Clubman Builders Resource



CRANFIELD UNIVERSITY

Wesley Linton

Analysis of Torsional Stiffness and design improvement study of a Kit Car Chassis Prototype

School of Industrial AND Manufacturing Science

MSc THESIS

CRANFIELD UNIVERSITY

School of Industrial AND Manufacturing Science

Motorsport Engineering and Management

MSc Thesis

Academic year 2001-2

Wesley Linton

Analysis of Torsional Stiffness and Design Improvement Study of a Kit Car Prototype

Supervisor: Mr. Jason Brown

September 2002

This thesis is submitted in partial fulfilment of the requirements

for the degree of Master of Science

© Cranfield University 2002. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner.

Abstract

The Luego prototype chassis was tested to determine the value of its global torsional stiffness. This value was calculated to be 1330Nm/deg. This value was to be improved upon by the following method:

• Creation of a Finite element baseline validation model

• Discussed modification of this model

• A design improvement study

• An optimisation study

The creation of a Finite Element baseline validation model using MSC Patran/Nastran software compared favourably with the physical test results with a torsional stiffness value of 1352Nm/deg for a mass of 120.1Kg and an efficiency of 88g/Nm/deg.

The discussed modifications had been suggested to Luego upon initial appraisal of the chassis were incorporated into this baseline model and resulted in increases in both torsional stiffness and efficiency.

Further, the design improvement study performed resulted in a maximum torsional stiffness of 6448Nm/deg, an increase of 377% over the baseline model. A maximum increase in efficiency of 286% to 23g/Nm/deg for a mass of 148.3Kg accompanied this increase in torsional stiffness.

Following optimisation of the model to gain minimum mass for a stiffness of 6000Nm/deg a torsional stiffness of 6030Nm/deg was realised for a mass of 127Kg, giving an increase in efficiency of 322% over the baseline model to 20.99g/Nm/deg.

Acknowledgements

First, I would like to thank my parents for their continual support and encouragement throughout my university career.

I would like to sincerely thank my supervisor Mr. Jason Brown for his unending support and enthusiasm for this thesis. Thanks also go to Grant and Matt at Luego Sports Cars Ltd for providing a very interesting thesis and great support throughout.

Finally, a special thanks to all my friends at Cranfield who have made this such a great year.

Contents

Abstract I

Acknowledgements II

Contents III

List of Figures V

1 Introduction 1

1.1 Luego Sports Cars Ltd 1

1.2 Aims of Project 1

2 Definition of a Chassis and Required Properties 2

2.1 Definition of a Chassis 2

2.2 Overview of Chassis Types 2

2.2.1 Ladder frame 2

2.2.2 Twin tube 3

2.2.3 Four tube 4

2.2.4 Backbone 5

2.2.5 Spaceframe 5

2.2.6 Stressed skin 6

2.3 Load Cases 7

2.4 Simple Structural Surfaces 9

3 The Locost Concept and the Competitors 11

3.1 The locost concept 11

3.2 Dimensions and constraints 12

3.3 The competitors and their structures 14

3.3.2 Caterham 14

3.3.3 Westfield 16

3.3.4 Quantum Xtreme 16

3.3.5 Robin Hood 17

4 Calculation of the Global Torsional Stiffness 18

5 Description of Prototype Chassis 20

6 Physical Testing of the Chassis 24

7 FE Modelling Description and Validation of Baseline Model 28

7.1 FE Model 28

7.2 Patran/Nastran 28

7.2.1 Bar element 29

7.2.2 Shell element 29

7.3 Model correction 29

7.4 Final Validation of Baseline Model 30

8 Design Improvement Study 32

8.1 Stage 1 – Discussed Modifications 32

8.1.1 One- piece floor 32

8.1.3 Cross bracing of engine bay tubes 34

8.1.4 Addition of rear firewall 35

8.1.5 Addition of bar across dash area 36

8.1.6 Panelled dash bar and footwell tops 37

8.1.7 Addition of aluminium side panels to passenger compartment 38

8.1.8 Conversion of dash panel, transmission panels and rear wall to Aluminium 39

8.1.9 Addition of Aluminium panels to engine bay sides 40

8.2 Stage 2 - Application of structures theory to bare chassis 41

8.2.1 Conversion of X-brace to W-brace on engine bay 41

8.2.2 Addition of X-brace to front of engine bay 42

8.2.3 Addition of triangulation from top of footwell bulkhead to lower main rails 43

8.2.4 Addition of ‘Ring Beam’ to engine bay 44

8.2.5 Addition of ‘Ring Beam’ to lower engine bay 45

8.2.6 Addition of lower triangulation to the suspension box 46

8.2.7 Vertical triangulation of the upper ring beam to the lower frame rails 47

8.2.8 Further triangulation of the upper ring beam to the engine plates 48

8.2.9 Triangulation of the front face of the suspension box 49

8.2.10 Y-brace conversion of lower engine beam 50

8.2.11 Conversion of 8mm flat bar to 2” x 1” RHS 51

8.3 Stage 3-Identical Modifications to Fully Panelled Chassis 52

8.4 Stage 4-Optimisation Study 54

8.4.1 Conversion of 5mm thick bar to 2” x 1” RHS 54

8.4.2 Conversion of mild steel floor to aluminium 55

8.4.3 Conversion of mild steel transmission tunnel panels to aluminium 56

8.4.4 Conversion of Transmission Tunnel Entrance Beams to 1” x 1” RHS 57

8.4.5 Conversion of Aluminium panels from 1.6mm to 1mm Thickness 57

9 Conclusions 60

9.1 Physical Testing 60

9.2 Creation of FE baseline model 60

9.3 Design Improvement Study 61

9.3.1 Discussed Modifications 61

9.3.2 Applications of Structures Theory to Bare Chassis 61

9.3.3 Inclusion of Design Improvements to Fully Panelled Chassis 61

9.4 Optimisation Study 62

References 63

List of Figures

Fig. 1 [Ref. 2] 3

Fig. 2 [Ref. 2] 4

Fig. 3 Lotus 21 [Ref. 4] 4

Fig. 4 1962 Lotus Elan backbone chassis [Ref.4] 5

Fig. 5 1952 Lotus Mk.IV spaceframe 6

Fig. 6 Bending Load case [Ref. 2] 7

Fig. 7 Torsion Load case [Ref. 2] 8

Fig. 8 Chassis and suspension as springs 9

Fig. 9 [Ref. 2]

Fig. 10 [Ref. 2] 10

Fig. 11 Chassis as Springs Between Bulkheads 13

Fig. 12 Dax Rush [daxcars.co.uk] 14

Fig. 13 Caterham Seven [caterham.co.uk] 15

Fig. 15 Westfield [westfieldcars.co.uk] 16

Fig. 16 Quantum Xtreme [quantumcars.co.uk] 17

Fig. 17 Robin Hood 2B [robinhoodengineering.co.uk] 17

Fig. 18 18

Fig. 19 19

Fig. 20 20

Fig. 21 21

Fig. 22 21

Fig. 23 22

Fig. 24 25

Fig.25 25

Fig. 26 26

Fig. 27 Dial Test Indicator measurement positions 27

Fig. 28 30

Fig. 29 31

Fig. 30 32

Fig 32 33

Fig. 33 34

Fig. 34 35

Fig. 35 36

Fig. 36 37

Fig. 37 38

Fig. 38 39

Fig. 40 40

Fig. 41 41

Fig. 42 42

Fig. 43 43

Fig. 44 44

Fig. 45 45

Fig. 46 46

Fig. 47 47

Fig. 48 48

Fig. 49 49

Fig. 50 50

Fig. 51 51

Fig. 52 52

Fig. 53 54

Fig. 54 55

Fig. 55 56

Fig. 56 58

Fig. 57 58

Fig. 58 59

1 Introduction

1.1 Luego Sports Cars Ltd

Luego Sports Cars Ltd has been involved in the motor sports industry for a number of years. They have produced work for Champion Motor Company (CMC) Spain, Tiger Racing, CMC USA, Ron Champion, and Locost ltd.

1.2 Aims of Project

The purpose of this thesis is:

- To perform a torsion test on the prototype chassis to determine its torsional stiffness;

- To create a finite element model of the chassis;

- To incorporate a design improvement study and note the effects on the global torsional stiffness of the chassis;

- To attempt an optimisation for maximum efficiency.

The following limitations are given for this project:

- The body shape is fixed and therefore the overall external shape of the chassis must not be altered;

- The engine bay must remain as open as possible to allow a variety of engines to be fitted;

- Complex assemblies are to be avoided, as Luego is a small manufacturer.

2 Definition of a Chassis and Required Properties

2.1 Definition of a Chassis

The chassis is the framework to which everything is attached in a vehicle. In a modern vehicle, it is expected to fulfil the following functions:

• Provide mounting points for the suspensions, the steering mechanism, the engine and gearbox, the final drive, the fuel tank and the seating for the occupants;

• Provide rigidity for accurate handling;

• Protect the occupants against external impact.

While fulfilling these functions, the chassis should be light enough to reduce inertia and offer satisfactory performance. It should also be tough enough to resist fatigue loads that are produced due to the interaction between the driver, the engine and power transmission and the road.

2 Overview of Chassis Types

1 Ladder frame

The history of the ladder frame chassis dates back to the times of the horse drawn carriage. It was used for the construction of ‘body on chassis’ vehicles, which meant a separately constructed body was mounted on a rolling chassis. The chassis consisted of two parallel beams mounted down each side of the car where the front and rear axles were leaf sprung beam axles. The beams were mainly channel sections with lateral cross members, hence the name. The main factor influencing the design was resistance to bending but there was no consideration of torsional stiffness. [Ref. 1]

A ladder frame acts as a grillage structure with the beams resisting the shear forces and bending loads. To increase the torsional stiffness of the ladder chassis cruciform bracing was added in the 1930’s. The torque in the chassis is reacted by placing the cruciform members in bending, although the connections between the beams and the cruciform must be rigid. Ladder frames were used in car construction until the 1950’s but in racing only until the mid 1930’s [Ref. 2]. A typical ladder frame is shown below in Fig. 1.

[pic]

Fig. 1 [Ref. 2]

2 Twin tube

The ladder frame chassis became obsolete in the mid 1930’s with the advent of all-round independent suspension, pioneered by Mercedes Benz and Auto Union. The suspension was unable to operate effectively due to the lack of torsional stiffness. The ladder frame was modified to overcome these failings by making the side rails deeper and boxing them. A closed section has approximately one thousand times the torsional stiffness of an open section. Mercedes initially chose rectangular section, later switching to oval section, which has high torsional stiffness and high bending stiffness due to increased section depth, while Auto Union used tubular section. The original Mercedes design was further improved by mounting the cross members through the side rails and welding on both sides. The efficiency of twin tube chassis’ is usually low due to the weight of the large tubes. They were still in use into the 1950’s, the 1958 Lister-Jaguar being an example of this type [Ref. 1]. A typical twin-tube chassis is shown in Fig. 2 opposite.

[pic]

Fig. 2 [Ref. 2]

3 Four tube

As designers sought to improve the bending stiffness of a chassis, the twin tube chassis evolved into the four tube chassis. The original twin tube design was modified by adding two more longitudinal tubes that ran from the front of the car, around the cockpit opening and on to the rear of the car. The top and bottom side rails are connected by vertical or diagonal members, essentially creating a very deep side rail and thus improving the bending characteristics. The two sides are joined by a series of bulkheads, normally located at the front, footwells, dash area, seatback, and rear of the chassis. [Ref.1]

A significant increase in bending stiffness was realised but there is little increase in the torsional stiffness due to the lack of triangulation causing lozenging of the bays.

[pic]

Fig. 3 Lotus 21 [Ref. 4]

4 Backbone

The backbone chassis has a long history in automobile design with its origins credited to Hans Ledwinka, an engineer with Czech automaker Tatra. Ferdinand Porsche worked with Ledwinka in the 1920’s and arguably learned much of his craft from him [Ref. 1].

When a chassis derives its torsional stiffness from one large central tube running the length of the car, the resistance to twist depends almost entirely on the cross-sectional area of that tube. Clearly, that cross section can be much larger than the typical drive shaft tunnel. Depending on the vehicle configuration it is possible to arrange for an approximately rectangular tube of substantial dimensions. This arrangement fits in well with conventional side-by-side seating, with the large central spine forming a centre console. Such an arrangement was utilised by Colin Chapman on the Lotus Elan (Fig. 4) of 1962-1973 [Ref. 1].

[pic]

Fig. 4 1962 Lotus Elan backbone chassis [Ref.4]

5 Spaceframe

Although the spaceframe demonstrated a logical development of the four-tube chassis, the space frame differs in several key areas and offers enormous advantages over its predecessors. A spaceframe is one in which many straight tubes are arranged so that the loads experienced all act in either tension or compression. This is a major advantage, since none of the tubes are subject to a bending load. Since space frames are inherently stiff in torsion, very little material is needed so they can be lightweight.

The growing realisation of the need for increased chassis torsional stiffness in the years following World War II led to the space frame, or a variation of it, becoming universal among European road race cars following its appearance on both the Lotus Mk IV [Fig.5] and the Mercedes 300 SL in 1952 [Ref. 1]. While these cars were not strictly the first to use space frames, they were widely successful, and the attention they received popularised the idea.

[pic]

Fig. 5 1952 Lotus Mk.IV spaceframe

6 Stressed skin

The next logical step for chassis development was the stressed skin design. This is more difficult to construct than a spaceframe with the accurate folding, forming, drilling and riveting of sheet steel or modern composite materials. The lessons learnt in the aircraft industry do not usually apply directly in automotive practice. The loads on aircraft are widely distributed – the lift that holds a plane up, for example, is spread over the entire area of its wings. On a race/sports car, the loads are much more concentrated, being focused on the suspension mounting points.

Even when a method is developed to accept forces and spread them over a load bearing skin, it becomes extremely inconvenient to make any modifications and may even require a major redesign. Analysis of the stresses in stressed skin construction is more difficult.

The continuous surface considerably complicates access for repair or replacement of the cars mechanical components. This may also explain why stressed skin construction was virtually unheard of in racecars before the modern mid-engined configuration. The majority of mid-engined racecars end their stressed skin construction at the back of the cockpit, with either a space frame or the engine itself forming the remainder of the structure. For all these drawbacks, stressed skin construction can potentially outperform any other form of racecar construction in terms of torsional stiffness.

3 Load Cases

A chassis is subjected to three load cases: bending, torsion and dynamic loads.

The bending (vertical symmetrical) load case occurs when both wheels on one axle of the vehicle encounter a symmetrical bump simultaneously. The suspension on this axle is displaced, and the compression of the springs causes an upward force on the suspension mounting points. This applies a bending moment to the chassis about a lateral axis. (See Fig. 6.)

[pic]

Fig. 6 Bending Load case [Ref. 2]

The torsion (vertical asymmetric) load case occurs when one wheel on an axle strikes a bump. This loads the chassis in torsion as well as bending. (See Fig. 7). It has been found both in theory and in practice that torsion is a more severe load case than bending.

[pic]

Fig. 7 Torsion Load case [Ref. 2]

The dynamic load case comprises longitudinal and lateral loads during acceleration, braking and cornering. These loads are usually ignored when analysing structural performance.

A torsionally stiff chassis offers a number of advantages:

1. According to vehicle dynamics principles for predictable and safe handling the geometry of the suspension and steering must remain as designed. For instance the camber, castor and toe angles could change with torsional twist or the steering geometry could change causing “bump steer.”

2. Once again according to vehicle dynamics principles a suspension should be stiff and well damped to obtain good handling. To this end the front suspension, chassis and the rear suspension can be seen as three springs in series as shown in Fig. 8. If the chassis is not sufficiently stiff in torsion then any advantages gained by stiff suspension will be lost. Furthermore, a chassis without adequate stiffness can make the suspension and handling unpredictable, as it acts as an undamped spring.

Fig. 8 Chassis and suspension as springs

3. Movement of the chassis can also cause squeaks and rattles, which are unacceptable in modern vehicles.

2.4 Simple Structural Surfaces

The simple structural surfaces method SSS originated from the work of Pawlowski [Ref. 3] and is described in the notes by Brown [Ref. 2] and the book by Brown, Robertson and Serpento [Ref.4]. These references should be consulted for a thorough understanding of this approach.

The SSS method provides a simple way of determining load paths through a structure. Each surface is assumed only to have in-plane stiffness and no out-of-plane stiffness. Each surface is acted on by forces, e.g. the engine mounts. For equilibrium, adjacent surfaces must provide reactions. This process is continued throughout the structure and determines the load on each SSS. It can then be realised if an SSS has insufficient supports or reactions and therefore determines the continuity of load paths and the structures overall integrity.

[pic][pic]

Fig. 9 [Ref. 2] Fig. 10 [Ref. 2]

As can be seen in the SSS example in Fig. 9 the box structure is loaded in torsion by the moment Ms, which causes the shear forces Q1 and Q3. All the surfaces are in complementary shear, and the structure is stiff in torsion.

If one shear surface is removed, as shown in Fig. 10, none of the complementary shear forces can exist. The torsion load is then transferred to the floor of the box via the edge forces Q, so the floor panel is loaded out of plane rather than in complementary shear.

3 The Locost Concept and the Competitors

3.1 The locost concept

Luego have become part of the cottage industry to emerge from the Locost concept. The locost concept began a number of years ago with the publication by Ron Champion of his book “Build Your Own Sports Car for as Little as £250.” This book details how he designed and built a Lotus Seven Inspired Sports car for his son and others in his capacity as a teacher of motor engineering at a public school [Ref. 5].

Due to the low budget on which the car was to be built, it was named the Lowcost, later shortened to Locost. This is a two seat open top sports car with a front mounted engine and gearbox linked by a propeller shaft to a rear mounted final drive.

The original Locost chassis was based around the running gear of the then cheap and plentiful rear wheel drive Ford Escort Mk.2. Many of the components of this “donor car” were used on the Locost with the major components being the engine and ancillaries, gearbox, propeller shaft and rear axle.

These items dictated the rear track of the car and the basis of the wheelbase. However, this led to the construction of a chassis that was relatively narrow. The rapid success of the book and the number of builders emulating Ron has led to a shortage of Mk.2’s. this has been exacerbated by the race class set up for running Locosts by the 750 Motor Club which dictates the chassis and running gear to be as per the book. Replica parts are available but do not adhere to the Locost ethos aspired to by many builders.

This shortage of available Mk.2 donors and the lack of space available in the original chassis has led many builders and chassis providers to use an alternative donor car. The favoured replacement for the Mk.2 Escort is the Ford Sierra. This is also front engined, rear wheel drive but comes with a range of engines from the 1.6 Pinto to the 2.8 Cologne and Essex V6’s and even the 2-litre Cosworth derived engine. It also benefits from a 5-speed transmission and independent rear suspension. This is all packaged in a slightly longer wheelbase and wider track. This allows a chassis to be designed with more room for passengers and a more varied drive train choice.

Luego were the chassis constructors for the Champion Motor Company as mentioned previously. Seeing the decline in parts availability and the popularity of the sierra based chassis’ they have constructed a prototype chassis to accept the Sierra running gear and provide fitment of a wide range of large displacement engines from the Pinto to the Rover V8, Ford and Chevrolet, small and big-block, V8s’ and the Jaguar V12.Motor

3.2 Dimensions and constraints

Many of the dimensions of the chassis have been determined by the choice of the Ford Sierra as the donor car. The larger rear track has meant a widening of the chassis by 153mm (6”) and the wheel base a lengthening of 306mm (12”) affording more room in the passenger compartment, footwells, transmission tunnel and engine bay. The chassis has also been made deeper by 76.5mm (3”) to solve the clearance problems of the larger engine sizes planned and to keep the silhouette similar to the original Locost.

These changes are in relation to the measurements given in Ref. 5 and could be beneficial to the torsional stiffness of the chassis if used correctly as they increase the enclosed area of the torsion boxes inherent in this type of frame.

The exterior dimensions of this chassis were not to be altered as moulds for the fibreglass components had already been taken. This meant any modifications had to remain on the inside of the chassis rails but still leave adequate room for engine installation.

The boxes formed by the bulkheads effectively split the chassis into a further series of springs. These can be represented by simple models as shown below in Fig. 11.

Fig. 11 Chassis as Springs Between Bulkheads

To examine how this affects the stiffness of the chassis we can look at the following example:

One stiff spring with stiffness Ks =1000

Two flexible springs with stiffness Kf1 = 500 and Kf2 =200

Due to continuity a load applied to the series springs, the loads in each spring are equal. Applying Hook’s Law (f = k(, ( = F/k), then each spring has its own deflection. The total deflection is the sum of the deflection of each spring, so the total stiffness is K = Ks Kf1 Kf2 / (Ks Kf1 + Kf1 Kf2 + Kf2 Ks). From the numerical example then the total stiffness is K = 125. This value is much lower than any of the original values. Therefore, it can be seen that stiffening the stiff spring further has little effect on the overall stiffness. The flexible springs must be stiffened first.

3.3 The competitors and their structures

3.3.1 Dax Rush

The Rush is front engined and rear wheel drive, claiming to offer more interior space than any of its competitors and has been designed to accept a wide variety of engines from Ford's OHC/DOHC and V8 ranges to the Sierra Cosworth Turbo or Rover V8.

The chassis is a multi-tubed triangulated space-frame chassis with integrated structural rear hoop. Additional stiffness is provided by bonded & riveted aluminium panels.

It uses Sierra 'running gear’ with the 4 x4 specifically using Sierra Cosworth 4 x 4 'running gear' [Ref. 7].

[pic]

Fig. 12 Dax Rush [daxcars.co.uk]

3.3.2 Caterham

Caterham Cars Ltd was founded in Caterham, England over 40 years ago and currently produces what can be considered as the ‘Original’ Seven using the Lotus 7 design [Ref. 8]. The chassis is a multi-tubed triangulated spaceframe design with riveted and bonded aluminium panels. The development of the Caterham has often been at the leading edge of the class. The running gear is all of a modern design with current generation engines and drive trains fitted. The Caterham is no longer available in kit form but only as turn key cars. The Caterham Seven is shown in Figs. 13 & 14 opposite.

[pic]

Fig. 13 Caterham Seven [caterham.co.uk]

[pic]

Fig. 14 [Ref. 4]

3.3.3 Westfield

The Westfield self-build kit is based upon a tubular triangulated chassis with bonded and riveted aluminium panels [Ref. 9]. The chassis is designed to accept different engine options. The chassis design provides two options for the final drive and rear suspension. The solid rear axle choice uses the Ford Escort Mk.2 rear axle located with trailing arms and panhard rod. The fully independent rear suspension version uses the Ford Sierra differential unit with Westfield manufactured drives shafts. All Westfield kits use the latest wide body chassis and body design as shown in Fig.15.

[pic][pic]

Fig. 15 Westfield [westfieldcars.co.uk]

3.3.4 Quantum Xtreme

The Quantum Xtreme is of Lotus 7 inspiration, but offers an innovative design of chassis for the class. The chassis is a stainless steel monocoque which its claimed has torsional stiffness far in excess of that obtainable from a traditional spaceframe chassis [Ref. 10]. The suspension is an inboard coil-over set up and a range of Ford engines are catered for fitment. The drive train and all other parts required are of Ford Sierra type. The Extreme is shown below in Fig.16.

[pic]

Fig. 16 Quantum Xtreme [quantumcars.co.uk]

3.3.5 Robin Hood

The chassis of the Robin Hood 2B is unique in that it is formed from large diameter bent tubing [Ref. 11]. This is claimed to offer increased torsional stiffness over a standard spaceframe however validation of this statement has not been possible as no figures or methods have been quoted. The Robin Hood development work has utilised the Ford Sierra 1600cc, 1800cc, or 2000cc (Pinto) as a donor vehicle. The Ford Sierra's rear wheel drive independent suspension is used and the car is shown below in Fig.17.

[pic]

Fig. 17 Robin Hood 2B [robinhoodengineering.co.uk]

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Rear Suspension

Front Suspension

Chassis

Chassis as Springs between bulkheads

Suspension box

Engine bay

Passenger compartment

Rear frame

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