1. Lecture 6 – Tyre Force and Moment Characteristics
Bergamo University
Italy
12th-14th June 2012
Lecture 6 – Tyre Force and Moment Characteristics mt kz cz
δ z
{Zsae} 1
{Xsae} 1 P
Professor Mike Blundell
Phd, MSc, BSc (Hons), FIMechE, CEng

2. SAE Tyre Axis System γ Angular Velocity (ω) Wheel Torque (T) Spin Axis
{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)

3. ISO Tyre Axis System {Ziso}1 Normal Force (Fz) γ Angular Velocity (ω)
{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)

4. Definition of Tyre Radiiω P V Ru A B Rl
Front
Rear Re C

5. Generation of Tyre Lateral Forces due to ConicityFY
YSAE
XSAE
Direction of Travel
Left
Right

6. Generation of Tyre Lateral Forces due to Plysteer
XSAE
YSAE FY
Left
Right
Direction of Travel

7. Frictional Force Component due to Adhesion
Direction of Sliding
Tyre Material
Road Surface
Adhesive Forces due to Molecular Bonding

8. Hysteresis in Rubber F δ
Unloading
Loading

9. Loading and Unloading of Tyre Rubber in the Contact Patch
Direction of Sliding
Road Surface
Unloading
Loading

10. Pressure Distribution in a Stationary Tyre Contact Patch
Over Inflation
Normal Inflation
Under Inflation
Pressure Distribution in the Tyre Contact Patch
Tyre Contact Patch

11. Tyre Forces and Moments Shown Acting in the SAE Tyre Axis System
{Ysae}1
{Zsae}1
{Xsae}1 P γ α
Spin Axis
Rolling Resistance
Moment (My) WC
Lateral Force
(Fy)
Normal Force
(Fz)
Tractive Force
(Fx)
Self Aligning Moment
(My)
Overturning Moment
(Mx)

12. Measurement of Stiffness in a Non-Rolling Tyreφ Fx Fy δy δx Tz
Longitudinal Stiffness
Lateral Stiffness
Torsional Stiffness

13. Vertical Tyre Force Model Based on a Linear Spring Dampermt kz cz δz
{Zsae}1
{Xsae}1 P

14. Generation of Slip in a Free Rolling Tyreω
V= ω Re Rl
Rear Re O
Vt = ω Ru Ru
Tread
Material
Compression
Front
Vt = ω Rl
Vt = ω Re
Direction of slip relative to the road surface
{Xsae}1
Longitudinal Shear Stress
Tangential velocity of tread relative to O B P D C A

15. Lateral Distortion of the Contact Patch for a Free Rolling Tyre
Lateral slip movement
(Moore, 1975)
Front
Rear
Un-deformed
Tyre
Deformed
Squirm through the contact patch (Gillespie, 1992)

16. Generation of Rolling Resistance in a Free Rolling Tyreω
FRx O δx Fz P Rl
Rear
{Xsae}1
Front
My = Fz δx

17. Generation of Force in a Braked Tyreω
V = ω Re
Rear O
Compression
Front
{Xsae}1
Tread Def. TB
Tension FB
Pressure
Distribution
Longitudinal
Slip
Shear Stress δx Fz

18. Braking Force versus Slip Ratio
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Braking Force versus Slip Ratio
Slip Angle = 0
Camber Angle = 0
Longitudinal Stiffness
Cs = tan φ φ
Braking
Force
Fx (N)

19. The Effect of Road Contamination on Braking
Slip Ratio
Aquaplaning
Good Tread on Wet Road
Dry Road
Braking Force versus Slip Ratio
Slip Angle = 0
Camber Angle = 0
Braking
Force
Fx (N)
Poor Tread on Wet Road

20. Generation of Force in a Driven Tyre
V = ω Re ω
Rear O
Compression
Front
{Xsae}1
Tread Def. TD
Tension FD
Longitudinal
Shear Stress
Pressure
Distribution δx Fz
Slip

21. Forces and Moments due to Slip and Camber Angle
Slip Angle
Camber Angle
Lateral Force
Camber Thrust
Pneumatic
Trail
Aligning Moment due to slip angle
Aligning
Moment due to camber angle γ α
Direction of Travel

22. Generation of Lateral Force and Aligning Moment due to Slip Angle
Limit Lateral Stress μp
Direction of Wheel Heading
Pressure p
Front
Rear
Direction of Wheel Travel α 
Slipping Starts
Lateral Stress Fy
Pneumatic Trail
xpt
Mz = Fy xpt
Side View
Top View
Tyre Contact Patch

23. Plotting Lateral Force versus Slip Angle
-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 Force
Fy (N)
Cornering Stiffness
Cs = tan φ φ

24. Plotting Aligning Moment versus Slip Angle
Slip Angle α (degrees)
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Aligning Moment versus Slip Angle
Camber Angle = 0
Aligning
Moment
Mz (Nm)
Aligning Moment Stiffness = tan φ φ

25. Generation of Lateral Force due to Camber Angle
Spin Axis
Camber Thrust Fy
{Ysae}1
{Zsae}1 γ 
Resultant Force FR
Tyre Load Fz

26. Plotting Lateral Force versus Camber Angle
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 Force
Fy (N)
Camber Stiffness
Cγ = tan φ φ

27. Generation of Self Aligning Moment due to Camber Angle A B C A C B
C
{Ysae}1
{Xsae}1
A Fy Mz
Front
Rear
Spin Axis
Camber Thrust Fy
{Zsae}1 γ

28. Plotting Aligning Moment Versus Camber Angle
Camber Angle γ (degrees)
Fz = -2 kN
Fz = -4 kN
Fz = -6 kN
Fz = -8 kN
Aligning Moment versus Camber Angle
Slip Angle = 0
Aligning
Moment
Mz (Nm)
Aligning Moment Camber Stiffness = tan φ φ

29. The Effect of Combined Camber and Slip Angle on Lateral Force
-Slip Angle α (degrees)
Lateral Force versus Slip Angle
Lateral Force
Fy (N)
Camber Angle = 0
Camber Angle = 5
Camber Angle = 10

30. Generation of Overturning Moment in the Tyre Contact Patchdy Fz P
YSAE
Wheel Plane O
Wheel Centre
ZSAE
Mx = Fz δy
Slip Angle
Camber Angle
Mx=Fzδy

31. Pure and Combined Braking and Cornering Forces
Direction of
Travel
YSAE
XSAE
Maximum Cornering Force
Fy = μ Fz
Large Slip Angle α
Pure Cornering α Fy
Direction of Travel
Maximum Braking Force
Fx = μ Fz
Contact
Patch
Pure Braking S
Maximum Road
Plane Force
FR = μ Fz Fx
Combined Braking and Cornering
Braking Force Fx
Moderate Slip
Angle α

32. Plotting Lateral Force Against Longitudinal Force (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

33. Development of Lateral Force Following Step Steering Input
Time (sec)
Lateral Force versus time
Lateral Force
Fy (N) t1 t0 t2
Fymax
0.632 Fymax
Steady State t

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

35. Flat Bed Tyre Test Machine at Coventry University

36. Lateral Force Fy with Slip Angle α
Courtesy of
Dunlop Tyres Ltd.

37. Aligning Moment Mz with Slip Angle α
Courtesy of
Dunlop Tyres Ltd.

38. Lateral Force Fy with Aligning Moment Mz (Gough Plot)
Courtesy of
Dunlop Tyres Ltd.

39. Cornering Stiffness with Load
Courtesy of
Dunlop Tyres Ltd.

40. Aligning Stiffness with Load
Courtesy of
Dunlop Tyres Ltd.

41. Lateral Force Fy with Camber Angle α
Courtesy of
Dunlop Tyres Ltd.

42. Aligning Moment Mz with Camber Angle α
Courtesy of
Dunlop Tyres Ltd.

43. Camber Stiffness with Load
Courtesy of
Dunlop Tyres Ltd.

44. Aligning Camber Stiffness with Load
Courtesy of
Dunlop Tyres Ltd.

45. Braking Force with Slip Ratio