Lecture notes on tire modelling - University of Waterloo

An Introduction to Tire Modelling
for Multibody Dynamics Simulation
SD 652
Professor John McPhee
University of Waterloo
March 2013

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

SAE Axis System

ISO Axis System

Rolling Resistance (M y )
Produced by hysteresis in tire tread
and sidewall rubber
M y = (Fz)(δx)

Braking Force (F x )
S = (V – wR) / V
0 < S < 1

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

Driving Force (F x )
S = (wR-V) / wR
0 < S < 1

Lateral Force (F y ) and
Aligning Moment (M z )

Lateral Force (F y ) and
Aligning Moment (M z )
Cornering Stiffness, C α , is the slope of the
F y vs. α curve at α=0

Effect of Camber Angle (γ)
on Lateral Force (F y )

Combined Slip (F x AND F y )

Overturning Moment (M x )

Characterizing a Pneumatic Tire:
Physical Testing

Characterizing a Pneumatic Tire:
Physical Testing

Data From Physical Tests
Consider how Fx varies with S: Fz, 20 and S,α, data S: γ : 20 20 points 24 =
160 400 000 data data points points
x5 = 800 000 data points

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

How Tire Forces are Included In
Multibody Vehicle Model
1. Define a point where tire forces and
moments will act on the multibody model
C2
C1
P
2
P
1

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.

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

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

MapleSim Demo

The Fiala Tire Model
The original tire model in MSC.ADAMS
Inputs:
1. Multibody model (mass, rotational inertia)
2. Tire parameters (C s , C α , etc.)
3. The current kinematic state (S, α ,γ, etc.)

Effect of Normal Force (F z )
on Lateral Force (F y )