Setting up and Solving the FEA System of Equations To obtain a system of equations which is suitable for calculating the unknown nodal displacements, the principle of the minimum of the potential energy should be used here. We provide an energy function that includes errors and then demand that the errors become minimal small.
The external energy is taken into account, which can be specified accurately. In contrast, the internal energy is written in the form of our approximate shape functions and will therefore be erroneous. It is required that the error is minimized by taking the derivative of the total potential energy and setting it equal to zero. These derivatives can be formed by every unknown. Thus, a linear system of equations is obtained for which the unknowns can be calculated. The internal energy or strain energy Π in a pull rod4 can for example be recognized through the elongation:
∏
=
pull_rod
1 EA 2 dx 2 ∫L ∂u
With ε = ∂x and the function for the area A ( x ) = 300 − x , as well as the two shape functions, the internal energies for the two elements as a function of the unknown nodal displacements can be specified:
∏
= El1
∏
=
El 2
2
L
1 N 2 ∂u ⋅ ( u2 − u1 ) E A( x) El1 dx = 262500 2 ∫0 ∂ x mm 2
2L
1 N 2 ∂u ⋅ ( u3 − u2 ) E A( x) El 2 dx = 472500 2 ∫L mm ∂x
The external energy W is the applied work from the undeformed to the deformed position: 4 Different notations for the strain energy per length in a pull rod [Schnell Gross Hauger] are: 1 1 N or EA 2 2
2
or
1 N2 2 EA
8.5 Setting up and Solving the FEA System of Equations 375
u
W = ∫Fdu 0
For the external energy is obtained: W=
1 ( u1F1 + u2 F2 + u3 F3 ) 2
+∏− −W W= = 00. The result is an ∏ + Now the energy portions can be assembled according to ∏ ∏ El1 El 2 El1 El 2 equation for the total potential energy P, which depends on the unknown nodal displacements:
P = 262500
N 1 N 2 2 ( u2 − u1 ) + 472500 ( u3 − u2 ) − ( u1F1 + u2 F2 + u3 F3 ) = 0 mm 2 mm
From the derivations ∂P = 0, ∂u1
∂P = 0, ∂u2
∂P =0 ∂u3
three equations arise, which can be represented in matrix form as follows: −4 ⋅ 262500 0 4 ⋅ 262500 u1 F1 − 4 ⋅ 262500 4 ⋅ 262500 + 472500 − 4 ⋅ 472500 ( ) ⋅ u2 = F2 0 −4 ⋅ 472500 4 ⋅ 472500 u3 F3
This energy function has errors because of our linear shape functions. To minimize the errors, we will set up derivatives and set them equal to zero. This results in e quations.
This system of equations can also be understood as overall stiffness matrix K, the displacement vector u and force vector F and be noted in the form kij ⋅ ui = Fj
In a finite element program, this form is generated directly by composing5 the individual element stiffness matrices to the overall stiffness matrix of the system. The deformation vector ui and the force vector Fi arise from boundary conditions. The following conditions are known6 in this example:
u1 = 0,
F2 = 0,
F3 = 1000 N
1000 N acting on the right node.
Thus, the system of linear equations can be resolved. The result is: u1 = 0mm u2 = 0, 00190476mm u3 = 0, 005079mm
5 Instead of “composing” it is also spoken of “assembling”. With the numerical values of the matrix representation of the example, the influence of the two elements can be seen on the overall stiffness matrix. 6 One of the two quantities, displacement or force, is always known at a node, the other can then be calculated.
These are the results of the FEM.
376 8 Manual Analysis of a FEM Example
■■8.6 Analytical Solution Compared with Solution from FEA The results, which are also shown in the figure below, show that the analysis at the nodes with FEM correspond relatively accurately with the analytical solution. Between the nodes, the solutions coincide worse, which is due to the chosen linear shape functions. Stress and strain results could now be derived from the calculated displacement magnitudes. This will be omitted here. Stress results differ more than displacements from the analytical result. Common methods to increase the accuracy of the results are: Finer meshing, i. e. smaller elements, higher element density7. Increase of the polynomial of the shape functions8. Displacement results in comparison: Analytical analysis and FEM.
The comparison of the analytical analysis with the FEM reveals the good compliance of the results, although they were produced with only small numbers of elements and linear shape functions because of the limited computational complexity. With the use of computers to solve the computational work, a much better compliance can be expected.
Bibliography [Bronstein] Bronstein I. N./Semendjajew K. A.: Taschenbuch der Mathematik. 24th Edition. Community Edition, Verlag Nauka, Moskau und Teubner Verlag, Leipzig, 1989 [Galerkin] Galerkin, B. G.: Stäbe und Platten. Reihen in gewissen Gleichgewichtsproblemen elastischer Stäbe und Platten. Vestnik der Ingenieure, Vol. 19, 1915, p. 897–908 7 This is also known as h-adaptivity. 8 This is also known as p-adaptivity.
8.6 Analytical Solution Compared with Solution from FEA 377
[Ritz] Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der Mathematischen Physik. In: Reine Angewendete Mathematik, Vol. 135, 1908, p. 1–61 [SchnellGrossHauger] Schnell, W./Gross, D. Hauger, W.: Technische Mechanik 2: Elastostatik. 3rd Edition Springer Verlag, Berlin/Heidelberg/New York 1989
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Index
2D Contact 19 3D contact 63 64-Bit 10
A Adams 10 ADINA 152 Ampere’s law 300 analytical solution 372 Animation 20 approval processes 354 Articulation 15, 31 automatic time stepping 265 AUTOMPC 182 axisymmetric 311
B beam 187 beam element 187 –190 beam theory 171 bolt load 220 boundary conditions 116 boundary layer resolution 282 Bushing 19
C Cable 19 CAEAnalysis 353, 364 CAEGeometry 353 CAEManager 364 – 368 CAEModel 353, 364 cams 12 capacitance 299 capacitor 299 CFD 271 CGAP 209 checking element shapes 128 clamping element 207 clamping seat 207
clamping situation 14 clearance 14 cloning 200 coil 299, 301, 303, 311, 314, 317 – 319, 321, 324, 326 – 329, 331, 334 coil spring 185 collision check 58 collisions 16 combination 176 Component-based Simulation 25 conduction losses 318, 331, 348 – 349 conflict situations 24 connection 166 conservation equations 272 Constant driver 31 Constant Velocity 18 Constraints 116 contact 249 contact non-linearity 84 convection boundary condition 146 convergence 135 convergence control 291 convergence criterion 275, 276 convergence validation 136 Co-Simulation 17, 24 coupled systems 150 coupling elements 177 Create Sequence 20 Curve on Curve 20 cylindrical joint 18, 43
D damper 12, 19 damping 64, 206 data model 354, 363 data protection 352 default settings 10, 66 determined degrees of freedom 15 dielectric permeability 302 dielectric relationship 302 Direct Matrix Abstraction Programming 151
384 Index
displacement function 371 displacement results 120 DMAP 151 DMU 3 – 4 driver 17, 30 dynamics 24, 59
E Eddy Current losses 318, 331, 348 – 349 Eddy Currents 304 edge subdivisions 233 eigenfrequencies 87, 199 electrical conductivity 302 electrical engineering components 297 electrical field theory 297 electrodynamics 299, 305 – 306 electrokinetics 299, 305 – 306 electromagnetic field analysis 150 electrostatics 299, 305 – 306 enforced displacement 194 Environment 17, 24 equilibrium condition 372 equivalent stress hypothesis 123 evaluation of accuracy 91 excitation 206
F f06 file 263 Faraday’s law 301 ferromagnetic 302 finite-volume method 272 fixed joint 18, 22, 63 Flexible Body Dynamics 17, 25 Flexible Link 19 flow analysis 272 flow boundary conditions 284 flow surfaces 284 Force 20 forced movement 338, 340 four-node tetrahedrons 127 friction 64 frictionless sliding 289 full wave 299, 305, 307 Full Wave (High Frequency) 299, 307 Function driver 31 Function Manager 19 FVM 272
G gap elements 152 gear 19, 31 General Motion 339 geometric nonlinear analysis 230 Graphing 20, 45
H Harmonic driver 31 heat flux 147 heat transfer 89 hexahedral elements 127 HEX Solid Meshing 252 high frequency 299, 307 Hooke’s law 83, 372
I induction law 301 inductivity 299, 326 inlet 286 Inline 18 installation 308 – 310 Interference 20 iron losses 348 – 349
J joint primitives 18
L large deformation 229, 249 large displacement 85, 229, 249, 261 leaf spring 229 learning tasks 5 library 61 licensing 308 lift force 293 lifting off contacts 60 linear buckling 90 linear statics 81 link 17, 25, 62 linked phase voltage 347 load transfer to FEM 20 load types 112 local mesh refinement 131 losses 318, 331, 348, 350
M machine portals 187 magnetic permeability 302 magnetic relationship 302 MAGNETICS 150 magnetodynamics 297 – 299, 305, 307 magnetostatics 297, 299, 303, 305, 307 Marker 18 mass properties 25 master model concept 21 Master Model Dimension 19 material equations 302 material law 372 material properties 109, 143, 283 MATLAB Simulink 17
Index 385
matrix form 375 maturity tracking 352 maximum distortion energy hypothesis 123 maximum principal stress 123 maximum tensile stress 196 Maxwell’s equations 298 MBD program 12 Measure 20 memory 10 mesh connections 144 mesh fineness 85 Mesh Mating Condition 144, 208 Mesh Point 189 middle node elements 127 midsurface 161 Motion Connections 28 motion-driven systems 15 Motion Joint Wizard 22 Motor Driver 24 motor libraries 17 Moving Band 332, 339 – 340 Multibody Dynamics 12 multi-processor 10
N named references 353, 362 Newton’s Method 261, 344 non-linear contact 208 – 209 non-linear effects 83 non-linear geometry 261 non-linear material 84 non-linear stress-strain behavior 256 notch factor 126 notch stress 91 NX Response Analysis 151 NX/Thermal 150
O ohm resistance 299, 303, 331, 348 – 349 Ohm’s law 302 Opel RAK2 5 opening 285 Orientation 18 outlet opening 287 over-determinations 24 over-determined degrees of freedom 24
P Parallel 18 parameterization 186 PDM 3, 5 perfect insulation 146 Phase Shift 342 phase voltage 343, 347 piece of cake 142
pivotable constraint 113 planar joint 18 Plant Input 20 Plant Output 20 plastic deformation 240 plasticity 241 PMDC-Motor 20 point mass 201 Point on Curve 19 Point on Surface 20 Poisson’s Ratio 110 polygon body 98 polygon geometry 133, 233 Populate Spreadsheet 20 post-processor 118 presetting 10 press fit 207 pressure distribution 293 pretensioned bearings 186 principle of linear FEM 82 principle of the minimum of the potential energy 374 principles of electromagnetic analysis 298 processor 10 process orientation 352
R Rack and Pinion 19 reaction force 186, 195 RecurDyn 10 redundant degrees of freedom 24, 41 release and change processes 352 residual tolerance 344 resistance 299, 303 restrictions of MBD 14 revising 365, 367 revisions 353, 362, 365 – 368 revolute joint 18, 26 ring-element-based method 141 rivet joints 176 rotational degrees of freedom 156, 179 rotational driver 13
S screw 18 Sensor 18 shape function 371, 373 – 376 sheet 162 shell elements 157 signal chart 20, 24 simulation data 351, 369 simulation data management 352 Simulation File View 97 singularities 86, 137 skin depth 304 slider 18, 56 Smart Point 18
386 Index
snap hook 249 soft spring bearing 217 – 218 Sol 101 151 Sol 103 151 Sol 106 152 Sol 601 152 space discretization 373 spherical joint 18, 55 spring 12, 19 standard meshing 108 starting behavior 340 Steinmetz formula 303 stiffness matrix 375 Stitch Edge 162 stress-strain behavior 372 structural mechanics 14 super elements 202 surface roughness 284 surface subdivisions 101 Surface to Surface Contact 209 Surface to Surface Gluing 208 symmetry 141 synchronization of the processes 352 system of differential equations 12
T TC_CAE_Defining 353, 362 TC_CAE_Source 353, 362 TC_CAE_Target 353, 362 Teamcenter 352 – 355, 357 – 359, 361, 363 – 366, 368 – 369 temperature boundary condition 145 temperature field 139 temperature gradient 147 ten-node tetrahedral elements 127 thermodynamic problem 150 time-dependent travel path 258
time step 291 time step size 275 TMG 150 tolerances 42 toolbar 16 top-down method 35 Torque 20 Trace 20 transport equations 272 traverse path 258 truss theory 372 turbulence model 276
U underdetermined 28 undetermined degrees of freedom 15 universal joint 18
V vents 285 version levels 352 virtual product development 3 – 5 von Mises 123
W wake space 296 wall thickness 165 weak springs 216 Whitney elements 314 without redundancy 24
Y Young’s Modulus 110
Correct Calculations d ok D an bo DV rora the On 8Au om Z8 s fr 8, le Z8 amp ex
all
Frank Rieg Reinhard Hackenschmidt Bettina Alber-Laukant
Finite Element Analysis for Engineers Basics and Practical Applications with Z88Aurora
Rieg/Hackenschmidt/Alber-Laukant Finite Element Analysis for Engineers Basics and Practical Applications with Z88Aurora 733 pages. With DVD € 79.99. ISBN 978-1-56990-487-9 Also available as ebook € 64.99. ebook-ISBN 978-1-56990-488-6
The Finite Element Analysis today is the leading engineer‘s tool to analyze structures concerning engineering mechanics, i.e. statics, heat flows, eigenvalue problems and many more. Thus, this book wants to provide well-chosen aspects of this method for students of engineering sciences and engineers already established in the job in such a way, that they can apply this knowledge immediately to the solution of practical problems. Over 30 examples along with all input data files on DVD allow a comprehensive practical training of engineering mechanics. Two very powerful FEA programs are provided on DVD, too: Z88, the open source finite elements program for static calculations, as well as Z88Aurora, the very comfortable to use and much more powerful freeware finite elements program which can also be used for non-linear calculations, stationary heat flows and eigenproblems, i.e. natural frequencies. Both are full versions with which arbitrarily big structures can be computed – only limited by your computer memory and your imagination.
More Information on Books: www.hanser-fachbuch.de
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