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The Multibody Systems Approach to Vehicle Dynamics

List of Chapters:

Preface Acknowledgements Nomenclature 1 Introduction 1.1 Overview 1.2 What is vehicle dynamics? 1.3 Why analyse? 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 2.8 2.9 2.10 2.11 2.12 2.13 Dynamics of a particle Linear momentum of a rigid body Angular momentum Moments of inertia Parallel axes theorem Principal axes Equations of motion

3 Multibody systems simulation software 3.1 Overview 3.2 Modelling 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 Modelling 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

The Multibody Systems Approach to Vehicle Dynamics

Quarter vehicle modelling approaches 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 centre and roll centre 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 Tyre characteristics and modelling 5.1 Introduction 5.2 Tyre axis systems and geometry 5.2.1 The SAE and ISO tyre axis systems 5.2.2 Definition of tyre radii 5.2.3 Tyre asymmetry 5.3 The tyre contact patch 5.3.1 Friction 5.3.2 Pressure distribution in the tyre contact patch 5.4 Tyre force and moment characteristics 5.4.1 Components of tyre force and stiffness 5.4.2 Normal (vertical) force calculations

4.3 4.4

5.5 5.6

5.7 5.8 5.9

Longitudinal force in a free rolling tyre (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 Experimental testing Tyre modelling 5.6.1 Overview 5.6.2 Calculation of tyre geometry and velocities 5.6.3 Road surface/terrain definition 5.6.4 Interpolation methods 5.6.5 The `Magic Formula' tyre model 5.6.6 The Fiala tyre model 5.6.7 Tyre models for durability analysis Implementation with MBS 5.7.1 Virtual tyre rig model Examples of tyre model data Case study 6 -- Comparison of vehicle handling tyre models

5.4.3

6 Modelling 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 Modelling of springs and dampers 6.5.1 Treatment in simple models 6.5.2 Modelling leaf springs 6.6 Anti-roll bars 6.7 Determination of roll stiffness for the equivalent roll stiffness model 6.8 Aerodynamic effects

The Multibody Systems Approach to Vehicle Dynamics

Modelling of vehicle braking Modelling traction Other driveline components The steering system 6.12.1 Modelling the steering mechanism 6.12.2 Steering ratio 6.12.3 Steering inputs for vehicle handling manoeuvres 6.13 Driver behaviour 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 underand 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

6.9 6.10 6.11 6.12

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-tonoise 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?

7.8

Appendix A: Vehicle model system schematics and data sets Appendix B: Fortran tyre model subroutines Appendix C: Glossary of terms References Index

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