Bergamo University Italy12th-14th June 2012

Professor Mike BlundellPhd, MSc, BSc (Hons), FIMechE, CEng

Lecture 6 – Tyre Force and Moment Characteristics

mt

kzcz

δ

z

{Zsae}

1

{Xsae}

1

P

SAE Tyre Axis System

2

{Ysae}1{Zsae}1

{Xsae}1

P

γ

α

Spin Axis

{V}1

Angular Velocity (ω)Wheel Torque (T)

WC

Direction of Wheel Heading

Direction of Wheel Travel

Lateral Force (Fy)Normal Force (Fz)

Tractive Force (Fx)

ISO Tyre Axis System

3

Normal Force (Fz)

{Yiso}1

{Ziso}1

{Xiso}1

P

γ

α

Spin Axis

{V}1

Angular Velocity (ω)Wheel Torque (T)

WC

Direction of Wheel Heading

Direction of Wheel Travel

Lateral Force (Fy)

Tractive Force (Fx)

Definition of Tyre Radii

4

ω

P

VRu

AB

Rl

FrontRear

Re

C

Generation of Tyre Lateral Forces due to Conicity

5

FY

FY

YSAE

YSAE

XSAE

XSAE

Direction of Travel

Left

Right

Generation of Tyre Lateral Forces due to Plysteer

6

XSAE

YSAE

XSAE

FY

Left

Right

Direction of Travel

YSAE

FY

YSAE

FY

YSAE

FY

Frictional Force Component due to Adhesion

7

Direction of Sliding

Tyre Material

Road Surface

Adhesive Forces due to Molecular Bonding

Hysteresis in Rubber

8

F

δ

F

δ

Unloading

Loading

Loading and Unloading of Tyre Rubber in the Contact Patch

9

Direction of Sliding

Road Surface

Unloading

Loading

Pressure Distribution in a Stationary Tyre Contact Patch

10

Over Inflation

Normal Inflation

Under InflationPressure Distribution in the Tyre Contact Patch

Tyre Contact Patch

Tyre Forces and Moments Shown Acting in the SAE Tyre Axis System

11

{Ysae}1

{Zsae}

1

{Xsae}1

P

γ

α

Spin Axis

Rolling ResistanceMoment (My)

WC

Lateral Force(Fy)

Normal Force(Fz)

Tractive Force(Fx)

Self Aligning Moment

(My)

Overturning Moment

(Mx)

Measurement of Stiffness in a Non-Rolling Tyre

12

φ

Fx

Fy

δy

δx

Tz

Fx

δx

Longitudinal Stiffness

Fy

δy

Lateral Stiffness

Tz

φ

Torsional Stiffness

Vertical Tyre Force Model Based on a Linear Spring Damper

13

mt

kzcz

δz

{Zsae}1

{Xsae}1

P

Generation of Slip in a Free Rolling Tyre

14

ω

V= ω Re

Rl

Rear

Re

O

Vt = ω Ru

Ru

TreadMaterial

Compression

Front

Vt = ω Rl

Vt = ω Re

Vt = ω Ru

Direction of slip relative to the road surface

{Xsae}1

Longitudinal Shear Stress

Tangential velocity of tread relative to O

B PD C A

Vt = ω Re

Lateral Distortion of the Contact Patch for a Free Rolling Tyre

15

Lateral slip movement(Moore, 1975)

FrontRear

Un-deformed Tyre

Deformed Tyre

Squirm through the contact patch (Gillespie, 1992)

Generation of Rolling Resistance in a Free Rolling Tyre

16

ω

FRxO

δx

Fz

Fz

FRx

P

Rl

Rear {Xsae}1Front

My = Fz δx

Generation of Force in a Braked Tyre

17

ω

V = ω Re

Rear

O

Compression

Front

{Xsae}1

Tread Def.

TB

TensionFB

PressureDistribution

LongitudinalSlip

LongitudinalShear Stress

δxFz

Braking Force versus Slip Ratio

18

0.0 Slip Ratio 1.0

Fz = -2 kN

Fz = -4 kN

Fz = -6 kN

Fz = -8 kN

Braking Force versus Slip Ratio

Slip Angle = 0Camber Angle = 0

Longitudinal Stiffness Cs = tan φφ

BrakingForceFx (N)

The Effect of Road Contamination on Braking

19

0.0 Slip Ratio 1.0

Aquaplaning

Good Tread on Wet Road

Dry Road

Braking Force versus Slip Ratio

Slip Angle = 0Camber Angle = 0

BrakingForceFx (N)

Poor Tread on Wet Road

Generation of Force in a Driven Tyre

20

V = ω Re

ω

Rear

O

Compression

Front

{Xsae}1

Tread Def.

TD

Tension

FD

LongitudinalShear Stress

PressureDistribution

δxFz

LongitudinalSlip

Forces and Moments due to Slip and Camber Angle

21

Slip Angle Camber Angle

Lateral Force Camber Thrust

Lateral Force

Camber ThrustPneumatic

TrailAligning Moment

due to slip angle

AligningMoment due to camber

angle

γ

α

Direction of Travel Direction of Travel

Generation of Lateral Force and Aligning Moment due to Slip Angle

22

Limit Lateral Stress μp

Direction of Wheel Heading

Pressure p

Front Rear

Direction of Wheel Travel

α

Slipping Starts

Slipping Starts

Lateral Stress

Lateral Stress

Fy

Pneumatic Trailxpt

Mz = Fy xpt

Side View

Top View

Tyre Contact Patch

Plotting Lateral Force versus Slip Angle

23

-Slip Angle α (degrees)

Fz = -2 kN

Fz = -4 kN

Fz = -6 kN

Fz = -8 kN

Lateral Force versus Slip Angle

Camber Angle = 0

Lateral ForceFy (N)

Cornering Stiffness Cs = tan φ

φ

Plotting Aligning Moment versus Slip Angle

24

Slip Angle α (degrees)

Fz = -2 kN

Fz = -4 kN

Fz = -6 kN

Fz = -8 kN

Aligning Moment versus Slip Angle

Camber Angle = 0

AligningMomentMz (Nm)

Aligning Moment Stiffness = tan φ

φ

Generation of Lateral Force due to Camber Angle

25

Spin Axis

Camber Thrust Fy

{Ysae}1

{Zsae}1

γ

Resultant Force FR

Tyre Load Fz

Plotting Lateral Force versus Camber Angle

26

Camber Angle γ (degrees)

Fz = -2 kN

Fz = -4 kN

Fz = -6 kN

Fz = -8 kN

Lateral Force versus Camber Angle

Slip Angle = 0

Lateral ForceFy (N)

Camber Stiffness Cγ = tan φφ

Generation of Self Aligning Moment due to Camber Angle

27

A B C

A C B C

{Ysae}1

{Xsae}1

A Fy

Mz

Front

Rear

Spin Axis

A C Camber Thrust Fy{Ysae}1

{Zsae}1

γ

B

Plotting Aligning Moment Versus Camber Angle

28

Camber Angle γ (degrees)

Fz = -2 kN

Fz = -4 kN

Fz = -6 kN

Fz = -8 kN

Aligning Moment versus Camber Angle

Slip Angle = 0

AligningMomentMz (Nm)

Aligning Moment Camber Stiffness = tan φ φ

The Effect of Combined Camber and Slip Angle on Lateral Force

29

-Slip Angle α (degrees)

Lateral Force versus Slip AngleLateral ForceFy (N)

Camber Angle = 0Camber Angle = 5Camber Angle = 10

Generation of Overturning Moment in the Tyre Contact Patch

30

y

Fz

PYSAE

Wheel Plane

OWheel Centre

ZSAE

Mx = Fz δy

Slip Angle

y

Fz

PYSAE

O

Camber Angle

ZSAE

Mx=Fzδy

Pure and Combined Braking and Cornering Forces

31

Direction ofTravel

YSAE

XSAE

Maximum Cornering ForceFy = μ Fz

Large Slip Angle α Pure Cornering

α

Fy = μ Fz

Fy

Direction of Travel

YSAE

XSAE

Maximum Braking Force Fx = μ Fz

ContactPatch

Pure Braking

S

Fx = μ Fz

Fy

Direction ofTravel

YSAE

XSAE

Maximum RoadPlane Force

FR = μ Fz

Fy

Fx

Combined Braking and Cornering

Large Slip Angle α

Direction of Travel

YSAE

XSAE Braking Force Fx

Fy

Combined Braking and Cornering

Moderate Slip Angle α

ContactPatch

ContactPatch

ContactPatch

Plotting Lateral Force Against Longitudinal Force (Friction Circle)

32

Friction Circle

Braking Force Fx Driving Force Fx

Lateral Force Fy

α =1

α =2

α =6

α =10

α =4

A B

C

D

Resultant Force FR

Development of Lateral Force Following Step Steering Input

33

Time (sec)

Lateral Force versus timeLateral ForceFy (N)

t1t0 t2

Fymax

0.632 Fymax

Steady State

High Speed Dynamics Machine for Tyre Testing Formerly at Dunlop Tyres Ltd.

34

Courtesy of Dunlop Tyres Ltd.

Flat Bed Tyre Test Machine at Coventry University

35

Lateral Force Fy with Slip Angle α

36

Courtesy of

Dunlop Tyres Ltd.

Aligning Moment Mz with Slip Angle α

37

Courtesy of

Dunlop Tyres Ltd.

Lateral Force Fy with Aligning Moment Mz (Gough Plot)

38

Courtesy of

Dunlop Tyres Ltd.

Cornering Stiffness with Load

39

Courtesy of

Dunlop Tyres Ltd.

Aligning Stiffness with Load

40

Courtesy of

Dunlop Tyres Ltd.

Lateral Force Fy with Camber Angle α

41

Courtesy of

Dunlop Tyres Ltd.

Aligning Moment Mz with Camber Angle α

42

Courtesy of

Dunlop Tyres Ltd.

Camber Stiffness with Load

43

Courtesy of

Dunlop Tyres Ltd.

Aligning Camber Stiffness with Load

44

Courtesy of

Dunlop Tyres Ltd.

Braking Force with Slip Ratio

45