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

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)

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)

Definition of Tyre Radii ω P V Ru A B Rl Front Rear Re C

Generation of Tyre Lateral Forces due to Conicity FY YSAE XSAE Direction of Travel Left Right

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

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

Hysteresis in Rubber F δ Unloading Loading

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

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

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)

Measurement of Stiffness in a Non-Rolling Tyre φ Fx Fy δy δx Tz Longitudinal Stiffness Lateral Stiffness Torsional Stiffness

Vertical Tyre Force Model Based on a Linear Spring Damper mt kz cz δz {Zsae}1 {Xsae}1 P

Generation of Slip in a Free Rolling Tyre ω 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

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)

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

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

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)

The Effect of Road Contamination on Braking 0.0 Slip Ratio 1.0 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Flat Bed Tyre Test Machine at Coventry University

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

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

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

Cornering Stiffness with Load Courtesy of Dunlop Tyres Ltd.

Aligning Stiffness with Load Courtesy of Dunlop Tyres Ltd.

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

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

Camber Stiffness with Load Courtesy of Dunlop Tyres Ltd.

Aligning Camber Stiffness with Load Courtesy of Dunlop Tyres Ltd.

Braking Force with Slip Ratio