1. University of Waterloo
An Introduction to Tire Modelling for Multibody Dynamics Simulation
SD 652
Professor John McPhee
University of Waterloo

2. Acknowledgement:
Kevin Morency, Automatic Generation of Real-Time Simulation Code for Vehicle Dynamics using Linear Graph Theory and Symbolic Computing, MASc Thesis, University of Waterloo, 2007

3. SAE Axis System

4. ISO Axis System

5. Rolling Resistance (My)
Produced by hysteresis in tire tread and sidewall rubber
Normal force Fz is integral of the distributed load
My = (Fz)(x)

6. Braking Force (Fx)
S = (V – wR) / V
0 < S < 1

7. Braking Force (Fx) S = (V – wR) / V 0 < S < 1
Longitudinal Stiffness, CS, is the slope of the Fx vs. S curve at S=0

8. Driving Force (Fx)
S = (wR-V) / wR
0 < S < 1

9. Lateral Force (Fy) and Aligning Moment (Mz)

10. Lateral Force (Fy) and Aligning Moment (Mz)
Cornering Stiffness, C, is the slope of the Fy vs.  curve at =0

11. Effect of Camber Angle () on Lateral Force (Fy)

12. Combined Slip (Fx AND Fy)

13. Overturning Moment (Mx)

14. Characterizing a Pneumatic Tire:
Physical Testing

15. Characterizing a Pneumatic Tire:
Physical Testing

16. Data From Physical Tests
Consider how Fx varies with S: 20 data points
Consider how Fx varies with Fz, S,,  : 204 =
data points
Consider how Fx varies with Fz and S: 202 =
400 data points
x5 = data points

17. Mathematical Functions to Fit Measured Data
Tire Models:
Mathematical Functions to Fit Measured Data
Fiala: 6 parameters needed to describe a tire
Easy to understand the physical significance of all parameters
Simple force and moment equations.
Does not handle combined slip
Effects of normal force and camber are largely ignored.
Pacejka 2002 : 117 parameters needed
Very good fit to experimental data
More complicated force and moment equations

18. How Tire Forces are Included In Multibody Vehicle Model
1. Define a point where tire forces and moments will act on the multibody model P2 P1 C2 C1

19. How Tire Forces are Included In Multibody Vehicle Model
2. Determine an expression for the vertical tire force, Fz, which is required as an input to the tire model.

20. How Tire Forces are Included In Multibody Vehicle Model
3. Establish vector directions for longitudinal and lateral components of tire force.

21. How Tire Forces are Included In Multibody Vehicle Model
4. Determine kinematic inputs to tire model (S, , )
5. Use a tire model to calculate Fx, Fy, Mx, My, Mz

22. MapleSim Demo

23. The Fiala Tire Model Inputs:
The original tire model in MSC.ADAMS
Inputs:
Multibody model (mass, rotational inertia)
2. Tire parameters (Cs, C, etc.)
3. The current kinematic state (S,  ,, etc.)

24. Effect of Normal Force (Fz) on Lateral Force (Fy)