A world-recognized expert in the science of vehicle dynamics, Dr. Thomas Gillespie has created an ideal reference book that has been used by engineers for 30 years, ranging from an introduction to the subject at the university level to a common sight on the desks of engineers throughout the world.
As with the original printing, Fundamentals of Vehicle Dynamics, Revised Edition, strives to find a middle ground by balancing the need to provide detailed conceptual explanations of the engineering principles involved in the dynamics of ground vehicles with equations and example problems that clearly and concisely demonstrate how to apply such principles. A study of this book will ensure that the reader comes away with a solid foundation and is prepared to discuss the subject in detail.
Ideal as much for a first course in vehicle dynamics as it is a professional reference, Fundamentals of Vehicle Dynamics, Revised Edition, maintains the tradition of the original by being easy to read and while receiving updates throughout in the form of modernized graphics and improved readability.
Inasmuch as the first edition proved to be so popular, the Revised Edition intends to carry on that tradition for a new generation of engineers.
Author(s): Thomas D. Gillespie
Edition: 2
Publisher: SAE International
Year: 2021
Language: English
Pages: 510
City: Warrendale
Cover
Table of Contents
Foreword
Preface
Acknowledgments
From the Publisher
About the Author
About the Editors
List of Symbols
CHAPTER 1 Introduction
Dawn of the Motor Vehicle Age
Introduction to Vehicle Dynamics
Fundamental Approach to Modeling
Lumped Mass
Vehicle-Fixed Coordinate System
ISO/SAE Z-up Vehicle-Fixed Coordinate System
Motion Variables
Earth-Fixed Coordinate System
Euler Angles
Forces
Newton’s Second Law
Dynamic Axle Loads
Static Loads on Level Ground
Low-Speed Acceleration
Loads on Grades
Climbing a Grade
Road Grade
Composite Mass
Moments of Inertia
Example Problems
References
CHAPTER 2 Acceleration Performance
Power-Limited Acceleration
Engines
Powertrain
Automatic Transmissions
Example Problems
Traction-Limited Acceleration
Transverse Weight Shift due to Drive Torque
Traction Limits
Parts of a Differential ( Figure 2.12)
Differential Rules
Example Problems
References
CHAPTER 3 Braking Performance
Basic Equations
Constant Deceleration
Deceleration with Wind Resistance
Energy/Power
Braking Forces
Rolling Resistance
Aerodynamic Drag
Driveline Drag
Grade
Brakes
Brake Factor
Tire-Road Friction
Velocity
Inflation Pressure
Vertical Load
Example Problems
Federal Requirements for Braking Performance
Brake Proportioning
Anti-lock Brake Systems
Braking Efficiency
Rear Wheel Lockup
Pedal Force Gain
Example Problem
References
CHAPTER 4 Road Loads
Aerodynamics
Mechanics of Air Flow around a Vehicle
Pressure Distribution on a Vehicle
Aerodynamic Forces
Drag Components
Aerodynamic Aids
Bumper Spoilers
Air Dams
Deck Lid Spoilers
Window and Pillar Treatments
Optimization
Drag
Air Density
Drag Coefficient
Side Force
Lift Force
Pitching Moment
Yawing Moment
Rolling Moment
Crosswind Sensitivity
Rolling Resistance
Factors Affecting Rolling Resistance
Tire Temperature
Tire Inflation Pressure/Load
Velocity
Tire Material and Design
Tire Slip
Typical Coefficients
Total Road Loads
Fuel Economy Effects
Example Problems
References
CHAPTER 5 Ride
Excitation Sources
Road Roughness
Tire/Wheel Assembly
Driveline Excitation
Engine and Transmission
Vehicle Response Properties
Suspension Isolation
Example Problem
Suspension Stiffness
Air Spring Suspensions
Suspension Damping
Tuning – Damping
Tuning – Unsprung Mass
Active Control
Wheel Hop Resonances
Suspension Nonlinearities
Rigid Body Bounce/Pitch Motions
Bounce/Pitch Frequencies
Special Cases
Example Problem
Perception of Ride
Tolerance to Seat Vibrations
Other Vibration Forms
Conclusion
References
CHAPTER 6 Steady-State Cornering
Introduction
Low-Speed Turning
High-Speed Cornering
Tire Cornering Forces
Cornering Equations
Understeer Gradient
Characteristic Speed
Critical Speed
Lateral Acceleration Gain
Yaw Velocity Gain
Sideslip Angle
Static Margin
Suspension Effects on Cornering
Roll Moment Distribution
Camber Change
Roll Steer
Lateral Force Compliance Steer
Aligning Torque
Effect of Tractive Forces on Cornering
Summary of Understeer Effects
Experimental Measurement of Understeer Gradient
Constant Radius Method
Constant Speed Method
Example Problems
References
CHAPTER 7 Suspensions
Solid Axles
Hotchkiss
Four Link
De Dion
Independent Suspensions
Trailing Arm Suspension
SLA Front Suspension
MacPherson Strut
Multi-link Rear Suspension
Trailing-Arm Rear Suspension
Semi-trailing Arm
Swing Axle
Anti-Squat and Anti-Pitch Suspension Geometry
Equivalent Trailing Arm Analysis
Rear Solid Drive Axle
Independent Rear Drive
Front Solid Drive Axle
Independent Front-Drive Axle
Four-Wheel Drive
Anti-Dive Suspension Geometry
Examples
Roll Center Analysis
Solid Axle Roll Centers
Four-Link Rear Suspension:
Three-Link Rear Suspension:
Four-Link with Parallel Arms:
Hotchkiss Suspension:
Independent Suspension Roll Centers
Positive Swing Arm Geometry:
Negative Swing Arm Geometry:
Parallel Horizontal Links:
Inclined Parallel Links:
MacPherson Strut:
Swing Axle:
Active Suspensions
Suspension Categories
Functions
Performance
References
CHAPTER 8 The Steering System
Introduction
The Steering Linkages
Steering Geometry Error
Toe Change
Roll Steer
Front-Wheel Geometry
Steering System Forces and Moments
Vertical Force
Lateral Force
Tractive Force
Aligning Torque
Rolling Resistance and Overturning Moments
Steering System Models
Examples of Steering System Effects
Steering Ratio
Understeer
Braking Stability
Influence of Front-Wheel Drive
Driveline Torque about the Steer Axis
Influence of Tractive Force on Tire Cornering Stiffness
Influence of Tractive Force on Aligning Moment
Fore/Aft Load Transfer
Summary of FWD Understeer Influences
Four-Wheel Steer
Low-Speed Turning
High-Speed Cornering
References
CHAPTER 9 Rollover
Quasi-Static Rollover of a Rigid Vehicle
Quasi-Static Rollover of a Suspended Vehicle
Transient Rollover
Simple Roll Models
Yaw-Roll Models
Tripping
Accident Experience
Dynamic Stability Testing
Electronic Stability Control (ESC)
Sine with Dwell: ESC Performance Requirements
Hardware-in-the-Loop Testing of ESC Systems
Fishhook Maneuver
Slowly Increasing Steer
Fishhook Maneuver
References
CHAPTER 10 Tires
Tire Construction
Size and Load Rating
Tire Load Index
Terminology and Axis System
Mechanics of Force Generation
Tractive Properties
Vertical Load
Inflation Pressure
Surface Friction
Speed
Relevance to Vehicle Performance
Cornering Properties
Slip Angle
Tire Type
Load
Inflation Pressure
Size and Width
Tread Design
Relevance to Vehicle Performance
Camber Thrust
Tire Type
Load
Inflation Pressure
Tread Design
Other Factors
Relevance to Vehicle Performance
Aligning Moment
Slip Angle
Path Curvature
Relevance to Vehicle Performance
Combined Braking and Cornering
Friction Circle
Variables
Relevance to Vehicle Performance
Conicity and Ply Steer
Relevance to Vehicle Performance
Durability Forces
Tire Vibrations
References
Appendix A: (R) Vehicle Dynamics Terminology
Rationale
Foreword
Introduction
1 Scope
2 References
2.1 Applicable Publications
2.1.1 SAE Publications:
2.1.2 ISO Publications:
2.2 Related Publications
2.2.1 SAE Publications:
2.2.2 ISO Publications:
2.2.3 Other Publications:
3 Axis and Coordinate Systems
4 Vehicle
4.1 Geometry and Masses
4.2 Kinematics
4.2.1 Translational Motion Variables:
4.2.1.1 Velocities
4.2.1.2 Accelerations
4.2.2 Angular Motion Variables
4.2.2.1 Angles.
4.2.2.2 Angular Velocities.
4.2.2.3 Angular Accelerations.
4.2.3 Vehicle Trajectory Measures
4.3 Forces and Moments
4.3.1 Forces
4.3.2 Moments
5 Suspension and Steering
5.1 General Nomenclature
5.2 Suspension Components
5.3 Steering Components
5.4 Masses and Inertias
5.5 Geometry
5.5.1 Steer and Camber Angles
5.5.2 Steering-Axis Geometry
5.6 Suspension Motions
5.7 Kinematics
5.7.1 Ride Kinematics
5.7.2 Roll Kinematics
5.7.3 Steering Kinematics
5.7.4 Anti- Characteristics:
5.8 Ride and Roll Stiffness
5.9 Compliances
5.9.1 Camber and Steer Compliances
5.9.2 Other Compliances
6 Brakes
6.1 General Nomenclature
6.2 Brake Components
6.3 Brake Proportioning
7 Tires and Wheels
7.1 Wheel Nomenclature
7.2 Pneumatic Tire Nomenclature
7.3 Wheel Plane Geometry
7.4 Tire Orientation Angles
7.5 Tire Rolling Characteristics
7.6 Wheel Spin and Tire Slip
7.7 Standard Loads and Inflation Pressures
7.9 Tire Forces and Moments
7.10 Pull Forces and Moments
7.11 Properties of Forces in the Road Plane
7.12 Normal Force Properties
7.13 Moment Properties
7.14 Tire/Road Friction
8 States and Modes
8.1 Equilibrium
8.2 Stability
8.3 Control Modes
9 Inputs and Responses
9.1 Inputs
9.2 Responses
10 Vehicle Longitudinal Response
10.1 Longitudinal Load Transfer
10.2 Descriptors of Steady-State Longitudinal Response
10.2.1 Gain Measures:
10.2.2 Gradient Measures:
10.3 Descriptors of Transient Longitudinal Response
10.4 Descriptors of Transient Brake System Response
10.5 Characterizing Descriptors of Braking Performance
11 Vehicle Lateral Response
11.1 Lateral Load Transfer
11.2 Ranges of Directional Response
11.3 Descriptors of Steady-State Directional Response
11.3.1 Gain or Sensitivity Measures:
11.3.2 Gradient Measures:
11.3.3 Understeer and Oversteer
11.3.4 Stability Measures
11.3.5 Characterizing Speeds
11.4 Descriptors of Transient Directional Response
11.4.1 Rise-Time Measures:
11.4.2 Overshoot Measures:
11.4.3 Other Transient Measures
11.5 Descriptors of Limit Response
11.5.1 Directional Response Limits
11.5.2 Rollover Resistance
11.6 Stability and Control Derivatives
12 Ride Vibration
12.1 Sprung-Mass Vibration
12.2 Unsprung-Mass Vibration
12.2.1 Wheel Vibration Modes
12.2.2 Axle Vibration Modes
12.2.3 Steering-System Vibration Modes
13 Notes
13.1 Marginal Indicia
Appendix B: SAE J6a Ride and Vibration Data Manual
Foreword
1. Basic Relationships
1.1 Acceleration versus Static Deflection
1.2 Undamped Natural Frequency of Sprung Mass
1.3 Relations in Simple Harmonic Motion
1.4 Resonant Speed on Uniformly Spaced Road Disturbances
2. Vibration Systems
2.1 List of Symbols
2.1.1 Vibrating System Parameters
2.1.2 Vibratory Motion
2.2 Free Vibration with Coulomb Damping
2.3 Free Vibration with Viscous Damping
2.4 Forced Vibration with Viscous Damping
2.4.1 Force Applied to Suspended Mass
2.4.1.1 Peak Exciting Force Constant.
2.4.1.2 Exciting Force Increasing as Square of Frequency.
2.4.1.3 Equivalent Impedance.
2.4.2 Excitation Applied to Spring Support
2.4.2.1 Absolute Amplitude Ratio.
2.4.2.2 Relative Amplitude Ratio.
2.5 Forced Vibration with Coulomb Damping
2.6 Force Transmission through Suspension
2.6.1 Direct Excitation of Mass with Viscous Damping
2.6.1.1 Constant Peak Driving Force.
2.6.1.2 Driving Force on Mass Proportional to Square of Speed with Viscous Damping .
2.6.1.3 Equivalent Impedance.
2.6.2 Comparison of Viscous and Coulomb Damping
2.6.3 Vibrating System with Two Degrees of Freedom:
2.7 References
3. Energy Absorption and Impact
3.1 List of Symbols
3.2 Mathematical Relations
3.2.1 Impact from Free Fall
3.2.2 Impact Without Gravity Acceleration
4. Vibration Limits for Passenger Comfort
4.1 Response to Vertical Vibrations
4.2 Vertical Vibration Limits for Passenger Comfort
4.3 Subjective Responses of the Human Body to Vibratory Motion
5. Bibliography
Appendix C: Ride Index Structure and Development Methodology
Rationale
Foreword
Introduction
1 Scope
1.1 Purpose
2 References
2.1 Applicable Documents
2.1.1 SAE Publications:
2.1.2 ISO Publications:
2.1.3 IEC Publications:
2.2 Related Publications
2.2.1 SAE Publications:
2.2.2 ISO Publications:
2.2.3 Other Publications:
3 Definitions
3.1 Motion
3.2 Psychometric
3.3 Rough Road Ride Event
3.4 Transient Ride Event
3.5 Vibration
4 Symbols, Subscripts and Abbreviations
4.1 Symbols
4.2 Subscripts
5 Subjective and Objective Data Requirements
5.1 Psychometric Ratings for Human Sensitivity Data
5.1.1 Discomfort Ratings:
5.1.2 Human Subjects:
5.1.3 Rating Scales and Usage
5.1.4 Subject Experimental Protocols:
5.1.4.1 Rating Interval and Description.
5.1.4.1.1 Rough Roads Ride Events.
5.1.4.1.2 Transient Ride Events.
5.2 Objective Motion and Vibration Measurement
5.2.1 General:
5.2.2 Motion and Vibration Measurement
5.2.2.1 Direction.
5.2.2.2 Location.
5.2.3 Signal Conditioning:
5.2.4 Duration of Measurement:
5.2.5 Vehicle Speed Measurement:
5.2.6 Reporting of Measurement Conditions:
5.3 Processing of Vibration Data
5.3.1 Basic Processing Method Using Weighted Root-Mean-Square and Root-Mean-Quad Acceleration:
5.3.2 Applicability of the Basic Processing Method
5.3.2.1 Categorizing Rough Versus Transient Specimens.
5.3.2.2 Determination of the Domain-of-Validity.
5.3.3 Frequency Weighting
5.3.3.1 Frequency Weighting of Acceleration Time History.
5.3.3.1.1 Frequency Band Limitation.
5.3.3.1.2 Tolerances.
5.3.3.2 Frequency Weighting of Acceleration Spectra.
5.4 Prediction of Discomfort Ratings
5.4.1 Rough Road Ride Specimens:
5.4.2 Transient Ride Specimens:
5.5 Statistical Method for Determining the Ride Discomfort Models
5.5.1 Jury Model:
5.5.2 RPRED Statistic:
5.5.3 Domain-of-Validity:
5.5.3.1 Z-Score Transformation Parameters.
5.5.3.2 Z-Score Domain-of-Validity.
5.5.3.3 Normally Distributed Z-Score Limits.
5.5.3.4 Not Normally Distributed Z-Score Limits.
6 Notes
6.1 Revision Indicator
APPENDIX A - MATHEMATICAL DEFINITION OF THE FREQUENCY WEIGHTINGS
A.1 Parameters of the Transfer Functions
A.2 Transfer Functions
APPENDIX B - OTHER PUBLICATIONS
APPENDIX C - SUPPORTING RATIONALE
C.1 Introduction
C.2 Discomfort
C.2.1 Environmental Context:
C.3 Objective Assessment of Motion andVibration Discomfort
C.3.1 Use of Weighted RMS Acceleration:
C.3.2 Use of Weighted RMQ Acceleration:
C.3.3 Use of RMQ/RMS Ratio for Categorizing Rough Versus Transient Specimens:
C.3.4 Use of Frequency Weightings:
Index
