The Multibody Systems Approach to Vehicle Dynamics

Transcription

1 The Multibody Systems Approach to Vehicle Dynamics A Short Course Lecture 4 Tyre Characteristics Professor Mike Blundell Phd, MSc, BSc (Hons), FIMechE, CEng

2 Course Agenda Day 1 Lecture 1 Introduction to Vehicle Dynamics Lecture 2 Multibody Systems Simulation Software Day 2 Lecture 3 Modelling and Analysis of Suspension Systems Lecture 4 Tyre Characteristics Lecture 5 Tyre Modelling Day 3 Lecture 6 Modelling and Analysis of the Full Vehicle Discussion and Wrap Up Close

3 Contents Lecture 4 Tyre Characteristics Tyre Axis- Systems Definition of Radii Friction Mechanisms Forces and Moments Combined Slip Tyre Testing Sample Data

4 SAE Tyre Axis System Angular Velocity (ω) Wheel Torque (T) γ Spin Axis P WC Direction of Wheel Heading Tractive Force {X sae } (F 1 x ) α {V} 1 Direction of Wheel Travel Normal Force (F z ) {Z sae } 1 {Y sae } 1 Lateral Force (F y )

5 ISO Tyre Axis System {Z iso } 1 Normal Force (Fz) Angular Velocity (ω) Wheel Torque (T) γ Spin Axis {Y iso } 1 WC Direction of Wheel Heading Tractive Force (Fx) {X iso } 1 Lateral Force (Fy) P α {V} 1 Direction of Wheel Travel

6 Definition of Tyre Radii ω R u V R l R e Rear B P C A Front

7 Generation of Tyre Lateral Forces due to Conicity X SAE Left F Y Y SAE Direction of Travel F Y X SAE Right Y SAE

8 Generation of Tyre Lateral Forces due to Plysteer Left X SAE Y SAE Y SAE F Y F Y Direction of Travel Right X SAE Y SAE Y SAE F Y F Y

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

10 Hysteresis in Rubber F F δ Loading Unloading δ

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

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

13 Tyre Forces and Moments Shown Acting in the SAE Tyre Axis System γ Spin Axis Overturning Moment (M x ) Tractive Force (F x ) WC {X sae } 1 α Self Aligning Moment (M y ) Normal Force (F z ) P {Z sae } 1 Rolling Resistance Moment (M y ) {Y sae } 1 Lateral Force (F y )

14 Measurement of Stiffness in a Non- Rolling Tyre F x F x Longitudinal Stiffness δ x F y Lateral Stiffness δ x F y δ y T z δ y Torsional Stiffness T z φ φ

15 Vertical Tyre Force Model Based on a Linear Spring Damper m t k z c z P δ z {X sae } 1 {Z sae } 1

16 Generation of Slip in a Free Rolling Tyre ω O R u V= ω R e V t = ω R u R l R e Tread Material V t = ω R u Compression Rear B D P C A Front {X sae } 1 Tangential velocity of tread relative to O V t = ω R l Direction of slip relative to the road surface Longitudinal Shear Stress V t = ω R e V t = ω R e

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

18 Generation of Rolling Resistance in a Free Rolling Tyre ω F z F Rx O R l M y = F z δx Rear P Front {X sae } 1 δx F z F Rx

19 Generation of Force in a Braked Tyre T B ω O V = ω R e Compression Rear Front Tread Def. Tension δx Fz F B {X sae } 1 Pressure Distribution Longitudinal Slip Longitudinal Shear Stress

20 Braking Force versus Slip Ratio Braking Force Fx (N) Slip Angle = 0 Camber Angle = 0 Braking Force versus Slip Ratio Fz = -8 kn Fz = -6 kn Fz = -4 kn Fz = -2 kn φ Longitudinal Stiffness C s = tan φ 0.0 Slip Ratio 1.0

21 The Effect of Road Contamination on Braking Braking Force Fx (N) Braking Force versus Slip Ratio Dry Road Slip Angle = 0 Camber Angle = 0 Good Tread on Wet Road Poor Tread on Wet Road Aquaplaning 0.0 Slip Ratio 1.0

22 Generation of Force in a Driven Tyre ω O T D V = ω R e Tension F D Pressure Distribution Rear Front Tread Def. δx F z Compression {X sae } 1 Longitudinal Slip Longitudinal Shear Stress

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

24 Generation of Lateral Force and Aligning Moment due to Slip Angle Side View Pressure p Limit Lateral Stress μp Slipping Starts Lateral Stress Front Tyre Contact Patch Rear Top View Lateral Stress M z = F y x pt F y Slipping Starts Direction of Wheel Heading α Direction of Wheel Travel x pt Pneumatic Trail

25 Plotting Lateral Force versus Slip Angle Lateral Force Fy (N) Camber Angle = 0 Lateral Force versus Slip Angle Fz = -8 kn Fz = -6 kn Fz = -4 kn Fz = -2 kn φ Cornering Stiffness C s = tan φ -Slip Angle α (degrees)

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

27 Generation of Lateral Force due to Camber Angle γ Spin Axis {Y sae } 1 Camber Thrust F y {Z sae } 1 Resultant Force F R Tyre Load F z

28 Plotting Lateral Force versus Camber Angle Lateral Force Fy (N) Slip Angle = 0 Lateral Force versus Camber Angle Fz = -8 kn Fz = -6 kn Fz = -4 kn Fz = -2 kn φ Camber Stiffness C γ = tan φ Camber Angle γ (degrees)

29 Generation of Self Aligning Moment due to Camber Angle γ Spin Axis {Y sae } 1 A B C Camber Thrust F y {Y sae } 1 {Z sae } 1 Rear A C B A C A B C Front {X sae } 1 M z F y

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

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

32 Generation of Overturning Moment in the Tyre Contact Patch Slip Angle Camber Angle Wheel Plane O Wheel Centre O M x = F z δy M x =F z δy dy P Y SAE P dy Y SAE F z Z SAE Z SAE F z

33 Pure and Combined Braking and Cornering Forces Y SAE F y Direction of Travel X SAE Contact Patch Pure Braking F x = μ F z S Maximum Braking Force F x = μ F z Direction of Travel Maximum Cornering Force F y = μ F z Large Slip Angle α X SAE Y SAE F y Contact Patch Pure Cornering Y SAE F y F y = μ F z α Maximum Road Plane Force F R = μ F z Large Slip Angle α Direction of Travel X SAE Contact Patch Combined Braking and Cornering Y SAE F y F x Direction of Travel Moderate Slip Angle α X SAE Contact Patch Combined Braking and Cornering Braking Force F x

34 Plotting Lateral Force Against Longitudinal Force (Friction Circle) C Lateral Force F y α =10 D Resultant Force F R α =6 α =4 Friction Circle α =2 α =1 A Braking Force F x Driving Force F x B

35 Development of Lateral Force Following Step Steering Input Lateral Force Fy (N) F ymax Lateral Force versus time Steady State F ymax t 0 t 1 t 2 t Time (sec)

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

37 Flat Bed Tyre Test Machine at Coventry University

38 Lateral Force F y with Slip Angle α Courtesy of Dunlop Tyres Ltd.

39 Aligning Moment M z with Slip Angle α Courtesy of Dunlop Tyres Ltd.

40 Lateral Force F y with Aligning Moment M z (Gough Plot) Courtesy of Dunlop Tyres Ltd.

41 Cornering Stiffness with Load Courtesy of Dunlop Tyres Ltd.

42 Aligning Stiffness with Load Courtesy of Dunlop Tyres Ltd.

43 Lateral Force F y with Camber Angle α Courtesy of Dunlop Tyres Ltd.

44 Aligning Moment M z with Camber Angle α Courtesy of Dunlop Tyres Ltd.

45 Camber Stiffness with Load Courtesy of Dunlop Tyres Ltd.

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

47 Braking Force with Slip Ratio