Steering Corruption Mechanisms

by

Peter Hewson B.Eng.

of

BMW Group

30/9/99

This thesis is submitted as part qualification for an MSc in Engineering

Business Management at the Warwick Manufacturing Group of the University

of Warwick.

ii

iii

iv

Contents Page No.

Contents iv

List of Diagrams, Tables and Illustrations vii

Acknowledgements and Declaration ix

Summary x

1 Introduction 1

2 Project Aims and Methodology 10

3 Principal Mechanisms

3.1 Symbols, and Typical Values 16

3.2 Vehicle, and Data Analysis 16

3.3 Bump Torque Steer 18

3.4 (Road) Camber Steer 25

3.5 Dry Park Torque 34

3.6 Feedback 42

3.7 Fight - Single Wheel Spin-Up and Snap 48

3.8 Kickback 54

3.9 On Centre Feel 61

3.10 Puddle Steer 61

3.11 Pull 63

3.12 Side Slope Steer 64

3.13 Side Wind Steer 74

3.14 Split Mu Steer 75

3.15 Tractive Torque Steer 76

3.16 Related Analyses

3.16.1 Turning Circle 78

3.16.2 Kerb Jacking 81

3.16.3 Suspension Bush Rate Analysis 83

v

3.16.4 Gyroscopic Steer 87

3.16.5 Ackerman Steer Geometry 88

3.16.6 Steering Universal Joint Phasing 91

3.16.7 Indicator Self-Cancelling Torque 93

3.16.8 Mass Measuring Procedure 93

3.16.9 Suspension Parameter Measurement Procedures 93

4 Conclusions

4.1 Summary of Work Done 95

4.2 Final QFD - Customer Focussed Development Tool 96

4.3 Case Studies 96

4.4 Final Comments and Discussion 97

5 Further Work 100

References 101

- Standards - Internal, National, International 103

- Papers 106

Bibliography 118

Abbreviations and Sample Data 124

Appendices

I Initial Steering Corruption QFD

II Final Steering Corruption QFD

III Geometry Data for Rover Vehicles

IV Mass Measuring Procedure

V Tyre Centre of Pressure Measurement Procedure

VI Hub Level Offset Measurement Procedure

VII Hub Level Trail Measurement Procedure

Index 149

vi

List of Diagrams, Tables and Illustrations

Diagram 1 Control system for path following ?

Diagram 2 All possible applied suspension forces ?

Diagram 3 Side view of suspension geometry and forces ?

Diagram 4 Front view of suspension geometry and forces ?

Diagram 5 Overall report structure ?

Diagram 6 Report structure of section 3 ?

Diagram 7 QFD House of quality ?

Diagram 8 Wavelength influence on longitudinal force component ?

Diagram 9 Radial tyre tread band influence on rolling circumference ?

Diagram 10 Dry Park steering torque results ?

Diagram 11 Pneumatic trail reduction with increasing cornering force ?

Diagram 12 Self-aligning torque reduction with increasing cornering force ?

Diagram 13 Steering torque characteristic with increasing cornering force ?

Diagram 14 Actual steering torque progression of a vehicle ?

Diagram 15 Longitudinal slip characteristic of a tyre ?

Diagram 16 The forces acting on a wheel encountering a transverse ridge ?

Diagram 17 Other forces acting on a wheel encountering a transverse ridge ?

Diagram 18 Vehicle kickback performance ?

Diagram 19 Tyre pneumatic trail against longitudinal force ?

Diagram 20 Side slope steer, no traction, run 1 ?

Diagram 21 Side slope steer, no traction, run 2 ?

Diagram 22 Side slope steer, no traction, run 3 ?

Diagram 23 Side slope steer, accelerating, run 1 ?

Diagram 24 Side slope steer, accelerating, run 2 ?

Diagram 25 Side slope steer, accelerating, run 3 ?

Diagram 26 Side slope steer, braking, run 1 ?

vii

Diagram 27 Side slope steer, braking, run 2 ?

Diagram 28 Side slope steer, braking, run 3 ?

Diagram 29 Pictorial representation of a drive shaft residual moment ?

Table 1 Tyre centre of pressure movement with camber change,

for various tyres ?

Table 2 Steer torque on a cambered road surface, for various conditions ?

Table 3 Worksheet for steer torque feedback during braking ?

Table 4 Spin up and snap test results ?

Illustration 1 Tyre contact patch at zero camber ?

Illustration 2 Tyre contact patch at 7 degrees camber ?

viii

Acknowledgements

I would like to thank all the many people at BMW Group UK whose knowledge and

experience I have drawn upon. Specifically I would like to thank R.A.M. Smith for his

support and technical input, J. Dunn for his invaluable advice, and M. Gallery for

giving me the inspiration and support to undertake the project. I would also like to

thank my academic and industrial supervisors, P. Kimber and J.T. Buckingham, for

providing much needed advice on the content of the project, and the layout and

structure of this report.

Declaration

Unless otherwise stated, the work contained herein is entirely my own. The contents

of this dissertation have not been previously published, in whole or in part.

ix

Summary

This report is the culmination of a two-year study into steering corruption

mechanisms. I have defined steering corruption as any steer torque feedback that is

unwanted by the driver. The project has been structured around the production of a

Quality Function Deployment, a methodology in which performance as perceived by

the customer is mapped against vehicle attributes. The individual steer corruption

performance mechanisms were generated using a “capture the universe” exercise,

and were then examined individually. For each mechanism a mathematical model

was derived to establish the theoretical relationship between the vehicle performance

and the steering parameters. The accuracy of the model was then checked by

testing the performance of an instrumented vehicle over appropriate test surfaces.

18 corruption mechanisms were identified, mapped against 33 vehicle

parameters, and 126 interrelationships were identified.

Prior to this project it had not been possible accurately to measure three of

the vehicle parameters; tyre centre of lateral pressure, hub level offset, and hub level

trail, so new measurement procedures have to be devised.

Models have been developed for 9 of the mechanisms.

Test work identified that the models for dry park torque, fight, and side slope

steer gave good correlation. Test work for feedback and kickback was successful but

could not be correlated with the modelling due to the extreme complexity of the tyre

behaviour.

1

1 Introduction

1.1 Statement of objectives

The prime objective of this report is to improve the understanding of steering

corruption mechanisms. This will be achieved by establishing the relationships

between the performance of a vehicle in circumstances known to generate steering

corruption and the parameters within the vehicle that affect its performance. The

technique known as Quality Function Deployment (QFD) will be used, as this is a

convenient means to visually represent these relationships. The development of the

QFD will be shown, from a basic representation of the Author's first thoughts to a

final, and fully validated, total representation.

The output from the investigation should offer a business benefit to BMW. For this

reason a "design handbook" will be issued internally at BMW, based on this report.

The first part will be the QFD, which allows the engineer to clearly understand the

implications of each aspect of his design, and the compromises that must be

resolved. The second part of the handbook incorporates the models developed in

this report. These models are written in simple MathCad software form, and are

designed to be used by the engineer to predict the performance of the design prior to

the construction of a vehicle. A similar process has successfully been used at BMW

Group UK in the design of new suspension systems. This "suspension blueprint"

process is now an established part of the design process.

A further objective of the project has been to develop test and measurement

processes where the existing procedures have either not existed, or have been

found to be lacking.

1.2 Background

The driver receives a great deal of information about the behaviour of the vehicle

from his environment, he can see the scenery changing, he can feel lateral and

2

longitudinal forces, he can hear tyre and road noise. In addition to these, the steering

wheel torques and displacements are very important feedbacks. The quality of these

feedbacks is crucial to providing the driver with a confidence inspiring, “good

handling” vehicle, and fall into two categories; feel and corruption. The only

difference between the two being that “feel” is any feedback wanted by the driver,

whereas corruption is any undesired feedback. Mechanisms that improve “feel” are

those which provide the driver with clear and useful information on the state of either

the vehicle or the environment (road, wind, weather etc.), an example being the

progression of the steering wheel torque as cornering speeds increase which gives

the driver feedback on the level of cornering and the potential remaining in the tyres.

Corrupting mechanisms are those which disturb the flow of useful information, and

introduce torques or displacements that relate to features of the vehicle or the

environment that the driver does not want to know about, an example being the

sharp feedback of steering torque as the vehicle passes over a transverse ridge.

The aim of the vehicle engineer is to maximise the steering feel, whilst minimising

steering corruption. The mechanisms are, however, highly complex and often

mutually exclusive. For these reasons a combination of modelling and vehicle

objective and subjective test work has been deployed within the industry to address

the issues. The result has been a gradual evolution of more refined vehicles, but

progress is slow and difficult due to the complex relationship between the many

corrupting mechanisms and the many vehicle parameters. The aim of this report is to

formally identify all these relationships, and formulate a strategy by which the

engineer may manage the design of the suspension and steering system.

The means of management will be the QFD and the means of relationship

identification will be modelling, validated with vehicle test work. There are many

modelling options available:

3

The steering and suspension could be modelled as a control system, the inputs

being the forces introduced by the environment, the transfer function being

coefficients relating to the vehicle, and the outputs being the handwheel torque and

displacement. However vehicles are highly complex systems. Diagram 1] shows the

complexity that results when just the simple case of path following is analysed. For

this reason I have chosen not to follow this approach.

4

Diagram 1]

Driver Input

(Handwheel Angle

& Torque

Steering

RatioFront Road Wheel

Steer (Slip Angle)

Front

Tyre

Char

Front Tyre

Side Force

Front Tyre

Self-Aligning

Moment

Vehicle

Yaw

Inertia

Front

Suspension

Compliance

Steer Char.

Front Suspension

Compliance

Steer

Road Wheel

Torque

Power

Sttering

Char.

Yaw Acceleration

-------------------------

Rear Slip Angle

Rear

Tyre

Char.

Rear

SideforceVehicle

mass

Rear Suspension

Compliance Steer

Yaw Velocity

-------------------------

Latac

Roll

Stiffness

(Inc.

Geometry)

Vehicle Roll

Rear Roll

Steer

Char.

Rear Roll

Steer

Desired Course

Change

Front Roll

Steer

Char.

Front Roll

Steer

Steering

Compliance

Char.

Rear

Suspension

Compliance

Steer Char.

Output = Actual

Course Change

Input

Control Chart Showing Driver

And Vehicle Control Mechanisms

Whilst Attempting To Follow A

Curved Path

Handwheel

Torque

Castor

Angle

Ft. Camber

Compliance

Char.

Camber Angle

Change

Rr. Camber

Compliance

Char.

Camber Angle

Change

Front Roll

Camber

Char.

Front Camber

Change

Rear Roll

Camber

Char.

Rear Camber

Change

Front Roll

Castor

Char.

Castor

Change

Tyre

Vertical

Force

Distribution

Rear Tyre Load

Change

Front Tyre Load

Change

Roll

Inertia

Roll Accel.

Roll

Damping

Roll Velocity

Net "Roll

Moment"

Net "Roll

Velocity"

Front

Damping

Char.

Rear

Damping

Char.

Key : Direct Connection / Strong

Factor

Strong Driver Feedback

5

The system could also be modelled in any of the proprietary multi-body modelling

codes (e.g. ADAMS, MEDYNA etc., see refs. 59], 60], 64] & 69]). These codes are

very good for predicting whole vehicle performance in response to definable

environment changes, but they are poor at providing the engineer with an

understanding of why the vehicle responds in such a way. Techniques such as

Design of Experiments can be used to start to map vehicle parameters to vehicle

behaviours, but for complex interrelated systems these techniques provide limited

information. Multi-body modelling is an invaluable tool in validating design proposals,

but it is not the ideal tool for fundamental research.

The limitations of the above two methods lead me to model the steering and

suspension using fundamental force analysis. I have defined the system as a

number of constraints in space, the corruption mechanisms have been examined to

establish the magnitude and direction of the excitation forces applied to the system,

and the output is the steering torque that results from the transmission of the applied

forces through the system.

1.3 Basic Suspension Theory

All applied steering forces are generated at the tyre contact patch. Additionally,

internal forces are generated within the system due to mass and inertial effects. This

report will concentrate on static analysis of the system (see section 2 for further

explanation) hence the dynamics of the system will be neglected. If the forces are

offset from the steering axis a steering wheel torque results. In a static force analysis

the magnitude of the resultant hand wheel torque is governed primarily by the

steering ratio and the efficiency of the steering mechanism. Therefore in order to

understand steering corruption in the "quasi-static" regime it is only necessary to

understand the magnitude and location of the applied force, the geometry of the

steering axis, the steering ratio, and the steering system efficiency. For ease, input

6

forces and moments are resolved into the three orthogonal axes. Also to aid analysis

it is often convenient to consider the force to act at wheel centre, since forces and

moments generated at the contact patch can often be resolved into a pure force at

the wheel centre. Hence diagram 2] represents all possible force inputs.

Diagram 2]

xgyg

z

xh yhxt yt

zt

All Possible Forces

The geometry of the steering axis is traditionally described by 2 angles and 2 offsets.

The side view angle is called the castor angle (Θ), and the offset most usually

referred to is the ground level trail (glt), although the hub level trail (hlt) could also be

used.

7

Diagram 3]

glthlt

xh

xg

yt

ΘΘΘΘ

zSide View

� Front

The front view angle is called the kingpin angle (Φ), and either the hub level offset

(hlo) or the ground level offset (glo) may be used.

Diagram 4]

glohlo

yh

yg

z

ΦΦΦΦ

zt

xt

Front View

Inboard�

8

1.4 Report Construction

Due to nature of the subject matter this report has many sections and subsections.

To aid the reader the report is constructed in a consistent and methodical fashion.

The report starts by introducing the reader to the important fundamentals of steering

performance (sections 1 & 2). The QFD is then introduced, since this is an ideal tool

to lead the reader into each individual corruption mechanism. Section 3 contains the

bulk of the substance, being a detailed examination of each of those mechanisms.

The QFD is then reintroduced to pull all the disparate mechanisms back together,

and offer a framework from which conclusions may be drawn.

Diagram 5]

Introduction

Conclusion

Final QFD

Initial QFD

Camber

SteerFightFeedbackBump

Steer

Puddle

Steer

Dry Park

Torque Etc.

Each mechanism is described in its own subsection of chapter 3, and is examined on

four levels. First is a general description of the background and important features of

the mechanism. Second, I develop a model in which I have attempted to include all

the key parameters, to produce an accurate predictive tool. Third, vehicle test work

9

that attempts to validate the model is described. On completion of the above three

tasks conclusions are drawn on the success (or otherwise) of the assumptions,

modelling, and test work. These four tasks are described in sub-divisions of each

subsection, see diagram 6]

Diagram 6]

Section 3

Subsection 3.1

Mechanism 1

Subsection 3.2

Mechanism 2

Subdivision 3.1.1

Description

Subdivision 3.1.2

Modelling

Subdivision 3.1.2

Test Work

Subdivision 3.1.3

Conclusion

Subdivision 3.2.1

Description

Subdivision 3.2.1

Modelling

Subdivision 3.2.1

Test Work

Subdivision 3.2.1

Conclusion

Etc.

10

2 Project Aims and Methodology

2.1 Scope

The principal aim of this project is to deliver a design “handbook”, that the engineer

can use to design vehicles that suffer less steering corruption. This handbook will be

a collection of mathematical models to calculate the magnitude of the steering torque

transmitted to the driver when the vehicle is subjected to various external conditions.

The handbook will be structured around a Quality Function Deployment (QFD) that

graphically represents the relationships between vehicle performance and vehicle

parameters.

The aim is to present a whole picture of steering corruption, rather than to focus on

any one aspect. Any mechanism that is shown to need a substantial amount of

individual work will be noted, and recommended for further work.

Vehicle behaviour can be analysed in many ways, including the “time domain”, the

“frequency domain”, or steady state. Through this project I will mostly be using

steady state analysis, since this permits the production of more simple mathematical

models suitable for inclusion in the handbook. The other benefit of steady state

analysis is that it allows the key drivers for the mechanism to be identified, separate

from any consideration of the wider dynamics of the vehicle. So, for instance, it is not

necessary to consider the whole vehicle dynamic performance, including yaw rates,

tyre cornering properties and so on, when analysing simple side slope steer. These

wider dynamic issues do not “cloud” the analysis, so the engineer can have a clear

view of all the key features affecting each mechanism.

Steady state testing of a vehicle’s response cannot be conducted “open loop”, i.e.

the driver cannot simply lock the hand wheel in position (fixed steer) or allow the

hand wheel to rotate freely (free steer), the testing must be closed loop. The driver

has to adjust the hand wheel angle to ensure that the vehicle follows the desired

path. Hence the testing is slightly driver dependant, the level of dependency being

11

governed by the complexity of the test manoeuvre. Since the key aim of this project

is to deliver of a series of mathematical models, the simplicity of closed loop

modelling outweighs the variability of the test work.

2.3 Initial QFD - Customer Focussed Target Setting

This report is intended to be an examination of steering corruption, it is beyond the

scope of this report to analyse the intricacies of the QFD process in any detail.

However, for the convenience of the reader a brief introduction to the principal

elements of a QFD will be described.

In 1972 Kobe Shipyard in Japan started to use structured quality tables (see ref. 83])

and, under the guidance of Yoji Akao, the QFD process was developed. The name

“Quality Function Deployment” is the unfortunate result of the initial translations of

the Japanese, and may have contributed to its slow adoption in the West. In Japan

“deployment” means the spreading of responsibility throughout the organisation. A

QFD is therefore an entire process by which the needs of the customer are

translated into targets and technical characteristics used throughout all sections of

the company. In 1977 Toyota adopted the QFD process as a cornerstone of its

quality drive, and impressive results have been claimed (see ref. 84]). Toyota

estimated that the cost of introducing new models was reduced by 61% in the 7

years following the instigation of the process. The key behind QFD is to build in

quality from the start of a project, rather than the traditional approach of reacting to

concerns as they are encountered.

The starting point for a QFD is the “House of Quality”, which is a 6 part matrix

representation of the relationships and correlations between the customer needs and

the technical product features (generally referred to as “Substitute Quality

Characteristics”, or SQCs). Diagram 7] shows a typical House of Quality.

12

Diagram 7]

Imp

ort

an

ce t

o C

ust

om

er

Cu

sto

mer

Sa

tisf

act

ion

Co

mp

etit

or S

ati

sfa

ctio

n

Go

al

Imp

ro

vem

ent

Ra

tio

Sa

les

Po

int

Ra

w W

eig

ht

!o

rm

ali

sed

Ra

w W

eig

ht

Correlations

Priorities

Competitive Benchmarks

Own Performance

Targets

Relationships

Technical Response

(Substitute Quality Characterisics)

Customer !eeds

House of Quality

This report constitutes the first steps on the path to a complete QFD. It details the

Customer's Needs, including a "capture the Universe" activity to ensure that all

customer needs are captured. Next the SQCs are established. Finally, the bulk of the

workload in this report is focused on establishing accurate relationships, by the

production of validated models of every Customer Need. These sections of the

"House of Quality" are highlighted in diagram 7]. The other three matrix parts are not

addressed in this report (but would make a fascinating subject for further study).

Further information on the QFD process can be found in references 81] to 85] & 140]

to 146].

13

The right hand matrix deals with translating the qualitative needs of the customer into

"quasi-quantitative" parameters. The Normalised Raw Weighting is an attempt to

assign relative importances to each Customer Need, and is used to prioritise the

ensuing workload. It is not addressed in this report since every Customer Need will

be addressed regardless of relative weighting. When the QFD presented at the

conclusion to this report is used by the design engineer some clear indications of the

importance of each Need will be required to allow proper establishment of the design

priorities. The lower matrix deals with target setting of the individual SQCs. Again it is

not dealt with in this report since targets are affected by issues that are external to

the generic nature of this report. For instance if the resultant QFD is used to analyse

a sports car the targets will have different values to if the QFD is used for an off-road

vehicle. The differences stem from the different technical benchmarks that would be

used, and the different Raw Weightings that would be decided upon.

The sixth matrix is concerned with Correlations between different SQCs. This has not

been carried out since this part of the matrix is designed to allow a visual

representation of the "informed opinion" of the engineer. The engineer will decide

whether two SQCs have high, medium or low correlation. The matrix developed in

this report has relationships developed by scientific, validated and quantifiable

methods, so the correlations are firmly established by the process followed and need

no further visual clarification (indeed a visual summary could lead to duplication and

confusion).

The initial QFD (shown in appendix I) details the "first guess" Customer Needs and

SQCs, and represented my best estimate of the likely Needs and SQCs at the

instigation of the project. The initial QFD was used as a tool to manage the project

and was developed and refined as the project progressed. This ultimately resulted in

the final QFD (shown in appendix II), which is a complete analysis of all identified

14

Customer Needs and relationships with every SQC. The QFD followed three

principal stages:

1) "Guessed" relationships, based on engineers skill and judgement

2) Validation of the "guesses" via modelling of the individual behaviours

3) Validation of the model via objective vehicle test work

This three-stage process was managed within the matrix by ensuring that each stage

was represented by a different coloured symbol:

- A black relationship is a suggested or possible relationship, based on

experience.

- Red indicates that a model or mathematical relationship has been developed

that indicates a probable relationship.

- Blue indicates that no model is required, either because the relationship is

trivially obvious, or so complicated as to be outside the scope of this project.

- Green indicates that the model has been developed, test work completed,

and a successful validation achieved. If a relationship is green then it may be

inferred that a “good understanding” of that mechanism has been achieved

My QFD varies from the standard format, as displayed in the literature, in two further

ways. I have chosen not to use the usual symbols for the strength of the

relationships. The usual format is; (blank)

for strong, moderate,

slight, and no relationship respectively. Since I intended to quantify the actual

relationship I did not feel it necessary to produce an initial approximation using these

symbols. Also, I have placed the SQCs on the vertical axis and the Customer Needs

on the horizontal axis (the converse would be normal practice). This was done simply

because I have many more SQCs than Needs, hence the matrix fits more easily on

15

the page. These variances from normal procedure cause no problems in use and, as

reference 142] (Pp 15) states: "QFD is what QFD practitioners do".

16

3 Principal Mechanisms

3.1 Symbols, and Typical Values

For the convenience of the reader all the abbreviations and symbols used throughout

this report are listed on a fold out flap in the section entitled "Abbreviations and

sample data" (page 124). For consistency I have used the same parameter values

for every model I have developed, and these are also listed on the chart. These

parameter values are correct for a Rover 800 Vitesse, so that a direct comparison

can be made between the model output and the test work.

Note: It is still common practice in the industry to specify imperial measurements for

some features (e.g. wheel dimensions). In this report I have always used SI units,

but where these are calculated from imperial I have shown those imperial figures in

brackets. Similarly I have used Radians throughout the report but these are often

translated from degrees, so I have shown degrees in brackets.

3.2 Vehicle, and Data Analysis

The vehicle chosen for the test work was a Rover 820 turbo. I chose this vehicle

because it has a high torque engine with a very flat torque curve, so the torque

output of the engine remains consistent over a wide range of engine revs. The

vehicle allows the option of a torsen (torque biasing) differential, and ABS, which

provides a convenient signal output for wheel speed sensing. The vehicle is also very

well understood, all details of the suspension kinematics and compliances are well

researched, and the vehicle has known steering corruptions issues including camber

steer and traction pull.

The car was fitted with the following instrumentation:

- 2 telemetry type drive shaft torque strain gauges

- 2 strain gauged track-rods

- strain gauged steering column (for hand-wheel torque)

17

- a pressure transducers in each brake line

- a pressure transducer in the PAS system

- 4 wheel speed sensors (via ABS sensors)

- torque/angle steering wheel

The data acquisition was done via a “Sorcus” board, and passed to DiaDem analysis

software for capture and analysis.

The vehicle was standard in all regards except that the power steering system was

disabled. Power steering systems magnify the torque between the hand wheel and

the road wheels, but they do so in a very non-linear manner. This non-linearity

means that when assessing the steering performance of a vehicle it is virtually

impossible to allow for the influence of the power steering characteristic, so the

easiest solution is to disable it. The other benefit of disabling the power steering is

that the steer torques are much higher, so the signal to noise ratio of the recorded

data is improved.

18

3.3 Bump Torque Steer

3.3.1 Discussion

Notes on ownership:

J. Buckingham of the BMW Group suggested the idea described in section 1). The

analysis of the mechanisms is my own.

R.A.M. Smith of the BMW Group suggested the ideas described in section 3). The

analysis is based on his original analysis.

Bump torque steer is the steer that results from a vertically acting road input. In order

to generate a net steer the inputs must be different on the left hand and right hand

sides of the vehicle. This sort of input might be encountered when driving along a

road with high wavelength high amplitude single wheel undulations, an example of

which would be the section of the Fosse Way between Coventry and Nuneaton. The

wavelength must be high since shorter wavelengths introduce an appreciable

longitudinal force component to the input.

Diagram 8]

High wavelength

Input primarily vertical

Low wavelength

Input has significant

longitudinal component

Longitudinal inputs will be discussed in the section on “Kickback”.

19

A vertical input is generated when a vehicle encounters the road condition described

above at sufficient speed to cause the vehicle’s body to have to accelerate vertically

over the surface. The vertical acceleration is a result of the body structure having

mass, and hence inertia, and the magnitude of the acceleration is governed by the

rate of the vehicle’s springs and dampers. With passive suspensions there is always

a compromise between reducing spring and damper rates to reduce vertical

accelerations aiding ride comfort, and increasing them to reduce the working

envelope of the suspension at the expense of ride comfort.

This input can generate steer via three independent mechanisms:

1) Steer torque is generated when the vertical force acts about a non-vertical

steering axis, resulting in a component of the torque about this axis. The analysis of

the forces and moments resulting is shown below. Suspension geometries are such

that if the left hand side of the vehicle encounters an upwards undulation the vehicle

will be steered right, i.e. the driver will be required to supply an anti-clockwise hand

wheel torque to keep the vehicle on a straight path.

2) Steer torque and angle displacement is generated when the vehicle exhibits “half

track change” with vertical suspension deflection. Half-track change is the lateral

movement of the tyre contact patch relative to the vehicle body. In reference 27] a

slip angle is defined as “The angle between the X’ axis and the direction of travel of

the centre of tire contact” (where the X’ axis is the “Direction of wheel heading”). If a

suspension exhibits half-track change the wheel’s direction of heading will remain

constant but the direction of travel will assume an angle relative to that heading. The

angle assumed will be that between the longitudinal and lateral velocities of the tyre.

The vehicle’s body has inertia and the track change may be assumed to be rapid

enough for the body not to move laterally or in yaw. In this case the tyre’s lateral

velocity may be measured relative to the body, and the tyre’s longitudinal velocity is

simply the vehicle’s longitudinal velocity. The analysis of the forces and moments

20

produced is shown below. The half-track may be increased but is more usually

decreased in response to suspension deflection into bump. If bump travel decreases

the track, when the left-hand wheel encounters the raised undulation the driver will

have to apply an anti-clockwise hand wheel torque to maintain a straight path,

otherwise the vehicle will deviate to the right. Hence this would be additive to

mechanism 1).

3) Steer angle displacement is generated when the vehicle has “bump steer”. This is

a feature of suspensions whereby they exhibit some steer change in response to

vertical displacement. A known amount of bump steer is invariably designed into a

suspension system as it is usually found to aid vehicle handling. Typically a front

suspension will toe-out into bump, and a rear suspension will toe-in into bump. It is

convention to consider the road wheel being steered in response to a suspension

deflection, but all tyres have self-aligning torque that causes them to resist deflecting

from a straight path. Hence in response to a vertical deflection bump steer will tend

to rotate the steering, without causing the vehicle to deviate. Of course, if the driver

holds the hand wheel firmly to prevent rotation the road wheel will be forced to steer,

the vehicle will deviate from its straight path, and the driver will experience a steer

torque as the tyres self-aligning torques are transmitted back to the hand wheel. If

the suspension is tuned to provide toe-out at the front the hand wheel will be steered

right in response to the left wheel encountering an upwards undulation. If the driver

holds the hand wheel he will experience an anti-clockwise torque. Hence this

mechanism is usually additive to mechanisms 1) and 2). The analysis of this

mechanism is also shown below.

4) Tyre vertical deflection. Since tyres have vertical compliance the rolling radius of

the tyre must reduce when the vertical load is increased. There is a school of thought

that this must cause the tyre to rotationally accelerate, and the inertia of the wheel

and tyre assembly will oppose the acceleration forcing the tyre into longitudinal slip.

21

If this were the case the longitudinal slip would generate a longitudinal force which

would act about the hub level offset creating a steer moment. I believe this to be a

flawed argument since radial tyres are constructed with an essentially inextensible

tread band, so the rotational speed of a tyre is governed by the rolling circumference

NOT the rolling radius. If a tyre is “squashed” the rolling radius will indeed reduce,

but the tread band will be forced into a new shape of the same length and the rolling

circumference will be maintained, the tyre will not accelerate, and no slip angles will

be produced, so no steer will be generated:

Diagram 9]

Summary of bump torque steer:

In summary it would be entirely conventional to design a vehicle with the following

characteristics:

- positive castor

- positive KPI

- positive hub level offset

- reducing half-track into bump

- toe-out into bump

All the above are additive and contribute, via the mechanisms described, to the

following behaviour (assuming a raised undulation on the left hand wheel):

- anti-clockwise holding torque required

22

- hand-wheel rotates clockwise

- vehicle deviates to the right

23

3.3.2 Bump Torque Steer

1) Due to vertical force Consider the following suspension arrangement:

In order to calculate the moment acting about the steering axis as a result of the applied force consider the view directly down the steering axis:

Since the track rods are mounted approximately horizontally to car line, the moment about the steering axis should be resolved to the vertical:

By similar triangles:

This is an important result, since it shows that the hub level trail is not a factor. Therefore:

Where r is the steering ratio. Simplifying:

Example calculation Using the Rover 800 Vitesse figures:

let:

(This force is equivalent to driving the "typical car" over a 40mm high road undulation)

Nm

24

2) Due to half-track change RAM Smith at Rover postulated the thought that half track change during bump travel can directly result in a slip angle being generated. Take a vehicle with a half track change of 0.1mm per mm of suspension travel being driven at 30m/s and encountering a 3m long undulation of 40mm height. The wheel has a forward velocity of 30m/s, and a lateral velocity of 4mm in 0.1s (or 0.04m/s). The slip angle may be calculated as follows:

Assuming a tyre self-aligning stiffness of 1500Nm/rad. the above slip angle could result in a road wheel torque of 19.5Nm, and a hand wheel torque of 0.08Nm.

3) Due to bump steer Bump steer can also generate tyre slip angles. If a vehicle has 0.02rad. of steer per 100mm of bump travel the above described undulation will generate a slip angle of 0.008rad., which will result in a hand wheel torque of 0.6Nm

Note: Mechanisms 2) and 3) relate to the generation of tyre slip angles, and their potential effect on handwheel torque. It should be noted that tyres have a strong tendency to self-align, and do not maintain slip angles unless an external force acts on them. In response to undulations a tyre will tend to track in a straight line unless the hand wheel is held very firmly, and even then steering compliances will tend to reduce the magnitude of the slip angles generated. Hence a driver will tend to see the hand wheel "wriggle" in his hands rather than notice large variations in torque. The analysis represents the worst case situation, when no steering compliance exists and the driver allows no hand wheel movement.

25

3.4 (Road) Camber Steer

3.4.1 Discussion

3.4.1.1 No Traction

A formula for steering torque due to road camber is developed below. It shows that,

in the absence of tractive or braking forces, a vehicle will pull DOWN a camber due

to the frictional force along the road surface and UP the camber due to the tyre

camber thrust. The amount by which the vehicle pulls is governed by the ratio of

mechanical to pneumatic trail, and generally reduces to zero when the pneumatic

and mechanical trails are equal. In typical straight line running a tyre may have about

30mm of pneumatic trail, but as cornering, braking, or tractive forces vary the

pneumatic trail will vary. At the limit of adhesion the pneumatic trail will drop to very

low levels, and may even go negative. This indicates that although most vehicles will

tend to pull down a camber, the amount will liable to fluctuate.

The analysis is done with “no tractive force”. In order to maintain a constant speed a

vehicle needs some tractive force to overcome wind and rolling resistance. The

amount of tractive force needed is dependant on the speed of the vehicle, and to

assess the influence of this factor see the section “Camber Steer - Under Traction”.

3.4.1.2 Braking

Notes on ownership:

R.A.M. Smith of the BMW Group suggested the idea that tyre centre of pressure

shift may be important to steer corruption. The theory developed below is all my own.

A. Sheppard of the BMW Group assisted me in the production of the tyre data shown

in table1])

It is well known that longitudinal braking forces produce a moment about the left and

right steering axes, with a moment arm given by the ground level offset. This will not

26

result in a net steer moment so long as the forces and moments remain in balance.

On a road camber the tyre is deformed and the centre of pressure moves up the

camber.

Illustration 1] shows a typical tyre contact patch at zero degrees camber angle.

Illustration 2] shows the tyre contact patch at a camber of 7 degrees. These images

were produced by lowering the tyre onto a special pressure sensitive carbon paper

(trade name “SPI Pressurex Micro”).

Illustration 1]

27

Illustration 2]

The images clearly indicate the significant movement of the centre of area of the

contact patch as the tyre is cambered relative to the road surface. The braking

forces transmitted by the tyre are frictional and hence act at the centre of pressure,

and a movement in this centre is equivalent to an increase of ground level offset on

one side of the vehicle, and a decrease on the other. This imbalance of offsets

produces a net steering moment up the camber. A simple pictorial representation is

useful for identifying the way in which the tyre deforms, but for modelling purposes it

28

is necessary to quantify the lateral shift per unit camber change, which required a

new procedure, a copy of which can be see in appendix V. Table 1] lists the

measured results obtained on a number of different tyres. It will be noted that the

tyres with the lowest profile aspect ratios also have the highest lateral pressure shift,

which confirms the subjective impression that these tyres cause vehicles to be

camber sensitive.

Table 1]

WHEEL

I!FO TYRE I!FORMATIO! MEASURED DATA VEHICLE DETAILS

WH

EE

L R

IM W

IDT

H

TY

RE

WID

TH

AS

PE

CT

RA

TIO

SP

EE

D R

AT

I!G

DIA

ME

TE

R

TY

RE

MA

KE

TY

RE

MO

DE

L

CA

MB

ER

max (

deg

)

CA

MB

ER

min

(d

eg)

C O

F P

MO

V m

ax (

mm

)

C O

F P

MO

V m

in (

mm

)

Cen

tre

of

Pre

ssu

re

Movem

ent

wit

h C

am

ber

Ch

an

ge

(mm

/deg

)

VE

HIC

LE

MA

!U

FA

CT

UR

ER

VE

HIC

LE

MO

DE

L

DO

OR

S

TY

RE

WE

AR

7" 205 40 ZR 17 DUNLOP SP SPORT 8000 10.00 -10 65.1 -86.5 7.58 ROVER R50

6.5" 205 45 ZR 16 DUNLOP SP SPORT 9000 8.75 -5.23 31.8 -50.5 5.89 ROVER 416oys 5DR NEWISH

6.5" 205 45 ZR 16 DUNLOP SP SPORT 9000 8.70 -5.27 31.8 -50.5 5.89 R0VER 416oys 5DR NEWISH

6" 205 55 ZR 16 MICHELIN MXV3A PILOT HX 10.00 -10 60.5 -55 5.78 ROVER R17 VIT 4DR

6" 195 50 VR 15 PIRELLI P6000 9.10 -5.75 35.2 -50.5 5.77 FORD PUMA COUPE PART WORN

6" 195 55 VR 15 PIRELLI P6000 9.93 -5.32 28.7 -58.2 5.70 ROVER 416 5DR PARTWORN

5.5" 185 60 HR 14 GOODYEAR EAGLE TOURING 10.23 -5.82 29.2 -50.5 4.97 ROVER 216CVT 5DR NEW

5" 185 60 HR 14 DUNLOP SP SPORT 200 9.63 -5.98 22.9 -46.4 4.44 ROVER 416 5DR NEWISH

5" 185 60 HR 14 DUNLOP SP SPORT 200 9.83 -5.92 22.9 -46.4 4.40 ROVER 416 5DR NEWISH

5" 185 60 HR 14 GOODYEAR EAGLE TOURING 9.00 -5.25 18.9 -42.5 4.31 ROVER 416 4DR WORN

5" 185 60 HR 14 GOODYEAR EAGLE TOURING 9.25 -5.28 18.9 -42.5 4.23 ROVER 416 4DR WORN

The figures from the modelling below (using Rover 800 Vitesse data) indicate that

the steer torque can be very large, and this is, without doubt, a very significant cause

of steering corruption. The figures are large because weight transfer allows 75% or

more of the vehicle mass to act on the front wheels during braking.

3.4.1.3 Traction

The arguments applied to camber steer under braking also apply to steer under

traction. Tractive forces produce their moments about the steer axis at hub level, but

the tyre’s centre of pressure movement produces an identical shift in offset, and

imbalance of moments. Tractive forces act in the reverse sense to braking forces,

hence traction tends to create a steer torque down the camber. Clearly the analysis

29

of tractive camber steer applies only to front or four-wheel drive vehicles. The

magnitude of peak force is lower than during braking since the weight transfer effect

limits the driving force on the front wheels to about 45% of the vehicle mass for a

typical front wheel drive vehicle.

The reversal of steering torque when moving from power on to braking is likely to be

the most disturbing aspect of the phenomenon to a driver since, although consistent

torques can be predicted and allowed for, transient changes are difficult to control.

Kato and Haraguchi of Toyota (ref. 106]) investigated steering pull on a rutted road,

although they only covered the case of braking. They looked at free steer and fixed

steer open loop control response, so their results are transient and therefore include

yaw rate. They identified that the key feature of the mechanism is the deformation of

the contact patch, and that this causes a lateral shift in the contact patch centre of

pressure, which they quoted as 6.83 mm per degree of camber angle. This agrees

very well with my results, which vary from 4.23 to 7.58 mm/deg. (see table 1]). The

magnitude of the steer torque resulting from the road camber is similar to that

derived in this report. This is the only paper I have found that properly analyses the

key factors behind this very important corruption mechanism.

Nagai and Koike (refs. 107] & 108]) have widely published their theoretical study on the wandering phenomenon of vehicles on damaged road cross profiles (ruts!). They do not consider braking or accelerating, do not include tyre centre of pressure lateral movement, and do not attempt to correlate their model with vehicle test work. The only significant conclusion is that the deeper the ruts are the worse the wander will be. I believe this paper is the inevitable result of excessive focus on the details of the modelling at the expense of a proper consideration of the fundamentals.

30

3.4.2 Camber Steer

No Tractive Force: Consider a vehicle travelling on a road surface such that both left and right wheels are on the same camber:

The mass acts vertically but the ground reaction is perpendicular to the ground, so a frictional component acts along the ground. The reaction normal to the ground acts longitudinally through the wheel centre, since the wheel is supported by a bearing in this plane so anything other would angularly accelerate the wheel. The normal reaction creates a steering moment UP the camber, with a moment arm given by the mechanical trail. The frictional component acts at the centre of pressure of the contact patch, and creates a steering moment DOWN the camber with a moment arm given by the mechanical trail plus the pneumatic trail. Hence:

Using Rover 800 Vitesse figures:

And let

deg.

Nm Down the camber.

31

Contribution from Tyres: It is well known that all tyres develop side force when at a camber to the road surface. This side force acts via the ground level and pneumatic trails to generate a steering torque UP the camber:

Nm Up the camber

With Tractive and Braking Force: The key to understanding camber pull in the presence of tractive (or braking) force is that the tyre's centre of pressure is displaced laterally. Since tyres transmit forces via the frictional contact between the tread and the road surface it is reasonable to deduce that the forces will act at the centre of pressure. It is well known that tractive and braking forces produce moments about the steer axis, but that these will not generate steer torques unless the left and right forces or moment arms are unbalanced. The lateral movement of the tyre contact patch does indeed unbalance the moment arms since on one side of the vehicle the centre of pressure will be displaced towards the centre-line of the vehicle, whilst on the other side it will be displaced towards the outside of the vehicle. A moment is produced equal to the amount of tractive (or braking) force multiplied by the movement of the centre of pressure.

Traction:

let:

Nm Down the camber.

Braking:

let:

Nm Up the camber

Notes: 1) The above results are from real Rover 800 Vitesse data, and clearly show that the level of steering torque generated on cambered road surfaces by the low profile tyres can be very high. This illustrates why steering fight, pull, and "white lining" (a tendency for the vehicle to follow raised road markings) is often reported on vehicles with low profile tyres. 2) For further details on a process that has been developed to measure tyre centre of pressure movement with camber see section 3.16.9

32

3.4.3 Test Work

The vehicle was driven on the Ride and Handling circuit of the Motor Industry

Research Association (MIRA). The back straight of the circuit has a surface that falls

away towards the verge at a constant 14-degree angle, and hence provides an ideal

surface for the testing. This surface is not, however, of sufficient length to be able to

guarantee achieving steady-state conditions, so the peak steer torque has been

used in the results. The test surface is cambered on only one side whereas the

modelling assumes camber on both wheels, so the results produced by the test work

will be should be doubled for comparison.

The first three tests were to drive at constant speed over the test surface. In future

testing it would be preferable to declutch, since driving at constant speed requires

engine torque. Tests were then done at maximum engine torque in both 2nd

and 3rd

gears. Finally the vehicle was braked over the test surface. The brake effort used

was just under lock-up, and the results have been “normalised” to 1’g’.

3.4.4 Results

Table 2] shows the results of the test work.

33

Table 2]

Steer Torque on a Cambered Road Surface

Traction Run Start time End time hwt (min.) hwt (max.) Mean Std. Deviation hwt (max.)

Peak Torque (Offset

Removed)

s s Nm Nm Nm Nm per 'g' Nm

No Traction 1 1.3 15.8 -2.11 2.21 0.35 0.83

2 8.1 19 -0.79 2.20 0.51 0.61

3 2.7 13.6 -1.92 2.61 0.59 0.81

Averages -1.61 2.34 0.48

Accelerating, 2nd gear 1 1 2.2 5.4 -4.96 3.27

2 12.2 14.2 -4.71 1.88

2 1 8.2 11.7 -4.62 3.26

2 17.1 19.5 -5.22 1.96

Averages -4.88 1.73 -5.36

Accelerating, 3rd gear 3 7.2 15.3 -4.57 1.81

4 6 12.4 -4.41 2.66

Averages -4.49 2.24 -4.97

Braking 1 13.2 14.2 1.97 4.92 6.91

2 5.2 7.3 0.58 7.59 11.14

3 8.4 10.4 -3.38 5.96 9.41

4 1 7.5 9.6 -1.08 6.02 8.70

2 17 18.8 -0.85 5.06 8.37

3 23.9 25.2 0.47 3.95 7.55

5 1 6.6 8.5 -0.25 3.86 6.88

2 15 16.4 -1.29 3.25 6.38

3 20.8 21.6 0.28 3.41 6.73

Averages -0.39 8.01 7.52

The results show the expected trends, with traction causing pull down the camber,

and braking causing pull up the camber. The zero traction case indicates (as

predicted) that the steer torque is very low, the model predicts a very small pull down

the camber, whereas the test work showed a slight tendency to pull up the camber.

This difference is probably due to not declutching during the test work, but the

results show large variability so more runs would be needed to confirm the trends.

However the model predicts that the steer torque in acceleration should be about

twice that measured, and the torque in braking should be about 3.5 times the

measured value. This is almost certainly due to the shortness of the test track, which

gave the driver insufficient time to achieve a genuine steady state condition. Whilst

carrying out the test it was impossible to reliably keep the vehicle on the test surface,

partly due to the very significant steer torques being produced. This test surface is

very good for looking at the subjective response of the vehicle over cambered road

surfaces, but if objective testing is to be done in the future then a dedicated test

surface, of sufficient length and width, must be built.

34

3.5 Dry Park Torque

3.5.1 Discussion

Notes on ownership:

J. Dunn of the BMW Group suggested the idea that an ellipse may be an appropriate

geometry on which to base an analysis of dry park torque. The analysis below is all

my own.

Dry park torque is simply the level of hand-wheel torque required to turn the steering

wheel when the vehicle is stationary on a typical high mu surface. On a manually

steered car this is of critical importance since it represents the peak steering torque

the customer will have to use to manoeuvre the vehicle. On a power steered car it is

equally important since it is one of the key drivers behind the amount of power that

the hydraulics of the steering must supply.

The torque applied by the driver causes the tyre to be “scrubbed” around an

approximately vertical axis, at a point near the centre of the contact patch. In order to

do the analysis a number of assumptions will be made. The validity of these

assumptions will be examined.

1) The axis of rotation is vertical.

In reality the axis of rotation is inclined to the vertical by the compound angle of

the castor and kpi. This error is in the order of 1-cos(12deg.), which is about

2%. It should be noted that the steer torque is increased due to the vehicle

being raised as the wheel rotates about the king pin axis, and this is allowed

for in the calculations below.

2) The tyre is scrubbed about its geometric centre of area (C of A).

The tyre is actually scrubbed about the point given by the intersection of the

steer axis with the ground, but this will generally be less than 40mm from the C

of A. More particularly, this distance is only important if it is ground level offset.

35

Ground level trail has no influence on the torques since the vehicle body has

an unrestrained degree of freedom to translate sideways, causing lateral

translation of the steering axis, and resulting in scrub about longitudinal centre

of the tyre. Positive or negative values of ground level offset will reduce the

torque to rotate the contact patch, since it introduces an element of rolling to

the contact patch.

3) The contact patch is an ellipse.

The shape of a tyre contact patch is obviously never a pure geometric shape.

The analysis is very much easier if the contact patch is assumed to be a circle,

and this would be nearly valid for narrower higher profile tyres, however in the

last two or three decades wide low profile tyres have become more and more

prevalent. The shape of this contact patch is usually considerably wider than it

is long, and this will cause a significant increase in dry park torque steering

efforts since more friction area is further from the axis of rotation. The keys to

choosing the right shape are to ensure that the total contact patch area is of

the correct size, and to chose a mathematically definable shape that is

scaleable to different tyre widths and whose defining equations facilitate

integration. For these reasons I have chosen the ellipse.

4) The pressure distribution is uniform across the entire tyre contact patch.

Whilst this is not the case, it is not an unrealistic assumption. Tyre designers

attempt to minimise stresses and uneven wear by ensuring that the pressure

distribution is as uniform as possible. The distribution is skewed towards the

outside of the tyre laterally since the tyre walls support some of the load, but

the distribution is skewed towards the centre longitudinally since the leading

and trailing edges of the tyre are close to zero load. These effects clearly

negate each other to a greater or lesser extent, rendering the assumption of

uniform pressure reasonable.

36

Literature:

The following formula is quoted in the literature (French, ref. 169], page 39; Dixon,

ref. 164], page 289; Bastow, ref. 154]):

m.lf

1.5

Torque at Road Wheel =

------------

3.p0.5

French states that “a close approximation is derived from the formula”, and Dixon

states that it “gives a fair estimate of the static steering torque at the road wheel”.

Neither French nor Dixon provides a source for the formula, however Bastow quotes

the source to be V. E. Gough in the discussions attached to ref. 110]. Gough states

that the formula only gives a “very approximate estimate of the static torque”.

Gough provides a proof for his formula. The fundamental assumptions are that the

contact patch is circular, and that the effective torque arm is about two thirds of the

radius of the contact patch. When Gough derived his formula tyres would have had

approximately circular contact patches, and his formula would have been, in his own

words, “near enough for the purpose”. However the formula does not suit modern

low profile tyres, a fact that should be commented upon in the more recent literature.

As proof of this, using Rover 800 Vitesse data the formula I derive below gives a

handwheel torque of 36.5Nm about centre, whereas the Gough formula gives a

torque of 23.5Nm. Test work supports my formula.

In my model below I derive the influence of KPI on the dry park steering torque. This

is a simple derivation, and is identical to those quoted in Dixon (ref. 164], page 291)

and Gillespie (Ref. 172], page 286).

Gillespie (ref. 172]) makes a slight error in stating with regard to castor jacking; “With

steer angle, one side of the axle lifts and the other drops, so that the net moment

37

produced depends also on the roll stiffness of the front suspension as it influences

the left and right wheel loads”. Castor jack does NOT raise one side of the axle and

lower the other, since the axle sits on the ground! Actually the body is forced to roll

and the net moment is hence dependant on the roll stiffness of BOTH the front and

rear suspensions (typically body stiffness is large, and may be ignored). Since castor

angles are small, and the net moment is governed by two compliances in series, the

steer torque effect of castor angles is very small and has been ignored in my

analysis.

The two further causes of increased steering effort are the loses due to inputting a

force to the non-vertical steering axis, and the application of the force via a steering

arm that is rotating from the perpendicular (and therefore foreshortening). These

effects are all modelled below, and are described by Bashford (ref. 109]).

Pellier (ref. 111]) carries out a more general analysis of steering efforts, in order to

give guidance on vehicle parameters. He recommends that manual steering systems

are appropriate only for vehicle with less than 500kg on the steered axle, a ground

level offset of 0 to 10mm, a hub level offset of 60 to 70mm, castor of 1 to 2 degrees,

and “appropriate” tyre pressures. Although the hub level offset seems unnecessarily

high, I would not disagree with these figures, however they are very prescriptive and

therefore remove the possibility of trade off and compromise by the Engineer. I

believe it is preferable to give the Engineer the tools to do the calculations and reach

the optimum solution for the situation, rather than simply quoting guidelines which

inevitably become out of date as the technology moves forward.

38

3.5.2 Dry Park Steering Torque

Put the appropriate parameters into the highlighted equations only

Vehicle Details: (alter only this section) Vehicle : Rover 800 Vitesse

Initial Calcs. (converting to SI units)

Calcs. to find the shape of the elipse of a tyre Equation of an Elipse :

Therefore :

And let b=c.a, giving:

(1) The major axis must be the contact patch width, so from (1):

And :

Therefore:

Using the vehicle parameters above:

39

Shape of contact patch:

Calcs. to find the resultant dry park steering torque

(due to tyre scrub) The length of a curve is given by:

Hence:

This integral has no closed form solution, so the analysis will continue with this integral as shown and a numerical solve will be done.

40

Therefore :

Nm

At each contact patch

Nm At the handwheel

Calc. to find the dry park steering torque (due to KPI lift)

Total Resultant Steer Torque :

41

Nm Full lock peak torque

Nm Hysteresis

42

3.5.3 Test Work

Dry park torque is very easy to measure. The Rover 800 Vitesse test vehicle had a

torque / angle measuring steering wheel fitted, was placed on a high mu surface

consisting of two sand paper pads glued to the floor, and the steering wheel was

rotated from full right lock to full left lock a number of times.

3.5.4 Results

The result of the above test is shown in diagram 10]. The black trace is a direct trace

of the measurement of hand wheel torque. For easy comparison I have included the

red trace, which is the output from the model described above. It will be noted that

the model provides a very good representation of the measured torque, however

there are some features of the real vehicle that are not included in the model. Firstly,

the measured trace shows a wave like characteristic that is typical of vehicles that

have a double universal joint arrangement in the steering column. The influence of

the universal joints is described in section 3.16.12. Second the measured trace

shows very clearly the hysteresis that all tyres show when reversing the direction of

their rotation. Tyres torsionally deform during the dry park manoeuvre, and as the

direction of rotation is reversed so the deformation has to reverse, which takes about

250 degrees of handwheel rotation.

43

Diagram 10]

-500 -250 0 250 500Angle [degrees]

-25

0

25

50

Torq

ue [N

m]

Rover 800 Dry Park Steering Torque

3.6 Feedback

3.6.1 Discussion

3.6.1.1 Braking and acceleration

Steer torque during braking and acceleration will occur whenever an asymmetry

exists. Assuming no wheel has locked or spun, possible asymmetries could include:

- vehicle lateral weight distribution

- tyre characteristics

- differential torque bias

- friction coefficient of the brake materials

- size of the brake material

- pressure in the brake lines

- ground level offset (for braking)

- hub level offset (for accelerating)

44

- steering axis geometry

- steering arm length and geometry

- non-centralised steering rack (unequal length track rods)

Most of these are unlikely to vary much, but the last two can, since all vehicles are

provided with front wheel alignment mechanisms that rely on altering the track rod

lengths individually and therefore adjusting the steer arm geometry. This asymmetry

is analogous to the left and right geometries being at different Ackerman angles.

Section 3.16.7 looks at Ackerman geometry in more detail.

More importantly these Ackerman asymmetries occur in normal driving whenever the

vehicle is steered. Table 3] is a worksheet showing the level of steering pull that

occurs in a Rover 800 Vitesse during a 1’g’ stop. In practice it would not be possible

to carry out a 1’g’ stop on full lock, but the sheet indicates that if the brakes are

applied whilst some steering is taking place this vehicle will tend to wind onto lock.

Using the work sheet some further conclusions can be drawn. Acceleration tends to

self-centre the steering. Higher levels of Ackerman cause the above tendencies to

be stronger. Conversely low levels of Ackerman can cause the vehicle to servo onto

lock during acceleration, which can be very disconcerting if the driver is attempting to

pull out of a T-junction quickly.

Steer torque effects during acceleration can also be the result of other factors, and

these are examined in section 3.15.

45

Table 3]

46

3.6.1.2 Cornering

Feedback during cornering is an essential property of vehicles, since it tells the driver

information about how much grip is available and hence how close he is to the limit

of cornering. The Engineer will specifically tune a vehicle to provide the driver with

the appropriate level of information. Thus this mechanism is more closely aligned

with “feel” rather than “corruption”, and hence only the basic principal will be

described here.

As a vehicle’s cornering speed is increased the lateral force builds linearly. Steer

torque is generated because the lateral force is applied offset from the steering axis

by a distance given by the ground level trail (glt) plus the pneumatic trail. The glt

remains almost constant, so this component of the steer torque build linearly with

lateral force, but the pneumatic trail reduces with increasing lateral force and may

even go negative. The reduction in pneumatic trail is tyre dependent, hence steering

feedback during cornering is tyre dependent. Diagram 11] shows a typical tyre

characteristic, and diagram 12] translates the reducing pneumatic trail into a

reducing self-aligning moment. Diagram 13] shows a typical steer torque progression

that results from the combination of the linearly increasing glt component and the

non-linear decreasing pneumatic trail component. It shows that a driver can detect

the approach of the limit of grip by the characteristic torque drop off that occurs near

the limit.

47

Diagram 11]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

20

20

40

60

80

Lateral Force ("g")

Pneumatic Trail (mm)

Diagram 12]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

40

30

20

10

10

20

30

Lateral Force ("g")

Self-Aligning Moment (Nm)

48

Diagram 13]

Lateral Acceleration

Ste

er T

orq

ue

3.6.2 Test Work

3.6.2.1 Cornering

The torque drop off is easy to measure during a steering pad test. Steering pad tests

are a common procedure, and have been formalised in an ISO standard (ref. 44])

3.6.3 Results

3.6.3.1 Cornering

Diagram 14] is a plot of the steering torque progression of a Rover 800 Vitesse, as

measured during a steering pad test. Note: to provide a clear view of the

mechanisms involved the test vehicle had its power steering disabled. The torque

drop off is clear, but there is also a considerable amount of hysteresis in the plot,

which tends to increase as the cornering forces build. This is probably due to level of

friction in the system, which would also increase as the cornering forces build due to

the higher loading in each component. The hysteresis could definitely be called a

corrupting mechanism, and the implication is that to provide the driver with a clear

49

stream of information (a good “feel”) the friction in the system should be minimised,

particularly whilst loaded in cornering.

Diagram 14]

0 2 4 6 8Vehicle latac (s [m/s/s]

0

5

10

15

20

25

30

Ha

nd

whe

el to

rqu

[N

m]

Steering Pad (right hand)

-10 -8 -6 -4 -2Vehicle latac (s [m/s/s]

-30

-25

-20

-15

-10

-5

Ha

nd w

hee

l to

rqu [

Nm

]

Steering Pad (left hand)

3.7 Fight - Single Wheel Spin

3.7.1 Discussion

An open differential will deliver approximately equal torques to both drive shafts. If a

single wheel looses traction it will not be able to transmit any more tractive force to

the ground, but if further engine torque is supplied the excess drive torque must be

reacted so the wheel will start to angularly accelerate. I shall refer to this as “spin-

up”. Indeed tyre characteristics are such that as the wheel starts to spin (develop

higher levels of longitudinal slip) the torque transmission ability of the tyre actually

reduces, increasing the tendency for the wheel to spin more quickly:

50

Diagram 15]

0 20 40 60 80 100

4000

3000

2000

1000

1000

Longitudinal Tyre Characteristic

Longitudinal Slip (%)

Longitudinal Force (N)

175/70R13

Vertical load: 350kg

As described previously, steer torque will be developed if the drive torques become

unbalanced, and the magnitude of this imbalance may be ascertained from the rate

at which the spinning wheel is accelerating.

It should be noted that drive torques are also unbalanced, but in the reverse sense, if

the wheel is decelerating, as it must do to re-establish parity with the non-spinning

wheel. I shall refer to this as “snap”.

Spin-up.

Consider a vehicle supplying maximum engine torque to the differential, with the

right wheel on a high friction surface and the left wheel on a zero friction surface.

The left wheel will achieve high angular acceleration, and the engine revs will climb

rapidly. The rate at which the revs climb will be governed by the rotational inertia of

the engine, transmission and spinning wheel. An amount of the available engine

torque will be used to accelerate the engine and transmission, the remaining amount

will reach the differential and will be equally split to each drive shaft. The left drive

51

shaft torque will cause the left wheel to angularly accelerate, the right drive shaft

torque will cause the right wheel to produce tractive force to accelerate the whole

vehicle. The tractive difference is hence given by the torque down one drive shaft,

and this may be calculated from the angular acceleration multiplied by the rotational

inertia of the spinning wheel. This quantifies the unbalanced steering moment, as

shown below.

Snap.

Snap occurs when the spinning wheel encounters a high friction surface and regains

grip. To regain grip the spinning wheel must obviously slow down, and the force

causing this slow down is a large rearwards friction force at the contact patch. This

friction force also produces large steer moment, which persists until the wheel speed

has reached parity with the vehicle speed. The steer torque during “spin-up” is

limited by a number of factors, however the steer torque during “snap” is only limited

by the tyre to ground friction. The analysis below shows the high level of steer torque

that can result from “snap”. Snap is made subjectively worse by the fact that the

steer torque is reversed. Using the Rover 800 Vitesse figures a driver may have to

cope with a reversal of (11.9+4.8) = 16.7Nm.

It will be evident that during spin-up the engine and transmission speed up, and that

during snap they must slow down again. This engine “overrun” cannot increase the

left hand drive torque (which is already limited by friction), but does increase the right

hand drive torque momentarily. This reduces the steer torque slightly during the brief

period of engine deceleration.

Notes:

1) The analysis has been done assuming that the vehicle is in first gear. If the

vehicle were in fifth gear, which is approximately 4 times higher, the suspension

52

rotating component inertias would have an apparent (to the engine) four fold

increase and the engine inertia would become less significant. The net result is that

the torque transmitted down the drive shafts stays approximately the same, as does

the steering torque. However, since the road wheel reach a higher rotation speed the

snap would be more prolonged, although of a similar magnitude since snap is friction

limited.

2) It is the engine “overrun”, mentioned above, that is responsible for the breaking of

drive shafts that can be a consequence of snap.

3) Traction control aids will transmit the torque of the spinning wheel to the non-

spinning wheel, improving traction but adding even more drive shaft torque to the

non-spinning wheel exacerbating the spin-up steer torque. They can, however,

restrict wheel spin, which will reduce the snap.

Dixon (ref. 2, page 37) recognises that torque required to accelerate a spinning

wheel will be matched by a thrust on the other tyre. He quantifies the effect as

“small”, partly because he chooses a very small rotating mass inertia (0.4 kg.m2).

53

3.7.2 Fight - Steer Moment During Spin-Up and Snap

Spin-up:

(1)

(2)

(3) From (1), (2) and (3):

Snap:

(1)

(2) From (1) and (2):

Example using Rover 800 Vitesse figures:

let: Spin-Up:

Nm Towards the low µ side

Snap:

Nm Towards the high µ side

54

3.7.3 Test Work

The vehicle was prepared with a torque measuring steering wheel. The idea surface

was found to be the low mu braking straights at MIRA. One front wheel could be

placed on low mu wet basalt tiles, whilst the other could be placed on high mu

Delugrip. This combination allowed single wheel spin up in any of the first 4 gear

ratios (the test vehicle being the Rover 800 Vitesse). To achieve “snap” the vehicle

was simply driven off the end of the test surfaces, onto a high mu area.

Note: in the lower gears the vehicle had sufficient torque to occasionally continue to

spin its wheel even after leaving the test surface. These occasions have been

discounted from the results.

3.7.4 Results

Table 4] shows the results of the spin/snap test. The results agree with the modelling

very well. The torque recorded during spin up is about 20% higher than the predicted

result, but the torque during snap appears to correlate very well. The test results

(particularly snap) are quite variable, as might be expected from such a rapid test

that relies on the friction properties of the tyre and road surface.

Table 4]

Spin Up: Snap:

Gear Run Steer Torque Gear Steer Torque (Nm)

Nm Power On Power Off

2 1 5.9Depress

Clutch0

2 5.4 1 12.2 11.61

3 6.4 2 14.3 9.5

4 5.5 3 16.6 13.9

3 1 6.6

2 5.5

4 1 5.6

Average: 5.8

55

3.8 Kickback

3.8.1 Discussion

There is no published general definition of kickback. Development engineers would

recognise kickback as a rapid fluctuation of steer torque in response to some road

input. Many different inputs and vehicle characteristics may give rise to this

behaviour. Steering or suspension systems may have insufficient compliance, or

have step changes in compliance. Power steering systems in which the frequency

response is insufficient to cope with inputs in the working range will suffer “hydraulic

lock up” over some surfaces. Large slip angles will present an angle to the direction

of travel, preventing the tyre from properly rolling over surface imperfections.

All the above mechanisms are excited by the application of a road input in the

longitudinal direction. The transmission from longitudinal force at the ground to steer

torque at the handwheel is relatively straight forward, the force simply acts about the

hub level offset, however the magnitude of the force is not easy to estimate. Diagram

16] shows the principal forces acting on a wheel as it encounters a transverse ridge:

Diagram 16]

A

BC

D

Emg

ua

ub Ic

Where: u = unsprung mass

56

a & b are linear wheel accelerations

c is the angular wheel acceleration

m is the mass carried by the wheel (including the mass of the wheel itself)

I is the rotational inertia of the wheel

A, B & C are the ground reaction forces

D & E are the ground frictional forces

The above system is highly complex to analyse for two fundamental reasons:

1) The system has two points of ground contact, and consequently is “statically

indeterminate”. The ratios of the forces can only be ascertained by reference to

the relevant component stiffnesses.

2) A “static” solve is not possible. The forces only exist transiently to produce

accelerations, so those forces are dependent on the masses and inertias in the

system.

A & B are the vertical ground reaction forces that must equal the total mass acting

on the ground plus the force required to accelerate the unsprung mass vertically. It

may be assumed that the vehicle’s body is sufficiently massive to allow neglection of

the body accelerations. Prior to the ridge A=mg. As the wheel travels over the ridge

B grows and A diminishes at rates governed by the vertical stiffness of the tyre and

road spring, the sprung and unsprung mass, the speed of the vehicle, and the

fore/aft compliance of the suspension.

C is the longitudinal force of interest. It starts at zero, quickly reaches a maximum,

then diminishes to zero again as the wheel centre passes vertically over the ridge. In

general ridges are not sufficiently large to cause vehicle deceleration, hence C=ub.

The magnitude of C is governed by the local belt stiffness of the tyre i.e. its ability to

“form” round the ridge, the vertical tyre and spring stiffness, the unsprung mass, and

particularly the fore/aft compliance of the suspension.

57

Since there is no relationship between A, B & C there can be a net torque on the

road wheel, which must be reacted by friction forces D & E. These friction forces are

likely to be small.

In order to find the magnitude of C it would be necessary to model the stiffnesses

and time dependant behaviour of all the components as the system traverses the

ridge. This is beyond the scope of this project.

Another contributory factor in the generation of longitudinal force input is the

necessity for the tyre to roll further when traversing a ridge than it would have done

on a flat road surface. There are three degrees of freedom between body and the

road surface that permit the relative motion:

1) rotation of the wheel

2) rearwards compliance of the wheel

3) slip between the wheel and the road surface

These are interdependent. The wheel is initially rotating too slowly for the new path it

is following, which causes a longitudinal slip. This slip is the mechanism by which the

tyre generates a force that starts to accelerate the wheel, rematching its speed to the

road surface. The rate at which the velocity can be modified is governed by the size

of this force and the rotational inertia of the wheel. The force both applies a moment

to rotationally accelerate the wheel and also applies a longitudinal force (‘A’) which

linearly accelerates the wheel centre backwards. However the magnitude of the force

is governed by the amount of longitudinal compliance which, if large, provides more

time for the angular acceleration of the wheel. Force ‘A’ acting around the hub level

offset is the potential source of kickback.

58

Diagram 17]

a

b

ub Ic

Simple geometry shows that

for a 10mm ridge the extra

distance traveled by the wheel

is:

b-a=0.87mm

Friction forces

Consider diagram 17) above. For a 10mm ridge the wheel (static laden radius

300mm) is required to travel 0.87mm further than it would have if it were on a flat

road. Clearly if the wheel centre complied this distance rearwards the wheel would

not have to angularly accelerate. A typical suspension may have a longitudinal

stiffness of 500N/mm, so the rearward displacement would need to be maintained

with a force of 0.87x500=435N. This is the maximum possible longitudinal force that

could be achieved via this mechanism. This force is created by the tyre longitudinal

slip, which starts to angularly accelerate the wheel and relieve the longitudinal force

as previously described.

The wheel, having now accelerated to a new higher angular velocity, must slow down

once again when on the flat surface after the ridge. This generates a forwards

steering moment, which is likely to be of significantly lower magnitude than the

rearwards moment, but may cause a noticeable reverse kick. It may be assumed

that the driver would feel a high frequency steering vibration, accompanied by a

tendency to be pulled towards the ridged surface.

Since the magnitude of the longitudinal force is highly complex to calculate (and

outside the scope of this project) the following analysis will, based on previous

59

experience of typical longitudinal inputs, assume an arbitrary peak longitudinal force

of 1000N.

Literature:

There are very few references to kickback in the literature. Higuchi, Yano and

Hashimoto (ref. 112]) state that “The amount of kick-back is reduced to a great

extent by reducing the amount of spindle offset” (spindle offset being hub level

offset). They reported that 60mm of hlo results in a steering wheel rim acceleration

of over 20m/s2, and reducing the hlo to zero reduces the rim acceleration to below

10m/s2. This seems entirely reasonable, but it only covers one of the parameters,

and the results are only for one vehicle.

60

3.8.2 Kickback

Due to a longitudinal force input The analysis is identical to that described in "Bump Torque Steer", only the force now acts horizontally at the hub level:

See "Bump Torque Steer" for derivation

Example calculation Using the values for a Rover 800 Vitesse:

let:

Nm

The actual magnitude of longitudinal force that results from a bump input is not directly calculable, however it may be noted that, on the "standard vehicle" the steer torque resulting from a given longitudinal force is considerably greater than the torque resulting from the same magnitude of vertical force.

61

3.8.3 Test Work

A Rover 800 Vitesse was driven as quickly as possible round a bend on the ride and

handling circuit at MIRA that has closely spaced longitudinal ridges. The response of

the steering torque was recorded, then analysed using the FFT (Fast Fourier

Transform) facility of the DiaDem software to convert the signal to the frequency

domain.

3.8.4 Results

Diagram 18] shows the results of the test work. Two frequency peaks are evident,

one probably coincides with the spacing of the ridges of the test track, the other may

also be due to ridge spacing or it may be a resonant peak of the steering response.

These peaks are a clear measure of the kickback performance of the vehicle, but

further work should be done to confirm the various features of the transmitted

frequencies.

Diagram 18]

0 10 20 30 40Frequency [Hz]

0

0.25

0.5

0.75

1

1.25

1.5

Am

pl_

-Pea

k [

Nm

] 11.7Hz

14.8Hz

Kick back, dominant frequency

62

The amplitude of the kickback is 1.75Nm, which is a little below that predicted by the

model. However the model used an arbitrary longitudinal force of 1000N. If the other

aspects of the model are correct the longitudinal force due to kick back in the above

vehicle test would have been about 700N.

3.9 On Centre Feel

3.9.1 Discussion

On centre handling mostly falls into the category of “feel”, but poor on-centre

handling can have a major impact on other corruption mechanisms. So this report

will be limited to explaining the key factors that effect the vehicle performance, and to

a list of references for further reading. On centre handling is commonly referred to as

the steer response of the vehicle at lateral accelerations below about 0.2’g’. At these

low accelerations the steer response is often non-linear, being both less responsive

to the hand wheel, and exhibiting hysteresis. These effects are caused by the

compliances in the steering, suspension and tyres, also by the free play in the

steering system, and by the static and dynamic friction in the system. A great deal of

work is currently being done in this field, and I refer the reader to references 54], 55],

74] to 77], & 113] to 115]. Reference 114] being a particularly comprehensive

analysis of the subject.

3.10 Puddle Steer

3.10.1 Discussion

Puddle steer can be a particularly serious form of corruption. Hight et al. (refs. 116] &

117]) report that “The retardation at 90 km/h (55 mph) in 5cm (2 inches) of water is

about 1’g’VV.. Suddenly running wheels on one side into a long 2 inch deep water

pool would give the driver significant control problems”. To do the subject proper

justice is beyond the scope of this report, since it would require specialised test track

63

surfaces, and detailed measurement of many tyres running through different water

depths at different speeds. However for the suspension engineer the mechanism is

relatively straightforward, and the discussion below will show that there is only one

aspect of the chassis that has any significant influence over puddle steer.

Assuming the tyre doesn’t aquaplane, it essentially acts as a “water paddle”, it’s

rotation being restrained by large externally applied moment. The vehicle’s yaw

response is governed only by the size of the restraining moment and the mass and

inertia of the vehicle, so there is little that the suspension Engineer can do the alter

this. However the steer response can be altered. The moment caused by the puddle

acts as a rearward force applied at the wheel centre, and hence creates a steer

moment via the hlo. It is clear from this why a vehicle subjectively responds strongly

to puddles; they often occur on only one side of the vehicle (hence an asymmetric

input) and they act at the hlo rather than the much smaller glo. The driver control

problem is made worse by the fact that hlo is always positive, so the steer response

will always tend to pull the vehicle further into the puddle.

Eventually the vehicle speed or water depth may be sufficient to cause the tyre to

aquaplane. This will occur just after the maximum drag, and hence just as the driver

feels the maximum steering torque towards the puddle. The problem for the driver

now suddenly reverses, not only does the drag due to the puddle disappear, but

almost all rolling resistance also disappears. Suddenly the driver will feel a complete

steering torque reversal, since the non-aquaplaning wheel will still have rolling

resistance. In addition the driver will have previously applied counter steering to

attempt to correct the previous pull, which will now cause the front wheels to steer

rapidly away from the puddle. Hence the vehicle rapidly alters its path from being

pulled towards the puddle, to being pulled away from it. The driver must respond

very quickly to maintain directional control of the vehicle.

64

From the above the engineer has only two routes for reducing puddle steer, he can

work with the tyre supplier to limit the water drag properties of the tyres and increase

their aquaplaning properties, and/or he can reduce the hlo as far as possible.

3.11 Pull

3.11.1 Discussion

Pull will only occur if an asymmetry exists in the vehicle. The most common

asymmetries are listed in section 3.6.1.1. In addition to these pull can occur, even

when no traction or braking is carried out, due to:

- castor difference side to side

- non-zero thrust angle

- power steering system unbalance

- tyre rolling resistance difference (may be caused by tyre pressure

difference)

- dragging brakes

Modern manufacturing techniques mean these asymmetries are rare, however more

vehicles are specified with adjustable rear toe than has previously been the case.

Rear toe adjustment is, to my knowledge, always done on each rear wheel

individually, which has the potential to cause thrust axis misalignment problems in

service should the required 4-wheel alignment facility not be available.

Literature:

Pull is a feature that customers can readily identify and tend to find very annoying, so

vehicle manufacturers have put a great deal of effort into curing. It is one aspect of

steering corruption for which a great deal of literature exists. References 118] to 123]

are some of the better-known papers and articles. There is now common agreement

65

on most of the causes and cures for pull, so none of the references given need

further comment.

3.12 Side Slope Steer

Notes on ownership:

R.A.M. Smith suggested the idea that pull on a side slope may be alter with traction

and braking due to the change in pneumatic trail of the tyre. All subsequent analysis

and test work is my own.

3.12.1 Discussion

3.12.1.1 No Traction

There are two mechanisms responsible for causing a vehicle on a side slope to have

a net steering torque:

1) The tyre to ground frictional forces cause a direct moment about the steer

axis, with a moment arm of the mechanical plus the pneumatic trails.

2) The increased load on the lower wheel causes asymmetric castor steer

exactly as described in section 3.3.1.

The analysis below shows that only mechanism 1) is significant in magnitude.

The frictional forces described in 1) are generated by tyre slip angles, and J.C. Dixon

(Ref. 164], pages 407-409) describes how these slip angles require a net hand

wheel angle, the magnitude of which is dependant on the basic handling

characteristics of the vehicle. It should be noted that although it is possible to design

an oversteering vehicle that will require zero hand wheel angle whilst traversing a

slope, that vehicle will still require a holding torque to the steering wheel that is

independent of the handling balance.

3.12.1.2 Traction and Braking

66

The amount of steer torque is governed by the amount of pneumatic trail. Tractive

forces reduce the pneumatic trail markedly, whereas braking forces tend to increase

it slightly as shown in diagram 19]. Note: heavy braking can cause the pneumatic

trail to start reducing again, and diagram 19] is just starting to show this tendency.

Diagram 19]

0.8 0.6 0.4 0.2 0 0.2 0.4 0.6

40

30

20

10

10

Tyre Characteristics

Longitudinal Force ("g")

Pneumatic Trail (mm)

Tyre: 185/65R14

Load: 350kg

Hence it would be expected that application of tractive forces would reduce the

moment arm and hence the amount of steer torque, and application of braking forces

would increase the steer torque.

The Doctoral Thesis by G. Roos (ref. 124], and its associated paper ref. 125])

examines a vehicle's stability on undulating road surfaces. Section 2.4 starts with a

very comprehensive description of a road surface, however he gradually introduces

the following assumptions:

- The road is flat in the area of the contact patch

- The tyre's forces act through the lateral centre line of the wheel

67

- Pneumatic trail effects are not considered (or even mentioned)

- The road has no longitudinal inclination

- There is no measurement of local lateral road inclination measurement

(camber)

- Suspension asymmetry is neglected

- Wheel load variation is assumed to be insignificant

So, from a very comprehensive initial description, his analysis is systematically

reduced to a simple examination of a vehicle driving on a side slope. He does

include a simple allowance for tyre camber force generation, but he states "the

response to the local road undulation will be very small". Despite these limitations he

seemed to achieve a reasonable correlation between his model and the measured

vehicle response.

68

3.12.2 Side Slope Steer

1) Due to Tyre frictional forces Consider a vehicle on a side slope:

The frictional forces simply act about the steer axis on a moment arm of the mechanical plus the pneumatic trail:

Using Rover 800 Vitesse figures:

And let:

Nm Down the slope

2) Due to Castor Steer The steer due to the lower wheel being more highly loaded is calculated by finding the difference in loads then putting this into the equation derived in "bump torque steer, section 1": Resolve normal to the road surface:

Take moments about the Centre of Gravity:

Therefore:

And:

Hence:

Putting into equation for "Bump Torque Steer due to Vertical Force", derived in section 3.3.2:

Using Rover 800 Vitesse figures:

69

Nm Up the slope

70

3.12.3 Test work

A Rover 800 Vitesse was driven on the 10-degree side slope of the MIRA ride and

handling circuit. In all tests the driver attempted to maintain a straight direction of

travel, perpendicular to the plane of the slope (closed loop). The first series of test

involved no acceleration or braking. In the second series of tests the vehicle was

accelerated at its maximum in 2nd

gear, through the period of the engines peak

torque generation. In the third series of tests the vehicle was braked from 50 miles

per hour to a stand still, at the maximum level of braking that the driver felt he could

comfortably avoid locking wheels (between 6 and 7 m/s2 appeared to be about right)

3.12.4 Results

The graphs below show the results of the test work.

3.12.4.1 No traction or braking

Diagram 20]

10.5 11 11.5 12 12.5 13 13.5Time [s]

-7

-6.5

-6

-5.5

-5

hw

t (s

mooth

ed)

[Nm

]

Side Slope. No traction, run 1.

5.87 Nm

Three run average: 5.5!m

71

Diagram 21]

10.5 11 11.5 12 12.5 13 13.5Time [s]

-7.5

-7

-6.5

-6

-5.5

-5

hw

t (s

mooth

ed)

[Nm

]

Side Slope. No traction, run 2.

5.59 Nm

Diagram 22]

8 9 10 11 12Time [s]

-6.5

-6

-5.5

-5

-4.5

hw

t (s

mo

oth

ed

) [N

m]

Side Slope. No traction, run 3.

4.98 Nm

The model predicted a steer torque of 3.54Nm, based on a (guessed) pneumatic trail

of 30mm. It is likely that the variance is because the tyres on the vehicle tested had

more pneumatic trail than was allowed in the model. The model would agree with the

test work if the pneumatic trail were assumed to be 50mm.

72

3.12.4.2 Traction

Diagram 23]

22.5 23 23.5 24 24.5 25 25.5Time [s]

-3

-2.5

-2

-1.5

-1

-0.5hw

t ( s

moo

thed)

[Nm

]

1.31Nm

Hand wheel torque. Side slope. Max. accel, 2nd gear

Average of 3 runs: 1.28Nm

Diagram 24]

13 14 15 16 17 18Time [s]

-2.5

-2.25

-2

-1.75

-1.5

-1.25

-1

-0.75

hw

t ( s

mo

oth

ed)

[Nm

]

1.49Nm

Hand wheel torque. Side slope. Max. accel, 2nd gear

73

Diagram 25]

15.5 16 16.5 17 17.5 18 18.5 19Time [s]

-2.25

-2

-1.75

-1.5

-1.25

-1

-0.75

-0.5

hw

t ( s

mo

oth

ed

) [N

m]

1.05Nm

Hand wheel torque. Side slope. Max. accel, 2nd gear

As predicted, the steer torque reduces when accelerating on a side slope. Using the

model the pneumatic trail during this manoeuvre appears to have reduced to about

4mm.

74

3.12.4.3 Braking

Diagram 26]

10 10.5 11 11.5 12Time [s]

-6

-5.5

-5

-4.5

-4

-3.5

-3hw

t (s

mooth

ed)

[Nm

]

4.30Nm

Hand wheel torque. Side slope. 7m/s deccel. Not held in straight line.

Average for 3 runs: 4.58Nm

Diagram 27]

10 10.5 11 11.5 12 12.5Time [s]

-7

-6

-5

-4

-3

hw

t (s

mo

oth

ed

) [N

m]

4.78Nm

Hand wheel torque. Side slope. 6.5m/s deccel.

75

Diagram 28]

13.5 13.75 14 14.25 14.5 14.75 15 15.25Time [s]

-5.25

-5

-4.75

-4.5

-4.25

hw

t (s

mooth

ed)

[Nm

]

4.65Nm

Hand wheel torque. Side slope. 6m/s deccel.

In this test the steer torque actually reduced during braking. As indicated above

some tyres loose pneumatic trail in heavy braking, and using the model the

pneumatic trail would seem to have dropped to about 40mm.

3.13 Side Wind Steer

3.13.1 Discussion

It is beyond the scope of this report to analyse side wind steer in any detail. Only the

broad mechanism will be described.

When a vehicle encounters a side wind it will be pushed sideways, but it will probably

also be pushed into a yawing motion. If the centre of aerodynamic pressure of the

vehicle is in front of the vehicle’s centre of gravity the yaw will cause the front of the

vehicle to be pushed further than the rear (I shall call this case 1), and the vehicle will

tend to be pushed further away from the wind. Conversely if the centre of pressure is

behind the centre of gravity (case 2) the rear of the vehicle will be pushed further,

and the vehicle will tend to drive into the wind. A steer torque results because as the

vehicle is pushed laterally the tyres see a slip angle, and hence generate a self-

aligning moment. In case 1 the self-aligning torque will be such that the vehicle will

76

try to steer away from the wind. In case 2 the initial steer torque may be away from

the wind, but once the vehicle has yawed the steer torque will tend to help the driver

resume his original course.

It is clear from the above that far less steer correction and vehicle deviation results if

the vehicle’s centre of pressure is behind the centre of gravity. This is certainly true

so long as the vehicle’s fundamental handling balance is understeer. If the vehicle

has a tendency towards oversteer (almost no modern vehicles do) then putting the

centre of pressure behind the centre of gravity would lead to a vehicle that would be

unstable in side-winds.

Literature:

Many studies have been carried out into vehicle side wind performance, and the

reader is directed to references 126] to 130] for further information.

3.14 Split Mu Steer

3.14.1 Discussion

The interesting thing about driving on split mu surfaces is that they cause absolutely

no vehicle handling problems until the wheel on the low mu side breaks traction.

If the wheel is locked, during braking, the vehicle will yaw towards the high mu

surface. Brake force distribution is always arranged to ensure that it is always a front

wheel that will lock first, so the wheel on the low mu surface will have reached

limiting friction and will not generate further braking effort, but the wheel on the high

mu side can continue to develop further braking force. If the vehicle has positive

ground level offset a steer pull towards the high mu side will also be developed,

exacerbating the vehicle yawing motion. This is the reason that most modern

vehicles have adopted negative ground level offset, where the steer torque will tend

to assist the driver in countering the vehicle’s yaw motion.

77

As explained in the section on “spin up and snap”, spin up can cause unbalanced

tractive forces, and these are largest if the vehicle is fitted with a torque biasing

differential. If the wheel is spun, during acceleration, the vehicle will yaw towards the

low mu surface. The tractive forces are transmitted to the steering via the hub level

offset, which is always positive, so the steer torque resulting from the unbalanced

tractive forces will always steer the vehicle towards the low mu surface.

These mechanisms are trivial, so no modelling or test work (beyond that done in the

section on “spin up and snap”) has been done.

3.15 Tractive Torque Steer

3.15.1 Discussion

The outboard end of a drive shaft is an assembly of two shafts joined by a CV joint. If

the joint is not articulated the two shafts will define a straight line. If the joint is

articulated the two shafts lie in a plane defined by the shafts. This plane is important

since when a drive shaft is articulated it produces a residual moment, and the

direction of this moment is perpendicular to the plane:

Diagram 29]

ibj

obj

stub

ε

dst

Plane

78

Hence with a knowledge of the input torque (dst), and the geometry of the two

elements of the shaft defined by three points:

inner joint

outer joint

stub axle

the magnitude and direction of a key forcing moment is known. In order to find the

steer corruption moment the only remaining task is to resolve the forcing moment

onto the steer axis, which is defined by a further two points. A mathematical analysis

rapidly becomes highly complex due to the three dimensional geometry of the

system, however the geometry may be easily analysed on a CAD system.

The equation given below for the residual couple is universally reported in the

literature (refs. 131] to 133], & 138]):

Couple=dst.tan(γ /2)

Note: this is not the steering moment, since for this the torque must be resolved onto

the steering axis. This extended analysis can be found reference 139].

Literature

In addition to those mentioned above, Gillespie (ref. 172], page 297-299) and “The

Universal Joint and Drive shaft Design Manual” (ref. 200], Appendix H, page 397)

contain particularly clear analyses of torque steer.

79

3.16 Related Analyses

During the course of the investigation of steering corruption mechanisms, I have had

to devise various models and techniques which, although not corruption mechanisms

in themselves, relate to or assist with the understanding of them.

3.16.1 Turning Circle

The equations developed below follow from the analysis of Ackerman steering

geometry.

The modelling of a vehicle’s turning circle is not quite as straightforward as it might

at first seem. The steering geometry of a vehicle is almost never pure 100%

Ackerman, so when the vehicle executes a tight turn the two front wheels fight each

other. Rover has had numerous ways of modelling the turning circle of vehicles,

some assume the left and right lock angles can be averaged, most assume the mid-

point of the projections of the two lock angles represents the turn centre. The best of

these “rough” formulas is one issued by New Vehicle Concept in October 1983,

which makes a “corrective displacement” which shifts the above mid-point by 10%.

Below I derive the turning circle based on the two wheels running round the circle

with the same (opposing) slip angles, which I believe is the correct assumption since

if they did not carry the same slip angles there would be a residual net force which

would have to be opposed either by some other force or by the generation of an

acceleration. My derived formula is actually a pair of simultaneous equations, which

have no direct solution and so must be solved numerically.

80

3.16.1 Turning Circle Calculation Sheet

Vehicle: Rover 800

UBJ

LBJ

OBJ

IBJ

Calcs. to find "Virtual" Steer Arm:

Lock Angle calcs:

Turning Circle calcs. Slip Angle calcs:

Average of Lock Angle calc.:

81

Ackerman calcs.

Results

m

m (Calculated from average of left and right road wheel steers)

m (Likely to be more representative. Calculated from same left and right slip angles)

deg. Slip angle (scrub) at full lock

82

Turning Circle Calcs.: "Average of Lock Angles" Method: Consider a vehicle on full lock:

From trivial geometry:

and:

tw/2 is required since turning circles are always quoted from "kerb to kerb", so allowance must be made for half the tyre width. The result is multiplied by two since diameter, not radius, is quoted.

therefore:

"Same Slip Angle" Method:

83

Therefore:

(1) And:

(2) (1) into (2) :

(3) Also:

(4) And:

(5) But same slip angle, therefore:

(6) (5) into (4) & (3) leads to :

(7)

The solution to may be found by simultaneous solving of (3) & (7). This is done using a numerical solve, since there is no symbolic solution to the two equations. Blueprint formula:

m

Vehicle Concepts formula (after simple manipulation, to allow comparison with above):

m

84

3.16.2 Kerb Jacking

The kerb jacking analysis is a simple extension to the dry park torque analysis. Kerb

jacking occurs when a driver parks his vehicle adjacent to, and in contact with, a tall

kerb and then attempts to rotate the steering. In order for the road wheels to steer

they must push the entire front of the vehicle away from the kerb. This is probably

the most severe steer manoeuvre that a vehicle will see.

85

3.16.2 Calcs. to find Kerb Jacking Steering Torque

Note: ec.tw/2 = eb

Nm Steer torque at zero lock

Nm Steer torque at full lock

86

3.16.3 Suspension Bush Rate Analysis

As described above, on centre handling characteristics are strongly affected by the

amount of compliance in the suspension and steering system. It is essential,

therefore, that the engineer has the tools to accurately predict the compliance rates

of every bush in the system. Up to now these have not been available to Rover.

Below I have derived models that predict bush rates and maximum permissible loads

and deflections in each of the three principal directions. I have derived models for

plain cylindrical bushes, and cylindrical interleaved bushes. I have checked the

models extensively against the many Land Rover Freelander suspension bushes,

and believe them to give accurate results.

87

3.16.3 Cylindrical Bush Rate Calculations

Bush : RBX101160

INPUTS :

(45 to 75 preffered)

N/mm^2

RESULTS :

RADIAL AXIAL TORSIONAL

N/mm N/mm Nm/deg

mm mm deg

N N Nm Note: 'def' signifies the maximum permissible bush deflection and 'load' signifies the maximum permissible bush load

88

3.16.3 Interleafed Bush Rate Calculations

INPUTS :

(45 to 75 preferred)

N/mm^2

89

RESULTS :

RADIAL AXIAL TORSIONAL

N/mm N/mm Nm/deg

mm mm deg

N N Nm Note: 'def' signifies the maximum permissible bush deflection 'load' signifies the maximum permissible bush load

90

3.16.4 Gyroscopic Steer

The road wheel of a vehicle is both large and rotates quickly (by convention about

the y-axis) hence it may be expected to suffer gyroscopic procession if rotated about

either the x or z-axis. Fortunately for vehicle engineers the x-axis of road wheel

rotation is very well constrained by the upper and lower suspension links, so

application of a steering input will not create significant camber change. The only

situation the engineer may need to be aware of is if the vehicle is designed with a

large camber change into bump and rebound. Should this be the case, when the

vehicle encounters a large undulation at high speed some level of steer torque will

occur. If both wheels see the same camber change the steer torques will cancel, but

if one wheel sees more camber change than the other the driver will feel a torque at

the steering wheel.

It has not been possible to cover this subject in any more detail in this report, but it

would make a very interesting study for some future work.

91

3.16.5 Ackerman Steer Geometry

The principals of Ackerman steer geometry are well known, and will not be repeated

here. The engineer must have a good knowledge of the amount of Ackerman a

steering system has throughout its travel since it is one of the factors governing steer

torque progression and traction steer (see section 3.6). The constructs to ascertain

the amount of Ackerman are not straight forward, so I have derived a model below to

simplify the process.

92

3.16.5 Ackerman Calculation Sheet Consider a track rod and steer arm being moved by some rack travel (rt):

The track rod and steer arm remain the same length, hence:

These may be simultaneously solved numerically to find a and b, which are then put into the equation for steer given by:

Using figures for a Rover 800 Vitesse:

Vehicle: Rover 800 Vitesse UBJ LBJ OBJ IBJ

Calcs. to find "Virtual" Steer Arm:

Lock Angle calcs:

Ackerman calcs.

93

Results

m

% Ackerman at full lock

94

% Ackerman on centre

Proof Ackerman Calcs: Consider a track rod and steer arm being moved by some rack travel (rt):

The track rod and steer arm remain the same length, hence:

These may be simultaneously solved numerically to find a and b, which are then put into the equation for steer given by:

95

3.16.6 Steering Column Universal Joint Phasing

It is well known that when two universal joints are placed in series on a shaft speed

fluctuations can occur between the input and the output. The fluctuations occur

whenever the joints are articulated, and the amount of fluctuation is strongly affected

by the phasing of the two joints. Just such a situation is often seen in the design of

steering columns, and can be noticed by the driver as an apparent variation in

steering ratio if the fluctuations exceed a given figure. Rover’s standard is to ensure

that the input and output velocities are never more than 7% different. Below is a

model to analyse these speed fluctuations.

96

3.16.6 Calc. Sheet for a double UJ shaft running at a

given Phase Angle

Inputs:

Initial Calcs:

Results:

97

3.16.7 Indicator Self Cancelling Torque

Steering system torque is a property entirely controlled by the Chassis department.

The only other part of the vehicle that has an influence on the torque is the indicator

self cancelling mechanism. In order to function, the mechanism requires a very small

steering wheel torque, which is conventionally ignored in the design of the steering

system. However with the introduction of power steering system, and the gradual

reduction of steering efforts that has resulted, the indicator self cancelling torque is

starting to become a noticeable feature. It has not been possible in this project to

analyse acceptable torque thresholds, but I believe this is now a piece of work that

should take place.

3.16.8 Mass Measuring Procedure

Many of the loads and torques in the steering system are governed by the front axle

mass of the vehicle. It is relatively easy to weigh a vehicle, but to repeatably

measure the corner weights of a range of different vehicles, in different seating

configurations, requires a robust procedure. During the course of this project I

rewrote the existing procedure to both improve on the old procedure, and to ensure

that it conformed to BMW’s mass measuring standards. The procedure has been

written with the ease of the user specifically in mind, thus with only 4 readings the

spreadsheet computes every possible mass configuration, and presents the data in

an easy visual format. See appendix IV for a copy of the procedure.

3.16.9 Suspension Parameter Measurement Procedures

Notes on ownership:

The hub level trail measurement procedure was developed an issued by A. Shepard

of BMW group UK under my guidance

98

From the discussions throughout this report it will be clear that the tyre centre of

lateral pressure, the hub level offset, and the hub level trail are all key aspects of

steer corruption. Up to the present there have been no reliable procedures for

measuring these parameters, hence as part of this project I have devised such

procedures. Two of these procedures are now issued internally within BMW group

UK as “Local Chassis Procedures” (see refs. 14] & 15]). These are self-explanatory

and copies are included in appendices V, VI, and VII.

99

4 Conclusions

4.1 Summary of Work Done

The relationships between customer perceived steering corruption

mechanisms and the relevant vehicle parameters was established in the form of a

QFD (Quality Function Deployment). This document followed three distinct phases;

initial engineer's "guess", preliminary confirmation via modelling, and final

confirmation by test work.

In the first phase eighteen mechanisms were identified. Nine of these were

identified as being suitable for investigation with mathematical modelling. Five

mechanisms were subject to detailed test work, and three mechanisms showed good

agreement with the model. The two mechanisms that did not show good agreement

with the model are conditions that are strongly influenced by the complex dynamic

performance of tyres, which are often the most difficult aspect of a vehicle's dynamic

behaviour to characterise.

A key objective of the project was to deliver a "design handbook" of simple

models, that can be used by the engineer to develop steering systems that suffer

less corruption. Throughout this report 12 models are presented, ranging from

fundamental corruption mechanisms such as camber steer and side slope steer, to

related analysis dealing with ackerman geometry and vehicle turning circle. These

models, together with the QFD as an index, will be issued internally at BMW group

UK as the "Steering Corruption Design Handbook".

A number of new test procedures were developed. These tests were closed

loop in nature, since this allowed the results of the testing to be directly compared

with the output of the models. Section 2.1 gives further details on the closed loop,

steady state nature of the analysis carried out in this report. All tests were carried out

with the same vehicle, a Rover 800 Vitesse. The vehicle's power steering system

100

was disabled, since this is a highly non-linear influence on the steer torque response

which clouds the basic vehicle performance.

During the course of the project I have issued 4 new vehicle parameter

measurement procedures. Three procedures define measurement processes for

suspension parameters that have not previously been easy to measure, the fourth

procedure describes a process for repeatably measuring vehicle mass.

4.1 Final QFD - Customer Focussed Development Tool

The final QFD is presented in appendix II. It shows that 126 interelationships

were identified and that there are, as might be expected, highly complex interactions

between the design parameters of a steering system and the vehicle's steering

performance. It should be remembered that this is actually only the first step on the

way to a complete QFD. The presented matrix is the "House of Quality" section of

the process. Completion of the QFD would require the weighting of all the

mechanisms and parameters, and the identification of appropriate targets.

The presented matrix allows the engineer to quickly identify the implications

of a particular design, and assess the likely effect of a change to any parameter.

Having identified the likely implication, the engineer can then refer to the

mathematical model to quantify the effect.

4.3 Case Studies

4.3.1 New Mini

One of the key features of the new Mini is its use of very low profile tyres. These

tyres have two key properties; they have high cornering stiffness, and tend to have a

greater lateral shift of the tyre centre of pressure. Reference to the QFD indicates

that these feature are likely to be affected:

101

1) The key corruption issue is likely to be camber steer. Unless special action is

taken, the tyres will cause the vehicle to pull during traction and braking on

cambered road surfaces.

2) Feedback under cornering. The tyres are likely to be less "progressive" and

provide less warning of the approach of the limit of grip.

3) Bump steer. If the vehicle has significant half-track change into bump the tyres

will translate this into higher levels steer torque

4) The dry park torque (or more specifically, the power steering forces) are likely to

be a little higher, since the tyre footprint is elongated.

4.3.2 Rover 600

Rover 600 has a very low hub level offset. Reference to the QFD indicates

that this should improve most of the corruption problems. In comparison to a vehicle

with "normal" hub level offset; bump steer, fight, kickback, puddle steer and torque

steer are all likely to be significantly reduced, and dry park torque and side slope

steer should be marginally better.

4.3.3 Rover Coupe Turbo

The Rover coupe turbo was notable for extremely high levels of steer corruption,

particularly during traction. The vehicle had a high torque engine, was fitted with a

torque biasing differential, and had fairly high hub level offset. Reference to the QFD

shows that all these features are strong causal factors behind tractive torque steer.

4.4 Final Comments and Discussion

The Rover coupe turbo was an object lesson in the need to provide

customers with vehicles that do not exhibit unpleasant steering corruption. The tools

presented in this report will allow the engineer to predict the steer performance of a

102

vehicle prior to the production of a prototype, and early enough in the design process

to allow any changes that may be required to address any problems found.

This project has highlighted the need to change our design focus away from

the traditionally used parameter of steering axis inclination (castor and kpi) towards

the four suspension offsets (hub level offset, ground level offset, hub level trail, and

ground level trail). The forces input by the tyre through the suspension system are

converted to steer torques by the offsets, the steer axis angle only modifies the

torques marginally.

The project has also highlighted the role of the tyre in steering corruption. Not

only is it a highly complex, difficult to model component, but it is also a critical factor

in the generation of some of the most significant of the corruption mechanisms. In

the design process there is often great concentration on ensuring that the ground

level offset is specified very accurately, but given that the tyre centre of pressure

lateral shift has been shown to be in the order of 50mm in either direction over badly

cambered road surfaces, and this makes a 2mm change in ground level offset seem

unimportant. The tyre, and particularly the lateral shift of the centre of pressure,

should form a key focus of the design and development of future chassis systems.

There is a general reluctance, within the vehicle dynamics community, to

undertake closed loop vehicle testing. It is certainly true that open loop testing,

whether it be fixed or free steer control, takes the driver out of the analysis and

permits more repeatable tests. However, even open loop test are not perfectly

repeatable since test surfaces, weather, tyre condition, vehicle loading and many

other variables can all affect the results. I have found that, for the special case of

steady state analysis, repeatability in closed loop testing is possible. The only

caveats are that the driver's task is not too arduous, and the test surface is of

sufficient size to allow time to reach steady state. Given these conditions vehicle

tests can be simplified to the point that modelling of those tests can be quite simple

103

mathematical models, rather than the more common but complex time domain based

multi-body modelling.

104

5 Further Work

There are many parts of the QFD that require further work. Feedback, on

centre feel, pull, side wind steer and split mu steer all need further modelling and test

work. Also, the QFD could be completed with weightings and targets.

Although I am confident that the camber steer model captures the key

aspects it was not possible to get good agreement with the test work. I believe that

this is due to the poor quality of the test surface. A longer stretch of consistent road

camber would need to be found to confirm the validity of the model. Given the

importance of this mechanism, I believe that such a test surface should either be

found or constructed.

Many of the models suffer from a lack of reliable tyre data. This is a common

issue in vehicle dynamic analysis. I would urge that the current effort to improve the

level of knowledge about tyres is redoubled.

Kickback is a complex issue. I have presented a simple analysis based on an

arbitrary longitudinal force, but I am aware that the issue is probably more complex

than this. Kickback would make an ideal project for future study.

Puddle steer (as opposed to aquaplaning) is not generally addressed in the

development of vehicles. There is an assumption that it is either "external, to do with

the weather", or "a tyre problem". I have shown that the steer response of the vehicle

is slightly affected by the design of the vehicle. Given that puddle steer can lead to

loss of control of the vehicle, I believe it should at least be the subject of overchecks

in the vehicle development phase.

Side wind steer has been extensively studied, but to my knowledge, the steer

response and the consequent driver task has not received the same focus. Side

wind steer has traditionally been analysed with fixed steer control, and the measure

has been lateral vehicle displacement. I believe this poorly represents the real world,

and that there is value in looking at steady state steer response analysis.

105

References

The references are arranged as follows:

BMW Group (Internal) Standards

Rover Chassis Local Processes (REFs)

Rover Engineering Standards (RESs)

BMW Engineering Standards (EHBs)

National Standards

American (SAE)

German (DIN)

Japanese (JASO)

International Standards (ISO)

Technical Papers

Sources:

Periodicals

Institutions/Societies

Conferences

General

General: Compliance

General: Feel

General: QFD

General: Steering as a control system

General: Testing

General: Vehicles

Camber steer

Dry park torque

Kickback

On centre feel

106

Puddle steer

Pull

Side slope steer

Side wind steer

Torque steer

Comments

There is no British section under “National Standards” since, although the BSI

(British Standards Institute) does issue vehicle dynamics standards, they are always

duplicates of ISO standards. Reference to relevant BS numbers can hence be found

in “International Standards”.

107

Rover (Internal) Standards

Chassis Local Processes:

1] REF30/001, Vehicle Analysis - Test Schedule

2] REF30/006, Index of Whole Vehicle Dynamic Tests

3] REF30/021, Vehicle Weights and Loading

4] REF38/023, Suspension and Steering Performance Test Rig

5] REF31/025, Bump Steer Measurements (Front & Rear)

6] REF31/026, Sideforce Steer

7] REF31/027, Steering Effort

8] REF31/028, Steer Turn Geometry (Ackerman)

9] REF31/033, Steering Subjective Analysis

10] REF31/035, Subjective Analysis - Handling

11] REF31/036, Wheel Balance (Shimmy) Sensitivity

12] REF35/039, Steering Gear Performance

13] REF31/043, Subjective Assessment - Vehicle Preparation

14] REF30/044, Hub Level Offset Measurement

15] REF30/045, Tyre Centre of Pressure Measurement

16] REF35/101, Use of Datron WVT RV3 5 Degree of Freedom Measurement

Head

17] REF35/102, Weigh Pad System

Rover Engineering Standards (RESs):

18] 50.01.506, Ride and Handling on Road - Subjective Appraisal

19] 50.31.500, Mass Schedule - Complete Vehicle

20] 50.31.501, Turning Circle - Vehicle - Measured

21] 61.02.510, Power Steering System - Catch-up Test

22] 61.11.500, Steering System Load and Effort Test

23] 61.21.503, Steering Pad - Test Procedure and Acceptance

108

BMW Engineering Standards (EHBs):

24] EHB 3 Whole Vehicle Dynamic Tests

25] EHB 43 Chassis Assessment - Subjective

National Standards

American:

26] SAE J266, “Steady-state directional control test procedures for passenger

cars and light trucks”, Society of Automotive Engineers, Warrendale, PA, June

1996

27] SAE J670e, “Vehicle Dynamics Terminology”, Society of Automotive

Engineers, Warrendale, PA, July 1979

28] SAE J1441, “Subjective Rating Scale”, Society of Automotive Engineers,

Warrendale, PA, June 1985

29] SAE J1574/1, “Measurement of Suspension Parameters”, Society of

Automotive Engineers, Warrendale, PA, May 1994

30] SAE J1574/2, “Measurement of Suspension Parameters - Rationale”,

Society of Automotive Engineers, Warrendale, PA, May 1994

31] SAE J1988, “Tyre Residual Aligning Moment Test”, Society of Automotive

Engineers, Warrendale, PA, Aug. 1994

German:

32] DIN 70 000, Same as ISO 8855 (See below)

33] DIN 70 020-1, “General Terms in automobile engineering: dimensions”

34] DIN 70 020-2, “General definitions for automotive engineering: weights”

35] DIN 70 020-5, “Automotive engineering; tyres and rims; terms and

conditions for measuring”

36] DIN 70 031, “Load distribution for passenger cars”

109

Japanese:

37] JASO Z108-76, “Test procedure of crosswind stability for passenger car”

38] JASO Z213-89, “Glossary of terms relating to steering systems of

automobiles”

International Standards

39] ISO 31, “Quantities”

40] ISO 611, “Braking of Automotive Vehicles & their trailers - Vocabulary”

41] ISO 612, “Road vehicles - Dimensions of motor vehicles and towed

vehicles - Terms and definitions”, 1978

42] ISO 1000, “SI - Units and Recommendations”

43] ISO 1176, “Road vehicles - Masses - Vocabulary and codes”, 1990

ISO 2416, “Passenger cars - Mass distribution”, 1992

44] ISO 4138 & BS AU 189, “Road vehicles - Steady state circular test

procedure”, 1996

45] ISO 7401 & BS AU 230, “Road vehicles - Lateral transient response test

methods”, 1988

46] ISO 7401 Part 2, “Road vehicles - Passenger cars - Free steer control test

procedure”, 1998 (Draft)

47] ISO/TR 8349, “Road vehicles - Measurement of road surface friction”, 1986

48] ISO/TR 8725, “Lateral Response (Single sine input transient test - open

loop)”, 1988

49] ISO/TR 8726, “Road vehicles - Transient open-loop response test method

with pseudo-random steering input”, 1988

50] ISO 8855 & BS AU 244, “Road vehicles - Vehicle dynamics and road-

holding ability - Vocabulary, 1991

51] ISO 11835, “ABS Performance”

110

52] ISO 12021-1, “Road vehicles - Sensitivity to lateral wind - Part 1: Open loop

test method using wind generator input”, 1996

53] ISO 12021-2, “Road vehicles - Sensitivity to lateral wind - Part 2: Natural

wind input”, (Not Issued)

54] ISO 13674-1, “Road vehicles - Test method for straight ahead directional

stability - Part 1, weave test”, (Draft)

55] ISO 13674-2, “Road vehicles - Test method for straight ahead directional

stability - Part 2, straight line test”, (Draft)

56] ISO 14512, “Passenger cars - Straight ahead braking on split coefficient of

friction surfaces - Open loop test procedure”, 1997 (Draft)

57] ISO 15037-1 & BS ISO 15037-1, “Passenger cars - Vehicle dynamics test

procedures - Part 1: General conditions”, 1997 (Draft)

58] ISO 17288, “Passenger cars - Free steer control test procedure”, (Draft)

Papers

There are three main sources of technical papers; periodicals, institutions/societies,

and conferences. Listed below are the primary sources for technical information on

vehicle dynamics and chassis systems. I have listed only those conferences that

regularly convened, not one off events.

Periodicals:

- ATZ (German. Monthly. Started 1898.)

- Automobil-Industrie (German)

- Automobile Engineering (Bi-Monthly. Proceedings of the IMechE-Automobile

Section)

- Automotive Engineering (Monthly. Journal of the IMechE. Started 1965)

- Automotive Engineering International (Monthly. Journal of the SAE. Started

1892)

111

- Automotive Technology International (Annual)

- Car Design & Technology (Monthly, published from Jun. 1991 to Oct. 1992)

- Ingens de L’Auto (French)

- International Journal of Vehicle Design (8 per year. Journal of the

International Association for Vehicle Design. Started 1988)

- JSAE J (Japanese. Journal of the JSAE)

- JSAE Review (Japanese. Quarterly. Review of JSAE J, in English. Started

1979)

- JSME International J (Japanese. Journal of the JSME)

- Machine Design (Monthly.)

- Vehicle System Dynamics (Bi-monthly, Journal of the IAVSD, Started 1968)

Institutions/Societies

- ASI (American Supplier Institute, for QFD expertise)

- FISITA (International Federation of Automotive Engineering Societies)

- GOAL/QPC (American, for QFD expertise)

- IAVD (International Association for Vehicle Design)

- IAVSD (International Association for Vehicle System Dynamics)

- IMechE (English. Institute of Mechanical Engineers)

- JSAE (Japanese Society of Automotive Engineers)

- JSME (Japanese Society of Mechanical Engineers)

- MIRA (English. Motor Industry Research Organisation. Has extensive

technical library)

- SAE (American. Society of Automotive Engineers)

Conferences

- Autotech (Bi-annually, odd years. Organised by IMechE. Birmingham,

England. November.)

112

- Autotechnologies Conference (Bi-annually, odd years. Organised by SAE.

Various locations. Started 1983. January)

- AVEC. International Symposium on Advanced VEhicle Control, (Bi-Annually,

even years.)

- FISITA. International Federation of Automotive Engineering Societies (Bi-

annually, even years. Various locations)

- IAVSD symposium. The Dynamics of Vehicles on Roads and Tracks.

International Association for Vehicle System Dynamics. (Bi-annually, odd

years. Various locations. Started 1969. August)

- International Conference on Experimental Safety Vehicles (Bi-annually, odd

years. Various locations. Started 1967. June)

- JSAE Convention (Twice yearly - spring and autumn, Japan)

- Novi QFD symposium (Annual. Organised by ASI & GOAL/QPC. Started

1989)

- SAE International Congress and Exposition (Annually. Detroit, USA, June)

General:

59] ADAMS - A Universal Program for the Analysis of Large Displacement

Dynamics, Ingens de l'Auto, Sep. 1985

60] ADAMS Theory and Application, “Vehicle System Dynamics”, 16, 1986

61] Bennison, M., Shimmy - A Case Study, Msc. Thesis, University of Warwick,

1992

62] Durstine, J.W., The Truck Steering System from Hand Wheel to Road

Wheel, Collection of SAE Technical Papers, SP-374, 1973

63] Fortunkov, D. F., An Investigation of Vehicle Steered-Wheel Stabilising

Torques, “Avtomobilnaya Promishlennost”, Oct. 1980

113

64] Full Vehicle Modelling and Simulation using the ADAMS Software System,

IMechE Technical Paper No. C427/16/170, 1991

65] Gillespie, T. D. & Segel, L., Influence of Front-Wheel Drive on Vehicle

Handling at Low Levels of Lateral Acceleration, IMechE Technical Paper No.

C114/83, 1983

66] Hays, D.F. & Browne, A.L. (eds.), The Physics of Tire Traction, Theory &

Experiment; Proceedings, Plenum, N.Y., 1974, ISBN 0-306-30806-1

67] Heydinger, G. J., Garrott, W. R. & Christos, J. P., The Importance of Tire

Lag on Simulated Transient Vehicle Response, SAE Technical Paper No.

910235, 1991

68] Jacobson, M. A., Vehicle Safety - Car Handling and Braking. Legislation

can not Cover Everything. 7th. International Conference on Experimental

Safety Vehicles, Paris, 5-8 Jun. 1979

69] MEDYNA An interactive Analysis and Design Program for Flexible

Multibody Vehicle Systems, “Vehicle System Dynamics”, 16, 1986

70] Niemann, K., Richter, K-H., Weiger, G., Wulf, H.,

Entwicklungsmöglichkeiten an Lenksystemen für Kraftfahrzeuge und ihr

Einfluß auf die Kurshaltung (Possibilities of Developing Steering Systems for

Motor Vehicles and their Influence on Directional Stability), ATZ, 82, 1980

71] Segel, L., Theoretical Prediction and Experimental Substantiation of the

Response of the Automobile to Steering Control, 1956

72] Shimomura, H., Haraguchi, T., Satoh, Y. & Saitoh, R., Simulation Analysis

on the Influence of Vehicle Specifications upon Steering Characteristics, Int. J.

of Vehicle Design, Vol. 12, No. 2, 1991

73] Wedlin, J., Tillback, L. R. & Bane, O., Combining Properties for Driving

Pleasure and Driving Safety: A Challenge for the Chassis Engineer, SAE

Technical Paper No. 921595, 1992

114

General: Compliance

74] Bergman, W., Effects of Compliance on Vehicle Handling Properties, SAE

Technical Paper No. 700369, 1970

75] Kuralay, N. S., The Effect of Chassis Elasticity and Tyre Parameters on

Passenger Car Handling, “Automobil-Industrie”, May 1986

76] Nozaki, H., The Effects of Steering System Rigidity on Vehicle Cornering

Characteristics in Power-Assisted Steering Systems, JSAE Review, Apr. 1985

77] Park, J. & Nikravesh, P. E., Effect of Steering-Housing Rubber Bushings

on the Handling Responses of a Vehicle, SAE Technical Paper No. 970103,

1997

General: Feel

78] Adams, F. J., Power Steering “Road Feel”, SAE Technical Paper No.

830998, 1983

79] Koide, M. & Kawakami, S., Analysis of “Steering Feel” Evaluation in

Vehicles with Power Steering, “JSAE Review”, Vol. 9, No. 3, Jul. 1988

80] Setright, L. J. K., The Mythology of Steering Feel, “Automotive

Engineering”, Jun. 1999

General: QFD:

81] Hayes, R., QFD: A Key Enabling Technology in Today's Advanced Product

Development Environments, "Industrial Engineering", 1994,pp.10-13

82] Kalageros, N. & Gao, J. X., QFD: Focusing on its Simplification and Easy

Computerization using Fuzzy Logic Principles, "Int. J. Of Vehicle Design", Vol.

19, No. 3, 1998, pp.315-325

115

83] Kogure, M. & Akao, Y., Quality Function Deployment and CWQC in Japan,

“Quality Progress”, Oct. 1983, pp.79-81

84] Sulivan, L. P., Quality Function Deployment, “Quality Progress”, Jun. 1986,

pp.39-50

85] Veraldi, L. C., The Team Taurus Story, Paper Presented at M.I.T. Conf.,

Chicago, 22 Aug. 1985

General: Steering as a Control System:

86] Bergman, W., Correlation between Open Loop and Closed Loop Vehicle

Handling Measurements, SAE Technical Paper No. 800846, 1980

87] Darrenberg, W., Panik, F. & Weidemann, W., Analysis of the Control

System “Driver - Vehicle - Road”, 7th International Conference on Experimental

Safety Vehicles, Paris, 5-8 Jun. 1979

88] Furukawa, Y. & Nakaya, H., Effects of Steering Response Characteristics

on Control Performance of Driver - Vehicle System, JSAE Review, Apr. 1985

89] Mayr, R., Automated Steering Control for Vehicles, “Int. J. of Vehicle

Design”, Vol. 16, Nos. 4/5, 1995

90] O’Hagan, J. T. & King, J. J., A New Procedure for Determining On-the-

Road Vehicle Directional Response Characteristics, SAE Technical Paper No.

700370, 1970

91] Segel, L. & MacAdam, C., The Influence of the Steering System on the

Directional Response to Steering, The Dynamics of Vehicles on Road and

Tracks, Proc. of 10th IAVSD Symposium, Prague, 24-28 Aug. 1987

92] Smiley, A., Reid, L. & Fraser, M., Changes in Driver Steering Control with

Learning, “Human Factors”, 22(4), 1980

93] Wade Allen, R., Stability and Performance Analysis of Automobile Driver

Steering Control, SAE Technical Paper No. 820303, 1982

116

General: Testing

94] Ashley, C. & Gibson, P. D., A Summary Report on Steering Pad and Steer

Frequency Response Tests carried out on 24 Cars, “VDI-Berichte”, No. 368,

1980

95] Barter, N. F., Measurement of Vehicle Handling by Tethered Testing, Proc.

IMechE, Vol. 184, Pt 2A, No. 11

96] Fancher, P. S., Winkler, C. B. & Nisonger, R. L., Analytical Comparisons of

Methods for Assessing the Transient Directional Response of Automobiles,

IAVSD

97] Jaksch, F. O., Vehicle Characteristics Describing the Steering Control

Quality of Cars, 7th. International Conference on Experimental Safety Vehicles,

Paris, 5-8 Jun. 1979

98] Nagiri, S., Doi, S., Matsushima, S. & Asano, K., Generating Method of

Steering Reaction Torque on Driving Simulator, “JSAE Review”, 15, 1994

99] Verma, M. K., Transient Response Test Procedures for Measuring Vehicle

Directional Control, “Vehicle System Dynamics”, 10, 1981

100] Zomotor, A., Braess, H. H., Ronitz, R., Methods and Criteria for the

Evaluation of Handling and Road Holding Properties of Passenger Cars,

“ATZ”, Dec. 1997

General: Vehicles

101] Anon., Nissan’s Multilink Front (Suspension), “Car Design & Technology”,

Mar. 1992

102] Bulmer, C. H., Analysis of the (Toyota Carena E) Super Strut, “Car Design

& Technology”, Apr. 1992

117

103] Jaksch, F. O., The Steering Characteristics of the Volvo Concept Car, 7th.

International Conference on Experimental Safety Vehicles, Paris, 5-8 Jun.

1979

104] Lijima, Y. & Noguch, H., The Development of a High-Performance

Suspension for the new Nissan 300ZX, SAE Technical Paper No. 841189,

1984

105] Miles, J., Sears, K. & Booen, J., High Performance Suspension for Front

Wheel Drive

Camber steer:

106] Kato, K. & Haraguchi, T., Improvement on Steering Pull during Braking on

Rutted Road, JSAE Review, 17, 1996

107] Nagai, M. & Koike, K., Analysis on Wandering Phenomenon of Vehicles

Influenced by Damaged Road Cross Profiles, SAE Technical Paper No.

931910, 1993

108] Nagai, M. & Koike, K., Theoretical Study of Vehicle Wandering

Phenomenon Induced by Dented Road Cross Profile, Int. J. of Vehicle Design,

Vol. 1, No. 2, 1994 (Note: this is an EXACT duplication of the above

publication, and has also been published in JSAE Review, Vol. 14, No. 2, Apr.

1993)

Dry park torque:

109] Bashford, G. D., Influence of King Pin Inclination on Steering Effort,

“Automotive Engineer”, Jun./Jul. 1978

110] Heacock, F. H. & Jeffery, H., The Application of Power Assistance to the

Steering of Wheeled Vehicles, IMechE Technical Paper, presented at General

Meeting of the Automobile Division, 9th Feb. 1954

118

111] Pellier, R., Critere d’optimisation d’une direction manuelle pour automobile

(Criteria for the Optimisation of a Manual Steering System for a Car), “Ingens

de L’Auto”, Mar. 1982

Kickback:

112] 34/ Higuchi, A., Yano, T. & Hashimoto, T., Trends of Suspensions of

Front-Wheel-Drive Vehicles, JSAE Review, Vol. 13, No. 2, Apr. 1992

On centre feel:

113] Farrer, D. G., An Objective Measurement Technique for the Quantification

of On-Centre Handling Quality, SAE Technical Paper No, 930827, 1993

114] Norman, K. D., Objective Evaluation of On-Center Handling Performance,

SAE Technical Paper No. 840069, 1984

115] Somerville, J., Farrer, D. G. & Whitehead, J. P., Improvements in the

Quantification of On-Centre Handling Quality, IMechE Technical Paper No.

C466/049, 1993

Puddle steer:

116] Hight, P. V., Fugger, T. F., Marcosky, J. & Varat, M., Asymmetric Water

Drag on Vehicle Trajectory and Human Response, IMechE Technical Paper

No. C462/39/106, 1993

117] Hight, P. V., Wheeler, J. B., Reust, T. J. & Birch, N., The Effects of Right

Side Water Drag on Vehicle Dynamics and Accident Causation, SAE Technical

Paper No. 900105, 1990

Pull:

118] Daniels, J., Offsets and Insets, “Motor”, 26th May 1984

119

119] Goddard, S., Elwood, P., Scrub Radius and SUV Handling, “Automotive

Engineering International”, Jul. 1999

120] Hanenberger, P. H., New Suspension for Small Front Wheel Driven Cars,

“The SAE-Australasia”, Sept./Oct. 1982

121] Heylen, V., How negative’s your off-set?, “Autocar”, 21 Aug. 1982

122] Morita, T. & Tanaka, T., Vehicle Stability during Braking and Influence of

Suspension Characteristics, “JSAE Review Vol. 10 No. 2”, Apr. 1989

123] Nedley, A. L., & Wilson, W. J., A new Laboratory Facility for Measuring

Vehicle Parameters Affecting Understeer and Brake Steer, SAE Technical

Paper No. 720473, 1972

Side slope steer:

124] Roos, G., Numerical Design of Vehicles with Optimal Straight Line

Stability on Undulating Road Surfaces, Doctoral Thesis, Technische

Universiteit Eindhoven, 1995

125] Roos, G., Rollet, R. & Kriens, R. F. C., Numerical Simulation of Vehicle

Behaviour during Straight Line Keeping on Undulating Road Surfaces, Vehicle

System Dynamics, 27, 1997

Side wind steer:

126] Alexandridis, A. A., Repa, B. S. & Wierwille, W. W., The Influence of

Vehicle Aerodynamic and Control Response Characteristics on Driver-Vehicle

Performance, SAE Technical Paper No, 790385, 1979

127] Harada, H. & Iwasaki, T., Stability Criteria and Evaluation of the Steering

Manoeuvre in Driver-Vehicle System - Handling and Stability against

Crosswind Gusts, “JSAE Review”, Vol. 13, No. 4, 1993

120

128] van den Hemel, H. J. M., Schuurman, R. E., Riemersma, J. B. J. &

Blaauw, G. J., The Way was Long, the Wind was Cold

129] Hiramatsu, K. & Soma, H., Response Parameters for Characterizing

Vehicle Behaviour under Lateral Wind Disturbance, IMechE Technical Paper

No. C466/009/93, 1993

130] Milner, P. J., Graphical Presentation of the Sensitivity of Cars to Windy

Conditions using Basic Wind Tunnel and Chassis Data, IMechE Technical

Paper No. C121/83, 1983

Torque steer:

131] Bulmer, C., Argumentative Torque, “Car Design & Technology”, Nov.

1991

132] Fergusson, J. H. & Woodruff, F., The Forgotten Forces in Couplings,

"Machine Design", 6th. Sept. 1973

133] Front Suspension Blueprint, Rover internal document, 1994

134] Hinds, J. M., Development of Vehicles for Directional Stability, IMechE

Technical Paper No. C120/83, 1983

135] Mabie, H. H., Constant Velocity Joints, "Machine Design", May 1948

136] Matschinsky, W., The Influence of Drive Shafts and Reduction Gears on

Wheel Suspension Characteristics

137] Pitts, S. & Wildig, A. W., Effect of Steering Geometry on Self-Centering

Torque and “Feel” during Low-Speed Manoeuvres, “Automotive Engineer”,

Jun./Jul. 1978

138] Platteau, R., Guidoni, S., Sacchettini, P. & Jesson, R., Traction and

Handling Safety Synergy of Combined Torsen Differential and Electronic

Traction Control, IMechE Technical Paper No. C498/30/144, 1995

121

139] Sutherland, G. H., Finding Bearing Loads caused by Constant-Velocity U

Joints, "Machine Design", 20 Apr. 1978

122

Bibliography

Books on QFD:

140] Akao, Y. (Ed.), Quality Function Deployment - Integrating Customer

Requirements into Product Design, Productivity Press, Cambridge, MA, ISBN

0-9152-9941-0, 1990

141] Bossert, J. L., Quality Function Deployment: a Practitioner’s Approach,

ASQC Press, 1991

142] Cohen, L., Quality Function Deployment: How to Make QFD Work for

You, Addison-Wesley, Reading, MA, ISBN 0-201-63330-2, 1995

143] Day, R., Quality Function Deployment: Linking a Company with its

Customers, ASQC Press, 1993

144] King, B., Better Designs in Half the Time, Methuen, MA, 1987

145] Mizuno, S. & Akao, Y. (Eds.), QFD - The Customer-Driven Approach to

Quality Planning and Deployment, Asian Productivity Organisation, Tokyo,

ISBN 92-833-1121-3 & 92-833-1122-1, 1994

146] Terninko, J., Step by Step QFD, 1997

Books on Vehicle Dynamics:

Very few books have been written on the subjects of vehicle dynamics, steering,

handling, aerodynamics and tyres. This section represents an attempt to list all

relevant books. Where information has been found on previous editions and

duplicate publishers these also have been listed.

147] Adams, H., Chassis Engineering, HPBooks, New York, NY, ISBN 1-

55788-055-7, 1993

148] Aird, F., Circle Track Suspension, Motorbooks International, Osceola, WI,

ISBN 0-87938-872-2, 1994

123

149] Artamonov, M.D., Ilarinov, V.A., Morin, M.M., Motor Vehicles -

Fundamentals and Design, (Trans. A. Troitsky), M.I.R. Publishers, Moscow,

1976

150] Automobile Engineering (6 volumes), American Technical Society,

Chicago, 1920

151] Barnard, R. H., Road Vehicle Aerodynamic Design, Longman, ISBN 0-

5822-4522-2, 1996

152] Bastow, D., Car Suspension and Handling, Pentech Press, London, ISBN

0-7273-0303-1 & 0-7273-0305-8, 1980

153] Bastow, D., Car Suspension and Handling, 2nd. Edition, Pentech Press,

London, 1987

154] Bastow, D., Howard, G., Car Suspension and Handling, 3rd. Edition,

Pentech Press, London, ISBN 0-7273-0318x, 1993

(also: Bastow, D., Howard, G., Car Suspension and Handling, 3rd. Edition,

Society of Automotive Engineers, Warrendale, PA, ISBN 1-56091-404-1, 1993)

155 Cambell, C., Automobile Suspensions, Chapman and Hall Ltd., London,

ISBN 412-16420-5 & 412-15820-5, 1981

156] Cambell, C., New Directions in Suspension Design, Robert Bentley,

Cambridge, MA, 1981

157] Clark, S.K. (ed.), Mechanics of Pneumatic Tires, National Bureau of

Standards, Washington DC, 1971

158] Clark, S.K. (ed.), Mechanics of Pneumatic Tires, 2nd Edition, US

Department of Transportation National Highway Traffic Administration, US

Government Printing Office, Washington DC, 1981

159] Cole D.E., Elementary Vehicle Dynamics, University of Michigan, Ann

Arbour, 1971

124

160] Costin, M. & Phipps, D., Racing and Sports Car Chassis Design, Albion

Scott, Brentford, ISBN 0-86255-035-1, 1962 & 1991

161] Daniels, J., Car Suspension at Work, Motor Racing Publications,

Croydon, 1998, ISBN 1-899870-31-8

162] Dean-Averns, R., Automobile Chassis Design, 2nd Edition, Iliffe & Sons

Ltd., London, 1952

163] Dixon, John C., Tires, Suspension and Handling (Cambridge Engineering

Series), 1st. Edition, ISBN 0-5214-0194-1

164] Dixon, John C., Tires, Suspension and Handling, 2nd. Edition, SAE R-

168, Society of Automotive Engineers, Warrendale, PA, ISBN 0-340-67796-1 &

1-56091-831-4, 1996

165] Dwiggins, B.H., Automotive Steering Systems, Delmar Publisher, Albany,

NY, 1968

166] Ellis, J.R., Vehicle Dynamics, Business Books Limited, London, 1969

167] Ellis, J.R., Road Vehicle Dynamics, John R. Ellis, Inc., Akron, OH, 1988

168] Ellis, J.R., Vehicle Handling Dynamics, MEP, London, ISBN 0-85298-885-

0, 1994

169] French, T., Tyre Technology, Adam Hilger, 1989, ISBN 0-85274-360-2

170] Fundamentals of Vehicle Dynamics, General Motors Institute, Flint, MI

171] Giles, J.G. (ed.), Steering, Suspension and Tyres, Iliffe, London, 1968

(Also: Giles, J.G. (ed.), Steering, Suspension and Tyres, Butterworths, London,

1968)

172] Gillespie, T.D., Fundamentals of Vehicle Dynamics, SAE R-114, Society

of Automotive Engineers, Warrendale, PA, ISBN 1-56091-199-9, 1992

173] Heldt, R.M., The Automotive Chassis, 1948

(OR: - Heldt, P.M., The Automotive Chassis, Chilton Co., 1952)

125

174] Howard, D., Chassis and Suspension Engineering, Osprey, London, ISBN

0-85045-775-0, 1987

175] Hucho, W-H. (ed.), Aerodynamics of Road Vehicles, Butterworths,

London, 1987

176] Hucho, W-H. (ed.), Aerodynamics of Road Vehicles, 4th. Edition, SAE R-

177, Society of Automotive Engineers, Warrendale, PA, ISBN 0-7680-0029-7,

1998

177] Katz, J., Race Car Aerodynamics: Designing for Speed, Robert Bentley,

Cambridge, MA, ISBN 0-8376-0142-8, 1995

178] Kovac, F.J., Tire Technology, The Goodyear Tire and Rubber Co., 1973

179] Milliken, W.F. & Milliken, D.L., Race Car Vehicle Dynamics, SAE R-146,

Society of Automotive Engineers, Warrendale, PA, 1995

180] Moore, D.F., The Friction of Pneumatic Tyres, Elsevier, Amsterdam, ISBN

0-444-41323-5, 1975

181] Nader, R., Unsafe at any Speed; the Designed-in Dangers of the

American Automobile, Grossman Publishers, New York, 1965

182] Newcomb, T.P., and Spurr, R.T., Braking of Road Vehicles, Chapman

and Hall, Ltd., London, 1967

183] Newton, K., & Steeds, W., The Motor Vehicle, 1st Edition, Iliffe & Sons,

London, 1929

(This has been constantly reissued, up to: Newton, K., Steeds, W., & Garrett,

K., The Motor Vehicle, 12th Edition, Butterworths-Heinmann, London, ISBN 0-

7506-3763-3 & 1-5609-1898-5, 1998)

184] Norbye, J.P., The Complete Handbook of Front Wheel Drive Cars, Tab

Books, ISBN 0-8306-2052-4, 1979

185] Norbye, J.P., The Car and its Wheels - A Guide to Modern Suspension

Systems, Tab Books, ISBN 0-8306-2058-3, 1980

126

186] Norbye, J.P., The Michelin Magic, Tab Books, ISBN 0-8306-2090-7, 1982

187] Reimpell, J. & Stoll, H., The Automotive Chassis: Engineering Principles,

Society of Automotive Engineers, Warrendale, PA, ISBN 1-56091-736-9, 1996

188] Scibor-Rylski, A.J., Road Vehicle Aerodynamics, 1st. Edition, ISBN 0-

4707-5920-8 & 0-4702-0097-9

189] Scibor-Rylski, A.J., Road Vehicle Aerodynamics, 2nd. Edition, Pentech

Press, London, ISBN 0-7273-1805-5 & 0-7273-1802-0, 1984

190] Setright, L.J.K., Automobile Tyres, Chapman and Hall, London, ISBN

0412-09850-4, 1972

191] Smith, S., Advanced Race Car Suspension Development, Steve Smith

Autosports Publications, Santa Ana, CA, ISBN 0-936834-05-6, 1992

192] Smith, S., Stock Car Chassis Technology, Steve Smith Autosports

Publications, Santa Ana, CA

193] Smith, S., Sprint Car Chassis Set-up, Steve Smith Autosports

Publications, Santa Ana, CA

194] Smith, S., Stock Car Racing Chassis, Steve Smith Autosports

Publications, Santa Ana, CA

195] Smith, S., Dirt Track Chassis Technology, Steve Smith Autosports

Publications, Santa Ana, CA

196] Staniforth, A., Competition Car Suspension, Haynes, Sparkford, ISBN 0-

85429-956-4, 1994

197] Steeds, W., Mechanics of Road Vehicles, Iliffe & Sons, London, 1960

198] Taborek, J.J., Mechanics of Vehicles, Towmotor Corporation, Cleveland,

OH, 1957

( Also: Taborek, J.J., “Mechanics of Vehicles”, Machine Design, May 30th -

Dec. 26 1957)

127

199] Tompkins, E. S., The History of the Pneumatic Tyre, Dunlop Ltd.

(Eastland Press), ISBN 0-903214-14-8, 1981

200] Universal Joint and Drive shaft Design Manual, AE7, Society of

Automotive Engineers, Warrendale, PA, 1979

201] Wong, J.Y., Theory of Ground Vehicles, John Wiley & Sons, New York,

ISBN 0-471-03470-3, 1978

202] Wong, J.Y., Theory of Ground Vehicles, 2nd. Edition, John Wiley & Sons,

New York, ISBN 0-471-52496-4, 1993

128

Abbreviations and Sample Data

Abbreviation

or Symbol Description Units

Nominal

Value

Used

Tyre cornering stiffness N/rad 50,000

Tyre self-aligning moment stiffness N.m/rad 1,500

a nominal tyre aspect ratio % 0.55

abs anti-lock braking system

cofg centre of gravity height m 0.45

cofp tyre centre of pressure movement with camber m/rad (0.315)

cs tyre lateral force generation with camber N/rad (2005)

cv joint constant velocity joint

d brake force distribution %

(front) 0.75

dst drive shaft torque N.m

ea ellipse major axis (half the tyre contact patch width)

eb ellipse minor axis (half the tyre contact patch length)

ec ratio of minor to major axis

et engine torque N.m

etmax maximum engine torque N.m 240

g acceleration due to gravity m/s2 9.81

gb acceleration in braking 'g'

glo ground level offset m

glt ground level trail m 0.0111

gr engine to road wheel gearing

gt acceleration in traction 'g'

hlo hub level offset m 0.048

hlt hub level trail m 0.001

ie inertia of engine rotating mass, including gearbox kg.m2 0.25

is inertia of suspension rotating mass, inc. driveshafts kg.m2 1.1

jx, jy, jz steer arm to steer axis (virtual) point

k height of "standard" kerb m 0.115

k & c kinematics and compliance

kpi king pin inclination (see Φ)

lf front corner force, M2 loading N (4654)

lfu unsprung front corner force N (456)

m vehicle mass, M2 loading kg 1646

mf front axle mass, M2 loading kg 948.9

mfu unsprung front axle mass kg 93

p tyre pressure N/m2 220000

pas power assisted steering

pt pneumatic trail m 0.03

qfd quality function deployment

r steering ratio (over centre) 18.35

res rover engineering standard

rtmax steering rack travel m 0.0735

rw half rim width m (0.076)

slr tyre static laden ratio m 0.293

tb torque bias of differential

tbmax maximum torque bias of differential 1.4

129

tc turning circle m

tf track width, front m 1.485

tr track width, rear m 1.485

tw nominal tyre width m 0.205

w wheelbase m 2.762

wr wheel radius m (203)

x1 to 4 kerb jacking radius (in increasing accuracy)

A suspension bush - Axial stiffness N/mm

AX, AY, AZ suspension geometry points - see appendix III for

to VX, VY, VZ

further details

CofP tyre Centre of Pressure movement with camber m/deg 0.0055

CS tyre lateral force generation with Camber N/deg 35

DII Inner Diameter - suspension bush Interleaf mm

DIO Outer Diameter - suspension bush Interleaf mm

DS Outer Diameter - suspension bush Sleeve mm

DT inner Diameter - suspension bush Tube mm

E shear modulus - suspension bush rubber mm

F input Force N

I thickness - suspension bush Interleaf mm

L Length - suspension bush rubber mm

P tyre Pressure psi (32)

R suspension bush - Radial stiffness N/mm

RW Rim Width inches 6

S hardness - suspension bush rubber shore

T suspension bush - Torsional stiffness N.m/deg

WD Wheel Diameter inches 16

β construction angle

εu strg column intermediate shaft upper joint angle rad

εl strg column intermediate shaft lower joint angle rad

χ road wheel camber rad (0.0032)

δ road wheel steer angle rad

δmax maximum road wheel steer angle rad 0.6

θ castor angle rad 0.03

µ tyre to road sliding friction coefficient 1

µmax tyre to road static friction coefficient 1.25

γ drive shaft angle rad

φ king pin inclination rad 0.14

κ road side slope rad

η hand wheel angle rad

ηmax max. hand wheel angle rad 9.8

λ road camber rad

Α tyre slip angle deg

Χ road wheel camber deg 0.18

130

∆ road wheel angle deg

∆max maximum road wheel angle deg (34.4)

Γ strg column intermediate shaft "out of co-planer" angle

deg

Θ castor angle deg (1.7)

Φ king pin inclination deg (8)

Κ road side slope deg

Λ road camber deg

131

Appendices

I Initial Steering Corruption QFD

STEERI!G SYSTEM QFD

Bump Torque Steer

(Road) Camber Steer - No Traction

(Road) Camber Steer - Under Braking

(Road) Camber Steer - Under Traction

Dry Park Torque

Feedback - Under Braking

Feedback - Under Cornering

Fight - Single Wheel Spin & Snap

Kickback

On Centre Feel

Puddle Steer

Pull - No Traction

Pull - Under Braking

Pull - Under Traction

Side Slope Steer

Side Wind Steer

Split Mu Steer - Under Braking

Tractive Torque Steer

Ackerman

Axle Mass - Front

Brake Intervention Traction Control

Brake Proportion Split

Camber

Castor

Centre of Gravity Height

Component Moments

CV Joint Angle

Diff. Bias

Engine Torque

Friction - Road

GLO

Handling Balance

HLO

Inertia - Suspension Rotating Parts

Inertia - Engine & Trans. Rotating Parts

KPI

PAS Characteristic

Pneumatic Trail

Steer Friction / Free Play

Steer Ratio

Suspension Compliances

Suspension Kinematics

(Bump Steer / Camber & Half Track Change)

Track

Trail (GLT)

Tyre Cornering Stiffness Characteristics

Tyre Footprint Shape / Coning Stiffness

Tyre Non-Uniformity

Tyre Pressure

Tyre Radial Flexibility

Tyre Relaxation Length

Tyre Water Clearnace Properties

Corruption or Feel mechanism : C C C C F F F F/C C F C C C C C C C C

Notes : 1) This chart describes steering effects, it does not include vehicle effects. i.e. The factors that affect puddle steer are different to the factors

that affect vehicle deviation when driving through a puddle, hence a vehicle with low puddle steer may have high puddle deviation, etc.

2) Feel is the desired transmission of a force or moment, from the tyre contact patch to the steering wheel.

Corruption is an unwanted alteration in handwheel torque or angle, that requires driver intervention to maintain the original path.

3) Feedback is transmission of forces or moments whilst applying a steer angle,

KEY : F : Mechanism is primarily steering feel

C : Mechanism is primarily steering corrurtion Peter Hewson (34792)

132

II Final Steering Corruption QFD

STEERI!G SYSTEM QFD

Bump Torque Steer

(Road) Camber Steer - No Traction

(Road) Camber Steer - Under Braking

(Road) Camber Steer - Under Traction

Dry Park Torque

Feedback - Under Braking

Feedback - Under Cornering

Fight - Single Wheel Spin & Snap

Kickback

On Centre Feel

Puddle Steer

Pull - No Traction

Pull - Under Braking

Pull - Under Traction

Side Slope Steer

Side Wind Steer

Split Mu Steer - Under Braking

Tractive Torque Steer

Ackerman √ Ο S S S

Axle Mass - Front √ √ √ √Brake Intervention Traction Control √ √Brake Proportion Split √ ΟCamber S S S

Castor √ √ S S S ΟCentre of Gravity Height ΟComponent Moments √ Ο Ο ΟCV Joint Angle S S S

Diff. Bias √ √Engine Torque √ √ √ √Friction - Road √ √GLO √ S √Handling Balance ΟHLO √ Ο √ √ √ S S Ο √Inertia - Suspension Rotating Parts √Inertia - Engine & Trans. Rotating Parts √KPI Ο Ο √ S S ΟPAS Characteristic √ Ο Ο √ √ √ Ο Ο √Pneumatic Trail √ √ Ο Ο √ √Steer Friction / Free Play √ Ο Ο √ √Steer Ratio √ √ √ √ √ Ο Ο √ √ Ο Ο √ √Suspension Compliances Ο √ S S Ο √Suspension Kinematics

(Bump Steer / Camber & Half Track Change) √ √ √ Ο Ο

Track ΟTrail (GLT) √ √ Ο Ο √ √Tyre Cornering Stiffness Characteristics √ √Tyre Footprint Shape / Coning Stiffness √ √ √ ΟTyre Non-Uniformity S

Tyre Pressure √ Ο Ο Ο S

Tyre Radial Flexibility √ ΟTyre Relaxation Length √Tyre Water Clearnace Properties √

Corruption or Feel mechanism : C C C C F F F F/C C F C C C C C C C C

Notes : 1) This chart describes steering effects, it does not include vehicle effects. i.e. The factors that affect puddle steer are different to the factors

that affect vehicle deviation when driving through a puddle, hence a vehicle with low puddle steer may have high puddle deviation, etc.

2) Feel is the desired transmission of a force or moment, from the tyre contact patch to the steering wheel.

Corruption is an unwanted alteration in handwheel torque or angle, that requires driver intervention to maintain the original path.

3) Feedback is transmission of forces or moments whilst applying a steer angle,

KEY : F : Mechanism is primarily steering feel

C : Mechanism is primarily steering corrurtion

√ : Strong causal factor

O : Weak causal factor

S : Only a factor if there is side to side difference

black : Suspected mechanism

red : Mathematical model developed

blue : No model required

green : Test work completed and correlation shown Peter Hewson (34792)

1

III Geometry data for Rover vehicles

Appendix III

Front Suspension Coordinates

Vehicle: ADO20 (Mini) UBJ LBJ Wheel Centre Stub Shaft Upper Arm Ft Upper Arm Rr

Lower Arm Ft Lower Arm Rr OBJ IBJ CVJ UJ

"Ralph's sheet" Data Sheet Data Sheet

145/70R12 175/50R13

Vehicle: HHR (400) UBJ LBJ Wheel Centre Upper Arm Ft Upper Arm Rr

Lower Arm Ft Lower Arm Rr OBJ IBJ

Strut Lower Strut Upper

Vehicle: R3 (200) UBJ LBJ Wheel Centre Stub Shaft

Lower Arm Ft Lower Arm Rr OBJ IBJ CVJ UJ

Strut Lower

2

Vehicle: PR3 (MGF) UBJ LBJ Wheel Centre Stub Shaft Upper Arm Ft Upper Arm Rr

Lower Arm Ft Lower Arm Rr OBJ IBJ

Vehicle: R17 (800) (Jim Forbes deck) UBJ LBJ Wheel Centre Upper Arm Ft Upper Arm Rr

Lower Arm Ft Lower Arm Rr OBJ IBJ

Strut Lower Spring Seat Lower Spring Seat Upper

(17" wheels)

Vehicle: R17 (800) (WENV deck) UBJ LBJ Wheel Centre Stub Shaft Upper Arm Ft Upper Arm Rr

Lower Arm Ft Lower Arm Rr OBJ IBJ CVJ UJ (LHS)

Strut Lower Spring Seat Lower Spring Seat Upper UJ (RHS)

(17" wheels)

3

Vehicle: R50 (New Mini) UBJ LBJ Wheel Centre

Lower Arm Ft Lower Arm Rr OBJ IBJ CVJ UJ

Strut Lower

Vehicle: L20 (Freelander) UBJ LBJ Wheel Centre Stub Shaft

Lower Arm Ft Lower Arm Rr OBJ IBJ CVJ UJ

Strut Lower Spring Seat Lower Gear Box Shaft

1

IV Mass Measuring Procedure

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V Tyre Centre of Pressure Measurement Procedure

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VI Hub Level Offset Measurement Procedure

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VII Hub Level Trail Measurement Procedure

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Index

Ackermann, v, 45, 80, 91, 92, 93, 98, 107

Bibliography, iii, vi, 122

Bush Rate Analysis, v, 86

Camber Steer, iv, 16, 25, 29, 98, 100, 103, 105,

117

Case Studies, vi, 99

Centre of Pressure, vii, ix, 25, 26, 28, 29, 30, 76,

77, 100, 101, 107, 141

Corruption, 1, vi, xii, 1, 2, 5, 8, 10, 11, 25, 29, 30,

47, 63, 65, 79, 80, 97, 98, 100, 101, 129, 130

Data Analysis, iv, 16

Dry Park Torque, iv, xii, 36, 37, 43, 84, 100, 105,

118

Feedback, iv, ix, xii, 2, 44, 47, 100, 103

Feel, 2, 14, 47, 50, 60, 63, 64, 90, 105, 114, 121

Fight, iv, xii, 50, 80, 100

Geometry, v, vii, viii, 5, 6, 36, 45, 79, 80, 91, 98,

107, 121, 131, 132, 133

Gyroscopic Steer, v, 90

Half Track Change, 19

Hub Level Offset, vii, xii, 7, 21, 39, 44, 56, 59, 60,

78, 97, 100, 101, 107, 145

Hub Level Trail, vii, xii, 6, 97, 101, 149

Indicator Self Cancelling Torque, 96

Kerb Jacking, v, 84

Kickback, iv, viii, xii, 19, 56, 59, 60, 62, 63, 100,

103, 105, 118

Mass, vi, vii, 5, 19, 29, 30, 53, 57, 58, 64, 96, 99,

107, 109, 134

Measurement Procedure, vi, vii, xii, 96, 97, 99,

141, 145, 149

Objectives, iii, 1

On Centre Feel, v, 63, 103, 106, 118

Papers, vi, 65, 105, 110, 113

Procedures, vi, vii, 1, 15, 29, 49, 96, 97, 98, 99,

108, 109, 110, 115, 116, 134

Puddle Steer, v, 63, 65, 100, 103, 106, 118

Pull, v, 8, 16, 25, 30, 35, 45, 64, 65, 66, 77, 100,

103, 106, 117, 119

QFD, vi, viii, 1, 3, 8, 10, 11, 12, 13, 14, 98, 99,

100, 101, 103, 105, 111, 112, 115, 122, 129,

130

Scope, 10, 11, 14, 58, 60, 63, 76

Side Slope Steer, v, viii, ix, xii, 10, 66, 98, 100,

106, 119

Side Wind Steer, v, 76, 103, 104, 106, 120

Single Wheel Spin, iv, 50, 55

Split Mu, 77, 103

Split Mu Steer, v, 77

Standards, vi, 96, 105, 106, 107, 108, 109, 123

Symbols, iv, 14, 16

Torque Steer, iv, v, 18, 21, 78, 80, 100, 101, 106,

120

Turning Circle, v, 80, 98, 107

Universal Joint Phasing, vi, 94