The Science of Vehicle Dynamics Massimo Guiggiani The Science of Vehicle Dynamics Handling, Braking, and Ride of Road and Race Cars Massimo Guiggiani Dip. di Ingegneria Civile e Industriale Università di Pisa Pisa, Italy ISBN 978-94-017-8532-7 ISBN 978-94-017-8533-4 (eBook) DOI 10.1007/978-94-017-8533-4 Springer Dordrecht Heidelberg New York London Library of Congress Control Number: 2013958104 © Springer Science+Business Media Dordrecht 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. 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While the advice and information in this book are believed to be true and accurate at the date of pub- lication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Disclaimer: This book is not intended as a guide for designing, building or modifying vehicles, and anyone who uses it as such does so entirely at his/her own risk. Testing vehicles may be dangerous. The author and publisher are not liable for whatsoever damage arising from application of any information contained in this book. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface Vehicle dynamics should be a branch of Dynamics, but, in my opinion, too often it does not look like that. Dynamics is based on terse concepts and rigorous reasoning, whereas the typical approach to vehicle dynamics is much more intuitive. Qualita- tive reasoning and intuition are certainly very valuable, but they should be supported and confirmed by scientific and quantitative results. I understand that vehicle dynamics is, perhaps, the most popular branch of Dy- namics. Almost everybody has been involved in discussions about some aspects of the dynamical behavior of a vehicle (how to brake, how to negotiate a bend at high speed, which tires give best performance, etc.). At this level, we cannot expect a deep knowledge of the dynamical behavior of a vehicle. But there are people who could greatly benefit from mastering vehicle dynam- ics. From having clear concepts in mind. From having a deep understanding of the main phenomena. This book is intended for those people who want to build their knowledge on sound explanations, who believe equations are the best way to for- mulate and, hopefully, solve problems. Of course along with physical reasoning and intuition. I have been constantly alert not to give anything for granted. This attitude has led to criticize some classical concepts, such as self-aligning torque, roll axis, understeer gradient, handling diagram. I hope that even very experienced people will find the book interesting. At the same time, less experienced readers should find the matter explained in a way easy to absorb, yet profound. Quickly, I wish, they will feel not so less experienced any more. Acknowledgments Over the last few years I have had interactions and discussions with several engineers from Ferrari Formula 1. The problems they constantly have to face have been among the motivations for writing this book. Moreover, their deep knowledge of vehicle dynamics has been a source of inspiration. I would like to express my gratitude to Maurizio Bocchi, Giacomo Tortora, Carlo Miano, Marco Fainello, Tito Amato (presently at Mercedes), and Gabriele Pieraccini (presently at Bosch). I wish to thank Dallara Automobili and, in particular, Andrea Toso, Alessandro Moroni, and Luca Bergianti. They have helped me in many ways. v vi Preface At the Università di Pisa there are an M.S. degree course in Vehicle Engineering (where I teach Vehicle Dynamics) and a Ph. D. program in Vehicle Engineering and Transportation Systems. This very lively environment has played a crucial role in the development of some of the most innovative topics in this book. In particular, I wish to acknowledge the contribution of my colleague Francesco Frendo, and of my former Ph. D. students Antonio Sponziello, Riccardo Bartolozzi, and Francesco Bucchi. Francesco Frendo and Riccardo Bartolozzi have also reviewed part of this book. During the last six years I have been the Faculty Advisor of E-Team, the Formula Student team of the Università di Pisa. I thank all the team members. It has been a very interesting and rewarding experience, both professionally and personally. Testing real vehicles is essential to understand vehicle dynamics. I wish to thank Danilo Tonani, director of FormulaGuidaSicura, for having given me the opportu- nity of becoming a safe driving instructor. Every year, he organizes an excellent safe driving course for the M.S. students in Vehicle Engineering of the Università di Pisa. My collaborators and dear friends Alessio Artoni and Marco Gabiccini have care- fully reviewed this book. I am most grateful to them for their valuable suggestions to correct and improve the text. Pisa, Italy Massimo Guiggiani October 2013 Contents 1 Introduction ............................... 1 1.1 Vehicle Definition ......................... 2 1.2 Vehicle Basic Scheme ....................... 3 References ................................ 6 2 Mechanics of the Wheel with Tire ................... 7 2.1 The Tire as a Vehicle Component ................. 8 2.2 Rim Position and Motion . .................. 9 2.3 Carcass Features ......................... 12 2.4 ContactPatch........................... 13 2.5 FootprintForce.......................... 14 2.5.1PerfectlyFlatRoadSurface................ 16 2.6 Tire Global Mechanical Behavior ................. 17 2.6.1TireTransientBehavior.................. 17 2.6.2 Tire Steady-State Behavior ................ 18 2.6.3 Rolling Resistance . .................. 20 2.6.4 Speed Independence (Almost) .............. 21 2.6.5 Pure Rolling (not Free Rolling) .............. 21 2.7 TireSlips............................. 26 2.7.1 Rolling Velocity ...................... 27 2.7.2 Definition of Tire Slips .................. 27 2.7.3SlipAngle......................... 30 2.8 GripForcesandTireSlips.................... 31 2.9 TireTesting............................ 33 2.9.1PureLongitudinalSlip.................. 34 2.9.2PureLateralSlip..................... 35 2.10MagicFormula.......................... 38 2.11 Mechanics of Wheels with Tire .................. 39 2.12Summary............................. 43 2.13 List of Some Relevant Concepts ................. 44 References ................................ 44 vii viii Contents 3 Vehicle Model for Handling and Performance ............ 47 3.1 MathematicalFramework..................... 48 3.2 Vehicle Congruence (Kinematic) Equations . ........ 48 3.2.1 Velocities ......................... 48 3.2.2YawAngleandTrajectory................ 49 3.2.3VelocityCenter...................... 51 3.2.4 Fundamental Ratios . .................. 52 3.2.5 Accelerations and Radii of Curvature . ........ 53 3.2.6 Acceleration Center . .................. 54 3.2.7TireKinematics(TireSlips)............... 56 3.3 Vehicle Constitutive (Tire) Equations ............... 58 3.4 Vehicle Equilibrium Equations .................. 59 3.5 ForcesActingontheVehicle................... 59 3.5.1Weight........................... 60 3.5.2 Aerodynamic Force . .................. 60 3.5.3 Road-Tire Friction Forces ................. 61 3.5.4 Road-Tire Vertical Forces ................. 63 3.6 Vehicle Equilibrium Equations (more Explicit Form) ...... 63 3.7 LoadTransfers.......................... 65 3.7.1LongitudinalLoadTransfer................ 65 3.7.2LateralLoadTransfers.................. 66 3.7.3 Vertical Loads on Each Tire ............... 66 3.8 Suspension First-Order Analysis ................. 67 3.8.1 Suspension Reference Configuration . ........ 67 3.8.2 Suspension Internal Coordinates ............. 68 3.8.3CamberVariation..................... 69 3.8.4VehicleInternalCoordinates............... 70 3.8.5RollandVerticalStiffnesses............... 71 3.8.6 Suspension Internal Equilibrium ............. 73 3.8.7EffectsofaLateralForce................. 74 3.8.8No-rollCentersandNo-rollAxis............. 75 3.8.9ForcesattheNo-rollCenters............... 77 3.8.10 Suspension Jacking . .................. 78 3.8.11RollAngleandLateralLoadTransfers.......... 79 3.8.12ExplicitExpressionsofLateralLoadTransfers....