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Generalized Vehicle Dynamics

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Author Daniel E. Williams, an industry professional with more 30 years of experience in chassis control systems from concept to launch, brings this experience and his unique approach to readers of Generalized Vehicle Dynamics.


This book makes use of nomenclature and conventions not used in other texts. This combination allows the derivation of complex vehicles that roll with multiple axles, any of which can be steered, to be directly predicted by manipulation of a generalized model. Similarly the ride characteristics of such a generalized vehicle are derived. This means the vehicle dynamic behavior of these vehicles can be directly written from the results derived in this work, and there is no need to start from Newton's Second Law to create such insight. Using new and non-standard conventions allows wider applicability to complex vehicles, including autonomous vehicles.


Generalized Vehicle Dynamics is divided into two main sections-ride and handling-with roll considered in both. Each section concludes with a case study that applies the concepts presented in the preceding chapters to actual vehicles. Chapters include Simple Suspension as a Linear Dynamic System, The Quarter-Car Model, The Pitch Plane Model, The Roll Plane Mode, Active Suspension to Optimize Ride, Handling Basics, Reference Frames, New Conventions, Two-Axle Yaw Plane Model, Rear Axle Steering and Lanekeeping, Two-Axle Vehicles that Roll, Three-Axle Vehicle Dynamics, Generalized Multi-Axle Vehicle Dynamics and Automated Vehicle Architecture from Vehicle Dynamics.

Author(s): Daniel Williams
Publisher: SAE International
Year: 2022

Language: English
Pages: 371
City: Warrendale

Cover
Contents
Foreword
Acknowledgments
1 Introduction
1.1 Overview
1.2 Historical Perspective
1.3 Structure of the Text
References
2 Simple Suspension as a Linear Dynamic System
2.1 Introduction
2.2 
The Simply Suspended Mass and Linear Systems Theory
2.3 A Suspended Mass with Damping
2.4 Basic Frequency Responses
2.5 
State Space and Block
Diagram Algebra
2.6 State Space Realization
2.7 
First-Order Matrix Differential
Equations
2.8 Summary
3
The Quarter-Car Model
3.1 Introduction
3.2 
Representing Reality with
the Quarter-Car Model
3.3 
Two Fundamental Frequencies
of Interest
3.4 The Conventional Quarter-Car Model
3.5  Stochastic Road Input and Human Sensitivity to Vibration
3.6 Nonlinear Damping
3.7 Summary
References
4
The Pitch-Plane Model
4.1 Introduction
4.2 Basic Pitch-Plane Model
4.3 Pitch-Plane-Free Response
4.4 Road Inputs to the Pitch-Plane Model
4.5 
Pitch-Plane Ride Quality and the Olley Ride Criteria
4.6 Pitch-Plane Model with Damping
4.7 
Generalized Pitch-Plane Model and Olley Solution
4.8 Three-Axle Vehicle Example
4.9 Summary
References
5
The Roll-Plane Model
5.1 Introduction
5.2 Simple Two-Axle Roll-Plane Model
5.3 The Roll Mode for a Single Axle
5.4 
The Roll-Plane Model with
Stabilizer Bar
5.5 Single-Wheel Inputs
5.6 Passenger Car Roll
5.7 Generalized Roll-Plane Model
5.8 Roll and Handling
5.9 Summary
6 Active Suspension to Optimize Ride
6.1 Introduction
6.2 Inertial Damping
6.3 Lotus Modal Control
6.4 Modal Inertial Damping
6.5 
Sprung Mass Acceleration Feedforward
6.6 Quarter-Car Optimal Control
6.7 Full Vehicle Optimal Control
6.8 Modal Inertial Damping and Handling
6.9 Summary
References
7 Handling Basics
7.1 Introduction
7.2 Ackermann Steering
7.3 Steering Efforts
7.4 Slip Angles
7.5 Tire Forces
7.6 The Conventional Bicycle Model
7.7 Summary
References
8
Reference Frames
8.1 Introduction
8.2 Reference Frames in General
8.3 
Velocity of a Point Translating
in a Rotating Reference Frame
8.4 
Velocity and Acceleration of a
Point in a Translating and Rotating Reference Frame
8.5 External Forces and Inertia
8.6 The Vehicle as a Rigid Body
8.7 Summary
Reference
9
New Conventions
9.1 Introduction
9.2 State-of-the-Art Conventions
9.3 New Axle Location Convention
9.4 New Attack Angle Convention
9.5 Summary
References
10 Two-Axle Yaw-Plane Model
10.1 Introduction
10.2 The Two-Axle Vehicle Model
10.3 
Drift Angle and Yaw Rate
Transfer Functions
10.4 Ideal Two-Axle Model
10.5 Steady-State Analysis
10.6 Pole Locations
10.7 Summary
References
11 Rear Axle Steering and Lanekeeping
11.1 Introduction
11.2 
Vehicle Model with Rear Axle Steering
11.3 
Determination of Rear
Axle Steer Control
11.4 
Open-Loop Response of Ideal Vehicle
11.5 Specified Preview
11.6  Determination of Rear Axle Control
of Ideal Vehicle
11.7 Numerical Results
11.8 
Theoretical Interpretation of
Practical Systems
11.9 Summary
References
12
Two-Axle Vehicles that Roll
12.1 Introduction
12.2 Roll Axis Definitions
12.3 Acceleration Equations
12.4 External Roll Forces on Sprung Mass
12.5 Camber Effects
12.6 Roll Steer Effects
12.7 
Differential Equations of
Motion with Roll
12.8 Roll Steer Compensation
12.9 
Including Steering Compliance
in Understeer
12.10 Inclusion of Nonlinear Tires
12.11 Summary
Reference
13
Three-Axle Vehicle Dynamics
13.1 Introduction
13.2 
Peculiarities of the
Three-Axle Vehicle
13.3 The Three-Axle Model
13.4 Third Axle Steering
13.5 Trajectory Tracking
13.6 Summary
References
14
Generalized Multiaxle Vehicle Dynamics
14.1 Introduction
14.2 General Model
14.3 An Arbitrarily Steered Axle
14.4 
All Arbitrary Axles Steered
Proportionally
14.5 The Multiaxle Vehicle with Roll
14.6 Summary
References
15 Automated Vehicle Architecture from Vehicle Dynamics
15.1 Introduction
15.2 
Properties of a Typical Three-Axle Commercial Vehicle
15.3 Control of Rear Axle
15.4 
Rear Axle Control for Yaw
Rate Equivalence
15.5 Vehicle Results
15.6 Proposed Three-Axle Vehicle
15.7 Summary
References
Afterword
Index
About the Author