Road Vehicle Dynamics Fundamentals and Modeling with MATLAB r 2nd edition By Georg Rill, Abel Arrieta Castro ISBN 0367493981 9780367493981

1. Introduction

1.1 Units and Quantities

1.1.1 SI System

1.1.2 Tire Codes

1.2 Terminology

1.2.1 Vehicle Dynamics

1.2.2 Driver

1.2.3 Vehicle

1.2.4 Load

1.2.5 Environment

1.3 Definitions

1.3.1 Coordinate Systems

1.3.2 Design Position of Wheel Center

1.3.3 Toe-In, Toe-Out

1.3.4 Wheel Camber

1.3.5 Design Position of the Wheel Rotation Axis

1.3.6 Wheel Aligning Point

1.4 Active Safety Systems

1.5 Multibody Dynamics Tailored to Ground Vehicles

1.5.1 Modeling Aspects

1.5.2 Kinematics

1.5.3 Equations of Motion

1.6 A Quarter Car Model

1.6.1 Modeling Details

1.6.2 Kinematics

1.6.3 Applied Forces and Torques

1.6.4 Equations of Motion

1.6.5 Simulation

Exercises

2. Road

2.1 Modeling Aspects

2.2 Deterministic Profiles

2.2.1 Bumps and Potholes

2.2.2 Sine Waves

2.3 Random Profiles

2.3.1 Statistical Properties

2.3.2 Classification of Random Road Profiles

2.3.3 Sinusoidal Approximation

2.3.4 Example

2.3.5 Shaping Filter

2.3.6 Two-Dimensional Model

Exercises

3. Tire

3.1 Introduction

3.1.1 Tire Development

3.1.2 Tire Composites

3.1.3 Tire Forces and Torques

3.1.4 Measuring Tire Forces and Torques

3.1.5 Modeling Aspects

3.1.6 Typical Tire Characteristics

3.2 Contact Geometry

3.2.1 Geometric Contact Point

3.2.2 Static Contact Point and Tire Deflection

3.2.3 Length of Contact Patch

3.2.4 Contact Point Velocity

3.2.5 Dynamic Rolling Radius

3.3 Steady-State Forces and Torques

3.3.1 Wheel Load

3.3.2 Tipping Torque

3.3.3 Rolling Resistance

3.3.4 Longitudinal Force and Longitudinal Slip

3.3.5 Lateral Slip, Lateral Force, and Self-Aligning Torque

3.4 Combined Forces

3.4.1 Combined Slip and Combined Force Characteristic

3.4.2 Suitable Approximation and Results

3.5 Bore Torque

3.6 Generalized or Three-Dimensional Slip

3.7 Different Influences on Tire Forces and Torques

3.7.1 Wheel Load

3.7.2 Friction

3.7.3 Camber

3.8 First-Order Tire Dynamics

3.8.1 Simple Dynamic Extension

3.8.2 Enhanced Dynamics

3.8.3 Parking Torque

Exercises

4. Drive Train

4.1 Components and Concepts

4.1.1 Conventional Drive Train

4.1.2 Hybrid Drive

4.1.3 Electric Drive

4.2 Eigendynamics of Wheel and Tire

4.2.1 Equation of Motion

4.2.2 Steady-State Tire Forces

4.2.3 Dynamic Tire Forces

4.3 Simple Vehicle Wheel Tire Model

4.3.1 Equations of Motion

4.3.2 Driving Torque

4.3.3 Braking Torque

4.3.4 Simulation Results

4.4 Differentials

4.4.1 Classic Design

4.4.2 Active Differentials

4.5 Generic Drive Train

4.6 Transmission

4.7 Clutch

4.8 Power Sources

4.8.1 Combustion Engine

4.8.2 Electric Drive

4.8.3 Hybrid Drive

Exercises

5. Suspension System

5.1 Purpose and Components

5.2 Some Examples

5.2.1 Multipurpose Systems

5.2.2 Specific Systems

5.2.3 Steering Geometry

5.3 Steering Systems

5.3.1 Components and Requirements

5.3.2 Rack-and-Pinion Steering

5.3.3 Lever Arm Steering System

5.3.4 Toe Bar Steering System

5.3.5 Bus Steering System

5.3.6 Dynamics of a Rack-and-Pinion Steering System

5.3.6.1 Equation of Motion

5.3.6.2 Steering Forces and Torques

5.3.6.3 Parking Effort

5.4 Kinematics of a Double Wishbone Suspension

5.4.1 Modeling Aspects

5.4.2 Position and Orientation

5.4.3 Constraint Equations

5.4.3.1 Control Arms and Wheel Body

5.4.3.2 Steering Motion

5.4.4 Velocities

5.4.5 Acceleration

5.4.6 Kinematic Analysis

5.5 Design Kinematics

5.5.1 General Approach

5.5.2 Example Twist Beam Axle Suspension

5.6 Race Car Suspension System

5.6.1 General Layout

5.6.2 Kinematics

Exercises

6. Force Elements

6.1 Standard Force Elements

6.1.1 Springs in General

6.1.2 Air Springs

6.1.3 Anti-Roll Bar

6.1.4 Damper

6.1.5 General Point-to-Point Force Element

6.1.5.1 Generalized Forces

6.1.5.2 Example

6.1.6 Rubber Elements

6.2 Dynamic Force Elements

6.2.1 Testing and Evaluating Procedures

6.2.1.1 Simple Approach

6.2.1.2 Sweep Sine Excitation

6.2.2 Spring Damper in Series

6.2.2.1 Modeling Aspects

6.2.2.2 Linear Characteristics

6.2.2.3 Nonlinear Damper Topmount Combination

6.2.3 General Dynamic Force Model

6.2.4 Hydro-Mount

Exercises

7. Vertical Dynamics

7.1 Goals

7.2 From Complex to Simple Models

7.3 Basic Tuning

7.3.1 Natural Frequency and Damping Ratio

7.3.2 Minimum Spring Rate

7.3.3 Example

7.3.4 Natural Eigenfrequencies

7.3.5 Influence of Damping

7.4 Optimal Damping

7.4.1 Disturbance Reaction Problem

7.4.2 Optimal Safety

7.4.3 Optimal Comfort

7.4.4 Example

7.5 Practical Aspects

7.5.1 General Remarks

7.5.2 Quarter Car Model on Rough Road

7.6 Nonlinear Suspension Forces

7.6.1 Progressive Spring

7.6.2 Nonlinear Spring and Nonlinear Damper

7.6.3 Some Results

7.7 Sky Hook Damper

7.7.1 Modeling Aspects

7.7.2 Eigenfrequencies and Damping Ratios

7.7.3 Technical Realization

7.7.4 Simulation Results

Exercises

8. Longitudinal Dynamics

8.1 Dynamic Wheel Loads

8.1.1 Simple Vehicle Model

8.1.2 Influence of Grade

8.1.3 Aerodynamic Forces

8.2 Maximum Acceleration

8.2.1 Tilting Limits

8.2.2 Friction Limits

8.3 Driving and Braking

8.3.1 Single Axle Drive

8.3.2 Braking at Single Axle

8.3.3 Braking Stability

8.3.4 Optimal Distribution of Drive and Brake Forces

8.3.5 Different Distributions of Brake Forces

8.3.6 Braking in a Turn

8.3.7 Braking on μ-Split

8.4 Anti-Lock System

8.4.1 Basic Principle

8.4.2 Demonstration Model

8.5 Drive and Brake Pitch

8.5.1 Enhanced Planar Vehicle Model

8.5.2 Equations of Motion

8.5.3 Equilibrium

8.5.4 Driving and Braking

8.5.5 Drive Pitch

8.5.6 Brake Pitch

8.5.7 Brake Pitch Pole

Exercises

9. Lateral Dynamics

9.1 Kinematic Approach

9.1.1 Kinematic Tire Model

9.1.2 Ackermann Geometry

9.1.3 Space Requirement

9.1.4 Vehicle Model with Trailer

9.1.4.1 Kinematics

9.1.4.2 Vehicle Motion

9.1.4.3 Entering a Curve

9.1.4.4 Trailer Motions

9.1.4.5 Course Calculations

9.2 Steady-State Cornering

9.2.1 Cornering Resistance

9.2.1.1 Two-Axled Vehicle

9.2.1.2 Four-Axled Vehicle

9.2.2 Overturning Limit

9.2.2.1 Static Stability Factor

9.2.2.2 Enhanced Rollover Model

9.2.3 Roll Support and Camber Compensation

9.2.4 Roll Center and Roll Axis

9.2.5 Wheel Load Transfer

9.3 Simple Handling Model

9.3.1 Modeling Concept

9.3.2 Kinematics

9.3.3 Tire Forces

9.3.4 Lateral Slips

9.3.5 Equations of Motion

9.3.6 Stability

9.3.6.1 Eigenvalues

9.3.6.2 Low-Speed Approximation

9.3.6.3 High-Speed Approximation

9.3.6.4 Critical Speed

9.3.6.5 Example

9.3.7 Steady-State Solution

9.3.7.1 Steering Tendency

9.3.7.2 Side Slip Angle

9.3.7.3 Curve Radius

9.3.7.4 Lateral Slips

9.3.8 Influence of Wheel Load on Cornering Stiffness

9.4 Mechatronic Systems

9.4.1 Electronic Stability Program (ESP)

9.4.2 Rear-Wheel Steering

9.4.3 Steer-by-Wire

Exercises

10. Driving Behavior of Single Vehicles

10.1 Three-Dimensional Vehicle Model

10.1.1 Model Structure

10.1.2 Position and Orientation

10.1.3 Velocities

10.1.4 Accelerations

10.1.5 Applied and Generalized Forces and Torques

10.1.6 Equations of Motion

10.2 Driver Model

10.2.1 Standard Model

10.2.2 Enhanced Model

10.2.3 Simple Approach

10.3 Standard Driving Maneuvers

10.3.1 Steady-State Cornering

10.3.2 Step Steer Input

10.3.3 Driving Straight Ahead

10.4 Coach with Different Loading Conditions

10.4.1 Data

10.4.2 Roll Steering

10.4.3 Steady-State Cornering

10.4.4 Step Steer Input

10.5 Different Rear Axle Concepts for a Passenger Car

10.6 Obstacle Avoidance and Off-Road Scenario

Exercises

Bibliography

Glossary

Index