Tyre Friction Potential Estimation by Aligning Torque and Lateral Force Information

137 Pages·2010·4.5 MB·English

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.)
AALTO UNIVERSITY ABSTRACT OF THE MASTER’S THESIS
SCHOOL OF SCIENCE AND TECHNOLOGY
PO Box 11000, FI-00076 AALTO
http://www.aalto.fi
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 DIPLOMITYÖN TIIVISTELMÄ
TEKNILLINEN KORKEAKOULU
PL 11000, 00076 Aalto
http://www.aalto.fi
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

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Acknowledgements

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

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Table of Contents

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

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Table of Contents

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
3.5 Conclusions of this Chapter .................................................................42
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
4.5 Conclusions of this Chapter .................................................................72

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Table of Contents

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
5.4 Conclusions of this Chapter .................................................................80
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

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Table of Contents

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

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Symbols and Definitions

Symbols and Definitions
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

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Symbols and Definitions

VELOCITIES
AND M EANING
ACCELERATIONS
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 MEANING
TORQUES
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

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