ANSYS Workbench 12官方中文培训教程--Dynamic动力学模块教程及实例
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Table of Contents
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
TOC-1
July 2009 Inventory #002666
Table of Contents
Training Manual
1. Introduction to Dynamics Definition & Purpose Types of Dynamic Analysis Basic Concepts and Terminology Damping Workshop 1 – Flywheel
1-1 1-6 1-9 1-15 1-21 1-33
5. Random Vibration Analysis Definition & Purpose Power Spectral Density Workbench capabilities Procedure Workshop 5 – Girder Assembly
5-1 5-3 5-5 5-9 5-10 5-22
2. Modal Analysis Definition & Purpose Terminology & Concepts Procedure Workshop 2A – Plate with Hole Workshop 2B – Prestressed Wing
2-1 2-3 2-5 2-21 2-40 2-40
3. Harmonic Response Analysis Definition & Purpose Terminology & Concepts Procedure Workshop 5 – Fixed-Fixed Beam
3-1 3-3 3-5 3-17 3-31
6. Transient Analysis Introduction Preliminary Modal Analysis Including Nonlinearities Part Specification and Meshing Nonlinear Materials Contact; Joints; and Springs Initial Conditions Loads; Supports; Joint Conditions Damping Analysis Settings Reviewing Results Workshop 6 – Caster
6-1 6-4 6-7 6-10 6-17 6-19 6-20 6-27 6-30 6-32 6-33 6-35 6-37
4. Response Spectrum Analysis Definition & Purpose Response Calculations Mode Combination Procedure Workshop 4 – Suspension Bridge
4-1 4-3 4-8 4-12 4-14 4-25
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TOC-2
July 2009 Inventory #002666
Chapter 1: Introduction
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Introduction
Welcome!
Training Manual
• Welcome to the Workbench Dynamics training course! • This training course covers the procedures required to perform dynamic analyses with ANSYS Workbench. • It is intended for novice and experienced users. • A related course is ANSYS Rigid and Flexible Dynamic Analysis, which covers multi-body analysis. • Several other advanced training courses are available on specific topics. – See the training course schedule on the ANSYS homepage: www.ansys.com under “Training Services”.
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July 2009 Inventory #002666
Introduction
Course Objectives
Training Manual
• This course is intended for users already familiar with the procedures for performing a linear static analysis in Workbench Mechanical environment. – Prerequisite is ANSYS Workbench – Mechanical Introduction
• By the end of this course, you will be able to use Mechanical to define, solve, and interpret the following dynamic analyses: – – – – –
Modal Harmonic Response Response Spectrum Random Vibration Transient
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July 2009 Inventory #002666
Introduction
Course Material
Training Manual
• The Training Manual you have is an exact copy of the slides. • Workshop descriptions and instructions are included in the Workshop Supplement. • Copies of the workshop files are available (upon request) from the instructor.
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July 2009 Inventory #002666
Introduction
Introduction to Dynamics
Training Manual
A. Define dynamic analysis and its purpose. B. Discuss different types of dynamic analysis available in Workbench Mechanical. C. Cover some basic concepts and terminology. D. Review the types of damping available in Workbench Mechanical. E. Do a sample dynamic analysis exercise.
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July 2009 Inventory #002666
Dynamics
A. Definition & Purpose
Training Manual
• A dynamic analysis is a technique used to determine the dynamic behavior of a structure or component. • It is an analysis involving time, where the inertia and possibly damping of the structure play an important role. • “Dynamic behavior” may be one or more of the following: – Vibration characteristics • how the structure vibrates and at what frequencies
– – – –
Effect of harmonic loads. Effect of seismic or shock loads. Effect of random loads. Effect of time-varying loads.
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July 2009 Inventory #002666
Dynamics
… Definition & Purpose
Training Manual
• A static analysis might ensure that the design will withstand steady-state loading conditions, but it may not be sufficient, especially if the load varies with time. • The famous Tacoma Narrows bridge (Galloping Gertie) collapsed under steady wind loads during a 42-mph wind storm on November 7, 1940, just four months after construction.
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July 2009 Inventory #002666
Dynamics
… Definition & Purpose
Training Manual
• A dynamic analysis usually takes into account one or more of the following: – free vibrations • natural vibration frequencies and shapes
– forced vibrations • e.g. crank shafts, other rotating machinery
– seismic/shock loads • e.g. earthquake, blast
– random vibrations • e.g. rocket launch, road transport
– time-varying loads • e.g. car crash, hammer blow
• Each situation is handled by a specific type of dynamic analysis.
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July 2009 Inventory #002666
Dynamics
B. Types of Dynamic Analysis
Training Manual
• Consider the following examples: – An automobile tailpipe assembly could shake apart if its natural frequency matched that of the engine. How can you avoid this? – A turbine blade under stress (centrifugal forces) shows different dynamic behavior. How can you account for it?
• A modal analysis can be used to determine a structure’s vibration characteristics.
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July 2009 Inventory #002666
Dynamics
… Types of Dynamic Analysis
Training Manual
– Rotating machines exert steady, alternating forces on bearings and support structures. These forces cause different deflections and stresses depending on the speed of rotation.
• A harmonic-response analysis can be used to determine a structure’s response to steady, harmonic loads.
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July 2009 Inventory #002666
Dynamics
… Types of Dynamic Analysis
Training Manual
– Spacecraft and aircraft components must withstand random loading of varying frequencies for a sustained time period.
A random-vibration analysis can be used to determine how a component responds to random vibrations.
Courtesy: NASA ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Dynamics
… Types of Dynamic Analysis
Training Manual
– Skyscrapers, power-plant cooling towers, and other structures must withstand multiple short-duration transient shock/impact loadings, common in seismic events.
• A response-spectrum analysis can be used to determine how a component responds to earthquakes.
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July 2009 Inventory #002666
Dynamics
… Types of Dynamic Analysis
Training Manual
– An automobile fender should be able to withstand low-speed impact, but deform under higher-speed impact. – A tennis racket frame should be designed to resist the impact of a tennis ball and yet flex somewhat.
• A transient analysis can be used to calculate a structure’s response to time varying loads.
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July 2009 Inventory #002666
Dynamics
… Types of Dynamic Analysis
Training Manual
• Choosing the appropriate type of dynamic analysis depends on the type of input available and the type of output desired. Type
Input
Output
Modal
• none
• natural frequencies and corresponding mode shapes • stress/strain profile
Harmonic
• sinusoidally-varying excitations across a range of frequencies
• sinusoidally-varying response at each frequency • min/max response over frequency range
Spectrum
• spectrum representing the response to a specific time history
• maximum response if the model were subjected to the time history
Random
• spectrum representing probability distribution of excitation
• response within specified range of probabilities
Transient
• time-varying loads
• time-varying response
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July 2009 Inventory #002666
Dynamics
C. Basic Concepts and Terminology
Training Manual
Topics discussed: • General equation of motion • Modeling considerations • Damping
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July 2009 Inventory #002666
Basic Concepts & Terminology
Equation of Motion
Training Manual
• The linear general equation of motion, which will be referred to throughout this course, is as follows (matrix form):
M u C u K u F u nodal accelerati on vector M structural mass matrix C structural damping matrix u nodal velocity vector K structural stiffness matrix u nodal displaceme nt vector F applied load vector • Note that this is simply a force balance: Finertial
Fdamping
Fstiffness applied F M u C u K u F ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Basic Concepts & Terminology
Equation of Motion
Training Manual
M u C u K u F • Different analysis types solve different forms of this equation. – Modal • F(t) set to zero; [C] usually ignored.
– Harmonic Response • F(t) and u(t) assumed to be sinusoidal.
– Response Spectrum • Input is a known spectrum of response magnitudes at varying frequencies in known directions.
– Random Vibration • Input is a probabilistic spectrum of input magnitudes at varying frequencies in known directions.
– Transient • The complete, general form of the equation is solved. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Modeling Considerations - Geometry and Mesh
Training Manual
• Generally same geometry and meshing considerations for static analysis apply to dynamic analysis. – Include as many details as necessary to sufficiently represent the model mass distribution. – A fine mesh will be needed in areas where stress results are of interest. If you are only interested in displacement results, a coarse mesh may be sufficient.
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July 2009 Inventory #002666
Basic Concepts & Terminology
Modeling Considerations - Nonlinearities
Training Manual
M u C u K u u F nonlinear • Nonlinearities, such as large deflections, nonlinear contact, material nonlinearities, etc, are allowed only in a full transient dynamic analysis with large deflection turned ON. • All other Workbench dynamic analysis types are linear. – the initial state of nonlinearities will be maintained throughout the solution; i.e., [K] = const.
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July 2009 Inventory #002666
Basic Concepts & Terminology
Modeling Considerations - Material properties
Training Manual
M u Cu K u F • Mass properties [M] – – – –
e.g. density, point mass required for all dynamic analysis types specify mass density when using metric units, and specify weight density when using British units
• Damping properties [C] – e.g. viscous, material (discussed later) – required for mode-superposition harmonic – optional but recommended for all other dynamic analysis types
• Stiffness (elastic) properties [K] – e.g., Young’s modulus, Poisson’s ratio, shear modulus – required for all flexible analysis types
• Note that Mechanical has display (interactive) units and solution units. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
D. Damping
Training Manual
• Damping is an energy-dissipation mechanism that causes vibrations to diminish over time and eventually stop. – e.g. vibrational energy that is converted to heat or sound
• The amount of damping may depend on the material, the velocity of motion, and/or the frequency of vibration. • Damping be classified as: – Viscous damping (e.g. dashpot, shock absorber) – Material / Solid / Hysteretic damping (e.g. internal friction) – Coulomb or dry-friction damping (e.g. sliding friction) – Numerical damping ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Damping
Training Manual
• If the amount of damping in a system becomes large, the response will no longer oscillate. • Critical damping is defined as the threshold between oscillatory and non-oscillatory behavior. • The damping ratio is the ratio of the damping in a system to the critical damping, given by
c cc cc 2m ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
k 2 km 2mn m 1-22
July 2009 Inventory #002666
Basic Concepts & Terminology
Damping
Training Manual
• The undamped natural frequency of a 1-DOF system is given by
n
k m
d 1 2 n
• The addition of viscous or solid damping slightly alters the natural frequency of a system.
d 1 2 n • Coulomb damping has no effect on frequency.
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Basic Concepts & Terminology
Viscous damping
Training Manual
• Viscous damping force is proportional to the velocity of the vibrating body.
Fd cu • Assuming the motion is harmonic,
Fd cu icnu • This type of damping occurs, for example, when a body moves through a fluid.
c k Fd ku i k n u
• For structural systems, a stiffness multiplier is often used in place of c for numerical simplicity. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Viscous damping
Training Manual
• The value of c in
Fd cu icnu can be input directly as element damping (Details section of Spring connection).
• The value of in
Fd ku iknu can be input directly as global damping value (Details section of Analysis Settings) or as materialdependent damping value (Material Damping Factor material property). ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Material / Solid / Hysteretic damping
Training Manual
• Solid damping is inherently present in a material (energy is dissipated by internal friction), so it is typically considered in a dynamic analysis. • Experience shows that energy dissipated by internal friction in a real system does not depend on frequency. • Not well understood and therefore difficult to quantify, so again a stiffness multiplier is used for numerical simplicity.
Fd 2iku ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Material / Solid / Hysteretic damping
Training Manual
• The value of in
Fd 2iku can be input directly as global damping value (Details section of Analysis Settings) or as material-dependent damping value (Constant Damping Coefficient material property).
• Damping ratio isn’t available in a transient analysis since the response frequency is not known in advance. – The value of can be calculated from a known value of (damping ratio) and a known frequency :
2 / n – Pick the most dominant response frequency to calculate . ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Coulomb or dry-friction damping
Training Manual
• Coulomb damping occurs when a body slides on a dry surface. • Damping force is proportional to the force normal to the surface.
Fd mmg sgn(x ) – – – –
m is the coefficient of friction m is the mass g is the gravitational constant sgn(y) is the signum function, defined as
1 for y 0 sgn( y ) 1 for y 0 0 for y 0 • Not considered in a linear dynamic analysis. Generally requires a nonlinear transient solution.
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Basic Concepts & Terminology
Numerical Damping
Training Manual
• Numerical Damping is not true damping. – Artificially controls numerical noise produced by the higher frequencies of a structure.
• Stabilizes the numerical integration scheme by damping out the unwanted high frequency modes. • The default value of 10% will damp-out spurious high frequencies and is a sensible value to try initially. • Use the lowest possible value that damps out nonphysical response without significantly affecting the final solution. High-frequency response
Primary Frequency undamped ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Damping – Summary
Training Manual
• In summary, Workbench allows the following four inputs for damping: – Beta damping (viscous) • Global or material-dependent. • Defines the stiffness matrix multiplier for damping.
– Element damping (viscous) • Defines the damping coefficients directly.
– Damping ratio (solid) • Global or material-dependent. • Defines the ratio of actual damping to critical damping.
– Numerical damping (artificial) • Defines the amplitude decay factor obtained through a modification of the time-integration scheme.
• NOTE: The effects are cumulative if set in conjunction. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Basic Concepts & Terminology
Damping
Training Manual
• Different industries specify damping in different ways: h Q D D A
= Viscous damping factor or damping ratio = Loss factor or Structural damping factor = Quality factor or simply = Log decrement = Spectral damping factor = Amplification factor
• The following table provides the conversions (note: U = strain energy) Measure
Spectral Damping
Amplification Factor
1/(2Q)
D/(4pU)
1/2A
D/p
1/Q
D/(2pU)
1/A
ph
D
p/Q
D/(2U)
p/A
1/2
1/h
p/D
Q
2pU/D
A
4pU
2pUh
2UD
2pU/Q
D
2pU/A
1/2
1/h
p/D
Q
2pU/D
A
Damping ratio
Loss Factor
Damping Ratio
h/2
D/2p
Loss Factor
2
h
Log Decrement
2p
Quality Factor Spectral Damping Amplification Factor ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
Log Decrement Quality Factor
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Dynamics
References & Bibliography
Training Manual
• S. S. Rao, Mechanical Vibrations. • K. Ogata, Modern Control Engineering. • B. J. Lazan, Damping of Materials and Members in Structural Mechanics. • A. K. Gupta, Response Spectrum Method: In Seismic Analysis and Design of Structures. • U.S. Nuclear Regulatory Commission Regulatory Guide 1.92, Combining Modal Responses and Spatial Components in Seismic Response Analysis. • D. E. Newland, An Introduction to Random Vibrations, Spectral & Wavelet Analysis. • Military Standard 810E, Environmental Test Methods And Engineering Guidelines.
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Dynamics
E. Introductory Workshop
Training Manual
• In this workshop, you will run a sample dynamic analysis of a flywheel. • Follow the instructions in your Dynamics Workshop supplement WS1: Intro (Flywheel) • The idea is to introduce you to the steps involved in a typical dynamic analysis. Details of what each step means will be covered in the rest of this seminar.
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July 2009 Inventory #002666
Chapter 2: Modal Analysis
ANSYS Mechanical Dynamics
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July 2009 Inventory #002666
Modal Analysis
Training Manual
A. Define modal analysis and its purpose. B. Discuss associated concepts, terminology, and mode extraction methods. C. Learn how to do a modal analysis in Workbench. D. Work on one or two modal analysis exercises.
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July 2009 Inventory #002666
Description & Purpose
Training Manual
• A modal analysis is a technique used to determine the vibration characteristics of structures: – natural frequencies • at what frequencies the structure would tend to naturally vibrate
– mode shapes • in what shape the structure would tend to vibrate at each frequency
– mode participation factors • the amount of mass that participates in a given direction for each mode
• Most fundamental of all the dynamic analysis types.
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Description & Purpose
Training Manual
Benefits of modal analysis • Allows the design to avoid resonant vibrations or to vibrate at a specified frequency (speaker box, for example). • Gives engineers an idea of how the design will respond to different types of dynamic loads. • Helps in calculating solution controls (time steps, etc.) for other dynamic analyses. Recommendation: Because a structure’s vibration characteristics determine how it responds to any type of dynamic load, it is generally recommended to perform a modal analysis first before trying any other dynamic analysis.
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July 2009 Inventory #002666
Description & Purpose
Terminology
Training Manual
• A “mode” refers to the pair of one natural frequency and corresponding mode shape.
mode 1 ← {f}1 f1 = 109 Hz
– A structure can have any number of modes, up to the number of DOF in the model.
mode 2 ← {f}2 f2 = 202 Hz
mode 3 ← {f}3 f3 = 249 Hz
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July 2009 Inventory #002666
Theory
Assumptions & Restrictions
Training Manual
• The structure is linear (i.e. constant stiffness and mass). • There is no damping. – Damped eigensolvers (MODOPT,DAMP or MODOPT,QRDAMP) may be accessed using Commands Objects, but will not be covered here.
• The structure has no time varying forces, displacements, pressures, or temperatures applied (free vibration).
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Theory
Development
Training Manual
• Start with the linear general equation of motion:
M u C u K u F • Assume free vibrations, and ignore damping: 0 0 M u C u K u F M u K u 0
• Assume harmonic motion:
u u u ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
f i i f i i2 f i
sin i t i cosi t i sin i t i
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July 2009 Inventory #002666
Theory
Development
Training Manual
• Substitute and simplify
M u K u 0 i2 M f i sin i t i K f i sin i t i 0 i2 M K fi 0 • This equality is satisfied if fi = 0 (trivial, implies no vibration) or if
det K i2 M 0 • This is an eigenvalue problem which may be solved for up to n eigenvalues, i2, and n eigenvectors, fi, where n is the number of DOF. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Theory
Extraction & Normalization
Training Manual
• Note that the equation
det K M 0 2 i
has one more unknown than equations; therefore, an additional equation is needed to find a solution. – The addition equation is provided by mode shape normalization.
• Mode shapes can be normalized either to the mass matrix
f M fi 1 T i
or to unity, where the largest component of the vector {f}i is set to 1. • Workbench displays results normalized to the mass matrix. • Because of this normalization, only the shape of the DOF solution has real meaning. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Theory
Eigenvalues & Eigenvectors
Training Manual
• The square roots of the eigenvalues are i, the structure’s natural circular frequencies (rad/s).
mode 1 ← {f}1 f1 = 109 Hz
• Natural frequencies fi can then calculated as fi = i/2p (cycles/s). – It is the natural frequencies, fi in Hz, that are input by the user and output by Workbench.
mode 2 ← {f}2 f2 = 202 Hz
• The eigenvectors {f}i represent the mode shapes, i.e. the shape assumed by the structure when vibrating at frequency fi.
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mode 3 ← {f}3 f3 = 249 Hz
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Theory
Equation Solvers • The equation
Training Manual
det K M 0 2 i
can be solved using one of two solvers available in Workbench Mechanical: – Direct (Block Lanczos) • To find many modes (about 40+) of large models. • Performs well when the model consists of shells or a combination of shells and solids. • Uses the Lanczos algorithm where the Lanczos recursion is performed with a block of vectors. Uses the sparse matrix solver.
– Iterative (PCG Lanczos) • To find few modes (up to about 100) of very large models (500,000+ DOFs). • Performs well when the lowest modes are sought for models that are dominated by well-shaped 3-D solid elements. • Uses the Lanczos algorithm, combined with the PCG iterative solver.
• In most cases, the Program Controlled option selects the optimal solver automatically. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Theory
Participation Factors (Solution Information)
Training Manual
• The participation factors are calculated by
i f Ti M D where {D} is an assumed unit displacement spectrum in each of the global Cartesian directions and rotation about each of these axes. – This measures the amount of mass moving in each direction for each mode. – The “Ratio” is simply another list of participation factors, normalized to the largest.
• The concept of participation factors will be important in later chapters.
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Theory
Participation Factors (Solution Information)
Training Manual
• A high value in a direction indicates that the mode will be excited by forces in that direction. mode 1
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mode 3
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Theory
Effective Mass (Solution Information)
Training Manual
• Also printed out is the effective mass.
M eff ,i
i2
f M f i T i
2 i
, if f M f i 1 T i
• Ideally, the sum of the effective masses in each direction should equal total mass of structure, but will depend on the number of modes extracted. • The ratio of effective mass to total mass can be useful for determining whether or not a sufficient number of modes have been extracted.
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Theory
Prestress Effects
Training Manual
• A prestressed modal analysis can be used to calculate the frequencies and mode shapes of a prestressed structure, such as a spinning turbine blade. – The prestress influences the stiffness of the structure through the stressstiffening matrix contribution.
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Theory
Prestress Effects
Training Manual
• In free vibration with prestress analyses, two solutions are required. – A linear static analysis is initially performed:
K u F s – Based on the stress state [s] from the static analysis, a stress stiffness matrix [S] is calculated (see Theory Reference for details):
s S – The free vibration with pre-stress analysis is then solved, including the [S] term:
K S M f 0 2 i
i
• Note that the prestress only affects the stiffness of the system. – i.e. the static prestress will not be added to the modal stress
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Remarks & Comments
Contact Regions
Training Manual
• Contact regions are available in modal analysis; however, since this is a purely linear analysis, contact behavior will differ for the nonlinear contact types, as shown below: Linear Dynamic Analysis Contact Type
Static Analysis Initially Touching
Inside Pinball Region
Outside Pinball Region
Bonded
Bonded
Bonded
Bonded
Free
No Separation
No Separation
No Separation
No Separation
Free
Rough
Rough
Bonded
Free
Free
Frictionless
Frictionless
No Separation
Free
Free
Frictional
Frictional
m = 0, No Separation m > 0, Bonded
Free
Free
• Contact behavior will reduce to its linear counterparts. – It is generally recommended, however, not to use a nonlinear contact type in a linear-dynamic analysis ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Remarks & Comments
Unconstrained Systems
Training Manual
• An unconstrained system is one that has no constraints or supports and can move as a rigid body in at least one direction. – Rigid-body motion can be considered to be a mode of oscillation with zero frequency. – In practice, these modes may not have a frequency of exactly zero.
“rigid-body” or “zero” modes
• Note that a well-connected system can have at most six rigid-body modes. – Obtaining more than six rigid-body modes may indicate that assemblies are not well connected. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Remarks & Comments
Symmetry Boundary Conditions
Training Manual
• Symmetry BC’s will only produce symmetrically shaped modes, so some modes can be missed. – It may be necessary to apply several different symmetry conditions to find all modes.
– The full model below results in the frequencies listed in the tabular view. – A quarter-symmetry model will require three sets of symmetry boundary conditions to find all modes (see next slide)...
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Remarks & Comments
Symmetry Boundary Conditions
Training Manual
Symm-Asym BC
Full Model Symmetry BC
etc
Anti-Symmetry BC
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Procedure: Modal
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Modal
Procedure
Training Manual
• Drop a Modal (ANSYS) system into the project schematic.
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Modal
Procedure
Training Manual
• Create new geometry, or link to existing geometry.
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• Edit the Model cell to bring up the Mechanical application.
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Modal
Preprocessing
Training Manual
• Verify materials, connections, and mesh settings. – This was covered in Workbench Mechanical Intro.
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July 2009 Inventory #002666
Modal
Preprocessing
Training Manual
• Add supports to the model. – Displacement constrains must have a magnitude of zero.
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July 2009 Inventory #002666
Modal
Solution Settings
Training Manual
• Choose the number of modes to extract. • If needed, upper and lower bounds on frequency may be specified to extract the modes within a specified range.
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July 2009 Inventory #002666
Modal
Solution Settings
Training Manual
• Stress and strain results may be turned on under Output Controls. • If the Program-Controlled solver selection is not appropriate, the solver type can be changed to either Direct or Iterative.
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July 2009 Inventory #002666
Modal
Postprocessing
Training Manual
• Total-deformation results may be quickly inserted by highlighting multiple rows in the tabular view or histogram view.
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July 2009 Inventory #002666
Modal
Postprocessing
Training Manual
• If stress/strain were requested, these results may also be access from the Solution Toolbar.
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July 2009 Inventory #002666
Procedure: Prestressed Modal
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July 2009 Inventory #002666
Prestressed Modal
Procedure
Training Manual
• The procedure to do a prestressed modal analysis is essentially the same as a regular modal analysis, except that you first need to prestress the structure by doing a static analysis. • The static analysis results in a stressed structure, which is used as the initial condition for the modal analysis.
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July 2009 Inventory #002666
Prestressed Modal
Procedure
Training Manual
• Drop a Static Structural (ANSYS) system into the project schematic.
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July 2009 Inventory #002666
Prestressed Modal
Procedure
Training Manual
• Drop a Modal (ANSYS) system onto the Solution cell of the Modal system.
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• Note the circular-ended connector, indicating a data transfer from the Static to the Modal analysis.
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July 2009 Inventory #002666
Prestressed Modal
Procedure
Training Manual
• Create new geometry, or link to existing geometry. • Edit the Model cell to bring up the Mechanical application.
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July 2009 Inventory #002666
Prestressed Modal
Preprocessing
Training Manual
• In the Static Structural system, insert the loads and supports that will cause the prestressed-state to occur.
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July 2009 Inventory #002666
Prestressed Modal
Postprocessing
Training Manual
• Review the static results before proceeding.
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July 2009 Inventory #002666
Prestressed Modal
Preprocessing
Training Manual
• Workbench will automatically setup the data transfer between the systems.
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• To verify the data transfer, one can ensure that – Future Analysis is set to Prestressed analysis in the Static Structural system – Pre-Stress Environment is set to Static Structural in the Modal system
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July 2009 Inventory #002666
Prestressed Modal
Postprocessing
Training Manual
• The modal results may be reviewed as described in the previous section.
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July 2009 Inventory #002666
Prestressed Modal
Postprocessing
Training Manual
• Note that the prestressed state increased the frequencies of this structure. – e.g. the first mode in this example increased from 108.3 Hz to 274.6 Hz Not Prestressed
Prestressed
• A prestress may not always increase the natural frequencies; a compressive load will decrease the frequencies. – In fact, a sufficiently-high compressive load will result in a natural frequency of zero, effectively replicating the results of a buckling analysis. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
D. Workshop - Modal Analysis
Training Manual
This workshop consists of two problems: 1. Modal analysis of a plate with a hole – A step-by-step description of how to do the analysis. – You may choose to run this problem yourself, or your instructor may show it as a demonstration. (WS2A: Modal Analysis - Plate with a Hole).
2. Pre-stressed Modal analysis of a model airplane wing – This is left as an exercise to you. (WS2B: Modal Analysis - Model Airplane Wing).
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July 2009 Inventory #002666
Chapter 3: Harmonic Response
ANSYS Mechanical
Dynamics
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3-1
July 2009 Inventory #002666
Harmonic Analysis
Harmonic Analysis
Training Manual
A. Define harmonic analysis and its purpose. B. Learn basic terminology and concepts underlying harmonic analysis. C. Learn how to do a harmonic analysis in Workbench. D. Work on a harmonic analysis exercise.
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July 2009 Inventory #002666
Harmonic Analysis
A. Definition & Purpose
Training Manual
What is harmonic analysis? • A technique to determine the steady state response of a structure to sinusoidal (harmonic) loads of known frequency. • Input: – Harmonic loads (forces, pressures, and imposed displacements) of known magnitude and frequency. – May be multiple loads all at the same frequency. Forces and displacements can be in-phase or out-of phase. Body loads can only be specified with a phase angle of zero.
• Output: – Harmonic displacements at each DOF, usually out of phase with the applied loads. – Other derived quantities, such as stresses and strains.
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July 2009 Inventory #002666
Harmonic Analysis
… Definition & Purpose
Training Manual
Harmonic analysis is used in the design of: • Supports, fixtures, and components of rotating equipment such as compressors, engines, pumps, and turbomachinery. • Structures subjected to vortex shedding (swirling motion of fluids) such as turbine blades, airplane wings, bridges, and towers.
Why should you do a harmonic analysis? • To make sure that a given design can withstand sinusoidal loads at different frequencies (e.g, an engine running at different speeds). • To detect resonant response and avoid it if necessary (by using dampers, for example).
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July 2009 Inventory #002666
Harmonic Analysis
B. Terminology & Concepts
Training Manual
Topics covered: • Assumptions and Restrictions • Equation of motion • Nature of harmonic loads • Complex displacements • Solution methods
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July 2009 Inventory #002666
Theory
Assumptions & Restrictions
Training Manual
• The entire structure has constant or frequency-dependent stiffness, damping, and mass effects. • All loads and displacements vary sinusoidally at the same known frequency (although not necessarily in phase). • Acceleration, bearing, and moment loads are assumed to be real (inphase) only.
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July 2009 Inventory #002666
Theory
Development
Training Manual
• Start with the linear general equation of motion:
M u C u K u F • Assume [F] and {u} are harmonic with frequency W:
F Fmax ei eiWt u umax ei eiWt Fmax cos i sin eiW t umax cos i sin eiW t F1 iF2 eiW t u 1 iu2 eiW t • Note: The symbols W an w differentiate the input from the output: W = input (a.k.a. imposed) circular frequency w = output (a.k.a. natural) circular frequency
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July 2009 Inventory #002666
Theory
Development
Training Manual
• Take two time derivatives:
u u u
iW W2
u 1 iu2 eiWt u 1 iu2 eiWt u 1 iu2 eiWt
• Substitute and simplify:
M u C u K u F W 2 M u 1 iu2 eiW t iWC u 1 iu2 eiW t K u 1 iu2 eiW t F 1 iF2 eiW t W 2 M iWC K u 1 iu2 F 1 iF2 • This can then be solved using one of two methods. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Theory
Development
Training Manual
• The full method solves the system of simultaneous equations directly using a static solver designed for complex arithmetic: – c denotes a complex matrix or vector Kc uc Fc W2 M iWC K u 1 iu2 F 1 iF2
K c uc Fc
• The mode-superposition method expresses the displacements as a linear combination of mode shapes (see Theory Reference for details).
W M iWC K u iu F iF 2
1
W ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
2
2
1
2
i 2w j W j w 2j y jc f jc 3-9
July 2009 Inventory #002666
Theory
Solution Methods
Training Manual
FULL
MSUP
• Exact solution.
• Approximate solution; accuracy depends in part on whether an adequate number of modes have been extracted to represent the harmonic response.
• Generally slower than MSUP.
• Generally faster than FULL.
• Supports all types of loads and boundary conditions.
• Does not support nonzero imposed harmonic displacements.
• Solution points must be equally distributed across the frequency domain.
• Solution points may be either equally distributed across the frequency domain or clustered about the natural frequencies of the structure.
• Solves the full system of simultaneous • Solves an uncoupled system of equations equations using the Sparse matrix solver for by performing a linear combination of complex arithmetic. orthogonal vectors (mode shapes).
• Prestressing is not available in either method in ANSYS Workbench 12.0. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Theory
Nature of Harmonic Loads
Training Manual
• Multiple loads and boundary conditions may be input, each with different amplitude and phase angles (interpreted as lag angle).
xi X i sin wt i where X amplitude
w freqency phase angle
• All loads and displacements, both input and output, are assumed to occur at the same frequency. • Calculated displacements will be complex if – damping is specified or – applied load is complex. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Remarks & Comments
Resonance
Training Manual
• When the imposed frequency approaches a natural frequency in the direction of excitation, a phenomenon known as resonance occurs. – This can be seen in the figures on the right for a 1-DOF system subjected to a harmonic force for various amounts of damping.
• The following will be observed: – an increase in damping decreases the amplitude of the response for all imposed frequencies, – a small change in damping has a large effect on the response near resonance, and – the phase angle always passes through ±90° at resonance for any amount of damping. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Remarks & Comments
Contact Regions
Training Manual
• Contact regions are available in harmonic analysis; however, since this is a purely linear analysis, contact behavior will differ for the nonlinear contact types, as shown below: Linear Dynamic Analysis Contact Type
Static Analysis Initially Touching
Inside Pinball Region
Outside Pinball Region
Bonded
Bonded
Bonded
Bonded
Free
No Separation
No Separation
No Separation
No Separation
Free
Rough
Rough
Bonded
Free
Free
Frictionless
Frictionless
No Separation
Free
Free
Frictional
Frictional
m = 0, No Separation m > 0, Bonded
Free
Free
• Contact behavior will reduce to its linear counterparts. – It is generally recommended, however, not to use a nonlinear contact type in a linear-dynamic analysis ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Remarks & Comments
Mode Superposition
Training Manual
• The Mode Superposition method will automatically perform a modal analysis first – The number of modes necessary for an accurate solution will be estimated if a frequency range is not supplied. • the default range is from zero to twice the ending frequency
– The harmonic analysis portion is very quick and efficient, hence, the Mode Superposition method is usually much faster overall than the Full method
• Since a free vibration analysis is performed, Mechanical knows what the natural frequencies of the structure are and can cluster the harmonic results near them (see next slide)
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July 2009 Inventory #002666
Remarks & Comments
… Solution Methods - Mode Superposition
Training Manual
• Cluster option captures the peak response better than evenly-spaced intervals.
Evenly spaced frequency points
Clustered frequency points
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July 2009 Inventory #002666
Procedure: Harmonic Response
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July 2009 Inventory #002666
Harmonic Analysis
C. Procedure
Training Manual
Four main steps: • Build the model • Choose analysis type and options • Apply harmonic loads and solve • Review results
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July 2009 Inventory #002666
Harmonic Analysis Procedure
Build the Model
Training Manual
Model • Nonlinearities are not allowed. • See also Modeling Considerations in Module 1.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
Choose Analysis Type & Options
Training Manual
Build the model Choose analysis type and options • Enter Solution and choose harmonic analysis. • Main analysis option is solution method - discussed next. • Specify damping - discussed next.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
… Choose Analysis Type & Options Analysis options • Solution method - full or mode superposition. • For large models (>1 million DOF), set Store Results at All Frequencies to “No”.
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Training Manual
Damping • Choose from beta damping and damping ratio (constant damping ratio is most commonly used).
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July 2009 Inventory #002666
Harmonic Analysis Procedure
Apply Harmonic Loads and Solve
Training Manual
Build the model Choose analysis type and options
Apply harmonic loads and solve • Structural loads and supports may also be used in harmonic analyses with the following exceptions: – Loads Not Supported: • • • • •
Gravity Loads Thermal Loads Rotational Velocity Pretension Bolt Load Compression Only Support (if present, it behaves similar to a Frictionless Support)
• Remember that all structural loads will vary sinusoidally at the same excitation frequency
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July 2009 Inventory #002666
Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• A list of supported loads are shown below:
– Not all available loads support phase input. Accelerations, Bearing Load, and Moment Load will have a phase angle of 0°. • If other loads are present, shift the phase angle of other loads, such that the Acceleration, Bearing, and Moment Loads will remain at a phase angle of 0°.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• Specifying harmonic loads requires: – Amplitude and phase angle – Frequency
• Amplitude and phase angle – The load value (magnitude) represents the amplitude Fmax. – Phase angle Y is the phase shift between two or more harmonic loads. Not required if only one load is present. Non-zero Y valid for force, displacement, and pressure harmonic loads.
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Imaginary
• Loads are applied all at once in the first solution interval (stepped). F2max
F1max
Real
July 2009 Inventory #002666
Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• Amplitude and phase angle (continued)
Imaginary
– Mechanical allows direct input of amplitude and phase angle into the Details window.
F2max
F1max
Real
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July 2009 Inventory #002666
Harmonic Analysis Procedure
… Apply Harmonic Loads and Solve
Training Manual
• Frequency of harmonic load: – Specified in cycles per second (Hertz) by a frequency range and number of substeps within that range.
– For example, a range of 0-50 Hz with 10 solution intervals gives solutions at frequencies of 5, 10, 15, …, 45, and 50 Hz. Same range with 1 substep gives one solution at 50 Hz.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
Review Results
Training Manual
Build the model Choose analysis type and options Apply harmonic loads and solve
Review results • Three steps: – Plot displacement vs. frequency at specific points in the structure. – Identify critical frequencies and corresponding phase angles. – Review displacements and stresses over entire structure at the critical frequencies and phase angles.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
Review Results
Training Manual
Displacement vs. frequency plots • Pick nodes that might deform the most, then choose the DOF direction. • Then graph the desired frequency response.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
… Review Results
Training Manual
Identify critical frequencies and phase angles • Bode plot shows frequency at which highest amplitude occurs. • The amplitude and phase angle at which the peak amplitude occurs are shown in the Worksheet tab.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
… Review Results
Training Manual
• Next step is to review displacements and stresses over the entire model at that frequency and phase angle. • The frequency and phase angle must be manually entered into the Details window.
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July 2009 Inventory #002666
Harmonic Analysis Procedure
… Review Results
Training Manual
• A harmonic analysis produces a real and imaginary solution as separate sets of results. • Plot deformed shape, stress contours, and other desired results at a specified frequency and phase angle.
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July 2009 Inventory #002666
Workshop
Harmonic Analysis
Training Manual
• In this workshop, you will examine the harmonic response of a fixed-fixed beam to harmonic forces caused by rotating machinery mounted on the beam. • See your Dynamics Workshop supplement for details WS3: Harmonic Analysis - Fixed-Fixed Beam
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July 2009 Inventory #002666
Chapter 4:
Response Spectrum
ANSYS Mechanical Dynamics
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July 2009 Inventory #002666
Response Spectrum Analysis
Training Manual
Topics covered: • Definition and purpose • Overview of Workbench capabilities • Procedure
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July 2009 Inventory #002666
Response Spectrum Analysis
Description & Purpose
Training Manual
• A response-spectrum analysis calculates the maximum response of a structure to a transient loading.
• It is performed as a fast alternative of approximating a full transient solution.
• The maximum response is computed as scale factor times the mode shape.
• These maximum responses are then combined to give a total response of the structure. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Response Spectrum Analysis
Types of Analyses
Training Manual
Types of Response Spectrum analysis: • Single-point response spectrum – A single response spectrum excites all specified points in the model.
• Multi-point response spectrum – Different response spectra excite different points in the model.
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July 2009 Inventory #002666
Response Spectrum Analysis
Common Uses
Training Manual
• Commonly used in the analysis of: – Nuclear power plant buildings and components, for seismic loading – Airborne Electronic equipment for shock loading – Commercial buildings in earthquake zones
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July 2009 Inventory #002666
Response Spectrum Analysis
Terminology & Concepts
Training Manual
• Instead of simulating the response of a structure to a full time history, we could figure out how each mode would respond to the time history, then combine the responses together. • In other words, the response of each mode of a structure is similar to a 1-DOF oscillator, just scaled by some amount. • If we know the natural frequencies and mode shapes of a structure, we can simply determine what the displacement would be for a 1-DOF oscillator, if it were subjected to the same transient loading, and scale the response by the appropriate amount. • If there is more than one load, each will have its own spectrum.
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July 2009 Inventory #002666
Response Spectrum Analysis
Assumptions & Restrictions
Training Manual
• The structure is linear (i.e. constant stiffness and mass). • For single-point response spectrum analysis, the structure is excited by a spectrum of known direction and frequency components, acting uniformly on all support points. • For multi-point response spectrum analysis, the structure may be excited by different input spectra at different support points. – Up to 20 different simultaneous input spectra are allowed.
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July 2009 Inventory #002666
Theory
Participation Factors
Training Manual
• A modal analysis must first be completed to determine the natural frequencies, mode shapes, and participation factors for each mode. – This procedure was covered in Chapter 2: Modal Analysis.
M K 0 2 i
i
i M D T i
mode
frequency
mode shape
spectrum value
participation factor
mode coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
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July 2009 Inventory #002666
Theory
Spectrum Values
Training Manual
• For each natural frequency, the spectrum value can be determined by a simple look-up from the response-spectrum table. – When values are needed between input frequencies, log-log interpolation is done in the space as defined.
mode
frequency
mode shape
spectrum value
participation factor
mode coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
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July 2009 Inventory #002666
Theory
Mode Coefficients
Training Manual
• The mode coefficients can be determined from the participation factors, depending on the type of spectrum input.
displaceme nt Ai Si i
velocity S Ai i i
i
accelerati on S Ai i 2i
i
– Recall: participation factors measure the amount of mass moving in each direction for a unit displacement.
mode
frequency
mode shape
spectrum value
participation factor
mode coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
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July 2009 Inventory #002666
Theory
Response
Training Manual
• The response (displacement, velocity or acceleration) for each mode can then be computed from the frequency, mode coefficient, and mode shape.
Ri Ri Ri
Ai i i Ai i
i2 Ai i
for displaceme nt response for veloci ty response for accelerati on response
• If there is more than one significant mode, the response for each mode must be combined using some method. mode
frequency
mode shape
spectrum value
participation factor
mode coefficient
response
1
1
{}1
S1
1
A1
{R}1
2
2
{}2
S2
2
A2
{R}2
3
3
{}3
S3
3
A3
{R}3
…
…
…
…
…
…
…
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Theory
Mode Combination
Training Manual
• In general, mode combinations take the form:
N N R e ij Ri Rj i 1 j 1
1 2
where R is the total modal response and RiRj is the entrywise product (a.k.a. Hadamard or Schur product) of modes i and j. • The modal correlation coefficients, eij, are uniquely defined, depending on the method chosen for evaluating the correlation coefficient. e ij 1 for partially correlated modes i and j 0 e ij 1 for uncorrelat ed correlated modes i and j e ij 0 for completely correlated modes i and j
• The methods for mode combination are SRSS, CQC, and ROSE. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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July 2009 Inventory #002666
Theory
Mode Combination
Training Manual
• The SRSS method is generally more conservative than the other methods. – assumes that all maximum modal values are uncorrelated
e ij 1.0 for i j e ij 0.0 for i j – for a structures with coupled modes, this assumption overestimates the responses overall
• The CQC and the ROSE methods providing a means of evaluating modal correlation for the response spectrum analysis. – accounting for mode coupling makes the response estimate from these methods more realistic and closer to the exact time history solution
SRSS
R Ri2 i 1 N
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CQC 1 2
R ke ij Ri Rj i 1 j 1 N
N
4-13
ROSE
1 2
R e ij Ri Rj i 1 j 1 N
N
1 2
July 2009 Inventory #002666
Procedure: Response Spectrum
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July 2009 Inventory #002666
Response Spectrum
Procedure
Training Manual
• Drop a Modal (ANSYS) system into the project schematic.
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July 2009 Inventory #002666
Response Spectrum
Procedure
Training Manual
• Drop a Response Spectrum system onto the Solution cell of the Modal system.
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July 2009 Inventory #002666
Response Spectrum
Procedure
Training Manual
• Create new geometry, or link to existing geometry.
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• Edit the Model cell to bring up the Mechanical application.
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July 2009 Inventory #002666
Response Spectrum
Preprocessing
Training Manual
• Verify materials, connections, and mesh settings. – This was covered in Workbench Mechanical Intro.
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July 2009 Inventory #002666
Response Spectrum
Preprocessing
Training Manual
• Add supports to the model. – Displacement constrains must have a magnitude of zero.
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July 2009 Inventory #002666
Response Spectrum
Solution Settings
Training Manual
• Choose the number of modes to extract. • If needed, upper and lower bounds on frequency may be specified to extract the modes within a specified range.
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July 2009 Inventory #002666
Response Spectrum
Postprocessing
Training Manual
• Review the modal results before proceeding.
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July 2009 Inventory #002666
Response Spectrum
Preprocessing
Training Manual
• Insert an Acceleration, Velocity, or Direction response spectrum. • Set the Boundary Condition, Spectrum (Tabular) Data, and Direction.
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July 2009 Inventory #002666
Response Spectrum
Postprocessing
Training Manual
• Insert Directional Deformation, Velocity, or Acceleration.
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July 2009 Inventory #002666
Response Spectrum
Postprocessing
Training Manual
• Stress (normal, shear, equivalent) and Strain (normal, shear) results can also be reviewed.
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July 2009 Inventory #002666
Workshop
Response Spectrum Analysis
Training Manual
• In this workshop, you will determine the response of a prestressed suspension bridge subjected to a seismic load. • See your Dynamics Workshop supplement for details WS4: Response Spectrum Analysis - Suspension Bridge
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July 2009 Inventory #002666
Chapter 5:
Random Vibration
ANSYS Mechanical Dynamics
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July 2009 Inventory #002666
Random Vibration Analysis
Random Vibration Analysis
Training Manual
Topics covered: • Definition and purpose • Overview of Workbench capabilities • Procedure
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July 2009 Inventory #002666
Random Vibration Analysis
A. Definition and Purpose
Training Manual
What is random vibration analysis? – A spectrum analysis technique based on probability and statistics. – Meant for loads such as acceleration loads in a rocket launch that produce different time histories during every launch .
Reference: Random vibrations in mechanical systems by Crandall & Mark
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July 2009 Inventory #002666
Random Vibration Analysis … Definition
and Purpose
Training Manual
• Transient analysis is not an option since the time history is not deterministic (sample is not repeatable). • Instead, using statistics the sample time histories are converted to Power Spectral Density function (PSD), a statistical representation of the load time history.
Image from “Random Vibrations Theory and Practice” by Wirsching, Paez and Ortiz.
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July 2009 Inventory #002666
Random Vibration Analysis
Power Spectral Density
Training Manual
• Sample time histories are converted to Power Spectral Density function (PSD), a statistical representation of the load time history.
Reference: Random vibrations in mechanical systems by Crandall & Mark
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Image from “Random Vibrations Theory and Practice” by Wirsching, Paez and Ortiz.
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Random Vibration Analysis
Statistical Representation
Training Manual
• A Random Vibration analysis computes the probability distribution of different results, such as displacement or stress, due to some random excitation • The analysis follows a modal analysis • An internal combination is done to compute the combined effect from each mode and their interactions.
Gaussian (normal) Distribution ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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3s
July 2009 Inventory #002666
Random Vibration Analysis
Power Spectral Density
Training Manual
• The Power Spectral Density is the mean square value of the excitation for a unit frequency band. – The area under a PSD curve is the variance of the response (square of the standard deviation). – The units used in PSD are mean square/Hz (e.g. an acceleration PSD will have units of G2/Hz). – The quantity represented by PSD may be displacement, velocity, acceleration, force, or pressure. Random Vibration curve by MIL-STD-202
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July 2009 Inventory #002666
Random Vibration Analysis
Common Uses
Training Manual
• Commonly used for – Airborne electronics – Acoustic loading of Airframe parts – Jitter in alignment of optical equipment – Relative deformation in large mirrors
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July 2009 Inventory #002666
Random Vibration
Workbench Capabilities
Training Manual
• Input: – Natural frequencies and mode shapes from a modal analysis – Single or multiple PSD excitations applied to ground nodes
• Output: – 1s results can be contoured like any other analysis. – Response PSD at one DOF (one point in one direction)
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Procedure: Random Vibration
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Random Vibration
Procedure
Training Manual
• Drop a Modal (ANSYS) system into the project schematic.
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July 2009 Inventory #002666
Random Vibration
Procedure
Training Manual
• Drop a Random Vibration system onto the Solution cell of the Modal system.
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Random Vibration
Procedure
Training Manual
• Create new geometry, or link to existing geometry.
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• Edit the Model cell to bring up the Mechanical application.
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Random Vibration
Preprocessing
Training Manual
• Verify materials, connections, and mesh settings. – This was covered in Workbench Mechanical Intro.
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Random Vibration
Preprocessing
Training Manual
• Add supports to the model. – Displacement constrains must have a magnitude of zero.
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July 2009 Inventory #002666
Random Vibration
Solution Settings
Training Manual
• Choose the number of modes to extract. • If needed, upper and lower bounds on frequency may be specified to extract the modes within a specified range.
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Random Vibration
Postprocessing
Training Manual
• Review the modal results before proceeding.
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Random Vibration
Preprocessing
Training Manual
• Insert an Acceleration, Velocity, or Direction PSD base excitation. • Set the Boundary Condition, Load (Tabular) Data, and Direction.
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Random Vibration
Postprocessing
Training Manual
• Insert Directional Deformation, Velocity, or Acceleration. – the direction and sigma value may be chosen here – note that results are always reviewed with scaling set to 0.0
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Random Vibration
Postprocessing
Training Manual
• Stress (normal, shear, equivalent) and Strain (normal, shear) results can also be reviewed.
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Random Vibration
Postprocessing
Training Manual
• Response PSD can be plotted at one DOF (one point in one direction, either absolute or relative to base excitation).
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Workshop – Random Vibration
Training Manual
• In workshop 5A, you will determine the displacements and stresses in a girder assembly due to an acceleration PSD. WS5A: Random Vibration (PSD) Analysis of a Girder Assembly
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Chapter 6:
Transient
ANSYS Mechanical Dynamics
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July 2009 Inventory #002666
Overview
Training Manual
• Transient structural analysis provides users with the ability to determine the dynamic response of the system under any type of time-varying loads. – Unlike rigid dynamic analyses, bodies can be either rigid or flexible. For flexible bodies, nonlinear materials can be included, and stresses and strains can be output. – Transient structural analysis is also known as time-history analysis or transient structural analysis.
– To perform Flexible Dynamic Analyses, an ANSYS Structural, ANSYS Mechanical, or ANSYS Multiphysics license is required
Assembly shown here is from an Autodesk Inventor sample model ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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Topics Covered
Training Manual
Background Information: A. Introduction to Transient Structural Analyses B. Preliminary Linear Dynamic Studies C. Background Information on Nonlinear Analyses Procedural Information: D. Demo – Impact Problem E. Part Specification and Meshing F. Nonlinear Materials G. Contact; Joints; and Springs H. Initial Conditions I. Loads; Supports; and Joint Conditions J. Damping K. Transient Structural Analysis Settings L. Reviewing Results
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A. Introduction
Training Manual
• Transient structural analyses are needed to evaluate the response of deformable bodies when inertial effects become significant. – If inertial and damping effects can be ignored, consider performing a linear or nonlinear static analysis instead – If the loading is purely sinusoidal and the response is linear, a harmonic response analysis is more efficient – If the bodies can be assumed to be rigid and the kinematics of the system is of interest, rigid dynamic analysis is more cost-effective – In all other cases, transient structural analyses should be used, as it is the most general type of dynamic analysis
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… Introduction
Training Manual
• In a transient structural analysis, Workbench Mechanical solves the general equation of motion:
M x C x K xx F t Some points of interest: – Applied loads and joint conditions may be a function of time and space. – As seen above, inertial and damping effects are now included. Hence, the user should include density and damping in the model. – Nonlinear effects, such as geometric, material, and/or contact nonlinearities, are included by updating the stiffness matrix.
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July 2009 Inventory #002666
… Introduction
Training Manual
• Transient structural analysis encompasses static structural analysis and rigid dynamic analysis, and it allows for all types of Connections, Loads, and Supports. • However, one of the important considerations of performing transient structural analysis is the time step size: – The time step should be small enough to correctly describe the timevarying loads – The time step size controls the accuracy of capturing the dynamic response. Hence, running a preliminary modal analysis is suggested in Section B. – The time step size also controls the accuracy and convergence behavior of nonlinear systems. Background information on the Newton-Raphson method is presented in Section C.
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B. Preliminary Modal Analysis
Training Manual
• While transient structural analyses use automatic time-stepping, proper selection of the initial, minimum, and maximum time steps is important to represent the dynamic response accurately: – Unlike rigid dynamic analyses which use explicit time integration, transient structural analyses use implicit time integration. Hence, the time steps are usually larger for transient structural analyses – The dynamic response can be thought of as various mode shapes of the structure being excited by a loading. The initial time step should be based on the modes (or frequency content) of the system. – It is recommended to use automatic time-stepping (default): • The maximum time step can be chosen based on accuracy concerns. This value can be defined as the same or slightly larger than the initial time step • The minimum time step can be input to prevent Workbench Mechanical from solving indefinitely. This minimum time step can be input as 1/100 or 1/1000 of the initial time step
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… Preliminary Modal Analysis
Training Manual
• A general suggestion for selection of the initial time step is to use the following equation:
tinitial
1 20 f response
where fresponse is the frequency of the highest mode of interest • In order to determine the highest mode of interest, a preliminary modal analysis should be performed prior to the transient structural analysis – In this way, the user can determine what the mode shapes of the structure are (i.e., how the structure may respond dynamically) – The user can also then determine the value of fresponse
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… Preliminary Modal Analysis
Training Manual
Points of Consideration: • The automatic time-stepping algorithm will increase or decrease the size of the time step during the course of the analysis based on the calculated response frequency. – Automatic time-stepping algorithm still relies on reasonable values of initial, minimum, and maximum time steps – If the minimum time step is being used, that may indicate that the initial time step size was too large. The user can plot the time step size by selecting “Solution Output: Time Increment” from the Details view of the Solution Information branch
• When performing a modal analysis to determine an appropriate response frequency value, it is not sufficient to request a certain number of modes, then to use the maximum frequency. It is a good idea to examine the various mode shapes to determine which frequency may be the highest mode of interest contributing to the response of the structure.
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C. Including Nonlinearities
Training Manual
• There are several sources of nonlinear behavior, and a transient structural analysis may often include nonlinearities: – Geometric nonlinearities: If a structure experiences large deformations, its changing geometric configuration can cause nonlinear behavior. – Material nonlinearities: A nonlinear stress-strain relationship, such as metal plasticity shown on the right, is another source of nonlinearities. – Contact: Include effects of contact is a type of “changing status” nonlinearity, where an abrupt change in stiffness may occur when bodies come in or out of contact with each other.
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July 2009 Inventory #002666
… Including Nonlinearities
Training Manual
• In a linear analysis, the applied force F and displacement x of the system are related such that doubling the force would double the displacement, stresses, and strains
F K
– This assumes that the change in the original and final deformed shapes is negligible since the same stiffness matrix [K] is used
x
• In a nonlinear analysis, the relationship between the applied force F and displacement x is not known beforehand – As the geometry undergoes deformation, so too, does the stiffness matrix [K] change – The Newton-Raphson method needs to be implemented to solve nonlinear problems
F
x ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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… Including Nonlinearities
Training Manual
• Nonlinear analyses require several solution iterations: – The actual relationship between applied load and deformation (dotted green line below) is not known a priori – The Newton-Raphson method, which can be thought of as a series of linear approximations with corrections, is performed (solid blue lines) • The load Fa is applied to the structure. Based on the new deformed shape, internal force F1 is calculated. If Fa ≠F1 then the system is not in equilibrium. A new stiffness matrix [K] (slope of blue line) is calculated based on the current conditions. • This process is repeated until Fa =Fi for iteration i, at which point the solution is said to be converged
• Oftentimes, the applied load Fa must be split into smaller increments in order for convergence to occur. Hence, for a ramped load, a smaller time step may be needed to ensure convergence
Fa 3 2
F1 1
x1 ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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x July 2009 Inventory #002666
… Including Nonlinearities
Training Manual
• As shown from the previous slides, the time step size will also have an influence on nonlinear analyses: – The time step size should be small enough to allow the Newton-Raphson method to obtain force equilibrium (convergence) – The user may also need to specify the initial, minimum, and maximum timesteps based on nonlinear considerations
• Usually, the dynamic considerations for picking a time step size as discussed in Section B is sufficient. – Since Workbench Mechanical only uses one set of time steps, resolving the dynamic response often provides a small enough time step to resolve nonlinear effects as well. – Determination of the time step size based on nonlinear considerations is often not as straightforward as choosing the dynamic time step size. Hence, the user may rely on automatic time-stepping algorithm to ensure convergence and accuracy.
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… Including Nonlinearities
Training Manual
• The automatic time-stepping algorithm takes into account the following nonlinear effects: – If force equilibrium (or some other convergence criterion) is not satisfied, bisection occurs – If an element has excessive distortion, bisection occurs – If the maximum plastic strain increment exceeds 15%, bisection occurs – Optional: if contact status changes abruptly, bisection occurs
• Bisection is part of the automatic time-stepping algorithm, when the solver goes back to the previously converged solution at time ti and uses a smaller time increment ti. – Bisections provide an automated means to solve nonlinear problems more accurately or to overcome convergence difficulties. – Note, however, that bisections result in wasted solver time since the solution returns to the previously converged solution and tries again with a smaller time step. Hence, choosing the right initial and maximum time step can minimize the number of bisections that occur
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… Including Nonlinearities
Training Manual
• By default, large deformation effects and automatic time-stepping will be active: – The user does not need to do anything special to account for nonlinearities. • However, as noted before, if nonlinear effects dominate, the time step size may be dictated by nonlinear considerations rather than dynamic concerns. • “Large Deflection” can be toggled in the Details view of the “Analysis Settings” branch
– If the user wants to turn on time step size checks based on contact status, this can be done in with “Time Step Controls” in the Details view of a given contact region. • Using this option may decrease the time step to ensure correct momentum transfer between parts in impact-type of situations • Note, however, that the time step may become excessively small, so this is not recommended in general, especially for preliminary analyses
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Procedure: Transient
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E. Part Specification
Training Manual
• In a transient structural analysis, parts may be rigid or flexible: – Under the “Geometry” branch, the “Stiffness Behavior” can be toggled from “Flexible” to “Rigid” on a per-part basis – Rigid and flexible parts can co-exist in the same model
• Consideration for flexible parts are the same as in static analyses: – Specify appropriate material properties, such as density, Young’s Modulus, and Poisson’s ratio – Nonlinear materials, such as plasticity or hyperelasticity, can also be included
• For rigid parts, the following apply: – Line bodies cannot be set to rigid – Multibody parts must have all bodies set to rigid – Density is the only material property needed to calculate mass properties. All other material specifications will be ignored. – An “Inertial Coordinate System” will automatically be defined at the centroid of the part ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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… Part Specification
Training Manual
• For flexible bodies, the mesh density is based on the following: – The mesh should be fine enough to capture the mode shapes of the structure (dynamic response) – If stresses and strains are of interest, the mesh should be fine enough to capture these gradients accurately
• For rigid bodies, no mesh is produced – Rigid bodies are rigid, so no stresses, strains, or relative deformation is calculated. Hence, no mesh is required – Internally, rigid bodies are represented as point masses located at the center of its “Inertial Coordinate System” On the figure on the right, one can see flexible bodies (meshed) and rigid bodies (not meshed) in the same model. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
Assembly shown here is from an Autodesk Inventor sample model
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F. Nonlinear Materials
Training Manual
• For flexible bodies, nonlinear materials may be defined: – Metal plasticity: • Define Young’s modulus and Poisson’s ratio • Select either isotropic or kinematic hardening law and either bilinear or multilinear representation of stress-strain curve – For multilinear stress-strain curve, remember that values should be logarithmic plastic strain vs. true stress
– Hyperelasticity: • Select a hyperelastic model based on strain invariants (neo-Hookean, Polynomial, Mooney-Rivlin, or Yeoh) or principal stretch (Ogden): – If material constants are not known, enter test data, then select hyperelastic model on which to perform curve-fit – If material constants are known, select hyperelastic model and enter constants
• To account for inertial effects, density should also be defined for both flexible and rigid bodies. • Material damping, discussed in Section I, may also be input for flexible bodies.
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G. Contact; Joints; Springs
Training Manual
• Contact, joints, or springs can be defined under the “Connections” branch in transient structural analyses – Contact is defined between solid and surface bodies (rigid parts must be single body). Contact is used when parts can come in and out of contact or if frictional effects are important. • Nonlinear contact (rough, frictionless, frictional) may be defined for faces of solid or surface bodies (flexible or rigid) at v12.
– Joints are defined for 3D rigid or flexible bodies only. Joints can be defined between two bodies or from one body to ground. Joints are meant to model mechanisms where the part(s) are connected but relative motion is possible. • Joints are defined faces, lines, or keypoints of 3D solid, surface, or line bodies, both flexible and rigid.
– Springs are defined for 3D rigid or flexible bodies. Springs provide longitudinal stiffness and damping for the scoped region(s), meant to represent stiffness/damping effects of parts not explicitly modeled. • Springs can be defined on vertices, edges, or faces of 3D bodies • Defined springs cannot have zero length ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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… Contact
Training Manual
• Contact regions can be defined between flexible bodies: – Contact is useful when the contacting area is not known beforehand or if the contacting area changes during the course of the analysis – Any type of contact behavior (linear, nonlinear) can be specified, including frictional effects • Play Animation
In the animation, some surfaces of two parts are initially not in contact, but as the analysis progresses, the surfaces come into contact, as shown on the right, allowing for forces to be transmitted between the two bodies. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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… Contact
Training Manual
• In contact, parts are prevented from penetrating into each other. The different type of contact describe behavior in the separation and sliding directions:
Contact Type Bonded No Separation Rough Frictionless Frictional
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Normal Direction Separate no no yes yes yes
Tangential Direction Slide no yes no yes yes (when Ft ≥mN)
July 2009 Inventory #002666
… Contact
Training Manual
• Different contact formulations allow for establishing the mathematical relationship between contacting solid bodies: – For bonded and no separation contact, the contacting areas are known beforehand based on the geometry and pinball region • The recommended contact formulation to use is either “Pure Penalty” (default) or “MPC”
– For rough, frictionless, and frictional contact, the actual contacting areas are not known a priori, so an iterative approach is required • The recommended contact formulation to use is “Augmented Lagrange”
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… Joints
Training Manual
• Joints can be defined between bodies or from a body to ground: – Joints define the allowed motion (kinematic constraint) on surface(s) – Various types of joints can be defined for flexible or rigid bodies: • Fixed, Revolute, Cylindrical, Translational, Slot, Universal, Spherical, Planar, or General Joints
– Definition and configuration of joints is covered in a separate training course named “ANSYS Rigid and Flexible Dynamic Analysis”. – Unlike rigid dynamic analysis, the actual – not relative – degrees of freedom are specified.
The animation on the right shows an assembly using cylindrical and revolute joints Assembly shown here is from an Autodesk Inventor sample model ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
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… Joints
Training Manual
• In transient structural analyses, the user has an additional option of specifying the behavior of the joint: – “Rigid” (default) behavior means that the scoped surface(s) will not deform but be treated as rigid surface(s). This means that a scoped cylindrical surface will remain cylindrical throughout the analysis. – “Deformable” behavior means that while the joint constraint is satisfied, the scoped surface(s) are free to deform. This means that a scoped cylindrical surface may not remain cylindrical throughout the analysis.
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… Springs
Training Manual
• Springs can be defined between bodies or from body to ground: – Springs define the stiffness and/or damping of surface(s) • Refer to Section I for additional details on damping
– Springs can be defined for rigid or flexible bodies – These are longitudinal springs, so the stiffness or damping is related to the change in length of the spring • The spring must not have zero length • Springs can be defined on vertices, edges, or surfaces • Definition and configuration of springs is covered in a separate training course named “ANSYS Rigid and Flexible Dynamic Analysis”.
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H. Initial Conditions
Training Manual
• For a transient structural analysis, initial displacement and initial velocity is required: – User can define initial conditions via “Initial Condition” branch or by using multiple Steps
• Defining initial displacement & velocity with the “Initial Condition” object: – Default condition is that all bodies are at rest • No additional action needs to be taken
– If some bodies have zero initial displacement but non-zero constant initial velocity, this can be input • Only bodies can be specified • Enter constant initial velocity (Cannot specify more than one constant velocity value with this method)
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… Initial Conditions
Training Manual
• Defining initial displacement & velocity by using multiple Steps: – This technique is required for all other situations – Leave “Initial Conditions” to “At Rest.” For “Analysis Settings,” use 2 Steps over a small time interval: • First Step should have very small “Step End Time” in Details view. Also, change “Time Integration: Off” and “Auto Time Stepping: Off” only for the first Step. Modify “Define by: Substeps” with “Number of Substeps: 1”.
– Apply a “Displacement” support with appropriate values (discussed in next slide) in Step 1. Deactivate this “Displacement” support in Step 2. – The idea behind such a technique is that the first Step, solved over a small time interval t1, will provide an initial displacement & velocity based on an imposed xinitial “Displacement” support.
v
initial
x1initial t1
If the time interval t1 is small enough, the effect on the actual ending time should be negligible.
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… Initial Conditions
Training Manual
– Initial displacement = 0, initial velocity ≠ 0 • Ramp a very small displacement value over a small time interval to produce the desired initial velocity. Deactivate it for Step 2.
– Initial displacement ≠ 0, initial velocity ≠ 0 • Ramp the desired initial displacement over a time interval to produce the desired initial velocity. Deactivate it for Step 2.
– Initial displacement ≠ 0, initial velocity = 0 • Step apply the desired initial displacement over a time interval to ensure that initial velocity is zero. Deactivate it for Step 2, if necessary.
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I. Loads; Supports; Conditions
Training Manual
• For rigid bodies, just as in a rigid dynamic analysis, only inertial loads, remote loads, and joint conditions are supported. – Rigid bodies do not deform, so structural & thermal loads do not apply
• For deformable bodies, any type of load can be used: – Inertial and structural loads – Structural supports – Joint (for defined joints) and thermal conditions
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… Time-Varying Loads
Training Manual
• Structural loads and joint conditions can be input as time-dependent load histories – When adding a Load or Joint Condition, the magnitude can be defined as a constant, tabular value, or function. – The values can be entered directly in the Workbench Mechanical GUI or entered in the Engineering Data page
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J. Damping
Training Manual
• As noted in Section A, the equations solved for in transient structural analyses also include a damping term • Since the response frequency is not known in advance of running the simulation, are only two types of damping available: – Viscous damping • beta damping (optionally material-dependent) or by element damping
– Numerical damping
• See Chapter 1 for more details. • The effect of damping is cumulative. Hence, if 2% materialdependent beta damping and 3% global beta damping is defined, that part will have 5% damping.
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K. Analysis Settings
Training Manual
• Besides damping, there are various other options the user can set under the “Analysis Settings” branch. • It is important that the user specify the solution times in the “Step Controls” section – The “Number of Steps” controls how the load history is divided. As noted in Section G, one can impose initial conditions with multiple load steps – use “Time Integration” to toggle whether inertial effects are active for that step – The “Step End Time” is the actual simulation ending time for the “Current Step Number” – The initial, minimum, and maximum timesteps should be defined as noted in Sections B & C
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… Analysis Settings
Training Manual
• The “Solver Controls” section allows the user to choose the equation solver, use of weak springs, and use of large deflection effects – Transient structural analyses may typically involve large deformations, so “Large Deflection: On” should be used (default behavior). – “Output Controls” allows users to control how frequently data is saved to the ANSYS result file. For multiple step analyses, one can save results only for the end of the step. Also, one can also save results at intervals that are as evenlyspaced as possible (depending on automatic time-stepping)
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L. Reviewing Results
Training Manual
• After completion of the solution, reviewing transient structural analysis results typically involves the following output: – Contour plots and animations – Probe plots and charts
• Generating contour plots and animations are similar to other structural analyses – Note that the displaced position of rigid bodies will be shown in the contour result, but the rigid bodies will not show any contour result for deformation, stress, or strain since they are rigid entities – Typically, animations are generated using the actual result sets, not distributed sets
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… Reviewing Results
Training Manual
• Probes are useful in generating time-history charts to understand the transient response of the system. Some useful probe results are as follows: – Deformation, stresses, strains, velocities, accelerations – Force and moment reactions – Joint, spring, and bolt pretension results
• Chart objects, based on probes, can also be added to include in reports or as independent figures
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D. Workshop – Transient Analysis
Training Manual
• In this workshop, you will determine the dynamic response of a caster wheel exposed to a side impact such as hitting a curb. WS6: Transient Analysis of a Caster Wheel
Striker Tool
Wheel ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
6-37
July 2009 Inventory #002666
Workshop 1: Intro (Flywheel)
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-1
July 2009 Inventory #002666
Workshop 1 – Introduction
Training Manual
• In this workshop, the vibration characteristics of a spinning flywheel will be investigated.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-2
July 2009 Inventory #002666
Workshop 1 – Project Schematic
Training Manual
• Drop a Static Structural system into the Project Schematic. • In this system, the rotational velocity will be applied.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-3
July 2009 Inventory #002666
Workshop 1 – Project Schematic
Training Manual
• Drop a Modal system onto the Results cell of the Static Structural system. • In this system, the prestressed modes will be found.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-4
July 2009 Inventory #002666
Workshop 1 – Project Schematic
Training Manual
• Drop a Harmonic Response system onto the Model cell of the Static Structural System. • In this system, a harmonic load will be applied to the static flywheel.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-5
July 2009 Inventory #002666
Workshop 1 – Project Schematic
Training Manual
• Import the geometry file – Flywheel.igs
• Edit the Model cell to open the Mechanical application.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-6
July 2009 Inventory #002666
Workshop 1 – Preprocessing
Training Manual
• Two coordinate systems will be added to align with the center of the shaft. • The origin of the first coordinate system can easily be located along the shaft axis by selecting two keypoints.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-7
July 2009 Inventory #002666
Workshop 1 – Preprocessing
Training Manual
• Duplicate the first coordinate system. – set the type of the newly-created coordinate system to Cylindrical
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-8
July 2009 Inventory #002666
Workshop 1 – Static Preprocessing
Training Manual
• Select the symmetry surfaces and insert a Frictionless support. – Since the geometry is 3D, a frictionless support is the same as applying a symmetry boundary condition.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-9
July 2009 Inventory #002666
Workshop 1 – Static Preprocessing
Training Manual
• Insert a Remote Displacement on the flywheel hub. – select the coordinate system that aligns with the axis of the shaft – fix the X Component, Z Component, and Rotation Y
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-10
July 2009 Inventory #002666
Workshop 1 – Static Preprocessing
Training Manual
• Insert a Rotational Velocity inertial load. – select the coordinate system that aligns with the axis of the shaft – set the Z component to 600 RPM
• Solve the model.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-11
July 2009 Inventory #002666
Workshop 1 – Static Preprocessing
Training Manual
• Insert a Directional Deformation. – set the Coordinate System to the Cylindrical Coordinate System that aligns with the axis of the shaft
• The X-Axis orientation is now the radial component.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-12
July 2009 Inventory #002666
Workshop 1 – Static Postprocessing
Training Manual
• Duplicate the Directional Deformation. – set the Orientation to Y Axis
• This is now the tangential component of deformation.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-13
July 2009 Inventory #002666
Workshop 1 – Static Postprocessing
Training Manual
• Using the cylindrical coordinate system again, insert radial and tangential components of stress.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-14
July 2009 Inventory #002666
Workshop 1 – Modal Postprocessing
Training Manual
• Move down to the Modal branch and Solve. • Insert some total deformation plots to review the mode shapes.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-15
July 2009 Inventory #002666
Workshop 1 – Harmonic Preprocessing
Training Manual
• Drag and drop the Frictionless Support and Remote Displacement from the Static Structural branch into the Harmonic Response Branch.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-16
July 2009 Inventory #002666
Workshop 1 – Harmonic Preprocessing
Training Manual
• Insert an Acceleration inertial load. – set the Z component to 2 G (~20000 mm/s^2)
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-17
July 2009 Inventory #002666
Workshop 1 – Harmonic Solution Settings
Training Manual
• Modify the Analysis Settings. – set the Range Maximum to 500 Hz – set Cluster Results to Yes – set Constant Damping Ratio to 5%
• Solve the model.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-18
July 2009 Inventory #002666
Workshop 1 – Harmonic Postprocessing
Training Manual
• Insert a Deformation Frequency Response result on the outer surface of the flywheel. – set the Spatial Resolution to Use Maximum – set the Orientation to Z Axis
• Make note of the frequency and phase angle at which the maximum amplitude occurs.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-19
July 2009 Inventory #002666
Workshop 1 – Harmonic Postprocessing
Training Manual
• Insert a Directional Deformation result. – set the Orientation to Z Axis – use the frequency and phase angle for the maximum amplitude, noted from the previous slide (229.28 Hz @ 92.859°)
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS1-20
July 2009 Inventory #002666
Workshop 2A: Modal Analysis (Plate with a Hole)
ANSYS Mechanical Dynamics ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-1
July 2009 Inventory #002666
Workshop 2A - Goals
Training Manual
• Our goal is to determine the first 10 natural frequencies and mode shapes for the plate with the hole shown. • The plate is made of Aluminum. • Assume the plate is fully constrained at the hole. – As if the plate is tightly bolted down at the hole.
Fixed Center
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-2
July 2009 Inventory #002666
Workshop 2A – Project Schematic
Training Manual
• From the project schematic, insert a new Modal system.
• Import the Geometry file – plate.iges
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-3
July 2009 Inventory #002666
Workshop 2A - Preprocessing
Training Manual
• Edit the Engineering Data cell. – add Aluminum Alloy from the General Materials library to Engineering Data
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-4
July 2009 Inventory #002666
Workshop 2A - Preprocessing
Training Manual
• Return to the Project, and Edit the Model cell to open the Mechanical application. – set the plate thickness to 0.1 in – set the plate material assignment to Aluminum Alloy
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-5
July 2009 Inventory #002666
Workshop 2A - Environment
Training Manual
• Constrain the center hole. – highlight the Modal Branch to >Insert>Fixed Supports.
• Switch to edge selection mode as necessary • Use Box Select, or drag single-select LMB around the hole to pick all applicable edge segments (4 edges).. – Click “Apply” in the Details window – Reorient model as necessary throughout.
8
9
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-6
July 2009 Inventory #002666
Workshop 2A – Modal Solution
Training Manual
• Check the Details of Modal Analysis Settings. – set Max Modes to Find to 10 – set Calculate Stress “Yes” – set Calculate Strain “Yes”
• If you just want frequencies and shapes, you don’t need to “calculate” stress or strain. It will save a little time to skip those calculations. • Solve the Modal analysis.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-7
July 2009 Inventory #002666
Workshop 2A - Results
Training Manual
• After the modal solution is completed, review the modal shapes for each frequency. • Click on the Modal Solution Branch in the Tree. Then LMB on the top of the Frequency Column in the “Tabular Data” region, and >RMB>Create Mode Shape Results – This will automatically insert “Total Deformation” objects in the Tree for all modes solved.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-8
July 2009 Inventory #002666
Workshop 2A - Results
Training Manual
• To get an overall view of the Modal results step thru (LMB) the Total Deformation result objects for each mode. – You can also Animate (Play & Stop) the mode from the Timeline window. – Note: Make a note of your highest natural Frequency mode: •
Max Indicated Freq = _________________Hz.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-9
July 2009 Inventory #002666
Workshop 2A - Comments
Training Manual
• Remember: – Displacements reported with mode shapes are “relative” and do not reflect the actual max magnitudes of the displacements. • The actual magnitudes will depend on the energy input to the system (depends on forcing function).
• Sometimes it is challenging to visualize the true mode shape from a simple contour plot. – Try the Vector Display instead. • Adjust the Vector Scale slider as desired. • You can also animate the vector plot too.
Arrows may be more intuitive in some cases.
Contour Plot. Difficult to determine deformation directions ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
Vector Plot
WS2-10
July 2009 Inventory #002666
Workshop 2B: Modal Analysis (Model Airplane Wing)
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-1
July 2009 Inventory #002666
Workshop 2B - Goals
Training Manual
• Our goal is to determine the first 5 natural frequencies and mode shapes for the prestressed model airplane wing shown. • Assume one end of the wing is fully fixed. • The wing is made of Titanium.
Fixed End
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-2
July 2009 Inventory #002666
Workshop 2B – Project Schematic
Training Manual
• From the project schematic, insert a new Static Structural system. • Drop a Modal system onto the Solution cell of the Static Structural.
• Import the Geometry file – wing.iges
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-3
July 2009 Inventory #002666
Workshop 2B - Preprocessing
Training Manual
• Edit the Engineering Data cell. – add Titanium Alloy from the General Materials library to Engineering Data
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-4
July 2009 Inventory #002666
Workshop 2B - Preprocessing
Training Manual
• Return to the Project, and Edit the Model cell to open the Mechanical application. – set the wing material assignment to Titanium Alloy
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-5
July 2009 Inventory #002666
Workshop 2B - Environment
Training Manual
• Constrain the far end of the wing. – – – – –
On the >Static Structural branch >Insert>Fixed Supports. Switch to face selection mode as necessary Use LMB to pick the applicable surface. Click “Apply” in the Details window Use “Depth Picking” and/or reorient the model as necessary throughout.
Depth Picking
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-6
July 2009 Inventory #002666
Workshop 2B - Environment
Training Manual
• Apply a pressure load to the underside of the wing. – – – –
On the >Static Structural branch >Insert>Pressure. Switch to face selection mode as necessary Use LMB to pick the applicable surface. Click “Apply” in the Details window
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-7
July 2009 Inventory #002666
Workshop 2B – Static Solution
Training Manual
• Solve the Static Structural model. • Review the results.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-8
July 2009 Inventory #002666
Workshop 2B – Modal Solution
Training Manual
• Check the Details of Modal Analysis Settings – set Max Modes to Find to 5 – set Calculate Stress to “Yes” – set Calculate Strain to “Yes”
• Solve the Modal analysis.
5
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-9
July 2009 Inventory #002666
Workshop 2B - Results
Training Manual
• After the modal solution is completed we’d like to review the modal shapes for each frequency. • Click on the Modal Solution Branch in the Tree. Then LMB on the top of the Frequency Column in the “Tabular Data” region, and >RMB>Create Mode Shape Results – This will automatically insert “Total Deformation” objects in the Tree for all modes solved. 13
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-10
July 2009 Inventory #002666
Workshop 2B - Results
Training Manual
• To get an overall view of the Modal results step thru (LMB) the Total Deformation result objects for each mode. – Remember to Animate (Play & Stop) the mode from the Timeline window. • You can typically rotate the model during animation too.
– Note: Make a note of your highest natural Frequency mode: •
Max Indicated Freq = _________________Hz.
• Experiment with the Vector Graphics and (vector) scale slider. Animation and rotation can also be performed on Vector plots.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS2-11
July 2009 Inventory #002666
Workshop 3:
Harmonic Response (Fixed-Fixed Beam)
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-1
July 2009 Inventory #002666
Workshop 3 - Goals
Training Manual
• Our goal is to determine the harmonic response of a fixed-fixed beam under the influence of two harmonic forces. – The forces represent rotating machines mounted at the “one-third” points along the beam. – The machines rotate at 300 to 1800 RPM.
• The Beam (3 m x 0.5 m x 25 mm) is made of Steel.
Constrain (Fix) Both Ends ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-2
July 2009 Inventory #002666
Workshop 3 – Project Schematic
Training Manual
• From the project schematic, insert a new Modal system. – we will first look at the natural frequencies and mode shapes of the system
• Drop a Harmonic Response system onto the Model cell of the Modal system to share the material properties, geometry, and mesh. – note that this system will not use the modes from the Modal system
• Import the Geometry file – beam.agdb
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-3
July 2009 Inventory #002666
Workshop 3 - Preprocessing
Training Manual
• Edit the Model cell to open the Mechanical application. – verify that the material assignment is Structural Steel
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-4
July 2009 Inventory #002666
Workshop 3 - Environment
Training Manual
• Constrain both ends of the Beam. – – – – –
Click on the Modal Branch and >Insert>Fixed Support. Switch to edge selection mode as necessary Use LMB to pick the two applicable edges. Hold to add to your selections Click “Apply” in the Details window
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-5
July 2009 Inventory #002666
Workshop 3 – Modal Results
Training Manual
• Solve the Modal analysis. • Create some Mode Shape Results to review the results. – note that modes 1 and 2 fall between 0 and 50 Hz
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-6
July 2009 Inventory #002666
Workshop 3 - Preprocessing
Training Manual
• Drag and drop the Fixed Support from the Modal branch to the Harmonic Response branch.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-7
July 2009 Inventory #002666
Workshop 3 - Environment
Training Manual
• In the Harmonic Response branch, apply one force to one edge. – – – – – –
There are two edges imprinted on the beam face. Switch to Edge selection mode as necessary and >Insert>Force. Use LMB and drag over surface to highlight to pick the applicable edge. Click “Apply” in the Details window In Details, change the “Defined By” to “Components” (i.e., XYZ). Enter 250 for “Y”. Leave Phase Angle = 0
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-8
July 2009 Inventory #002666
Workshop 3 - Environment
Training Manual
• Apply another force to the other edge. – set Y Component to 250 N – leave Phase Angle = 0 – We will investigate the results as the phase angle between these loads changes.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-9
July 2009 Inventory #002666
Workshop 3 – Harmonic Response Solution
Training Manual
• Edit the Analysis Settings. – – – –
set the Range Minimum to 0 Hz set the Range Maximum to 50 Hz set the Solution Intervals to 50 set the Constant Damping Ratio to 2%
• Solve the Harmonic analysis.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-10
July 2009 Inventory #002666
Workshop 3 – Results
Training Manual
• Insert a Deformation Frequency Response. – set the scoping to all faces on the beam – set the Spatial Resolution to Use Maximum – set the Orientation to Y Axis
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-11
July 2009 Inventory #002666
Workshop 3 - Results
Training Manual
• You can also plot contours at specific frequencies. • Click RMB on the solution object and >Insert> Stress, Strain, or Deformation – This will insert the result object(s) – Step thru the Details for each and specify the Geometry and other details. – It is necessary to specify a specific frequency and phase angle.
Contours at a specific Frequency
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-12
July 2009 Inventory #002666
Workshop 3 – Results
Training Manual
• Return to the second harmonic force applied. – set the Phase Angle to 90° (we will try to excite different modes) – resolve the Harmonic Response
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-13
July 2009 Inventory #002666
Workshop 3 – Results
Training Manual
• Return once more to the second harmonic force applied. – set the Phase Angle to 180° – resolve the Harmonic Response
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS3-14
July 2009 Inventory #002666
Workshop 4:
Response Spectrum (Suspension Bridge)
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-1
July 2009 Inventory #002666
Workshop 4 - Goals
Training Manual
• Our goal is to determine the response of a prestressed suspension bridge subjected to a seismic load.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-2
July 2009 Inventory #002666
Workshop 4 – Project Schematic
Training Manual
• From the project schematic, insert a new Static Structural system. • Drop a Modal system onto the Solution cell of the Static Structural system. • Drop a Response Spectrum system onto the Solution cell of the Modal system.
• Import the Geometry file – simple_bridge.agdb
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-3
July 2009 Inventory #002666
Workshop 4 - Project Schematic
Training Manual
• Right click on Geometry, choose Properties, then check Line Bodies under Basic Geometry Options.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-4
July 2009 Inventory #002666
Workshop 4 - Project Schematic
Training Manual
• Edit the Model cell to open the Mechanical application.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-5
July 2009 Inventory #002666
Workshop 4 - Preprocessing
Training Manual
• Insert a fixed support on the vertex of all four tower foundations. – the Modal and Response Spectrum systems will inherit this support
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-6
July 2009 Inventory #002666
Workshop 4 - Preprocessing
Training Manual
• Insert a zero-displacement constraint in the Y and Z directions on the three outer edges at both ends of the bridge deck.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-7
July 2009 Inventory #002666
Workshop 4 - Preprocessing
Training Manual
• Finally, insert Standard Earth Gravity from the Inertial loads toolbar button.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-8
July 2009 Inventory #002666
Workshop 4 – Modal Solution
Training Manual
• Change the Max Modes to Find to 10, then run the Modal solution. – verify in Solution Information that a significant portion of the total mass has been accounted for
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-9
July 2009 Inventory #002666
Workshop 4 - Preprocessing
Training Manual
• Insert an RS Acceleration load in the Response Spectrum branch. Then, change Boundary Condition to All BC Supports and Direction to Y Axis.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-10
July 2009 Inventory #002666
Workshop 4 - Preprocessing
Training Manual
• Open the supplied seismic data from the Savannah River Earthquake, copy the spectrum data, and paste it into the Tabular Data.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-11
July 2009 Inventory #002666
Workshop 4 - Results
Training Manual
• Since the seismic data were supplied in units of G acceleration, insert a Scale Factor equal to the acceleration due to gravity of the working units.
– Finally, run the solution and insert the result item of your choice. – Note that the bridge deck may need some mesh refinement. Try changing the mesh settings and resolving. ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS4-12
July 2009 Inventory #002666
Workshop 5A: Random Vibration (Girder Assembly)
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-1
July 2009 Inventory #002666
Workshop 5A - Goals
Training Manual
• Our goal is to investigate the vibration characteristics of a Girder Assembly. • In this workshop, we will examine the displacements and stresses in a steel assembly due to an acceleration spectrum. • A PSD spectrum can be specified via Acceleration, Velocity, or Displacement. A2
Acceleration
– The spectrum will typically be measured during physical tests or documented in a written specification relating to the system or component. – The data points can be entered for each Freq & Amplitude, or a function can be entered.
A3
A1 A4
F1
F2
F3
F4
Frequency ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-2
July 2009 Inventory #002666
Workshop 5A – Project Schematic
Training Manual
• From the project schematic, insert a new Modal system. • Drop a Random Vibration system onto the Solution cell of the Modal system.
• Import the Geometry file – girder.agdb
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-3
July 2009 Inventory #002666
Workshop 5A – Preprocessing Thickness
Training Manual
• The first preprocessing task is to specify the thickness of all the surfaces. • Select all the bodies to assign a uniform thickness – LMB to select the top Body in the Part list. – Hold and LMB on the last Surface Body. • Note: By highlighting “all”, we can set the thickness on the first one, and the same thickness gets assigned to all of them.
– Left click in the thickness field and set the Thickness = 0.5 in
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-4
July 2009 Inventory #002666
Workshop 5A – Preprocessing Mesh Size
Training Manual
• The assembly consists of multiple slender bodies plus a large flat Roof plate. • We want to specify a relatively fine mesh size on the slender members but a larger element up top. – – – – – –
select the roof body Mesh >Insert >Sizing set Element Size to 2 in select all other bodies Mesh >Insert >Sizing set Element Size to 4 in
• Preview the mesh, >Mesh>Generate Mesh – If desired, repeat the steps above to increase or decrease element sizes as desired to enhance the model or reduce CPU time.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-5
July 2009 Inventory #002666
Workshop 5A - Environment
Training Manual
• For the lower edges of the truss, highlight the “Modal” branch in the Outline and >Insert >Fixed Supports. • Switch to edge selection mode as necessary – Reorient model as necessary throughout. – Using the “Extend to Limits” feature is probably the most convenient.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-6
July 2009 Inventory #002666
Workshop 5A - Environment
Training Manual
• For the PSD Base Excitation loads, at the Random Vibration Branch, >Insert>PSD Acceleration – set Boundary Condition to Fixed Support – this is a reference to the Fixed Support in the modal Branch
Acceleration
A2
A3
A1 A4
F1
F2
F3
F4
Frequency ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-7
July 2009 Inventory #002666
Workshop 5A – PSD Loads
Training Manual
• Enter the following tabular data for the PSD Acceleration load
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
Frequency [Hz]
Acceleration [(in/s^2)^2/Hz]
5
150
20
200
30
200
45
100
WS5-8
July 2009 Inventory #002666
Workshop 5A – Modal Results
Training Manual
• After the solution is completed you can review the (precursor) modal shapes for each frequency. – In the Outline Tree pertaining to Modal, click on Solution (within the Modal branch) – Click on the Modal Solution Branch in the Tree. Then LMB on the top of the Frequency Column in the “Tabular Data” region, and >RMB>Create Mode Shape Results – This will insert “Total Deformation” objects in the Tree for all modes solved.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-9
July 2009 Inventory #002666
Workshop 5A – Random Vibration Results
Training Manual
• Now review Random Vibration results. • Due to the applied spectrum, you can >Insert – Deformations – Strains – Stresses
• >Insert>Deformation>Directional – Specify the Z “Orientation” direction in the Details Pane
• >Insert>Strain>Normal – For instance, specify Y “Orientation” in the Details Pane
• >Insert>Stress>Equivalent (von Mises)
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-10
July 2009 Inventory #002666
Workshop 5A - Comments
Training Manual
• Review the evaluated results. • Remember: – Modal displacements reported with mode shapes are “relative” and do not reflect the actual max magnitudes of the displacements. – The PSD simulation generates statistically “Probable” resultant magnitudes that depend on the energy input magnitude and spectrum applied to the system. • The Damping data also plays a roll in the magnitude of the response.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS5-11
July 2009 Inventory #002666
Workshop 6A:
Transient (Caster Wheel Test)
ANSYS Mechanical Dynamics
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-1
July 2009 Inventory #002666
Workshop 6A - Goals
Training Manual
• Our goal is to determine the dynamic response of a caster wheel exposed to a side impact such as hitting a curb. • This may be simulated in a physical test by dropping a heavy Striker Tool on the side of the wheel. – The dropped weight represents side impact on the wheel.
Striker Tool
• The Wheel and Striker Tool are made of Steel. – Assume the far face of the Wheel/Axle is constrained. – Assume the sides of the Striker are constrained to slide up and down vertical rails. – Assume a damping ratio of 0.02 (i.e. 2%)
Wheel
Constrain End ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-2
July 2009 Inventory #002666
Workshop 6A – Project Schematic
Training Manual
• From the project schematic, insert a new Transient Structural system.
• Import the Geometry file – caster_test2.agdb
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-3
July 2009 Inventory #002666
Workshop 6A - Preprocessing
Training Manual
• Edit the Model cell to open the Mechanical application. – verify that the material assignment is Structural Steel
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-4
July 2009 Inventory #002666
Workshop 6A - Preprocessing
Training Manual
• Suppress the upper Striker. – Expand the geometry Branch, and determine which part is the upper Striker. >RMB>Suppress Body • We will incorporate the lower Striker in the simulation only. • We will apply an initial velocity to the lower Striker to account for it’s momentum due to the drop height & force.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-5
July 2009 Inventory #002666
Workshop 6A - Preprocessing
Training Manual
• Define the contact between the bottom of the Striker Tool and the top Edge of the Caster Wheel – LMB on >Connections in the Outline Tree. – >Insert>Manual Contact Region – Use Face select – Change “Update Stiffness” to “Each Equilibrium Iteration”
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
8
WS6-6
July 2009 Inventory #002666
Workshop 6A - Environment
Training Manual
• Apply constraints on the end of the bore to oppose loads on the wheel. – Within the Flexible Dynamic Branch >Insert>Fixed Support – Use Face Select, LMB and pick four annular surfaces on the bottom of the axle hole.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-7
July 2009 Inventory #002666
Workshop 6A - Environment
Training Manual
• The Striker Tool is guided on rails so it can only travel up and down when dropped on the wheel. – >Insert>Frictionless Support – Use LMB and pick all four sides of the Striker Tool block. – Note: The “four sides” of the block may consist of more than “four” total faces depending on how the (CAD) geometry was originally generated.
a Face a Face ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-8
July 2009 Inventory #002666
Workshop 6A - Environment
Training Manual
• Apply a gravity inertial load – RMB >Insert>Standard Earth Gravity to account for weight (mass) and to accelerate the Striker downward towards the Wheel. – In the Details window, change the Direction in this case to +X (look at the XYZ Triad to understand global orientation)
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-9
July 2009 Inventory #002666
Workshop 6A - Environment
Training Manual
• Apply an initial velocity on the Striker. – – – – –
Change “At Rest” to “Constant Velocity” Use Body Select and pick and >Apply the Striker Part. Change the Direction “Defined By” to “Components” Enter 10 m/s for “X” initial velocity is assigned to the picked Striker but not the Caster Wheel
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-10
July 2009 Inventory #002666
Workshop 6A – Solution Settings
Training Manual
• Check on >Analysis Settings in the Outline Tree – define the analysis settings in the “time domain” – Verify “1” for Number of Steps – Verify “1” for Current Step Number – Verify “0.001” for Step end time – Enter “0.0001” for Initial Time Step – Enter “3e-5” for Minimum Time Step – Enter “2e-4” for Maximum Time Step
• Solve the Transient analysis. …it may take some hand calculations and/or trial & error to find values that are appropriate for the scale and severity of your non-linear problem.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-11
July 2009 Inventory #002666
Workshop 6A - Results
Training Manual
• After the Solution is completed review the results. • Very important in many problems like this… – Set Result Scale to “ 1.0 (True Scale) “
• >Insert additional solution objects of interest
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
WS6-12
July 2009 Inventory #002666
Workshop 6A - Results
Training Manual
• To get an overall view of the Dynamic (transient) results step thru the TimeLine for each result plot of interest. – Evaluate any objects that have lost their Green Checkmark (possibly because the Display time has changed due to changes in the Timeline. – Remember to Animate (Play & Stop) the mode from the Timeline window. • You can typically rotate the model during animation too.
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
If time permits, make a note of your results, and >Insert>Sizing (at the mesh object in the outline) and enter a smaller “Element Size” (refer to the Graphics Ruler). Then >Solve again and compare results.
WS6-13
July 2009 Inventory #002666
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