ES410 Report

Technical Report
1111585 1213744 1220902 1220258 1218923 1219529
FS Chassis: The Research, Design and
Development of the FSAE Electric Prototype
WRe

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Table of Contents
Table of Figures ........................................................................................................................vi
Table of Tables........................................................................................................................... x
Acknowledgements ...................................................................................................................xi
Declaration ...............................................................................................................................xii
Abstract ...................................................................................................................................xiii
1 Introduction ........................................................................................................................ 1
1.1 Electric Powertrains..................................................................................................... 2
1.2 Tractive System Component Selection........................................................................ 3
1.2.1 Inverters................................................................................................................ 3
1.2.2 Motors .................................................................................................................. 4
1.2.3 Battery Pack ......................................................................................................... 5
1.3 Characteristic Differences from Internal Combustion................................................. 5
2 Packaging the System......................................................................................................... 6
2.1 Powertrain Housing..................................................................................................... 6
2.2 Rear Bulkhead ............................................................................................................. 7
2.2.1 Benchmarking ...................................................................................................... 7
2.2.2 Design Considerations.......................................................................................... 9
2.3 Completing the Cradle............................................................................................... 11
2.4 Spaceframe Conceptual Design................................................................................. 11
3 Load Case Calculation ..................................................................................................... 15
3.1 Tyre Data................................................................................................................... 15
3.2 Chassis Loads ............................................................................................................ 16
3.2.1 Load Scenarios ................................................................................................... 16
3.2.2 Cornering............................................................................................................ 18
3.2.3 Braking............................................................................................................... 19

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3.2.4 Bump .................................................................................................................. 20
3.2.5 Combining Scenarios ......................................................................................... 20
3.2.6 Forces at Each Tyre............................................................................................ 20
3.2.7 Calculating the Force Applied By Individual Suspension Members ................. 21
3.2.8 Calculating the Force at Chassis Mounting Points............................................. 22
3.2.9 Improvement of this Approach .......................................................................... 22
3.3 Powertrain Calculations............................................................................................. 23
4 Design Methodology........................................................................................................ 24
4.1 Computer Aided Design ............................................................................................ 24
4.2 Meshing ..................................................................................................................... 24
4.3 Finite Element Analysis............................................................................................. 26
4.4 Topology Optimisation.............................................................................................. 27
5 Powertrain Cradle............................................................................................................. 27
6 Bulkhead........................................................................................................................... 31
6.1 Design Intent.............................................................................................................. 31
6.2 Initial Design ............................................................................................................. 32
6.3 Initial Verification ..................................................................................................... 33
6.4 Weight Optimisation (FEA) ...................................................................................... 33
6.5 FEA Results............................................................................................................... 34
6.6 Topology Optimisation.............................................................................................. 35
6.7 Final Design............................................................................................................... 36
6.8 Final Simulations....................................................................................................... 37
6.9 Assembled Rear Cradle, Driveline and Motors......................................................... 38
7 Spaceframe Design........................................................................................................... 38
7.1 Design Mentality ....................................................................................................... 38
7.2 Member Selection and Modes of Failure .................................................................. 40
7.3 Spaceframe Geometry and Frame Analysis .............................................................. 44

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7.4 Final Simulations....................................................................................................... 47
8 Controlling the Electrical Systems................................................................................... 48
8.1 Vehicle System Controller (VSC) ............................................................................. 48
8.1.1 Other options considered.................................................................................... 49
8.1.2 FPGA vs RT....................................................................................................... 49
8.1.3 Additional VSC Features ................................................................................... 50
9 Tractive System................................................................................................................ 51
9.1 Ashwoods ELMO-S112 Motor ................................................................................. 51
9.1.1 Encoder Converter.............................................................................................. 51
9.2 Sevcon Gen4, Size 4, 72V Inverter ........................................................................... 53
9.2.1 Configuration ..................................................................................................... 53
9.3 Potenza Lithium Iron Phosphate Battery................................................................... 53
10 GLV System..................................................................................................................... 54
10.1 Shutdown Circuit ................................................................................................... 54
10.1.1 Brake System Plausibility Device (BSPD) ........................................................ 55
10.2 Human Interface..................................................................................................... 55
10.2.1 Pedal Box ........................................................................................................... 55
10.2.2 Dashboard........................................................................................................... 55
11 Wiring, Signals and Communication ............................................................................... 55
11.1 CAN bus between VSC, Sevcons and Battery....................................................... 55
11.2 Galvanic Isolation Module..................................................................................... 56
11.2.1 Control Signals and UVW Encoder Signals (Low Frequency).......................... 56
11.2.2 CAN Bus (High Frequency)............................................................................... 56
11.2.3 Analogue Signals................................................................................................ 57
12 Start Up Sequence ............................................................................................................ 57
13 Performance Optimisation................................................................................................ 57
13.1 Results.................................................................................................................... 59

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14 Cooling Model for WRe................................................................................................... 59
14.1 Motor Cooling........................................................................................................ 60
14.2 Inverter Cooling..................................................................................................... 60
14.3 Radiators ................................................................................................................ 61
14.4 Conclusion ............................................................................................................. 62
15 Project Costings................................................................................................................ 62
16 Conclusions...................................................................................................................... 63
17 Recommendation for Further Work ................................................................................. 64
References ................................................................................................................................ 65
Glossary.................................................................................................................................... 71
Appendices............................................................................................................................... 73
Appendix A. Load Cases.......................................................................................................... 73
Appendix B. Motor Mount Forces ........................................................................................... 78
Appendix C. Meshing .............................................................................................................. 79
Appendix D. Topology Optimisation....................................................................................... 81
Appendix E. Motor Mount FEA Iteration Design Process ...................................................... 89
Appendix F. Bulkhead FEA Iteration Design Process............................................................. 92
Appendix G. Engineering Drawings ........................................................................................ 96
Appendix H. Spaceframe Chassis Analysis ............................................................................. 99
Appendix I. Full Spaceframe Dynamic Model ...................................................................... 115
Appendix J. Full Spaceframe Crash Simulation Load Cases................................................. 118
Appendix K. Motor Mount Manufacture.................................................................................119
Appendix L. Spaceframe Manufacture and Assembly........................................................... 122
Appendix M. Inverter Comparison Matrix ............................................................................ 129
Appendix N. Encoder Converter Implementation on the MyRIO FPGA.............................. 129
Appendix O. Sevcon Electrical Connections ......................................................................... 131
Appendix P. Brake System Plausibility Device..................................................................... 132

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Appendix Q. VSC Start-up Sequence .................................................................................... 133
Appendix R. VSC Software ................................................................................................... 134
Appendix S. Tyre Data Acquisition and Processing.............................................................. 138
Appendix T. Steady-State Simulator...................................................................................... 146
Appendix U. Simulink Model ................................................................................................ 150
Appendix V. Simulink Validation.......................................................................................... 153
Appendix W. Cooling System................................................................................................ 155
Appendix X. Category Costing.............................................................................................. 159
Appendix Y. Full Car Renders.................................................................................................167

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Table of Figures
Figure 1. Key tractive system components. ............................................................................... 2
Figure 2. Comparison of common electric drive architectures. ................................................. 2
Figure 3. Sevcon Gen4 AC Motor Controller............................................................................ 3
Figure 4. Two candidate motors: Left: Motenergy ME115 (axial flux). Right: Ashwoods ELMO
S112 (radial flux). ...................................................................................................................... 4
Figure 5. Torque curve comparison between WR-5 and WRe .................................................. 5
Figure 6. Comparison of motor packaging: (Left) hub mounted on “Grimsel” (Right) In board
motors on “Umbrail.” (AMZ, 2015) .......................................................................................... 6
Figure 7. Packaging chosen for WRe, the motor cradle............................................................. 7
Figure 8 L: Bulkhead from the MUR13 (MUR Motosports, 2013). R: The bulkhead assembled
on the MUR13 (MUR Motorsports, 2013)................................................................................. 7
Figure 9. Bulkhead assembly of the TBR14 (Team Bath Racing, 2014)................................... 8
Figure 10. Bulkhead used on the Monash Motorsports team from 2005 (Monash Motorsport,
2016)........................................................................................................................................... 8
Figure 11. The drivetrain layout of the WR3 (Team WR4, 2014)............................................. 9
Figure 12. WR3 damper-rocker mounts (Team WR4, 2014) .................................................... 9
Figure 13. Difference in chassis tube mounting positions. ...................................................... 10
Figure 14. Initial Non-optimised Rear Cradle Assembly......................................................... 10
Figure 15. Umicore Luna's Carbon Monocoque Chassis (Left) (Umicore Luna, 2014-2015),
Dalhousie University's Tubular Spaceframe (Right) (Carrodus, 2014). .................................. 11
Figure 16 AMZ Racing's 'Julier Drivetrain' - Battery and Invertor Package stored in rear of car.
(Huber, 2014) ........................................................................................................................... 12
Figure 17. AMZ Racing ‘Furka’ Concept, Battery and Invertor Package stored in sidepods.
(Thrainer, 2008) ....................................................................................................................... 13
Figure 18. Stuba Green Teams' Integrated Battery Box stored beneath driver (Benkovský, 2010)
.................................................................................................................................................. 14
Figure 19. WR5's bulkhead (left) WRe bulkhead billet (right); manipulating trigonometry to
confirm suspension bracket coordinates .................................................................................. 15
Figure 20. graph displaying the longitudinal force produced by the tyre at different slip ratios.
.................................................................................................................................................. 16
Figure 21. Coordinate System Used (Kemna, 2011) ............................................................... 17

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Figure 22. Lateral Force Against Slip Angle for Several Reaction Forces (Adapted from
Kasprzak & Gemtz (Kasprzak & Gentz, 2006)........................................................................ 19
Figure 23. Friction Circle for Tyre Forces (Ramani, 2006)..................................................... 20
Figure 24. Graphs showing the effect the number of nodes has on a simulation: (Left) Max
Stress vs No. Nodes (Right) Displacement vs No. Nodes. ...................................................... 25
Figure 25. Comparison meshes: (Left) Structured (Right) Unstructured................................. 25
Figure 26. FEA Design process. (C.T.Shaw, 1996)................................................................. 26
Figure 27. Comparison of analyses: (Left) Non-linear analysis (Right) Linear analysis ........ 26
Figure 28.An example of the possible design process using topology optimisation. (Left) Un-
optimised part; (Middle) Suggested material by algorithm; (Right) Optimised part.
(Triantaphyllou, 2015) ............................................................................................................. 27
Figure 29. Un-optimised powertrain cradle. ............................................................................ 28
Figure 30. Topology optimisation output without un-optimisable regions.............................. 28
Figure 31. Topology models: (Left) Before simulation (Middle) 0.4 Mass fraction output
(Right) 0.25 Mass fraction output. ........................................................................................... 28
Figure 32. FEA reduction process: (Left) Initial geometry (Middle) 1st
iteration (Right) 8th
iteration..................................................................................................................................... 29
Figure 33. Graphic representation of the change in displacement under motor forces through
the motor mount iterations. ...................................................................................................... 30
Figure 34. Motor mount final model: (Top) 3/4 view render. (Bottom) Von Mises result from
linear Nastran analysis. ............................................................................................................ 30
Figure 35. Render of the forward bulkhead ............................................................................. 31
Figure 36. Comparison of the WR5 bulkhead with that of WRe............................................ 32
Figure 37. L: The bulkhead with mounting point for ancillaries and mock-up of the sprocket
dimensions; R: Complete initial bulkhead design................................................................... 32
Figure 38. Motor torque validation on the initial bulkhead (exaggerated distortion). L:
Maximum Displacement: 0.09 mm R: Maximum Stress: 16.48 MPa ..................................... 33
Figure 39. Progressively light-weighted iterations of the bulkhead......................................... 34
Figure 40. FEA to verify the displacement of the iterations under the torque from the motors
.................................................................................................................................................. 34
Figure 41. Progression of topology optimisation. Left to Right: 100%, 51% and 34% of initial
mass.......................................................................................................................................... 35
Figure 42. Topology optimisation of the bulkhead. L to R: 3G Bump, Pure Braking, Pure
Cornering and All Forces ......................................................................................................... 35

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Figure 43. Superimposed images of the topology optimised bulkheads under the various
scenarios L to R: Front and Rear.............................................................................................. 36
Figure 44. Final weight-optimised bulkhead design ................................................................ 36
Figure 45. FEA to verify the displacement of the iterations under different scenarios. Left to
Right: Motor Forces, 3G Bump & Motors, Pure Cornering and Pure Braking. ...................... 37
Figure 46. Graphic representation of the change in displacement under motor forces through
the bulkhead iterations. ............................................................................................................ 37
Figure 47. WRe powertrain and cradle assembly. ................................................................... 38
Figure 48. Radar Chart displaying design considerations for current race vehicles................ 39
Figure 49. WRe chassis with labelled diction.......................................................................... 39
Figure 50. Essential rules dictating the design of the rear spaceframe. ................................... 40
Figure 51 Instron tensile testing welded ChroMoly 4130 tubing (Coveney, et al., 2015)....... 40
Figure 52. Testing results for 4130 ChroMoly steel (Coveney, et al., 2015)........................... 40
Figure 53. Previous WR5 tubular tensile testing for 4130 ChroMoly steel and 1010 steel tubing
(Coveney, et al., 2015). ............................................................................................................ 41
Figure 54. Torsional shear deformation in a cylinder (Negahban, 2000) ................................ 42
Figure 55. Torsional force acting on the chassis...................................................................... 42
Figure 56. Normal shear stress................................................................................................. 43
Figure 57. (Left to right): Strain energy from thin, medium and thick tubes for safety-critical
frame members under motor loading)...................................................................................... 45
Figure 58. Frame member designation, thick tubes (left), medium tubes (middle) and thin tubes
(right)........................................................................................................................................ 45
Figure 59. Torsional validation for full spaceframe, full displacement at 4.065mm............... 47
Figure 60. Side impact validation for full spaceframe, maximum displacement at 19.98mm.
.................................................................................................................................................. 47
Figure 61. Full Dynamic Simulation type: Displacement (mm), maximum displayed
displacement of 11.21mm. ....................................................................................................... 47
Figure 62. Breakdown of the electrical system........................................................................ 48
Figure 63. Block level diagram of the WRe electrical system................................................. 48
Figure 64: VSC Diagram.......................................................................................................... 49
Figure 65. VSC package design ............................................................................................... 49
Figure 66. Comparison between FPGA and RT processors on the MyRIO. ........................... 50
Figure 67. WRe tractive system diagram................................................................................. 51
Figure 68. Required relationship between sin/cos encoder signal and UVW encoder signals.52

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Figure 69. Resulting input and output waveforms of the encoder converter. .......................... 52
Figure 70. GLVS system level diagram................................................................................... 54
Figure 71. Re-routing the CAN signals past the isolation barrier............................................ 56
Figure 72. Bruntingthorpe Go-kart Tack Map (Google Maps, 2015)...................................... 58
Figure 73. Simulink model block diagram............................................................................... 58
Figure 74. Velocity against time for various vehicle masses................................................... 59
Figure 75. Change in Current Output Against Temperature For the Sevcon Gen 4................ 60
Figure 76. Cooling simulation model for WRe powertrain ..................................................... 61

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Table of Tables
Table 1. Vehicle Centre of Gravity.......................................................................................... 17
Table 2. Weight at Each Wheel While Cornering.................................................................... 18
Table 3. Tyre forces at contact patch. ...................................................................................... 21
Table 4. Summary of simulations to verify the performance of the iterations under the torque
from the motors........................................................................................................................ 35
Table 5. Summary of simulations to verify the performance of final weight-optimised
bulkhead under various load scenarios..................................................................................... 37
Table 6. ChroMoly steel tube nomenclature ............................................................................ 41
Table 7. Torsional test for the 4130 ChroMoly tubes. ............................................................. 43
Table 8. Shear stress results. .................................................................................................... 44
Table 9. Developing the rear space frame................................................................................ 46
Table 10 -GLV system’s largest power draws......................................................................... 54
Table 11. The characteristics of air and water cooled motors.................................................. 60
Table 12. Inverter temperature results for one or two radiators............................................... 62
Table 13. Categorised costing for WRe ................................................................................... 62

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Acknowledgements
The completion of this project was due various supporters, and therefore the individuals
involved recognise and gratefully thank the input from the following parties:
 Mr Howard Neal, Project Supervisor
 Mr David Cooper, Technical Advisor
 Professor David Greenwood, Advanced Propulsion Centre
 Warwick Racing
 Warwick Manufacturing Group
 Potenza Technology
 GRM Consulting
 AquaJet Profiles
 Baileigh Industrial
 RS Components
 Santander

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Declaration
We, the undersigned, hereby declare the project entitled “FS Chassis: The Research, Design
and Development of the FSAE Electric Prototype WRe” submitted to the University of
Warwick, is a record of the original work done under the guidance of Mr Howard Neal,
Warwick Manufacturing Group, and this project work is submitted in the partial fulfilment of
the requirements for the award of the degree of Masters of Engineering. The results embodied
in this thesis have not been submitted to any other University or Institute for the award of any
other degree or diploma.
Aditya Gupta
Araan Mohanadass
Brandon Soutter
Nick Emery
Laurence Parkins
Matt Dent

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Abstract
This report ascertains the requirements for developing an electric Formula Student FSAE
electric race vehicle, WRe. This prototype was to be developed from donor chassis WR5, the
competition vehicle for the 2015 Formula Student season. Focus is drawn towards the
recognition of design changes deemed necessary to implement a prototype vehicle, with the
desired intent to compete in future years.
Preliminary research was performed to characterise the powertrain system, which was
developed to pioneer the foundation for future research, and to set the design mentality. Further
chassis design is oriented around the powertrain.
The development of the powertrain dictated initial chassis concepts, as packaging for the new
system were detrimental to project success. Through extensive analysis of leading electric
FSAE teams it was possible to benchmark initial concept designs for both the chassis and an
innovative powertrain cradle.
To increase the accuracy and reliability of the design work, it was deemed essential to
consolidate a series of four load scenarios that represent a realistic racing environment. These
scenarios were braking, cornering, bump and a final worst case event whereby all scenarios
occurred at once. Tire Testing Consortium data was further utilised to strengthen the
understanding of vehicular behaviour under certain loading conditions.
The forces from the racing environment directly influenced the design for various chassis and
powertrain packaging components, and this project focused on three primary components: an
innovative motor cradling assembly, the rear bulkhead and the tubular spaceframe. Various
software tools were considered for the use of CAD, FEA and topology optimisation. The aim
was to introduce the new components to be fit for purpose, maintaining strength yet adhering
to weight reduction where possible.
The final focus for the project was to confirm all theoretical expectations through the use of a
lap simulator, which would accurately represent the testing of WRe at Bruntingthorpe race
circuit. The program would allow for the variation of inputs such as radiator and cooling jacket
sizes for performance optimisation, and would provide an understanding for vehicular
behaviour.
To conclude, the project saw the creation of a prototype vehicle which houses a bespoke electric
powertrain system, packaged within a modified chassis that provides improved performance
under the calculated loading conditions compared to WR5. The use of the lap simulator allowed
for academic judgements to be made considering the performance likelihood, and the
foundation for a future electric Formula Student entry was laid.

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1 Introduction
The Formula Student competition, organised by the Formula Society for Automotive Engineers
(FSAE), offers a single seated, open-wheeled amateur race series, whereby groups of students
around the globe partake in the sponsorship, design, manufacture and assembly of a competitive
vehicle. Warwick Racing is the University of Warwick’s Formula Student team, and has
participated in the competition since 2002 with an Internal Combustion entrant (Warwick
Racing, 2016).
In recent years, it has become apparent that teams boasting an electric powertrain exhibit more
advantageous characteristics than the gasoline counterpart, and as such, an exploration into the
field should provide tangible benefits. This report aims to manipulate a powertrain oriented
methodology, whereby the chosen system will dictate the design of the surrounding
components, leading to the foundation for an electric Formula Student prototype.
The Formula Student competition is bound by a series of rules, and therefore the approach for
the creation of an electric prototype will be governed by such guidelines. Other considerations
will assume safety a top priority, as the introduction of electric systems is a relative unknown
to Warwick Racing, and furthermore adopt a competitive mentality, enhancing performance
and manipulating weight reduction where possible.
The electric prototype will be utilised to develop the technology to provide a competitive
advantage, with the hopes to provide the necessary tools to enter an electric Formula Student
vehicle into competition within the near future.

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1.1 Electric Powertrains
The powertrain and associated electrical systems were developed in accordance with the FSAE
rules and supporting documentation, which provide a solid and safe framework to work from.
According to the guidelines, the car’s electrical system should be considered in two parts:
 Tractive system: The high voltage system delivering power to the motors. Comprises of
all points with an electrical connection to the accumulator.
 Grounded Low Voltage System (GLVS): The control system and any human interface
electronics.
A typical FS tractive system contains three key components:
Figure 1. Key tractive system components.
The accumulator is typically a battery, utilizing Li-ion chemical cell technology to provide DC
current. An inverter, one per motor, takes the DC current and uses a transistor switching
arrangement to convert this to three phases (3Ø) of AC current. The AC current excites the pole
pairs of the motor’s stator, driving the rotor which is mechanically coupled to the wheels.
At this point, the number of motors and the mechanical drivetrain architecture through which
they deliver power must be defined by the team, see Figure 2. The tractive system and drivetrain
together make up the powertrain.
Figure 2. Comparison of common electric drive architectures.
DC
Power
Accumulator
3Ø AC
Power
Inverter
Mechanical
Torque
PMAC
Motor
A B C D
Complexity

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The most basic of electric drive architectures is a single motor, acting on a fixed rear axle (A).
To increase traction during cornering, a team could add a mechanical differential (B) – an
architecture which is very similar to a classic IC based RWD powertrain in a road car. For more
control over vehicle dynamics, a team could add a second motor, and drive the two wheels
separately (C). Finally, for maximum traction and dynamic control, each wheel can be driven
by an independent motor (D).
Recent FS results have shown that independent AWD (D) gives the best performance (the top
3 electric cars at FSUK 2015 featured this architecture), primarily because it offers the ability
to develop powerful electronic traction and driver aids. Non-pro drivers in FS benefit greatly
from this.
However, because of the prohibitive initial cost of four motors, the decision was made to use
independent rear wheel drive (C), which is a very similar architecture from a control systems
perspective. Consequently, the framework presented here can be built upon in future years
without having to make any changes to the fundamentals. For example, torque vectoring works
in a very similar manner for both independent RWD and AWD.
1.2 Tractive System Component Selection
As a prototype, flexibility is the primary driver for most of WRE’s component selections. It
must be possible to modify powertrain characteristics quickly and easily as the vehicle takes
shape.
Most of the tractive system flexibility in an electric car is dictated by the inverters, because they
have the most interactions with the rest of the system. They were therefore the first of the three
main components to be decided upon. Next, motors were selected to match the inverter voltage.
Finally, the battery specification can be defined.
1.2.1 Inverters
A variety of candidate inverters were identified, based
on: range of features, physical and electrical
characteristics, and performance. A comparison matrix
can be found in Appendix M; from which it was
concluded that the Sevcon Gen4 is the most suitable
choice. It hosts a broad range of integrated features to
streamline tractive system development (such as pre- Figure 3. Sevcon Gen4 AC Motor Controller.

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charge circuitry to prevent inrush currents when the system is activated), while also offering
relatively good electrical and thermal performance in a convenient physical package.
Once the requirements of the powertrain are better understood, it may be possible to develop
an inverter in-house. However, the ability to experiment with a range of features in these early
stages is more important than a minimalistic, optimised design for this test vehicle.
Four voltage configurations for the Gen4 exist, from 24-36V to 96-120V. The higher the
tractive voltage, the more efficient the system, because ‘copper losses’ are reduced. Copper loss
is power P dissipated in the cables and stator windings, and is related to resistance R and current
I in the system by P=I^2
R. Therefore, a high tractive voltage (which requires correspondingly
less current) wastes exponentially less power than a low one. Unfortunately, the 96-120V Gen4
was unavailable, so the 72-80V version was chosen instead.
1.2.2 Motors
After the tractive system voltage had been determined, there remained two candidate pairs of
motors available to us. We had to make a fundamental choice between radial and axial flux
motors (known colloquially as ‘cylinder’ and ‘pancake’ respectively, indicating their shape, see
Figure 4). There is a strict width constraint at the rear of the car, so we decided on the axial flux
motors because it would be possible to mount them with their axes inline. This improves weight
and force balance in the rear of the car.
All brushless motors must feed their position back to the inverter, so that phase currents can be
commutated. The Ashwoods motor (unlike the Motenergy) outputs an analogue feedback
signal, so additional signal conditioning is required to interface with the Sevcon (which only
accepts digital encoder outputs for position feedback). This process is described in Section
5.1.1.
Figure 4. Two candidate motors: Left: Motenergy ME115 (axial flux). Right: Ashwoods ELMO S112 (radial flux).

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1.2.3 Battery Pack
The battery has far fewer system interactions than the other powertrain components, so design
changes have minimal knock on effects. Thus, to avoid unnecessarily broadening the scope of
the project, it was decided that the battery be sourced as a ‘black box’ unit from Potenza
Technology. Discussions were held early in the project to establish the key requirements of the
battery system. It was not discovered until later in the project that the 96-120V Sevcon Gen4
was unavailable, so the battery was designed to the higher voltage. Fortunately, the pack’s
voltage range of 80V – 116.8V is still within the 72-80V Gen4’s operating range.
As the project progressed we collaborated with Potenza Technology on the external form and
dimensions of the pack to integrate it into our chassis.
1.3 Characteristic Differences from Internal Combustion
PMAC motors are capable of delivering full torque at very low rotational speeds, as low as 0
RPM. This lends them well to the low speed corners of a FS track, as it enables the car to “burst”
from corner to corner along the short straights.
IC engines deliver their useful torque over a much smaller RPM range, so a gearbox is used,
allowing discrete ratios of speed and torque to be selected. Figure 5 shows the torque at the
wheels from the KTM 450 SX-F versus the electric powertrain.
Figure 5. Torque curve comparison between WR-5 and WRe
From a drivability perspective, the electric system makes it much easier for the driver to
smoothly apply power whilst exiting a corner. This is important because large torque impulses,
as experienced during non-ideal gear shifts, may cause the tyres to lose traction and the car to

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spin out of control. Therefore, whilst the magnitude of torque available is slightly smaller, the
nature of its delivery is much better suited to racing.
2 Packaging the System
2.1 Powertrain Housing
The FSAE rules allow two primary methods of propulsion system: internal combustion engines
and electrical power systems. (SAE International, 2014). As past Warwick Racing teams have
only produced internal combustion engine vehicles, the design and manufacture of an
electrically propelled vehicle this year produced a number of unique challenges. One important
consideration is the packaging of the motors that propel the vehicle.
Research into Formula Student competitors that have produced electrically powered vehicles
shows the diversity in packaging methods, with the type and number of motors considerably
changing the packaging method. Figure 6 compares AMZ racing’s “Grimzel”, which uses four
hub mounted motors, to the “Umbrail,”, powered by two in-board motors. It is clear that hub
mounted motors increase the available space at the rear for the other components. The
disadvantage of hub mounted motors are their added cost and increased un-sprung mass
(Formula 1 Dictionary, 2016).
Figure 6. Comparison of motor packaging: (Left) hub mounted on “Grimsel” (Right) In board motors on “Umbrail.” (AMZ,
2015)

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Due to the implementation of two inboard
Ashwoods ELMO-S motors, the packaging shares
some characteristics with “Umbrail.” A
spaceframe is used in place of the monocoque on
“Umbrail”, resulting in greater packaging space
limitations. Similar to “Umbrail”, the motors are
packaged side by side. To adapt this concept for a
spaceframe a rear cradle was designed. This
allows both easy access to the motors for
maintenance purposes and a strong support for the motors during peak torque output. Figure 7
shows the packaging of the motors in the rear cradle assembly.
2.2 Rear Bulkhead
2.2.1 Benchmarking
The rear bulkhead is an integral part of the WRe chassis as all the suspension, powertrain and
driveline components attach to it. As a result, the bulkhead must support the rear weight of the
car and withstand the torsional and dynamic forces provided by the motors and spaceframe
under racing conditions. In this instance, the bulkhead will be manufactured from a 25.4mm
thick billet of Aluminium 7075
Figure 8 L: Bulkhead from the MUR13 (MUR Motosports, 2013). R: The bulkhead assembled on the MUR13 (MUR
Motorsports, 2013)
The Warwick Racing Formula Student vehicles utilise the same rear bulkhead design, with no
change from WR4 (2014) to WR6 (2016). A number of teams have fabricated similar bulkhead
structures for their FSAE entries. For example, the University of Melbourne MUR Motorsport
team used a bulkhead made from Aluminium billet on their MUR13 car (MUR Motosports,
2013). As seen in Figure 8, the suspension uprights, wishbones, sprocket, differential and
Figure 7. Packaging chosen for WRe, the motor cradle

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driveline of the car are accommodated. Substantial weight optimisation is observed by the
removal of excess material.
Team Bath Racing also adopted a bulkhead in their TRB14 chassis design. Similar to the
aforementioned bulkhead, suspension and drivetrain ancillaries are attached. The bulkhead
structure however incorporates aluminium honey comb and a carbon-fibre shell for rigidity
(Team Bath Racing, 2015). This is depicted in Figure 9109.
In Figure 10, Monash Motorsports have integrated their rear braking system into the differential
assembly on the bulkhead instead of the wheel hubs. This reduces the unsprung mass at the
wheel hub, improving the handling and stability of the car (Formula 1 Dictionary, 2016). Hence
it can be concluded that the bulkhead plays a key role in the overall design direction of the
chassis and dynamics of an FSAE car.
To build upon previous chassis, work prior Warwick Racing bulkhead designs have been
studied. For instance, the WR3 bulkhead design affected a number of crucial performance
factors (Team WR4, 2014). The layout of the drivetrain, depicted in Figure 11, caused the
bulkhead to buckle as the chain tension and resultant bending moment were inaccurately
considered. As a result, a 3mm plate of steel was welded on to the bulkhead as reinforcement,
incurring a weight penalty.
Figure 910. Bulkhead assembly of the TBR14 (Team
Bath Racing, 2014)
Figure 10. Bulkhead used on the Monash Motorsports
team from 2005 (Monash Motorsport, 2016)
9.
9.

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Figure 11. The drivetrain layout of the WR3 (Team WR4, 2014).
Furthermore, key suspension rocker brackets were welded to the frame (Team WR4, 2014).
The asymmetry of these welds resulted in poorly aligned suspension, summarised by Figure 12.
This adversely affected the dynamics and adjustability of the WR3 suspension system,
providing an additional design consideration for the integration of the WRe bulkhead with the
suspension system.
Figure 12. WR3 damper-rocker mounts (Team WR4, 2014)
2.2.2 Design Considerations
Introducing a cradle design for housing the new powertrain warranted the redesign of the main
rear bulkhead. The first change being the repositioning of the chassis mounting points on the
bulkhead. In order to adapt the cradle, the rear spaceframe structure was widened; this
difference in geometry is depicted in Figure 13. Consequently, this defined the dimensions of
the new bulkhead, used as the basis of the forthcoming design.

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Figure 13. Difference in chassis tube mounting positions.
As the electric powertrain requires two large sprockets instead of the single chain drive of an
IC powertrain, two large cut-outs within the bulkhead are required. This poses a risk of
substantially reducing the stiffness of the entire bulkhead. Additionally, the bulkhead needs to
withstand 4 times the torque, 120 Nm, from the motors compared to 40 Nm of torque from the
IC engine. The design challenge and proposed solution is discussed in Section 6.
It was decided that the suspension set up would be carried over from the WR5, hence the
mounting points for components would remain virtually the same. The geometries were
measured manually from the previous bulkhead, then verified and updated in CAD. Minor
changes were required to incorporate the brackets for the suspension uprights, however this will
be discussed in Section 2.4.
Figure 14. Initial Non-optimised Rear Cradle Assembly

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In addition to driveline components, the motor mount assembly also attaches to the bulkhead
as depicted in Figure 14. Bulkhead robustness is therefore more critical as it acts as the
backbone for the entire vehicle. A thorough design methodology was followed to achieve the
optimal bulkhead design, reducing weight for performance advantage. This is detailed later in
the report.
2.3 Completing the Cradle
Completion of the cradle assembly required a support further forward in the car. Previously, for
the internal combustion vehicle, this was achieved using a bracket welded to the base member
of the main roll hoop. The combined peak torque of two motors would provide a force three
times that of the internal combustion engine on the bracket, causing failure. The chosen solution
is a 5mm sheet of mild steel welded to the inside of the main roll hoop with machined holes for
the motor mounts to attach to, referred to throughout this report as the forward bulkhead. The
cradle is shown in Figure 14.
The chosen solution is a 5mm sheet of mild steel welded to the inside of the main roll hoop
with holes for the motor mounts to attach to, as can be seen in Figure 7.
2.4 Spaceframe Conceptual Design
The main structure of any vehicle is provided by its chassis. With regards to the Formula
Student competition, few distinctive chassis configurations are seen: the tubular spaceframe,
the composite Carbon-Fibre-Reinforced-Polymer (CFRP) monocoque, and a hybrid of the two.
Figure 15. Umicore Luna's Carbon Monocoque Chassis (Left) (Umicore Luna, 2014-2015), Dalhousie University's Tubular
Spaceframe (Right) (Carrodus, 2014).

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Within the confines of FSAE regulations, the monocoque structure is considered favourable as
the fibrous layup of the composite provides a lightweight structure that maintains the optimal
strength and energy dissipation characteristics of a tubular spaceframe (Davies, et al., 2011).
Another advantage of the monocoque structure is in the packaging of ancillaries. As it is less
constrained by geometric packaging, the structure acting as a ‘supportive skin’ allows engineers
to form-fit vehicular components into the optimal locations, and within reason, design the load-
bearing skin around the structure.
The tubular spaceframe, although heavier and more limiting in terms of packaging than the
monocoque structure (Davies, et al., 2011), offers decreased design complexity and
manufacture. Historically, Warwick Racing have produced race vehicles using a ChroMoly
4130 tubular chassis, wih all tools required for manufacture being available in-house.
Warwick Racing’s previous competition entrants were powered using a KTM 450cc engine,
whereas the aim for this project is to adapt the rear structure of WR5 to house an electric
powertrain. The new drivetrain consists of two motors, making adjustment of the rear
spaceframe geometry necessary allow for the increased width of the powertrain package.
The next consideration was the battery system packaging. Research into FSAE Electric teams
revealed three prospective solutions to battery storage:
1. Stored within the rear of the car
2. Stored within sidepods either side of the car
3. Stored beneath the driver/integral part of the seating arrangement
Each solution has associated benefits and these are evaluated to decide upon an approach for
this project.
The first example considered is the
inboard, rear mounted, battery
management system. This method is
typical for hub-mounted motor drive
systems, as seen in AMZ’s ‘Julier
Drivetrain’ in Figure 16. This system
allows the greatest packaging space,
as motors occupy volume within the
unsprung mass of the vehicle. Figure 16 AMZ Racing's 'Julier Drivetrain' - Battery and Invertor
Package stored in rear of car. (Huber, 2014)

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Although the relocation of large components allows room for a larger battery-cell, the increased
sprung mass can adversely affect performance through greater force feedback in a bump
scenario. Thus reducing the tyre contact patch and increasing wheel-slip, leading to loss of
traction and control (Smith, 1978).
Figure 17. AMZ Racing ‘Furka’ Concept, Battery and Invertor Package stored in sidepods. (Thrainer, 2008)
This system removes the high volume package from the occupant area, allowing more space
for the powertrain system. Furthermore, the centre of gravity is shifted to below the driver
which enhances the handling characteristics. Since these battery systems are heavy and require
stabilisation, the structural integrity of the vehicle must be considered. The monocoque chassis,
as used by AMZ Racing, is ideal for this application. This would not be an option for Warwick
Racing, however, due to the added mass the tubular structure would require.
Placing the battery system outside of the safety structure of the chassis also poses undesirable
risks in an impact. Considering the high likelihood of impact in motorsport, the consequences
of external battery packaging could be severe. As a result, this is considered a non-viable option
for battery packaging.
The final solution is to store the battery system behind the driver. A sufficiently insulated
firewall that provides a barrier between the battery and occupant must be employed for safety.
This system is beneficial as added mass is sprung instead of unsprung. The design also does not
require additional mass in the form of tubing to support sidepods. The centre of mass is also
moved closer to the driver. A combination of methods are used by the Stuba Green FS Team,
shown in Figure 18. Here, the battery systems are stored both within a sidepod and behind the
driver’s seat

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Figure 18. Stuba Green Teams' Integrated Battery Box stored beneath driver (Benkovský, 2010)
For WRe the chosen design was a battery system placed behind the driver. However, in order
to house the volume of the Potenza battery system, the dual Ashwood motors, and the Sevcon
invertors at the rear of the chassis, it was necessary to widen the rear of the car. This allows the
motors to be housed along the same lateral plane, optimising the available space.
This project focused on the addition of an electric powertrain to the existing WR5 chassis, as
well as any required chassis redesign due to this powertrain. The original suspension system
from WR5 is carried over, as it had been optimised for the chassis setup. Using key reference
points, it was possible to adapt the original suspension geometry for WRe.
The newly widened chassis posed limitations to its use, however. The original pickup points
for the upper wishbones and shock absorbers conflicted with the geometric space required for
the chassis tubes.
Basic understanding of dynamic principles and trigonometry were used to alter the suspension
pickup coordinates without affecting component lengths. The billet material used to represent
the initial rear bulkhead is displayed in Figure 19, where initial extruded cuts are required for
mounting essential components; the four chassis tubes, the two sprockets and all driveline
bracket mounting points.

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Figure 19. WR5's bulkhead (left) WRe bulkhead billet (right); manipulating trigonometry to confirm suspension bracket
coordinates
Declining the angle connecting to the upper wishbone would reduce the anti-squat
characteristics of the vehicle, which in turn decreases the centre of gravity over the rear axle
(Gillespie, 1992). The shock absorber mounts would require raising slightly, this increases the
angle between the sprung mass and the road profile, thus increasing the feedback performance
of the dampers during bump. The outcome is therefore a raised damper bracket (as seen in gold
on Figure 19) along the suspension trigonometric arc, as well as a lowered upper wishbone. The
changes made to vehicular dynamics are therefore advantageous to its performance attributes.
3 Load Case Calculation
3.1 Tyre Data
Tyres provide the fundamental grip between a car and the road. Data was obtained from the
FSAE Tire Testing Consortium for the tyres used on the car, the Hoosier R13 6.5” (Kasprzak
& Gentz, 2006). Using a self-developed Matlab script, data such as longitudinal forces in
relation to slip angles for given reaction forces were plotted, as depicted in Figure 20. The
longitudinal and lateral data of the tyre are essential for the creation of load cases.

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Figure 20. graph displaying the longitudinal force produced by the tyre at different slip ratios.
The data depicted required analysis of varying camber angles, reaction forces and tyre
pressures. It is observed in Figure 20 that longitudinal and lateral forces are proportional to the
reaction force, with peak forces occurring at zero camber. Further explanation is provided in
Appendix S.
3.2 Chassis Loads
Ascertaining specific load cases applied to the chassis for the pre-established vehicle design is
a necessity for validating new components. Accurate loads are particularly significant for more
complex Finite Element Analysis and topology optimisation.
To begin, the forces applied to the vehicle are calculated for a number of driving scenarios.
These forces are applied at the point where the wheel contacts the road surface, known as the
contact patch. If each scenario is modelled in a state of static equilibrium, the forces and
moments generated at the contact patch are reacted solely by the chassis, through the suspension
geometry. The location of the suspension fixing points to the chassis and wheel hub are defined,
hence these forces and matrices can be setup as simultaneous equations and thereby solved
using matrix mathematics (Borg, 2009).
3.2.1 Load Scenarios
The driving scenarios most stressful upon the suspension, and therefore most considered across
FSAE literature for component design, are: cornering, braking and driving over a bump (Borg,
2009; Riley & George, 2002). For each scenario, weight transfer has a notable effect on the
forces imposed on the chassis. Therefore, the estimation of the vehicles centre of gravity is
required.

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Centre of Gravity Estimation
For this section, the coordinate system depicted in Figure 21 is used. Coordinate values are
specified in mm, with the origin being placed at the Bottom Dead Centre (BDC) of the vehicle
roll hoop.
Figure 21. Coordinate System Used (Kemna, 2011)
To calculate the centre of mass, coordinates for each component and sub-assembly have been
assumed from a CAD model. Appendix A lists the components used, as well as mass and
coordinate estimates. Each coordinate along each axis is multiplied by the items’ established
weight. Summing, and then averaging, these moments per axis determines the coordinates for
the vehicle centre of gravity, as seen in Table 1.
Axis X (mm) Y (mm) Z (mm)
Center of Gravity Coordinates 252 0 191
FR Wheel Contact Patch Coordinates 1140 -600 -50
Table 1. Vehicle Centre of Gravity
To translate these coordinates into the front to back weight distribution used for load case
scenarios, each coordinate is substracted from those of the front right wheel contact patch,
which is used a reference point. Dividing this value by the length, width or height of the vehicle
respectively then establishes the weight distribution as a ratio. The initial weight distribution
along the X -axis is most significant for the load cases. Given a vehicle length of 1640mm the
weight distribution is 46% at the front tyres and 54% at the rear.

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3.2.2 Cornering
When turning through a corner, the steady state forces at each tyre change in both the Y and Z
directions. The lateral force in Y must exist for the vehicle to turn, while the force in Z changes
as weight shifts from the tyres at the inside of the turn to the tyres at the outside of the turn.
To calculate this weight transfer, described by Milliken and Milliken as Lateral Load Transfer
(LLT) (Milliken & Milliken, 1995), an estimate for the lateral force is required. Riley and
George propose that 1.5 multiplied by gravity (1.5G) multiplied by the mass of the entire
vehicle is an appropriate estimation of lateral force in this instance (Riley & George, 2002).
Equation 1 is used to calculate the final weight distribution from cornering as a fraction. In
Table 2 this fraction has been multiplied by the vehicle weight to display the load at each wheel
while cornering.
𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝐿𝑜𝑎𝑑 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟
=
(𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝐺′𝑠) × (𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝐶𝑒𝑛𝑡𝑟𝑒 𝑜𝑓 𝐺𝑟𝑎𝑣𝑖𝑡𝑦)
(𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑇𝑟𝑎𝑐𝑘 𝑊𝑖𝑑𝑡ℎ)
Equation 1
Weight at Inside Wheel (N) Weight at Outside Wheel (N)
Front 293 990
Rear 1192 3249
Table 2. Weight at Each Wheel While Cornering
In calculating the lateral force applied to the tyre, data from the Tire Testing Consortium
(Kasprzak & Gentz, 2006) has been used for the WRe model of tyre. This data has been graphed
in Figure 22.

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Figure 22. Lateral Force Against Slip Angle for Several Reaction Forces (Adapted from Kasprzak & Gemtz (Kasprzak &
Gentz, 2006)
Analysing the peak lateral force for each curve suggests that 2.5 times the reaction force is an
appropriate measure of lateral force. The cornering forces calculated for each tyre are
demonstrated in Table 3, which summarises all scenario tyre forces.
3.2.3 Braking
In braking the vehicle experiences a negative force in the x direction as it is slowing. Weight
also transfers from the rear tyres to those at the front due to the deceleration (Milliken &
Milliken, 1995). Forces are therefore expected in the X and Z directions for a braking scenario.
Riley and George propose that braking force can be estimated at -1.5G. As WRe is estimated
to weigh 310kg (Appendix A), the total braking force is -4561N. A brake bias of 60% at the
front and 40% at the rear is set as this is the same as WR5, establishing the braking forces found
in Table 3.
Milliken and Milliken describe the weight transfer under braking as longitudinal weight
transfer. Using Equation 2 it is established that 640N transfer from the rear tyres to the front
tyres under the proposed 1.5G braking condition.
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝐿𝑜𝑎𝑑
=
(𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝐻𝑒𝑖𝑔ℎ𝑡) × (𝑊𝑒𝑖𝑔ℎ𝑡) × (𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛)
(𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝐿𝑒𝑛𝑔𝑡ℎ)
Equation 2

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3.2.4 Bump
Costin and Phipps state that a 3Gg force appropriately represents driving over a six-inch-high
bump (Costin & Phipps, 1965), while Riley and George propose a 3.5G force for an FSAE
bump scenario (Riley & George, 2002). Using the higher estimate of 3.5G, the total bump force
experienced is the weight at the tyre multiplied by 3.5. For a front tyre this is 2448N and for a
rear tyre it is 2873N. No changes in force are applied in the X or Y directions.
3.2.5 Combining Scenarios
The most stressful scenario on a chassis is a combination of cornering, braking and driving over
a bump. An estimate for this scenario is produced by summing the forces in each axes for each
tyre, shown in Table X. This is an overestimate as in reality forces generated at the tyre cannot
exceed the frictional force at the tyre, μFz (Ramani, 2006). Figure 23 is an example of a friction
circle diagram where μFz = 3000N. As this data will be used solely for design of the chassis,
overestimating in this case will increase the strength of the components designed while also
increasing their weight.
Figure 23. Friction Circle for Tyre Forces (Ramani, 2006)
3.2.6 Forces at Each Tyre
Table 3 lists the calculated forces at each tyre, with outer and inner referring to the tyre location
when turning a corner. These forces are now used to solve static equations for the force applied
by individual suspension members.

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Axes Scenario
Cornering (N) Braking
(N)
Bump (N) Mixed
(N)
Tyre
Outer Front X 0 -1368 0 -1368
Y 2477 0 0 2477
Z 990 1140 2448 4578
Inner Front X 0 -1368 0 -1368
Y 732 0 0 732
Z 293 1140 2448 3881
Outer Rear X 0 -912 0 -912
Y 3249 0 0 3249
Z 1299 380 2448 4127
Inner Rear X 0 -912 0 -912
Y 1192 0 0 1192
Z 477 380 2448 3305
Table 3. Tyre forces at contact patch.
3.2.7 Calculating the Force Applied By Individual Suspension Members
To calculate the force applied for each suspension member, simultaneous equations are
developed and then solved using matrices. These calculations use suspension fixing point and
tyre contact patch coordinates generated from CAD, shown in Appendix A.
Equation 3 is used to calculate the force applied by each suspension member in X, Y and Z that
must sum with the force at the tyre to zero. Equation 4 is used to calculate the moments applied
by each suspension member as these must sum with the moment generated at the tyre to zero
(Borg, 2009). The Moment Arm Vector of Equation 4 is calculated through the cross product
of the unit vector with the coordinate where the suspension arm joins the wheel upright.
𝑈𝑛𝑖𝑡 𝑉𝑒𝑐𝑡𝑜𝑟 × 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝐹𝑜𝑟𝑐𝑒 = 𝐹𝑜𝑟𝑐𝑒 𝑉𝑒𝑐𝑡𝑜𝑟 Equation 3
𝑀𝑜𝑚𝑒𝑛𝑡 𝐴𝑟𝑚 𝑉𝑒𝑐𝑡𝑜𝑟 × 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝐹𝑜𝑟𝑐𝑒
= 𝑀𝑜𝑚𝑒𝑛𝑡 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 𝑏𝑦 𝑆𝑢𝑠𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝐴𝑟𝑚
Equation 4
The matrix equation 𝐴𝑥 = 𝐵 can be used to form and solve simultaneous equations for the
magnitude of force applied by each suspension member, where;
A = Unit vectors and moment arm vectors for each suspension member

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x = Magnitude of force applied by each suspension member
B = Forces and moments of the chosen tyre in X, Y and Z
A:
Unit Vector ⌈
𝑢𝑥1 𝑢𝑥2 … 𝑢𝑥 𝑛
𝑢𝑦1 𝑢𝑦2 … 𝑢𝑦𝑛
𝑢𝑧1 𝑢𝑧2 … 𝑢𝑧 𝑛
⌉
Moment Arm
Vector
⌊
𝑟𝑥1 𝑟𝑥2 … 𝑟𝑥 𝑛
𝑟𝑦1 𝑟𝑦2 … 𝑟𝑦𝑛
𝑟𝑧1 𝑟𝑧2 … 𝑟𝑧 𝑛
⌋
x: B:
Magnitude of Force
Reacted by Suspension
Member
[
𝐹1
𝐹2
𝐹3
𝐹4
𝐹5
𝐹6]
Force Applied at Tyre
Contact Patch
⌈
𝐹𝑥 𝐶𝑃
𝐹𝑦 𝐶𝑃
𝐹𝑧 𝐶𝑃
⌉
Moment Generated at
Tyre Contact Patch
⌊
𝑀𝑥 𝐶𝑃
𝑀𝑦 𝐶𝑃
𝑀𝑧 𝐶𝑃
⌋
The components of matrix A can be calculated using suspension coordinate geometry
(Appendix A), while those of matrix B are calculated in Section 3.2.6 and Appendix A. To
solve for x, Equation 5 is therefore used.
𝑥 = 𝐴−1
𝐵 Equation 5
For reference, an example calculation of matrix x is shown in Appendix A.
3.2.8 Calculating the Force at Chassis Mounting Points
To establish the force that each suspension member applies to the chassis in X, Y and Z,
Equation 3 is used again with a different matrix as A. In this case, the Moment Arm Vectors of
A are generated through the cross product of the suspension member unit vector with the
coordinate that the suspension member attaches to the chassis.
3.2.9 Improvement of this Approach
In calculating the moment arm vectors, Borg subtracts the point where the suspension arm
meets the chassis from the point it meets the suspension upright for X, Y and Z (Borg, 2009).

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While a standard method for a two dimensional moment problem, this is inaccurate for a three
dimensional moment as described by Whiteman (Whiteman, 2015). Instead, a cross product
approach is used for this report as previously described.
Core limitations of this method are the use of static calculations to model the dynamic scenarios
of cornering, braking and driving over a bump. This will affect the final accuracy of results
however with appropriate factors of safety in design this can be mitigated.
Final suspension forces applied to the chassis are available in Appendix A.
3.3 Powertrain Calculations
To run simulations, the forces acting on the motor supports must be calculated. The coordinate
system used is the same as that of Figure 21
The Ashwoods ELMO-S motors have a peak torque of 60𝑁𝑚 (𝑇) each when running at 72𝑉
and 550𝐴 (Ashwoods, 2015). The mounting holes on the casing for the motor are 0.13𝑚 (𝑟𝑇)
from the centre. The peak force turning the mounting bolts about the centre of the motor shaft
can be calculated using:
𝐹𝑇 =
𝑇
4𝑟𝑇
Equation 6
Where 𝐹𝑇 is the force acting on one mounting bolt due to the torque of the motor.
The motor output shaft is attached to a small sprocket driving the larger sprocket on the
driveshaft through a chain. The connection creates a pulling force on the motor mounts and an
equal and opposite force on the bulkhead. The radius of the small sprocket is 0.016𝑚 (𝑟𝑠). The
maximum exhibited force from the chain acting on the motor can be calculated using:
𝐹𝑐 =
𝑇
4𝑟𝑠
Equation 7
Where: 𝐹𝑐 is the force on the motor due to the chain.
Finally, the sprocket is offset from the centre of the motor mounts by a maximum distance
of 0.0497𝑚 (𝑑). This will provide a moment on the motor about the z-axis. This can be
calculated using:
𝑀 = 𝐹𝑐 𝑑 Equation 8
Where: 𝑀 is the moment due to the sprocket offset.

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This can then be converted into a force on each of the motor mount bolts using:
𝐹 𝑀𝑖 =
𝑀
4𝑥𝑖
Equation 9
Where: 𝐹 𝑀 and x are the force on the bolt and the distance of the corresponding bolt from the
centre of the motor, in the x-axis.
The forces then have to be broken down into vector components and summed, to be applied to
various models in order to run simulations. The forces applied to the motor mounts can be found
in Appendix B.
4 Design Methodology
Models are created and simulations performed to ensure that all designed components would
fit together and be capable of withstanding the calculated loads. CAD modelling, FEA and
topology optimisation are tools primarily used to validate design work and secondarily used to
optimise components for their respective applications. In this project CAD was utilised for all
components, FEA was used to simulate stresses, deflections or weight reductions and topology
optimisation sped up the FEA process. Consequentially, it is important to recognise the
advantages and limitations of these tools.
4.1 Computer Aided Design
CAD, short for computer aided design, has become commonplace in industry due to its
applicability to most forms of engineering. Assemblies in CAD allow designers to create
complex models with confidence, as relevant component dimensions must be correct for the
virtual assembly. It is an important tool for this project as FEA and topology optimisation would
not be possible without a computational model to perform their respective analyses on.
This project presented a primary limitation in the user’s competency with the software due to
training and practice, however all users demonstrated sufficient competency.
4.2 Meshing
Meshing is essential for use of finite element analysis (FEA), topology optimisation and many
other simulations. The user should aim to produce a mesh that optimises the accuracy of the
simulation. To improve the mesh, the user should aim to replicate regularly shaped elements

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and increase the number of nodes in the mesh. (C.T.Shaw, 1996) Tests conducted in Abaqus
demonstrate that the number of nodes directly affects the deflection and maximum stress for a
simulation. These results are plotted in the graphs of Figure 24. It is observed that the
displacement trends towards a value at a substantially lower number of nodes relative to the
stress, confirming that for accurate stresses a large number of nodes must be used. However,
increasing the number of nodes also increases simulation run time. For this reason, coarse
meshes are manipulated on iterative models, with final model simulations using higher mesh
node counts.
Figure 24. Graphs showing the effect the number of nodes has on a simulation: (Left) Max Stress vs No. Nodes (Right)
Displacement vs No. Nodes.
The type of mesh used also makes a difference to the accuracy of the results, with structured
meshes demonstrating improved accuracy over unstructured meshes. The issue with structured
meshes manifests itself in the time required to fit a structured mesh to a model. The advantage
of an unstructured mesh is related to the algorithm programmed to automatically generate the
mesh for any shape, saving large amounts of time. (C.T.Shaw, 1996). Creating a structured
mesh for every component on a car would require
either significant time or a larger team of trained
users to generate them. Instead, automatically-
generated, unstructured, tetrahedral meshes were
used. The test conducted in Figure 25 was repeated
for structured and unstructured meshes, also
showing a small difference in results. For more
information on meshing used in this project, see
Appendix C.
Figure 25. Comparison meshes: (Left) Structured
(Right) Unstructured.

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4.3 Finite Element Analysis
Finite element analysis (FEA) is used to demonstrate how the design of a component will
perform under the subjected loads, such as peak static force and dynamic fatigue loading. FEA
can also be used to optimise components through the use of a good iterative design process,
such as in Figure 26. Effective use of FEA will lead to components with minimal weight for
the chosen performance target; normally a safety factor of the material yield stress or a
maximum displacement. Good design practice is required when removing material from the
model for efficient optimisation. The drawback of this optimisation method is that it can be
time consuming, especially when considering every component which this could be used for on
a car.
The greatest limitation of FEA is the accuracy with which the simulation
replicates the real situation. This is dependent on a number of factors: the
accuracy of the CAD model geometry; the impact the mesh has on the
results; and the accuracy with which the simulation replicates the loads
and constraints. The CAD dimensions are accurate, because the parts are
manufactured using the CAD models and drawings. The meshes were
unstructured but verified as described in Section 4.2. The simulations
were for the most part linear and worst-case; these are suitable because
the components, upon which simulations were run, should not deflect
excessively. To further verify this, a non-linear test was conducted on the
motor mounts in which the difference in maximum stresses was less than 6% of the maximum
linear stress. Considering the assumed safety factor of at least two for the majority of the cradle
components, the linear analysis is deemed sufficiently accurate.
Figure 27. Comparison of analyses: (Left) Non-linear analysis (Right) Linear analysis
Figure 26. FEA Design
process. (C.T.Shaw, 1996)

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4.4 Topology Optimisation
Topology optimisation is a development upon the FEA design process, whereby an organic
three-dimensional model that contains a minimal amount of material is produced by the
software. The output of the software is dependent upon the input loads and the topology
objective. This means that the output from topology optimisation is the best suited material
layout for the given loading and objective. (GRM, 2016) The process offers the advantage of
reducing the component design time to a fraction of that required for an iterative FEA design
process.
Topology optimisation software has three major limitations. Licences for the software are
expensive, however a sponsorship package from GRM provided six Genesis licences to aid in
the development of the car. The software is complex and requires extensive training, provided
by GRM, to practice and master. Further consultation was required to gain further
understanding for software usage and to ensure that the simulations were accurately set up.
Finally, the output from the software requires adjustment before the component can be
manufactured and assembled. Manufacturing and design constraints must be considered when
adapting the output for a CAD model, as depicted in Figure 28. The model should then be tested
using FEA to verify the design. For further explanation, see Appendix D.
Figure 28.An example of the possible design process using topology optimisation. (Left) Un-optimised part; (Middle)
Suggested material by algorithm; (Right) Optimised part. (Triantaphyllou, 2015)
5 Powertrain Cradle
Incorporating two motors into the chassis design presented a unique challenge requiring a
number of considerations: peak torque output of the motors, forces from the chassis and
bulkhead, packaging, mass, manufacture, serviceability.

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Figure 29 shows the chosen design, a cradle in
which the motors are housed using motor mounts
between the bulkhead and a steel plate welded into
the main roll hoop. Each motor has a separate
housing to reduce the overall weight. This has the
added benefits of reduced twisting stresses caused
by the motors not outputting the same torque and
improved air flow over the motors for cooling. The
components of the design were then optimised with the aim of weight reduction and the
objective of the material yield stress.
The forces on the motor mounts are explained in Section 3.3 and are tabulated in Appendix B.
To optimise the motor mounts, as mentioned
previously, a combination of topology
optimisation and finite element analysis were
used. Initially a model was created in Genesis
replicating the loads due to the motor torque.
Figure 30 shows the first simulation run that
allowed the software to remove material from
anywhere on the model. The output suggests that
the motor housing could be made from two parts.
This design was not carried forward because the motors are designed to have a face in contact
with the support for rigid alignment.
To obtain a reliable output from the simulation, non-optimisable regions were applied to the
model, highlighted in red in Figure 31. For a full breakdown of the topology optimisation
process for the motor mounts, see Appendix D.
Figure 31. Topology models: (Left) Before simulation (Middle) 0.4 Mass fraction output (Right) 0.25 Mass fraction output.
Figure 29. Un-optimised powertrain cradle.
Figure 30. Topology optimisation output without un-
optimisable regions.

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The output from Genesis software suggests a design similar to that of a truss structure, however
it also includes varying the depth of material, which would pose manufacturing difficulties.
Therefore, using topology simulations as a guide, a model was created in Autodesk, shown in
Figure 31 (Middle). The model created has more material than the optimisation output. This is
so that the motor mounts would be able to withstand regenerative forces from the motors, should
regenerative braking be used on the car. An iterative FEA reduction process was then carried
out on the design. For the full breakdown of the FEA design process, see Appendix E.
Figure 32. FEA reduction process: (Left) Initial geometry (Middle) 1st
iteration (Right) 8th
iteration.
For each iteration, simulations were run to confirm whether the design specifications were
exceeded. If they were not exceeded further material was removed, if they were exceeded a
varying value for mass-fraction was tested. Figure 32 shows the initial geometry created from
the Genesis output, the third iteration and the final iteration, the full FEA process is shown in
Appendix D. The mass of the initial geometry is 6.227𝑘𝑔 and the mass of the eighth iteration
is 1.650𝑘𝑔, equating to a 74% reduction in mass. Figure 33 illustrates the changes in mass and
displacement through the iterative FEA process. The mass of the component was reduced at the
cost of increasing the deflection. When the iterative design surpassed the maximum allowable
deflection, the iteration process stopped. The final design has a delflection significantly below
the maximum allowable to build in a safety factor.

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Figure 33. Graphic representation of the change in displacement under motor forces through the motor mount iterations.
The final design for the motor mounts, shown
in Figure 34, has a mass of 1.891𝑘𝑔 which is
slightly heavier than the final iteration. This is
to account for unpredictable forces and
imperfections in both the material and
component geometry, created during
manufacture. The maximum stress on the
component is 90𝑀𝑃𝑎, resulting in a factor of
safety of 2.7 for the material yield stress. The
maximum deflection of the component
is 0.3𝑚𝑚. The engineering drawing for the
component can be found in Appendix G.
The motor mounts were initially designed for
manufacture using a CNC milling machine. In
practice, water jetting was used due to the
shorter lead time and reduced cost. The limitations of water jetting are that it cannot cut to a
defined depth, and the process can leave a taper on the material. For these reasons, water jetting
removed the bulk of material prior to finishing with a CNC milling machine, see Appendix K.
0
1
2
3
4
5
6
7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 1 2 3 4 5 6 7 8 Final
Mass(kg)
Deflection(mm)
Iteration
Displacement vs Mass through Motor Mount Iterations
Displacement Max Allowable Displacement Mass
Figure 34. Motor mount final model: (Top) 3/4 view render.
(Bottom) Von Mises result from linear Nastran analysis.

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The forward bulkhead, shown in Figure 35
completes the constraint of the motor mounts. It is
essential to the cradle for this reason but has
limited opportunity for optimisation. As a result,
the design was created using topology
optimisation and verified using FEA. The process
is shown in Appendix D.
6 Bulkhead
The main purpose and application of a bulkhead has been briefed in Section 2.2. However, the
intent, challenges and methodology of the bulkhead design for WRe will be detailed in this
section.
6.1 Design Intent
The new powertrain dictates a redesign of the rear chassis and therefore the bulkhead. Priority
is given to ensuring that the bulkhead can withstand the torque from the motors while
supporting the dynamic loads of common racing conditions.
Having ensured the requisite robustness, light-weighting can be performed. This would
contribute towards reducing the vehicle weight, hence increasing the power-to-weight ratio of
the car and resulting in competitive advantage.
To comply with FSAE rule T6.6, the rear of the car must have a jacking rod distinctly painted
in orange (SAE International, 2015). This has been incorporated into the design. Other FSAE
rules that govern the bulkhead design are linked to spaceframe regulations and therefore not
considered.
Figure 35. Render of the forward bulkhead

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6.2 Initial Design
As mentioned in Section 2.2.2, the chassis
bolting points were used as the basis for this
design. A 600 x 400 mm billet of 25.4mm
thickness was chosen, setting the dimensional
boundaries of the entire design process.
The next step was to ensure that the dynamic
setup was appropriately accounted for on the
new bulkhead. The accuracy of these
locations was crucial; any differences in the
geometry would result in non-optimal performance of the car, as discussed in Section 2.4. Using
CAD, the suspension points from the older bulkhead were directly projected onto the new one.
Following this, the points for the motors mounts were implanted and dimensioned relative to
the sprocket mounts. The resultant design can be seen in Figure 36, along with a mock-up of
the sprocket and driveline geometries. The mass at this stage was 15.8kg.
Figure 37. L: The bulkhead with mounting point for ancillaries and mock-up of the sprocket dimensions;
R: Complete initial bulkhead design
Upon implementing the adapted damper mounting points and the associated design changes
discussed in Section 2.4, the initial design was complete. This is depicted in Figure 36. Material
was removed in order to adapt the damper mounting points, reducing the mass to 11.5kg.
Figure 36. Comparison of the WR5 bulkhead
with that of WRe

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6.3 Initial Verification
Figure 38. Motor torque validation on the initial bulkhead (exaggerated distortion).
L: Maximum Displacement: 0.09 mm R: Maximum Stress: 16.48 MPa
To ensure the capability of the design under the expected load conditions, a basic simulation
was conducted using the resultant forces of the motor torque. The results can be seen in Figure
38. The displacement is minimal and stress is far below 414 MPa, the Yield Strength of
Aluminium 7075 Plate (Alcoa, 2016). This confirmed that the bulkhead would not be over-
stressed under motor forces, leaving ample scope for weight optimisation.
6.4 Weight Optimisation (FEA)
The areas marked in dark blue of Figure 38 (R) demonstrate that a large proportion of the
bulkhead is not load-bearing. An iterative process was followed to progressively remove
material and verify robustness.

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Figure 39. Progressively light-weighted iterations of the bulkhead
This iterative process involved performing FEA with the motor forces and removing low stress
areas. Compared to the initial billet of mass 15.8 kg, the extensively light-weighted iteration
achieved an optimised mass 3.4 kg. A drastically light-weighted design has therefore been
achieved whilst fulfilling requirements for torsional stiffness under from initial simulations.
Table 4 summarises the results from simulations for the models under the forces imposed by
the motors. Further simulations and results can be found in Appendix F.
6.5 FEA Results
Figure 40. FEA to verify the displacement of the iterations under the torque from the motors
It can be seen from Table 4 that from Iteration 1 through to 4, there has been a weight saving
of 3.28 kg. However, compared to the Initial Design of 11.5 kg, there has been a 70.4% saving
down to 3.4 kg. Under forces imposed by torque from the motors, the Safety Factor is 9.93 with
respect to Maximum Stress experienced and the Yield Strength of Aluminium 7075 Plate, as
mentioned in Section 6.3.

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Model Maximum
Displacement (mm)
Maximum
Stress (MPa)
Safety Factor Mass (kg)
Iteration 1 0.14 22.69 18.25 6.68
Iteration 2 0.22 32.29 12.82 5.43
Iteration 3 0.27 38.51 10.75 3.97
Iteration 4 0.34 41.70 9.93 3.40
Table 4. Summary of simulations to verify the performance of the iterations under the torque from the motors.
6.6 Topology Optimisation
Similar to the motor mounts, the bulkhead underwent topology optimisation. This was
performed concurrently to the FEA process, further facilitating light-weighting as well as
adding credibility to the FEA work.
Figure 41. Progression of topology optimisation. Left to Right: 100%, 51% and 34% of initial mass
Using a fine, high-quality mesh, the optimisation was significantly more accurate compared to
the coarser mesh with fewer nodes and elements that Nastran typically uses. In the case of the
bulkhead, simulations were conducted with the aim of achieving 0.25 mass fraction whilst
maintaining the 414MPa Yield Stress of Aluminium 7075 (Alcoa, 2016). In Figure 41, a
progression of the topology process is demonstrated, whereby the software cycles through
various iterations, removing mass whilst confirming the structural rigidity of each node.
Figure 42. Topology optimisation of the bulkhead. L to R: 3G Bump, Pure Braking, Pure Cornering and All Forces
The four simulated scenarios mentioned in Section 3.2.1, were extrapolated to investigate the
optimised bulkhead design under various racing scenarios. The worst case scenario simulated
all the maximum loads occurring at once. The results for each simulation are exhibited below
in Figure 42. A detailed summary of these topology results can be found in Appendix D.

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Figure 43. Superimposed images of the topology optimised bulkheads under the various scenarios L to R: Front and Rear
Finally, results of each scenario were combined, with the aim of producing guidelines for the
final bulkhead design. This is depicted in Figure 43. This was then compared to the results from
the FEA simulation in Nastran. Appropriate modifications were made to ensure the reliability
of the design, using the robust guidelines set by the Genesis results.
6.7 Final Design
In Figure 44, the final design for the bulkhead is depicted.
This is based on findings from both FEA using Nastran
and Topology-optimisation using Genesis.
The chosen design is heavier than the lightest FEA
iteration. This is to offset the limitations of the software
and ensure an appropriate safety factor.
Nastran uses linear analysis, which assumes linearity in
the elastic behaviour of a material (MIT , 2010). Although the loads are modelled accurately,
the simulations may not be fully accurate; additionally, it does not consider unexpected forces
that the spaceframe may impose on the bulkhead.
Genesis is industry-standard topology-optimisation software used by automotive and
motorsport firms. In this case the output from Genesis recommended density reductions within
the plate that were not manufacturable. Hence, guidelines from both analyses were considered
to arrive at the final design.
The design is therefore marginally over-engineered however the greater mass, 4.7 kg compared
to 3.4 kg, is offset by the safety of the vehicle, especially considering the fact that the driver is
likely to be an amateur with limited experience in race-car driving.
Figure 44. Final weight-optimised
bulkhead design

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6.8 Final Simulations
Figure 45. FEA to verify the displacement of the iterations under different scenarios. Left to Right: Motor Forces, 3G Bump
& Motors, Pure Cornering and Pure Braking.
It can be seen from Table 5 that the final, weight-optimised bulkhead design at 4.7 kg is robust
in a range of scenarios that may manifest under racing conditions. Compared to the Initial
Design of 11.5 kg, there has been a 59.1% saving. The lowest Safety Factor is 9.72, with respect
to the Yield Strength of Aluminium 7075 Plate, and the Maximum Displacement is 0.29mm.
Scenarios Maximum
Displacement (mm)
Maximum Stress
(MPa)
Safety Factor
Motor Forces 0.26 42.50 9.74
3G Bump & Motors 0.26 42.61 9.72
Pure Cornering 0.09 35.17 11.77
Pure Braking 0.29 10.01 41.36
Table 5. Summary of simulations to verify the performance of final weight-optimised bulkhead under various load scenarios.
Figure 46. Graphic representation of the change in displacement under motor forces through the bulkhead iterations.
0
2
4
6
8
10
12
14
16
18
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Billet Initial Initial
w/DM
1 2 3 4 Final
Mass(kg)
Deflection(mm)
Iteration
Displacement vs Mass through Bulkhead Iterations
Displacement Max. Allowable Displacement Mass

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6.9 Assembled Rear Cradle, Driveline and Motors
Figure 47. WRe powertrain and cradle assembly.
7 Spaceframe Design
7.1 Design Mentality
Due to the skeletal function of the tubular spaceframe, design work was performed concurrently
with the design of all other components. For this project, the main focus was on modifying the
rear section of WR5’s chassis. Due to the project requiring redesign of an existing chassis,
design compromises are expected.
The following radar chart (Figure 48) displays the current design focus for Warwick Racing’s
current vehicles WRe and WR6, the 2015-2016 competitive IC vehicle. The main
considerations for the prototype are feasibility of manufacture and the safety of the product

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Figure 48. Radar Chart displaying design considerations for current race vehicles
Full adherance to the competition rules would require refrabrication of the chassis, as teams are
deducted points for reusing spaceframe designs. However, the limited interaction of the new
powertrain with the front of the car led to a decision to focus only on the rear of the spaceframe
for this project. Figure 49 depicts the final WRe spaceframe with major components listed
Figure 49. WRe chassis with labelled diction.
Figure 50 illustrates all FSAE rules dictating the final design of a steel tubular spaceframe
chassis. The guidelines also set the geometric location and packaging of relative components
as well as requirements for the impact zones.
Feasibility and Cost
Lightweighting
Safety ConsiderationsPerformance
Adheration to Rules
Chart Title
WR-e (Ideal) WR-e (Actual) WR6

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Figure 50. Essential rules dictating the design of the rear spaceframe.
7.2 Member Selection and Modes of Failure
Due to high stresses during racing, the metallurgic composition and forming of the SAE/AISI
4130 ChroMoly steel tubes must be understood.
In previous years, primary failure mode was considered
to be through tensile load leading to peel stress along a
bonded line; a common cause of failure in welded joints
(Fisher, 2005). Previous testing results are displayed
below in Figure 51 for the 4130 ChroMoly, with the final
results displayed in Table 6.
Figure 52. Testing results for 4130 ChroMoly steel
(Coveney, et al., 2015)
Figure 51 Instron tensile testing welded
ChroMoly 4130 tubing (Coveney, et al., 2015).

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Figure 53. Previous WR5 tubular tensile testing for 4130 ChroMoly steel and 1010 steel tubing (Coveney, et al., 2015).
Table 6 compares the performance of the 4130 steel tubes against traditional 1010 tubing
expressed as a fraction, and conclude that the medium and thick tubes exhibit performance
benefits over the thin tubes. This dictates a purpose for the tube thickness as shown below in
Table 6.
Steel tube
nomenclature
Outer diameter
(mm)
Inner diameter
(mm)
Wall thickness
(mm)
Traditionally used for
Thick 25.4 20.574 4.826 Structural and safety
critical members
Medium 25.4 22.1 3.3 Load bearing members
Thin 25.4 22.9 2.5 Non-load bearing
members
Table 6. ChroMoly steel tube nomenclature
Tensile stress is not the only method of failure for the tubing, however, and this report section
provides a quantitative method for analysing spaceframe joints, justifying the ChroMoly tube
size of each member.
The main concern for a race car spaceframe is structural integrity, so consideration must be
given to the shear stress within the material. In this instance shear stress can be defined as a
materials tendency to translate perpendicularly to a uniaxial load, which will be measured for
WRe by the mixed forces defined in Section 3.2.1 acting upon the bulkhead at the rear of the
car (Roylance, 2000). Torsional failure is manifested as crack propagation under torsional
loading. The frame member measured was the main roll hoop bracing (Figure 49); a primary
load bearing and critical safety structure.

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Shear is measured through the following
equation: 𝜏 = 𝑇𝑟
𝐽⁄ , where:
𝜏 = Shear Stress (MPa)
T = Twisting Moment/Torque (Nmm)
r = Distance from acting member to stressed
surface (mm)
J = Second polar moment of area (mm4
)
The torsional impact on the chassis is illustrated
below, based on defined load cases (Figure 54).
The shear modulus of mild carbon steel is 77 GPa
(Engineering Toolbox, 2015), which suggests the
material will fail above this shear force. The force
simulated is the upward force reaction from the road
profile, calculated to be 2214N. The direction of torsion
acting upon the chassis is displayed in Figure 55. The
value of r is the distance between the rear tubes, and the
twisting moment is found to be 64,502Nmm. Therefore,
the torsional force is 819,180 Nmm2
. The full
calculation can be found in Appendix H.
The second polar moment of area, also known as the second moment of inertia, is defined as a
materials ability to resist bending through its cross section.
𝐽 =
𝜋
2
𝑟𝑜
4
−
𝜋
2
𝑟𝑖
4
Where:
𝑟𝑜 = Outer tube diameter (mm)
𝑟𝑖 = Inner tube diameter (mm)
This gives rise to the following results for the three steel tubes:
𝐽 𝑇ℎ𝑖𝑐𝑘 = 2.3273𝑒5
𝑚𝑚4
𝐽 𝑀𝑒𝑑𝑖𝑢𝑚 = 1.7444𝑒5
𝑚𝑚4
𝐽 𝑇ℎ𝑖𝑛 = 1.3864𝑒5
𝑚𝑚4
Therefore, the values for τ are calculated as follows:
𝑇ℎ𝑖𝑐𝑘 𝑇𝑢𝑏𝑒 τ = 35.2GPa 𝑀𝑒𝑑𝑖𝑢𝑚 𝑇𝑢𝑏𝑒 τ = 47.0GPa 𝑇ℎ𝑖𝑛 𝑇𝑢𝑏𝑒 τ = 59.1GPa
Figure 54. Torsional shear deformation in a cylinder
(Negahban, 2000)
Figure 55. Torsional force acting on the chassis

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This assumes that the load forces applied are the maximum loads established in the load cases.
In reality, during a rollover scenario, the forces would be greater so a factor of safety is included.
For analysing failure of an untested structure, a factor of safety of 2.00 is recommended (Oregon
State University, 2008). This provides the following results (Table 7), (considering the shear
modulus for ChroMoly steel to be 77GPa):
Tube Τ (GPa) With safety factor (GPa) Result
Thick 35.2 70.4 Structurally sound
Medium 47.0 94.0 Delaminated
Thin 59.1 118.2 Delaminated
Table 7. Torsional test for the 4130 ChroMoly tubes.
Using the estimated safety factor, the thick tubing remains structurally in-tact while the medium
and thin tubes delaminate (fail). An accurate factor of safety can be confirmed using the
following calculation:
𝑓𝑠 =
𝑠 𝑚
𝑠 𝑤
⁄ = 77
35.2⁄ = 2.19 Equation 10 Calculating factor of safety
(Engineers Edge, 2016)
Where 𝑓𝑠 = factor of safety, 𝑠 𝑚 = Allowable working stress (GPa) and 𝑠 𝑤 = Actual working
stress (GPa)
The final failure mechanism to be considered is
the normal shear stress, whereby the force
acting on the frame member causes welded
joints to crack and fail (Figure 56).
For theoretical calculations, the main roll-hoop
brace was considered to be a safety-critical
member, and therefore was chosen for
simulation. The force chosen was the 2214N
reaction force from the load cases (Section
3.2.1). The shear force is acting upon the
uppermost welded joint on the main roll-hoop,
as the reaction force attempts to shear the connected faces.
To calculate normal shear force acting in a perpendicular plane to the welded joint at the roll
hoop, the following equation for pipe shear stress is calculated:
Figure 56. Normal shear stress

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𝑓𝑣 = 𝑉𝑄/𝐼𝑡 Equation 11. Shear stress in a circular pipe (Eng-Tips,
2004)
Whereby: (calculation spreadsheet found in Appendix J):
𝑄 =
2𝑟
𝜋
(𝜋𝑟𝑡)
𝑄 = 3.113𝑒−8
𝑚𝑚4
𝐼 = 𝜋𝑟3
𝑡 𝐼 = 6.211𝑒−6
𝑚𝑚4
𝑡 = 2(𝑊𝑎𝑙𝑙 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠) 𝑡 = 0.0097𝑚𝑚
𝑉 𝑉 = 2214𝑁
Applying the calculated factor of safety:
Calculated shear stress (GPa) Factor of Safety Inclusive Result
11.5 25.2 Structurally sound
Table 8. Shear stress results.
The results from both tests prove that structural failure is due to torsional forces rather than
shear stress, and prove the need for thick tubes on safety-critical members.
7.3 Spaceframe Geometry and Frame Analysis
Having considered the ChroMoly thickness variants (calculated in Section 7.2) and the relevant
spaceframe rules, it was possible to begin formulating the spaceframe geometry. Genesis was
chosen as appropriate FEA software, as it allows easy redefinition of tubular sizes and
geometric coordinates. The methodology for design was to create nodes in Cartesian space from
the wireframe geometry, then connect coordinates using straight elements with ChroMoly tube
properties.
The initial testing verified the use of thick tubes for the safety critical components: the tubes to
brace the main roll-hoop and the members supporting the rear bulkhead. The FEA software was
configured to report strain energy (J) and displacement (mm), providing an understanding of
stored member energy during deformation. The first tests confirmed the choice of thick tubes
for safety-critical components, minimising energy transfer to the driver (Figure 57).

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