Finite element analysis and improvement of an Ultima GTR Racing car chassis
May 29, 2016 | Author: josbaema | Category: N/A
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School of Technology MASTER OF SCIENCE DISSERTATION Title: Surname: First Name: Supervisor: Student Number: Module Nu...
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School of Technology
MASTER OF SCIENCE DISSERTATION Title:
Surname: First Name: Supervisor:
Student Number:
Date Submitted:
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José Manuel Baena
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26 August 2010
STATEMENT OF ORIGINALITY
Except for those parts in which it is explicitly stated to the contrary, this project is my own work. It has not been submitted for any degree at this or any other academic or professional institution.
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Regulations Governing the Deposit and Use of Master of Science Dissertations in the School of Technology, Oxford Brookes University.
1. The ‘top’ copies of projects submitted in fulfilment of Master of Science course requirements shall normally be kept by the Department. 2. The author shall sign a declaration agreeing that, at the supervisor’s discretion, the dissertation may be submitted in electronic form to any plagiarism checking service or tool. 3. The author shall sign a declaration agreeing that the dissertation be available for reading and copying in any form at the discretion of either the project supervisor or in their absence the Head of Postgraduate Programmes, in accordance with 5 below. 4. The project supervisor shall safeguard the interests of the author by requiring persons who consult the dissertation to sign a declaration acknowledging the author’s copyright. 5. Permission for anyone other than the author to reproduce in any form or photocopy any part of the dissertation must be obtained from the project supervisor, or in their absence the Head of Postgraduate Programmes, who will give his/her permission for such reproduction only to the extent which he/she considers to be fair and reasonable.
I agree that this dissertation may be submitted in electronic form to any plagiarism checking service or tool at the discretion of my project supervisor in accordance with regulation 2 above.
I agree that this dissertation may be available for reading and photocopying at the discretion of my project supervisor or the Head of Postgraduate Programmes in accordance with regulation 5 above.
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José Manuel Baena
Date
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ABSTRACT This project is about the analysis and improvement of an Ultima GTR Racing car chassis in the framework of the build project EGOUltima based in Gerona, Spain. An accurate and easy adaptable Finite element model has been created in order to analyze the influences of the different parts of the chassis in the overall torsional stiffness and undertake an iterative process of including tubes, plates and changes in the configuration and testing the improvement in terms of torsional stiffness.
The different approaches and the utilized methodology for the different tasks have been explained and compared. The simplifications made as well as the difficulties appeared have been explained and discussed. This project explains how the data acquisition of the geometry could be carried out in order to create a CAD model of the chassis for later elaboration of a model based on the finite element method and once validated against data obtained from mechanicals trials, start an iterative process of improving the chassis increasing the stiffness.
Although there are many difficulties in creating an accurate and reliable model for improving a racing car chassis, the model has been successfully validated against data obtained from mechanical trials and a new configuration of the frames has been presented and characterized improving the torsional stiffness of the chassis in a higher percentage than estimated.
ACKNOWLEDGEMENTS I would like to thank Adrián Martínez and Enrique Garcia, mechanical engineers and EGOUltima build team for offering me the possibility of working on such interesting project, their advice and all the data provided. I would also like to thank, the Spanish bank Cajastur and the F1 driver Fernando Alonso for their sponsorship, giving me the opportunity of such a great experience, my supervisor Shpend Gerguri for helping me and discussing with me all the different aspects of the project and all the colleagues of the Master for sharing with me a great time. Finally I would like to thank my parents for giving me the opportunity of getting an education and to my family and friends.
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TABLE OF CONTENTS STATEMENT OF ORIGINALITY ........................................................................................... 2 ABSTRACT .......................................................................................................................... 3 ACKNOWLEDGEMENTS ..................................................................................................... 3 TABLE OF CONTENTS ........................................................................................................ 4 LIST OF FIGURES ............................................................................................................... 6 LIST OF TABLES ................................................................................................................. 8 1
2
INTRODUCTION........................................................................................................ 10 1.1
Introduction ...................................................................................................................... 10
1.2
Objectives ........................................................................................................................ 12
1.3
Background ...................................................................................................................... 12
1.4
Structure of the report ...................................................................................................... 13
LITERATURE REVIEW .............................................................................................. 15 2.1 Introduction ........................................................................................................................... 15 2.2 Data acquisition of the chassis´ geometry............................................................................ 16 2.3 Computer aided design ........................................................................................................ 18 2.4 Finite element method analysis ............................................................................................ 19 2.5 Chassis design for improving the performance of a racing car ............................................ 23 2.6 Summary .............................................................................................................................. 26
3
EXPERIMENTAL / NUMERICAL METHODOLOGY ................................................... 29 3.1 Introduction ........................................................................................................................... 29 3.2 Geometry measures acquisition ........................................................................................... 29 3.3 Computer aided design of the chassis ................................................................................. 31 3.4 Finite element analysis and torsional rigidity ........................................................................ 37 3.5 Validation of the model ......................................................................................................... 48 3.6 Influence of the riveted plates............................................................................................... 52 3.7 Linearity and Convergence of the model .............................................................................. 54 3.8 Improvements of the ultima GTR chassis frame .................................................................. 56 3.9 Summary .............................................................................................................................. 61
4
RESULTS AND DISCUSSION ................................................................................... 63 4.1 Introduction ........................................................................................................................... 63 4.3 Improvement of the chassis.................................................................................................. 63 4.5 Summary .............................................................................................................................. 71
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5
CONCLUSIONS ......................................................................................................... 73
6
REFERENCES .......................................................................................................... 75
7
APPENDICES ............................................................................................................ 79 A) Steel AISI 1018 Characteristics sheet ................................................................................... 79 B) NS4 Aluminium Alloy ............................................................................................................. 80 C) Section Types Commands ..................................................................................................... 81 D) Section Types Plots ............................................................................................................... 82 E) Characterisation of the plates ................................................................................................ 85
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LIST OF FIGURES Figure 1. EGOUltima build project Figure 2. Layout of the structure of the project Figure 3. Finite element method widely used in chassis design and evaluation Figure 4. Handy VIU Scanner Figure 5. Configuration of the torsional trial Figure 6. Hand measures on an Ultima GTR chassis. Figure 7. Difficulties to measure the chassis when devices are set Figure 8. Data acquisition of the geometry. Figure 9. Reconstruction of the chassis Figure 10. 3D Representation of the chassis. Figure 11. Different profiles of the chassis Figure 12. Configuration of the riveted aluminium plates in the chassis Figure 13. CAD of the chassis without riveted plates Figure 14. Riveted plates attached to the tubes Figure 15. CAD of the chassis with riveted plates Figure 16. Exporting lines as IGES file configuration options. Figure 17. Lines of the chassis exported into ANSYS Figure 18. Aluminium Plates Figure 19. Welded cockpit plate Figure 20. Constraints at the rear Figure 21. Loads and constraint at the front Figure 22. Configuration of the trials usually applied in a lab Figure 23. Model meshed Figure 24. Model of the rivets Figure 25. Rivets in the plates of the left side of the chassis Figure 26. Mesh and verification Figure 27. Gearbox Figure 28. LS7 corvette engine Figure 29. Riveted plates at the bottom of the Ultima GTR chassis Figure 30. Adding Silkafex to add the riveted plates
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Figure 31. Linearity of the model Figure 32. Convergence of the model Figure 33. Von Mises stress distribution of the frames Figure 34. Von Mises stress distribution of the plates Figure 35. Displacement Vector sum of the standard chassis Figure 36. X braces improvement Figure 37. Triangulation of the arc Figure 38. Carbon fibre plate Figure 39. X braces above the gearbox Figure 40. CAD of the redesigned chassis Figure 41. Mesh of the redesigned chassis Figure 42. Von Mises stress distribution, redesigned chassis Figure 43. Plates Von Mises stress distribution, redesigned chassis Figure 44. Displacement Vector sum of the redesigned chassis
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LIST OF TABLES Table 1. Different approaches when designing a chassis frame Table 2. Material properties Table 3. Gear ratios Table 4. Displacement of the two nodes and validation of the results Table 5. Linearity trial Table 6. Convergence of the model Table 7. Properties of Steel, Aluminium and Carbon fibre
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LIST OF SYMBOLS AND ABBREVIATIONS CAD Computer Aided Design GRP Glass reinforced plastic CAM Computer Aided Manufacturing FEM Finite element method FEA Finite element analysis UK
United Kingdom
3D
Three-dimensional
STL
Stereolithography file
CT
Computer tomography
MRI
Magnetic resonance imaging
IGES Initial Graphics Exchange Specification Lb
Pound (0,453 Kg)
Ft
Foot
Deg
Degree
N
Newton
M
meter
DOF Degree of freedom INTA National institute for aerospace technology NURB Non Uniform Rational B-Spline
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1 INTRODUCTION 1.1
INTRODUCTION
This project is a part of the Ultima GTR racing car build project EGOUltima based in Gerona (Spain) and deals with the practical ant technical issues to create a FE model of the chassis and improve the torsional stiffness of the Ultima GTR racing car chassis. The build of the car has been based in Gerona (Spain) and the work has been undertaken between Spain and the Oxford Brookes University (United Kingdom) as a MSc dissertation. EGOUltima has born as a private initiative to build the second Ultima GTR racing car in Spain and the present project has been created in order to improve the torsional stiffness of the chassis frame towards the homologation in Spain.
http://egoultimagtr.blogspot.com/ Figure 1. EGOUltima build project The chassis frame of a racing car is a very important part as has influence on the performance of the car. An ideal chassis is one that has high stiffness with low weight and cost. Torsional stiffness plays an important role in the behaviour of the racing car since affects parameters as weight transfer, vibration, strength, safety and handling (Thompson et al., 1998). The improvement of the chassis design is a key part in
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racing and all the improvements made can help to obtain better results and to win races (Raju, 1998).
The Ultima GTR Racing car manufactured by the company Ultima Sport Ltd is a mid engine, rear wheel drive layout, with a tubular steel space frame chassis and GRP bodywork, and is considered one of the fastest super cars (Internet site Ultima Ltd, 2009, Internet site of the present project, 2009). In order to improve the performance and the dynamic behaviour of the Ultima GTR an analysis and improvement of the tubular steel space frame will be carried out. As first step a modern geometry data acquisition system is presented in order to obtain the CAD model of the standard Chassis. As second step an ANSYS model and simulation to obtain the torsional stiffness will be made in order to obtain the mechanical performance and the torsional stiffness of the Ultima GTR. Once the model has been validated against data obtained in real trials and the influence of welded, riveted joints and the aluminium plates characterised, a redesign of the tubular frame will be performed with the aim of reducing the weight, increasing the torsional stiffness and the safety of the car without affecting the structural frames supporting parts of the bodyworks and other devices.
Improving the chassis of the Ultima GTR will lead to an improvement of the performance of the car, adding quality to the product as well as improving the safety conditions and handling of the car towards a homologation process. In addition the importance of obtaining the geometric data accurately and in a short period of time is vital in racing where the deadlines are very strong and the time to redesign and develop the car very short. Furthermore the importance of Finite element analysis for engineering research has been increased in the last years as a powerful tool improving products, reducing costs and decreasing the design time (Lewis and Ward, 1991). A thorough understanding of the finite element method, his accuracy and his applications is vital for the development of the technology. All research and introduction of the approach will lead to improving the knowledge and the technology for the present and future applications.
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1.2
OBJECTIVES
The main aim of the project is to improve the chassis of an Ultima GTR Racing car. To achieve this aim a Finite element Analysis of the standard chassis of the Ultima GTR Racing car will be run to find out the possible improvement ways. The main tasks to achieve the aim of the project are: •
Geometric data acquisition system and a stereolithography reconstruction
•
A computer aided design of the standard chassis with CAD package.
•
A literature Research to find out the boundary condition of the simulation.
•
FEA to work out the stiffness, setting the optimal attributes of the mesh, characterisation of the rivets and plates and his influence on the results.
•
Validation of the FEM model.
•
Redesign and improvement of the chassis.
•
Influence of Changing materials, configuration of the original riveted sheets and the tubes, changing rivets and materials to stick the plates to the frames.
•
Interpretation of the results
As a result a comparison between the standard chassis and the possible improvements will be given as well as, the best chassis configuration obtained as a result of an iterative process. An improvement of around 10-20% is aimed to be achieved towards the homologation of the car in Spain, within the duration of the project.
1.3
BACKGROUND
The goal of the project is to create a finite element model and improve the chassis frame of an Ultima GTR racing car. The chassis of a racing car is a very important part of the car as has a huge influence in the dynamic and mechanical performance of the car. The present work starts at the point of data acquisition of the geometry of the chassis, in order to create a CAD model to be exported to a finite element method package to work out the torsional stiffness of the frame. After the model has been created and validated against mechanical trials data, an iterative process of improving the chassis frame will be developed. In order to do that, the influence of
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secondary parts as riveted plates will be characterised as well as the influence of welding profiles and different most common used materials. After doing that a new configuration of the chassis will be presented.
The present work start with a deep literature review of the main projects realized on the topics and present, using different technologies, an approach for undertaking a design and improvement of a racing car chassis.
1.4
STRUCTURE OF THE REPORT
The report of the project is divided in five main parts that represent the main steps to be undertaken in order to improve a chassis of a racing car. The first part is the literature review in order to investigate all the relevant works undertaken about the topic, the problems, the solutions and the future trends in the field in order to gain a good knowledge that can be useful when undertaken the own investigation . The second part is about the data acquisition of the chassis´ geometry. The different techniques and which is the most useful when developing and improving a chassis of a racing car. The third part is about the computer aided design of the standard chassis from the data obtained in the precedent section. The fourth part is about the preparation of the finite element analysis (FEA), the realization of the model in order to obtain the mechanical performance of the chassis and the torsional stiffness and the validation of the model. As the last part, once the FEA data is studied the work will propose the changes made in the standard chassis in order to improve the performance of the car and will present the influence of the changes made in the torsional stiffness and a result of the different effects of the new configuration and secondary structures as plates and joints in the results obtained and the performance of the chassis (Figure 2).
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Literature review
Data acquisition
Final design
CAD model
Validation of the model
FE Model
Results analysis
FE simulation
Redesign of the chassis
FE model
Figure 2. Layout of the structure of the project
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2 LITERATURE REVIEW 2.1 INTRODUCTION The chassis of a racing car is very important as it is the structure that supports all the main parts of the car, connect the wheel sufficiently rigidly that contact patch position is under control, support the structure and the occupants and it is the main barrier in case of crashing. There are many kind of chassis design, but tubular space frames are the most common in racing cars as they provide an optimal rigidity / weight ratio and they are very strong in any direction (Gillespie, 1992).
Finite element models can help to predict the mechanical performance of the chassis of a racing car. Finite element analysis (FEM) is a technique nowadays widely used in engineering because of the good accuracy and reduction of the time and costs in comparison than building a real model (Lewis and Ward, 1991). A thorough understanding of the finite element method, the accuracy and his applications is vital for the development of the technology. All research and introduction of the approach will lead to improving the knowledge and the technology for the present and future applications.
Figure 3. Finite element method widely used in chassis design and evaluation (Thompson. et al, 1998)
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The present project has both an industrial and research relevance. The UK motorsport industry is a global leader. The country’s dominant role in both managing and serving the F1 and other international racing series has led to a wealth of worldclass design, precision and high-performance engineering companies (Beck-Burridge and Walton, 1999). Motorsport is a very important sector for the UK, exemplifying its strengths in R&D, advanced materials and engineering and sophisticated services. It is constantly developing new components, products and services for worldwide applications, with spin-offs into the wider automotive industry and other related sectors such as aerospace (internet site of UK trade and investment).
Improving the chassis of the Ultima GTR will lead to an improvement of the performance of the car, adding quality to the product as well as improving the safety conditions and handling of the car. This, in turn, will help to improve the motorsport industry of the United Kingdom (UK) and creating engineering knowledge will lead to an improvement of the technology and the overall quality of life.
2.2 DATA ACQUISITION OF THE CHASSIS´ GEOMETRY There are many different physical ways of acquiring data of a racing car chassis. However the high accuracy required and the difficulties of accessing to the chassis frame without the disassembly of the bodywork and other important devices as the engine, suspension, cooling system, etc. makes the data acquisition of the geometry to be an important issue to consider when planning for time and cost in a project (Bernardini and Rushmeier, 2002).
Instead of the widely used hand measuring of a chassis car, when attempting to model it in a CAD package, a different technique for the data acquisition of the geometry of the chassis frame is presented in the present work. “Three-dimensional (3D) image acquisition systems are rapidly becoming more affordable, especially systems based on commodity electronic cameras and laser sensors. Furthermore personal computers with powerful graphic cards with the capacity of displaying complex 3D models are also becoming cheaper to the point that are inexpensive enough to be available to a large quantity of person and professionals (Weik, 1997).
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Although there are many different computers based techniques for acquiring 3D data—including laser scanners, structured light and time-of-flight—there is a basic pipeline of operations for taking the acquired data and producing an usable numerical models (Curless, 2000).Furthermore in the last years the prices of 3D scanning equipment have been decreased due to the new technologies development in the area as well as in other related areas as the computers science mentioned above. Three-dimensional scanning has been widely used for many years for reverse engineering and part inspection towards the fabrication using rapid manufacturing techniques that offer a reliable way for the redesign and fabrication in the motorsport industry (V´arady et al., 1997).
A 3D scanner is a device that analyzes a real-world object or environment to collect data on its shape. The collected data can then be used to construct digital, three dimensional models useful for a wide variety of applications. These devices are used extensively by the design industry as well as other important industries, as the entertainment industry in the production of movies and video games. Other common applications of this technology include, orthotics and prosthetics, reverse engineering and prototyping, quality control/inspection and documentation of cultural artefacts. There are many different technologies in order to get a scanned shape of a body, each of them with his advantages, disadvantages and costs (Benjemaa, 1997).
Figure 4. Handy VIU Scanner Laser scanners is one of the most used technologies in the auto industry. They send a huge quantity of light photons towards the object and receive the percentage of
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reflected by the body via the optics that they use. Those 3D scanners are used to create a point cloud representing the geometry of the body. These points, as a stereolithography file (stl) can be used to recreate the shape of the body in a CAD package (Marschner et al., 1999).
Another interesting technology, when the chassis frame is very difficult to access due to the bodywork, is the use of X-ray. X-ray are widely used in biomedicine for acquiring internal shapes and using the computer tomography and an imageprocessing package with 3D visualization functions to create a solid of the chassis frame is a good approach. These methods use the different threshold values of the density in the image for creating masks that can be converted to polylines or solids. CT, MRI, or Micro-CT scanners do not produce point clouds but a set of 2D slices which are then joined to produce a 3D representation. There are several ways to do this depending on the output required (Chelule et al. 2000).
Once the chassis geometry has been scanned the stl file can be imported into a CAD package as Catia and SolidWorks in order to reconstruct the geometry with a high accuracy.
2.3 COMPUTER AIDED DESIGN From an engineering and manufacturing perspective, the representation of shapes in a digitalized, editable and parametric form is a CAD. In CAD, geometries are described by parametric features which are easily edited by changing a value. From point clouds stl file produced by 3D scanners can be used directly for measurement and visualization in the architecture and construction of the chassis of a racing car with high level of accuracy (Bernardini and Rushmeier, 2002).
Once the stl is imported into CAD software it is straightforward to set the points in the frame joints. After the frame has been located, the location of those can be exported as an IGES file that can be imported to a finite element analysis software as ANSYS or ABAQUS. It is also possible to export the file as a txt with the location of the points and it can be directly introduced in MATLAB or in the command bar of programs as ANSYS.
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Once the joint frame points have been located we can model each frame as a line and with the weld profile option it is possible to create a frame with different profile for each part of the chassis. This polygonal representation of a shape, as curved solid is useful for visualization and for some Computer Aided Machining (CAM) purpose but are generally a big set of data, very difficult to manipulate and unreliable to create a meshing based simulations ( ANSYS Online Documentation).
As a chassis is a structure composed of many thin tubes and complex geometries near the corners, it is not recommended to use the polygonal representation of the frame profile as these structural models are very heavy and meshing, analyzing and simulating it could be a hard and very resource consuming in terms of time and computationally. Instead of that a CAD design reconstruction based on lines could be made in the CAD software and exported as IGES file and imported by the FE software (Raju, 1998).
When modelling curved shapes Non Uniform Rational B-Splines (NURBS) are to be used as is a true mathematical sphere. These patches are lighter when exported to a CAD software (Aird, 1997).
Some main ideas about the geometric profiles of the chassis frame when designing are that tubular chassis may use square-section tubes for easier connection to the body panels, though circular section provides the maximum strength. The main disadvantages of the tubular space frames are that they are very complex, costly and time consuming to be built. Furthermore, it is impossible for robotised production, engages a lot of space raise the door sill and result in difficult access to the cabin (Bernardini and Rushmeier, 2002).
2.4 FINITE ELEMENT METHOD ANALYSIS The Finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it is a very good approach for analyzing the mechanical behaviour of complex systems with complex shapes (Zienkiewicz and Taylor, 1967).
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In this finite element approach the system modelled is divided into finite elements interconnected at points that receive the name of nodes. Different elements may have different number of nodes and different physical properties such as thickness, density, Young's modulus, coefficient of thermal expansion, shear modulus and Poisson's ratio. The elements are interconnected only at the exterior nodes; they should cover the entire domain as accurately as possible. Different element sizes or refinement may be needed in different parts of the body in order to meet the shape and obtain the better accuracy as possible, always keeping in mind the compromise time consuming- accuracy. Nodes have nodal degrees of freedom and displacement that may include all the translation and rotations.
A node affected will have an
influence in the connected nodes and this influence will be dictated by the nodal equations of the elements. The importance of Finite element analysis for engineering research has been increased in the last years as a powerful tool, improving products, reducing costs and decreasing the design time (Yang, 1986).
In order to improve the stiffness/weight ratio a Finite elements model of the chassis has to be created and once validated, used to work out the torsional stiffness of the new chassis designs (Lewis and Ward, 1991). The chassis is a structure composed of many thin tubes and complex geometries near the corners. Therefore, it is not recommended to use a solid or shell element mesh type when conducting a stress analysis, even though it may be acceptable for frequency analysis. These structural models have to use beam elements for the tubular and box beam frame members and thin shell elements for the floor pan and firewall sheet metal. These models are currently being used to evaluate torsional stiffness of competing chassis designs (Raju, 1998). Using beam elements we make the assumption that welded tubes have stiffness in bending and torsion and using link elements the assumption made is that the connection does not offer resistance to bending or torsion. Another advantage of the beam elements in ANSYS is that the transverse shear is automatically included (Riley and George, 2002).
If a finite element analysis with the welding profile polygonal geometry is to be undertaken the meshing of the data could be too time consuming and intractable in
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terms of virtual memory for complex topologies. The approach to be used is the image-based meshing, an automated process of generating an accurate and realistic geometrical description of the scanned data (Young et al., 2008).
Furthermore to get a good accuracy care has to be taken when analysing the influence of welded joints, which is fundamental to perform a reliable simulation of multi-joint structures and a good estimate of loads acting on the joints (Deng et al., 2000). Another important characteristic of the chassis are the riveted aluminium plates that play an important role in the rigidity of the car. They have to be analysed and characterised the influence that they have on the torsional stiffness of the chassis (Vivio, 2009).
Meshing is a very important part in the process of simulating a racing car chassis. Accuracy, speed of the solution and convergence are affected by the quality of the mesh. Furthermore the time to create a mesh could be very significant in the designing, modelling and simulating process. ANSYS provides a very good solution due to his capability of automation and adaptability to new geometries and flexibility to produce meshes (Siegler et al., 1999).
Some consideration on how to measure the torsional stiffness has to be given that the best place to make the measurements are the suspension anchorages and since the length of the component in torsion affects the deflection, consideration needs to be given to whether the torque is applied between the front anchorages of the rear suspension and the rear anchorages of the front; or between the rear of the rear and the front of the front, a rather longer distance. In general organisations do not all use the same method and so care should be taken when comparing figures (Balkwill, 2009).
In order to produce an accurate analysis to predict the stiffness of the Ultima GTR chassis we have to consider the constraints to add to the model as the chassis frame receive a lot of load inputs from the suspension. One approach is to constraint the back four nodes of the rear and apply two equal and opposite forces at the front of the front suspension nodes. After obtaining the angular deflection caused by the
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forces, the torsional stiffness can be calculated by finding the applied torque dividing by the angular deflection a shown by the Figure 5 (Riley and George, 2002).
Figure 5. Configuration of the torsional trial The torsional stiffness is worked out from the equation:
In which K is the torsional stiffness, T is the Torque applied calculated as the Force applied at each corner (F) multiplied by the dimension L and divided by the angle of deflection ( θ ). The angle of deflection has been calculated using the mean value of the vertical displacement at each point of the applied forces; ∆y1 , ∆y2 .
In order to validate the analysis, the torsional stiffness of the chassis has to be measured by means of mechanical trials. Few apparatus have been designed in order to measure the stiffness of different chassis. Some designs include the ability to twist the chassis in both clockwise and counter-clockwise direction, and the ability
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to measure the error as well as being light for transport and adjustable and reliable for different measures of different chassis geometries (Keiner, 1995).
“To twist the chassis about the longitudinal axis, the bases of the front posts are translated in the vertical direction, equal and opposite on each side. The vertical reactions at the bases of the front posts are used to calculate the torque. Stiffness is calculated from the torque divided by the applied twist angle” (Thompson, 1998b).
In order to validate the model, have to be taken into account the differences between the numerical and the experimental data due to binding in the suspension, gradual drift in the load cells and inaccuracy of the equipment to measure (Riley and George, 2002).
2.5 CHASSIS DESIGN FOR IMPROVING THE PERFORMANCE OF A RACING CAR “An ideal chassis is one that has high stiffness; with low weight and cost”. If there is considerable twisting, the chassis will vibrate, complicating the system of the vehicle and sacrificing the handling performance. Thinking on the chassis as a large spring connecting the front and rear suspensions, if the chassis torsional stiffness is weak, attempts to control the lateral load transfer distribution will be confusing at best and impossible at worst (Milliken and Milliken, 1995).
Considering the load cases, the deflection in each of them and the factor of safety, once the chassis has been designed strong enough in torsion it will be also strong enough in the other load cases. This is because a chassis of a racing car is a deflection limited structure and not a stress limited structure (Riley and George, 2002).
Predictable handling is best achieved when the chassis is stiff enough to be approximated as a rigid structure. There are numerous reasons for high chassis stiffness. A chassis that flexes is more susceptible to fatigue and subsequent failure, and “suspension compliance may be increased or decreased by bending or twisting
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of the chassis”. Torsional stiffness’ range from 3000 lb-ft/ deg (4068 Nm/ deg) for a small race car to 12 000 lb-ft/ deg (16 272 Nm/ deg) and up for a Formula 1 car, quoted in 1995 (Milliken and Milliken, 1995).
Improving the design of the tubular chassis of a racing car, the performance, the weight distribution and the dynamic behaviour will be improved, optimizing the stiffness / weight ratio, reducing the complexity, the quality of the joints, reducing the fabrication time and consequently the costs, the accessibility and the safety and handling of the car (Thompson., 1998).
There are many approaches when designing a chassis of a racing car. In the present project, in order to improve the performance of the Ultima GTR supercar an investigation about the possible improvements of the chassis to be made has to be undertaken. Table 1 shows different approaches when designing a chassis with the advantage and disadvantages of each approach (Balkwill, 2009).
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Chassis design Simple ladder
Advantages Simple, cheap easy.
Disadvantages Poor dynamic performance limits use to basic vehicles with low maneuvering forces
Steel Monocoque good rigidity to weight, possible to design in good crash performance
Tooling very expensive indeed, joining processes complex
Space frame
Easy to manufacture using basic welding Not suitable for high volume manufacture – high techniques, cheap, possible to achieve reasonably labour content, would require additional paneling good torsional rigidity to weight ratio for road use.
Honeycomb
Superior torsional rigidity to weigh ratio possible. Requires use of inserts etc. for mounting. Requires Better crash performance possible. Assembly time bonding capability. More expensive material costs for batch production lower than space frame than space frame
Carbon fibre
Best torsional rigidity to weight ratio. Can easily Very expensive indeed. Requires detailed be formed into any shape. Good crash understanding of material properties. Manufacture performance possible. Fantastically strong complex. material
Table 1. Different approaches when designing a chassis frame The designers of racing car have to design cars with high dynamic and mechanical performance as well as safe. One of the most important issue in racing, is to keep the contact patches located as desired when the car is accelerating in a straight line, decelerating under braking or cornering, since the forces that act together on the car are transmitted to the chassis through the wheels. Furthermore the effects of weight transfer have to be taken into account in order to improve the performance of the car (Milliken and Milliken, 1995).
The wheels therefore travel up and down within the body in a way prescribed by the suspension. In a racing car the positional accuracy with which the contact patch is controlled is in the range 1-0.1mm. “Clearly there is no point in having a chassis structure which is so floppy that under the forces, the car experiences deformations in the chassis structure greater than these values otherwise all the accuracy build into the suspension will be lost by the chassis. On the other hand there is also no point in having a chassis so rigid that it limits the movement of the suspension
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anchorages to a much greater degree than this since this would mean that the chassis was unnecessarily rigid and therefore too heavy” (Balkwill, 2009).
The basic considerations about designing a frame for being stiff structure in torsion are to triangulate where possible, to place material as far as the neutral axis as possible, and improve the stiffness keeping in mind the aim stiffness-weight increased ratio (Deakin et al., 2000)
It is worth to consider that the engine is a very stiff part in comparison to the car frame and can be mounted as being a stressed part of the chassis to reduce the frame weight keeping the stiffness. Furthermore additional parts as aluminium plates, considered as stressed skins are composed of either 0.020” or 0.040” thick aluminium sheet bonded and riveted to the space frame and are important when evaluating the torsional stiffness of a chassis (Mitschke, 1996).
In racing application where cost don´t allow the use of carbon fibre or even honeycomb materials, steel is more appropriate than aluminium as the chassis of a racing car is a deflection limited structure and his young´s modulus to density ratio is more important than the yield stress to density ratio (Fenton, 1996).
Finally when designing a racing car chassis other important requirements of the chassis have to be taken into account as the ride height for aerodynamic reasons and the natural frequencies for the dynamic performance (Katz, 1995)
2.6 SUMMARY The chassis of a racing car is a very important part of the car that connect the wheels sufficiently rigidly that contact patch position is under control, support the structure and the occupants and it is the main barrier in case of crashing. Three-dimensional (3D) image acquisition systems as 3D scanners are a very good approach when acquiring geometrical data from a chassis. These devices produce a point cloud representing the geometry of the body. These points, as a stereolithography file (stl) can be used to recreate the shape of the body in a CAD package.
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After the joint points of the chassis has been located, the location of those can be exported as a IGES file that can be imported to a finite element analysis as ANSYS or ABAQUS. It is also possible to export the file as a txt with the location of the points and it can be directly introduced in MATLAB or in the command bar of programs as ANSYS. As chassis is a structure composed of many thin tubes and complex geometries near the corners, it is not recommended to use the polygonal representation of the frame profile as these structural models are very heavy and meshing, analyzing and simulating it could be a hard and very resource consuming in terms of time and computationally. The Finite element method (FEM) is a powerful technique for analyzing the mechanical behaviour of complex systems with complex shapes. In order to improve the stiffness/weight ratio a Finite elements model of the chassis has to be created and once validated used to work out the torsional stiffness of the new chassis designs. It is not recommended to use a solid or shell element mesh type when conducting a stress analysis, even though it may be acceptable for frequency analysis. These structural models have to use beam elements for the tubular and box beam frame members and thin shell elements for the floor pan and firewall sheet metal.
The approach of image-based meshing can be useful when necessary to mesh complex shapes or polygonal welding profiles. Accuracy, speed of the solution and convergence are affected by the quality of the mesh, ANSYS provides a very good solution due to his capability of automation and adaptability to new geometries and flexibility to produce meshes. In order to produce an accurate analysis, the position of the constraints, to add to the model of the chassis frame, has to be studied. One approach is to constraint the back four nodes of the rear and apply to equal and opposite forces at the front of the front suspension nodes. After obtaining the angular deflection caused by the forces, the torsional stiffness can be calculated by finding the applied torque dividing by the angular deflection.
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In order to validate the analysis, the torsional stiffness of the chassis has to be measured by means of mechanical trials and the sources of differences between the numerical and the experimental data have to be taken into account.
The chassis frame of a racing car is a deflection limited structure and not a stress limited structure then, if the chassis has been designed strong enough in torsion it will be also strong enough in the other load cases. Improving the design of the tubular chassis of a racing car, the performance, the weight distribution and the dynamic behaviour will be improved, optimizing the stiffness / weight ratio, reducing the complexity, the quality of the joints, reducing the fabrication time and consequently the costs, the accessibility and the safety and handling of the car. One of the most important issue to keep in mind when designing a racing car is to keep the contact patches located as desired when the car is accelerating in a straight line, decelerating under braking or cornering, since the forces that act together on the car are transmitted to the chassis through the wheels as well as the effects of weight transfer have to be taken into account in order to improve the performance of the car.
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3 EXPERIMENTAL / NUMERICAL METHODOLOGY 3.1 INTRODUCTION The present section will explain the experimental and numerical procedures to undertake the investigation. The existent approaches will be analyzed and the most interesting will be used in order to undertake the work, linking the results obtained in the simulation with the real experience of the Ultima GTR build. The difficulties will be explained and discussed as well as the methodology to overcome the problems faced in order to improve the chassis of the Ultima GTR supercar under the framework of the EGOUltima project.
3.2 GEOMETRY MEASURES ACQUISITION The first step, in order to create a reliable model of the Ultima GTR racing car to work out the torsional stiffness is the data acquisition of the chassis geometry. There are few different approaches in order to obtain the geometrical data of the chassis. From the rudimentary hand measurements, when the chassis is accessible, to the new technologies of 3D scan.
52cm
Figure 6. Hand measures on an Ultima GTR chassis
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In the present work hand measures on the Ultima GTR chassis have been done in the province of Gerona, Spain. Figure 6 shows an image of the Ultima GTR chassis and one of the obtained measures. However, once the build advance and more devices are set in the car as shown in Figure 7 it becomes very difficult to access to the main frame to take any measure, so due to the problems of getting the data from an already in construction car a new approach of stl reconstruction has been undertaken (Bernardini and Rushmeier, 2002) and is presented in the present work.
Figure 7. Difficulties to measure the chassis when devices are set (EGOUltima) The process of generating and stl file is very simple. Just a laser hand scan is needed in order to acquire a cloud of points that will be logged in a computer with a CAD package as Catia or Solidworks (Marschner et al., 1999). For the good data acquisition it could be necessary to pass the scan few times over the geometry in order to get the best results (see Figure 8).
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STL
CAD
Figure 8. Data acquisition of the geometry Once the stl file has been obtained, the file can be imported into CAD software as Solidworks to set the lines and reconstruct the geometry of the frames in order to create a CAD file of the Ultima GTR chassis.
3.3 COMPUTER AIDED DESIGN OF THE CHASSIS Once the stl file has been imported into a CAD software it is straightforward to reconstruct the geometry of the chassis by setting the points in the joints and drawing lines representing the bars, as shown in Figure 9 .Care has to be take when setting the joining points and the lines as any small inaccuracy on the configuration of the model will lead to a non connected finite element model and the results obtained in the simulation will be incoherent. It is also very important to take care on the correct segmentation of the frame.
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Figure 9. Reconstruction of the chassis Once the lines have been obtained there are two different approaches to act next, depending on the kind of model to be created in Finite elements and the way of meshing. One is to export the lines as an IGES file and import the IGES files into the FEM software where the section of each frame can be given at the same time when creating the mesh. In this first approach the aluminium plates can be modelled either in the CAD software or in the Finite element package. The second approach is to reconstruct the entire geometry in the CAD software using the welding profiles function of the CAD software (see Figure 10). This polygonal representation is very useful for CAM and very graphical, but the geometries obtained are very heavy and problematic when meshing and simulating using FEM.
In the present work in order to create a reliable, not too time consuming and easily adaptable model the first approach has been adopted in order to create a FE model as described by Raju (1998). This approach will allow us to create a more simple and easy to mesh model with a solving time of around 4 minutes and will be helpful when undertaking the iterative process of testing different configuration to work out the
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influence of the different new tubes and changes made in the overall torsional stiffness of the Ultima GTR chassis. Although the approach selected has been creating a FE model based on the lines representing the frames, the polyhedral representation of the chassis with the frames using welding profiles and the aluminium plates will be made for visual reasons and in order to better measure the weight of the different configurations.
Figure 10. 3D Representation of the chassis The standard chassis of the Ultima GTR racing car is composed by 5 different frame profiles and riveted aluminium plates in the frontal and cockpit of the chassis. Figure 11 show the different profiles of the Ultima GTR chassis.
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Frame profiles
Figure 11. Different profiles of the chassis (all units in mm) The first delivery of the Ultima GTR provided the standard chassis of the car and the builders have to set the plates by using standard rivets situated each 30mm. Care has to be taken when riveting the plates and the use of a plastic guide can be helpful.
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Figure 12. Configuration of the riveted aluminium plates in the chassis Although rivets can also be modelled in the polyhedral representation by using the joint facilities of Solidworks or a shape design and mirror options, in the present work and due to the high amount of rivets needed and that the approach adopted is to export just the lines into the FE model the rivets have not been included in the polyhedral CAD file.
The Figure 13 shows the polyhedral representation of the Ultima GTR chassis without the aluminium plates and the suspension, created in Solidworks and with the different colours representing the different frame profiles.
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Figure 13. CAD of the chassis without riveted plates Once the tubes have been modelled it is time to model the aluminium plates of the chassis. These plates have structural, holding and isolating functions and are riveted to the tubes.
Figure 14. Riveted plates attached to the tubes
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Figure 15 shows the configuration of the aluminium plates in the chassis.
Figure 15. CAD of the chassis with riveted plates Care has to be taken when setting the aluminium plates and a strict order has to be followed when building a kit car in order to all the devices are properly mounting as detailed by the manufacturer.
3.4 FINITE ELEMENT ANALYSIS AND TORSIONAL RIGIDITY Once the CAD model has been created, one of the most important parts of the present project is the creation of a FE model of the chassis to work out the torsional stiffness and to carry out an iterative process of changing and adding tubes in order to increase the torsional stiffness of the car. In the present work it is need a reliable and easy adaptable model, not too time consuming when meshing and solving and easy to change the configuration of the tubes in order to test the influences of the changes in the configuration and the effect of the aluminium plates with or without rivets. In order to do that and as described in
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the bibliography different simplifications have to be made in the FE element model. The approach of creating a model with the polyhedral configuration has also been tested, but has been rejected due to the problems presented when meshing, the lack of adaptability and the too high consumption of time. In order to overcome the meshing difficulties, advanced meshing software has been tried to create a good importable mesh to import into ANSYS obtaining unsuccessful results and due to the other approach selected this approach has been abandoned. In futures works an approach of image-based meshing from the stl has to be tried in order to improve the automation of the simulations. Instead of that and as mentioned before, the approach of exporting the lines and meshing the tubes with BEAM 188 elements, given the different sections and meshing the aluminium plates with SHELL181 elements, has been undertaken. Related to the quality of the mesh, by default, ANSYS uses a mesh density that provides accurate results for torsional stiffness and even for nonlinear material calculations. Increasing cross-section mesh size, does not imply larger computational cost if the associated material is linear (ANSYS Online Documentation).
The configuration options for exporting into ANSYS the lines obtained in the last section are shown in the Figure 16. It is very important, once the model has been imported, to check the dimensions of the model by checking the distance of two key points known and if necessary, to use the scale option to scale the model to the correct dimensions.
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Figure 16. Exporting lines as IGES file configuration options. The next step is to define the element type, the materials models and the different sections of the different tubes of the chassis. As mentioned above in the selected approach, BEAM188 elements for the tubes and SHELL181 elements for the plates will be used (Raju, 1998). One of the most important characteristics of ANSYS is the possibility of automation of the process of creating a model. Once the IGES file with the lines of the chassis has been imported a txt file with all the commands can be created. This can be useful when starting other models and when doing smooth changes. Figure 17 shows the lines imported into ANSYS.
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Figure 17. Lines of the chassis exported into ANSYS Once the element types have been defined, the next thing to do is to define the sections used with the beam element to model the frame sections of the chassis. This can be made using instructions to define the 5 section types, thus each smooth change could be made in a txt file and easily pasted in the command bar (see Appendices for the commands and sections defined).
The next thing to do is to set the real constraint for the SHELL181 elements to give the thickness of 1.5 mm to the aluminium plates and the material properties of the materials. In order to create the model of the standard chassis of the Ultima GTR, two materials models have been created, one is steel for the dia tube MIG welded frames and the second one NS4 aluminium alloy. In order to create the material models in ANSYS, the Poisson coefficient and Young module have been inserted. See the Appendix for more detailed specification of the materials used. The aluminium and steel used in the standard chassis have the following Young module and Poisson coefficient:
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Young´s modulus (GPa) Steel Aluminium
205 70
Poisson coefficient ν 0.29 0.33
Table 2. Material properties Once the parameters have been set, the next step to do is to model the aluminium plates, this can be made directly in ANSYS with the modelling options or in Solidworks and exported into ANSYS. The Aluminium plates have been modelled as areas (see Figure 18 )
Figure 18. Aluminium Plates The plate at the bottom of the cock pit is welded and will be modelled in ANSYS as attached to the frames (see Figure 19).
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Figure 19. Welded cockpit plate The next step is to apply the boundary conditions and loads. The boundary conditions have to be set to model the mechanical trials for working out the torsional stiffness. The computer simulation has the advantage of the possibility of applying the loads in any direction but in real trials applying forces in any direction is not that easy. Following the instruction of the configuration of the trial from Milliken and Milliken (1995), the chassis will be constraint in 4 key points at the rear, deleting the 6 degree of freedom of each node and other constrain is set at the front acting as a hinge joint with the displacement in the three axles eliminated and just allowing the roll. Two forces have also been applied in different directions to twist the chassis in the x axle. It is preferred to set the loads and constraints to the key points as are geometrical entities, better than applying it to nodes that could be removed when remeshing. The two forces have been applied in the key points of the front-front suspension. These forces twist the chassis and this movement produces a variation in the z axle of the key points where forces are applied (Figure 20 and Figure 21). By measuring this displacement we can get the angle the chassis has been moved and relating it to the force applied we can easily work out the torsional stiffness of the chassis (see Figure 5).
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Figure 20. Constraints at the rear
Figure 21. Loads and constraint at the front The torque applied is the product of the force applied at one key point and the distance from the point of application to the centerline of the car. The deflection is taken to be angle formed from the center of the car to the position of the deflected
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corner. In order to work out the torsional stiffness we take the average of the right and left deflections so we are generating a more accurate estimate of the total angular deflection of the chassis of the Ultima GTR (Riley, 2002). Though this trial is easy to be done in FE software as Ansys this configuration is difficult to reproduce in a laboratory as it is quite difficult to apply a vertical load counter to the direction of gravity. Instead of that in many torsional stiffness trials a known weight is hanged on the corner of the chassis to allow it to pivot about a roller. This method can be seen in the Figure 22.
Figure 22. Configuration of the trials usually applied in a lab (Riley, 2002) In the present work and due the facility of setting the loads in the direction required the approach of setting one force in each corner has been carried out. Once the geometrical configuration of the model, the constraints and the loads have been set the next step is to mesh the model. It is important to explain here a bit the approach followed to model the rivets. As said before the FE model made in the present work aims to be reliable and easy adaptable, not too time consuming when meshing and solving and easy to change the configuration of the tubes in order to test the influences of the changes in the configuration and the effect of the aluminium plates with or without rivets. In order to achieve that a simplification when modelling
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the rivets has to be carried out, otherwise if we would like to create a more realistic model of the rivets we should made a model based on the polyhedral representation of the CAD of the chassis, but this would lead to a high time consuming and not easy to adapt model that is not what we are aiming in the present project. Future works should compare the results with the two different approaches and characterize the influence of the simplifications made. In order to model the rivets, nodes can be located every 30 mm both in the plates and in the tubes. This can be made by giving the manual size of the entities with the command LESIZE and AESIZE and setting the element edge length to 30mm. Once the manual size has been given it is time to mesh the model. It is important to be careful when selecting the elements types, the materials models, the real constant and the section numbers as any mistake will lead to confusing results. Figure 23 shows the model meshed with the aluminium plates with the ESHAPE command (ANSYS Online Documentation) activated to display the elements with shapes of the section defined.
Figure 23. Model meshed with sections geometry activated
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Once the model is meshed it is time to model the rivets, this has been made in the present project by coupling degrees of freedom of the nodes representing the rivets in the lines and in the plates. The coupling option of ANSYS is very useful when modeling forming pins, hinges, universal, and slider joints between two coincident nodes. This option force two or more degrees of freedom (DOFs) to take on the same unknown value forcing the nodes in the frames and in the aluminium plates of the model to behave as rigid bodies. A set of coupled DOFs contains a prime DOF, and one or more other DOFs. Coupling will cause only the prime DOF to be retained in the analysis' matrix equations, and will cause all the other DOFs in a coupled set to be eliminated. The value calculated for the prime DOF will then be assigned to all the other DOFs in a coupled set (Figure 24).
Figure 24. Model of the rivets In the present job, the rivets of the two plates of the cock pit have been modeled and at the front, one plate has been modeled as a riveted plate and at the opposite corner the other one has been modeled as a plate attached to the tube by all his nodes, in
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order to compare the difference of modeling the plate transmitting the forces just by points situated every 30 mm (with rivets) and simply attached to the tube (without modeling rivets) as a completely attached part (Figure 25).
Figure 25. Rivets in the plates of the left side of the chassis One very important thing to do is to verify the connectivity of the different elements. One of the causes that lead to a very confusing results is when two adjacent elements are not joint together because of two key points situated in the same position have not been merged correctly or inaccuracies when modelling the lines and the joint points in the CAD software. This is an important step to be done. As looking for non connected frame in the model could be quite tiring due to the high amount of nodes and elements a simple program called grow up will be written and used to show that all the elements are connected. This program select all the elements attached to a selected node and select the nodes of the selected elements
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and replot the new entities selected. Figure 26 shows verification steps of the mesh connectivity.
Mesh and “grow up verification”
esln !grow up nsle /replot
Figure 26. Mesh and verification Once the connectivity of the elements has been verified it is time to solve the model by using the current LS solver. After about 4 minutes the solution is done and we can check the results in the general post processer.
3.5 VALIDATION OF THE MODEL Once the model has been solved we have to work out the torsional stiffness and validate the model against the torsional stiffness of the standard chassis. In order to do that and as mechanical trials of the chassis are beyond the scope of the EGOUltima project we will take the results from mechanicals trials that have been already undertaken to work out the torsional stiffness. The decision of not doing our own mechanical trials have been reached due to the EGOUltima racing car was already in building process and creating the mounting for the trials would have delayed the building process and would have increased the costs of the project.
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Instead of that there are many initiatives easily accessible in the communities of Ultima GTR of users that need to work out the torsional stiffness in order to meet the requirements of the homologation in their respective countries. In the special case of Spain, there are no specifics standards for the homologation of kit cars. The organism responsible for the homologation of customized racing cars is the National institute for aerospace technology (INTA, http://www.inta.es). In order to homologate the car it is needed to meet the requirement that involve things as the gearbox, the engine and the torsional stiffness in order to meet the requirement of safety. It is important to choose carefully the gearbox and the engine towards the homologation in a specific country as the regulations may be quite different in each country. Now it is a good point to explain more about the characteristics of the complements that have been chosen for the EGOUltima build:
The gearbox used in the EGOUltima build will be the Porsche GT3 RS Cup 6 gears (Figure 27), limited Slip Racing differential oil cooled, 321 km/h at 7100 rpm with the following ratios:
Gear
ratios 1 2 3 4 5 6
13/41 20/40 25/36 30/36 33/32 35/31
Table 3. Gear ratios
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Figure 27. Gearbox The engine chosen is the 7 litres corvette LS7 shown in the Figure 28 (Appendices).
Figure 28. LS7 corvette engine (courtesy of Corvette) In order to validate our model we will use the mechanical trials that have been carried out by an Ultima GTR builder last July in Perth, Western Australia. As we are still
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waiting for the requirements from the INTA in terms of torsional stiffness, in the present work, we will use as a reference the Australian standards. Homologation of kit cars can be a very time consuming process.
The Australian vehicle standards bulletin 14, says that “torsional rigidity should be at least 4000 Nm per degree over the wheelbase at least the vehicle has been professionally designed to operate at lower stiffness levels or 6000 Nm per degree in case the capacity of the engine mounted is higher than 2 litres” (Internet site of the department of infrastructure, transport, regional development and local government of Australia, 2006). As in EGOUltima the chosen engine is a 7 litres capacity we will take the 6000 Nm per degree as a reference for the improvement of the chassis.
The mechanical trials undertaken last July in Australia have given a torsional stiffness of the standard chassis of the Ultima GTR of 4180 Nm per degree. We will take this torsional stiffness as a reference for validating our model.
It is important to notice the high influence of smooth variation in the geometrical data of the frames on the results of torsional stiffness. Increments of less than one millimetre in the thickness, diameter of edge of the frames could lead to a high increment in the torsional stiffness. It is important here to make clear that in order to create a high accurate model to work out the torsional stiffness it is necessary to measure with high accuracy the geometry of the chassis and each frame. As mentioned before the approach of measuring with laser scanner is a good approach in order to get the desired accuracy. Once the solution is done we have to select the nodes 260 and 277 where the loads have been applied, list the nodal solution in the general postprocessor of the displacement in the z axle and work out the torsion stiffness with the equation given in Table 4. These points have been taken to apply the forces and to measure the displacement as are the suspension anchorage points that transmit the forces from the wheels to the chassis frame.
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Table 4. Displacement of the two nodes and validation of the results As shown in the last table the torsional stiffness of 3813 Nm per degree given by the FEM is a bit lower than the worked out in the mechanical trials. These differences of 8.77% may be due to the assumptions made in the model, the inaccuracies between the mechanical trials and the model created, as well as other effects as gradual drift in the load cells, inaccuracies in the geometrical measures and inaccuracies of the equipment to measure described in the bibliography (Riley and George, 2002).
3.6 INFLUENCE OF THE RIVETED PLATES In this section the influence of the riveted plates on the torsional stiffness of the chassis will be explained. The aluminium plates are important structural elements of the chassis of the Ultima GTR and increase the torsional stiffness of the chassis in a 31% from 2631 Nm per degree for the chassis without plates to 3813 Nm per degree for the standard chassis with the riveted plates. It is important to notice that though plates add some torsional stiffness to the chassis the influence of each aluminium plate in the overall chassis stiffness is not so high than adding new bars but, as they are easy to set and there are few different materials to be used as carbon fibre with very high strength/weight ratio it is important to take plates into account when redesigning the chassis and aiming to improve torsional stiffness.
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No all the plates have the same influence in the torsional stiffness as plates situated orthogonal to the direction of the applied forces applied more resistance and have a better contribution in the overall torsional stiffness of the chassis. The difference in modelling the plates as continuously attached elements or as riveted every 30 mm, as in the reality, offer an overall torsional stiffness difference of around 10 Nm per degree each meter of riveted plate. This is because riveted plates transmit stress only by the attached points and not through all the attached line. For this reason in order to increase the accuracy of a chassis skinned model, all the rivets have to be modelled as every meter of plate simplified and attached continuously will introduce an error of around 10 Nm per degree each meter of riveted plate. Patient and care have to be taken when modelling the rivets as every plate has many rivets as shown in Figure 29.
Figure 29. Riveted plates at the bottom of the Ultima GTR chassis One important point to note about the riveted plates, that have been found in mechanical trials at Oxford Brookes University is that the rivets loosen over time and the torsional stiffness added to the chassis when riveting the plates is lost over the time.
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One way of reducing this torsional stiffness loss is using an adhesive material when attaching the plates to the frames. This has been taken into account when building the Ultima GTR in the EGOUltima build and an adhesive material called Silkafex has been used. Care has to be taken when using it because it comes out soft and the surface to be bonded have to be carefully prepared before using the adhesive (see Figure 30).
Figure 30. Adding Silkafex to add the riveted plates
3.7 LINEARITY AND CONVERGENCE OF THE MODEL It is important, once the model in FE has been created, to check the linearity and convergence of the model within the linear behaviour of the materials, in order to detect possible errors and that the model is consistent. The yield stress of the steel is 370 MPa and 75.8 MPa for the Aluminium. Then we will take forces that produce maximum stress of Von Mises smaller than these yield stresses in order to avoid the nonlinear range of the materials. It is said in the Ansys guide that BEAM188 and SHELL 181 elements used in the model of the present are linear, this means that the relationship between force
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applied and displacement obtained has to be linear and no matter which force is applied the torsional stiffness worked out will be the same. In order to check that we have created and easy trial, changing the forces, reading the displacements and working out the torsional stiffness for each force applied. In the model created we have applied a force of 450 Newton in each corner, and now we will test the linearity of the model trying with different load values, in order to assure that the model is working properly. The linearity trial has been done with the standard chassis and the aluminium plates. Figure 31 and Table 5 show the linearity of the model.
Force(N)
ANSYS torsional stiffness Nm/deg 1 100 450 1000 5000
angular displacement
3797,40 3797,40 3812,59 3797,41 3797,56
9,85E-05 9,85E-03 4,41E-02 9,85E-02 4,92E-01
Table 5. Linearity trial
Torsional stiffness Nm/deg vs applied force 4500,00 4000,00 3500,00 3000,00 2500,00 Torsional stiffness Nm/deg
2000,00 1500,00 1000,00 500,00 0,00 1
100
450
1000
5000
force in N
Figure 31. Linearity of the model
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Furthermore, a simple convergence trial has been undertaken in order to check the consistent of the results when increasing the amount of elements in the model. Three different mesh sizes have been used of the standard chassis of the Ultima GTR without plates, as coupled elements present difficulties when remeshing. Figure 32 and Table 6 show the convergence of the model.
number of elements in the model torsional stiffness Nm/deg
1684
2520
2631,30
3293
2627,02
2625,85
Table 6. Convergence of the model
Torsional stiffness Nm/deg vs number of elements 3000,00 2500,00 2000,00 1500,00
Torsional stiffness Nm/deg
1000,00 500,00 0,00 1684
2520
3293
number of elements
Figure 32. Convergence of the model
3.8 IMPROVEMENTS OF THE ULTIMA GTR CHASSIS FRAME In this section the methodology of improvement of the Ultima GTR chassis will be outlined before the obtained results are presented. Many are the changes that could be made to the standard chassis; the use of other materials as carbon fibre; adding new plates, adding new tubes and changing frames profiles. The present project aims to achieve an improvement of the standard chassis of the Ultima GTR adding torsional stiffness towards to the homologation process without
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adding too much weight. No huge changes in the standard structural configuration that support important parts of the car as the bodywork or devices as the cooling systems will be made, just smooth improvements that add torsional stiffness without compromising the stiffness/weight ratio and inside the budget possibilities of the build project.
The main criterion to follow will be to change the position of the standard frames, to add frames and plates in different position as well as using new materials for the plates as carbon fibre and honeycomb materials. As a starting point the influence of the different parts of the chassis in the torsional stiffness will be analyzed focused on the red and blue bars as they play a more important role in the overall chassis stiffness than the black, yellow and green that mainly act as supports of the different devices. The reason of increasing the torsional stiffness is that a chassis that flectes too much is less easy to handle and less safe as well as must be prone to fatigue. Increasing the stiffness of the chassis doesn’t have any disadvantage unless the chassis is made overweight. Modifying the chassis stiffness will change the set-up; different springs, anti-roll bar settings etc may be required (Milliken and Milliken, 1995).
A good approach to follow when redesigning for stiffness is to arrange the tubes to form triangles with the major loads applied at the intersections of tubes, otherwise the structure will work in bending which is much less efficient than tension/compression. It is also a good approach to use composite stressed skins further than aluminium or steel stressed skins where economy is not so important than performance.
Other recommendations extracted from Milliken and Milliken (1995) are: •
Adding diagonals in the roll cage. This is the thing to do if the vehicle is already built and found to be flexible. Diagonals work best if they connect to major lead points such as suspension/spring mounts.
•
The engine can function as stressed part of the chassis provided that the loads are not so high that the block is distorted.
•
If tubes must be used in bending, plate reinforcements may be used at the joints to pass loads more effectively from one tube to another
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•
Adding additional cross members to the chassis
In order to start with the process of improving the standard chassis it is important to have a look at the displacement (m) and Von Mises stress distribution (N/m2) to work out how the frame is working. It is important to activate the ESHAPE command (ANSYS Online Documentation) to display the elements with shapes of the section defined. For better analysis of the data obtained we will separate the frames and the plates.
Figure 33. Von Mises stress distribution of the frames (units in N/m2) Figure 33 shows the Von Mises stress distribution of the Ultima GTR chassis. In order to improve the chassis of the ultima we will have to add tubes to the connection points that are more stressed, that occurs at the rear due the near constraints applied and at the top of the chassis. The redesign of the chassis will have to add diagonals to the more stressed joints.
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We can also look at the aluminium plates Von Mises stress distribution to work out how they are working (Figure 34)
Figure 34. Von Mises stress distribution of the plates (units in N/m2) Another important plot to look at is the displacement vector sum to see which bars and plates have greater displacements (Figure 35).
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Figure 35. Displacement Vector sum of the standard chassis (units in m) In order to redesign the chassis and add torsional stiffness we will add bars and triangulate the more affected elements and check the increment in torsional stiffness that changes produce. First of all a characterization of the effect of the standard chassis plates has been undertaken in order to check the effect of the plates on the overall torsional stiffness (see Appendices for the characterization of the plates) Adding and changing the aluminium plates to carbon fibre plates will increase the torsional stiffness of the chassis as the chassis of a car is a deflection limited structure and therefore it is the young’s modulus to density ratio (specific modulus) of the material that is important rather than yield stress to density ratio and on this criteria, carbon fibre offers a superior performance as can be seen in the Table 7. For this reason adding thicker carbon fibre will add more stiffness without increasing the weight. Nevertheless, as carbon fibre is more expensive than aluminium plates, it is important to have equilibrium between costs and performance.
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Young module (GPa) Steel Aluminium Carbon fibre
205 70 135
Poisson coefficient 0.29 0.33 0.25
density (g/cc) 8 2.7 1.6
Young module to density ratio 25.63 25.93 84.38
Table 7. Properties of Steel, Aluminium and Carbon fibre Related to the FE analysis of composite materials as carbon fibre it is important to notice here that modelling carbon fibre in Ansys is not straight forwards as it is not an isotropic material but an orthotropic material with Ex ≠ Ey ≠ Ez ≠ E1 ≠ E2 ≠ E3 and the orientation of the fibers influence the stiffness of the material. In this project in order to add torsional stiffness by using carbon fibre and keeping in mind to have an adaptable model not too time consuming we will model the carbon fiber plates as isotropic SHELL 181 elements with Young modulus of 135 GPa and adding thickness as it will add torsional stiffness decreasing the weight (compared to the aluminum standard plates). In future works where carbon fiber is used in many parts of the chassis a more realistic analysis and model of the carbon fiber should be made. In order to redesign the chassis an iterative process of adding and changing the configuration of the chassis will be undertaken simulating the changes with the validated model to work out the increment in torsional stiffness and measuring weight increments. There are many changes that can be made; we will focus the present project in achieving the torsional stiffness of 6000 Nm per degree as described before without changing too much the configuration of the car and without increasing too much the weight. Having an easy adaptable model for working out the torsional stiffness is very important for such analysis and this is the main goal we aimed when creating the model.
3.9 SUMMARY This section has explained the progress of creating a Finite element model to work out the torsional stiffness of the chassis of the Ultima GTR racing car; the approaches adopted, the difficulties, the problems to be overcome and the solutions
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given. It is very important in order to work out the torsional stiffness of a chassis and the changes made in the configuration to have an easy adaptable FE model, no too time consuming with high accuracy to increase the torsional stiffness to homologate the car or to improve the safety and the handling.
The main steps of the creation of the model and improvement of the chassis have been explained, as first step the data acquisition of the geometry where the use of 3D scanner have been proposed
because of the high accuracy required and
specially in case the chassis is difficult to access. The approach of creating the model in the CAD software with the lines representing the frames of the chassis and defining the section of the frames in ANSYS has been followed because of the advantage in terms of easy adaptability and low time consuming.
BEAM188 elements for the tubes and SHELL181 elements for the plates have been used and a simplification of the rivets has been added to the model in order to increase the accuracy. Loads and boundary condition have been added to represent the mechanical trials done. A simple program for looking for unconnected element has been developed and tested.
The designing of the model has been linked to the real experience when building the Ultima GTR in the project EGOUltima and an adhesive material called SIlkafex have been used in order to avoid the looses of the rivets after use. Linearity and convergence studies have been carried out in order to check the consistence of the model and the model has been successful validated against mechanical data.
Once the model has been validated the improvement of the chassis process has been presented with the criterion to be followed in order to increase the torsional stiffness of the chassis as adding frames and triangulating the structure and using news material with higher specific modulus as carbon fibre.
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4 RESULTS AND DISCUSSION 4.1 INTRODUCTION This section will show the results obtained in the process of analyzing and improving the chassis of an Ultima GTR racing car and the improvements made in order to increase the torsional stiffness. The aim is to achieve the torsional stiffness to 6000 Nm per degree without adding too much weight in order to meet the homologation requirements, to increase the safety and the performance of the car.
The influence of the different parts has been characterized and different improvements and configuration have been tested. No huge changes in the standard structural configuration will be presented as results. The project achieves to increase the torsional stiffness without increasing too much the costs and no structural parts supporting devices have been modified.
The redesigned chassis will be modelled and simulated in order to work out the new torsional stiffness and the increment in weight will be calculated using the sensors facilities in Solidworks starting from the standard chassis with a weight of 123.88 kg and a torsional stiffness of 3813 Nm per degree.
4.3 IMPROVEMENT OF THE CHASSIS The first improvement introduced is the X braces above the engine in order to triangulate and give more strength to the more stressed joints saw in the section before. This improvement has been tested with the created model of Ansys and has been very successful as has increased the torsional stiffness of the standard chassis to 5568 Nm per degree and just add 3.3 kg to the weight of the chassis. Figure 36 shows the configuration of the X braces triangulating and connecting the section above the engine. The use of these bars don’t need any modification of the bodywork, as aimed and although it has to be fixed after the engine has been installed increase a lot the torsional stiffness of the standard chassis.
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X Bars above the engine
Figure 36. X braces improvement The second improvement introduced is a redesign of the part behind the driver in order to increase the safety of the car and used with the X braces above the engine increase the torsional stiffness. The redesign proposed is the elimination of the structure and the triangulation of the arc as shown in Figure 37. This new configuration increases the safety while keeping the same weight of the chassis. The use of this new configuration used with the X braces increase the torsional stiffness from 3813 Nm per degree to 5626 Nm per degree.
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X Bars behind the driver
Figure 37. Triangulation of the arc The next improvement in order to increase the torsional stiffness and once the midrear part of the car has been improved is to add stiffness to the cockpit. To achieve that, a carbon fibre plate have been added joining the two bars above the cockpit as shown in Figure 38. Carbon fibre has been selected as has a higher specific modulus and the chassis of a car is a deflection limited structure. A 3mm thickness has been selected in order to increase the torsional stiffness without adding too much weight. With this improvement the torsional stiffness of the car reaches to 5907 Nm per degree with just adding 800 gram to the overall chassis weight.
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Carbon fibre plate
Figure 38. Carbon fibre plate The next improvement to be made in order to reach the aimed torsional stiffness of 6000 Nm per degree is to add two X bars at the rear of the car above the gearbox, as shown in Figure 39. This improvement will bring the torsional stiffness to a 6325 Nm per degree adding 2 kg to the overall weight.
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X Bars at the rear
Figure 39. X braces above the gearbox The weight of the new design of the chassis calculated by Solidworks is 130.137kg just 7 kg more with an increment in torsional stiffness of 2513 Nm per degree reaching a total torsional stiffness of 6326 Nm per degree higher by 326 Nm/degree than the 6000 taken as objective and having increased the torsional stiffness of the chassis in 39.72% twice than the 20% aimed at first. The chassis with all the modification integrated is shown in Figure 40. Once the improvements have been made a new model of the chassis will be created, meshed (Figure 41) and solved in order to check the stress distribution of the redesigned frames.
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Figure 40. CAD of the redesigned chassis Figure 42 shows the Von Misses distribution of the chassis (in N/m2), for simplicity the plates have been removed and are shown in Figure 43. The same scale of colours has been applied than for the standard chassis (Figure 33 and Figure 34). As can be seen, strength has been added to the rear of the chassis and the leading points are less stressed. This decrease the overall displacement of the bars and the torsional stiffness given in the trials is higher.
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Figure 41. Mesh of the redesigned chassis
Figure 42. Von Mises stress distribution, redesigned chassis (units in N/m2)
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Figure 43. Plates Von Mises stress distribution, redesigned chassis (in N/m2)
Figure 44. Displacement Vector sum of the redesigned chassis (units in m)
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At this stage is very important to discuss the results obtained and to make clear the simplification made, the successes of the project and the future needs to improve the model created and the chassis redesigned. The model implemented in the present project is a very useful model for testing the changes and redesigns of racing car chassis in order to work out the increment or decrement in torsional stiffness that produce the changes, when installing complementary devices that could need higher requirements of torsional stiffness both for regulation or safety reasons. It is an easy adaptable model not time consuming at all in terms of simulation time, as aimed, and offers an optimal accuracy for working out the torsional stiffness in order to prepare the homologation trials and avoid to have to repeat the trials with the additional high costs that it would produce. Furthermore the redesigned chassis has been successful and offers a superior performance in comparison of the standard chassis in terms of torsional stiffness and safety, just adding 7 kg.
Though the accuracy of the model is good, in order to improve the model and increase the accuracy of it further work directions should be followed. A higher accuracy in the data acquisition of the geometry has to be attempted as any small inaccuracy in the acquisition of the geometry of the chassis frame can lead to changes in the results. In addition a more complex model of the riveted joints should be added as well as a complex model of the welded joint in order to make the results more realistic. Furthermore a more realistic model of the carbon fiber should be made, taking into account the orthotropic properties of the material.
4.5 SUMMARY In this section the results of the improvement of the Ultima GTR chassis have been presented discussing the main results of the projects, the outcome and the other aspects that could be improved in future work in order to increase the accuracy of the model. Four new improvements have been added to the standard chassis in order to increase the torsional stiffness from 3813 Nm per degree to 6326 Nm per degree, higher than the 6000 taken as objective and having increased the torsional stiffness of the chassis in 39.72% twice than the 20% aimed at first with just 7kg added. The
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chassis with all the modification integrated is likely to presents a better performance in terms of handling and safety and meet the requirement for the homologation. Furthermore the plots of displacement vector sum and Von Mises stress distribution have shown the decrement in the frames displacements and the improved tension distribution in the main tubes.
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5 CONCLUSIONS
•
Torsional stiffness plays an important role in the behaviour of the racing car since affects parameters as weight transfer, vibration, strength, safety and handling
•
Using 3D Scanners is a good approach to obtain the geometrical data of a chassis when the chassis is difficult to access due to the bodywork or other devices.
•
A model implemented from a IGES file with lines representing the frames and meshing the lines as BEAM elements defining the different sections and the plates as SHELL elements is a better approach when aiming to create an easy adaptable model not time consuming.
•
Small inaccuracies in the CAD lead to high variation in the results, for this reason it is important high accuracy when creating the CAD of the chassis.
•
One very important thing to take into account is to verify the connectivity of the different elements as the lack of connectivity leads to very confusing results.
•
In order to validate the FE model it is important to take into account the inaccuracies of the measurement devices and the smooth differences between the mechanical trials and the FE model.
•
Having an easy adaptable FE model for working out the torsional stiffness is very important in order to easily work out the torsional stiffness of the chassis before to the expensive homologation trials to meet the requirements that are different in each country.
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•
The coupling option of ANSYS is very useful when modelling forming pins, hinges, universal, and slider joints between two coincident nodes.
•
Rivets of plates loosen over time and this torsional stiffness added to the chassis when riveting the plates is lost. One way of reducing this torsional stiffness loss is using an adhesive material as Silkafex when attaching the plates to the frames.
•
A good approach to follow when redesigning for stiffness is to arrange the tubes to form triangles with the major loads applied at the intersections of tubes, otherwise the structure will work in bending which is much less efficient than tension/compression.
•
Adding and changing the aluminium plates to carbon fibre plates will increase the torsional stiffness of the chassis as the chassis of a car is a deflection limited structure and therefore it is the young’s modulus to density ratio (specific modulus) .
•
A lot of changes can be made to the standard chassis of the Ultima GTR in order to increase the torsional stiffness of the chassis.
•
In future works, the complexity of the model should be increased in order to check the differences in the results. Futures works could improve the automation capacity of the model in order to create a standard model for every racing car chassis.
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6 REFERENCES Thompson, L. L. Soni, Pipasu H.; Raju, Srikanth and Law, E. Harry. (1998). The effects of Chassis Flexibility on Roll Stiffness of a Winston Cup Race Car. Motorsports Engineering, Conference and Exposition, Dearborn, Michigan,November 16-19.
S. Raju,.(1998).Design and Analysis of a Winston Cup Stock Car Chassis for Torsional Stiffness using the Finite Element Method, Master of Science Thesis, Department of Mechanical Engineering, Clemson University.
Internet site Ultima Ltd: http://www.ultimasports.co.uk/Content.aspx?f=gtrintro
Internet site of the present project http://egoultimagtr.blogspot.com/
P.E, Lewis and J.P. Ward. (1991). The Finite Element Method: Principles and Applications. New York: Addison-Wesly Publishing Company.
T. D. Gillespie, (1992).Fundamentals of vehicle dynamics. SAE Inc. Warrendale. PA 15096-0001. ISBN 1-56091-199-9.
M. Beck-Burridge, J. Walton. (1999). Britain's Winning Formula: Achieving World Leadership in Motorsports. Palgrave Macmillan (18 Nov 1999). ISBN-10: 0333712706. ISBN-13: 978-0333712702
Internet site of UK trade and investment: http://www.anella.cat/c/document_library/get_file?folderId=552813&name=DLFE2201.pdf
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F. Bernardini, H.E. Rushmeier (2002). The 3D Model Acquisition Pipeline. Comput. Graph. Forum 21 (2): 149–172
S. Weik. Registration of 3D partial surface models using luminance and depth information. In Proceedings of the International Conference on Recent Advances in 3D Digital Imaging and Modeling, Ottawa, Canada: pp. 93–100. May, 1997.
B. Curless (November 2000). From Range Scans to 3D Models. ACM SIGGRAPH Computer Graphics 33 (4): 38–41
T. V´arady, R. R. Martin and J. Cox. Reverse engineering of geometric models—an introduction. Computer Aided Design, 29(4):255–268, 1997.
R. Benjemaa and F. Schmitt. Fast global registration of 3D sampled surfaces using a multi-z-buffer technique. In Proceedings of the International Conference on Recent Advances in 3D Digital Imaging and Modeling, Ottawa, Canada: pp. 113–120. May, 1997.
S. Marschner, S. Westin, E. Lafortune, K. Torrance and D. Greenberg. Image-based BRDF measurement including human skin. In Proceedings of the 10th Eurographics Workshop on Rendering, Granada, Spain:pp. 131–144. June, 1999.
K. L. Chelule, Dr. T. Coole, D.G. Cheshire (2004), Fabrication of medical models from scan data via rapid prototyping techniques
ANSYS Online Documentation
F.
Aird.
(1997).Race
Car Chassis: Design
and
Construction.
Motorbooks
International. ISBN-10: 0760302839. ISBN-13: 978-0760302835.
O. C. Zienkiewicz and R .Taylor. The Finite Element Method for Solid and Structural Mechanics L ISBN-13:978-0-7506-6321-2 1967, McGraw Hill, New York
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T.Y. Yang. Finite Element Structural Analysis , Prentice-Hall, Inc, Englewood, NJ, 1986.
W. B. Riley and Albert R. George. Design, Analysis and Testing of a Formula SAE Car Chassis.Cornell University.Proceedings of the 2002 SAE Motorsports Engineering Conference and Exhibition (P-382), 2000.
Young et al, 2008. An efficient approach to converting 3D image data into highly accurate computational models. Philosophical Transactions of the Royal Society A, 366.
X., Deng; W., Chen; G., Shi. (2000). Three-dimensional finite element analysis of the mechanical behaviour of spot welds. Finite Elements in Analysis and Design 35, 17– 39.
F. Vivio. (2009). A new theoretical approach for structural modelling of riveted and spot welded multi-spot structures. International Journal of Solids and Structures 46 (2009) 4006–4024.
B. P.Siegler, Butler L., Deakin A. J., Barton D. C., The Application of Finite Element Analysis to Composite Racing Car Chassis Design, Sports Engineering (1999) 2 pp 245-252, September 1999.
J. Balkwill, (2009). Advanced chassis engineering. Student handbook. Oxford Brookes University.
H. Keiner, “Static Structural Analysis of a Winston Cup Chassis Under a Torsional Load”, Report # TR-95-100-MEMSP, Department of Mechanical Engineering, Clemson University, 1995.
Thompson, L. L. Jon K. Lampert and E. Harry Law (1998b). Design of a Twist Fixture to Measure the Torsional Stiffness of a Winston Cup Chassis. Department of
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Mechanical Engineering, Clemson Univ. 1998 Motorsports Engineering Conference ProceedingsVolume 1: Vehicle Design and Safety (P-340/1)
F. Milliken, William and Milliken, Douglas L. (1995). Race car vehicle Dynamics. Society of Automotive Engineer; ISBN: 1-56091-526-9. ISBN-13: 9781560915263
A. Deakin, Crolla D., Ramirez J. P., Hanley H., The Effects of Chassis Stiffness on Race Car Handling Balance, This Proceedings, 2000.
M. Mitschke, “Dynamik Der Kraftfahrzeuge: Band A: Antrieb Und Bremsung”, 1996
J. Fenton, “Handbook of Vehicle Design Analysis”, Society of Automotive Engineers, 1996
J. Katz, (1995) Race Car Aerodynamics, Robert Bentley Publishers, ISBN 0-8376-01428.
J.K. Lampert, “Design and Analysis of a Twist Fixture to Measure the Torsional Stiffness of a Winston Cup Chassis”, Masters Thesis, Department of Mechanical Engineering, Clemson University, August 1998.
Materials Database http://www.matweb.com
Internet site of the department of infrastructure, transport, regional development and local government of Australia http://www.infrastructure.gov.au/roads/vehicle_regulation/bulletin/pdf/NCOP12_Secti on_LT_Test_Procedures_3Feb2006.pdf
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7 APPENDICES A) STEEL AISI 1018 Characteristics Sheet
Source http://www.matweb.com
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B) NS4 Aluminium Alloy
Source http://www.matweb.com
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C) Section Types Commands SECTYPE, 1, BEAM, CTUBE, , 0 !Beam Section for tubes diameter 38,5 SECOFFSET, CENT SECDATA,0.0175,0.019,0.010,0,0,0,0,0,0 SECTYPE, 2, BEAM, CTUBE, , 0 !Beam Section for tubes diameter 26 SECOFFSET, CENT SECDATA,0.0115,0.013,0.010,0,0,0,0,0,0 SECTYPE, 3, BEAM, HREC, , 0 !Beam Section for tubes 39x39 SECOFFSET, CENT SECDATA,0.038,0.038,0.0015, 0.0015, 0.0015, 0.0015 SECTYPE, 4, BEAM, HREC, , 0 !Beam Section Type for tubes 25x25 SECOFFSET, CENT SECDATA,0.026,0.026,0.0015, 0.0015, 0.0015, 0.0015 SECTYPE, 5, BEAM, HREC, , 0 !Beam Section Type for tubes 39x19 SECOFFSET, CENT SECDATA,0.038,0.020,0.0015, 0.0015, 0.0015, 0.0015
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D) Section Types Plots 1 = Centroid
SECTION ID 1 DATA SUMMARY
= ShearCenter
.019
.0095
0
-.0095
-.019 -.019
-.0095
0
.0095
.019
1 = Centroid
Section Name = Area = .172E-03 Iyy = .286E-07 Iyz = 0 Izz = .286E-07 Warping Constant = 0 Torsion Constant = .573E-07 Centroid Y = -.385E-18 Centroid Z = -.173E-17 Shear Center Y = .361E-18 Shear Center Z = .915E-18 Shear Corr. YY = .500895 Shear Corr. YZ = -.214E-13 Shear Corr. ZZ = .500895
SECTION ID 2 DATA SUMMARY
= ShearCenter
.013
.0065
0
-.0065
-.013 -.013
-.0065
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.0065
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.013
Section Name = Area = .115E-03 Iyy = .868E-08 Iyz = 0 Izz = .868E-08 Warping Constant = 0 Torsion Constant = .174E-07 Centroid Y = .516E-18 Centroid Z = .315E-18 Shear Center Y = -.669E-18 Shear Center Z = -.286E-18 Shear Corr. YY = .502608 Shear Corr. YZ = -.373E-13 Shear Corr. ZZ = .502608
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1 = Centroid
SECTION ID 3 DATA SUMMARY
= ShearCenter
.038
.0285
.019
.0095
0 0
.0095
.019
.0285
.038
1 = Centroid
Section Name = Area = .219E-03 Iyy = .487E-07 Iyz = 0 Izz = .487E-07 Warping Constant = .104E-13 Torsion Constant = .752E-07 Centroid Y = .019 Centroid Z = .019 Shear Center Y = .019 Shear Center Z = .019 Shear Corr. YY = .430927 Shear Corr. YZ = -.888E-13 Shear Corr. ZZ = .430927
SECTION ID 4 DATA SUMMARY
= ShearCenter
.026
.0195
.013
.0065
0 0
.0065
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.0195
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.026
Section Name = Area = .147E-03 Iyy = .148E-07 Iyz = 0 Izz = .148E-07 Warping Constant = .263E-14 Torsion Constant = .230E-07 Centroid Y = .013 Centroid Z = .013 Shear Center Y = .013 Shear Center Z = .013 Shear Corr. YY = .437044 Shear Corr. YZ = .624E-13 Shear Corr. ZZ = .437044
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1 = Centroid
SECTION ID 5 DATA SUMMARY
= ShearCenter
.02
.015
.01
.005
0 0
.0095
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.019
.0285
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.038
Section Name = Area = .165E-03 Iyy = .110E-07 Iyz = 0 Izz = .307E-07 Warping Constant = .198E-12 Torsion Constant = .258E-07 Centroid Y = .019 Centroid Z = .01 Shear Center Y = .019 Shear Center Z = .01 Shear Corr. YY = .622074 Shear Corr. YZ = .104E-13 Shear Corr. ZZ = .242112
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E) Characterisation of the plates
1 2 3 4 5 6 7 8 9
node 260 277 node 260 277 node 260 277 node 260 277 node 260 277 node 260 277 node 260 277 node 260 277 node 260 277
displacement(m)
displacement(m)
2,631E+03
ANSYStorsional stiffness Nm/deg
-4,02E-04 3,95E-04
displacement(m)
2,755E+03
ANSYStorsional stiffness Nm/deg
-3,40E-04 3,34E-04
displacement(m)
3,262E+03
ANSYStorsional stiffness Nm/deg
-3,39E-04 3,34E-04
displacement(m)
3,265E+03
ANSYStorsional stiffness Nm/deg
-3,35E-04 3,30E-04
displacement(m)
3,305E+03
ANSYStorsional stiffness Nm/deg
-3,30E-04 3,24E-04
displacement(m)
3,356E+03
ANSYStorsional stiffness Nm/deg
-3,19E-04 3,13E-04
displacement(m)
3,477E+03
ANSYStorsional stiffness Nm/deg
-2,92E-04 2,87E-04
displacement(m)
3,795E+03
ANSYStorsional stiffness Nm/deg
-2,90E-04 2,86E-04
3,813E+03
2
1
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ANSYStorsional stiffness Nm/deg
-4,20E-04 4,14E-04
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4
3
5
6
8
7
9
END OF DOCUMENT
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