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School of TechnologyMASTER OF SCIENCE DISSERTATIONTitle:Surname: First Name: Supervisor:Student Number: Module Number: Course Title:Date Submitted:José Manuel Baena1 of 8626 August 2010STATEMENT OF ORIGINALITYExcept 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.Signature of AuthorDateRegulations Governing the Deposit and Use
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José Manuel Baena 1 of 86 26 August 2010
School of Technology
MASTER OF SCIENCE DISSERTATION Title:
Surname:
First Name:
Supervisor: Student Number: Date Submitted:
Module Number:
Course Title:
José Manuel Baena 2 of 86 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.
Signature of Author Date
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.
Signature of Author Date
José Manuel Baena 3 of 86 26 August 2010
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.
José Manuel Baena 4 of 86 26 August 2010
TABLE OF CONTENTS
STATEMENT OF ORIGINALITY ........................................................................................... 2
ABSTRACT .......................................................................................................................... 3
ACKNOWLEDGEMENTS ..................................................................................................... 3
TABLE OF CONTENTS ........................................................................................................ 4
LIST OF FIGURES ............................................................................................................... 6
LIST OF TABLES ................................................................................................................. 8
1 INTRODUCTION ........................................................................................................ 10
1.1 Introduction ...................................................................................................................... 10
1.2 Objectives ........................................................................................................................ 12
1.3 Background ...................................................................................................................... 12
1.4 Structure of the report ...................................................................................................... 13
2 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
José Manuel Baena 5 of 86 26 August 2010
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
José Manuel Baena 6 of 86 26 August 2010
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
José Manuel Baena 7 of 86 26 August 2010
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
José Manuel Baena 8 of 86 26 August 2010
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
José Manuel Baena 9 of 86 26 August 2010
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
José Manuel Baena 10 of 86 26 August 2010
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.
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
http://egoultimagtr.blogspot.com/
José Manuel Baena 11 of 86 26 August 2010
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.
José Manuel Baena 12 of 86 26 August 2010
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
José Manuel Baena 13 of 86 26 August 2010
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).
José Manuel Baena 14 of 86 26 August 2010
Figure 2. Layout of the structure of the project
Literature review Data acquisition
CAD model
FE ModelValidation of the
modelRedesign of the
chassis FE model
FE simulation
Results analysisFinal design
José Manuel Baena 15 of 86 26 August 2010
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)
José Manuel Baena 16 of 86 26 August 2010
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 world-
class 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).
José Manuel Baena 17 of 86 26 August 2010
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
José Manuel Baena 18 of 86 26 August 2010
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 image-
processing 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.
José Manuel Baena 19 of 86 26 August 2010
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).
José Manuel Baena 20 of 86 26 August 2010
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
José Manuel Baena 21 of 86 26 August 2010
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
José Manuel Baena 22 of 86 26 August 2010
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; 1y∆ , 2y∆ .
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
José Manuel Baena 23 of 86 26 August 2010
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
José Manuel Baena 24 of 86 26 August 2010
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).
José Manuel Baena 25 of 86 26 August 2010
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
Chassis design Advantages DisadvantagesSimple ladder Simple, cheap easy. 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 techniques, cheap, possible to achieve reasonably good torsional rigidity to weight ratio
Not suitable for high volume manufacture – high labour content, would require additional paneling for road use.
Honeycomb Superior torsional rigidity to weigh ratio possible. Better crash performance possible. Assembly time for batch production lower than space frame
Requires use of inserts etc. for mounting. Requires bonding capability. More expensive material costs than space frame
Carbon fibre Best torsional rigidity to weight ratio. Can easily be formed into any shape. Good crash performance possible. Fantastically strong material
Very expensive indeed. Requires detailed understanding of material properties. Manufacture complex.
José Manuel Baena 26 of 86 26 August 2010
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.
José Manuel Baena 27 of 86 26 August 2010
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.
José Manuel Baena 28 of 86 26 August 2010
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.
José Manuel Baena 29 of 86 26 August 2010
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.
Figure 6. Hand measures on an Ultima GTR chassis
52cm
José Manuel Baena 30 of 86 26 August 2010
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).
José Manuel Baena 31 of 86 26 August 2010
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.
STL
CAD
José Manuel Baena 32 of 86 26 August 2010
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
José Manuel Baena 33 of 86 26 August 2010
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.
José Manuel Baena 34 of 86 26 August 2010
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.
Frame profiles
José Manuel Baena 35 of 86 26 August 2010
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.
José Manuel Baena 36 of 86 26 August 2010
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
José Manuel Baena 37 of 86 26 August 2010
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
José Manuel Baena 38 of 86 26 August 2010
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.
José Manuel Baena 39 of 86 26 August 2010
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.
José Manuel Baena 40 of 86 26 August 2010
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:
José Manuel Baena 41 of 86 26 August 2010
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).
Young´s modulus (GPa)
Poisson coefficient ν
Steel 205 0.29Aluminium 70 0.33
José Manuel Baena 42 of 86 26 August 2010
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).
José Manuel Baena 43 of 86 26 August 2010
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
José Manuel Baena 44 of 86 26 August 2010
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
José Manuel Baena 45 of 86 26 August 2010
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
José Manuel Baena 46 of 86 26 August 2010
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
José Manuel Baena 47 of 86 26 August 2010
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
José Manuel Baena 48 of 86 26 August 2010
and replot the new entities selected. Figure 26 shows verification steps of the mesh
connectivity.
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.
Mesh and “grow up verification”
esln !grow upnsle/replot
José Manuel Baena 49 of 86 26 August 2010
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:
Table 3. Gear ratios
Gear ratios1 13/412 20/403 25/364 30/365 33/326 35/31
José Manuel Baena 50 of 86 26 August 2010
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
José Manuel Baena 51 of 86 26 August 2010
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.
José Manuel Baena 52 of 86 26 August 2010
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.
José Manuel Baena 53 of 86 26 August 2010
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.
José Manuel Baena 54 of 86 26 August 2010
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
José Manuel Baena 55 of 86 26 August 2010
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.
Table 5. Linearity trial
Figure 31. Linearity of the model
Force(N) ANSYS torsional stiffness Nm/deg angular displacement1 3797,40 9,85E-05
100 3797,40 9,85E-03450 3812,59 4,41E-02
1000 3797,41 9,85E-025000 3797,56 4,92E-01
0,00
500,00
1000,00
1500,00
2000,00
2500,00
3000,00
3500,00
4000,00
4500,00
1 100 450 1000 5000
Torsional stiffness Nm/deg vs applied force
Torsional stiffness Nm/deg
force in N
José Manuel Baena 56 of 86 26 August 2010
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.
Table 6. Convergence of the model
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
number of elements in the model
1684 2520 3293
torsional stiffness Nm/deg 2631,30 2627,02 2625,85
0,00
500,00
1000,00
1500,00
2000,00
2500,00
3000,00
1684 2520 3293
Torsional stiffness Nm/deg vs number of elements
Torsional stiffness Nm/deg
number of elements
José Manuel Baena 57 of 86 26 August 2010
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
José Manuel Baena 58 of 86 26 August 2010
• 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.
José Manuel Baena 59 of 86 26 August 2010
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).
José Manuel Baena 60 of 86 26 August 2010
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.
José Manuel Baena 61 of 86 26 August 2010
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
Young module (GPa)
Poisson coefficient
density (g/cc) Young module to density ratio
Steel 205 0.29 8 25.63Aluminium 70 0.33 2.7 25.93Carbon fibre 135 0.25 1.6 84.38
José Manuel Baena 62 of 86 26 August 2010
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.
José Manuel Baena 63 of 86 26 August 2010
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.
José Manuel Baena 64 of 86 26 August 2010
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.
X Bars above the engine
José Manuel Baena 65 of 86 26 August 2010
Figure 37. Triangulation of the arc
The next improvement in order to increase the torsional stiffness and once the mid-
rear 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.
X Bars behind the driver
José Manuel Baena 66 of 86 26 August 2010
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.
Carbon fibre plate
José Manuel Baena 67 of 86 26 August 2010
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.
X Bars at the rear
José Manuel Baena 68 of 86 26 August 2010
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.
José Manuel Baena 69 of 86 26 August 2010
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
José Manuel Baena 72 of 86 26 August 2010
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.
José Manuel Baena 73 of 86 26 August 2010
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.
José Manuel Baena 74 of 86 26 August 2010
• 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.
José Manuel Baena 75 of 86 26 August 2010
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=DLFE-
2201.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 0-8376-0142-
8.
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
José Manuel Baena 79 of 86 26 August 2010
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
José Manuel Baena 82 of 86 26 August 2010
D) Section Types Plots
SECTION ID 1DATA SUMMARY
Section Name =Area = .172E-03Iyy = .286E-07Iyz = 0Izz = .286E-07Warping Constant = 0Torsion Constant = .573E-07Centroid Y = -.385E-18Centroid Z = -.173E-17Shear Center Y = .361E-18Shear Center Z = .915E-18Shear Corr. YY = .500895Shear Corr. YZ = -.214E-13Shear Corr. ZZ = .500895
1
-.019
-.0095
0
.0095
.019
-.019 -.0095 0 .0095 .019
= Centroid = ShearCenter
SECTION ID 2DATA SUMMARY
Section Name =Area = .115E-03Iyy = .868E-08Iyz = 0Izz = .868E-08Warping Constant = 0Torsion Constant = .174E-07Centroid Y = .516E-18Centroid Z = .315E-18Shear Center Y = -.669E-18Shear Center Z = -.286E-18Shear Corr. YY = .502608Shear Corr. YZ = -.373E-13Shear Corr. ZZ = .502608
1
-.013
-.0065
0
.0065
.013
-.013 -.0065 0 .0065 .013
= Centroid = ShearCenter
José Manuel Baena 83 of 86 26 August 2010
SECTION ID 3DATA SUMMARY
Section Name =Area = .219E-03Iyy = .487E-07Iyz = 0Izz = .487E-07Warping Constant = .104E-13Torsion Constant = .752E-07Centroid Y = .019Centroid Z = .019Shear Center Y = .019Shear Center Z = .019Shear Corr. YY = .430927Shear Corr. YZ = -.888E-13Shear Corr. ZZ = .430927
1
0
.0095
.019
.0285
.038
0 .0095 .019 .0285 .038
= Centroid = ShearCenter
SECTION ID 4DATA SUMMARY
Section Name =Area = .147E-03Iyy = .148E-07Iyz = 0Izz = .148E-07Warping Constant = .263E-14Torsion Constant = .230E-07Centroid Y = .013Centroid Z = .013Shear Center Y = .013Shear Center Z = .013Shear Corr. YY = .437044Shear Corr. YZ = .624E-13Shear Corr. ZZ = .437044
1
0
.0065
.013
.0195
.026
0 .0065 .013 .0195 .026
= Centroid = ShearCenter
José Manuel Baena 84 of 86 26 August 2010
SECTION ID 5DATA SUMMARY
Section Name =Area = .165E-03Iyy = .110E-07Iyz = 0Izz = .307E-07Warping Constant = .198E-12Torsion Constant = .258E-07Centroid Y = .019Centroid Z = .01Shear Center Y = .019Shear Center Z = .01Shear Corr. YY = .622074Shear Corr. YZ = .104E-13Shear Corr. ZZ = .242112
1
0
.005
.01
.015
.02
0 .0095 .019 .0285 .038
= Centroid = ShearCenter
José Manuel Baena 85 of 86 26 August 2010
E) Characterisation of the plates
node displacement(m) ANSYStorsional stiffness Nm/deg 260 -4,20E-04277 4,14E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -4,02E-04277 3,95E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -3,40E-04277 3,34E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -3,39E-04277 3,34E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -3,35E-04277 3,30E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -3,30E-04277 3,24E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -3,19E-04277 3,13E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -2,92E-04277 2,87E-04node displacement(m) ANSYStorsional stiffness Nm/deg 260 -2,90E-04277 2,86E-04
3,356E+03
3,477E+03
9 3,813E+03
1 2,631E+03
2 2,755E+03
3,262E+03
3,795E+03
345678
3,265E+03
3,305E+03
1 2
José Manuel Baena 86 of 86 26 August 2010
END OF DOCUMENT
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