tyre friction potential estimation by aligning torque …atuonone/files/tyre friction...

AALTO UNIVERSITY SCHOOL OF SCIENCE AND TECHNOLOGY Faculty of Engineering and Architecture Department of Engineering Design and Production

Mika Matilainen

Tyre Friction Potential Estimation by

Aligning Torque and Lateral Force Information

Thesis submitted in partial fulfilment of the requirements for the degree of

Master of Science in Technology.

Espoo, November 24, 2010

Supervisor Professor Matti Juhala Thesis Instructor Ari Tuononen Doctor of Science (Tech.)

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AALTO UNIVERSITY SCHOOL OF SCIENCE AND TECHNOLOGY PO Box 11000, FI-00076 AALTO http://www.aalto.fi

ABSTRACT OF THE MASTER’S THESIS

Author: Mika Matilainen

Title: Tyre Friction Potential Estimation by Aligning Torque and Lateral Force Information

Faculty: Faculty of Engineering and Architecture

Department: Department of Engineering Design and Production

Professorship: Vehicle Engineering Code: Kon-16

Supervisor: Professor Matti Juhala

Instructor(s): Ari Tuononen Doctor of Science (Tech.)

Abstract:

The modern active systems and the advanced driver assistance systems have certainly re-duced the amount of accidents. However these systems are still lacking one major informa-tion, which is the friction between the tyre-road interface. The performance of these systems could be enhanced substantially if this information was known. Rather simple methods can be used to determine the friction coefficient at the current operating point of the tyre. The challenge arises from the friction potential, which is the maximum friction coefficient that the tyre-road interface can produce. The objective of this master's thesis is to study the feasibility of estimating the friction potential by using the information of lateral force and the self align-ing torque of the tyre. The well-known bicycle model of the vehicle is used to determine the lateral force of the front axle, which is divided to left - and right side in accordance with the normal load distribution of the wheels. The normal loads of the wheels are calculated from the angle sensors, which are assembled in the transverse control arms of the vehicle. The same sensors are also ex-ploited to determine the inclination angles of the steering axes. The heart of the estimation method is the brush tyre model. It receives the self aligning torque, lateral - and normal force of the tyre as inputs and outputs the friction potential. The proving ground tests are done with a typical small family estate car (VW Golf Variant Mk5). Two distinguishing proving grounds are chosen for illustrating the operation of the

estimation method on high - and low friction level surfaces. Tests also in μ-split conditions and in situation where the vehicle is travelling from high friction level surface to low friction level surface are implemented. Results from both the high - and low friction level surface illustrate that the estimation method is able to detect the friction states of the front tyres in steady state cornering ma-

noeuvres. Remarkable and interesting results are found from the μ-split and surface transi-tion tests were the estimation method distinguishes the difference between the high- and low friction level surfaces. The presented friction estimation method has potential. However lots of work and further studies have to be conducted before this method can assist the modern active safety systems and the upcoming ADAS systems.

Date: 24.11.2010 Language: English Number of pages: 137

Keywords: Friction estimation, self aligning torque, brush tyre model, bicycle model

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AALTO-YLIOPISTO TEKNILLINEN KORKEAKOULU PL 11000, 00076 Aalto http://www.aalto.fi

DIPLOMITYÖN TIIVISTELMÄ

Tekijä: Mika Matilainen

Työn nimi: Renkaan kitkapotentiaalin arvioiminen palauttavan momentin ja sivuttaisvoiman avulla

Tiedekunta Insinööritieteiden ja arkkitehtuurin tiedekunta

Laitos: Koneenrakennustekniikan laitos

Professuuri: Auto- ja työkonetekniikka Koodi: Kon-16

Työn valvoja: Professori Matti Juhala

Työn ohjaaja(t): Tekniikan tohtori Ari Tuononen

Tiivistelmä:

Nykyaikaiset aktiiviset turvajärjestelmät ovat vähentäneet liikenneonnettomuuksien määrää

merkittävästi. Näiltä järjestelmiltä puuttuu kuitenkin tieto rengas–tie-rajapinnan kitkapotenti-aalista. Tämän tiedon avulla kyseisten järjestelmien suorituskykyä pystyttäisiin parantamaan huomattavasti. Renkaan hetkellisen toimintapisteen kitkakerroin voidaan määrittää suhteelli-

sen yksinkertaisilla menetelmillä. Kitkapotentiaalin eli rengas–tie-rajapinnan maksimikitka-kertoimen määrittäminen on huomattavasti haasteellisempaa. Tämän diplomityön tavoite on tutkia renkaan sivuttaisvoiman ja palauttavan momentin käyttökelpoisuutta kitkapotentiaalin arvioimiseen.

Etuakselin sivuttaisvoima määritetään yleisesti käytetystä kaksipyörämallista. Tämä sivut-taisvoima jaetaan vasemmalle ja oikealle renkaalle pyöränkuormien suhteessa. Pyörän-kuormat lasketaan alatukivarsiin asennettujen kulma-anturien tietojen perusteella. Samoja antureita käytetään myös kääntöakselin pitkittäis- ja poikittaiskulmien määrittämiseen. Kitka-potentiaalin arvioimismenetelmä hyödyntää renkaan harjamallia. Se ottaa syötteenä renkaan palauttavan momentin, sivuttaisvoiman sekä pystykuorman ja antaa ulostulona arvion kitka-potentiaalista.

Käytännön testit suoritettiin pienellä farmariautolla (VW Golf Variant Mk5). Kaksi erilaista ajorataa valittiin käytännön testejä varten, jotta kyseisen menetelmän toimintaa voitiin tutkia sekä korkea - että matala kitkaisella tienpinnalla. Testejä suoritettiin myös kitkajakautuneella tienpinnalla, jossa ulkokaarteen renkaat olivat liukkaalla päällysteellä ja sisäkaarteen renkaat pitävällä päällysteellä. Tämän lisäksi tehtiin testejä, jossa ajoneuvolla ajettiin pitävämmältä päällysteeltä liukkaalle päällysteelle.

Tulokset vakiotilan kaartotesteistä osoittavat, että menetelmä pystyy arvioimaan renkaiden kitka-arvot sekä korkea - että matala kitkaisilla tienpinnoilla. Mielenkiintoisia tuloksia saatiin myös kitkajakautuneen tienpinnan - ja päällysteeltä toiselle ajetuista testeistä. Näistä tulok-sista nähtiin selkeästi, että menetelmä kykenee erottelemaan korkean kitkan omaavan tien-pinnan matalammasta sekä antamaan uskottavia arvoja kitkapotentiaaleille. Tässä työssä esitellyllä kitkapotentiaalin arviointimenetelmällä on ehdottomasti mahdollisuuksia auttaa aktiivisia turvajärjestelmiä toimimaan vieläkin tehokkaammin tulevaisuudessa. Paljon työtä ja monia lisätutkimuksia on kuitenkin vielä tehtävä ennen kuin tähän tavoitteeseen päästään.

Päivämäärä: 24.11.2010 Kieli: Englanti Sivumäärä: 137

Avainsanat: Kitkan arvioiminen, renkaan palauttava momentti, renkaan harjamalli, ajoneu-von kaksipyörämalli

Acknowledgements

4

Acknowledgements

This master’s thesis was done in Aalto University School of Science and Tech-

nology. First of all I want to give my appreciations to Henry Ford Foundation for

providing me a scholarship to carry out this interesting study.

Special thanks are reserved for Professor Matti Juhala, researcher Ari Tuononen

and senior laboratory manager Panu Sainio. These appreciations aren’t only for

encouraging and supporting me throughout my master’s thesis, but also for giv-

ing me interesting working possibilities at the Laboratory of Automotive Engineer-

ing. My compliments go also to senior laboratory technicians Pekka Martelius

and Keijo Kallio, who helped me with the sensor calibrations and mounting of the

sensor equipment to the research vehicle. Thanks also to Professor Petri Kuos-

manen for reading my almost finished master’s thesis with a short notice and

giving valuable comments about it.

Thanks to all fellow master’s thesis workers at the open-plan office for keeping

the atmosphere relaxed and pleasant.

Finally but certainly not for least I want to thank my parents, who have been sup-

porting me throughout my studies.

Espoo November 24, 2010

Mika Matilainen

Table of Contents

5

Table of Contents

ABSTRACT OF THE MASTER’S THESIS .......................................................... 2

DIPLOMITYÖN TIIVISTELMÄ ............................................................................. 3

Acknowledgements ............................................................................................. 4

Table of Contents ................................................................................................ 5

Symbols and Definitions ...................................................................................... 9

Abbreviations .....................................................................................................12

1 Introduction .................................................................................................13

1.1 Motivation and Background ..................................................................13

1.2 Problem Statement ..............................................................................17

1.3 Outline .................................................................................................19

1.4 Main Results ........................................................................................20

2 The Rubber-Road Interface: Phenomena Involved in Friction .....................21

2.1 Introduction ..........................................................................................21

2.2 Characteristics of Rubber .....................................................................21

2.2.1 Visco-elastic Behaviour .................................................................21

2.2.2 Influence of Stress Frequency .......................................................24

2.2.3 Influence of Temperature ..............................................................25

2.3 Characteristics of Road Surfaces .........................................................26

2.3.1 Texture..........................................................................................26

2.3.2 Influence of Surface Conditions ....................................................29

2.4 Friction Mechanisms ............................................................................31

2.4.1 Adhesion .......................................................................................31

2.4.2 Hysteresis .....................................................................................32

2.5 Conclusions of this Chapter .................................................................33

Table of Contents

6

3 Background and Theory of Friction Estimation ............................................34

3.1 Introduction ..........................................................................................34

3.2 Friction Coefficient ...............................................................................34

3.2.1 Definition .......................................................................................34

3.2.2 Terminology ..................................................................................37

3.3 Classification of Friction Estimation Methods .......................................39

3.3.1 Direct Methods ..............................................................................39

3.3.2 Indirect Methods ...........................................................................40

3.4 Previous Studies ..................................................................................41


4 Research Vehicle and Sensor Equipment ...................................................44

4.1 Introduction ..........................................................................................44

4.2 Front Suspension Geometry ................................................................45

4.2.1 Overview .......................................................................................45

4.2.2 Steering Axis .................................................................................47

4.2.3 Caster Angle .................................................................................47

4.2.4 Kingpin Inclination Angle ...............................................................51

4.2.5 Camber Angle ...............................................................................52

4.3 Steering System ...................................................................................54

4.3.1 Overview .......................................................................................54

4.3.2 Forces and Torques ......................................................................55

4.3.3 Evaluation of the Force Lever Arm ................................................57

4.4 Sensor Equipment................................................................................59

4.4.1 Overview .......................................................................................59

4.4.2 Piezoelectric Force Sensor ...........................................................60

4.4.3 Hall Effect Angle Sensor ...............................................................67

4.4.4 Two-Axis Optical Velocity and Slip Angle Sensor ..........................71


Table of Contents

7

5 Proving Grounds and Experimental Tests ...................................................74

5.1 Introduction ..........................................................................................74

5.2 Proving Ground of Nokian Tyres ..........................................................74

5.2.1 Overview .......................................................................................74

5.2.2 Experimental Tests .......................................................................75

5.3 Test Driving Track of Uudenmaan Ajoharjoitteluradat ..........................77

5.3.1 Overview .......................................................................................77

5.3.2 Experimental Tests .......................................................................78


6 Friction Estimation Method ..........................................................................81

6.1 Introduction ..........................................................................................81

6.2 The Bicycle Model ................................................................................81

6.2.1 Definition and Assumptions ...........................................................81

6.2.2 Equations of Motion ......................................................................82

6.2.3 Lateral Tyre Forces and Slip Angles .............................................83

6.3 The Brush Tyre Model ..........................................................................86

6.3.1 Definition and Assumptions ...........................................................86

6.3.2 Determination of Normal Load Distribution and Contact Length ....88

6.3.3 Complete Adhesion .......................................................................90

6.3.4 Adhesion and Sliding ....................................................................91

6.3.5 Complete sliding ...........................................................................93

6.4 Friction Estimation in Pure Lateral Slip Situation ..................................94

6.4.1 Principle ........................................................................................94

6.4.2 Requirements and Limitations .......................................................97

6.4.3 Proof of Concept ......................................................................... 101

6.4.4 Implementation ........................................................................... 102

6.5 Conclusions of this Chapter ............................................................... 103

Table of Contents

8

7 Proving Ground Results and Discussion ................................................... 105

7.1 Introduction ........................................................................................ 105

7.2 Steady-State Cornering ...................................................................... 105

7.2.1 High Friction Level Road Surface ................................................ 105

7.2.2 Low Friction Level Road Surface................................................. 109

7.2.3 -split Road Surface ................................................................... 113

7.3 Ramp Steer from High - to Low Friction Level Road Surface ............. 117

7.4 Conclusion of this Chapter ................................................................. 121

8 Conclusions and Recommendations ......................................................... 123

Bibliography ..................................................................................................... 126

Appendix A1: Vehicle and tyre parameters ....................................................... 130

Appendix A2: Contact pressure distribution and contact patch length .............. 131

Symbols and Definitions

9


ANGLES MEANING

Slip angle of the front or the rear tyre

Slip angle of the vehicle centre of gravity

Caster angle

Kingpin inclination angle

Camber angle

Angle of the transverse control arm

Steering angle

DIMENSIONS MEANING

Length of the transverse control arm

Wheel base

Distance of the centre of gravity from the front axle

Distance of the centre of gravity from the rear axle

Height of centre of gravity above the ground

Track width (or time)

Dynamic rolling radius

Caster offset

Kinematic caster trail (the distance on the ground between the centre point of the contact patch and the steering axis)

Kinematic pneumatic trail (pneumatic trail on the ground)

Caster trail

Pneumatic trail

Total trail

Longitudinal force lever arm in braking situation

Longitudinal force lever arm in tractive - or rolling resistance situations

Scrub radius

Half of the tyre’s contact length

Diameter


10

VELOCITIES AND

ACCELERATIONS MEANING

Velocity of the centre of gravity

Lateral velocity of the centre of gravity

Longitudinal velocity of the centre of gravity

Velocity of the front or the rear tyre

Angular velocity around the -axis (Yaw rate)

Angular acceleration around the -axis

Angular velocity of the wheel

Longitudinal acceleration

Lateral acceleration

acceleration due to gravity

FORCES AND

TORQUES MEANING

Total aligning torque around the steering axis

Torque arising from the caster angle

Torque arising from the pneumatic trail

Torque arising from the kingpin inclination angle

Longitudinal force

Lateral force

Vertical force

Tractive friction force between the tyre and the road surface

Braking friction force between the tyre and the road surface

Rolling resistance force

Force of the left or the right hand side tie rod

Normal load distribution of the tyre

Lateral force distribution of the tyre


11

DIMENSIONLESS FACTORS

MEANING

Slippage rate

The length of the adhesion region in percentage

The friction coefficient at the current operating point of the tyre

The maximum achievable friction coefficient

The friction coefficient amount that the used friction coeffi-cient can still increase before saturation

Steering ratio

OTHERS MEANING

Curb weight of the vehicle

Total -moment of inertia

Rubber brush element stiffness per unit area

Stiffness coefficient of a spring

Viscosity constant of the fluid

Composite tyre model parameter

SUFFIXES MEANING

Front

Rear

Left

Right

Tie rod left

Tie rod right

Inside

Outside

Adhesive

Sliding

Abbreviations

12

Abbreviations

ABBREVIATION MEANING

ESC Electronic Stability Control

ABS Anti-lock Braking System

TCS Traction Control System

ACC Adaptive Cruise Control

ADAS Advanced Driver Assistance Systems

SAT Self Aligning Torque

IVSS Intelligent Vehicle Safety Systems

FFT Fast Fourier Transform

CAN Controller-Area Network

GPS Global Positioning System

INS Inertial Navigation System

CG Centre of Gravity

PIARC Permanent International Association of Road Congresses

VW Volkswagen

SWA Steering Wheel Angle

Introduction

13

1 Introduction

1.1 Motivation and Background

The basic relationship between the driver and the vehicle has remained the same

from the early stages of automotive history. Still today the driver sits in the vehicle

and gives his/her desires to vehicle’s systems such as power transmission and

steering. Figure 1 represents a generalized block diagram of the driver-vehicle

relationship, where all the other systems have been omited except the steering.

The other systems aren’t greatly involved in this work and can therefore be

omited.

Figure 1 Block diagram of driver-vehicle relationship (figure is based on [1])

In a driving situation the driver gives an input to the steering system by rotating

the steering wheel into a particular angle with a certain amount of angular speed

and acceleration. The steering system then changes the steering angle of the

front wheels, which generates lateral slip to all four tyres. The lateral slip of the

tyres induces lateral forces, which on the other hand gives lateral acceleration to

the vehicle’s center of gravity ( ). Angular velocity around the vertical axis of the

vehicle is also generated. The driver senses these two factors with his/her sense

of balance and makes his/her own judgements about the state of the vehicle. In

other words, is the vehicle going the desired path and is the vehicle still under

driver’s control. From this feedback the driver can make some adjustements to

the steering wheel position if he/she consideres it neccesary. The driver receives

Introduction

14

another feedback from the steering system. The induced lateral forces at the

tyres don’t act at the steering axis, but a distance from it, which generates a

torque on both front tyres that attempts to return the wheels back in straight

ahead driving position. This torque is transmitted to the steering wheel via the

steering system and thus to the sense of feeling of the driver’s hands. Againg the

driver makes his/her own judgements about whether adjustments are required or

not. The driver gains also a lot of feedback via his/her sense of sight and hearing.

For example judgements of the road surface and its environmental conditions are

made by vision. Hearing on the other hand can be exploited for listening tyre

noises.

The only instruments that the driver has for evaluating the current state of the

vehicle are his/her own senses. Obviously the driver is placed under a challeging

task, since there comes a surge of information, which has to be evaluated imme-

diately. Fortunately modern vehicles are equipped with such active safety

systems as ESC, TCS, ABS and ACC. These systems utilize mostly the same

principles as the senses of the driver for gathering information about the state of

the vehicle. The difference is that these embedded system are more accurate

and consistent of making decisions than the driver. The senses and decisions

that the driver makes are always subjective and depend of many things such as

state of alertness and mental motivation. With the aid of these systems the

workload of the driver is relified and some of the mistakes that the driver makes

can be corrected. Altough the modern active safety systems work rather well,

they are lacking one major information, which is the knowledge of the tyre-road

friction potential. The maximum force that the tyre can generate is affected by the

friction potential of the specific tyre-road interface. Therefore the full performance

of the active safety systems and the upcoming advanced driver assistance

systems (ADAS) can be achieved only with the knowledge of friction potential.

The driver of course makes his/her own conclusions of the friction conditions

(Figure 2). Studies have nevertheless proved the drivers’ friction estimation ca-

pabilities being rather poor [2]. In addition the drivers’ conclusions can’t be

exploited to active safety systems. Therefore several different approaches for

estimating friction potential have been studied in research projects. These

different approaches are briefly discussed in Chapter 3.

Introduction

15

Figure 2 Driver's friction estimation methods

There obviously exists a clear relation between the tyre-road interface friction

potential and traffic accident risk. Several studies have concluded that the

accident risk increases substantially after the friction potential value has dropped

under a certain threshold (Figure 3). It’s evident that under slippery conditions the

vehicle is more difficult to handle, but it doesn’t explain the reason why the

accident risk increases substantially. The main reason for the increase in

accident risk at low friction surfaces is the drivers ability to adapt friction

variations. Studies on the same highway, where the speed limit is 90 km/h, have

shown that drivers decrease their driving speed only about 6…10 km/h as the

friction potential has dropped from 0.9 to 0.25 [2]. The stopping distance is

almost doupled with the impaired friction surface, since the drivers don’t

decrease their driving speed sufficiently. Therefore it’s self-evident that accident

risk increases dramatically with low friction surfaces. The task of friction

estimation is unfeasible for the driver, since the friction potential may vary to a

great extent with different periods of the year and also with different places on the

road. Thus there is a need for a technology that could reliably estimate the

friction potential of the tyres.

Introduction

16

Figure 3 Relation between road friction and accident risk [2]

Figure 4 represents a bar graph of fatalities in Finnish traffic arranged by the type

of the accident. The blue bars illustrate the situation of year 2010 until august and

the dark green bars illustrate the statistics of the whole year 2009. The light

green bars depict the average of fatalities between years 2006-2008. As it can be

seen, swerving of the road is one of the most fatal type of accidents in Finnish

traffic. The cause of swerving of the road is mostly too high driving speed for that

specific manouvre and road conditions. The driver assumes that the friction

potential (limit of tyre forces) is much higher that it actually is and therefore the

vehicle might not handle as the driver would expect.

Figure 4 Fatalities in Finnish traffic arranged by the type of the accident [3]

Introduction

17

1.2 Problem Statement

All the forces that enable the vehicle to negotiate a bend or brake/accelerate are

generated in the tyre-road interface. Obviously the magnitude of the forces that

the tyre-road interface can produce has a limit. Beyond this limit, the whole con-

tact area of the tyre is sliding and therefore full control over the vehicle might be

lost. The maximum forces that the tyre-road interface can produce depends

mainly of the tyre - and road surface properties. The load - and the orientation of

the tyre relative to road surface have also a significant influence to the force limit.

The last two factors can be determined rather easily, but the detection of tyre-

road interface properties and conditions is much more challenging. In addition the

properties and conditions of the tyre-road interface may vary a lot in short term.

In order to get the full performance out of the active safety systems and ad-

vanced driver assistance systems, the maximum achievable forces of each tyre

should be known. For attaining this ambitious goal, the friction potential of each

tyre has to be evaluated in real-time. Several different approaches have been

studied over the years, which can be categorized into direct - and indirect meth-

ods. The categorization of estimation methods is discussed more detailed in

Chapter 3, but briefly, the direct methods are directly involved with the friction

process by measuring e.g. forces and accelerations of the vehicle or the tyre.

The indirect methods on the other hand are just related to the friction process in

some way. Figure 5 illustrates the methods that have been implemented for

sensing the friction potential. The tyre - and vehicle sensors belong to the direct

methods, where physical quantities such as forces, accelerations and deforma-

tions have been used for the estimation. The indirect methods of friction estima-

tion are illustrated in the horizontal ellipses of Figure 5. The basic principle of

indirect methods is that they monitor some parameters that are related to the

friction process such as temperature of the road. The monitoring of these pa-

rameters can be done either on-board of the vehicle or at the road side. The con-

tribution of this master’s thesis is put to direct estimation methods, since they are

directly involved with the friction process. Although it must be mentioned that the

direct - and indirect methods of friction estimation should not be thought as rivals,

but as instruments of completing each other.

Introduction

18

Figure 5 Methods of sensing friction potential

The objective of this master’s thesis is to study the feasibility of estimating friction

potential by using the information of forces and torques that are generated in the

tyre-road interface. The Self Aligning Torque (SAT) that develops around the

wheel’s steering axis in a cornering manoeuvre is evaluated by measuring the

force of the tie rod. This torque is obviously induced by the lateral force, which

doesn’t act at the steering axis but at a distance from it. The planar motion of the

vehicle and thus the lateral forces of the front tyres are determined by exploiting

the famous bicycle model. Both the self aligning torque and the lateral force of

the tyre are given as inputs for the well-known brush tyre model, which ultimately

is used for the estimation of friction potential. The self aligning torque that is

evaluated from the tie rod force measurement can’t be given directly to the brush

tyre model, because it contains an additional torque, which arises from the

alignment of the steering axis. In order to subtract this additional torque from the

total self aligning torque, the lateral - and longitudinal inclination angles of the

steering axis have to be determined. The basic principle of the brush tyre model

is illustrated on the left hand side picture of Figure 6. A more detailed description

of the brush tyre model is represented in Chapter 6. The graph on the right-hand

side represents the behaviour of the lateral force and the self aligning torque as a

function of the slip angle. Both the lateral force and the self aligning torque are

normalised for the vertical load of the tyre. The objective of this master’s thesis is

Introduction

19

also clarified with the terminology of friction coefficients in Figure 6. The currently

used friction can be determined rather easily if the lateral force and the vertical

load of the tyre are known. The problem arises from the friction potential, which

would have to be evaluated without requiring the tyre to reach its limits.

a

yF

a txpx

0

Fv

x

)(xqz

)(xq y

y

Figure 6 Brush tyre model and terminology of friction coefficients

1.3 Outline

Since the friction is mainly affected by the characteristics of the tyre and road

surface, an in-depth examination of both is represented in Chapter 2. Also a brief

introduction to the friction mechanisms involved in tyre-road interface is given in

the same chapter. A more precise definition of the terminology concerned with

friction coefficients is introduced in Chapter 3. The same chapter depicts also the

classification of the friction estimation methods and gives a brief review of the

methods used in the previous studies. Chapter 4 is devoted for presenting the

research vehicle and sensor equipments used in this master’s thesis. The pres-

entation of the research vehicle is focused on the front suspension and the steer-

ing system, since they are greatly involved in this master’s thesis. The proving

grounds used to perform experimental tests are represented in Chapter 5. The

methods concerned in the friction estimation are introduced in Chapter 6, which

includes the bicycle model of the vehicle and the brush tyre model. Chapter 7

presents the results of experimental tests at the proving grounds. Conclusions

and suggestions for improvements are given in Chapter 8.

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Introduction

20

1.4 Main Results

In this master’s thesis a typical small family estate car is used for proving ground

tests, where the feasibility of the estimation method is studied. Two distinguishing

proving grounds are chosen for illustrating the operation of the estimation method

on high - and low friction level surfaces. Tests also in -split conditions and in

situation where the vehicle is travelling from high friction level surface to low fric-

tion level surface are implemented. The friction estimation method considers only

a pure lateral slip situation and therefore all the test were performed with clutch

disengaged.

Results from the high friction level surface illustrate that the estimation method is

able to detect the friction states of the front tyres in steady state cornering ma-

noeuvres. The same tests at the low friction level surface provide also plausible

values of the front tyres friction state. Remarkable and interesting results are

found from the -split and surface transition tests were the estimation method is

able to distinguish the difference between the high- and low friction level sur-

faces.

The Rubber-Road Interface: Phenomena Involved in Friction

21

2 The Rubber-Road Interface: Phenomena Involved

in Friction

2.1 Introduction

Besides gravity and aerodynamic forces, the rubber-road interface is the place

where all the significant forces that act on a vehicle are generated. The area of

contact between these components is around the size of an average mans palm.

An in-depth examination of the interface components (rubber and road) and the

friction mechanisms involved in the contact are essential for understanding how

the vehicle is able to manoeuvre relying only to these relatively small contact

patches.

2.2 Characteristics of Rubber

2.2.1 Visco-elastic Behaviour

Many different materials are used for making tyres, but the main construction

materials are the natural and synthetic rubbers (Figure 7). They are elastomeric

materials constituting from many elastic polymers, which have a specific property

called viscoelasticity. [4]

Figure 7 Natural and synthetic elastomeric materials [4]

The nomination viscoelasticity yields that the behaviour of rubber lies between

that of viscous liquid and elastic solid. For understanding the behaviour of rubber

more thoroughly, the examination can be divided to these specific cases. Con-

sidering first the rubber only as an elastic solid, it can be represented as a spring

with a stiffness coefficient (Figure 8). The initial position of the spring in Figure

8 is at . The same situation is also illustrated in the right-hand side graph

with an orange circle. At this position no forces are applied to the spring. Thus

the displacement and the force in the graph are both zero. In the next phase, a


22

compressive type force is applied to the spring, which causes the beginning of

the spring to move from the initial position by amount of . The green circle in

Figure 8 represents this situation. It’s noticed that the displacement of the spring

is directly proportional to the applied force. Hence the well-known equation of the

spring force can be written as:

(2.1)

In the third phase, denoted with a purple circle in Figure 8, the applied force has

diminished back to zero and the displacement is also back in its initial

tion . Since the spring returned to its initial position, the supplied energy is

restored.

F

0x

Figure 8 Elastic behaviour of rubber (figure is based on [4])

The examination of rubber as an elastic solid is now familiar. Next the rubber is

considered purely as a viscous liquid and as the Figure 9 illustrates, the viscous

behaviour can be modelled with a damper. A similar excitation force is applied to

the damper as it was the case with the spring. However, now the displacement of

the damper doesn’t follow the curve of the applied force. The movement of the

piston of the damper seems to lag behind the force. The maximum of the applied

force is achieved when the displacement is at its minimum and vice-versa. There-

fore the phase lag between the displacement and the applied force is 90 . The

phase lag is also known as the hysteresis of the rubber, which is one of the key

factors of producing friction.

The applied force is proportional to the excitation velocity of the piston and to

the viscosity constant of the fluid inside the damper.

0 50 100 150 200 250 300 350

Force Displacement


23

(2.2)

The orange circle in the Figure 9 represents the initial situation where the applied

force is at its maximum. Therefore the velocity of the piston is also at its maxi-

mum. However, at this position the piston of the damper has hardly moved. The

resistance arises from the viscosity of the fluid inside the damper. The faster the

piston is forced to move, the larger the friction between the constituent molecules

of the fluid becomes. At moderate excitation velocity of the piston, the friction

between the constituent molecules is lower and the piston experiences little resis-

tance to movement (green circle in Figure 9). If the applied force is removed, the

piston doesn’t return to its initial position as it was the case with a spring. The

input energy has dissipated to the friction between the constituent molecules of

the fluid. In other words the energy has dissipated in the form of heat.

0x

1F

2F

3F

Figure 9 Viscous behaviour of rubber (figure is based on [4])

As mentioned above, the behaviour of rubber lies between that of viscous liquid

and elastic solid. The previous examination of these components separately has

to be combined as a whole to derive the real behaviour of rubber. The combining

of these components is done by connecting them in parallel (Figure 10). As it can

be seen from the right-hand side graph of Figure 10, there still exists phase lag

between the applied force and the displacement, but it’s smaller than in the case

of a damper. The effect of the spring causes the combined assembly to return to

its initial position after the applied force is removed. However the damper resists

the movement and therefore it doesn’t occur instantaneously. The delay that it

takes to revert back to the initial position is directly proportional to the phase an-

gle between the force and displacement. Again some of the energy is dissipated

in the damper to form of heat.

0 50 100 150 200 250 300 350

Force Displacement


24

1F

2F

3F

Figure 10 Visco-elastic behaviour of rubber (figure is based on [4])

The characteristics of the spring and the damper depend of the ingredients used

to the manufacturing process of rubber. Therefore by using different types of

compounds, the energy loss, hysteresis and modulus of the rubber can be modi-

fied. However the behaviour of rubber for a specific compound isn’t static. It

changes according to the excitation frequency and temperature at which it’s ex-

posed to. [4]

2.2.2 Influence of Stress Frequency

Figure 11 illustrates the energy loss and modulus of a specific rubber compound

in respect to the stress frequency, which it’s exposed to. Since the purpose of the

graphs is to illustrate the frequency behaviour of a rubber compound, the tem-

perature is considered to be constant. The stress frequency behaviour of rubber

divides to three zones: rubbery, viscoelastic and glassy. The most desirable zone

for good friction is the viscoelastic zone, because there the hysteresis of rubber is

at its maximum.

Considering the spring and damper assembly, the curves in Figure 11 are easy

to understand. At low stress frequencies, the damper gives almost no resistance

at all to the movement and the spring is the dominant part. Therefore both the

energy loss and the modulus of rubber are low. By raising the stress frequency to

moderate level, the effect of damper increases. The behaviour of rubber is

brought to the viscoelastic zone, where the energy loss is at the maximum range

and the modulus at the moderate range. At high frequencies the effect of damper

increases even more. As explained previously, the resistance force of the

damper depends of the excitation velocity. Therefore at high frequencies, the

0 50 100 150 200 250 300 350

Force Displacement


25

damper resists the movement exceedingly. The rubber appears to be rigid, with

glass-like mechanical properties. In other words hard and brittle.

2.2.3 Influence of Temperature

The increase in temperature has the opposite effect to the behaviour of rubber

than the increase in stress frequency. In Figure 12, the same energy loss and

modulus graphs are illustrated as above, but now in respect to temperature.

Again the graphs are for a specific rubber compound and now the frequency is

constant.

In low temperatures, rubber has the same properties as with high frequencies.

The modulus is at the maximum level and the energy loss at the minimum level.

Therefore the behaviour of rubber lies in the glassy zone, where it appears to be

hard and brittle. As the temperature rises to moderate level, the behaviour of

rubber changes to the desirable viscoelastic zone. The temperature, at which the

energy loss attains the highest value and the modulus is around the moderate

level, is called the glass transition temperature. Below this temperature, the be-

haviour of rubber tends toward the glassy zone and over it towards the rubbery

zone. In high temperatures, the behaviour of rubber changes to the rubbery

zone, where both the modulus and the energy loss are in the minimum level.

Frequency

RU

BB

ER

Y

GLA

SS

Y M

od

ulu

s

VIS

CO

EL

AS

TIC

Frequency

VIS

CO

EL

AS

TIC

RU

BB

ER

Y

GLA

SS

Y

En

erg

y lo

ss

Figure 11 Influence of stress frequency to the behaviour of rubber (figure is based on [4])


26

2.3 Characteristics of Road Surfaces

2.3.1 Texture

The other component of the contact is obviously the road surface, which texture

is one of the key factors in friction generation. The Permanent International As-

sociation of Road Congresses (PIARC) has classified the road surface textures

into three major categories: micro-, macro- and mega-texture (Figure 13).

Figure 13 Classification of road surface textures [5]

The definition of road surface texture is done by evaluating the deviation of the

road surface from a true planar surface. The three major road surface texture

categories are determined by the wavelength and the peak-to-peak (pp) values of

the deviation, which are represented in Table 1.

Temperature

RU

BB

ER

Y

GLA

SS

Y M

od

ulu

s

VIS

CO

EL

AS

TIC

Temperature

VIS

CO

EL

AS

TIC

RU

BB

ER

Y

GLA

SS

Y

En

erg

y lo

ss

Figure 12 Influence of temperature to the behaviour of rubber (figure is based on [4])


27

Table 1 Determination of road surface textures

Micro-texture Macro-texture Mega-texture

Wavelength 0,5 mm 0,5 50 mm 50 500 mm

Amplitude (p-p) 0,001 0,5 mm 0,1 20 mm 0,1 50 mm

One of the main construction components of road surfaces are mineral aggregate

particles, which are manufactured by crushing hard rocks. The macro-texture

quality of road surfaces is affected by the size, shape and gradation of these ag-

gregate particles. [4] The roughness of the individual aggregate particles can be

considered as the micro-texture quality of road surfaces. The third road surface

quality is the mega-texture, which is considered as the waviness of the surface in

the scale of contact patch. [5]

As Figure 14 illustrates, the micro- and macro-texture quality of road surfaces are

the main components involved in friction generation. Micro-texture provides the

circumstances for adhesion friction mechanism and macro-texture for hysteresis

friction mechanism. The friction mechanisms are discussed more thoroughly later

on in this chapter.

Figure 14 The influence of road surface texture to interactions between the tyre and road surface [5]

Since only the micro- and macro-texture quality of road surfaces are concerned

in friction generation, the presence of them can be divided to four categories,

which are illustrated in Figure 15. Obviously, in reality road surfaces don’t strictly


28

belong to one specific category. The micro- and macroroughness of an actual

road surface can be at any point in the illustrative graph (Figure 15).

Figure 15 The presence of micro- and macro-texture [4]

A previous study has examined the effects of the four distinguished micro- and

macro-texture road surface qualities to friction. A graph from the previous study

represents the sliding friction coefficient in respect to the sliding speed with the

distinguished road surface qualities of micro- and macro-texture (Figure 16). At

low sliding speeds, high micro-texture quality of the road surface improves the

adhesive friction mechanism. Therefore, the sliding friction coefficient has a lar-

ger value with high micro-texture quality road surfaces at low sliding speeds. With

greater sliding speeds, the lack of macroroughness reduces the value of sliding

friction notably. This is due to the fact that high macro-texture quality of road sur-

face provides the circumstances for hysteresis friction mechanism and at higher

sliding velocities hysteresis is the dominant friction mechanism.


29

Figure 16 Influence of micro- and macroroughness of road surface to the sliding coefficient of friction [5]

2.3.2 Influence of Surface Conditions

Besides the texture of the road surface, another factor influencing friction is the

condition in which it is. The state of repair, water, slush, snow, ice and other con-

taminants on the road surface have a substantial effect to the friction generation.

Water in its all forms (liquid, slush, snow and ice) is one of the most dangerous

substances on road surfaces. E.g. in Finland water can always be present on

road surfaces in some form. Therefore it has to be taken into account when de-

signing and constructing road surfaces.

Figure 17 illustrates the influence of micro- and macro-texture road surface quali-

ties to friction coefficient in wet conditions. The highest friction coefficient is

achieved on micro- and macrorough surfaces. There the macroroughness of the

road surface enables a drainage place for the water. Thus the microroughness of

the road surface is able to penetrate through the water layer and produce friction

forces.


30

Figure 17 Influence of micro- and macro-texture road surface quality to friction coefficient in wet conditions [4]

The water on the road surface can be considered as a lubricant, which signifi-

cantly reduces the friction between the tyre and road surface. The effect of water

to friction is affected by several things, but the most important factors are the

speed of the vehicle, the water layer thickness and the tyre tread depth. With

high driving speeds and substantial water layer thicknesses, there is a significant

risk of aquaplaning. In aquaplaning the tyre isn’t capable of dispersing the water

away from the contact area and thus the water pressure begins to rise in the

leading edge part of the tyre. The whole tyre can lift up on to the water layer, if

the speed of travel is high enough and the water layer thickness is sufficient. In

full aquaplaning situation the friction coefficient is almost zero and therefore the

driver hasn’t got any control over the vehicle. Hence the drainage of the road

surfaces should be designed in such a way that large water layer thicknesses

can’t be generated. [6]

At winter time slush, snow and ice are found on the road surfaces frequently. The

behaviour of slush on the road surface can almost be compared to water. There-

fore its existence on the road surface is really dangerous. Snow on the other


31

hand can mould to the shape of the tread pattern of a tyre, but because of the

low shear strength of snow, it leaves the friction considerably low. [7] Ice at very

low temperatures can be compared to road surfaces with moderate micro-texture

quality. Therefore in these very cold conditions, the microroughness of the ice

can provide sufficient circumstances for traction. However, if the temperature of

ice rises around -5 to 0 C, the microroughness can be covered with water and

thus disable the friction generation. The slipperiness of ice originates from the

water layer, which can be produced mainly with two ways. In Figure 18 the first

two sub pictures from the left explain how the water layer is produced under a

skate. The same principles are however valid for a tyre and gives therefore a

clarified picture to the slipperiness of ice.

Figure 18 Slipperiness of ice [8]

2.4 Friction Mechanisms

2.4.1 Adhesion

Adhesion friction mechanism requires a direct, clean and dry contact to the road

surface. These circumstances are provided by the micro-texture quality of the

road surface. Adhesion friction mechanism arises from the molecular bonding of

the tread rubber and the road surface. The operating principle of the adhesion

friction mechanism is represented in Figure 19. The first molecular bond is gen-

erated at the leading edge of the tread rubber (denoted with number 1 in Figure

19). As the bond is made, the spring-damper assembly begins to stretch and be-

cause of the visco-elastic behaviour, it resists the movement (denoted with num-

ber 2 in Figure 19). Thus a friction force is generated in the opposing direction of

the speed of slippage. The molecular bond can hold only a certain amount of


32

force and then it breaks (denoted with number 3 in Figure 19). After the break-up,

the bond forms again further on. [4] & [5]

Figure 19 Adhesion friction mechanism [4]

2.4.2 Hysteresis

The hysteresis friction mechanism is generated through the stress frequency ex-

citation of the tread rubber, which is provided by the macro-texture quality of the

road surface. The operating principle of the hysteresis friction mechanism is rep-

resented in Figure 20. As the tread rubber slips on the road surface the

macrorough spots penetrate into it and the spring-damper assembly experiences

a compressive-relaxation type stress cycle. The viscous behaviour of the tread

rubber, or in other words the damper part, generates hysteresis and therefore

also an energy loss is introduced at each cycle. The occurrence of hysteresis

causes an asymmetrical deformation of the tread rubber over the rough spot,

which also effects in an asymmetrical force field. Since the force field is signifi-

cantly larger at the compressive side of the rough spot, an opposing friction force

to the speed of slippage is generated (denoted with symbol X and yellow arrow in

Figure 20). [4] & [5]

Figure 20 Hysteresis friction mechanism [4]


33

2.5 Conclusions of this Chapter

The examination of the rubber and road surfaces properties illustrated that both

of them have a significant influence to the friction generation process. Also the

excess medium, such as water, between the tyre and road surface plays a major

role on the attainable friction. Several essential issues have to be taken into ac-

count when designing tread rubbers for tyres and surfaces for roads. These in-

clude such issues as the temperature at which the tread rubber compound is de-

signed to operate (summer - or winter tyre). In the road surface design process

the most important issue is to consider the effect of water. The surface texture

should have high microroughness to ensure traction in wet conditions and the

drainage of water should be designed in a way that no high water layers are gen-

erated.

Background and Theory of Friction Estimation

34

3 Background and Theory of Friction Estimation

3.1 Introduction

The attainable traction between the tyre and the road surface depends always of

the specific rubber-road interface properties and the conditions that they are ex-

posed to. It’s obvious that there are several different types of road surfaces,

which state of repair and surface conditions vary a lot between each other. Each

vehicle on the roads has their own specific set of tyres, which conditions vary

also from vehicle to vehicle. Since the circumstances for traction are so variable,

it would be essential to evaluate the current traction conditions in real-time.

There have been several studies concerning friction estimation of rubber-road

interface with various different methods. The purpose of this chapter is to give an

insight to the theory and methods that has been discovered during these previ-

ous studies.

3.2 Friction Coefficient

3.2.1 Definition

Figure 21 illustrates the basis of the well known Coulomb’s friction model. It con-

sists of two rigid bodies, which in this simple case are the ground and a box. In

the illustration gravitation pulls the box against the ground with a force propor-

tional to the mass of the box . A horizontal force is also applied to the box,

which attempts to move it to the right . However assuming the applied

force increases gradually from zero, the box doesn’t begin to move instantane-

ously. A resistive force is generated in the contact, which is proportional to the

normal force pushing the bodies together. As the applied force increases it over-

takes the static friction force and begins to slide on the ground surface. The resis-

tive force is smaller when the box is actually moving. This is known as the kinetic

friction force. [9]


35

The definition of the friction force is presented in Equation 3.1. As mentioned be-

fore, it’s directly proportional to the normal force pushing the two bodies together.

In the equation there is also a factor called the friction coefficient, which is de-

fined as the ratio of the friction force and the normal force. It expresses the

amount of friction force generated in respect to the normal force. Therefore it

characterises the nature of the contact surfaces and is a good representative of

the traction quality.

(3.1)

Coulomb’s friction model ignores the area of the contact and it’s also largely in-

dependent of the relative velocity of sliding. Despite of these generalizations,

Coulombs’ friction model works relatively well for most engineering models.

Hence it’s commonly accepted and used in engineering. [7]

Considering the vehicle as a rigid body moving on a planar surface, the Cou-

lomb’s friction model can be used to estimate the average friction coefficient of

the whole vehicle. The forces that are generated in the tyre-road interfaces are

summed up, which means that the calculated friction coefficient is an average of

these contact points. Thus the expression average friction coefficient. The friction

estimation is divided to pure lateral and longitudinal acceleration situations of the

vehicle. The left-hand side of Figure 22 illustrates the vehicle in a pure cornering

manoeuvre, where each tyre of the vehicle produces a certain amount of lateral

force. The sum of these lateral friction forces is denoted with a symbol , which

can also be written as the product of the centripetal acceleration and the mass of

the vehicle. The normal force of the vehicle can also be written as the product of

the gravitational acceleration and the mass of the vehicle. Thus the average lat-

eral friction coefficient of the vehicle is reduced to a ratio between the lateral

- and the gravitational acceleration (Equation 3.2).

Figure 21 Coulomb’s friction model

Fapplied

µFz

Fz


36

Figure 22 Evaluating average friction coefficient of the whole vehicle with Cou-lomb's friction model

The same holds true for the longitudinal acceleration situation. The right hand-

side of Figure 22 illustrates the vehicle in a braking manoeuvre, where only longi-

tudinal forces are generated. The sum of the individual tyre forces is denoted with

a symbol , which can also be written as a product of the longitudinal accelera-

tion and the mass of the vehicle. Thus the longitudinal friction coefficient is

derived in the same kind of form as the lateral friction coefficient, but now the

longitudinal acceleration is in the numerator (Equation 3.2).

(3.2)

It’s common that the vehicle experiences both lateral and longitudinal accelera-

tions at the same time. Hence the average friction coefficient of the vehicle is

shared between the lateral - and longitudinal accelerations. Therefore the maxi-

mum traction in either direction can’t be achieved at the same time. The total av-

erage friction coefficient of the vehicle is calculated as presented in Equa-

tion 3.2.

As the previously derived equations illustrate, friction coefficient is depended of

the acceleration of the vehicle. Therefore fierce braking or cornering manoeuvres

would be required to estimate the maximum achievable friction coefficient. These

kinds of fierce manoeuvres on public roads aren’t sensible in any way and they

would have to be carried out frequently for an accurate estimation. Hence the

previous representation of friction estimation is feasible only for evaluating the

Fx,R Fx,F mg

Fy,l Fy,r mg

may max

Fz,l Fz,r Fz,F Fz,R


37

friction coefficient that is currently used. Another downside of the previous repre-

sentation of friction estimation is that it doesn’t take into consideration the friction

situation of the individual tyres.

3.2.2 Terminology

The terminology concerned in friction coefficients can be confusing, because dif-

ferent studies have used various terms signifying the same things. Hence the

terms used in this work are defined as follows [10].

Friction used

Friction potential

Friction available

Figure 23 clarifies the use of these terms with three illustrative graphs. The mid-

dle graph represents the well known friction circle, where the longitudinal friction

coefficient is plotted against the lateral friction coefficient. Usually the maximum

of the longitudinal friction coefficient is higher than the lateral friction coefficient

[7]. Therefore the shape of the friction circle isn’t actually round, but more of an

ellipse. The blue dot in the friction circle illustrates the current operating point of

the tyre. The friction coefficient at the current operating point is nominated as the

friction used (Equation 3.3).

z

xx

F

F

0

25.0

50.0

75.0

00.1

Fric

tion

Po

ten

tialF

rictio

n

Use

d

Fric

tion

Ava

ilab

le

x

y

Friction Potential

Friction Used

Friction Available

z

y

yF

F

0

25.0

50.0

75.0

00.1

Fric

tion

Po

ten

tialF

rictio

n

Use

d

Fric

tion

Ava

ilab

le

Figure 23 Definition of friction coefficients

The graphs on both sides of the friction ellipse illustrate the lateral - and longitu-

dinal friction components of the same situation relative to slip angle and slip-

page rate respectively. For clarifying purposes, all the colours of the graphs

are signifying the same things.


38

(3.3)

The red circle and the red arrows in Figure 23 indicate the maximum friction that

the tyre-road interface can produce. The friction coefficient at this boundary line

is nominated as friction potential (Equation 3.4). In pure lateral - or longitudinal

slip situations, friction potential can be obtained by forcing the tyre to produce its

maximum force in that specific direction.

(3.4)

The yellow colour in Figure 23 illustrates how much the friction coefficient can still

increase from the current operating point before it reaches the maximum limit of

friction potential. The friction coefficient of the zone in question is nominated as

the friction available. The definition of it is simply the subtraction of the friction

potential and friction used (Equation 3.5).

(3.5)

The previous equations illustrated that for evaluating the overall state of the tyre,

both the friction used and the friction potential should be known. From these two,

the evaluation of friction used is much more straightforward. It requires only the

current lateral -, longitudinal - and normal load information of the tyre. The most

challenging task is to evaluate the friction potential, which would need the forces

of the tyre-road interface to reach their maximum. However this isn’t feasible in

any way and therefore the friction potential has to be evaluated with different

methods. The objective of this master’s thesis is to introduce a method that could


39

estimate the friction potential in a pure lateral slip situation. Thus no longitudinal

forces are produced in the tyre-road interface.

3.3 Classification of Friction Estimation Methods

There have been several different approaches to friction estimation in previous

studies, which can be classified to direct and indirect methods as illustrated in

Figure 24. The direct methods are directly involved with the friction process, by

measuring physical quantities such as forces and torques of the tyre or the vehi-

cle. Indirect methods are merely related to the friction process, by some environ-

mental or tyre/vehicle conditions.

Figure 24 Classification of friction estimation methods used in previous studies (figure is based on [11])

3.3.1 Direct Methods

As represented in Figure 24, the direct friction estimation methods are divided to

deliberate - and accidental excitation categories. The measured physical behav-

iours and quantities are the same in both of these categories, but the distinguish-

ing factor is found from the excitation manner. The input in deliberate excitation

category is given intentionally by a control system, which can acceler-

ate/brake/steer the individual wheels of the vehicle. The physical responses of

the input given by the control system are measured with different sensors. From

the sensor data, friction estimation algorithms can be conducted to attain the fric-


40

tion used and - potential values. Although deliberate excitation methods provide

accurate estimates for friction, they hold major drawbacks. The disadvantages

arise from the fact that the deliberate excitation of the wheels has a significant

influence to vehicle dynamics and therefore to safety and driving dynamics. Also

an additional tyre wear is introduced, which involves energy loss and therefore

increase to the fuel consumption. Thus the use of deliberate excitation methods

can be accepted only for research purposes.

Feasible friction estimation methods are found in the accidental excitation cate-

gory. The inputs in this category are generated by the normal driving manoeu-

vres. Therefore no additional tyre wear or influences to the driving dynamics are

created. However since the friction estimation depends of the inputs given by the

driver, it’s valid only, if there actually exists excitation. Also for accurate friction

estimation the magnitude of the excitation has to be sufficient. Therefore draw-

backs exist, but they are still small compared to deliberate excitation methods.

Since common trips with a vehicle include several cornering situations, it gives

potential circumstances for friction estimation. Therefore this master’s thesis is

concerned with the cornering situation of the accidental excitation methods.

The actual measurements of the physical responses of the inputs can be con-

ducted with three different methods, which are illustrated with green rectangular

boxes in Figure 24. The first method is to measure the deforma-

tions/accelerations of the tyre tread or inner liner. The second method considers

the wheel and the tyre as one packet, which forces and torques are measured.

The third method examines the behaviour of the whole vehicle, which includes

measurements of accelerations and angular -/translational velocities. All of these

methods have been investigated in previous studies to some extent. The focus of

this work is in the second method, measuring the forces and torques of the whole

wheel.

3.3.2 Indirect Methods

Indirect methods aren’t strictly involved with the friction process, but somehow

related to it. Therefore the accuracy of the friction estimation isn’t as good as with

direct methods. However studies have been performed to estimate friction from

environment - and tyre/vehicle conditions. As mentioned previously the traction

between the tyre-road interface is depended of the surface texture quality

(macro-/microroughness), surface conditions (dry/wet/ice) and surface tempera-


41

ture. Therefore these factors can be utilised to estimate friction potential. Espe-

cially optical sensors have been studied for distinguishing the surface conditions.

The advantage of these optical sensors is that they can be positioned to observe

the upcoming surface. Hence the alterations of surface conditions are updated

before the actual contact.

Conditions of the vehicle and the tyre can also be exploited to friction estimation.

E.g. the temperature - and the inflation pressure of tyre are related to the friction

process. The influence of these factors to friction is however limited and the al-

teration of them can be small. Therefore making the friction estimation difficult

and impairing the accuracy.

3.4 Previous Studies

There have been several studies, which have approached the topic of friction

potential estimation with exploiting the information of self aligning torque and lat-

eral force of the tyre. One of the first studies that utilized self aligning torque for

friction estimation was conducted in the Netherlands by Wim R. Pasterkamp. He

assembled a strain gauge in the lower ball joint of the transverse control arm for

evaluating the lateral force of the front tyre. The self aligning torque of the tyre

was attained by measuring the force of the tie rod with a load cell. The vertical

load of the tyre was evaluated by measuring the sway angle of the transverse

control arm. Two different friction estimation methods were implemented. The

first friction estimation method utilized look-up tables and the second neural net-

works. The effect of two different tyre models was also experimented. The first

one was the brush tyre model, which is also used in this master’s thesis and the

other one was the Magic Formula tyre model. Results showed that the imple-

mented estimation methods had potential and thus gave also motivation for this

master’s thesis. [11]

Another similar study performed by The University of Michigan, demonstrated

that the self aligning torque can be exploited to rather accurate friction potential -

and slip angle estimation. For more in-depth description of the estimation meth-

ods see [12].

The self aligning torque is also available at the steering wheel axis and can there-

fore be measured from there. Mitsubishi Electric has conducted a study, where

they have exploited the electronic power steering system as a sensor for estimat-


42

ing the friction potential of the tyre-road interface. This rather simple and cost

effective method showed good accuracy and robustness for the estimation. A

more detailed description can be found from [13].

The researchers in the University of Stanford have also devoted themselves to

several studies, where they have utilized the self aligning torque information to

estimation of friction potential and slip angle. In [14] an algorithm is introduced,

which exploits the steering torque information from the steer-by-wire system for

evaluating the cornering stiffness of the tyre and the friction potential of the tyre-

road interface. The slip angle of the tyre in the same study is derived from

GPS/INS measurements. Another study from the same University utilized the

pneumatic trail information of the self aligning torque for estimating the peak lat-

eral force ( ) and the slip angle of the tyre. This particular estimation method

doesn’t require the knowledge of the normal force of the tyre. More detailed

presentation of this study can be found from [15].

A Swedish Intelligent Vehicle Safety Systems (IVSS) programme has investi-

gated different approaches for evaluating the friction potential of the tyre-road

interface [16]. One part of this study was devoted to estimating friction potential

by utilizing the self aligning torque together with the lateral force of the tyre. The

employed algorithms indicated that a reliable estimate of friction potential re-

quired a lateral acceleration of around 0.3 g. More about the issued friction esti-

mation method together with the other methods concerned in this study is avail-

able in [16].


The friction forces generated between two rigid bodies are commonly modelled

with the Coulomb’s friction model. It suggests that the produced friction forces

are directly proportional to the normal force, which compresses the bodies to-

gether. The nature of the contact surfaces and the traction quality is represented

with a dimensionless factor called the friction coefficient. It’s defined as the ratio

of the produced friction force and the normal force. Therefore it expresses the

amount of friction force generated in respect to the normal force. Coulomb’s fric-

tion model is commonly accepted and used in engineering, although it has many

generalizations.


43

The evaluation of the overall traction state of the tyre requires the knowledge of

both the friction used and the friction potential. The information of the current lat-

eral -/longitudinal - and normal force of the tyre are the only factors needed for

evaluating the friction used. Thus making it a straightforward task compared to

the evaluation of friction potential, which would require the tyre-road interface to

reach the maximum achievable friction force. These forces are produced only in

fierce braking/acceleration/cornering manoeuvres, which normally occur only in

hazard situations. Therefore the evaluation of friction potential has to be con-

ducted with different methods.

The classification of friction estimation methods can be done according to previ-

ous studies. The main division is done to two categories: direct - and indirect

methods. The first main category includes estimation methods that are directly

involved with the friction process. These methods are implemented by measuring

forces, torques and acceleration of the wheel or the vehicle. The direct methods

are also subdivided to two categories according to the excitation manner (delib-

erate - and accidental excitation). A deliberate toe-in alteration of the front wheels

or a braking of an individual wheel is carried out by a control system in the first

subcategory. The excitations in the other subcategory are produced due to nor-

mal driving manoeuvres. The second main category holds the indirect friction

estimation methods, which are somehow related to the friction process. The ad-

vantage of these methods is that they don’t require any driving inputs for the es-

timation. However since these methods aren’t strictly involved with the friction

process, the accuracy of the estimation can be low.

The friction estimation of this master’s thesis belongs to the direct method cate-

gory and to the accidental excitation subdivision. Concerning only the cornering

situation, where the forces and torques of front wheels are measured.

Research Vehicle and Sensor Equipment

44

4 Research Vehicle and Sensor Equipment

4.1 Introduction

The upcoming subchapters will give an insight to the research vehicle and to the

equipment used in this master’s thesis. The research vehicle is a fifth generation

(Mk5) Volkswagen (VW) Golf Variant, which is a typical small family estate-car

(Figure 25). The front wheel suspension and steering system of the research ve-

hicle are examined in detail, because they have a significant influence on the

aligning torque.

Figure 25 Volkswagen Golf Mk5 Variant

Vehicle axis system together with the essential dimensions of the VW Golf is rep-

resented in Figure 25. The longitudinal position of the centre of gravity ( ) from

the front - and rear axle is denoted as and respectively. The height of the

above the ground is denoted as and the track width is denoted as . The fun-

damental parameters of the VW Golf are given in Appendix A1.

CG

h

t lR lF

z y

x


45

4.2 Front Suspension Geometry

4.2.1 Overview

The McPherson type independent front wheel suspension is without a doubt the

most common front axle suspension solution in front-wheel driven cars and VW

Golf Mk5 Variant is no exception. Assembly of the VW Golf Mk5 Variant front axle

suspension is illustrated in Figure 26. As can be seen, the McPherson suspen-

sion is a compact packet including the following main parts:

Transverse control arm

Suspension strut (spring and damper)

Wheel hub carrier

Anti-roll bar and coupling rod

Figure 26 VW Golf Mk5 variant front axle suspension [17] (figure modified)

The McPherson assembly attaches to the vehicle body at three different locations

(yellow circles in Figure 27 and Figure 28). The transverse control arm is joined

to the subframe via two bonded rubber bushes, which allow a rotational degree of

freedom for the control arm. The dashed-dotted line in Figure 27 represents the

axis of rotation of the wishbone. A ball joint is bolted to the other end of the

wishbone, which attaches to the wheel hub carrier (red circle in Figure 27).

Wheel hub carrier

Transverse control arm

Suspension strut

Anti-roll bar

Coupling rod

Subframe


46

Figure 27 Mounting of the lower wishbone

The suspension strut is mounted to the wheel hub carrier by a clamp-type con-

nection. Therefore it can be considered as a rigid junction. The upper strut mount

is a bonded rubber bush and it forms the third connection to the vehicle body.

The upper strut mounting can be considered as a universal joint, because the

strut can rotate around its axle and sway in any direction.

Figure 28 Wheel hub carrier and suspension strut [17] (figure modified)

Wheel hub carrier

Lower spring seat

Suspension strut

Coil spring

Ball joint

Steering arm

Lower strut mount

Upper strut mount


47

4.2.2 Steering Axis

Detailed examination of the McPherson type suspension geometry is extremely

important, because it defines the steering axis, which about the wheel assembly

rotates and the aligning moment is generated. In McPherson the steering axis

goes through the upper strut mount and the lower ball joint of the trans-

verse control arm (Figure 29) [18]. The upcoming subchapters represent the lon-

gitudinal - and lateral inclination angles of the steering axis and examine the ef-

fect of these angles to self aligning torque.

1Bz

xy

2A

r

dynr

C

x px

pr

Cx ,

1B

1A2A

xy

z

y

br

ar

Figure 29 McPherson strut suspension geometry of left front wheel

4.2.3 Caster Angle

The longitudinal inclination angle of the steering axis is denominated as the

caster angle . It’s defined as the angle between the steering axis and a

vertical drawn trough the wheel centre (Figure 29) [18]. Caster angle is con-

sidered to be positive, when the steering axis is inclined backwards as illustrated

in Figure 29. The backward inclination of the steering axis is a desired design

concept, because it brings a stabilizing effect to the wheel. The stabilizing effect

arises from the position of the lateral force, which is behind the steering axis. The


48

lateral force together with the lever arm generate a torque around the steering

axis, which tries to bring the wheel back to straight a head driving position.

The lateral force lever arm divides to caster trail and pneumatic trail of

the tyre. Considering first only the effect of caster trail, the point of application of

the lateral force is assumed to be at centre point of the contact patch [18]. For

clarifying the terminology, the denomination caster trail signifies the normal dis-

tance from the steering axis to the point of application of the lateral force. The

distance on the ground between the centre point of the contact patch and the

steering axis is denominated as the kinematic caster trail. Obviously the lateral

force lever arm is the shortest distance from the axis of rotation, which is the

caster trail. The length of the caster trail as function of the caster angle can be

evaluated from the suspension geometry by using trigonometric functions. For

the evaluation of the caster trail, two other variables have to be determined and

they are the dynamic rolling radius of the tyre and the caster offset. The dynamic

rolling radius of the tyre is defined as the ratio of the longitudinal velocity and the

angular velocity.

(4.1)

The longitudinal distance between the wheel centre and the steering axis is de-

fined as the caster offset. Typically designers drive for negative caster offset,

which is also the case in the Figure 29. The negative caster offset shortens the

kinematic caster trail, which reduces the steering effects arising from uneven

road surfaces. [18] The length of the caster offset depends of the caster angle

and the distance between the wheel centre and the ball joint. The latter is a static

measure and hence can be evaluated with measurements. Therefore the caster

offset is defined as follows.

(4.2)

Now that the dynamic rolling radius and the caster offset are defined, the caster

trail is evaluated by using trigonometric functions (Figure 29).

(4.3)

However the lateral force distribution of the tyre isn’t symmetrical about the con-

tact patch. It depends of the slip angle, friction coefficient and the normal load


49

distribution of the tyre. Therefore the resultant lateral force doesn’t act at centre

point of the contact patch, but at a distance from it called the pneumatic trail. The

length of the pneumatic trail on the ground ( -plane) is derived by using the

brush tyre model, which is discussed thoroughly in the next chapter. Obviously

the force lever arm isn’t the pneumatic trail on the ground, but the normal drawn

from the line, which goes trough the centre point of the contact patch and is par-

allel with the steering axis. The length of this normal can be evaluated with trigo-

nometric functions from the suspension geometry (Figure 29).

(4.4)

The total lateral force lever arm is simply the sum of the caster - and pneumatic

trails.

(4.5)

The total self aligning torque about the steering axis is the product of the lateral

force and the total lateral force lever arm.

(4.6)

The brush tyre model concerns only the self aligning torque that arises from the

pneumatic trail. Therefore the total lateral force lever arm has to be differentiated

to caster - and pneumatic trails in order to subtract the self aligning torque

emerging from the caster trail. For clarifying the equations, the self aligning

torque arising from the caster trail is denoted as and the self aligning torque

arising from the pneumatic trail is denoted as .

(4.7)

The total self aligning torque is evaluated from the tie rod forces and the self

aligning torque arising from the caster trail can be calculated. Thus the desired

self aligning torque emerging from the pneumatic trail is obtained.

(4.8)

As the previous equations have shown, the lateral force lever arm depends of the

caster angle and therefore also the self aligning torque is dependent of it. By ob-

serving the right side of Figure 30, it's obvious that the caster angle alters as


50

function of the transverse control arm's angle. The ball joint bolted to the end of

the transverse control arm moves along an arc, which path is determined by the

physical length of the control arm. The length of the control arm is static and is

therefore a parameter, but the angle of the control arm has to be measured for

the evaluation of the caster angle. The measurement of the control arm’s angle is

done with an angle sensor, which is discussed later on in this chapter.

A coordinate system has to be established for evaluating the position of the ball

joint. The rear joint of the transverse control arm is chosen to be the origin for the

coordinate system. Therefore all the other coordinates are measured in respect

to the rear joint of the control arm.

z

xy

C

),( 11 AfA zx ),( 11 ArA zx

),( 22 AA zx

),( 11 BB zx

xy

z

),( 11 BB zy

),( 11 AA zy

),( 22 AA zy

C

A

Figure 30 Evaluation of the caster and kingpin inclination angles

The vertical - and lateral positions of the ball joint are calculated from the left side

of the Figure 30. These coordinate points are also needed for evaluating the

kingpin angle, which is discussed more thoroughly in the next chapter.

(4.9)


51

The -coordinate of the ball joint doesn’t alter, because it moves parallel to the -

axis. Also the upper strut mount and the joints of the transverse control arm are

assumed to be rigidly attached to the vehicle body. Both the caster angle and the

kingpin angle are derived from the Figure 30 by using trigonometry.

(4.10)

4.2.4 Kingpin Inclination Angle

The lateral inclination angle of the steering axis is denominated as the kingpin

angle . It’s defined as the angle between the steering axis and a vertical drawn

trough the ground plane (Figure 29). The point of application of the longitudinal

forces is assumed to be at the centre of the contact patch. The extension of the

steering axis line doesn’t necessarily intersect with the centre point of the contact

patch. The distance between these points is denoted as the kingpin offset .

The sign of the kingpin offset is considered to be negative, when the extension of

the steering axis line intersects the ground outside of the centre point of the con-

tact patch. Since the longitudinal forces don’t act at the steering axis, but at a

distance from it, a torque is produced, which is proportional to the kingpin offset.

The larger the kingpin offset is the larger torque around the steering axis is pro-

duced by the longitudinal forces. Therefore the design aim is to keep the kingpin

offset as small as possible. Obviously kingpin offset isn’t the actual longitudinal

force lever arm. [18]

The actual longitudinal force lever arm is different for braking - and tractive

forces. In the case of braking, the brake cylinder joins the wheel and the wheel

hub carrier as a whole. Therefore the longitudinal force lever arm is achieved

by drawing a normal from the steering axis to the centre of the contact patch

(Figure 29).

(4.11)

Since the steering axis is also inclined in the longitudinal direction by the amount

of caster angle, the braking force at the tyre-road interface has to be resolved

into components. One component is in the direction of the steering axis and the


52

other is vertical to it. The vertical component of the braking force together with

the force lever arm generates the torque around the steering axis.

(4.12)

The direction of this torque depends of the sign of the kingpin offset. If it’s posi-

tive, the resulting torque from the braking force at the tyre-road interface pushes

the wheel into toe-out and if it’s negative the resulting torque pushes the wheel

into toe-in. It’s therefore desired that this torque remains small under braking

situation, because it brings disturbance forces to the steering system.

Tractive - and rolling resistance forces generated in the tyre’s contact patch are

supported by the wheel bearing (wheel centre). Therefore the point of application

of these forces has to be considered at the wheel centre, but in the opposite di-

rection than in the contact patch. In this case, the longitudinal force lever arm

is determined by drawing a normal from the steering axis to the wheel centre

(Figure 29). As in the braking situation, the tractive- and resistance force has to

be resolved around the caster angle. The vertical component produces the

torque around steering axis. The equations for the torques generated by the trac-

tive and resistance force are represented below.

(4.13)

4.2.5 Camber Angle

Camber angle is defined as the angle between the wheel centre plane and

the vertical drawn through the ground plane (Figure 31). The sign of the camber

angle is considered to be positive, when the top dead centre of the tyre is inclined

outwards. The camber angle in the illustration is negative, because the top dead

centre is leaning inwards. Zero - or slight negative camber angle is common in

vehicles nowadays. Slight negative camber angle improves the lateral grip of the

tyre and therefore it has a positive influence to the handling of the vehicle. [18]


53

xy

z

od

id

Figure 31 Camber angle

The lateral grip of the tyre is improved, because the tyre produces a lateral force

even when it’s travelling a straight path and without a slip angle. The lateral force

emerges from the deformation of the tyre contact patch. Considering the brush

tyre model (see Chapter 5), the rubber brush elements deflect and produce a

force proportional to their deflection.

The lateral force distribution arising from the camber angle is assumed to be

symmetrical. Therefore the point of application of the lateral force is at the centre

of the contact patch. Together with the caster trail, this force produces an equal

torque on both wheels, which is absorbed by the tie rods. However another

source of torque emerges from the camber angle. Observing the Figure 31, it’s

noted that the circumference of the outside and inside of the tyre differs with each

other. Yet the tyre is forced to travel a straight path and the angular velocity of

the wheel is constant. Since the circumference of the tyre is smaller on the in-

side, it should rotate faster than the outside of the tyre. Therefore it denotes that

there must exist opposite longitudinal slips on both sides of the tyre, which arises

a torque around the steering axis. [11]


54

4.3 Steering System

4.3.1 Overview

The investigation of the steering system is relevant, because all the forces gen-

erated around the steering axis of the wheels are supported by the tie rods,

which have a mechanical connection to the steering wheel. Therefore the torque

generated on both steering axis is transferred to the steering wheel and to the

knowledge of the driver.

The main components of the steering system of the VW Golf Mk5 are illustrated

in Figure 32. The most interesting part of the steering system is the power steer-

ing, which is electro-mechanical. The electro-mechanical power steering system

enables to eliminate all the hydraulic components that were needed to the old

hydraulically assisted steering system. Therefore no hydraulic oil pump is re-

quired and energy is saved. The electronic motor of the electro-mechanical

power steering is actuated only when needed. The assisting force of the steering

depends of the driving speed, the amount of steering force applied and the steer-

ing angle. Thus the amount of assisting force can be optimized for different driv-

ing conditions. [19]

Figure 32 Steering system components of the VW Golf Mk5 [19] (figure modified)

Steering wheel

Steering column

Tie rod

Universal joint shaft

Power steering control unit

Steering gear

Electro-Mechanical power steering motor

Tie rod end

Steering angle sender

Steering torque sender


55

The construction of the electromechanical power steering is illustrated in Figure

33. As the figure shows, the steering rack has two pinions (steering - and drive

pinion). Hence the name dual pinion type electro-mechanical power steering sys-

tem. The steering force applied by the driver is transferred to the steering rack via

the steering pinion. The assisting steering force generated by the electric motor is

transferred to the steering rack via the drive pinion. Therefore the total steering

force that the steering rack imparts is the sum of the forces that the pinions trans-

fer.

Figure 33 Electro-mechanical power steering [19] (figure modified)

The basic operational principle of the electro-mechanical power steering is

straightforward. When the driver turns the steering wheel, the power steering

control unit acquires the following data from the sensors:

Steering torque (steering torque sender) [19]

Steering wheel angle and speed (steering angle sender) [19]

Driving speed (wheel speed sensor/ESC control unit) [19]

Engine speed (engine speed sensor/engine control unit) [19]

The memory of the power steering control unit contains maps for determining the

required assisting force from the acquired input data.

4.3.2 Forces and Torques

A simplified model of the steering system is presented in Figure 34. In this par-

ticular situation the driver turns the steering wheel to counter clockwise direction

with a torque . The universal joint shaft imparts this torque to the steering pin-

ion, which pushes the steering rack with a force . The assisting force is de-

Drive pinion Steering pinion

Steering rack

Power steering control unit

Electric motor Steering torque sender

Steering angle sender


56

livered to the steering rack by the electric motor of the power steering system.

Thus the sum of these two forces is shifting the steering rack to the right-hand

side in the Figure 34.

ltotzM ,,

DFMF

TRLFTRRF

DMx

y

rtotzM ,,

Figure 34 Simplified model of the steering system

The steering action produces lateral tyre forces, which on the other hand arises

self aligning torques ( , ) around the steering axes. The wheels and

the steering rack are connected via the tie rods, which support the self aligning

torques that are generated at the steering axes. The yellow squares in Figure 34

represent the piezoelectric force sensors, which are discussed more detailed in

the upcoming chapters. For now they can be considered as devices, which can

measure the forces of the tie rods. In this simplified illustration of the steering

system, the tie rods are drawn parallel with the steering rack. Thus the following

force equilibrium equation can be written (Equation 4.14). The left-hand side tie

rod is put under a tensile stress and the right-hand side tie rod under a compres-

sive stress.

(4.14)

By considering the steering system without the power steering system, the follow-

ing equation of torque equilibrium can be represented (Equation 4.15). Hence the

total self aligning torque of both wheels can be detected from the steering wheel.

(4.15)


57

4.3.3 Evaluation of the Force Lever Arm

The forces of the tie rods are measured with the piezoelectric force sensors.

However the force itself doesn’t reveal the self aligning torque, which is the re-

quired information for the estimation. Therefore the force lever arm of the tie rod

has to be evaluated in some way. Figure 35 illustrates the factors that are con-

cerned with the evaluation of the force lever arm and the self aligning torque.

0,0

x

y

1x x

TRLF

r

y

TRL

2x

yTRLF ,

xTRLF ,

as

ltotzM ,,

Figure 35 Evaluation of the force lever arm

The tie rod is joined to the steering arm with a ball joint and it’s considered to

move a circular path, which is drawn in the Figure 35. The other end of the tie rod

is joined to the steering rack and can therefore move only transversally. First of

all, the position of the ball joint of the steering arm has to be evaluated as a func-

tion of the steering angle. The origin of the reference system, in this specific

situation, is determined to be at the steering axis. Thus the positions are pre-

sented against this point. The - and -distances between the steering arm ball

joint and the reference system are actually the force lever arms (Equation 4.16).

Obviously the tie rod force has to be resolved to - and -directions before the

self aligning torque can be extracted from these distances.


58

(4.16)

The ball joint of the steering arm doesn’t locate at the bottom dead centre, when

the steering angle is zero. Therefore there exists a static angle , which can

easily be solved from basic trigonometry. Depending of the sign of the steering

angle, it’s either added or subtracted from this static angle.

For resolving the tie rod force to - and -directions, the angle of the tie rod

has to be evaluated. The distance between the steering rack and the ball joint of

the steering arm is needed before the angle can be extracted (Equation 4.17).

Obviously the distance is dependent of the steering angle.

(4.17)

The angle of the tie rod can now be solved by utilising basic trigonometry.

(4.18)

The same angle is evident between the forces and , which enables the

actual tie rod force to be extracted to - and -directions.

(4.19)

The self aligning torque consists of these two force components and from the two

lever arm components (Equation 4.20). The lateral force component and the lon-

gitudinal lever arm component produce a torque, which attempts to bring the

wheel back to straight a head position. The longitudinal force component and the

lateral lever arm component produce a much smaller torque, which points to the

opposite direction.

(4.20)

Although the previous presentation of the lever arm evaluation was to the left-

hand side wheel, it’s obviously easily modified to the right-hand side wheel as

well.


59

4.4 Sensor Equipment

4.4.1 Overview

The sensor equipment setup of the research vehicle is illustrated in Figure 36.

The coloured circle callouts point the locations of the individual sensors. For the

friction estimation, the following sensor information is needed.

Steering wheel angle (orange circle)

Steering axle torque (orange circle)

Longitudinal- and lateral velocity of the vehicle (green circle)

Lateral acceleration and yaw-velocity (brown circle)

The angle of the transverse control arm (yellow circle)

Tie rod forces (blue circle)

Industrial charge amplifier for the piezoelectric tie rod force sensor (purple

circle)

Analogue- to digital-signal converter (black circle)

Rapid prototyping computer, MicroAutoBox (red circle)

Figure 36 The sensor equipment setup of the research vehicle


60

The steering wheel angle, lateral acceleration and yaw velocity are acquired from

the vehicle’s ESC (Electronic Stability Control) system. A contactless 2-axis opti-

cal velocity sensor (Correvit S350) is used for the longitudinal and lateral velocity

measurement. The bicycle model, which is described later on, requires these

information for evaluating the lateral tyre forces and slip angles.

The alignment of the steering axis determines the force lever arm of the self

aligning torque. Therefore the longitudinal and lateral inclination angles of the

steering axis have to be evaluated. For this purpose angle sensors (Bosch

Rexroth, Angle Sensor WS1) are installed on both transverse control arms of the

front suspension. These angle sensors are also used for approximating the wheel

load distribution of the front axle.

The lateral- and longitudinal tyre forces don’t act at the axis of rotation (steering

axis), but at a distance from it. Hence a self aligning torque is generated around

the steering axis. Piezoelectric force sensors are mounted to both tie rods, for

acquiring the force of the self aligning torque. Another possibility for evaluating

the self aligning torque is by using a torque sensor at the steering axis. Both of

these are implemented to the research vehicle. An industrial charge amplifier is

needed for the piezoelectric sensors and for the steering axis torque sensor. The

amplified signals are converted to digital form with an AD-converter and send to

the MicroAutoBox by CAN-bus.

There are three individual CAN-busses, which communicate with the rapid proto-

typing computer (MicroAutoBox). The lateral acceleration and yaw velocity are

acquired from the vehicle CAN-bus, the optical velocity sensor has an own can-

bus and the data of the piezoelectric sensors and the steering axis torque sensor

are acquired from the third CAN-bus. Hence only the transverse control arm’s

angle data is transmitted in analogical form.

4.4.2 Piezoelectric Force Sensor

Since the tie rod supports the forces generated around the wheel’s steering axis,

it’s a logical place to evaluate the aligning torque. However it’s not the ideal

measuring solution, because the forces generated at the tyre contact patch are

transmitted through joints to the tie rod. As well known, all joints contain friction

and inertia, which can distort the force information. An ideal measurement place

would be the wheel centre, because it’s close to the contact patch where the

forces and torques are generated. Actually there exist measurement wheels that


61

can determine longitudinal -, lateral - and vertical forces of the wheel centre as

well as the torques around all of the three axes (Figure 37). However these

measurement wheels are extremely expensive and not practical in vehicles.

Therefore the use of measurement wheel was excluded from this master’s thesis.

Figure 37 6-component measuring wheel [20]

In a previous study [21], two different measurement solutions were examined for

evaluating the tie rod force. The first measurement solution was a strain gage

load sensor, which was attached to the tie rod. In proper measurement locations

where the deformation of the force detector is sufficient, strain gages can be ac-

curate and therefore a cost effective measurement solution. However it was

noted by experiments and calculations that the deformation of the tie rod was too

small. The other measurement solution was a piezoelectric force sensor, which

was installed in between a split tie rod. Based on the good experience found in

the previous study [21], the piezoelectric force sensor is also used in this mas-

ter’s thesis for measuring the tie rod force. The chosen piezoelectric sensor is

manufactured by Kistler and it’s the same type as used in the previous study.

Construction of the Kistler piezoelectric force sensor (typre 9102A) is illustrated in

Figure 38. It consists of two crystal washers , an electrode and

ing with a connector . The Kistler type 9102A is a single component force

sensor and therefore it measures forces only in the -direction. [22]


62

Figure 38 Kistler piezoelectric force sensor (type 9102A) [22] & [23]

In Figure 38, the applied force to the sensor is denoted with a symbol, which in

this case is the tie rod force. As the sensor is subjected to a compressive force,

the crystal washers inside the housing deform and generate negative charge,

which is proportional to the applied mechanical compression. The electrical

charge value has to be converted into voltage form and for that purpose a charge

amplifier is required. The charge amplifier used in this master's thesis is a Kistler

type 5073A411, which has four channels [24]. Since both tie rods are equipped

with piezoelectric force sensors, two channels of the charge amplifier are

needed. The piezoelectric force sensor by itself doesn't require a power supply,

but the charge amplifier has to be connected to a 24 V power supply. As the ve-

hicle's own electrical system supplies only 12 V, a DC-DC-converter is installed.

The charge amplifier requires also a reset/measure signal for resetting the drift of

the piezoelectric sensors to zero (Figure 39). The reset/measure signal is ac-

quired from the MicroAutoBox.

The whole measurement chain is illustrated in Figure 39. It consists of the piezo-

electric force sensor, highly insulated coaxial cable and the charge amplifier. As a

force is applied to the piezoelectric sensor, it produces an electrical charge ,

which is transmitted to the charge amplifier via the cable. The charge amplifier is

basically a charge integrator, which constantly compensates for the sensor’s

electrical charge with a charge of equal magnitude and opposite polarity of the

range capacitor . Therefore the voltage across the range capacitor is propor-

tional to the charge generated by the piezoelectric sensor. [25] The output volt-

age of the charge amplifier ranges from -10 V to +10 V.


63

Figure 39 Measurement chain [24] & [25]

For even pressure distribution and accurate measurements, the piezoelectric

force sensor has to be mounted in between two finely machined surfaces [22].

The surface of the split tie rod isn’t that fine and rigid. Therefore a stress distribu-

tion ring is required on both sides of the contact surface. For measuring both

compressive and tensile forces, the sensor has to be preloaded. The manufac-

turer recommends preloading the sensor to 50 % of the measuring range, which

is 25 kN [22]. For preloading the sensor a preloading bolt, a centring sleeve and

two insulating washers are needed (Figure 40).

Figure 40 Mounting equipment (left: preloading elements, right: stress distribution ring) [26]

The preloading force is measured by the sensor itself and for that purpose the

charge amplifier is set to the sensitivity specified in the sensor’s datasheet [22].

However after preloading the sensor, the mechanical load is divided between the

preloading bolt and the sensor. Thus the whole measurement setup has to be

calibrated after the preloading procedure with a reference force sensor. Figure 41

illustrates the situation before the calibration and as it can be seen, the output of

the piezoelectric sensor doesn’t follow the output of the reference force sensor.


64

Figure 41 Reading before the calibration (red line: piezoelectric sensor, white line reference force sensor)

The calibration setup is illustrated in Figure 42. The calibration is done dynami-

cally by using a hydraulic cylinder as an actuator. The reference force sensor is

a strain gage manufactured by Hottinger. It’s assembled mechanically in series

with the piezoelectric force sensor. Hence both sensors experience the same

force applied by the hydraulic cylinder. The reference force sensor has been cali-

brated beforehand and it’s considered to be accurate.

Figure 42 Calibration setup

Stress distribution rings

Piezoelectric sensor

Hydraulic cylinder

Reference force sensor

Inner end of the tie rod

Outer end of the tie rod


65

The sensitivity of the charge amplifier is set to 1 pC/N in the beginning of the

calibration procedure. Therefore the output of the piezoelectric sensor gives the

amount of charge generated on specific force. The specific force is measured

with the reference force sensor and with these two measurements it’s possible to

evaluate the sensitivity of the whole measurement setup. It’s considered that the

maximum force the tie rod encounters is around 5000 N. Hence the amplitude of

the excitation force of the hydraulic cylinder is set to be 5000 N. The frequency of

the excitation is set to be 0.5 Hz. Other frequencies are also implemented after

the calibration procedure to assure the success of the calibration.

The hydraulic cylinder is set to produce the excitation explained above and data

of a 10 second measurement is gathered. The data is then analysed in DIAdem

by calculating a Fast Fourier Transform (FFT) of both measurement signals.

Figure 43 Evaluation of the sensitivity of the whole measurement setup

In Figure 43, the blue curve represents the output of the reference force sensor in

N and the red curve represents the output of the piezoelectric sensor in pC. The

lower graph of the Figure 43 illustrates the result of the FFT. The sensitivity of the

whole measurement setup is evaluated from the peak values of the first fre-

quency components.


66

(4.21)

The sensitivity of the charge amplifier is set to the acquired value and the outputs

of both sensors are examined as before the calibration. Figure 44 illustrates

clearly that the sensor readings are the same after the calibration procedure.

Figure 44 Reading after the calibration (red line: piezoelectric sensor, white line reference force sensor)

As mentioned previously, the output of the charge amplifier produces a voltage,

which ranges from -10 V to +10 V. However the analogue inputs of the Micro-

AutoBox are limited to signals that range from 0 V to +5 V. Therefore the ana-

logue output of the charge amplifier can’t be connected to the analogue input of

the MicroAutoBox. At first, a voltage converter was considered, but analogue

signals are in general very sensitive to electrical interferences. Therefore the

length of the analogue cables should be kept as short as possible. The solution

was to digitise the output of the charge amplifier straight away and send the in-

formation to the MicroAutoBox through a CAN-bus. Industrial fieldbus compo-

nents, manufactured by Beckhoff, provided an advantageous and straightforward

answer for implementing the digitizing and CAN-format conversion. All the field-

bus components required for the implementation are illustrated in Figure 45. The

first block from the left is a BK5150 CANopen bus coupler, which converts the

digitized data to CAN-format and then sends the data as CAN-messages to the

MicroAutoBox [27]. The second block in the middle is a 2-channel analog input

terminal KL3132, which attaches to the CANopen bus coupler [28]. The input


67

range of the KL3132 is from -10 V to +10 V, which matches with the output of the

charge amplifier. The 2-channel analog input terminal digitizes the data from the

charge amplifier with a resolution of 16 bits. The last block on the right is an end

terminal KL9010, which is always needed at the end of the assembly [29].

Figure 45 Beckhoff equipment (BK5150 [27], KL3132 [28] and KL9010 [29])

4.4.3 Hall Effect Angle Sensor

The angle of the transverse control arm is essential information for determining

the caster - and kingpin inclination angles. It’s also needed for approximating the

front axle wheel load distribution. Therefore a Bosch Rexroth angle sensor WS1

is mounted on the axis of rotation of the transverse control arm (Figure 46) [30].

It’s designed specially for automotive application and thus the structure of the

sensor satisfies the requirements in its mounting location.

Figure 46 Bosch Rexroth, Angle Sensor WS1 [30]


68

The block circuit diagram of the sensor is represented on the left hand-side of

Figure 47. The sensor consists of two measurement systems, which both contain

a hall-element and an amplifier. As outputs the sensor produces two voltage sig-

nals, which are proportional to the angle of rotation. The measuring range of the

sensor is from -45 degrees to +45 degrees, which is more than enough for de-

termining the angle of the transverse control arm. Since there are two opposing

output signals, the measurement can be done differentially by subtracting the

signals with each other (Figure 47). [30]

Figure 47 Block circuit diagram and angle vs. output voltage [30]

The assembly of the left side transverse control arm is illustrated in Figure 48.

The angle sensor is mounted on the axis of rotation by using a piece of rectangu-

lar tubing. For attaching the guide lever of the sensor in line with the transverse

control arm, an aluminium extension bar together with a corner piece had to be

constructed. The sensor is aligned perpendicularly in respect to the frame, which

signifies that the measured angle is zero when the guide lever is parallel with the

sensor.

Figure 48 Assembly of the angle sensor to the transverse control arm

Bosch Rexroth, Angle Sensor WS1

Transverse control arm Sub frame


69

The angle of the transverse control arm is determined from the measuring range

and the output voltage of the sensor (Figure 47). The output voltage is linear in

between the measuring range -45 V…+45 V. Therefore the sensitivity of the sen-

sor in differential measurement becomes as follows.

(4.22)

The wheel load of the front tyres can also be approximated from the angle sen-

sors data. The experimental setup needed for determining the wheel load of the

front tyres is illustrated in Figure 49. The bonnet of the research vehicle had to be

removed in order to carry out the experiment. As the Figure 49 represents an I-

beam is assembled on the upper strut mounts of the front suspension. The ends

of the I-beam contain holes where the hooks of the turnbuckles are attached. The

other end of the turnbuckle is bolted to the ground. Therefore by tightening the

turnbuckle the wheel load is forced to increase. Scales are placed under each

wheel although only the load of the front wheels is measured.

Figure 49 Experimentally defining the vertical load of the front wheels

The experiment was carried out by tightening the turnbuckles in such a manner

that a specific wheel load on both scales was established. It was noticed that the

compliance of the tyre would cause the output of the angle sensor to saturate

Scale

Turnbuckle

I-beam


70

around 200 kg and 700 kg. Therefore the detectable measurement range is be-

tween these wheel load values. Another issue arose from the friction of the joints,

which brought hysteresis to the measurement. In Figure 50 the green line repre-

sents the downward movement of the suspension and the orange line represents

the upward movement.

Figure 50 Hysteresis caused by the friction of the joints

It was clear that the measurements would have to be done multiple times in both

directions, because of the hysteresis. Five measurements were conducted in

both directions and an average voltage value of the sensor was calculated at

each measured wheel load. From the average voltage values a lookup-table is

implemented to Simulink, which takes the voltage value of the sensor as an input

and gives out the corresponding wheel load. It’s obvious that this implementation

gives an approximated wheel load, which contains errors. But as the Figure 51

illustrates the curves are quite linear between the ranges of 300 kg to 500 kg.

Therefore the approximated wheel load is more accurate at small wheel load

changes, which is sufficient in this master’s thesis.

150

250

350

450

550

650

750

-1,00 -0,80 -0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00

Wh

eel l

oad

[k

g]

Output of the angle sensor [V]


71

Figure 51 Approximated wheel load by using the angle sensor

4.4.4 Two-Axis Optical Velocity and Slip Angle Sensor

The task of evaluating the actual longitudinal and especially the lateral velocity of

the vehicle has always been demanding. The longitudinal velocity of the vehicle

can be approximated relatively well from the angular velocity sensors of the

wheels, but the evaluation of the lateral velocity is difficult. Both the actual longi-

tudinal - and lateral velocity is essential information for calculating the slip angles

of the , front - and rear tyres by using the bicycle model, which is discussed

later on. Therefore it was decided that a two axis optical velocity sensor is used

for determining the longitudinal and lateral velocities (Figure 52).

Figure 52 Correvit S350 [31]

0

100

200

300

400

500

600

700

800

-1,00 -0,80 -0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00

Wh

eel l

oad

[k

g]

Output of the angle sensor [V]

Left Wheel Right Wheel


72

The two-axis optical velocity sensor is assembled to the right front door of the

research vehicle. Longitudinally it’s positioned to the , but laterally there exists

an offset to the . Hence under cornering manoeuvre the lateral velocity of the

is directly the measured lateral velocity component. However the longitudinal

velocity of the isn’t directly the measured longitudinal signal. Since the sensor

isn’t positioned laterally to the , the yaw rate of the vehicle brings an additional

velocity component to the longitudinal velocity signal. The lateral position of the

of the research vehicle is assumed to be in the middle of the vehicle. There-

fore the distance from the sensor to the is measured to be m. The

velocity components of the are evaluated from the data of the two-axis optical

velocity sensor and the yaw rate sensor of the vehicle [32].

(4.23)


A detailed examination of the research vehicle and the equipment required for

this master’s thesis was represented. Especially the front wheel suspension and

the steering system were discussed carefully. The inclination angles of the steer-

ing axis (caster- and kingpin angle) were defined and their effects to the self

aligning torque were discussed. Also a brief insight to the camber angle was

given.

The electromechanical power steering system of the research vehicle was ex-

plained in order to get better understanding from it. The actual steering event

together with forces and torques that occur in the steering system were illus-

trated. The method of evaluating the force lever arm and the self aligning torque

was rather simple and could be improved with a more precise model.

The most important sensor equipments considered with this master’s thesis are

the piezoelectric force sensor and the hall effect angle sensor. The tie rods of the

research vehicle were cut in half and the piezoelectric force sensors were as-

sembled in between these cut tie rods. Before they were installed to the vehicle

they were dynamically calibrated with a reference force sensor. The hall effect

angle sensors were assembled to the transverse control arms in order to deter-

mine their angles and the normal load of the front tyres. The angle information


73

was also utilised to define the caster - and kingpin inclination angles of the steer-

ing axis. The compliance of the tyre defined the detectable measuring range of

the normal load to be around 200…700 kg.

The two axis velocity - and slip angle sensor was used for attaining the real ve-

locities in longitudinal and especially in lateral direction. Also it provided the op-

portunity to evaluate the axle-specific slip angles and obviously the slip angle of

the vehicle.

Proving Grounds and Experimental Tests

74

5 Proving Grounds and Experimental Tests

5.1 Introduction

For evaluating the operation of the friction estimation method, different road sur-

face conditions are needed. A brief investigation of the proving grounds near the

capital area showed that there isn’t any single track, which could provide both

high - and low friction circumstances for conducting steady-state cornering ma-

noeuvres. Thus two different proving grounds are chosen for performing the ex-

perimental tests.

The first experimental tests are performed at the Nokian Tyres plc proving

ground, which is located in Finland at the town of Nokia. The proving ground of

Nokian Tyres plc provides the circumstances for conducting steady-state corner-

ing manoeuvres on a typical Finnish road surface, which has high micro- and

macro-texture qualities. The second experimental tests are performed at the test

driving track of Uudenmaan Ajoharjoitteluradat plc, which is also located in

Finland at the town of Vantaa. The road surface of the test driving track of Uu-

denmaan Ajoharjoitteluradat plc is divided to three lanes. The inner- and outer-

most lanes of the circle are constructed from asphalt, which has almost similar

properties as the road surface of the circle in Nokia. The middle lane on the other

hand is constructed from a special type concrete, which provides extreme slip-

pery conditions. The three different types of experimental tests conducted at the

test driving track of Uudenmaan Ajoharjoitteluradat are explained thoroughly in

this chapter.

5.2 Proving Ground of Nokian Tyres

5.2.1 Overview

Figure 53 illustrates a view from the proving ground of Nokian Tyres plc. The

main objective of this work is to estimate the friction state of the front tyres in

steady-state cornering manoeuvre. The circle (number 2 in Figure 53) of the

proving ground of Nokian Tyres provides perfect circumstances for conducting

these manoeuvres on a typical Finnish road surface. The radius of the circle is

around 40 m and it contains also a system, which can make the surface wet.

Therefore tests both in dry - and wet conditions are performed.


75

Figure 53 The proving ground of Nokian Tyres plc [33]

5.2.2 Experimental Tests

The experimental tests at the proving ground of Nokian Tyres plc were executed

at the 12th of august in 2010. The weather at the proving ground site was sunny,

wind speed near zero and the ambient temperature around 25 C. Before the

tests began the inflation pressure of the tyres was set to 2.2 bars. Obviously the

inflation pressure of the tyres wouldn’t remain constant during tests, since the

tyres warm up. However the rise of the inflation pressure can be considered rela-

tively small. Altogether the inflation pressure shouldn’t have a major factor to the

friction estimation method presented in this master’s thesis. The tyres used in the

experimental tests were rather new non-studded Nokian WR G2 205/55R16 91H,

which are designed for Central European winter conditions (Figure 54). The tread

depth of the tyres was around 7 mm and the overall condition good.

Figure 54 Nokian WR2 [34]

Since the research vehicle was a front wheel driven car, the experimental tests

were performed with the clutch engaged and disengaged. Longitudinal forces


76

produce additional torques around the steering axis and therefore the clutch dis-

engaged tests represent the pure lateral slip situation. Although both tests with

clutch disengaged and engaged were performed, only the results of clutch disen-

gaged are presented in this master’s thesis, because the estimation method

doesn’t consider the combined slip situation.

The steady-state cornering tests at the circle followed the same pattern. First the

vehicle was accelerated to the specified speed and then the clutch was either

disengaged or not. The chosen driving speed was 60 km/h. It was empirically

tested that the maximum attainable driving speed in the circle was around 70

km/h (the peak of the blue curve in Figure 55). In the same empirical test it was

also noted that the friction potential with this specific road surface and tyres was

around 1.0 (the peak of the green curve in Figure 55), which was an anticipated

result.

Figure 55 Maximum attainable driving speed and the friction potential value in the circle on dry road surface

Obviously the experimental tests at the circle were initiated on dry conditions and

after that, the watering system was activated for gaining the wet conditions. Fig-

ure 56 represents the graphs of maximum attainable driving speed (the peak of

the blue curve) and the friction potential (the peak of the green curve) in wet con-

ditions. It wasn’t surprising that the graphs were almost identical with the graphs

of dry conditions. The high micro- and macro-texture qualities of the road surface

enabled a good contact with the tyre despite of the presence of water (Figure 17).

Since the results of the wet conditions were almost identical with the results of

0 20 40 60 800

10

20

30

40

50

60

70

80

[km

/h]

[s]

0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

[-]

[s]

Vx

potential


77

the dry condition, they don’t give any additional information and were therefore

left aside.

Figure 56 Maximum attainable driving speed and the friction potential value in the circle on wet road surface

5.3 Test Driving Track of Uudenmaan Ajoharjoitteluradat

5.3.1 Overview

Figure 57 gives an illustrative view of the test driving track of Uudenmaan Ajohar-

joitteluradat plc. The circle of the test driving track (number 1 in Figure 57) is di-

vided to three different types of road surfaces. The inner and outer lanes of the

circle are coated with similar asphalt as in the proving ground of Nokian Tyres

plc, thus providing high friction levels. The middle lane on the other hand is con-

structed from the previously mentioned special type of concrete, which enables

tests on low friction level road surface. In addition, the two distinctive road sur-

faces give an opportunity to test the friction estimation method in -split condi-

tions and in a situation where the vehicle is travelling from high - to low friction

level surface.

0 20 40 60 800

10

20

30

40

50

60

70

[km

/h]

[s]

Vx

0 20 40 60 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

[-]

[s]

potential


78

Figure 57 The test driving track of Uudenmaan Ajoharjoitteluradat plc [35]

5.3.2 Experimental Tests

The experimental tests at the test driving track of Uudenmaan Ajoharjoitteluradat

plc were executed at the 3rd of September in 2010. The weather at the test driv-

ing track was rainy, wind speed high and the ambient temperature around 7 C.

Thus the conditions of the test driving track were perfect for low friction level

tests. The setup of the research vehicle was identical to the tests at the proving

ground of Nokian Tyres plc.

The experimental tests were divided to three different manoeuvres:

Steady-state cornering on the slippery concrete

Steady-state cornering on -split road surface

Ramp steer from high - to low friction level road surface

Steady-state cornering manoeuvres on the slippery concrete followed the same

pattern as the tests at the proving ground of Nokian Tyres plc. First the vehicle

was accelerated to a specific driving speed (40 km/h) and then the clutch was

either disengaged or not. Since the estimation method doesn’t consider the com-

bined slip situation, only the results where the clutch was disengaged are illus-

trated in this master’s thesis.

In the -split experimental test, the vehicle was accelerated to the same driving

speed as in the steady-state cornering manoeuvre. After the desired driving

speed of 40 km/h was achieved, clutch was disengaged and the path of the vehi-

cle was kept in the middle of the different road surfaces. The left-hand side

wheels were on the high friction level surface and the right-hand side wheels on

the low friction level surface (Figure 58).


79

Figure 58 Steady-state cornering on μ-split road surface

The ramp steer manoeuvres were conducted between the outer high friction level

- and the middle low friction level surface. The driving direction was chosen to

counter clockwise direction for attaining better comparison between the previous

tests at the same test driving track. The manoeuvre itself began by accelerating

the vehicle to a driving speed of about 60 km/h on the high friction level surface.

After this the clutch was disengaged and the driver began to increase the steer-

ing wheel angle gradually. Thus the vehicle shifted towards the low friction level

surface. Obviously since the vehicle was travelling to counter clockwise direction,

the left-hand side wheels reached the low friction level surface before the right-

hand side wheels (Figure 59).

Figure 59 Ramp steer from high - to low friction level surface

LOW FRICTION LEVEL SURFACE

(CONCRETE)

HIGH FRICTION LEVEL SURFACE

(ASPHALT)


80


The experimental tests were implemented on two distinctive proving grounds.

The first experimental tests were performed at the proving ground of Nokian

Tyres plc. It provided the circumstances for testing the estimation method in typi-

cal Finnish road surface conditions. Steady-state cornering tests both in dry and -

wet conditions were executed. However since the road surface and the tyres pro-

vided good grip also in the wet conditions, no difference compared to the dry

conditions were observed. Therefore the results of the wet conditions were left

aside of this master’s thesis. The second experimental tests were conducted at

the test driving track of Uudenmaan Ajoharjoitteluradat plc. It provided the cir-

cumstances for steady-state cornering tests on low friction level road surface.

The circle at the test driving track of Uudenmaan Ajoharjoitteluradat plc was con-

structed of three different lanes. The inner - and outer lanes were coated with

asphalt and the middle lane with slippery concrete. Therefore it provided the op-

portunity for trying out the estimation method in -split conditions and in situation

where the vehicle was travelling from high friction surface to low friction level sur-

face.

Friction Estimation Method

81

6 Friction Estimation Method

6.1 Introduction

Chapter 4 introduced the required equipment and input signals for the friction

estimation. This chapter explains how the required input signals are exploited in

order to derive the complete friction state of the tyre. To start with the models of

the vehicle and the tyre are introduced.

The planar motion of the vehicle is modelled with the well-known single track

model, which provides the axle specific lateral force - and slip angle information

[1]. Literature is also familiar with the brush tyre model, which explains the force

generation of a tyre under lateral -, longitudinal - or combined slip situations [36].

Only the pure lateral slip situation is examined here, since the friction estimation

introduced in this master’s thesis assumes a pure cornering manoeuvre.

However the brush tyre model isn’t used to derive the forces and torques of the

tyre, but they are given to it as inputs. This provides an opportunity to exploit the

brush tyre model for estimating friction potential, - used and - available. The es-

timation principle together with the requirements and limitations are given in the

last subchapter. A proof of concept is also represented.

6.2 The Bicycle Model

6.2.1 Definition and Assumptions

There has to be a mathematical model of the actual vehicle for analysing its pla-

nar motion and handling characteristics. The bicycle model is in many cases a

sufficient tool for studying the handling of a vehicle. Since the bicycle model sim-

plifies the actual vehicle in many ways, there are several assumptions and re-

quirements that have to be taken into consideration. The assumptions and re-

quirements are listed below:

No lateral load transfer [1]

No longitudinal load transfer [1]

No rolling or pitching motions [1]

No chassis or suspension compliance effects [1]

Tyres have the same slip angle on the same axle [1]

Steering wheel angle and slip angles are small [1]


82

Constant forward velocity of the vehicle [1]

Resistance forces imposed on the vehicle are negligible [1]

Model is position controlled [1]

Despite the fact that, the model is called the bicycle model, it hasn’t got anything

to do with bicycles, motorcycles or any other kind of two-wheeled vehicles. The

bicycle model describes the planar motion of a four-wheeled vehicle, with the

assumptions listed above.

The free body diagram of the bicycle model in a cornering manoeuvre is illus-

trated in Figure 60. The origin of the vehicle axis system is fixed in the centre of

gravity of the vehicle. The orientation of the vehicle axis system is right-handed,

with -axis pointing forwards, -axis pointing rightwards and -axis pointing

downwards. In a cornering manoeuvre, the vehicle has longitudinal -, lateral -,

and angular velocity as illustrated in the Figure 60. Since the bicycle model as-

sumes constant forward velocity of the vehicle, there exist no longitudinal accel-

eration and therefore the model can be reduced to two degrees of freedom. The

remaining motion variables are the lateral velocity and the angular velocity

around the -axis (yaw velocity).

xv

yv

F

R

FlRl

v

Y

FyF ,

FFRF

FxF ,

X

Figure 60 The Free body diagram of the bicycle model

6.2.2 Equations of Motion

Equations of motion can be derived from the free body diagram (Figure 60). The

left hand side of the equation of motion contains the resultant lateral and longitu-

dinal forces and yawing moment that the tyres apply to the vehicle. Since there


83

don’t exist longitudinal accelerations, the applied longitudinal force by the tyres to

the vehicle is zero. The inertia terms are represented on the right-hand side of

the equations of motion.

(6.1)

Steering wheel angle and slip angles are assumed to be small and therefore the

sine - cosine - and tangent of an angle can be approximated in the following way.

(6.2)

With these approximations the front wheel lateral force can be evaluated from the

free body diagram.

(6.3)

The equations of motion can now be derived in the following form.

(6.4)

6.2.3 Lateral Tyre Forces and Slip Angles

By examining the equations of motion, it can be seen that the axle specific-lateral

tyre forces and are the only unknown variables. The determination of

the vehicle parameters and can be performed with simple meas-

urements. Vehicles equipped with ESC have sensors that can measure the lat-

eral acceleration and angular velocity about the -axis of the vehicle.

Hence the axle-specific lateral tyre forces are derived from the equations of mo-

tion.


84

(6.5)

For the friction estimation there is a need to determine the distribution of the

overall axle-specific lateral force to individual tyres. The approximation of the in-

dividual lateral tyre forces is done in respect to the normal load of the wheel in

question. Only the front axle’s individual tyre forces are of interest for the friction

estimation. It is suggested that the lateral force of the individual tyre is linearly

depend of the normal load ratio of the whole axle to the normal load of the single

wheel.

(6.6)

The velocity vector presentation of the bicycle model is illustrated in Figure 61. In

a cornering manoeuvre there exists a point called the instant centre of rotation,

which around the vehicle is moving. The position of this point is determined with

the sideslip angles of the vehicle and the front and rear tyres. These

three sideslip angles are defined by the ratio of lateral - and longitudinal velocities

at the position in question. Yet it has to be noticed that the front tyre is inclined by

the amount of steering angle . Therefore the sideslip angle in respect to the

tyre's direction of heading is the steering angle subtracted by the angle enclosed

by the lateral - and longitudinal velocity . At there exists only lateral- and

longitudinal velocity components. However the yawing velocity around the -axis

in , arises an additional component for the lateral velocity at the front

and rear tyre. Thus the sideslip angles are as illustrated in Figure 61.


85

xv

yv

F

R

X

FRRR

FlRl

v

CGR

yR vl

yF vl

Y

Instant center of

rotation

Rv

Fv

Figure 61 Velocity vector presentation of the bicycle model

The equations for the three sideslip angles can now be determined from the Fig-

ure 61. The assumption of small angles made in Equation 6.2 is still valid and

therefore the tangent of an angle is approximated to be equal with the angle.

(6.7)


86

6.3 The Brush Tyre Model

6.3.1 Definition and Assumptions

Brush tyre model is a simple and well-known approach to model the force gen-

eration of a tyre [36]. The investigation of force generation can be divided to pure

lateral -, pure longitudinal - and combined slip situations. A more detailed expla-

nation of the pure lateral slip situation will be given here.

Figure 62 represents a vehicle in a cornering manoeuvre, where no braking - or

tractive forces are transmitted through the tyres. Of course there always exists

some micro-slippage in the longitudinal direction, because of the natural forces

such as wind, surface irregularities, etc. However the effect of micro-slippage to

lateral force generation is small and can therefore be neglected.

F

Rv

X

Y

R

a

yF

a txpx

0

Fv

x

)(xqz

)(xq y

y

F

R

Fv

v

Fv

Rv

Figure 62 The brush tyre model (pure lateral slip situation)

The contact between the tyre and the road surface is modelled with a contact

line, which consist of rubber brush elements or bristles. These rubber brush ele-

ments are attached to the contact line (rim) at one end and the other end is


87

touching the road surface. The stiffness of the tyre carcass is therefore assumed

to be infinite, which implies inaccurate results compared to reality. A more realis-

tic behaviour can be obtained by modelling also the deformation of the carcass or

reducing the stiffness of the rubber brush element. [11] There are also several

other assumptions concerning brush tyre model and they are listed below:

Stiff carcass [37]

Rubber is linearly elastic [37]

Each brush element deforms independently in lateral and longitudinal di-

rections [37]

Normal load distribution follows a symmetric parabolic function [37]

An enlargement of the brush tyre model is illustrated on the right-hand side of

Figure 62. The angle enclosed by the centre line of the wheel and the direction of

wheel heading is defined as the slip angle . Wheel rolling with a slip angle

causes the rubber brush elements to deflect from their initial position ( ). The

first rubber brush element touches the road surface at the leading edge of the

contact line ( ) and the last brush element leaves the road surface at the

trailing edge of the contact line ( ). Thus the whole length of the contact

line is . The deflection of a rubber brush element at the point of the contact

line is defined as:

(6.8)

As the Figure 62 illustrates, the deflection of the individual rubber brush elements

enlarge from the leading edge to the trailing edge. However there’s a limit for the

maximum deflection, which is governed by the friction coefficient and normal load

distribution. The position, at the contact line, where the rubber brush element

meets the maximum deflection limit is called the transition point. The denomina-

tion, transition point, arises from the two regions that govern the contact line. Be-

fore the transition point, the rubber brush elements adhere to the road surface

and generate force directly proportional to their deformation and stiffness per unit

area . After the transition point, the rubber brush elements start to slide and the

force of individual rubber brush elements decrease to the maximum deflection

limit. Hence the names for these zones are adhesive – and sliding regions re-

spectively.


88

6.3.2 Determination of Normal Load Distribution and Contact Length

As mentioned previously, the normal load distribution of the tyre is commonly

assumed to follow a parabolic function. [37]

(6.9)

For a situation, where the tyre isn’t rolling, this assumption holds relatively well.

However, in a dynamic situation, where the tyre has to generate longitudinal and

lateral forces, the form of the normal load distribution will no longer be symmetric.

The effect of rolling resistance causes the position of the resultant vertical force

to shift closer to leading edge of the contact patch. Yet the position of the vertical

force resultant under longitudinal and lateral forces isn’t that obvious. It has been

suggested that the position of the resultant vertical force shifts towards the oppo-

site direction as the generated tyre force is working. However previous studies

have shown that the benefit from modelling the normal load distribution more

accurately is small compared to the complexity of resulting formulas. Therefore

the parabolic function for normal load distribution is also used in this master’s

thesis.

Obviously the length of the contact patch depends on the resultant vertical force

and therefore it had to be approximated experimentally. The measurements were

made with a static tyre footprint device, which is an outcome of another master’s

thesis. The main components of the static tyre footprint device are the two hy-

draulic cylinders and a glass plate. As the Figure 63 illustrates, the tyre is bolted

to a sledge, which is actuated by one of the hydraulic cylinders. The purpose of

the other hydraulic cylinder is to move the glass plate horizontally against the

tyre. Hence only the cylinder that presses the tyre against the glass plate was

needed for the contact patch length measurements.

Figure 63 Determining Contact Patch Length


89

The length of the contact patch was determined by using Fujifilm’s Prescale

measurement film. It consists of two sheets (A- and C-film), which are placed

facing each other between the place were the contact pressure is to be meas-

ured [38]. Here the sheets were attached to the glass plate of the static tyre foot-

print device. The operating principle of the measurement film is rather simple

(Figure 64). The A-film consists of colour forming microcapsules, which are bro-

ken under pressure. There are small and large microcapsules, which are broken

by low and high pressure respectively. The C-film contains the colour developing

material and together with the colour forming material of the microcapsules, red

patches appear on the C-film [38].

Figure 64 Operating principle of the Fujifilm Prescale measurement film [38]

The contact patch length measurements were made with eight different vertical

forces. After the measurements, all the figures were scanned in greyscale format

and processed in MATLAB. The upper left corner of Figure 65 illustrates the con-

tact pressure distribution with a vertical force of 3217 N. The graph in the lower

left corner of Figure 65 represents the mean values of the contact pressure dis-

tribution in the longitudinal direction and the graph in the upper right corner

represents the mean values of the contact pressure distribution in the lateral di-

rection. The longitudinal length of the contact patch is evaluated from the graph

with data cursors as shown. The other graphs from different vertical forces are

represented in Appendix A2.


90

Figure 65 Contact pressure distribution and contact patch length with a vertical force of 3217 N

6.3.3 Complete Adhesion

Rubber brush elements are assumed to generate force directly proportional to

their deformation and stiffness per unit area . The deflection of a rubber brush

element as a function of contact patch position was determined previously in

Equation 6.8. Thus the lateral force distribution is defined as:

(6.10)

The above equation for lateral force distribution holds true for the entire contact

area, if the frictional force is large enough to deflect the rubber brush elements.

This denotes that the friction coefficient tends to infinity and the slip angle tends

to zero. Therefore the rubber brush elements adhere to the road surface and no

sliding is occurring. The resultant lateral force and self aligning torque are

attained by integrating the lateral force distribution over the contact length. The

500 1000 1500 2000

500

1000

1500

2000

2500

0 20 40 60 80 100 120 1400

20

40

60

80

100

X: 120.1

Y: 2.121

x[mm]

X: 6.858

Y: 1.738

0 20 40 60 80 100

-160

-140

-120

-100

-80

-60

-40

-20

0

y[m

m]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a

[m

m]

100 150 200 250


91

force lever arm, pneumatic trail , is obtained by dividing the self aligning torque

with the resultant lateral force.

(6.11)

In the case of complete adhesion the resultant lateral force and self aligning

torque depend only of the slip angle, contact length and lateral tread element

stiffness. Pneumatic trail has a constant value, which is one third of half of the

contact length.

6.3.4 Adhesion and Sliding

In reality the friction coefficient has a finite value and the slip angle of the tyre can

reach much larger values than close to zero. Hence the contact patch is divided

to adhesion and sliding regions as explained previously. The lateral force distri-

bution is governed by the friction coefficient and the normal load distribution, in

the sliding region.

(6.12)

The resultant lateral force and self aligning torque are obtained similarly as in the

complete adhesion case, but now the integration divides obviously to adhesive -

and sliding regions.

(6.13)

By calculating the integrals of Equation 6.13, the resultant lateral force and self

aligning torque become:


92

(6.14)

The above equations can be described in simpler forms by introducing a factor ,

which represents the length of the adhesion region in percentage.

(6.15)

The transition point is solved from the Equation 6.15 and substituted in Equation

6.14. Thus the transition point is eliminated and the resultant lateral force and self

aligning torque is derived in the following form.

(6.16)

The next step is to eliminate the lateral tread element stiffness factor and for this

a composite tyre model parameter is introduced.

(6.17)

The tread element stiffness factor is solved and substituted in Equation 6.16.

Hence the resultant lateral force and self aligning torque become:

(6.18)

By substituting , the equations for resultant lateral force and self

aligning torque become depended only from the normal load, friction coefficient,

half of the contact length and the factor .

(6.19)

As in the complete adhesion case, the lateral force distribution isn’t symmetrical

and therefore the resultant lateral force doesn’t act in the middle of the contact

area, but at a distance, pneumatic trail , from the origin.


93

(6.20)

Friction coefficient is eliminated in the calculation of the pneumatic trail and it

depends only of the contact length and the factor .

6.3.5 Complete sliding

All the rubber brush elements are sliding, if the friction coefficient is low and/or

the slip angle is very large. As the Figure 66 implies, the larger the slip angle is,

the larger the sliding region becomes and the closer to the origin the pneumatic

trail diminishes. Simultaneously the self aligning torque diminishes to zero, be-

cause the force lever arm tends to zero.

a

yF

a txpx

0

Fv

x

)( xq z

)(xq y

y

a2a2

a2

a

0

0px

tx

aa

)(xq z

y

yF

)(xq y

x

a

yF

y )(xq y)( xq z

tx

x

Fv

Fv

Figure 66 Brush Tyre Model with different slip angles: small - (left), moderate - (middle) and large slip angle (right)

The resultant lateral force is governed only by the friction coefficient and the

normal load distribution. Because the normal load distribution is assumed to be

symmetrical, the resultant lateral force acts in the middle of the contact and

hence pneumatic trail and self aligning torque are zeros.

(6.21)


94

6.4 Friction Estimation in Pure Lateral Slip Situation

6.4.1 Principle

The previous subchapters introduced the fundamental tools for the friction esti-

mation. Figure 67 clarifies how these tools are implemented in order to derive the

friction potential, - used and - available. The large red arrows in Figure 67 repre-

sent the required input signals for the friction estimation. They are divided to five

categories by the origin of the signal. The blue boxes inside the grey friction es-

timation box, illustrates the main tools for the estimation. The needed input sig-

nals of each tool are represented with small red arrows. The output of each tool

is illustrated with small green arrows.

Figure 67 Principle of friction estimation

All of the tools have been introduced previously in the work. Therefore they aren’t

examined again in this subchapter. However since the brush tyre model is the

heart of the friction estimation, its behaviour is looked through carefully. To start

with the previously introduced equations for lateral force, aligning torque (Equa-

tion 6.19) and pneumatic trail (Equation 6.20) are made independent of the nor-

mal force of the tyre.


95

(6.22)

As it can be seen from the previous equations, the new dimensionless variables

are only depended of the friction coefficient and the factor . Figure 68 illus-

trates the behaviour of these dimensionless variables with various friction coeffi-

cient values against the slip angle of the tyre. The primary -axis of Figure 68 is

divided between the normalised lateral force (upper part) and the normalised

pneumatic trail (lower part). The secondary -axis is devoted to the normalised

aligning torque, which are represented with dash-dotted lines. The line styles of

the normalised lateral force and - pneumatic trail are solid and dashed respec-

tively.

Figure 68 Normalised lateral force (solid), aligning torque (dash-dotted) and pneu-matic trail (dashed) versus the slip angle

A noticeable fact from the previous Figure 68 is that the normalised aligning

torque reaches its maximum well before the normalised lateral force saturates.

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

-0,50

-0,40

-0,30

-0,20

-0,10

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0 5 10 15 20 25 30 35 40 45 50

Mz/

aFz

Fy/

F z

α[°]

mu = 0,25 mu = 0,5 mu = 0,75 mu = 1,0

x p/a


96

Therefore the normalised aligning torque provides a possibility to estimate friction

potential before the tyre is totally sliding. On the other hand when the tyre is to-

tally sliding, both the normalised pneumatic trail and the aligning torque tends to

zero, which hinders the use of aligning torque to friction estimation. The sensitiv-

ity of the normalised lateral force and - aligning torque are discussed in the next

subchapter.

By observing the previously derived equations of normalised lateral force, - align-

ing torque and - pneumatic trail (Equation 6.22), it’s noticed that there are three

equations and only two unknown variables. This provides a possibility to evaluate

the friction potential separately as a function of normalised lateral force and -

aligning torque. Equation 6.23 represents the friction potential as function of the

normalised lateral force and the factor .

(6.23)

The friction potential derived from the normalised aligning torque is represented

in Equation 6.24.

(6.24)

Both of the previous equations contain also the other unknown variable, which is

the factor . One approach of solving the factor would be placing the previ-

ous equations equal, but the result is a 3rd degree function, which doesn’t have

an unambiguous solution. However the equation of normalized pneumatic trail

can be exploited for evaluating the factor . The equation of normalised pneu-

matic trail is only depended of the factor , which signifies that a specific value

of normalised pneumatic trail corresponds to a specific value of the factor .

Therefore a look-up table can be constructed, which takes the normalised pneu-

matic trail as an input and gives out the corresponding value of factor (Table

2).

Table 2 Factor and the corresponding value of normalised pneumatic trail

λ [-]

0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00

xp / a [-]

0,0000 0,0009 0,0065 0,0194 0,0410 0,0714 0,1102 0,1566 0,2098 0,2690 0,3333


97

The above table can also be illustrated as a graph, which is presented in Figure

69.

Figure 69 Factor as a function of normalised pneumatic trail

6.4.2 Requirements and Limitations

There are several requirements and limitations that have to be taken into consid-

eration when estimating friction by using the brush tyre model. First of all the fric-

tion estimation is only eligible when there actually exists lateral slip, which gives

arise to the required input signals lateral force and aligning torque. Therefore a

part of the contact area must be in the sliding region in order to get eligible fric-

tion estimates. Figure 70 illustrates the degree of adhesion region in percentages

with various friction values. Together with the sensitivity graph (Figure 71), it can

be observed that the normalised aligning torque is most sensitive to friction coef-

ficient, when the adhesion region is around 70…80 % of the whole contact area.

Hence normalised aligning torque provides good estimates of the friction poten-

tial without forcing the tyre to its limits.

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0,0000 0,0500 0,1000 0,1500 0,2000 0,2500 0,3000 0,3500

λ[-

]

xp / a [-]


98

Figure 70 Size of the adhesion region in percentages as a function of the slip angle

However, the sensitivity of the normalised aligning torque to friction coefficient

begins to deteriorate after the adhesion region drops under 70 % values. The

dashed-dotted curves in Figure 71 represent the sensitivity of the normalised

aligning torque to friction coefficient. On the other hand the sensitivity of the nor-

malised lateral force to the friction coefficient increases as the adhesion region

diminishes. The solid curves in Figure 71 represent the sensitivity of the normal-

ised lateral force to friction coefficient.

As it can be observed from Figure 71, the sensitivity of the normalised aligning

torque diminishes to zero as the sensitivity of the normalised lateral force

reaches the maximum. Therefore a conclusion can be made that the normalised

aligning torque is more eligible for friction potential estimation under small slip

angles and moderate driving manoeuvres. The normalised lateral force is more

favourable under larger slip angles and fierce driving manoeuvres to the friction

potential estimation.

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0 5 10 15 20 25 30 35 40 45 50

λ[-

]

α[°]

mu = 0,25 mu = 0,50 mu = 0,75 mu = 1,00


99

Figure 71 Sensitivity of Fy and Mz to friction coefficient

The previous conclusion is also visible in the Gough-plot, which illustrates the

normalised lateral force as a function of the normalised aligning torque (Figure

72). The fierce cornering manoeuvre can be observed from the Gough-plot, when

the normalised aligning torque is zero. At this position the whole contact area is

in the sliding region and the full friction potential is in use. As the aligning torque

is zero it’s useless for the friction estimation. However under moderate cornering

manoeuvres, where there actually exists aligning torque it can be used to the

friction estimation. Especially when the aligning torque reaches its maximum, it’s

more favourable to the estimation than the lateral force. The transition to full ad-

hesion occurs swiftly after the normalised aligning torque has reached its maxi-

mum and the normalised lateral force is decreasing. In the full adhesion region

the curves with different friction coefficient values coincide and therefore the fric-

tion estimation is impaired.

0,00

0,02

0,04

0,06

0,08

0,10

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0 5 10 15 20 25 30 35 40 45 50

Sen

siti

vity

of M

zto

µ

Sen

siti

vity

of F

y to

µ

α[°]

mu = 0,25 mu = 0,50 mu = 0,75 mu = 1,00


100

Figure 72 Gough plot with varying friction coefficients and brush element stiffness

Figure 72 holds another interesting fact about the friction estimation. In the brush

tyre model the individual bristles are assumed to generate force directly propor-

tional to the deformation and the stiffness of the bristles. An intuition would say

that the friction estimation is depended of the stiffness of the bristle, but this isn’t

the case. The red squares, yellow circles and black triangles illustrate different

stiffness of the bristles in Figure 72. As it can be seen the curves with the same

friction coefficient values, but varying bristle stiffness are overlapping. Thus, as-

serting that the estimation of friction is invariant of the bristle stiffness.

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,10 0,11 0,12

Fy/

F z

Mz/aFz

mu = 0,25 | c_y = 0,5 mu = 0,25 | c_y = 0,8 mu = 0,25 | c_y = 1,1

mu = 0,50 | c_y = 0,5 mu = 0,50 | c_y = 0,8 mu = 0,50 | c_y = 1,1

mu = 0,75 | c_y = 0,5 mu = 0,75 | c_y = 0,8 mu = 0,75 | c_y = 1,1

mu = 1,00 | c_y = 0,5 mu = 1,00 | c_y = 0,8 mu = 1,00 | c_y = 1,1


101

6.4.3 Proof of Concept

The graphs illustrated in this chapter have been plotted with four different friction

potential values ( 0,25, 0,50, 0,75 and 1,00). The proof of con-

cept of the friction estimation can be demonstrated by attaining these friction po-

tential values from the normalised lateral force and aligning torque. Figure 73

illustrates the friction potential estimation only from the normalised aligning

torque data. Obviously with zero slip angle the estimation of friction potential is

infeasible, since the aligning torque is zero. Similarly the estimation is impaired

after the whole contact area is sliding. Between these limits the aligning torque

provides information for estimating friction potential.

Figure 73 Friction potential estimation of the normalised aligning torque

Actually both the lateral force and the aligning torque are essential information for

attaining the complete friction state of the tyre. Figure 74 depicts the friction po-

tential (solid lines), - used (dashed lines) and - available (dashed-dotted lines)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5 10 15 20 25 30 35 40 45 50

µ[-

]

α[°]

mu = 0,25 mu = 0,50 mu = 0,75 mu = 1,00


102

values in respect to the slip angle. Friction potential is attained quickly after the

slip angle arises from the zero point. Obviously friction available is high in the

beginning, since very little amount of the friction potential is in use. However, as

the friction used increases, the friction available decreases with same phase.

Figure 74 Simulation results of friction potential, - used and – available

6.4.4 Implementation

The introduced friction estimation method is implemented with Matlab/Simulink

software (MathWorks, Inc.). The developed Simulink model is compiled to an

executable file and uploaded to the rapid prototyping computer (Figure 75).

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5 10 15 20 25 30 35 40 45 50

µ[-

]

α[°]

mu = 0,25 | Friction potential mu = 0,25 | Friction used mu = 0,25 | Friction available


mu = 0,75 | Friction potentia mu = 0,75 | Friction used mu = 0,75 | Friction available



103

Figure 75 Simulink model of the entire friction estimation method

A user interface is created with ControlDesk software (dSPACE), which repre-

sents all the essential sensor information and the estimated friction states of the

front tyres. In addition to the illustrative user interface, ControlDesk software

(dSPACE) is exploited to data acquisition for processing the information later on.


The bicycle model represented the methods to evaluate the axle specific forces

and slip angles. The individual lateral forces of the front tyres were suggested to

be directly proportional to the normal load distribution of the front axle. The axle

specific slip angles were assumed to be the same with left- and right-side tyres.

The equations of lateral force, aligning torque and pneumatic trail were derived

by using the brush tyre model. Only the pure lateral slip situation was repre-

sented, with three different cases (complete adhesion, adhesion and sliding,

complete sliding).

Since the brush tyre model is the heart of the friction estimation, its behaviour

was further explained together with the principle of the estimation procedure. The


104

equations of lateral force, aligning torque and pneumatic trail were made inde-

pendent of load. These three equations provided an opportunity to solve the fric-

tion potential as a function of the normalised lateral force or the - aligning torque.

The sensitivity of the normalised lateral force and - aligning torque to friction coef-

ficient was investigated with various different friction coefficient values. A conclu-

sion was drawn that the normalised aligning torque is most sensitive to friction

coefficient, when the size of the adhesion region is around 70…80 % of the

whole contact area. Therefore providing feasible conditions for friction estimation

without, forcing the tyre to its limits. The sensitivity of the normalised lateral force

to the friction coefficient was found to increase as the adhesion region diminished

to zero. The effects of different brush element stiffness to the friction estimation

were investigated. It was noted that the friction estimation is invariant to varying

brush element stiffness.

The proof of concept from simple simulated data illustrated that the friction esti-

mation by using the brush tyre model is feasible.

Proving Ground Results and Discussion

105

7 Proving Ground Results and Discussion

7.1 Introduction

The proving grounds and the experimental tests were presented thoroughly in

Chapter 5. The purpose of this chapter is to illustrate the results from these ex-

perimental tests and discuss about them.

As described in Chapter 5, two distinctive proving grounds are used for investi-

gating the operation of the friction estimation method. The proving ground of

Nokian Tyres plc provided the circumstances for conducting steady-state corner-

ing manoeuvres on high friction level surface. The second experimental tests

were performed at the test driving track of Uudenmaan Ajoharjoitteluradat plc.

The circle at the test driving track of Uudenmaan Ajoharjoitteluradat gave an op-

portunity to three distinguished test manoeuvres, which were explained thor-

oughly in Chapter 5.

For clarification purposes, the blue curves of the graphs presented in this chapter

denote always to the properties of the left-hand side wheel and the red curves to

the properties of the right-hand side wheel. The green coloured curves, which

appear in the brush tyre model graphs, represent the averages of the left- and

right-hand side curves.

7.2 Steady-State Cornering

7.2.1 High Friction Level Road Surface

The steady-state cornering manoeuvres on high friction level road surface were

performed at the proving ground of Nokian Tyres plc. Measurements were re-

peated several times to both counter clockwise - and clockwise directions. How-

ever since the results were almost identical to both directions, only the results of

the clockwise direction are presented here.

The sensor data of the vehicle and the optical velocity sensor are illustrated in

Figure 76. As it can be seen, first the vehicle was accelerated to a driving speed

of about 55 km/h and then the clutch was disengaged at 1.516 s. Obviously

from this point forward the vehicle started to decelerate, which is also visible in

the lateral acceleration graph ( ) and the longitudinal velocity graph ( ). The

aspiration was to keep the radius of the steady-state cornering manoeuvre at a


106

constant level, which was the reason why the driver had to make some adjust-

ments to the steering wheel angle during the manoeuvre.

Figure 76 Vehicle data (60 km/h and clutch disengaged at t = 1.516 s)

The total self aligning torque ( ) together with the torques that arise from the

caster trail ( ) and the pneumatic trail ( ) are illustrated in Figure 77. The

evaluation of these torques were represented in Chapter 4. In addition Figure 77

contains the tie rod forces ( , ) -, lateral forces ( , ) - and normal

forces ( , ) of the front wheels. Obviously, since the cornering manoeuvre

was performed to clockwise direction, the normal - and lateral force of the outside

(left) wheel was higher. The total self aligning torque together with the torques

that arose from the caster - and the pneumatic trail were also higher on the left

side, since the normal - and lateral force of the left wheel was higher.

1 2 3 4 5 6 7 8-8

-6

-4

-2

0[m

/s2]

[s]

ay

1 2 3 4 5 6 7 8151719212325

[deg/s

]

[s]

psidot

1 2 3 4 5 6 7 8-80

-75

-70

-65

-60

[deg]

[s]

swa

1 2 3 4 5 6 7 80

1

X: 1.516

Y: 0[on/o

ff]

[s]

clutch

1 2 3 4 5 6 7 840

45

50

55

60

[km

/h]

[s]

Vx

1 2 3 4 5 6 7 8-1

-0.8-0.6-0.4-0.2

0

[km

/h]

[s]

Vy

1 2 3 4 5 6 7 8-10

-5

0

5

10

[deg]

[s]

F

R


107

Figure 77 Torque and force data (40 km/h and clutch disengaged at t = 1.516 s)

The factors that are related to the brush tyre model are represented in Figure 78.

One of the most interesting graphs in Figure 78 is the area of adhesion region.

As noticed in the sensitivity examination of the self aligning torque and lateral

force to the friction estimation, the ideal range of the area of adhesion region was

about 70…80 % (Chapter 6). In this particular experimental test, the area of ad-

hesion region of the left-hand side tyre was just around this ideal zone. Thus pro-

viding, perfect circumstances to friction estimation. The area of adhesion region

of the right-hand side tyre was around 60 %, which wasn’t in the best possible

range, but still adequate for friction estimation. By observing all of the graphs in

Figure 78, it can be concluded that the brush tyre model was modelled correctly.

The variables are within reasonable range and compared with each other they

have plausible values.

1 2 3 4 5 6 7 80

30

60

90

120

150

[Nm

]

[s]

Mz,totL

Mz,totR

1 2 3 4 5 6 7 80

20

40

60

80

100

[Nm

]

[s]

Mz,L

Mz,R

1 2 3 4 5 6 7 80

10

20

30

40

50

60

[Nm

]

[s]

Mz,pL

Mz,pR

1 2 3 4 5 6 7 8500

1000

1500

2000

2500

[N]

[s]

FTRL

FTRR

1 2 3 4 5 6 7 81000

1500

2000

2500

3000

3500

4000

[N]

[s]

FyFl

FyFr

1 2 3 4 5 6 7 83000

3500

4000

4500

5000

5500

6000

[N]

[s]

FzFl

FzFr


108

Figure 78 Brush tyre model data (60 km/h and clutch disengaged at t = 1.516 s)

The friction state curves of the front tyres are presented in Figure 79. Although

the road surface of the proving ground was homogeneous, there was clearly a

slight difference between the estimation of friction potential on the left- and right-

hand side tyre. The estimated friction potential value of the right-hand side was a

bit lower than of the left-hand side. One conceivable reason inflicting this differ-

ence was that the measured and calculated inputs for the estimation weren’t ab-

solutely correct. Other reason for the difference could have been the fact that the

sensitivity of the right-hand side tyre’s self aligning torque to the friction estima-

tion wasn’t in the best possible zone, which impaired the friction estimation.

1 2 3 4 5 6 7 80.06

0.062

0.064

0.066

0.068

0.07

0.072

0.074

0.076

[m]

[s]

aL

aR

1 2 3 4 5 6 7 8-0.02

-0.018

-0.016

-0.014

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

[m]

[s]

xpL

xpR

xp

1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

[-]

[s]

L

R

1 2 3 4 5 6 7 8-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

[m]

[s]

xtL

xtR

xt


109

Figure 79 Friction state of the front tyres (clutch disengaged at t = 2.104 s)

There were two friction potential estimates for both left- and right-hand side tyres

(Chapter 6). The friction potential graphs denoted with subscript 01 were derived

from the self aligning torque (Equation 6.24) and the friction potential graphs de-

noted with subscript 02 were derived from the lateral force (Equation 6.23). The

definitions of the subscripts are the same in the upcoming friction state graphs.

Friction used of both front tyres was around 0.6 in the beginning of the experi-

ment. Obviously as the driving speed and the lateral acceleration began to de-

crease, the friction used diminished also. Friction available on the other hand

started to increase, in the same phase as the friction used was decreasing.

7.2.2 Low Friction Level Road Surface

The steady-state cornering manoeuvres on low friction level surface were per-

formed at the test driving track of Uudenmaan Ajoharjoitteluradat plc. Measure-

ments were conducted to both directions as on the high friction level surface.

Demonstrating that the estimation method works regardless of the cornering di-

rection, the results of the low friction level surface are presented to the opposite

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

potentialL01

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

potentialR01

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

potentialL02

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

potentialR02

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

usedL

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

usedR

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

availableL

1 2 3 4 5 6 7 80

0.20.40.60.8

11.2

[-]

[s]

availableR


110

direction as on the high friction level surface. Thus the sensor data of the vehicle

and the optical velocity sensor in Figure 80 are to counter clockwise direction,

which appears also from the sign of the steering wheel angle. In the high friction

level surface tests, the radius of the cornering manoeuvre was attempted to be

kept at a constant level. Therefore the driver had to make some adjustments to

the steering wheel angle during the cornering manoeuvre. Since these adjust-

ments seemed to produce additional noise to the measurements, an effort was

made to hold the steering wheel in constant position in the low friction surface

tests. The disengagement of the clutch occurred at 5.272 s (Figure 80). Since

the estimation method didn’t consider the combined slip situation, the graphs

should be examined from this point forward.

Figure 80 Vehicle data (clutch disengaged at t = 5.272 s)

On the low friction level surface, lateral force and self aligning torque were sub-

stantially smaller compared to the high friction level surface (Figure 81). Also the

differences of the forces and torques between the left- and right-hand sides were

notably smaller on the low friction level surface. Still, since the vehicle was cor-

5 6 7 8 9 102

2.5

3

3.5

4

[m/s

2]

[s]

ay

5 6 7 8 9 10-20-18-16-14-12-10

[deg/s

]

[s]

psidot

5 6 7 8 9 1070

80

90

100

[deg]

[s]

swa

5 6 7 8 9 100

1

X: 5.272

Y: 0[on/o

ff]

[s]

clutch

5 6 7 8 9 10303234363840

[km

/h]

[s]

Vx

5 6 7 8 9 101

2

3

[km

/h]

[s]

Vy

5 6 7 8 9 10-10

-5

0

5

10

[deg]

[s]

F

R


111

nering to counter clockwise direction, the forces and torques of the right-hand

side were larger.

Figure 81 Torque and force data (clutch disengaged at t = 5.272 s)

The graphs related to the brush tyre model illustrate the same facts that the dif-

ferences between the right- and left-hand sides were rather small (Figure 82).

The approximated half of the contact length was only about 5…6 mm longer on

the right-hand side tyre. The area of the adhesion region, pneumatic trail and

transition point were also of the same size on both sides. After the disengage-

ment of the clutch, the area of the adhesion region began to rise up as the driving

speed decreased. Pneumatic trail was near zero in the beginning of the test, but

as the area of adhesion region expanded, it moved closer to the trailing edge of

the tyre. Obviously the behaviour of the transition point followed the behaviour of

the pneumatic trail and moved towards the trailing edge of the tyre.

5 6 7 8 9 1040

45

50

55

60

65

70[N

m]

[s]

Mz,totL

Mz,totR

5 6 7 8 9 1020

25

30

35

40

45

50

[Nm

]

[s]

Mz,L

Mz,R

5 6 7 8 9 100

5

10

15

20

25

30

[Nm

]

[s]

Mz,pL

Mz,pR

5 6 7 8 9 10600

700

800

900

1000

[N]

[s]

FTRL

FTRR

5 6 7 8 9 101000

1200

1400

1600

1800

2000

[N]

[s]

FyFl

FyFr

5 6 7 8 9 104000

4200

4400

4600

4800

5000

[N]

[s]

FzFl

FzFr


112

Figure 82 Brush tyre model data (clutch disengaged at t = 5.272 s)

The friction states of the front tyres on the low friction level surface are repre-

sented in Figure 83. The evaluated friction potential values were almost exactly

the same on both sides. However for some reason the approximated friction po-

tential values increased towards the end of the experiment. The area of the ad-

hesion region was in the ideal range, which signifies that it wasn’t the reason for

the incorrect approximation. Therefore the most likely source of error was found

from the measurements and the evaluation of some variables as the force lever

arm of the self aligning torque.

5 6 7 8 9 100.062

0.063

0.064

0.065

0.066

0.067

0.068

0.069

0.07

0.071

0.072

[m]

[s]

aL

aR

5 6 7 8 9 10-0.02

-0.018

-0.016

-0.014

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

[m]

[s]

xpL

xpR

xp

5 6 7 8 9 10

0.2

0.4

0.6

0.8

1

[-]

[s]

L

R

5 6 7 8 9 10-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

[m]

[s]

xtL

xtR

xt


113


Friction used was around 0.4 in the beginning of the experiment, but it decreased

as the driving speed decreased. Friction available gave rather plausible values

for the whole experiment. In the beginning of the experiment it was around 0.1

and in the end of the experiment it rose up to around 0.35-0.40 level (Figure 83).

7.2.3 -split Road Surface

Since the circle at the Uudenmaan Ajoharjoitteluradat was divided to three differ-

ent lanes, it gave a possibility to test the friction estimation method in -split

situation. The left-hand side tyres were on the inner high friction level surface and

the right-hand side tyres on the middle low friction level surface. Thus the driving

direction was to counter clockwise direction.

Figure 84 illustrates the exact time, when the clutch was disengaged in this par-

ticular -split manoeuvre ( 5.248 s). During the steady-state cornering ma-

noeuvre, the driver had to make some adjustments to the steering wheel angle

for attaining the -split situation.

5 6 7 8 9 100

0.20.4

0.60.8

1

[-]

[s]

potentialL01

5 6 7 8 9 100

0.20.4

0.60.8

1

[-]

[s]

potentialR01

5 6 7 8 9 100

0.20.40.60.8

1

[-]

[s]

potentialL02

5 6 7 8 9 100

0.20.40.60.8

1

[-]

[s]

potentialR02

5 6 7 8 9 100

0.20.40.60.8

1

[-]

[s]

usedL

5 6 7 8 9 100

0.20.40.60.8

1

[-]

[s]

usedR

5 6 7 8 9 100

0.20.40.60.8

1

[-]

[s]

availableL

5 6 7 8 9 100

0.20.40.60.8

1

[-]

[s]

availableR


114


The torque and force graphs in Figure 85 provide many interesting observations

of the -split experiment. Obviously, as the vehicle was travelling to counter

clockwise direction, the normal force of the right-hand side tyre was larger than of

the left-hand side tyre. However, by examining the tie rod force graph, an obser-

vation can be made that the force of the left-hand side tie rod was higher. This

fact alone tells that the friction level on the left-hand side must have been consid-

erable higher.

Another interesting fact is found from the lateral force graph (Figure 85). The lat-

eral force of the front axle was derived from the bicycle model and the distribution

of this force to left - and right side was made according to the normal load of the

tyre (Chapter 6). Since the normal load of the right tyre was higher, the model

distributed a greater amount of lateral force to the right-hand side tyre. In this

particular -split situation, the distribution method can be questioned, since the

tie rod force of the left hand side was higher. The torque arising from the caster

trail was also derived from the lateral force information and therefore the torque

5 6 7 8 9 103

3.5

4

4.5

5

[m/s

2]

[s]

ay

5 6 7 8 9 10-30

-25

-20

-15

-10

[deg/s

]

[s]

psidot

5 6 7 8 9 10507090

110130150

[deg]

[s]

swa

5 6 7 8 9 100

1

X: 5.248

Y: 0[on/o

ff]

[s]

clutch

5 6 7 8 9 10303234363840

[km

/h]

[s]

Vx

5 6 7 8 9 100

1

2

3

[km

/h]

[s]

Vy

5 6 7 8 9 10-10

-5

0

5

10

[deg]

[s]

F

R


115

on the right hand side was probably too high. In any case the torques arising

from the pneumatic trail seemed to get plausible values on both sides.


The half of contact length on the right-hand side tyre was about 7…8 mm longer

than on the left-hand side tyre (Figure 86). Although the contact area was larger

on the right-hand side tyre, it was completely sliding for the first three seconds.

Since the clutch was disengaged, the driving speed dropped gradually and the

sliding region of the right-hand side tyre began to diminish. At the same time, the

area of the adhesion region of the left-hand side tyre was near 100 %, which sig-

nified that the friction potential on that side had to be much higher.

The same facts can also be observed from the transition point graph (Figure 86).

For the first three seconds, the transition point of the right-hand side tyre was

located at the leading edge of the contact, which signified that the whole contact

was sliding. After the first three seconds, the transition point shifted towards the

trailing edge of the contact. On the other hand the left-hand side tyre was under

full adhesion since the transition point was located at the trailing edge of the con-

tact.

5 6 7 8 9 1040

60

80

100

120[N

m]

[s]

Mz,totL

Mz,totR

5 6 7 8 9 1030

40

50

60

70

[Nm

]

[s]

Mz,L

Mz,R

5 6 7 8 9 100

10

20

30

40

50

60

[Nm

]

[s]

Mz,pL

Mz,pR

5 6 7 8 9 10500

700

900

1100

1300

1500

[N]

[s]

FTRL

FTRR

5 6 7 8 9 101000

1300

1600

1900

2200

2500

[N]

[s]

FyFl

FyFr

5 6 7 8 9 104000

4200

4400

4600

4800

5000

[N]

[s]

FzFl

FzFr


116

Since the right-hand side tyre was totally sliding for the first three seconds, the

torque arising from the pneumatic trail and therefore the pneumatic trail itself

should have been zeros. However by examining the graphs they weren’t. The

incorrectness rose presumably from the previously mentioned derivation of the

lateral force distribution.


The friction states of the front tyres in -split experiment are illustrated in Figure

87. The most interesting and expected result can be seen from the right-hand

side tyre’s friction potential graph, which was derived by using the self aligning

torque information. As it was noticed already in the proof of concept chapter, the

total sliding situation prohibited the use of self aligning torque for the friction po-

tential estimation. For the first three seconds, the friction potential of the right-

hand side tyre was incorrect. After that, some adhesion was attained and the

friction potential of the right-hand side tyre was plausible. However the friction

potential derived by using the lateral force information provided plausible esti-

mates of the friction potential for the whole time of the experiment.

The friction potential values evaluated from the left-hand side self aligning torque

and lateral force gave the same result, which was 1.0. The area of adhesion on

5 6 7 8 9 100.062

0.063

0.064

0.065

0.066

0.067

0.068

0.069

0.07

0.071

0.072

[m]

[s]

aL

aR

5 6 7 8 9 10-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

[m]

[s]

xpL

xpR

xp

5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

[-]

[s]

L

R

5 6 7 8 9 10-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

[m]

[s]

xtL

xtR

xt


117

the left-hand side was almost 100 %, which itself signified a good contact be-

tween the tyre and the road surface.


Friction used was around 0.4 on both the left- and right-hand side tyre. On the

right-hand side tyre, the friction potential was fully utilised and therefore there

wasn’t any friction available. However on the left-hand side there was still about

0.6 friction available, since it was on the high friction level surface.

7.3 Ramp Steer from High - to Low Friction Level Road

Surface

The outer high friction level surface and the middle low friction level surface of

Uudenmaan Ajoharjoitteluradat plc were used to the ramp steer manoeuvres. In

this particular test the vehicle was driven to counter clockwise direction. Thus the

left hand tyres entered the low friction level surface before the right hand side

tyres. As Figure 88 illustrates the vehicle was accelerated to a driving speed of

about 60 km/h and the clutch was disengaged at 1.156 s. For the time inter-

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialL01

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialR01

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialL02

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialR02

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

usedL

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

usedR

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

availableL

5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

availableR


118

val 0…5 seconds, the vehicle travelled entirely on the high friction level surface.

At the point 5.0 s, the driver began to steer the vehicle towards the low friction

level surface.


Lots of interesting information is again found from the torque and force graphs

(Figure 89). First observation is that after the disengagement of the clutch, all the

curves are rather constant until the ramp steering input at 5.0 s. Obviously

some descend of the curves is evident, since the driving speed was decreasing.

The first significant change in the curves occurs at the point 6.0 s, where the

tie rod force of the left-hand side wheel drops considerably. The same fact is

clearly visible in the total self aligning torque graph. At this specific point, the left-

hand side tyre shifted to the low friction level surface. At the same time, the force

of the right-hand side tie rod increased notably. This was due to the fact that as

the left hand side tyre entered the low friction surface it couldn’t transmit the

same size lateral as before. Therefore since the right hand side tyre was still on

the high friction level surface, it was able to counteract to the loss of left-hand

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

[m/s

2]

[s]

ay

0 1 2 3 4 5 6 7 8 9 10-30

-20

-10

0

[deg/s

]

[s]

psidot

0 1 2 3 4 5 6 7 8 9 1060

90

120

150

180

[deg]

[s]

swa

0 1 2 3 4 5 6 7 8 9 100

1

X: 1.156

Y: 0[on/o

ff]

[s]

clutch

0 1 2 3 4 5 6 7 8 9 100

20

40

60

[km

/h]

[s]

Vx

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

[km

/h]

[s]

Vy

0 1 2 3 4 5 6 7 8 9 10-15-10-505

1015

[deg]

[s]

F

R


119

side’s lateral force. However at the point 7.5, the force of the right-hand side

tie rod began to drop also. As both of the front tyres entered the low friction level

surface, the torques that arose from the pneumatic trails descended to near zero

values. This signified a total sliding situation as explained in Chapter 6.


The same conclusion of the full sliding situation is evident in the data related to

the brush tyre model (Figure 90). The left-hand side tyre’s area of adhesion curve

drops to zero after the point 6.0 s, which was the point of transition to the low

friction level surface. The area of adhesion of the right-hand side tyre began to

descend towards zero at the point 7.5, which clearly indicated that it entered

to the low friction surface.

Also the pneumatic trail and transition point graphs illustrate the fact of full sliding

situation (Figure 90). Until the change of the surface, the pneumatic trail of the

left-hand side tyre was around -10 mm and after the surface changed it shifted

towards zero. The pneumatic trail of the right-hand side tyre behaved in the same

way. First it was around -15 mm and after the change of the surface it shifted

0 1 2 3 4 5 6 7 8 9 100

50

100

150

200

[Nm

]

[s]

Mz,totL

Mz,totR

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

[Nm

]

[s]

Mz,L

Mz,R

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

[Nm

]

[s]

Mz,pL

Mz,pR

0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

2000

2500

[N]

[s]

FTRL

FTRR

0 1 2 3 4 5 6 7 8 9 100

500100015002000250030003500

[N]

[s]

FyFl

FyFr

0 1 2 3 4 5 6 7 8 9 103800

4100

4400

4700

5000

5300

5600

[N]

[s]

FzFl

FzFr


120

towards zero. Both the left-hand - and right-hand sides’ transition points moved

towards the leading edge of the contact as the surface changed to the slippery

concrete.


In the previous -split experiments it was noted, that the full sliding situation pro-

hibited the use of self aligning torque to estimation of the friction potential. The

same fact was also evident in this experiment. The topmost graphs in Figure 91

represent the results of the friction potentials, which were evaluated from the self

aligning torque information. As the tyre entered to the slippery surface, the friction

potential estimated from the self aligning torque was incorrect. However the fric-

tion potential evaluated by using the lateral force information gave plausible val-

ues for the whole time of the experiment.

0 1 2 3 4 5 6 7 8 9 100.06

0.062

0.064

0.066

0.068

0.07

0.072

0.074

0.076

[m]

[s]

aL

aR

0 1 2 3 4 5 6 7 8 9 10-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

[m]

[s]

xpL

xpR

xp

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

[-]

[s]

L

R

0 1 2 3 4 5 6 7 8 9 10-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1[m

]

[s]

xtL

xtR

xt


121


Friction used on the high friction level surface was around 0.6, but as the tyre

entered the low friction level surface, it dropped to about 0.4. Until the transition

of the surface there was about 0.4 friction available, but after the transition, fric-

tion potential was fully utilised.

7.4 Conclusion of this Chapter

The estimation method functioned rather well in the steady-state cornering tests

at the proving ground of Nokian Tyres plc. The operating point of the tyres, that is

the friction used, was around 0.6 and the evaluated friction potential showed a

value around 1.0. However the approximated friction potential of the right-hand

side tyre was a bit lower than of the left-hand side tyre. The most likely reason

inflicting this difference was that the measured and calculated inputs for the esti-

mation weren’t absolutely correct.

The steady-state cornering tests on the low friction level surface at the test driv-

ing track of Uudenmaan Ajoharjoitteluradat plc gave also plausible results. One

interesting observation was that the differences between the torques and forces

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialL01

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialR01

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialL02

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

potentialR02

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

usedL

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

usedR

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

availableL

0 1 2 3 4 5 6 7 8 9 100

0.20.40.60.8

11.2

[-]

[s]

availableR


122

of left and right side were considerably smaller than on the high friction level sur-

face. The friction potential of both tyres showed a value around 0.4, which

seemed plausible for that surface and that set of tyres.

A clear distinction between the left- and right-hand side friction potential esti-

mates was observed in the -split experimental tests. The left-hand side tyre was

on the high friction level surface and the estimated friction potential was around

1.0, which was plausible in those conditions. The right-hand side tyre was on the

low friction level surface and the estimated friction potential was around 0.4,

which was also plausible. However the derivation and distribution method of the

lateral tyre forces were questioned in this particular case.

In the experimental tests, where the vehicle was travelling from the high friction

level surface to the low friction level surface, the estimated friction potential

changed according to the road surface. However the same fact was observed as

in the -split tests, that the total sliding situation of the tyre prohibited the use of

self aligning torque information to the friction estimation. Still the lateral tyre force

information could be exploited to the estimation of friction potential in this situa-

tion.

Conclusions and Recommendations

123

8 Conclusions and Recommendations

The objective of this master’s thesis was to study the feasibility of using the front

tyres lateral force and aligning torque information to friction potential estimation.

Since the estimation method exploited the actual forces and torques that were

generated in the tyre-road interface, it classifies to the direct friction estimation

method category. The direct estimation methods need a certain amount of excita-

tion before the obtained friction potential can be considered eligible. Suitable ex-

citation method for this study was the steady-state cornering manoeuvre.

Mathematical models of the vehicle and the tyre were required for this particular

estimation method. The planar behaviour of the vehicle was modelled with the

bicycle model, which provided the axle specific lateral forces. The lateral force of

the front axle was differentiated between left- and right side in accordance with

the normal load distribution of the front tyres. The normal load of the front tyres

were attained from the angle sensors, which were installed to the transverse con-

trol arms. The same angle sensors were exploited for deriving the caster - and

kingpin inclination angles of the steering axes. The caster angle produces an

additional torque around the steering axis, which had to be subtracted from the

total aligning torque. Hence the torque that arose from the tyre itself was distin-

guished. The tie rods of the front wheels were assembled with piezoelectric force

sensors for gaining the total aligning torques around the steering axes.

The force generation of the tyre-road interface was modelled with the brush tyre

model. Thus it can be considered as the heart of the estimation method. Often

the brush tyre model is used for attaining the lateral force and the aligning torque

information as outputs, but in this master’s thesis they were given as inputs to it.

Therefore the brush tyre model could be exploited for evaluating the friction po-

tential of the tyre-road interface.

There were several assumptions concerning the brush tyre model, which most

likely introduced inaccuracy to the estimation. Especially the assumption of stiff

carcass and symmetric parabolic normal load distribution were substantial gen-

eralizations compared to reality. Both of these have an effect to the estimation,

but in what way and how significant they are requires further investigations. One

method for modelling the carcass flexibility can be found from [36]. Examination

of this method is one of the starting points for future studies. Another foundation


124

for future work is to upgrade the brush tyre model to combined slip situation. The

pure lateral slip model works well for rear wheel driven cars, since the longitudi-

nal slip of the front wheels is rather small. However with front wheel driven cars,

the longitudinal slip has a substantial effect to the lateral force and especially to

aligning torque.

The accuracy of the presented friction estimation method was directly depended

of the measured and calculated input variables:

Lateral force

Normal force

Aligning torque

These forces and torques were measured and calculated with various methods,

which undoubtedly produced error to the estimation. Therefore they should have

been validated with reference sensors. Perfect tool for this purpose would have

been the 6-component measuring wheel. For future studies, it’s essential to per-

form the validation of these input variables before conducting the actual proving

ground tests. In addition the estimation method should have been tested with

some simulation software (e.g. IPG: CarMaker) before proceeding to the experi-

mental phase. Attention especially for modelling the front suspension and the

steering system should be paid. The tie rod moves as a function of the steering

angle and the suspension travel, which makes the derivation of the force lever

arm of the aligning torque rather challenging. Thus by modelling the front sus-

pension and the steering system accurately with CarMaker or ADAMS, the force

lever arm can be attained as a function of the steering angle and the suspension

travel.

The experimental tests of the estimation method were divided to two different

proving grounds. The proving ground of Nokian Tyres plc provided the circum-

stances for conducting experimental tests on a typical Finnish road surface. The

second experimental tests were performed at the test driving track of Uuden-

maan Ajoharjoitteluradat plc, which provided extreme slippery conditions. There-

fore the estimation method was tested on both high - and low friction level sur-

faces. In addition, the second proving ground gave an opportunity to try the esti-

mation method in -split conditions and in a situation where the vehicle was trav-

elling from a high friction level surface to a low friction level surface.


125

Steady-state cornering manoeuvres from both proving grounds showed that the

estimation method was able to give plausible values of friction used, - potential

and - available. However some deviation between the friction estimates of inner -

and outer tyre was observed. Measurement - and calculation errors were the

most likely reasons for this deviation. Especially the simplified calculation of the

force lever arm may have caused error to the self aligning torque and thus to the

estimation. The most interesting results were found from the -split - and the sur-

face transition tests. The different road surfaces in the -split situation were dis-

tinguished and both (left - and right side) estimates were in the range of plausi-

ble. Yet it was also discovered that the method for deriving the lateral tyre forces

might not have been adequate in this heterogeneous road surface situation.

Therefore the previously suggested reference sensor system would have been

essential for validating that the input signals are realistic even in these kinds of

road conditions. The results from the surface transition tests illustrated also

clearly the points where the front wheels shifted from one surface to another.

The results gathered from the proving ground tests showed that this particular

friction estimation method has potential. However lots of work and further studies

have to be conducted before this method can assist the modern active safety

systems and the upcoming ADAS systems.

Bibliography

126

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Appendix A1: Vehicle and tyre parameters

130

Appendix A1: Vehicle and tyre parameters

General

Make Volkswagen (VW)

Model Golf Variant 1,9 Comfort

Dimensions

Curb weight 1590 kg

Total -moment of Inertia 3156,6 kgm2

Wheelbase 2,57 m

distance from the front axle

1,09 m

distance from the rear axle

1,48 m

Height of the above ground

0,58 m

Track width 1,60 m

Steering ratio 14,96

Tyres

Make and model Nokian WR G2

Size 205/55R16 91 H

Tyre pressure 2,2 bar

Appendix A2: Contact pressure distribution and contact patch length

131

Appendix A2: Contact pressure distribution and

contact patch length

Fz = 1608 N

0.5 600.5 1200.5

500

1000

1500

2000

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

X: 81.6

Y: 1.206

x [mm]

X: 6.16

Y: 1.165

0 20 40 60 80-160

-140

-120

-100

-80

-60

-40

-20

0

y [

mm

]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a

[m

m]

100 150 200 250


132

Fz = 2413 N

500 1 000 1 500

500

1000

1500

2000

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

X: 6.032

Y: 1.208

x[mm]

X: 102

Y: 1.424

0 20 40 60 80-160

-140

-120

-100

-80

-60

-40

-20

0

y[m

m]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a [m

m]

100 150 200 250


133

Fz = 3217 N

500 1000 1500 2000

500

1000

1500

2000

2500

0 20 40 60 80 100 120 1400

20

40

60

80

100

X: 120.1

Y: 2.121

x[mm]

X: 6.858

Y: 1.738

0 20 40 60 80 100

-160

-140

-120

-100

-80

-60

-40

-20

0

y[m

m]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a

[m

m]

100 150 200 250


134

Fz = 4021 N

500 1000 1500 2000

500

1000

1500

2000

2500

0 20 40 60 80 100 120 1400

20

40

60

80

100

X: 8.7

Y: 1.471

x[mm]

X: 135.3

Y: 1.763

0 20 40 60 80 100-170

-150

-130

-110

-90

-70

-50

-30

-10

y[m

m]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a

[m

m]

100 150 200 250


135

Fz = 4825 N

500 1000 1500 2000

500

1000

1500

2000

2500

0 20 40 60 80 100 120 140 1600

20

40

60

80

100

X: 6.858

Y: 1.62

x[mm]

X: 146.1

Y: 1.601

0 20 40 60 80 100

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

y[m

m]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a

[m

m]

100 150 200 250


136

Fz = 5630 N

500 1000 1500 2000 2500

500

1000

1500

2000

2500

0 20 40 60 80 100 120 140 1600

20

40

60

80

100

X: 7.43

Y: 1.432

x[mm]

X: 158

Y: 1.328

0 20 40 60 80 100-180

-160

-140

-120

-100

-80

-60

-40

-20

0

y[m

m]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a

[m

m]

100 150 200 250


137

Fz = 6434 N

500 1000 1500 2000 2500

500

1000

1500

2000

2500

0 20 40 60 80 100 120 140 160 1800

20

40

60

80

100

X: 174

Y: 1.279

x[mm]

X: 7.62

Y: 1.059

0 20 40 60 80 100-180

-160

-140

-120

-100

-80

-60

-40

-20

0

y[m

m]

0 2000 4000 6000 800060

70

80

90

100

110

120

130

140

150

160

170

180

Fz [N]

2a [m

m]

100 150 200 250

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