Vehicle Structures - Development of the Sports Car Chassis and Stiffness Analysis of the Westfield Sports Car

VEHICLE STIFFNESS ANALYSIS with a focus on Sports Car Structures and a detailed study of the Westfield Sports Car Spaceframe Chassis

Wayne Prangnell November 1992

SUMMARY The purpose of a vehicle chassis, the different type of vehicle structures and the analysis of vehicle structures is discussed by way of introduction to a detailed investigation of a Westfield Sports Car space frame chassis. The bending and torsional stiffness of a spaceframe chassis was tested in the laboratory and was modelled using finite element analysis software. Laboratory testing was carried out to establish the validity of the finite element model. The model was then used to investigate methods of improving the torsional stiffness of the chassis without altering the layout of the car. A number of recommendations were made to improve the torsional stiffness of the chassis with some simple modifications.

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TABLE OF CONTENTS List of Figures ..................................................................................................................................................4 List of Tables ....................................................................................................................................................6 1 Introduction ..................................................................................................................................................8 1.1 Outline of Project .........................................................................................................................8 2 Background ..................................................................................................................................................9 2.1 Introduction ..................................................................................................................................9 2.2 Purpose of the Chassis .................................................................................................................9 2.3 Basics of Vehicle Structural Actions ............................................................................................10 2.4 Requirements of a Chassis ...........................................................................................................15 2.4.1 Strength Requirements ................................................................................................15 2.4.2 Chassis Stiffness Requirements ..................................................................................17 2.4.3 Determining Torsional Stiffness ................................................................................19 2.5 Relationship of Suspension and Chassis Stiffness .......................................................................20 2.6 Vehicle Structure Analysis ...........................................................................................................20 2.7 Development of the Structure of Sports and Racing Cars ..........................................................22 2.8 Background of Clubman Cars ......................................................................................................28 3 Analysis of the Westfield Sports Car ............................................................................................................30 3.1 Introduction ..................................................................................................................................30 3.2 Determination of Chassis Geometry ............................................................................................31 3.2 Chassis Bending Stiffness ............................................................................................................32 3.2.1 Laboratory Test Description and Procedure................................................................32 3.1.2 Theoretical Analysis Description ................................................................................34 3.3 Chassis Torsional Stiffness ..........................................................................................................36 3.3.1 Laboratory Test Description and Procedure................................................................36 3.3.2 Theoretical Analysis Description ................................................................................38 4 Results and Discussion .................................................................................................................................39 4.1 Bending Test and Bending Analysis ............................................................................................39 4.2 Torsional Test and Torsional Analysis..........................................................................................41 4.3 Torsional Stiffness - Chassis Variations .......................................................................................45 5 Conclusions ..................................................................................................................................................54 5.1 Recommendations ........................................................................................................................57 5.2 Further Study................................................................................................................................58 6 Acknowledgments ........................................................................................................................................59 7 References ....................................................................................................................................................60 8 Appendices ...................................................................................................................................................61 Appendix A - Westfield Sports Car Data............................................................................................61 Appendix B - Westfield Sports Car Chassis Drawing........................................................................63 Appendix C - Computer Model Data File..........................................................................................64 Page 2

Appendix D - Laboratory Testing Observations ................................................................................76 Appendix E - Diagrams and Information for Chassis Modifications ................................................77 Appendix F - Components of the Westfield Sports Cars ...................................................................91 Appendix G - Calculations ................................................................................................................92

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LIST OF FIGURES Figure 2.1 - Chassis Design Considerations ..........................................10 Figure 2.2 - Exploded View of Girder Chassis ......................................12 Figure 2.3 - Twin Tube Chassis of Triumph TR4 with Cross Bracing ..12 Figure 2.4 - Spaceframe Chassis ...........................................................13 Figure 2.5 - Multitubular Chassis ..........................................................13 Figure 2.6 - Torsion Box Stressed Skin Construction, Ford GT40........14 Figure 2.7 - Monocoque Stressed Skin Construction ............................14 Figure 2.8 - Composite Structure of Mass Produced Renault 16 ..........15 Figure 2.9 - 1966 McLaren Grand Prix Car..........................................20 Figure 2.10 - Lola T92/10 Rollbox Model ............................................24 Figure 2.11 - Live Axle, Swing Axle and Independent Suspension ......26 Figure 2.12 - Independent Suspension Attached to Vehicle Structure...27 Figure 2.13 - Lotus Mark Six ................................................................27 Figure 2.14 - Mercédès-Benz 300SL .....................................................28 Figure 2.15 - Mercédès-Benz W196 ......................................................28 Figure 2.16 - Structure of the Lotus 25 Grand Prix Car ........................29 Figure 2.17 - 1989 Ferrari Grand Prix Car (bodywork cut away) .........29 Figure 2.18 - 1988 McLaren MP4/4 GP Car, Bodywork Removed ......30 Figure 2.19 - Modern Cars with Space Frames .....................................31 Figure 2.20 - Monocoque Chassis Road Cars .......................................32 Figure 2.21 - Westfield Sports Car ........................................................33 Figure 2.22 - Ginnetta G2 ......................................................................33 Figure 2.23 - Lotus Seven Body ............................................................34 Figure 2.24 - Elfin Clubman Car ...........................................................35 Figure 3.1 - Layout of Chassis Survey ..................................................38 Figure 3.2 - Axes System ......................................................................39 Figure 3.3 - Chassis Bending Test .........................................................39 Figure 3.4 - PAFEC 34000 Beam Element ............................................41 Figure 3.5 - Standard Chassis Model Member Groups .........................42 Figure 3.6 - Chassis Bending Model .....................................................43 Figure 3.7 - Chassis Torsional Test ........................................................44 Figure 3.8 - Pattern of Loading for Torsional Test ................................45 Figure 3.9 - Chassis Torsional Test Model ............................................46 Figure 4.1 - Load Deflection Response of Chassis Bending .................47 Figure 4.2 - Shape of Chassis for Calculated Bending Test ..................49 Figure 4.3 Torsional Load Deflection Response....................................51 Page 4

Figure 4.4 - Scatter of Measured Torsional Stiffness ............................52 Figure 4.5 - Torsional Deflections Along Chassis .................................53 Figure 4.6 - Torsional Stiffness Plots of Changes to Member Sizes .....55 Figure 4.7 - Torsional Stiffness Plots of Engine Bay Changes ..............56 Figure 4.8 - Torsional Stiffness Plots for Chassis with Extra Bracing ..58 Figure 4.9 - Torsional Stiffness Plots of Centre Tunnel Changes ..........59 Figure 4.10 - Torsional Stiffness Plots for Changes Using Plates .........60 Figure 4.11 - Torsional Stiffness Plots for Other Changes ....................61

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LIST OF TABLES Table 2.1 - Measured Peak Accelerations of Vehicles ...........................18 Table 2.2 - Chassis Torsional Stiffness ..................................................22 Table 4.1 - Standard Chassis Models ....................................................54 Table 4.2 - Category I, Changes to Member Sizes ................................55 Table 4.3 - Category II, Changes to the Engine Bay .............................56 Table 4.4 - Category III, Addition of Bracing Chassis Nose .................58 Table 4.5 - Category IV, Changes to the Centre Tunnel ........................59 Table 4.6 - Category V, Use of Plates ....................................................60 Table 4.7 - Category VI, Other Changes ...............................................61

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"You have to have passion to go deep inside, where you can then experience special feelings, very special moments which trigger some of the unique sensations, unique touch and feelings that give you something extra when you are right on the limit." Ayrton Senna, December 1991 The analysis of a vehicle structure takes the designer deep inside, looking for something extra to give the driver when he is right on the limit.

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1 INTRODUCTION The motor car is an important part of our lives that most of us use every day. Usually considered as a mechanical product because of all the mechanisms attached to it, the car is also an important structure. The motor car is subject to such a variation of loads and a severe fatigue life. For efficiency and performance reasons the car must weigh as little as possible, thus the design and analysis of this structure is essential. The analysis of vehicle structures is also very important because the public who use cars will tolerate the occasional mechanical breakdown, but they expect never to have any problems with the structure of the vehicle regardless of the severity of conditions the vehicle has been subject through its life. The analysis of vehicle structures is an area where Civil Engineers, or more specifically Structural Engineers are well equipped to tackle. The analysis of vehicle structures was researched and a fairly broad overview provided. A detailed stiffness analysis of the Westfield Sports Car chassis was then carried out using a finite element computer model and validated with laboratory testing. Potential modifications to the chassis and their effect of vehicle stiffness using the computer model.

1.1 Outline of Project Many ideas were pursued with this project and the aims often shifted with new information that was learned and new ideas, but the basic goal of this project has remained the same: To learn about the structure of vehicles. The subject of this project was narrowed by the authors interest in motor sport and sports cars which led to acquaintances with one of two vehicle manufacturers in Western Australia, Westfield Sports Cars Australia. Stephen Fox from Westfield Sports Cars showed enthusiasm at learning more about the structure of the sports car that his company produces and he agreed to lend a completed chassis for testing. Early plans for the project were ambitious and some of the activities planned were: Track testing of the Westfield Sports car to determine the loads on a vehicle, analysis of the chassis for stiffness, analysis of the vehicle for stresses and laboratory testing of chassis stiffness and stresses. Unfortunately track testing was not viable due to the cost of the equipment that would be required such as strain gauges and high speed multi channel data loggers. With improvements in data logger technology and availability, measuring the loads on a vehicle may make an interesting project in the future. On a simpler level, it was attempted to measure vehicle loads with brake meters. Brake meters work on a principal of lateral accelerations causing an angular deflection of a pendulum in a damping fluid. These devices which were used by British authorities for testing the brakes of commercial vehicles were found to be inaccurate for measuring car accelerations as the pitch and roll of a car about its horizontal axes and the slope of a road visibly affected the angle of the pendulum. The laboratory program was limited to stiffness testing because strain gauges for measuring stresses were not able to be supplied and fitted at the University for financial reasons. In hindsight it was sensible to carry out laboratory testing for stiffness only for reasons of simplicity and the limited time available to the project. Page 8

To establish computer models for stress and stiffness analysis of the chassis, various data was collected. The geometry of the chassis was measured using optical surveying techniques in the first instance and then using a tape measure. Around thirty of the major components of the Westfield Sports car were weighed, measured and drawn for use with a lumped mass finite element stress model. However the stress analysis did not proceed because laboratory stress measurements would not have been available to confirm any model results and the time available would not have allowed the use of a detailed stress model. A model for stiffness analysis was created and analysed for bending and torsion load cases. A number of variations to the standard Westfield Sports Car were also investigated. All models were created for and analysed using the PAFEC finite element software, running on an Apollo workstation at Curtin University of Technology. Some of the results of testing and analysis have been interesting, others were what was expected, but the overall result was learning a lot about vehicle structures and learning of the potential of computer analysis as a tool for the development of motor vehicle structures. The author has found this subject very interesting and hopes that this report conveys its information in a way that will pass on this interest to the reader.

2 BACKGROUND 2.1 Introduction Information is presented here as background on vehicle structures. The purpose of a vehicle chassis, its effect on the performance of a vehicle, the different types of vehicle structures and how analysis of the vehicle structure is approached is explained. The importance of stiffness of a vehicle structure is also discussed in this section. The chassis of a vehicle is frequently referred to throughout this project. The intended meaning is the main structural parts of the vehicle. This does not include suspension components or non structural bodywork, eg fibreglass cladding. A background on the structural developments of racing and sports cars is given as racing and sports cars are usually at the forefront of chassis development. Background on Clubman cars has been included to help understanding of the analysis of the Westfield Sports Car chassis which is a Clubman car. Clubman is the name given to a particular style car and this is explained in the background on Clubman cars.

2.2 Purpose of the Chassis A car chassis may be thought of as a large bracket. This bracket must keep all the parts of the car rigidly in place for the normal loads to which a car is subjected. Additionally this bracket must protect the driver in situations of abnormal loading such as crash loading. A summary of considerations for chassis design is given in Figure 2.1.

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Figure 2.1 - Chassis Design Considerations

Strength is required for safety and long life.

Rigidity or stiffness is required for servicability reasons to

eliminate low frequency shaking, fatigue problems, door closure problems on uneven ground.

For

performance reasons adequate chassis stiffness ensures that the full road holding and handling potential of the suspension system and tyres is reached.

2.3 Basics of Vehicle Structural Actions The vehicle structure is required to be strong and stiff in bending between the front and rear wheels and strong and stiff in torsion between the front and rear wheels. In addition the vehicle structure must have sufficient strength and stiffness in local areas where loads are applied by components mounted to the structure. These include loads from the pedals, steering wheel, seats, engine, fuel tank, differential, aerodynamic devices etc. In dealing with vehicle loads there are a number of structural systems employed by the different types of chassis. Looking at the predominant structural action, the four main types of structural actions for vehicle structures are discussed in the following order: i) Beam structures, ii) Framed structures,

iii) Stressed

skin construction and iv) Compound structures. i)

Beam structures Bending and torsional, are carried by relatively thick walled beams. There are usually two beams longitudinally along the base of the car. Essentially there have been two types of beam structures used for vehicles. Historically the first type was the conventional girder chassis which consisted of two longitudinal steel girders of channel section spaced by transverse members of similar construction. A girder chassis is shown in Figure 2.2. Vehicles which commonly employ this structural system are trucks. It is unusual to find this structural system in a new car today.

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Figure 2.2 - Exploded View of Girder Chassis The second type of beam structure is the twin tube or ladder chassis. This chassis has two large section hollow members joined by lateral or diagonal bracing or a combination of both which increases the torsional stiffness of the structure. The torsional stiffness of a twin tube chassis is far superior to a girder chassis of similar weight. A twin tube chassis with diagonal bracing is shown in Figure 2.3.

Figure 2.3 - Twin Tube Chassis of Triumph TR4 with Cross Bracing

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ii)

Framed Structures Loads are carried by either a partially or nearly fully braced frame system. Because of the complexity of loading and the number of components which must be accommodated within a car, a fully braced frame would be impractical and almost impossible. A vehicle with a frame as its main structure is called a spaceframe when the frame is well triangulated. It is called a multitubular chassis when the frame is only poorly braced and the loads are carried partly by the bending of the members and joints and partly by tension and compression in the members.

A spaceframe chassis is shown in Figure 2.4 and a

multitubular chassis in Figure 2.5.

Figure 2.4 - Spaceframe Chassis

Figure 2.5 - Multitubular Chassis

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iii)

Stressed skin construction With stressed skin construction loads are carried by a series of thin walled panels. The panels are usually stabilised with stiffeners and reinforced locally in regions of high stress such as near suspension mountings. The panels are most commonly sheet steel or aluminium, moulded glass fibre composites, carbon fibre composites. Stressed skin construction can be categorised into two main forms. Firstly those chassis consisting of two closed boxed sections down either side of the car, essentially a very large diameter, twin tube chassis. Figure 2.6 illustrates this type of construction.

Figure 2.6 - Torsion Box Stressed Skin Construction, Ford GT40

Secondly chassis which are like a closed top bath tub; a nearly closed single shell with apertures for driver and engine. This is illustrated in Figure 2.7 by the Lotus 25 structure.

Figure 2.7 - Monocoque Stressed Skin Construction

These forms of chassis have both been called monocoque, unitary, bath tub, torsion box and stressed skin bodies. Torsion box probably best describes the former, while the latter fits the definition of a monocoque. Monocoque comes from French: mono- + coque, shell, from Latin.

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iv)

Compound structures Many vehicles employ a combination of these principal structural actions.

Almost all modern

production cars are a composite structure of frame members such as the roof and door pillars and stressed skins such as the roof, floor and other panels in the engine bay and boot. Figure 2.8 illustrates with an exploded view of a Renault production car. Commercial vehicles such as buses and coaches often use a basic frame, very flexible on its own which is stiffened by the addition of exterior body panels. The structures of many light buses and four wheel drive wagons are similar in principal to this. Tray backed vehicles usually have two longitudinal beams along their length and a stressed skin cabin, often with a frame inside the skin.

Some of the more limited volume production sports cars are

composite structures with a braced frame, further stiffened and strengthened with stressed panels.

Figure 2.8 - Composite Structure of Mass Produced Renault 16

The loads in a beam structure are carried by flexure of the main beams, in a braced frame system loads are carried primarily by tension and compression in the members as in a truss. A partially braced frame carries load by bending moment and tension and compression in the members and with stressed skin construction, loads are carried by in plane stresses in the skin.

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2.4 Requirements of a Chassis 2.4.1 Strength Requirements The strength requirements of any vehicle structure depend upon : i)

The magnitude of the loads to which it is subject

ii)

Whether the loads are dynamic or static.

iii)

The method of transmission of the loads into the structure.

iv)

The variability of the loading.

v)

The factor of safety which is required against failure.

Vehicle structure loadings are generally specified in terms of peak accelerations to which the vehicle is subject. This is independent of the weight of the vehicle thus allowing uniform comparison between loads on cars of different weight. The magnitude of peak accelerations to which a vehicle is subject and the use of these accelerations to determine the loads on a vehicle structure is described by Garrett (1953).

He suggests that the worst

combinations of loading which could affect a vehicle structure are represented by four design cases. These four load cases do not include any consideration for crash loading, a separate area of vehicle design which is not considered in this report. The four load cases are based on peak accelerations of 1g for forward acceleration or braking, 1g for lateral acceleration due to cornering and 3g for vertical acceleration. These accelerations should be multiplied by 1.5 as a safety factor in arriving at maximum loads for design. A safety factor of 1.5 which is relatively high for steel structures is used due to uncertainty as to the actual magnitude of the loads. The four loading cases which should be considered are: i)

Hitting a bump / kerbing while braking in a straight line.

ii)

Cornering.

iii)

Hitting a bump while accelerating straight ahead.

iv)

Hitting a bump while cornering.

Costin and Phipps (1965) used a similar approach in an example of the design of a racing sports car chassis. The peak accelerations and the safety factor used in arriving at loads they used were identical to those suggested by Garrett. Other methods of analysing loads include determining serviceability loads from spring and damper actions and and analysis of the tyre / road interface. Vertical loading for normal operation would be through determining the relationship between compression of the spring damper unit and loading which is a combination of simple elastic deformation of the spring plus dynamic force from the damper unit, whereas strength or ultimate load cases are invariably outside of the normal spring

and suspension movement range

and may be more

dependent on other factors including tyre, bump stop and bushing deformation. Analysing the tyre contact Page 15

patch and tyre deflection may provide an envelope of the longitudnal, lateral and vertical forces potentially transmitted from the road into the vehicle. With steady improvements in suspension design, tyre properties, aerodynamics and downforce, vehicle weight, torsional stiffness and engine outputs, the peak accelerations that a modern production car, sports car or racing car can generate has increased. Examples of the peak accelerations that can be generated by several different cars are given in Table 2.1. Table 2.1 - Measured Peak Accelerations of Vehicles Peak Accelerations, g Longitudinal Lateral . Wheels, October 1992 - Road and race Nissan GTR's Standard Nissan GTR

.87

1.17

Australian Group A Nissan GTR

1.22

1.46

Ferrari 1992 Formula 1 Car

3.4

4.31

Ferrari F40

1.17

1.29

Ferrari 348

1.14

1.0

Holden Commodore

1.0

1.4

Nissan GTR

1.0

1.7

1.09

1.01

BMW M5

N/A

1.05

Ferrari Mondial t348

N/A

1.03

Honda NSX

N/A

1.07

Nissan GTR

N/A

1.10

Porsche Carrera 4

N/A

1.06

1953 Grand Prix Car

N/A

0.7

1965 Grand Prix Car

N/A

1.4

Wheels, May 1992

Wheels, October 1991 - Australian Group A Racing Cars

Motor, July 1991 - Tyre Testing Feature Nissan 300zx, Dunlop D40 M2 225/50 ZR16 Tyres Dry, low friction, smooth concrete track Wheels, May 1991 - Handling Test Tested with Valentine Research Inc. G-analyst

L J K Setright1968

Note that comparisons between these results will not be accurate as factors such as coefficient of friction of road, temperature, test circuit and driver are variables.

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Modern cars, in particular sports and racing cars commonly achieve higher peak accelerations than those given in references by Garrett (1953) and Costin and Phipps (1965). Consequently the loads on a modern car will be larger, however may be slightly offset by reduction of the safety factor due to: i) More accurate determination of loads using modern measuring equipment ii) Better understanding of the vehicle structure through computer structural analysis techniques iii) Better quality control of materials and manufacturing processes used in vehicle construction This project is concerned with chassis stiffness rather than strength. This discussion about vehicle loads is intended to provide background for vehicle strength. Strength analysis of vehicle structures requires further more detailed information of the loads that apply to a particular vehicle and a range of different load cases apply ranging from serviceability where fatigue stress is a primary consideration to impact loads where controlled failure and permanent plastic deformation occurs. Further discussion focuses on chassis stiffness which can be analysed independently of loads and stresses, thus detailed load cases are not further developed.

2.4.2 Chassis Stiffness Requirements Chassis stiffness is important in any vehicle for reasons such as door aperture tolerance, durability of fitments, occupant comfort and impression of safety, but most importantly for a performance car, chassis stiffness is fundamental to cornering performance. Bending stiffness of a chassis is typically expressed as a maximum vertical deflection of a chassis resulting from a certain mid span load. Fenton (1980) suggests that the maximum deflection for a 680 kg mid span load should be 1.27 mm. Fenton has not discussed the type or weight range of the vehicles that this would be applicable to and this would be necessary where deflection is the design criteria. For instance if two cars meet the requirement of a maximum mid span deflection of 1.27 mm for a 680 kg load, yet one of these cars is very heavy and the other is much lighter, the in service deflections of the heavier car will be larger approximately in proportion to the difference in weight. Chassis torsional stiffness is expressed in vehicle publications and by automotive engineers as the amount of torque required to twist the chassis one degree over the length of its wheelbase. Metric units are Nm/degree and imperial units are ft.lb/degree. This expression of chassis stiffness is independent of the wheelbase of the car, allowing direct comparison between cars of different length.

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To obtain good road holding and handling, the suspension geometry of a car is carefully designed and often refined to sub millimetre accuracy. For the suspension system to be most effective, the mounting points for the suspension on the chassis must be held rigidly in place by a stiff chassis. For this reason torsional stiffness is most important. Torsional stiffness is almost always more important than bending stiffness for performance reasons because in bending there is very little deflection at the supports, which in the case of a vehicle are the suspension mountings. However with torsional deformation the maximum deflections are likely to occur at the suspension mounting points. A good illustration of the effect of chassis torsional stiffness is documented by Setright (1968). The 1966 McLaren Grand Prix car was uncompetitive with the leading teams of that season because the engine was large, heavy and underpowered. However the chassis which was designed by young Aerospace Engineer, Robin Herd, which had an aluminium skin over a balsa wood core was of exceptional torsional stiffness. The McLaren had a torsional stiffness of about 13500 Nm/deg compared to about 3300 Nm/deg for a competitive Lotus 33. Setright timed the McLaren of Bruce McLaren shown in Figure 2.9 through Hunzberg Corner at the Zandervoort Grand Prix circuit faster than that achieved by Jim Clark in his Lotus although Clark's lap times were significantly faster than McLaren's.

Figure 2.9 - 1966 McLaren Grand Prix Car

Another illustration of the importance of chassis torsional stiffness was the Porsche 904 Bergspyder developed for the 1965 European Hillclimb Championship. Its structure was very poor for torsional loads and as a result the handling was erratic and the car was called 'Kangaroo'. Heavy modifications were needed to make the car competitive (Cotton 1988).

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2.4.3 Determining Torsional Stiffness There are two common strategies for measuring the torsional stiffness of a chassis which are: i)

Fit solid bars in place of spring and shock absorber units and mount either the front or rear suspension uprights to a rigid datum. Measure the torque required to twist the unrestrained end of the car one degree, or a similar measured amount. Thus the chassis stiffness is deduced from the rotation of the unrestrained suspension uprights for the particular torque applied.

ii)

Reasonably restrain one end of the chassis from rotation about the centreline at its suspension mounting points at that end. Apply a known torque to the unrestrained end of the chassis through the chassis mounting points, measuring the rotations on the chassis at the front and the rear. The chassis stiffness may be deduced from the relative rotation of the unrestrained end of the chassis to the restrained end for the torque applied.

The measured torsional stiffness of the chassis may vary if the torsional stiffness is calculated from rotations at the ends of suspension members as in i) or if the stiffness is calculated from rotations measured at the front and rear of the actual chassis as in ii). Table 2.2 summarises literature review of recommendations and observations for chassis torsional stiffness.

Table 2.2 - Chassis Torsional Stiffness Source

Vehicle

Setright 1968

1962 Lotus 25/33 GP car

Recommendation or Observation 3300 Nm/deg

(basic structure weighed 32kg complete) Setright 1968

1966 Brabham GP car

about 1400 Nm/deg

multitubular chassis Setright 1968

1966 McLaren GP car

over 13 500 Nm/deg

chassis of thin aluminium alloy, chemically bonded to end grain balsa core. Fenton 1980

typical family saloon,

Minimum: Recommended:

6100 Nm/deg 6500 - 7500 Nm/deg

Webb 1984

family size saloon

most cars range 4000 9000 Nm/deg

Gard 1992

Ford Falcon EBII 1992

8200 Nm/deg

Campbell 1978

Lotus Elan (about 1963) backbone chassis only

6870 Nm/deg

Fenton 1980

Ford GT40

13560 Nm/deg Page 19

Fothergill 1984

Open sports car

4000 Nm/deg is design aim

light road racing car

4070 Nm/deg suitable

Gard 1992

any performance car

ideally 10 times the suspension roll stiffness

Gard 1992

early 1990's F1

estimated 35 000 to 45 000 Nm/deg

Qld Govt.

Low volume cars:

4 cyl

4000 Nm/deg

(Road registration)

6 cyl

6000 Nm/deg

8 cyl

8000 Nm/deg

Gard 1992 Jaguar 2013

English kit Cobra

300 Nm/deg

RMC racing Cobra

8300 Nm/deg

2014 F Type aluminium body Jaguar

2.5 Relationship of Suspension and Chassis Stiffness An improvement in roadholding and cornering performance may be possible by increasing the stiffness of the suspension, but often increasing the spring stiffness gives no improvement or even worse overall performance. The reason for this may be that the torsional stiffness of the chassis has not been considered. For instance where springs are already quite stiff, or the chassis is quite flexible much of the suspension movement may be as a result of flexure of the chassis and in such a case stiffer springs are unlikely to increase cornering capacity. The other problem of fitting stiffer springs, also associated with the torsional stiffness of the car is that stiffer springs transfer bigger loads into the chassis resulting in larger chassis deflections. When these deflections become large enough to affect a carefully designed suspension geometry, cornering performance will be lost. In order to achieve the full potential of the suspension system and the tyres, the torsional stiffness of the chassis should be ten times the roll stiffness of the suspension. The roll stiffness of the suspension is the torsional stiffness of the car minus the flexibility of the chassis, measured at the wheel positions with springs in place and the suspension movement unrestricted.

2.6 Vehicle Structure Analysis Traditional engineering statics and mechanics formula can be applied relatively easily to early beam and tubular chassis however manual methods become more difficult with complex three dimensional geometry of

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space frames, stressed skin and composite construction. Model or prototype testing provided an early solution but testing numerous iterations of loads and design options is time consuming and expensive. With modern vehicle design and construction, the structural actions of vehicle structures have become quite complex. Sports and racing car structures are usually either thin walled (shell) structures or of spaceframe construction. With many members, joints, load paths and a high degree of indeterminacy, manual analysis becomes difficult, often impractical and more susceptible to errors.

This is further aggravated by the

variability of loading imposed on a vehicle. Thus analysis of these structures has tended toward approximate analysis techniques, design by rules of thumb, prototype or model analysis (not usually thought of as an analysis technique). More detailed calculations for localised areas which are important parts of the structure are usually made. Approximate methods of analysis for thin wall vehicle structures, based on predicting onset of shear instability are described by Bruhn (1958). With developments in computer hardware in the 80's and 90's, computers with adequate power for structural analysis have become more affordable and most major car companies are now using computer finite element techniques to improve and refine their structural designs. Finite element analysis is also becoming a powerful design tool for a number of specialist vehicle constructors. For instance Lola Cars who are leading English constructors of sports and racing car chassis have used finite element analysis in the design of the composite structure for the rollbox for crash loads of the T92/10 sports car (Baxter-Smallwood J. , Advanced Composite Engineering, 1992). Figure 2.10 is a diagram of the model used for the analysis of the Lola rollbox. Stress contours are superimposed on the model.

Figure 2.10 - Lola T92/10 Rollbox Model

The finite element method has become one of the most important tools for vehicle structural analysis. It deals with structural analysis problems by breaking down a structure which consists of a few complex elements into many simple elements.

Mathematical solution of the systems of simple elements by recognised stiffness

matrix techniques is readily performed using commercial software and a workstation or powerful personal computer. Current developments in personal computers is leading software companies to produce affordable finite element software for the PC, effectively bringing this tool within the reach of most engineers. A finite element software package generally consists of modules which: i) Assist with creating a model of the structure to be analysed. Interactive graphics is preferable, and graphics essential for checking input. Page 21

ii) Perform the solution iii) Communicate the results of the analysis. Interactive graphics could be considered essential for this purpose. Factors which make the analysis of vehicle structures complex have been discussed, but a factor which can greatly simplify the structural design and analysis of many vehicles is that the design of a vehicle structure is usually controlled by deflections rather than stresses. That is, if the car is designed to achieve a suitable stiffness, the stresses will be below safe limits. This simplifies design because interpreting the results of a stiffness analysis is generally much simpler and less time consuming than with the analysis of stresses. Hence most analysis work during the design stage is for stiffness and a stress analysis is carried to check the final structural details.

2.7 Development of the Structure of Sports and Racing Cars The historical course of the development of the car chassis has been led in the past by racing and sports car designers who have either failed or achieved glory in applying new technology and new ways of thinking to their car designs. In the past it was thought that the car engine embodied the main technology in the car, but in this era of motor car development and with the benefit of hindsight, the importance of the role that the vehicle chassis has played in successful cars can be seen. The following brief history pays particular attention to developments in Grand Prix racing, as this is seen as the show case for automotive technology. The earliest cars were built on a steel girder frame which supported a timber body. It didn't matter whether the car was a Grand Prix racing car or a family saloon, the structural action of chassis was the same. This technology had come straight from the coach building industry and it was generally believed that a degree of flexing of the chassis was a necessary part of the suspension.

If built along substantial lines, the girder

chassis possessed adequate bending stiffness, but its torsional stiffness was very poor. The conventional girder chassis consisted of two longitudinal steel girders of channel section spaced by transverse members of similar construction. This was used almost exclusively in sports and racing cars up until the 1930's. Even racing cars are subject to Newton's laws of motion, and so it is that a heavy racing car requires more power to accelerate and brake and has a greater desire to continue in a straight line when the driver is trying to turn a corner. In pursuit of better performance from their racing cars, designers recognised the need to reduce weight. As these early chassis were particularly heavy for their strength and stiffness, the chassis was an ideal place to reduce weight. The move to tubular ladder chassis was led by racing car designers when in 1934 the German Auto Union team introduced a Grand Prix racing car with a twin tube chassis, Mercédès-Benz also introducing a chassis of similar layout that year. This considerably increased the torsional stiffness of the chassis with minimal change in the bending stiffness. The types of suspension in use at the time, namely live axles and later swing axles, were not dependent on a stiff chassis to preserve the suspension geometry. These suspension types have the wheels connected to axles Page 22

and the wheel and axle assembly moves a single unit. Torsional deformation of the car structure has little effect on the wheel angles whereas the mechanism of wishbone independent suspensions rely on the relative positions of suspension member pivots to determine the angular positions of the wheels. Figure 2.11 shows typical independent wishbone, swing axle and live axle suspension systems.

Figure 2.11 - Live Axle, Swing Axle and Independent Suspension

Around 1934 came the application of independent suspension to racing cars. Whereas before this the angular relationship of the wheels was determined by a live axle acting as a beam joining the wheels, now the car itself was part of the structure required to preserve the angular relationship of the wheels. Figure 2.12 is a simplified diagram of the connection of independent suspension to the vehicle structure.

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Figure 2.12 - Independent Suspension Attached to Vehicle Structure

The need for increased torsional stiffness was recognised by designers and attempts were made to improve the basic ladder chassis with extra tubular super structure, however this was generally not effective. It was not until 1952 that two new sports cars that were to be very successful, designed on space frame principals appeared; the Lotus Mark Six, see Figure 2.13 and the Mercédès-Benz 300SL, see Figure 2.14.

Figure 2.13 - Lotus Mark Six

Figure 2.14 - Mercédès-Benz 300SL

Spaceframe chassis construction was introduced to Grand Prix racing in 1954 by the Mercédès-Benz W196 which had a significant weight and stiffness advantage over rivals whose car structure were based on the ladder chassis.

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Figure 2.15 - Mercédès-Benz W196

The spaceframe chassis and multitubular chassis were used exclusively in Grand Prix racing until in 1962. Fuelled by the desire to win races, the search for further chassis stiffness and light weight brought about the introduction of the stressed skin construction Lotus 25 Grand Prix car. The Lotus 25, later becoming the Lotus 33 with its stressed skin structure achieved a torsional stiffness of around 2 to 2½ times that of the a conventional Grand Prix. It also achieved a typical weight saving of around 10 kg. The benefits of weight saving, excellent torsional stiffness and improved driver safety offered by this form of construction were soon recognised and followed by the majority of Grand Prix teams. The basic structure of the Lotus 25 Grand Prix car is shown in Figure 2.16.

Figure 2.16 - Structure of the Lotus 25 Grand Prix Car

The excellent stiffness and strength to weight ratio achievable with stressed skin construction currently sees all Grand Prix teams building their racing cars this way. It has also proven ideal for construction with new materials that have since become available such as aluminium honeycomb and currently carbon fibre. Figures 2.17 and 2.18 show modern Grand Prix car chassis.

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Figure 2.17 - 1989 Ferrari Grand Prix Car (bodywork cut away on top)

Figure 2.18 - 1988 McLaren MP4/4 Grand Prix Car, Bodywork Removed

In Australia today, ladder chassis for cars are common only in go-karts, vintage cars and some drag racing cars. Space frame chassis are popular for many types of racing cars, for example; Formula Ford and Formula Vee are restricted to tubular steel construction, Clubman racing cars must be of the "space frame" type and many original sports cars and sports sedans use space frame chassis. Many of the kit cars that are available in Australia are of space frame type construction such as Westfield Sports Car and the PRB Clubman and the AT Riciardi. In contrast to these budget sports cars is the Lamborghini Diablo, currently one of the fastest road cars it employs a space frame chassis (Sports Car World, 1990/91). Two cars with aluminium space frame chassis currently undergoing development for mass production are the Pininfarina Ethos (Motor, 1992) and the Audi Avus (Chiton's Automotive Industries, 1992).

Audi Avus

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Pininfarina Ethos Figure 2.19 - Modern Cars with Space Frames

Aluminium monocoques are required in Australia's premier open wheeler racing category, Formula Holden, and carbon fibre monocoques are found in Formula 2, Formula Libre and Sports Sedan cars in Australia. Carbon fibre monocoques provide the basic structure for many of the latest breed of supercars such as Ferrari F40, Jaguar XJ220, Bugatti EB110, McLaren F1 and the Yamaha OX99-11.

Yamaha OX99-11

McLaren F1

Jaguar XJ220 Figure 2.20 - Monocoque Chassis Road Cars

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2.8 Background of Clubman Cars As part of this project theoretical and laboratory analysis of the Westfield Sports Car chassis was carried out. As this is a clubman style car, background on clubman cars has been included in this report. The basic formula that defines a clubman car would be: A front longitudinally mounted engine, two seats in an open cockpit with no doors, live rear axle, multitubular space frame chassis and front wheels separate from the main body of the car. A typical car is shown in Figure 2.21.

Figure 2.21 - Westfield Sports Car Two of the earliest clubman cars were the Lotus Mark 6, which was being produced in 1954 and the Ginnetta G2 which was put into production in 1958. Based around multitubular space frames with aluminium body panels, these cars were designed to provide an unprecedented level of performance at a price affordable to the average motoring enthusiast. Their appointments were sparse, with little concession to comfort. They were suitable for transport during the week and could perform well on the racing track or in trials at the weekend.

Figure 2.22 - Ginnetta G2 Many specials' constructors and limited production manufacturers have since produced similar clubman cars, some copies of the more recognised designs, others of more original design, but the principals of the clubman have led to these cars often looking similar and usually performing well. The structural design of these cars is often very similar, many being based on a Lotus design for the Lotus Seven which first appeared in 1957. Since this time engine power outputs have risen, the price of steel has dropped, spring rates of the suspension have risen and there have been significant advances in tyre technology. Hence there is the desire to improve the chassis to gain the most advantage from these changes. Page 28

Figure 2.23 - Lotus Seven Body

Elfin Sports Cars first produced the clubman car shown in Figure 2.20 in Australia in 1962.

Currently

clubman cars are available in Australia in kit form from Westfield Sports Cars (WA), PRB Motors (NSW), Tilke Engineering (NSW) and Fraser Cars Ltd (New Zealand).

Specifications and general information

concerning the Westfield Sports Car is included in Appendix A.

Figure 2.24 - Elfin Clubman Car

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3 ANALYSIS OF THE WESTFIELD SPORTS CAR 3.1 Introduction To investigate vehicle chassis analysis, a Westfield SEi chassis supplied by Westfield Sports Cars Australia was used. The stiffness of this chassis was investigated using a finite element computer model. The computer model was validated using the results of laboratory testing. Two tests were carried out for evaluation of the computer model. i)

Bending stiffness of the chassis.

ii)

Torsional stiffness of the chassis.

The effect of variations on the torsional stiffness of the chassis was investigated using a computer model. The model was created for, and analysed with PAFEC finite element software on an Apollo workstation. Variations that were tested were aimed at either improving the torsional stiffness of the chassis or reducing construction costs. Only the stiffness of the chassis was investigated because of the following reasons: i)

The strength of the Westfield Sports Car has been well proven

ii) Measurement of stresses is expensive and was beyond the finances available to this project iii) Computer stress analysis of a vehicle requires a much more complicated model than does stiffness analysis. The number of load cases that must be considered for stress analysis also extends the time required to set up and analyse a model. iv) Stresses predicted by a model can only be as accurate as the loads that are used. To determine loads with reasonable accuracy would require special measuring equipment, unavailable to this project. Alternatively loads may be used as determined from other peoples work, however it appeared that the references that were available (Garrett 1953 and Costin and Phipps 1965) were somewhat dated as are the analysis methods that were used when these load cases were first suggested. v) Developments in suspension and tyre technology mean that the cornering performance of the car is likely to benefit from improved chassis stiffness.

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A quick overview of the activities that were involved in testing and analysis follows: Laboratory Testing Construction of sub frames for attachment of chassis to testing frame. Setting up the chassis, loading devices and measuring equipment for testing. Carrying out the test. Recording observations and the results of the test for later analysis and scrutiny. Theoretical Model Analysis Determining the geometry of the model Creating a data file that describes the geometry of the chassis, member and section properties, loads and restraints. Checking the data for errors Analysis of the model Interpretation of the results of analysis.

3.2 Determination of Chassis Geometry The physical characteristics of the chassis were required for a theoretical model of the chassis to be generated. Information such as section types and plate thicknesses were available from the management of Westfield's, however no plans or drawings of the chassis were available. Two methods of determining chassis geometry were considered: i)

Survey using optical surveying instruments.

ii)

Tape measure, measuring from reference beams.

At the time it was thought that an optical survey would provide the most accurate measurement of the chassis geometry, so with the assistance of Associate Professor L. A. White a survey of the chassis was commenced. Two theodolites, two subtense bars and the chassis were layed out as shown in Figure 3.1. A subtense bar is a bar with markings accurately calibrated to two metres.

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Figure 3.1 - Layout of Chassis Survey

Vertical and horizontal angles to each end of the subtense bars and several of the nodes were observed and the distance between stations A and B was measured. This data enabled calculation of positions of the nodes in three dimensional space. However the chassis survey technique of measurement was found unsuitable for the following reasons: i)

Making the observations was very time consuming.

ii) A check on measurements determined by the survey with a tape showed errors of 4 to 7mm. The time consuming nature of the theodolite observations and the large errors were partly to the level of skill of the operator. The geometry of the chassis was subsequently measured using a tape. Beams were clamped to the chassis to act as a reference for measurements. A one fifth scale orthogonal drawing was produced as a reference for further work. A copy of this drawing has been included in Appendix B. The geometry of the theoretical model was compiled into standard file format for the PAFEC finite element software by typing the node coordinates, member connectivities and other information defining loads, restraints and member properties. A graphics interface was used for checking that information was correct. The following diagram, Figure 3.2 shows the global axes of the model.

This is the axes system used

consistently in this report.

Figure 3.2 - Axes System

3.2 Chassis Bending Stiffness 3.2.1 Laboratory Test Description and Procedure The chassis bending test of the Westfield Sports Car involved simply supporting the chassis on its front and rear extremities as shown in Figure 3.3 and applying loads near the middle of the chassis while the deflections at known positions were measured.

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Figure 3.3 - Chassis Bending Test

The chassis was placed on timber blocks in the four restraint positions shown in Figure 3.3. The blocks were supported on a smooth concrete floor. Dial gauges were set up to measure deflections at nodes 12 and 24 relative to the concrete floor. A load hanger was placed midway between nodes 151 and 154 on which dead weights were placed. The following steps were carried out during testing: i)

The chassis was first proof loaded to with 50 kg to bed in the chassis at the supports and to ensure the chassis was sitting evenly on its supports.

ii)

The proof load was removed and dial gauge readings were observed at nodes 12 and 24.

iii)

A load of 10 kg was applied and dial gauge readings at nodes 12 and 24 were observed. This was repeated for loads of 10 kg, 20 kg, 40 kg, 50 kg and 60 kg. Observations were made as the load was increased to 60 kg and then reduced in the same increments back to zero.

iv)

Dial gauge deflections were then observed for a loading pattern of 0 kg, 50 kg, 0 kg, 50 kg, 0 kg.

v)

The average deflections of the gauges at nodes 12 and 24 were calculated for the load increments. These are plotted in Figure 4.1 in the results section.

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3.1.2 Theoretical Analysis Description The chassis model was created using primarily PAFEC type 34000 beam elements.

These elements are

straight uniform beams with two nodes. They cater for bending in two principal directions, axial forces and twisting about the shear centre. The beam section is described by second moments of area Iyy and Izz, area A and torsional constant C (same as J). The flexural and shear centres of this element must coincide.

Six

degrees of freedom are modelled at each of the two nodes of this element; Ux, Uy, Uz, φx, φy and φz. Figure 3.4 shows the degrees of freedom of the 34000 element.

Figure 3.4 - PAFEC 34000 Beam Element The theoretical basis of this model is that bending displacements in each direction vary as a cubic along the length, giving linearly varying bending moments. Axial force and twisting moment are constant along the length. Results produced by this element are exact in statics. The beam members in the model are represented by the member centre lines. Other elements used in the model were the suspension members which were only axial force elements and plate elements for the engine and gearbox mounts. The plate elements were capable of accepting both in plane and out of plane forces. The elements of the model were separated into eleven groups of similar members with the same sectional properties. This was done to enable quick and simple specification and changing of member properties. A diagram showing the node numbering and the data file which defined the chassis model is included in Appendix C.

Figure 3.5 on the following page shows the member groups and their colours with brief

explanations of each of the groups used in the model.

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Figure 3.5 - Standard Chassis Model Member Groups

The restraints and loading used for the chassis bending analysis as a model of the chassis bending test are shown in Figure 3.6.

Figure 3.6 - Chassis Bending Model A load of 1000 N was applied mid way between nodes 151 and 154. The chosen value of the load was not important, just that the value was known because the theory used to analyse the model assumed linear elastic response.

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3.3 Chassis Torsional Stiffness 3.3.1 Laboratory Test Description and Procedure The torsional stiffness test was carried out in the Curtin University of Technology Civil Engineering concrete laboratory, using a substantial reaction frame designed for testing concrete beams. The chassis was supported on the frame at three points; one front and two rear simulated wishbones. The connections to the wishbones were retained by loosely fitting bolts that allowed the connections to act as joints pinned in three dimensions. The simulated wishbones along with solid links replacing the spring and shock absorber units distribute test loads into the chassis similarly to how loads in a car are transmitted through the suspension. At the rear of the chassis, restraint from rotation about the longitudinal X axis was provided by the wishbone connections. At the front of the chassis the one wishbone connection prevented mechanistic rotation of the chassis and facilitated the application of a torque loading to the front of the chassis. The load was applied at the unsupported front wishbone and deflections of the chassis were measured by dial gauges supported from the reaction frame. Loads were applied as steel dead weights in 20 kg and 18.1 kg increments with deflections observed at selected node points for each increment. Figure 3.7 shows the chassis with simulated wishbones and the loading and restraint conditions.

Figure 3.7 - Chassis Torsional Test The test was carried out on two occasions; after the first test was carried out, inspection of the results indicated inconsistent load - deflection behaviour. To rectify this two steps were taken before and during the second test: i)

The removal of a pulley through which the load was initially being applied. The pulley allowed the vertical load to be applied upwards, however it appeared that the pulley was jamming when load was applied.

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ii)

After incrementing the load, the chassis was tapped with a small block of wood until the dial gauge readings became steady, before deflections were observed.

The testing procedure was carried out as follows: i)

The chassis and subframes were set up in the test frame as shown in Figure 3.7.

ii)

Dial gauges were set up at selected nodes on the chassis. Two dial gauges at the front measured rotation at the front while two dial gauges at the rear measured rotation of the rear of the chassis. Deflections were measured at the rear of the chassis because although the rear was prevented from mechanistic rotation, elastic deformations of the sub frame and wishbones allowed some rotation.

iii)

Distances between dial gauges and the load lever arm were measured with a tape.

iv)

A 60 kg proof load was applied to settle in the chassis at its supports. Loads were applied at the front wishbone as shown in Figure 3.7.

v)

Dial gauge readings were observed before loading was commenced.

Loads were then applied and

removed in the pattern shown in Figure 3.8. Before observing dial gauge readings and after the load was applied, the chassis was tapped with a small block of wood until dial gauge readings stabilised. vi)

Measurements of distance between dial gauges and load lever arm distance were checked.

A full set of observations from the laboratory tests is given in Appendix D.

Figure 3.8 - Pattern of Loading for Torsional Test

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3.3.2 Theoretical Analysis Description The chassis model was the same as that used for the bending analysis but the loads and supports were changed to model the torsion test conditions. The restraints and loading used for the chassis torsional analysis are shown in Figure 3.9.

Figure 3.9 - Chassis Torsional Test Model The load applied to the front wishbone was 1000 N.

Where deflections for other loads are required the

deflections obtained from analysis with the 1000 N load may be scaled directly proportionally to the change of load because the computer model was linear.

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4 RESULTS AND DISCUSSION

4.1 Bending Test and Bending Analysis The chassis bending test was a simple test which was carried out to help establish the accuracy of the theoretical model of the chassis. The chassis was loaded between nodes 151 and 154 with deflections at nodes 12 and 24 being observed. (These nodes have been identified previously in Figure 3.6). The average vertical deflections of nodes 12 and 24 are plotted for different loads in Figure 4.1.

Figure 4.1 - Load Deflection Response of Chassis Bending

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The relationship between load and deflection observed in the test followed a linear pattern with a coefficient of correlation, r2 = 0.995. The measured stiffness of the chassis in bending is less than the calculated stiffness by about 11%. The linear relationship between load and deflection from Figure 4.1 being: Observed stiffness:

Δ = load ∗ 0.70

Theoretical stiffness:

Δ = load ∗ 0.62 where Δ = deflection in mm, load = load in kN

The linear relationship for observed stiffness ignores the permanent set which is labelled in Figure 4.1. The permanent set was probably the result of local crushing of the timber supports where high spots of welds were in contact with the supports. The difference in stiffness between the model and the measured stiffness of 11% may be due at least partly to the following reason. The chassis was supported on timber blocks into which stresses were transmitted across the grain. These timber blocks were quite thick and supported the chassis on a relatively small bearing area. As any deflections at the supports will be reflected in the measured deflections, compression of the supports will result in measured stiffness apparently less than the actual stiffness of the chassis. A quick check for elastic compression of the supports indicates that up to 1 - 3% of the difference may be as a result of deformation in the supports. This does not include local deformation of the supports which may occur where there are local high spots in the chassis above the supports. Other reasons for the model stiffness differing from the observed stiffness were: The supports used in the test may not have been properly level. Some member eccentricities were difficult to include in the model and where they were not large they were excluded. This would increase the effectiveness of the bracing and slightly increase the stiffness of the model. Angular deformation of the members to which the dial gauges were attached may have caused increases to the observed deflections. The shape of the deflected chassis undergoing bending was determined from the model. Deflections for the bottom plane outer edge members are plotted in Figure 4.2 for a load of 1000 N between nodes 151 and 154.

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Figure 4.2 - Shape of Chassis for Calculated Bending Test

The average deflections of nodes 12 and 24 are shown in Figure 4.2 by a dashed line. The maximum vertical deflection of the chassis between front and rear wheel centres of 0.26mm is shown on Figure 4.2. The observed vertical deflection of 0.26 mm per 1000 N can be linearly extrapolated to 1.73 mm per 680 kg mid span load. This compares to a recommended bending stiffness of not more than 1.27mm deflection for a mid span load of 680 kg by Fenton (1980). The bending stiffness achieved by the Westfield Sports Car chassis is obviously less than that recommended by Fenton, however Fenton's recommendations include no discussion on the weight of the vehicle for which his recommendation is made. It would be logical to include the weight of a car in a recommendation for bending stiffness as the bending deflections are likely to increase proportionally to the weight of the car. The sharp change in stiffness graph of Figure 4.2 at point A is as a consequence of the presentation of the data for this graph. Point A is an external node on the bottom plane of the chassis, point B is a node on the same member as point A, but it is closer to the longitudinal centreline of the chassis and directly under the rear support. Also there is no reason for concern over a sharp decrease in the stiffness of the chassis in this position because this part of the structure is outside of the wheelbase of the car and only subject to small loads.

4.2 Torsional Test and Torsional Analysis The chassis torsional stiffness test was carried out to establish the accuracy of the theoretical model of the chassis. As mentioned earlier the torsional stiffness test was carried out on two occasions. In the first instance there was large scatter of the results and virtually no consistency. This was thought to be the result of applying the load through a pulley in the first test. The pulley was not of good quality and although it appeared to run Page 41

smoothly and freely when unloaded, it was likely that the pulley was binding against the pulley shaft when load was applied. Thus the pulley was discarded for the second test. Another precaution that was taken for the second test was to tap several times checking that dial gauge positions did not fluctuate before dial gauge readings were recorded. The results of the first torsional test are not included in this report because due to their inconsistent nature, they are of little use. The torsional deflection response for the second torsion test of the Westfield Sports Car chassis is shown in Figure 4.3. The load deflection response calculated from the chassis model is also shown on this graph for comparison with the measured response.

Figure 4.3 Torsional Load Deflection Response

The results of the second torsional stiffness test show very little scatter. A response which is clearly linear may be observed. For the torsional stiffness test, deflections were measured at the front and rear of the chassis on each side of the chassis at nodes 102 and 123 at the front and nodes 105 and 111 at the rear. Figure 3.9 previously defined these node numbers. To calculate the torsional stiffness, the rotation at the rear of the chassis was subtracted from the rotation at the front of the chassis. The torque applied at the front of the chassis was calculated from the magnitude and lever arm of the load. Thus the torsional stiffness was the Torque applied divided by the rotation between the front and rear of the chassis.

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The torsional stiffness of the chassis in the test calculated in this way was 1134 Nm/deg on average (see Figure 4.4) and the stiffness of the model was 1121 Nm/deg.

Figure 4.4 - Scatter of Measured Torsional Stiffness For the torsional test errors such as error of measurement of the chassis geometry, approximations in the model by ignoring some eccentricities and error in reading dial gauges should be the same as those for the bending stiffness test.

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The difference between the measured torsional stiffness of 1134 Nm/deg and the model torsional stiffness of 1121 Nm/deg of 1.2% was extremely good and suggests that the model was a good representation of the chassis. The range of torsional stiffness observed during testing was from +5.4% to -10.4% of the model stiffness.

The biggest difference of 10.4% between model and test is still within the average difference

observed for the bending test.. When the torsional stiffness of the model was calculated from the rotation of the front suspension wishbones with the rear wishbone restrained from movement by the supports, the torsional stiffness of the chassis was found to be 1050 Nm/degree. The difference between the two calculated stiffnesses is due to the position of the load relative to where the stiffness was measured. Measuring the torsional stiffness from the wishbones resulted in an apparently more flexible structure because the loads and supports were attached directly to the wishbones. Nodes 102, 123, 111 and 115 were away from the loads and supports which were the most highly stressed regions, thus the measured stiffness was higher. The graph of angular deflections along the chassis in Figure 4.5 highlights the most flexible areas of the chassis. The most flexible areas, which are where the curve is steepest are the first 70mm from the front of the chassis and 200mm to 500mm from the front of the chassis which is in the engine bay area. The stiffest parts of the chassis is the 250mm directly behind the hoop on which the steering wheel is mounted and the very front of the chassis, after the first 70mm and where there is corner bracing in the front, top plane of the engine bay. If the entire chassis was able to be increased to the same stiffness as directly behind the steering hoop, the chassis would have a torsional stiffness of over 2000 Nm/deg.

Figure 4.5 - Torsional Deflections Along Chassis Page 44

4.3 Torsional Stiffness - Chassis Variations A number of variations to the standard chassis have been considered. Mostly these variations are intended to be suitable for production at some time in the future, however some less practical variations have been considered on the basis that they may help understanding of the structural actions of the chassis. Table 4.1 to Table 4.7 describe the various changes made and the effect of these changes on the torsional stiffness and weight of the chassis. Following each table is a graph with the torsional stiffness along the length of the chassis plotted.

In each case Car1, the standard chassis configuration is included as a reference.

The

variations to the chassis are shown graphically in Appendix E along with information about masses, centres of mass and moments of inertia of the chassis variations. The types of variations to the basic chassis structure are grouped together according to the type of change which was made. In general terms the changes which resulted in a worthwhile increase in chassis stiffness were extra centre tunnel bracing, increased member section sizes with same or even reduced wall thicknesses, extra engine bay bracing and extra bracing in the nose. The changes which were least desirable were the removal of the existing main engine bay brace and attaching steel plates to various areas such as the front of the drive train tunnel and the sides of the engine bay.

Table 4.1 - Standard Chassis Models File

Description

Car1

Standard chassis with minimum three point restraint Torsional stiffness calculated as per laboratory test Torsional stiffness calculated from wishbones deflections

Car20 Car23

As Car1, but using PIGS generated data file (as a check) This file models the bending stiffness test

Torsional Stiffness (Nm/deg)

Weight (kg)

1121

63.3

1050

63.3

0.0

0.0

16.6

1050

63.3

0.0

0.0

16.6

63.3

% Change from Stiffness Car1 to Weight Stiffness Weight Ratio

0.0

Hereafter all files are the same as the standard Westfield Sports Car chassis except for those variations specified. Minimum three point restraint and torsional stiffness calculated from deflections at the wishbones is used consistently.

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Table 4.2 - Category I, Changes to Member Sizes File

Description

Car2

Top plane members changed to 31.8 x 1.6 SHS Bottom plane members changed to 31.8 x 1.6 SHS Top and bottom plane members changed to 40 x 1.2 SHS Bottom side members changed to 40 x 1.6 SHS Bottom and top side members changed to 40 x 1.6 SHS All member changed to 40x40x1.0 SHS

Car3 Car 16 Car26 Car27 Car29

Torsional Stiffness (Nm/deg) 1152

Weight (kg)

1112

65.2

5.9

3.0

17.1

2051

71.0

95.3

12.2

28.9

1185

67.0

12.9

5.8

17.7

1412

69.4

34.5

9.6

20.3

2845

74.6

171

17.9

38.1

64.4

% Change from Stiffness Car1 to Weight Stiffness Weight Ratio 9.7 1.7 17.9

Figure 4.6 - Torsional Stiffness Plots of Changes to Member Sizes

Changes to member sizes produced the biggest increases in torsional stiffness to weight ratio when the section sizes of the members were increased significantly and the wall thicknesses of the hollow members decreased. Comparing changes of the top longitudinal members to changes to the bottom longitudinal members showed that changes to the top longitudinal members produced a more pronounced effect on torsional stiffness.

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Table 4.3 - Category II, Changes to the Engine Bay File

Description

Car4 Car5 Car6

Extra brace in top plane of engine bay

Car9 Car10 Car11 Car15 Car 18

Side bracing in engine bay changed Extra lateral member across top of engine bay Extra top, right hand engine bay brace Normal engine bay brace removed Normal engine bay brace replaced by LH and RH braces Engine bay side braces replaced by 1mm steel panels Extra cross members in engine bay

Torsional Stiffness (Nm/deg) 1261 1040 1105

Weight (kg)

1060 683 1148

63.8 62.5 63.5

1.0 -35.0 9.3

0.8 -1.3 0.3

16.6 10.9 18.1

1061

66.9

1.0

5.7

15.9

1475

64.9

40.5

2.5

22.7

63.8 63.5 64.0

% Change from Stiffness Car1 to Weight Stiffness Weight Ratio 20.1 0.8 19.8 -1.0 0.3 16.4 5.2 1.1 17.3

Figure 4.7 - Torsional Stiffness Plots of Engine Bay Changes

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The changes around the engine bay consisted of changes to the top plane bracing, changes to the bracing in the side of the engine bay and use of plates instead of bracing in the sides. Additional bracing in the top plane, correctly positioned achieved an excellent increase in torsional stiffness for a simple change. When the added bracing was not well positioned only insignificant increases to torsional stiffness were observed. The removal of the main top plane engine bay brace caused a dramatic reduction in the torsional stiffness of the chassis. Changes to the the bracing in the side of the engine bay was carried out so that the degree of triangulation was not reduced. Consequently there was no large changes to the torsional stiffness for the variations analysed. Using plates instead of bracing was a solution which increased the weight of the chassis with no significant gain in torsional stiffness.

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Table 4.4 - Category III, Addition of bracing to Chassis Nose File

Description

Car8

Nose fully braced (some of this may not be practical) Extra nose bracing

Car17 Car24 Car25

Some extra nose bracing Some extra nose bracing

Torsional Stiffness (Nm/deg) 1453

Weight (kg)

1334 1149 1215

65.0 64.0 64.6

65.8

% Change from Stiffness Car1 to Weight Stiffness Weight Ratio 38.4 3.9 22.1 27.0 9.4 15.7

2.7 1.1 2.1

20.5 18.0 18.8

Figure 4.8 - Torsional Stiffness Plots for Chassis with Extra Bracing

Bracing added to the nose of the chassis produced some worthwile increases in torsional stiffness. The fully braced nosed produced a 38% increse in torsional stiffness, and while this may not be practical for production, each of the other changes that were more suitable for production resulted in an increased stiffness to weight ratio. The nose is a relatively short part of the overall length of the chassis so the magnitude of these increases in stiffness was unexpected.

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Table 4.5 - Category IV, Changes to the Centre Tunnel File

Description

Car12

1mm steel plates added to front of tunnel Extra centre tunnel bracing, except on bottom plane Extra centre tunnel bracing all around

Car19 Car21 Car28

Tunnel members changed to 25 x 1.6 SHS

Torsional Stiffness (Nm/deg) 1157

Weight (kg)

1450

67.6

38.1

6.8

21.4

1504 1183

68.4 65.9

43.2 12.7

8.1 4.1

22.0 18.0

71.1

% Change from Stiffness Car1 to Weight Stiffness Weight Ratio 10.2 12.3 16.3

Figure 4.9 - Torsional Stiffness Plots of Centre Tunnel Changes

Fully bracing the centre tunnel section, which had external dimensions of 220mm x 140mm over the main part of its length produced a 43% increase in torsional stiffness. This shows that the centre tunnel section plays an important part in the overall torsional stiffness of the chassis. Fully bracing the centre tunnel may not be practical in that it would restrict access to the driveshaft which passes through this tunnel. Bracing the tunnel on all but the bottom plane also resulted in a large increase in torsional stiffness of 38%. Welding plates to the tunnel section was a solution which was not analysed but could be worthwhile considering in the future.

Table 4.6 - Category V, Use of Plates File

Description

Car12

1mm steel plates added to front of tunnel Altered engine support beams webbed with 1mm plate

Car14

Torsional Stiffness (Nm/deg) 1157

Weight (kg)

1179

64.4

71.1

Page 50

% Change from Stiffness Car1 to Weight Stiffness Weight Ratio 10.2 12.3 16.3 12.3

1.7

18.3

Car15

Engine bay side braces replaced by 1mm steel panels

1061

66.9

1.0

5.7

15.9

Figure 4.10 - Torsional Stiffness Plots for Changes Using Plates

The increases in torsional stiffness that were achieved by adding plates to the chassis were generally offset by the increases in weight and reduction in accessibility that resulted from using plates.

The plated engine

support beams gave a torsional stiffness increase of 12% but the engine support beams were also modified in this case. The modified engine support beams increased torsional stiffness by 11% without the use of plates. These results should not be construed to suggest that plate solutions will not be viable, rather that the variations which were tested were not particularly viable.

Page 51

Table 4.7 - Category VI, Other Changes File

Description

Car7

Member added under gearbox (Node 61 to 63) Geometry of engine support beams altered Altered engine support beams webbed with 1mm plate

Car13 Car14

Torsional Stiffness (Nm/deg) 1066

Weight (kg)

1163

63.3

10.8

0.0

18.4

1179

64.4

12.3

1.7

18.3

63.6

% Change from Stiffness Car1 to Weight Stiffness Weight Ratio 1.5 0.5 16.8

Figure 4.11 - Torsional Stiffness Plots for Other Changes

The modified engine support beams gave an 11% increase of torsional stiffness for a relatively simple change in geometry and no increase in weight. The member under the gearbox was a change that would be difficult to put into production. The effect of this member was minimal.

Page 52

The changes that have been considered are only a sample of the changes that could be considered in a serious effort to improve the torsional stiffness of this chassis. For instance no additional bracing was considered for the rear part of the chassis. The changes that were considered targeted the more flexible areas of the chassis, as indicated by the torsional stiffness diagram, Figure 4.5 where changes could be made without disrupting the layout of the chassis. Where positive improvements to the chassis have been determined, these changes could be refined by further analysis with the computer model.

Page 53

5 CONCLUSIONS The first objective of this project that was carried out was to investigate the use of a computer model for predicting the stiffness of a vehicle chassis. The space frame type chassis of the Westfield Sports Car was modelled using finite element software. The model consisted of mainly beam elements and it was found that a beam model predicted the stiffness of the chassis with good accuracy. The accuracy of the computer model was established from carrying out the same tests both in the laboratory and with the computer model and comparing the results. Two distinct tests were carried out that were bending stiffness and torsional stiffness. The bending stiffness test showed that the computer model was within 11% of the laboratory observations. This difference may be partly accounted for by a problem with the way the laboratory test was carried out. The chassis was supported on compressible timber supports and because this was not foreseen as a problem, no measurement of the deflections at the supports were taken during the test. Consequently the results of the test indicated the chassis was more flexible than it actually was. The computer model was stiffer than the results of the bending test so at least some of the 11% difference was due to compression at the supports in the laboratory test. The torsional stiffness test did not have the problems of the bending test and comparison between model and average measured stiffnesses was of the order of 1%. The torsional stiffness was measured a number of times for different loads and the range of all measurements was about 10% if the extremes are discarded. The 1% difference between the model and average observed stiffness is well within this 10% range.

Hence the

accuracy to which the model can be confirmed is limited by the accuracy of test measurements. The load deflection response of the chassis was consistent and linear for both laboratory tests which further confirms the use of a simple beam model based on linear elastic theory. The second objective that was carried out was to make use of the computer model for testing changes to the chassis. The torsional stiffness only was tested for the chassis modifications because it was desirable for the torsional stiffness of the chassis to be improved, where as the bending stiffness was already adequate.

Page 54

There were a number of changes that Westfield Sports Cars may test further on a full scale chassis and there were a number of other changes that may be beneficial. The changes fell into five broad categories: i)

Changes to member sizes

ii) Addition or removal of bracing in the engine bay iii) Addition of bracing to the nose of the chassis iv) Addition of members to the centre tunnel v) Use of plates instead of bracing vi) Other changes The first category which was changes to member sizes showed excellent improvements to torsional stiffness for a minimal weight penalty with increased section sizes.

Reducing the wall thicknesses of the hollow

members when the section sizes were increased minimised increases of weight in the chassis. The most pronounced effects of changing member sizes were observed where members in areas with a lack of bracing were changed such as the top and bottom plane members in the engine bay and cockpit. The largest increase of stiffness of all the changes analysed, changing all members to 40x40x1.0 SHS, was in this category. Although this change could not be directly incorporated into manufacture of new Westfield’s because there is physically not enough space in some places for these larger members, it demonstrates the efficiency of larger section sizes and smaller wall thicknesses for this type of chassis. The second category which was the addition and removal of bracing in the engine bay showed that the bracing in the top plane of the engine bay was very significant. The removal of the existing main engine bay brace in the top plane reduced torsional stiffness by 35% while adding a second main engine bay brace in the top plane increased the torsional stiffness by 20%. No major changes were made to the side bracing of the engine bay but presumably there is little potential for increased torsional stiffness by adding bracing to the sides because the sides are already well braced.

Significant decreases in torsional stiffness would be likely if the side

bracing of the engine bay is partly or wholly removed.

Page 55

Bracing in the nose of the chassis was the third category and some worthwhile increases in torsional stiffness were obtained with nose bracing. However at the nose of the car there are other requirements which limit the use of bracing. Steering arms protrude through the side of the nose and the engine cooling system limits bracing in the front plane. Thus the benefits of nose cone bracing indicated by the model would not achievable on a finished car. Extra bracing of the centre tunnel was very effective in increasing the torsional stiffness of the model. The largest increase in torsional stiffness was observed when the centre tunnel was braced on the sides and top and bottom planes. The torsional stiffness increased by 43% for only an 8% increase in weight for this case. Changing the member section sizes of the tunnel increased torsional stiffness by 13% and while this increase is much less than that achieved with extra bracing, it would require less labour for construction than would the extra bracing. If additional bracing and increased section size is applied to the centre tunnel, the individual increases are very unlikely to be cumulative. The reason why increased member sizes gave such an increase in torsional stiffness was because the centre tunnel was poorly braced. With a well braced tunnel, section sizes will be much less significant. The use of plates in the place of hollow section bracing was generally not structurally advantageous. Flat plates 1mm thick were analysed with the model. Where plates were used instead of hollow section bracing, the plated solution was heavier and the model suggested only a small increase in torsional stiffness. Plates of 1mm thickness were used because thinner plates may have been difficult to weld. It may be beneficial to investigate the use of thinner plates and also the use of profiled plates. Plate solutions have the advantage that they are simpler to fabricate than tubular members when no services are required to pass through the plate and disadvantages of restricting access through the chassis and difficulty of fabrication where services are required to pass through the plate. The final category considered two unrelated changes; addition of a member under the gearbox and alteration of the engine support beams. The member under the gearbox would be a difficult member to add in practice and had little effect on torsional stiffness. Alteration of the engine support beams did not affect the weight of the chassis but produced a worthwhile increase in torsional stiffness of 11%. This change would be relatively simple and it should be considered for incorporation into production. The further addition of 1mm steel plates to the altered engine support beams had little effect. Only a small number of the possible changes to the chassis have been analysed. With the work in creating and verifying the model already done, it would not require much more work to investigate numerous other changes. Testing a large number of changes to the chassis would have been a relatively simple task but in the context of this project it was seen as more advantageous to concentrate on establishing the accuracy of the model and showing how this was done. The results of a smaller number of variations could also be presented in more detail, making the use of a computer model for testing vehicle structures more clear. With the importance of light weight and good stiffness for a car chassis and the high cost of building a testing prototype vehicles computer model analysis is likely to be cost effective method of determining upgrades to an existing chassis.

Computer model analysis can be effective for large production and special production

vehicles alike. Page 56

5.1 Recommendations From analysis of the computer model, there are a number of changes to the chassis that should be investigated for immediate inclusion into the production of the Westfield Sports Car chassis.

The most practical and

effective changes were: i)

Additional top plane engine bay brace

ii)

Additional bracing of the centre tunnel

iii)

Increased top plane member section size with same or reduced wall thickness.

iv)

Geometry of the engine support beams altered

v)

Extra nose bracing. Suitable bracing geometry may be determined by investigation of complete car and further analysis with the computer model.

In general for a structure of this type the stiffness will be increased for any given weight when section sizes are increased and wall thicknesses decreased.

Such changes should be subject to further investigation to

determine if welding thinner walls will cause a problem and if particular wall thicknesses are required for withstanding rust, abrasion and local stresses around mounting brackets such as suspension mounting brackets. A recommendation not associated with the analysis of the Westfield Sports Car, comes from applying an engineering knowledge to the background information given in this report. It very beneficial to consider the weight of vehicle as well as the vehicle's purpose or engine size when recommending or legislating for stiffness of the vehicle. Whether torsional stiffness or bending stiffness is considered, the reason stiffness is required is to limit deflections. The deflections of a structure are just as dependent on the applied loads as the stiffness of the structure. In the case of a vehicle, the loads are as a direct result of the weight of the vehicle, thus any sensible recommendations or legislation for vehicle stiffness should include consideration for vehicle weight.

Page 57

5.2 Further Study With the limited amount of time and resources available for a final year project, there remains much on the analysis of vehicle structures that could be investigated of the structure of the Westfield Sports Car. This project should provide a good background for any further work investigating vehicle loads, structures and dynamic response. The original intention to carry out a detailed stress analysis was not carried out, however diagrams were drawn and masses measured for around thirty components, covering the major components of the Westfield Sports Car. A lumped mass model from this data was partially completed for stress analysis work and could be made available. Information about the components of the Westfield Sports Car has been included in Appendix F.

Page 58

6 ACKNOWLEDGMENTS Atkinson, Scott

Mr Atkinson provided a great deal of assistance with numerous computing problems, writing programs for manipulating data, fixing up sick computers, processing information for plotting and printing and transferring information between different computers.

Chandler Dr I

Dr Chandler was always prepared to talk about ideas and problems encountered in the course of the project. I have enjoyed these discussions, often being infected with his positive attitude. His time spent sifting through computer print outs or laboratory results to try a find where I had gone wrong was invaluable. Dr Chandler has also helped to improve the standard of this report by his efforts in proof reading several draft copies, making valuable comments.

Fox, Stephen

I wish to thank Mr Fox for his interest in my project and specially thank him for supplying the Westfield Sports Car chassis on which my project was based.

It has also been a privilege talking to Mr Fox and

learning from his experiences building road and racing cars. Gard, Jaime

I would like to thank Mr Gard for the interest he has shown in my project and for the time he has spent discussing vehicles and vehicle structures with me, in particular his work chassis torsional testing and race car suspensions. Mr Gard has also spent time checking the accuracy of information in my report and I greatly appreciate this and express my sincere thanks.

Kong, Paul

Mr Kong has helped me by checking computer models for errors. I would like to thank him for this.

Curtin University of Technology Civil Engineering laboratory technical staff The laboratory staff have provided assistance in carrying out laboratory tests, different to the testing normally carried out in the Curtin Civil laboratories. Sceresini, Robert

I would like to thank Mr Sceresini for helping with physical problems such as moving chassis and lifting engines.

Associate Professor L.A. White

I extend my thanks for assistance in carrying out the survey of the chassis.

Page 59

7 REFERENCES Baxter-Smallwood, J (1992) "FEA gets Lola rolling", Advanced Composites Engineering June Beermann, H J (1989) The Analysis of Commercial Vehicle Structures, Mechanical Engineering Publications Ltd, London. Bruhn, E F (1958) Analysis and Design of Flight Vehicle Structures Bureau of Transport and Communications Economics (1990) Cost of Road Crashes in Australia - 1988 Campbell, Colin (1973) Design of Racing Sports Cars, Robert Bentley Inc., Cambridge. Campbell, Colin (1978) The Sports Car,: Its Design and Performance, Robert Bentley Inc., Cambridge. Carey J (1991) "The G Force", Wheels Magazine, May Carey, J (1992) "Max Factor", Wheels Magazine, May Costin, M and Phipps, D (1965) Racing and Sports Car Chassis Design, B. T. Batsford Ltd, London Cotton, M (1988) Classic Porsche Racing Cars, Patrick Stephens Ltd, England. Coulter, J (1986) The Lotus and Caterham Sevens, Motor Racing Publications Ltd., England. Crombac, G (1986) Colin Chapman. The Man and His Cars, Patrick Stephens Ltd, England. Dubensky, R G (1986) What Every Engineer Should Know About Finite Element Analysis Methods, Chrysler Motors Corp. Federal Office of Road Safety (1989) Australian Design Rules for Motor Vehicles and Trailers, Third Edition, Federal Department of Transport and Communications. Fenton, J (1980) Vehicle Layout and Analysis, Mechanical Engineering Publications, London. Fothergill, D J, Southall, R, Osmond, E, (1984) "Computer Aided Concept Design of a Sports Car Chassis System", Proceedings of Institution of Mechanical Engineers Gard, J (1992) Oral Communication Garrett, K (1953) "Automobile Dynamic Loads", Automobile Engineer, February Garrett, T K (1953) "Structure Design", Automobile Engineer, March/April General Motors Holden's (1990) FEM of Motor Body Structures, ACADS Seminar, 25 June 1990 Greenway, W R, (1969/70) "Automobile Body Testing Techniques", Proceedings of Institution of Mechanical Engineers Lake, B (1992) "Budget Barnstormers", Motor Magazine, September McCarthy, M, (1987) Great Australian Sports Cars and Specials, Australian Consolidated Press, Sydney. National Council of CAMS, (19992) CAMS 1992 Manual of Motor Sport 1992, Confederation of Australian Motor Sport. Page 60

Niemi, E, Makelainen, P (1990) Tubular Structures, Third International Symposium, PAFEC Limited (1984) Data Preparation User Manual Level 6.1 PAFEC Limited (1984) PAFEC Theory Page, E (1991) "Two Way Stretch", Wheels Magazine, October Palmer Tube Mills Australia Pty Ltd (1991) Catalogue 1991, Palmer Tube Mills, Australia. Rose, J (1988) Ginetta The Illustrated History, Haynes Publications Inc., California. Setright, LJK (1968) The Grand Prix Car 1954-1966, George Allen and Unwin Ltd, London. Setright, LJK (1976) The Designers, Weidenfeld and Nicolson, London. Sturz, W D, (1990/91) "Hell Fire", Sports Car World, Summer pp 14-21 Timishenko and Gere (1968) Elements of Strength of Materials, Webb, G G

(1984)

"Torsional Stiffness of Passenger Cars", Proceedings of Institution of Mechanical

Engineers Westerman, A (1991) "Tyre Supertest", Motor Magazine, July Westfield Sports Cars Ltd, Westfield SE - SEi Instruction Manual, Westfield Sports Cars Ltd Williams, G (1991) McLaren. A Racing History, The Crowood Press Ltd, Wiltshire.

8 APPENDICES Appendix A - Westfield Sports Car Data Motor magazine recently conducted tests of four clubman cars available and able to be licensed in Australia (September 1992). The following information about the Westfield Sports Car is sourced from tests conducted by Motor. Kits sold in Australia

60

Cars registered in Australia

14

Engine

Front, longitudinally mounted 1.6L, 88kW (Toyota Corolla)

Suspension

front - independent double wishbones rear - double wishbones or live axle

Tyres

Yokohama A-008R, 205/60 R13 85H

Wheelbase

2270mm

Front Track

1310mm

Rear Track

1330mm

Overall Length

3515mm

Overall Width

1580mm

Height

1040mm

Ground Clearance

105mm Page 61

Kerb Weight

580kg

Weight/Power

6.6 kg/kW

Acceleration

0 - 100m

6.53s

Standing 400m

14.85s

Member Properties of Westfield Sports Car Chassis Tubemakers B.T.M. Square Hollow Sections Section

Size mm

Wall

Area

Thickness

mm²

kg/m

Ixx mm4 J

mm4

2020

20

mm 1.6

111

0.873

6080

10300

2525

25

1.6

143

1.12

12800

21200

Page 62

Appendix B - Westfield Sports Car Chassis Drawing

Page 63

Appendix C - Computer Model Data File (diagrams showing nodes and elements at end of data file listing) C C Standard Chassis C Generally units are in Newtons, N and metres, m CONTROL CONTROL.END C C .......1.........2.........3.........4.........5.........6.........7.........8 BEAMS MATERIAL=1 C (NOTE THAT SECTION.NUM IS THAT REFERRED TO BY PROPERTY NO. IN ELEMENTS MODULE) SECTI IYY IZZ TORSION AREA KY KZ ZY ZZ 1 12.8E-9 12.8E-9 21.2E-9 143E-6 .9 .9 816E-9 816E-9 C BOTTOM PLANE 2 6.08E-9 6.08E-9 10.3E-9 111E-6 .9 .9 608E-9 608E-9 C CENTRE TUNNEL 3 12.8E-9 12.8E-9 21.2E-9 143E-6 .9 .9 816E-9 816E-9 C TOP PLANE 4 5.36E-9 5.36E-9 10.7E-9 103E-6 .9 .9 487E-9 487E-9 C 5 6.08E-9 6.08E-9 10.3E-9 111E-6 .9 .9 608E-9 608E-9 C 6 5.36E-9 5.36E-9 10.7E-9 103E-6 .9 .9 487E-9 487E-9 C 7 6.08E-9 6.08E-9 10.3E-9 111E-6 .9 .9 608E-9 608E-9 C SUSP'N MEMBERS 8 12.8E-9 12.8E-9 21.2E-9 143E-6 .9 .9 816E-9 816E-9 C UPRIGHTS 9 16.1E-9 16.1E-9 1.0E-9 111E-6 .9 .9 800E-9 800E-9 C BRACKETS 10 16E-9 810E-9 20E-9 492E-6 .3 .7 100E-9 12.1E-6 C FLOORPANS C C MATERIAL MATE.NUM E NU RO 1 200E9 0.3 7850 C C C *** THE NODES MODULE IS PRINTED C *** USING GLOBAL CARTESIAN AXES C NODES NODE X Y Z C C NODES ON PERIMETER OF BOTTOM PLANE C 1 0 0.000 0.000 3 0.000 -.123 0.000 4 0.000 -.145 0.000 5 .196 -.182 0.000 6 .257 -.199 0.000 7 .341 -.224 0.000 8 .499 -.272 0.000 9 .585 -.297 0.000 10 .962 -.411 0.000 12 1.553 -.517 0.000 13 2.307 -.517 0.000 14 2.293 -.517 0.000 16 2.930 -.442 .127 17 2.930 -.126 .127 Page 64

18 19 20 21 22 23 36 24 26 27 28 29 30 31 32 33 34 35 38 37 C C C

2.930 2.930 2.930 2.930 2.930 2.307 2.293 1.553 .962 .585 .499 .341 .257 .196 0 0 1.809 1.809 .542 .542

0.000 -.456 .126 .442 .456 .517 .517 .517 .411 .297 .272 .224 .199 .182 .145 .123 -.517 .517 -.2845 .2845

.127 .127 .127 .127 .127 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

OTHER NODES ON BOTTOM PLANE 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

C C C

.257 .341 .499 .585 .962 .962 .585 .499 .341 .257 .962 .962 .962 .962 2.306 2.306 2.306 2.306 2.306 2.306 2.306 2.306 .542 .542

-.180 -.203 -.213 -.218 -.243 .253 .218 .213 .203 .180 -.162 -.156 .107 .097 -.432 -.140 -.124 -.088 .088 .124 .140 .432 -.2155 .2155

.003 .003 .003 .003 .003 .003 .003 .003 .003 .003 0 -.003 0 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 .003 .003

NODES FOR CENTRE TUNNEL 75 76 77 78 79 80 81 82

1.558 1.558 1.580 1.580 2.052 2.052 2.122 2.122

-.067 .055 -.064 .054 -.059 .055 -.059 .055

.191 .191 .191 .191 .196 .196 .197 .197 Page 65

83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

1.553 1.553 1.553 1.553 1.553 1.553 1.286 1.286 1.386 1.386 2.282 2.282 2.307 2.307 1.336 1.336

C C C

-.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003 -.003

PERIMETER NODES ON TOP PLANE 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129

C C C

-.065 .055 -.143 .135 -.434 .432 -.100 .073 -.087 .065 -.060 .060 -.060 .060 -.0935 .069

.069 .069 .069 .069 .167 .277 .282 .967 1.222 1.553 2.197 2.489 2.489 2.489 2.489 2.489 2.197 1.553 1.222 .967 .290 .167 .069 .069 .069 .276 2.489 2.489 1.537 1.537

0 -.046 -.250 -.281 -.267 -.288 -.289 -.411 -.457 -.517 -.517 -.517 -.299 0 .299 .517 .517 .517 .457 .411 .289 .267 .281 .250 .043 .285 -.325 .325 -.5 .5

.324 .324 .324 .324 .322 .320 .320 .308 .303 .297 .297 .515 .515 .515 .515 .515 .297 .297 .303 .308 .319 .322 .324 .324 .324 .319 .515 .515 .392 .392

OTHER NODES ON TOP PLANE 150 151 152 153 154 155

.967 1.222 .967 .967 1.222 .967

-.143 -.107 .087 .095 .075 -.161

.310 .305 .310 .310 .305 .310 Page 66

156 C C C

.967

.108

.310

EXTRA NODES FOR THE BRACING 200 201 202 203 204 205 206 207 208 209 210 211

C C C

.275 .275 .959 .959 1.551 1.551 1.551 1.551 2.183 2.183 2.312 2.312

-.280 .280 -.411 .411 -.517 .517 -.517 .517 -.517 .517 -.517 .517

.287 .287 .029 .029 .266 .266 .280 .280 .288 .288 .020 .020

NODES FOR REAR INTERNAL FRAME (UP TO BEHIND SEAT BACK) 220 225 221 224 222 223 226 227 228 229 230 231 232 233 234 235 236 237

C C C

2.372 2.372 2.687 2.687 2.697 2.697 2.387 2.387 2.387 2.387 2.387 2.387 2.387 2.387 2.697 2.697 2.412 2.412

-.203 .203 -.124 .124 -.124 .124 -.135 .135 -.120 .120 -.088 .088 -.055 .055 -.203 .203 -.203 .203

.208 .208 .077 .077 .0795 .0795 .250 .250 .250 .250 .250 .250 .250 .250 .208 .208 .208 .208

NODES FOR SUSPENSION MOUNTINGS AND SUSPENSION 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267

.005 .005 .074 .074 .167 .167 .267 .267 .315 .315 .008 .008 .057 .057 .315 .315 .273 .273

-.195 .195 -.293 .293 -.265 .265 -.293 .293 -.192 .192 -.163 .163 -.262 .262 -.195 .195 -.275 .275

.033 .033 .261 .261 .288 .288 .265 .265 .032 .032 .046 .046 .278 .278 .003 .003 .270 .270 Page 67

268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294

2.327 2.327 2.694 2.694 2.414 2.414 2.693 2.693 .170 .170 .170 .170 2.550 2.550 2.550 2.550 2.497 2.497 .170 .170 2.550 2.550 .17 .17 2.550 2.550 .17

-.120 .0425 .120 .0425 -.120 .045 .120 .045 -.231 .225 .231 .225 -.231 .225 .231 .225 -.492 .275 .492 .275 -.487 .070 .487 .070 -.55 .23 .55 .23 -.55 .04 .55 .04 -.325 .478 .325 .478 -.49 .17 .49 .17 -.55 .17 .55 .17 -.55 -.1 .55 -.1 -.60 -.1 .60 -.1 0 -.1

C RIGID.LINK N1 N2 7 51 29 58 C C ELEMENTS ELEM= 34100 NUMB GROUP PROP TOPO C C BOTTOM PERIMETER PLANE C 1 1 1 1 3 2 1 1 3 4 3 1 1 3 5 4 1 1 5 6 5 1 1 6 7 6 1 1 7 8 7 1 1 8 38 33 1 1 38 9 8 1 1 9 10 9 1 1 10 12 10 1 1 12 34 11 1 1 34 14 12 1 1 14 13 14 1 1 16 19 15 1 1 16 17 16 1 1 17 18 17 1 1 18 20 18 1 1 20 21

ELEMENTS

Page 68

19 21 22 23 24 25 26 34 27 28 29 30 31 32 C C C

1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1

21 23 36 35 24 26 27 37 28 29 30 31 33 33

22 36 35 24 26 27 37 28 29 30 31 33 32 1

BOTTOM PLANE INTERNAL ELEMENTS 50 51 52 53 54 93 55 56 452 57 58 59 60 61 453 62 63 94 64 70 71 72 73 99 74 66 67 68 69 75 76 450 77 78 96 79 80 451 81 82 97

1 1 1 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2

1 1 1 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2

5 31 6 50 50 59 59 30 50 264 264 51 51 52 52 72 72 53 53 54 10 54 55 26 55 56 56 73 73 57 57 58 58 265 265 59 12 87 87 85 85 83 83 84 84 86 86 88 88 24 54 60 60 61 55 62 62 63 63 90 90 98 98 92 92 84 84 94 94 96 61 89 89 97 97 91 91 83 83 93 93 95 Page 69

65 83 84 85 86 87 88 89 90 91 92 C C C

1 1 1 1 1 1 1 1 1 1 1

13 64 65 66 67 95 96 68 69 70 71

64 65 66 67 95 96 68 69 70 71 23

TOP PLANE PERIMETER ELEMENTS 100 101 102 103 104 105 106 107 108 109 110 111 126 112 113 114 127 115 116 117 118 119 120 125 121 122 123 124

C C C

1 1 1 1 1 1 1 1 1 1 1

3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3

100 101 101 102 102 103 102 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 126 126 112 112 113 113 114 114 127 127 115 115 116 116 117 117 118 118 119 119 120 120 125 125 121 121 123 123 122 123 124 124 100

TOP PLANE INTERNAL ELEMENTS 150 151 152 153 154 155 156 157 158 159 160 161 162

3 3 3 3 3 3 3 3 3 2 2 3 3

3 3 3 3 3 3 3 3 3 2 2 3 3

101 106 124 120 120 153 107 155 155 150 150 152 152 153 153 156 156 119 150 151 152 154 108 151 151 154 Page 70

163 164 165 166 177 167 168 169 170 171 172 173 174 175 176 C C C

3 5 5 2 2 2 2 2 2 2 2 2 4 4 4

154 118 111 16 115 21 151 77 77 78 154 78 77 79 78 80 79 81 80 82 81 232 82 233 109 128 128 129 129 117

UPRIGHTS (WELL THOSE THERE ABOUT) 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 250 274 275 252 276 277 251 280 278 253 279 281

C C C

3 5 5 2 2 2 2 2 2 2 2 2 4 4 4

8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8

8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8

10 202 202 107 26 203 203 119 12 204 204 206 206 109 24 205 205 207 207 117 14 210 36 211 210 111 211 115 62 156 60 155 83 77 84 78 93 79 94 80 4 260 260 262 262 103 32 261 261 263 263 122 6 200 200 266 266 105 30 267 267 201 201 125

MEMBERS REPRESENTING SUSPENSION COMPONENTS 300 301 302 303 304

9 9 9 9 9

9 9 9 9 9

104 254 121 255 260 250 261 251 262 252 Page 71

305 306 307 308 309 310 311 312 313 314 315 316 317

9 9 9 9 9 9 9 9 9 9 9 9 9

9 9 9 9 9 9 9 9 9 9 9 9 9

263 253 256 266 257 267 258 264 259 265 274 234 275 235 270 221 271 224 268 66 269 69 236 272 237 273

C Front Suspension ELEMENTS ELEM= 34400 NUMB GROUP PROP TOPO 318 7 7 250 278 319 7 7 251 279 320 7 7 278 258 321 7 7 279 259 326 7 7 254 278 327 7 7 255 279 C Rear Suspension 328 7 7 268 282 329 7 7 269 283 330 7 7 270 282 331 7 7 271 283 336 7 7 282 126 337 7 7 283 127 C Uprights ELEMENTS ELEM= 34100 NUMB GROUP PROP TOPO C C BRACING MEMBERS C 200 6 6 200 202 201 6 6 201 203 202 6 6 202 204 203 6 6 203 205 204 5 5 206 34 205 5 5 207 35 206 3 3 34 208 207 3 3 35 209 208 3 3 208 110 209 3 3 209 116 214 3 3 14 208 215 3 3 36 209 216 2 2 154 84 C TUNNEL FRONT BRACE C C MEMBERS OF THE REAR INTERNAL BACK) C 350 1 1 66 221 351 1 1 221 222 352 1 1 222 17 Page 72

FRAME (UP TO BEHIND SEAT

353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 377 368 376 369 370 371 372 379 378 380 373 374 375 C C C

1 1 1 5 5 3 3 3 3 3 3 3 2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1

1 1 1 5 5 3 3 3 3 3 3 3 2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1

69 224 224 223 223 20 221 19 224 22 226 228 228 230 230 232 232 233 233 231 231 229 229 227 226 112 227 114 228 220 220 210 229 225 225 211 67 230 68 231 234 235 220 236 236 234 225 237 237 235 234 222 222 223 223 235

FLOOR PAN MEMBERS 400 401 402 403

10 10 10 10

10 10 10 10

87 85 86 88

64 65 70 71

C ELEMENTS ELEM=46210 NUMB GROUP PROP TOPO 425 11 11 8 9 52 53 38 0 0 72 426 11 11 57 56 28 27 73 0 0 37 427 11 11 89 91 90 92 97 0 0 98 C C PLATES.AND.SHELLS PLATE.OR.SHELL MATER.NUMB THICKNESS 11 1 0.0030 LOADS CASE NODE DIRE VALUE 1 279 3 1000 C C RESTRAINTS NODE.NUM DIRECTION 278 123 282 23 283 3 C Page 73

C REACTIONS C NODE.NUM C 278 C 279 C 282 C 283 C C STRESS.ELEMENT C START FINISH STEP C 1 9999 1 C END.OF.DATA

Page 74

Page 75

Appendix D - Laboratory Testing Observations

Page 76

Appendix E - Diagrams and Information for Chassis Modifications i) Diagrams Showing Changes to Chassis

Page 77

Page 78

Page 79

Page 80

Page 81

Page 82

Page 83

Page 84

Page 85

Page 86

Page 87

ii) Summary of Calculated Masses for Chassis Modifications CAR1 - Masses and Moments of Inertia About Global Axes GROUP

CENTRE OF MASS

NUMBER MASS ALL 63.3

1.60

X

Y

MOMENTS OF INERTIA

Z

Ixx

Iyy

Izz

0.155E-02 0.130

9.35

206.

CENTRE OF MASS

MOMENTS OF INERTIA

210.

CAR2 GROUP NUMBER MASS ALL 64.4

1.58

X

Y

Z

0.152E-02 0.133

Ixx

Iyy

Izz

9.64

207.

212.

CAR3 GROUP

CENTRE OF MASS

NUMBER MASS ALL 65.2

1.58

X

Y

MOMENTS OF INERTIA

Z

0.148E-02 0.126

Ixx

Iyy

Izz

9.67

209.

214.

CAR5 GROUP

CENTRE OF MASS

NUMBER MASS ALL 63.5

1.60

X

Y

MOMENTS OF INERTIA

Z

0.155E-02 0.130

Ixx

Iyy

Izz

9.36

206.

211.

CAR6 GROUP

CENTRE OF MASS

NUMBER MASS ALL 64.0

1.59

X

Y

MOMENTS OF INERTIA

Z

0.154E-02 0.132

Ixx

Iyy

Izz

9.44

206.

211.

CAR7 GROUP

CENTRE OF MASS

NUMBER MASS ALL 63.6

1.60

X

Y

MOMENTS OF INERTIA

Z

0.142E-02 0.129

Ixx

Iyy

Izz

9.36

206.

211.

CAR8 GROUP

CENTRE OF MASS

NUMBER MASS ALL 65.8

1.54

X

Y

MOMENTS OF INERTIA

Z

0.356E-02 0.131

Ixx

Iyy

Izz

9.50

206.

211.

CAR9 GROUP

CENTRE OF MASS

MOMENTS OF INERTIA

Page 88

NUMBER MASS ALL 63.8

1.59

X

Y

Z

0.326E-02 0.131

Ixx

Iyy

Izz

9.44

206.

211.

CAR10 GROUP

CENTRE OF MASS

NUMBER MASS ALL 62.5

1.61

X

Y

MOMENTS OF INERTIA

Z

-0.850E-03 0.127

Ixx

Iyy

Izz

9.24

206.

210.

CAR11 GROUP

CENTRE OF MASS

NUMBER MASS ALL 63.5

1.60

X

Y

MOMENTS OF INERTIA

Z

-0.959E-03 0.131

Ixx

Iyy

Izz

9.41

206.

211.

CAR12 GROUP

CENTRE OF MASS

NUMBER MASS ALL 71.1

1.53

X

Y

MOMENTS OF INERTIA

Z

0.780E-03 0.134

Ixx

Iyy

Izz

10.1

214.

219.

CAR13 GROUP

CENTRE OF MASS

NUMBER MASS ALL 63.3

1.60

X

Y

MOMENTS OF INERTIA

Z

0.141E-02 0.130

Ixx

Iyy

Izz

9.34

206.

210.

CAR14 GROUP

CENTRE OF MASS

NUMBER MASS ALL 64.4

1.59

X

Y

MOMENTS OF INERTIA

Z

0.159E-02 0.128

Ixx

Iyy

Izz

9.42

207.

211.

CAR15 GROUP

CENTRE OF MASS

NUMBER MASS ALL 66.9

1.55

X

Y

MOMENTS OF INERTIA

Z

0.141E-02 0.131

Ixx

Iyy

Izz

9.86

208.

212.

CAR16 GROUP

CENTRE OF MASS

NUMBER MASS ALL 71.0

1.59

X

Y

MOMENTS OF INERTIA

Z

0.205E-02 0.133

CAR17

Page 89

Ixx

Iyy

Izz

10.6

231.

236.

GROUP

CENTRE OF MASS

NUMBER MASS ALL 65.0

1.56

X

Y

MOMENTS OF INERTIA

Z

0.218E-02 0.132

Ixx

Iyy

Izz

9.51

206.

211.

CAR18 GROUP

CENTRE OF MASS

NUMBER MASS ALL 64.9

1.57

X

Y

MOMENTS OF INERTIA

Z

0.499E-03 0.133

Ixx

Iyy

Izz

9.55

207.

211.

CAR19 GROUP

CENTRE OF MASS

NUMBER MASS ALL 67.6

1.58

X

Y

MOMENTS OF INERTIA

Z

0.240E-03 0.132

Ixx

Iyy

Izz

9.55

216.

220.

CAR20 GROUP

CENTRE OF MASS

NUMBER MASS ALL 63.3

1.60

X

Y

MOMENTS OF INERTIA

Z

0.155E-02 0.130

Ixx

Iyy

Izz

9.35

206.

210.

CAR21 GROUP

CENTRE OF MASS

NUMBER MASS ALL 68.4

1.59

X

Y

MOMENTS OF INERTIA

Z

0.209E-03 0.131

Ixx

Iyy

Izz

9.55

219.

223.

CAR22 GROUP

CENTRE OF MASS

NUMBER MASS ALL 67.5

1.54

X

Y

MOMENTS OF INERTIA

Z

0.151E-02 0.136

Page 90

Ixx

Iyy

Izz

9.86

208.

213.

Appendix F - Components of the Westfield Sports Cars

Page 91

Appendix G - Calculations i) Chassis Torsional Stiffness The deflections at four dial gauges are as follows:

Node

102

123

111

115

DZ

-5.77

-14.01

0.84

-1.15

Load = 94.4 kg lever arm of load = 974mm

ii) Measure of Effectiveness of WSC Spaceframe

Page 92

As a means to evaluating the effectiveness of the geometry of a space frame in resisting torsional loading, it would be helpful to consider: How much does the torsional stiffness of the members independently contribute to the overall torsional stiffness of the chassis. Note that a low percentage contribution from individual members will suggest an effective geometry of the overall chassis. A typical cross section of the chassis would consist of four 25x1.6 SHS and four 20x1.6 SHS. The chassis alone was calculated as having a stiffness of 1121 Nm/deg over a length of 2420mm. Consider member stiffnesses alone over this length:

The percentage to which the members alone contribute to torsional stiffness is: 6.5% Hence the stiffness of the chassis is primarily derived from the members "acting as a team" within the structure rather than from the individual member stiffnesses, as would be the case with a ladder type chassis.

ii) Equivalent Structures It may be helpful in understanding the improvements in chassis technology over the years to consider the typical torsional stiffness of different types of chassis of the same weight. Westfield Chassis:

weight = 63 kg wheelbase = 2420 mm torsional stiffness = 1121 Nm/deg

Girder Chassis of Equivalent Weight Two girders 2.9 m long and three 0.8 m cross members of the same section, weighing 63 kg combined would require a member of 7.7 kg/m. Page 93

Using 100 TFB (Taper Flanged Beam); 7.20 kg/m the weight of the chassis will be 59 kg and the torsional stiffness of the chassis will be:

Page 94

Ladder Chassis of Equivalent Weight (ignoring the effect of lateral bracing) Use 102 CHS 3.2 7.77kg/m. Two 2.9m beams and three 0.8m laterals weigh 63.7 kg.

Stressed Skin Chassis of Equivalent Weight Using 0.9mm steel skin, the dimensions for two boxes with a combined weight of around 63 kg are: 430mm x 300mm x 0.9mm thick; two 3m boxes would weigh 62kg

Page 95