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The Multibody Systems Approach to Vehicle Dynamics - 1st Edition - ISBN: 9780750651127, 9780080473529

The Multibody Systems Approach to Vehicle Dynamics

1st Edition

Authors: Michael Blundell Damian Harty
Paperback ISBN: 9780750651127
eBook ISBN: 9780080473529
Imprint: Butterworth-Heinemann
Published Date: 14th July 2004
Page Count: 288
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Multibody Systems Approach to Vehicle Dynamics aims to bridge a gap between the subject of classical vehicle dynamics and the general-purpose computer-based discipline known as multibody systems analysis (MBS). The book begins by describing the emergence of MBS and providing an overview of its role in vehicle design and development. This is followed by separate chapters on the modeling, analysis, and post-processing capabilities of a typical simulation software; the modeling and analysis of the suspension system; tire force and moment generating characteristics and subsequent modeling of these in an MBS simulation; and the modeling and assembly of the rest of the vehicle, including the anti-roll bars and steering systems. The final two chapters deal with the simulation output and interpretation of results, and a review of the use of active systems to modify the dynamics in modern passenger cars.

This book intended for a wide audience including not only undergraduate, postgraduate and research students working in this area, but also practicing engineers in industry who require a reference text dealing with the major relevant areas within the discipline.

Key Features

  • Full of practical examples and applications
  • Uses industry standard ADAMS software based applications
  • Guides readers from modelling suspension movement through to full vehicle models able to perform handling manoeuvres


Practicing vehicle design engineers and analysts; Postgraduates in Automotive Engineering. Other undergraduates in civil engineering or transport studies studying automotive option units.

Table of Contents




1 Introduction

1.1 Overview

1.2 What is Vehicle Dynamics?

1.3 Why Analyze?

1.4 Classical Methods

1.5 Analytical Process

1.6 Computational Methods

1.7 Computer-Based Tools

1.8 Commercial Computer Packages

1.9 Benchmarking Exercises

2 Kinematics and Dynamics of Rigid Bodies

2.1 Introduction

2.2 Theory of Vectors

2.2.1 Position and Relative Position Vectors

2.2.2 The Dot (Scalar) Product

2.2.3 The Cross (Vector) Product

2.2.4 The Scalar Triple Product

2.2.5 The Vector Triple Product

2.2.6 Rotation of a Vector

2.2.7 Vector Transformation

2.2.8 Differentiation of a Vector

2.2.9 Integration of a Vector

2.2.10 Differentiation of the Dot Product

2.2.11 Differentiation of the Cross Product

2.2.12 Summary

2.3 Geometry Analysis

2.3.1 Three Point Method

2.3.2 Vehicle Suspension Geometry Analysis

2.4 Velocity Analysis

2.5 Acceleration Analysis

2.6 Static Force and Moment Definition

2.7 Dynamics of a Particle

2.8 Linear Momentum of a Rigid Body

2.9 Angular Momentum

2.10 Moments of Inertia

2.11 Parallel Axes Theorem

2.12 Principal Axes

2.13 Equations of Motion

3 Multibody Systems Simulation Software

3.1 Overview

3.2 Modeling Features

3.2.1 Planning the Model

3.2.2 Reference Frames

3.2.3 Basic Model Components

3.2.4 Parts and Markers

3.2.5 Equations of Motion for a Part

3.2.6 Basic Constraints

3.2.7 Standard Joints

3.2.8 Degrees of Freedom

3.2.9 Force Elements

3.2.10 Summation of Forces and Moments

3.3 Analysis Capabilities

3.3.1 Overview

3.3.2 Solving Linear Equations

3.3.3 Non-Linear Equations

3.3.4 Integration Methods

3.4 Systems of Units

3.5 Pre- and Post-Processing

4 Modeling and Analysis of Suspension Systems

4.1 The Need for Suspension

4.1.1 Wheel Load Variation

4.1.2 Body Isolation

4.1.3 Handling Load Control

4.1.4 Compliant Wheel Plane Control

4.1.5 Kinematic Wheel Plane Control

4.1.6 Component Loading Environment

4.2 Types of Suspension System

4.3 Quarter Vehicle Modeling Approaches

4.4 Determination of Suspension System Characteristics

4.5 Suspension Calculations

4.5.1 Measured Outputs

4.5.2 Suspension Steer Axes

4.5.3 Bump Movement, Wheel Recession and Half Track Change

4.5.4 Camber and Steer Angle

4.5.5 Castor Angle and Suspension Trail

4.5.6 Steering Axis Inclination and Ground Level Offset

4.5.7 Instant Center and Roll Center Positions

4.5.8 Calculation of Wheel Rate

4.6 The Compliance Matrix Approach

4.7 Case Study 1 – Suspension Kinematics

4.8 Durability Studies (Component Loading)

4.8.1 Overview

4.8.2 Case Study 2 – Static Durability Loadcase

4.8.3 Case Study 3 – Dynamic Durability Loadcase

4.9 Ride Studies (Body Isolation)

4.9.1 Case Study 4 – Dynamic Ride Analysis

4.10 Case Study 5 – Suspension Vector Analysis Comparison with MBS

4.10.1 Problem Definition

4.10.2 Velocity Analysis

4.10.3 Acceleration Analysis

4.10.4 Static Analysis

4.10.5 Dynamic Analysis

4.10.6 Geometry Analysis

5 Tire Characteristics and Modeling

5.1 Introduction

5.2 Tire Axis Systems and Geometry

5.2.1 The SAE and ISO Tire Axis Systems

5.2.2 Definition of Tire Radii

5.2.3 Tire Asymmetry

5.3 The Tire Contact Patch

5.3.1 Friction

5.3.2 Pressure Distribution in the Tire Contact Patch

5.4 Tire Force and Moment Characteristics

5.4.1 Components of Tire Force and Stiffness

5.4.2 Normal (Vertical) Force Calculations

5.4.3 Longitudinal Force in a Free Rolling Tire (Rolling Resistance)

5.4.4 Braking Force

5.4.5 Driving Force

5.4.6 Generation of Lateral Force and Aligning Moment

5.4.7 The Effect of Slip Angle

5.4.8 The Effect of Camber Angle

5.4.9 Combinations of Camber and Slip Angle

5.4.10 Overturning Moment

5.4.11 Combined Traction and Cornering (Comprehensive Slip)

5.4.12 Relaxation Length

5.5 Experimental Testing

5.6 Tire Modeling

5.6.1 Overview

5.6.2 Calculation of Tire Geometry and Velocities

5.6.3 Road Surface/Terrain Definition

5.6.4 Interpolation Methods

5.6.5 The 'Magic Formula' Tire Model

5.6.6 The Fiala Tire Model

5.6.7 Tire Models for Durability Analysis

5.7 Implementation with MBS

5.7.1 Virtual Tire Rig Model

5.8 Examples of Tire Model Data

5.9 Case Study 6 – Comparison of Vehicle Handling Tire Models

6 Modeling and Assembly of the Full Vehicle

6.1 Introduction

6.2 The Vehicle Body

6.3 Measured Outputs

6.4 Suspension System Representation

6.4.1 Overview

6.4.2 Lumped Mass Model

6.4.3 Equivalent Roll Stiffness Model

6.4.4 Swing Arm Model

6.4.5 Linkage Model

6.4.6 The Concept Suspension Approach

6.5 Modeling of Springs and Dampers

6.5.1 Treatment in Simple Models

6.5.2 Modeling Leaf Springs

6.6 Anti-Roll Bars

6.7 Determination of Roll Stiffness for the Equivalent Roll Stiffness Model

6.8 Aerodynamic Effects

6.9 Modeling of Vehicle Braking

6.10 Modeling Traction

6.11 Other Driveline Components

6.12 The Steering System

6.12.1 Modeling the Steering Mechanism

6.12.2 Steering Ratio

6.12.3 Steering Inputs for Vehicle Handling Manoeuvres

6.13 Driver Behavior

6.13.1 Steering Controllers

6.13.2 A Path Following Controller Model

6.13.3 Body Slip Angle Control

6.13.4 Two-Loop Driver Model

6.14 Case Study 7 – Comparison of Full Vehicle Handling Models

6.15 Summary

7 Simulation Output and Interpretation

7.1 Introduction

7.2 Case Study 8 – Variation in Measured Data

7.3 A Vehicle Dynamics Overview

7.3.1 Travel on a Curved Path

7.3.2 The Classical Treatment Based on Steady State Cornering

7.3.3 Some Further Discussion of Vehicles in Curved Path

7.3.4 The Subjective/Objective Problem

7.3.5 Mechanisms for Generating under- and Oversteer

7.4 Transient Effects

7.5 Steering Feel as a Subjective Modifier

7.6 Roll as an Objective and Subjective Modifier

7.7 Frequency Response

7.8 The Problems Imposed By

7.8.1 Circuit Racing

7.8.2 Rallying

7.8.3 Accident Avoidance

7.9 The Use of Analytical Models with a Signal-to-Noise Ratio Approach

7.10 Some Consequences of Using Signal-to-Noise Ratio

8 Active Systems

8.1 Introduction

8.2 Active Systems

8.2.1 Active Suspension and Variable Damping

8.2.2 Brake-Based Systems

8.2.3 Active Steering Systems

8.2.4 Active Camber Systems

8.2.5 Active Torque Distribution

8.3 Which Active System?

Appendix A: Vehicle Model System Schematics and Data Sets

Appendix B: Fortran Tire Model Subroutines

Appendix C: Glossary of Terms




No. of pages:
© Butterworth-Heinemann 2004
14th July 2004
Paperback ISBN:
eBook ISBN:

About the Authors

Michael Blundell

Michael Blundell

Mike Blundell is Professor of Vehicle Dynamics and Impact, Mechanical & Automotive Engineering, Coventry University, UK. He specializes in vehicle dynamics and safety teaching and research, and has worked with multibody systems applications in vehicle dynamics in industry and academia, publishing many papers on the topic.

Affiliations and Expertise

University of Coventry, UK

Damian Harty

Damian Harty

Damian Harty is a Senior Staff Engineer at Polaris Industries based in Minnesota. He was formerly Director of the Vehicle & System Dynamics Group at Coventry University, a Technical Specialist for vehicle dynamics with Prodrive on the Mini WRC, as well as a freelance consultant.

Affiliations and Expertise

Senior Staff Engineer at Polaris Industries, Minnesota, USA.

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