Vehicle Handling Dynamics Theory and Application Second Edition Masato Abe Kanagawa Institute of Technology AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Butterworth-Heinemann is an imprint of Elsevier Butterworth-Heinemann is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK 225 Wyman Street, Waltham, MA 02451, USA Copyright © 2015, 2009 Masato Abe. Published by Elsevier Ltd. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-08-100390-9 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress For Information on all Butterworth-Heinemann publications visit our website at http://store.com/ Preface This book intends to give readers the fundamental theory and some applications of automotive vehicle dynamics.
The book is suitable as a text book of vehicle dynamics for undergraduate and graduate courses in automotive engineering. It is also acceptable as a reference book for re- searchers and engineers in the field of R&D of vehicle dynamics and control, chassis design and development. The vehicle motion dealt with in this book is generated by the tire forces, which are produced by the vehicle motion itself. The motion on the ground is possible in any direction by the driver’s intention.
This is a similar feature to flight dynamics and ship dynamics. In Chapter 1, the vehicle motion studied in this book is defined. Chapter 2 examines the tire mechanics. The vehicle motion depends on the forces exerted upon tires and this chapter is the base of the book.
However, if the reader experiences difficulties in the detailed description of the tire mechanics, they can skip to the next chapter, while still understanding the fundamentals of vehicle dynamics. In Chapter 3, the fundamental theory of vehicle dynamics is dealt with by using a two degree of freedom model. The vehicle motions to external disturbance forces are described using the two degree of freedom model from Chapter 4. This motion is inevitable for a vehicle that can move freely on the ground.
In Chapter 5, the effect of the steering system on vehicle motion is studied. The vehicle-body roll effect on the vehicle dynamics is described in the Chapter 6. Chapter 7 looks at the effect of the longitudinal motion on the lateral motion of the vehicle and the fundamental vehicle dynamics with active motion controls is described in the Chapter 8. The vehicle motion is usually controlled by a human driver.
The vehicle motion controlled by the human driver is dealt with in the Chapter 9 (Chapter 10 in the second edition) and relations between the driver’s evaluation of handling quality and vehicle dynamic characteristics are described in the Chapter 10 (Chapter 11 in the second edition). For readers who need only to understand the fundamental aspects of the vehicle dynamics and the human driver, it is possible to skip to Chapter 9 after reading from Chapter 1 to Chapter 4. The readers who like to understand and are interested in more in detail of vehicle dynamics should continue to read through the book from the Chapters 5 to 10, depending on their interests. The original book is written by the author in Japanese and published in Japan.
The book was once translated into English by Y. Chai when he was a masters-course student of the author. The author has added new parts such as examples in each chapter and problems at the end of the chapters. Manning has revised the whole text for the English version.
The publication process started according to a suggestion by the author’s old friend, D. He has consistently continued to give us useful advises from the beginning to the final stage of the publication. The author has to confess that without any support of the above mentioned three, the publication is not accomplished. The author would like to express his deep gratitude to their contributions to publishing the book.
The author is indebted as well to J. Ishio, a former master- course student of the author for his assistance in arranging the examples for each chapter. Also special thanks should go to Yokohama Rubber Co. for the preparation of some tire data in the Chapter 2.
Finally, author thanks the editorial and production staff of Elsevier Science & Technology Books for their efforts for the publication. Masato Abe March 2009 xi Preface to Second Edition Five years have passed since the first edition was published. During this period, more and more requirements of understanding the fundamental knowledge of vehicle handling dynamics arise especially for the application to research and development of vehicle active motion controls aim- ing at vehicle agility and active safety. In view of the situation, the publication of the second edi- tion was pursued in order to make the first edition a still more solid one.
The Chapters 1–8 in the first edition are revised for the second edition by putting the addi- tional parts with correcting existing errors and careless-misses. As a fundamental knowledge of the active vehicle motion control, a description on active front wheel steer controls and an addi- tional note on DYC (Direct Yaw-moment Control) are added in the Chapter 8 and also the new Chapter 9 is provided for the second edition. The Chapter 9 deals with all wheel independent control for full drive-by-wire electric vehicles which is a very updated issue of vehicle dy- namics and control for the vehicles of new era. The previous Chapters 9 and 10 in the first edition are also revised for the Chapters 10 and 11 respectively in the second edition, in which driver-vehicle system behaviors and driver’s evalu- ation of handling qualities are dealt with.
The new Chapter 12 is for dealing with a very classical issue which has not been solved yet generally and theoretically in the field of the vehicle handling dynamics. The point is handling quality evaluation and its contribution to the vehicle design for fun-to-drive. The Chapter 12 is a challenge to a fundamental and theoretical approach to this area. The author thanks the editorial and production staffs of Elsevier Science & Technology Books for their efforts for the publication of the second edition.
Finally the author’s old friend, Professor Dave Crolla, who consistently gave us useful sug- gestions and advices from the beginning to the final stage of the publication of the first edition, regrettably died on 4th September, 2011. The author would like to dedicate this book to the memory of David Anthony Crolla. Masato Abe November 2014 xiii Symbols The following symbols are commonly used throughout from Chapter 3 to Chapter 12 consistently in this book, because they are fundamental symbols for representing the vehicle dynamics and it is rather convenient for the readers to be able to use them consistently. So these symbols are sometimes used without any notice on the symbols.
When it is impossible to avoid using these symbols for other meanings than the following, some notice will be given at each part of the chapters where they are used. m vehicle mass l vehicle yaw moment inertia l wheel base lf longitudinal position of front wheel(s) from vehicle center of gravity lr longitudinal position of rear wheel(s) from vehicle center of gravity Kf cornering stiffness of front tire Kr cornering stiffness of rear tire V vehicle speed d front wheel steering angle b side slip angle r yaw rate q yaw angle x vehicle longitudinal direction y vehicle lateral direction and lateral displacement t time s Laplace transform variable The symbols other than the above adopted in each chapter are defined at the first places where they are used in each chapter. It should be notified that though, in general, x€ and y€ mean the second order time derivative of the variables x and y, they are expediently used in this book for the symbols to represent the vehicle longitudinal and lateral accelerations respectively. In addition, d(s), for example, generally means d as a function of variable, s, however, it represents in this book the Laplace transformation of variable, d, and this way of representation is applied to all the variables used throughout this book.
xv CHAPTER VEHICLE DYNAMICS AND CONTROL 1 1.1 DEFINITION OF THE VEHICLE Ground vehicles can be divided into two main categories: vehicles that are restricted by a track set on the ground (e., railway vehicles) and vehicles that are unrestricted by tracks, free to move in any direction on the ground by steering the wheels (e. Aircraft are free to fly in the air, while ships can move freely on the water’s surface. In the same way, the road vehicle is free to move by steering its wheels, and it shares similarities with aircraft and ships in the sense that its movements are unrestricted. From the viewpoint of dynamic motion, the similarity lies in the fact that these three moving bodies receive forces generated by their own movement that are used to accomplish the desired movement.
Aircraft depend on the lift force caused by the relative motion of its wings and the air; ships rely on the lift force brought by the relative motion of its body and the water; and ground vehicles rely on the lateral force of the wheels created by the relative motion of the wheels and the road. In the above described manner, the dynamics and control of the three moving bodies is closely related to their natural function, whereby for an airplane, it is established as flight dynamics, for a ship as ship dynamics, and for a vehicle, similarly, as vehicle dynamics. The vehicle studied in this book is a vehicle similar to the airplane and ship that is capable of independent motion on the ground using the forces generated by its own motion.2 VIRTUAL FOUR-WHEEL VEHICLE MODEL For the study of vehicle dynamics and control, a typical vehicle mathematical model is assumed. This vehicle model has wheels that are steerable: two at the front and two at the rear, which are fitted to a rigid body.
Passenger cars, trucks, buses, and agricultural vehicles all fall into this category. At first sight, it may seem there are no common dynamics among these vehicles, but by applying a simple four-wheeled vehicle model, as in Figure 1.1, it is possible to obtain funda- mental knowledge of the dynamics of all these vehicles. In the vehicle mathematical model represented in Figure 1.1, the wheels are regarded as weightless, and the rigid body represents the total vehicle weight.