Advanced Brush Tyre Modelling (SpringerBriefs in Applied Sciences and Technology)

✍ Scribed by Luigi Romano

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 137
• Edition: 1st ed. 2022
• Category: Library

✦ Synopsis

This book provides an in-depth understanding of tyre dynamics. In the first three chapters, new concepts are introduced in respect to the classic theory. Analytical results are derived step-by-step to guide the reader through the governing equations of the model. Transient phenomena are explained in a relatively simple way according to the brush theory. The analysis is extended to cover the case of large camber angles, which is often disregarded. The principal mechanisms behind the transient generation of tyre forces and moment are discussed in general terms, and exact solutions to the rolling contact problem are given for simple contact geometries.
The last part of the book is dedicated to the approximated theories of transient generation of tyre forces and moment. Two different models, suitable for use in vehicle dynamics applications, are presented and compared.

✦ Table of Contents

Preface
Acknowledgements
Contents
Nomenclature
Forces and Moments
Displacements
Speeds
Slip Parameters
Rotation Matrices and Tensors
Geometric Parameters
Stiffnesses and Compliances
Friction Parameters
Functions and Operators
Sets
1 The Tyre as a Nonlinear System
1.1 Reference Frame and Wheel Velocities
1.2 Slip Variables
1.2.1 Theoretical Slip Variables
1.2.2 Practical Slip Variables
1.2.3 Geometrical Slip Variables
1.2.4 Transient Slip Variables
1.3 General Tyre-Slip Relationships
1.4 Steady-State Relationships
1.4.1 Tyre-Slip Steady-State Relationships
1.4.2 Relationships Between Slip Stiffnesses
1.4.3 Slip-Tyre Steady-State Relationships
References
2 Tyre-Road Contact Mechanics Equations
2.1 Friction Model
2.2 Constitutive Relationships
2.2.1 Constitutive Relationships for the Tyre Tread
2.2.2 Constitutive Relationships for the Tyre Carcass
2.3 Tyre-Road Kinematic Equations
2.3.1 Exact Brush Theory for Large Camber Angles
2.3.2 Classic Brush Theory
2.3.3 Brush Models with Compliant Carcass
2.4 Boundary and Initial Conditions
2.4.1 Boundary and Initial Conditions for the Adhesion Zone
2.4.2 Boundary Condition for the Sliding Zone
2.5 Equilibrium Equations
References
3 Steady-State Brush Theory
3.1 Assumptions and Hypotheses
3.2 Vanishing Sliding
3.3 Pure Translational Slip
3.4 Pure Spin Slip
3.5 Lateral Slip and Spin
References
4 Unsteady-State Brush Theory
4.1 Vanishing Sliding
4.2 Effect of Limited Friction
4.2.1 Pure Lateral Slip
4.2.2 Pure Spin Slip
4.2.3 Lateral Slip and Spin
4.3 Effect of Carcass Compliance
4.3.1 Pure Translational Slips
4.3.2 Effect of Spin Slip
References
5 Theory for Large Spin Slips
5.1 Vanishing Sliding
5.1.1 Steady-State Solution
5.1.2 Transient Solution
5.1.3 Explicit Solutions for Some Contact Shapes
5.2 Limited Friction
References
6 Theories of Transient Generation of Tyre Forces and Moment
6.1 Single Contact Point Models
6.1.1 Model Equations
6.1.2 Relationships Between Relaxation Matrices
6.2 Two-Regime Theory
6.2.1 Derivation of the Sliding Functions
6.2.2 Model Equations
6.3 Model Comparison
References