DEVELOPMENT OF AN OFF-ROAD CAPABLE TIRE MODEL FOR VEHICLE DYNAMICS SIMULATIONS by Brendan Juin-Yih Chan Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy In Mechanical Engineering Dr. Corina Sandu Dr. Mehdi Ahmadian Dr. Saied Taheri Dr. Dennis Hong Dr. Marte Gutierrez Dr. Harry Dankowicz Mr. David Glemming 14th January 2008 Blacksburg, Virginia Keywords: Terramechanics, tire model, vehicle dynamics, off-road © Copyright 2008 Brendan J. Chan DEVELOPMENT OF AN OFF-ROAD CAPABLE TIRE MODEL FOR VEHICLE DYNAMICS SIMULATIONS Brendan Juin-Yih Chan (ABSTRACT) The tire is one of the most complex subsystems of the vehicle. It is, however, the least understood of all the components of a car. Without a good tire model, the vehicle simulation handling response will not be realistic, especially for maneuvers that require a combination of braking/traction and cornering. Most of the simplified theoretical developments in tire modeling, however, have been limited to on-road tire models. With the availability of powerful computers, it can be noted that majority of the work done in the development of off-road tire models have mostly been focused on creating better Finite Element, Discrete Element, or Boundary Element models. The research conducted in this study deals with the development of a simplified tire brush-based tire model for on-road simulation, together with a simplified off-road wheel/tire model that has the capability to revert back to on-road trend of behavior on firmer soils. The on-road tire model is developed based on observations and insight of empirical data collected by NHSTA throughout the years, while the off-road tire model is developed based on observations of experimental data and photographic evidence collected by various terramechanics researchers within the last few decades. The tire model was developed to be used in vehicle dynamics simulations for engineering mobility analysis. Vehicle-terrain interaction is a complex phenomena governed by soil mechanical behavior and tire deformation. The theoretical analysis involved in the development of the wheel/ tire model relies on application of existing soil mechanics theories based on strip loads to determine the tangential and radial stresses on the soil-wheel interface. Using theoretical analysis and empirical data, the tire deformation geometry is determined to establish the tractive forces in off-road operation. ii To illustrate the capabilities of the models developed, a rigid wheel and a flexible tire on deformable terrain is implemented and output of the model was computed for different types of soils; a very loose and deformable sandy terrain and a very firm and cohesive Yolo loam terrain. The behavior of the wheel/tire model on the two types of soil is discussed. The outcome of this work shows results that correlate well with the insight from experimental data collected by various terramechanics researchers throughout the years, which is an indication that the model presented can be used as a subsystem in the modeling of vehicle-terrain interaction to acquire more insight into the coupling between the tire and the terrain. iii ACKNOWLEDGEMENT I wish to thank my advisor Dr. Corina Sandu, who, over the course of my time as a graduate student, has been a great source of inspiration. Throughout my time here, Dr. Sandu has served as both a mentor and friend, and I greatly appreciate her support. I wish to also thank the members of my Ph.D. committee for their guidance and support throughout the entire research effort, and for their counsel in my work during my time at Virginia Tech. My gratitude goes forth to Dr. Mehdi Ahmadian, Dr. Saied Taheri, Dr. Dennis Hong, Dr. Marte Gutierrez, Dr. Harry Dankowicz and Mr. David Glemming from Goodyear Tire and Rubber Company. Their input to my work has often provided me with guidance that steered me in the right direction. In addition to the faculty, I would also like to thank the department and the various sources of funding that has graciously funded my studies. I would also like to thank Dr. Steve Southward and Dan Reader in PERL for allowing the use of the equipment in the quarter car rig in Danville. Their assistance during the time we were assembling the tire mechanics rig are greatly appreciated. My gratitude also goes to Scott Israel for his hospitality during my time in Danville. Special thanks also go to Dr. Kamel Salaani from NHTSA for on-road tire testing data used in this dissertation. I would like to thank all my colleagues at AVDL for their contributions and input to my work. Amongst the group of friends and colleagues that have helped me throughout the years, many of you have helped me in your own little ways. The list of colleagues that have helped me includes but is not limited to Dr. Jeong-Hoi Koo, Dr. Fernando Goncalves, Emmanuel Blanchard, Dr. Mohammad Elahinia, Lin Li, Brian Southern and Brent Ballew. I would like to express my deepest gratitude to my family, and in particular to my mother, Mdm. Sim Kui Hua, for her tireless devotion and love can never be repayed. Finally, I would like to express my sincerest gratitude to my dearest Ing-Ling for putting up with everything. Her support and encouragement has been a constant source of inspiration to me, through the late nights and the long days. I am forever indebted to her. iv “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.” - Sir Isaac Newton Newton’s First Law of Motion Philosophiae Naturalis Principia Mathematica (1687) v CONTENTS (ABSTRACT).................................................................................................................... ii ACKNOWLEDGEMENT................................................................................................ iv LIST OF TABLES............................................................................................................. x LIST OF FIGURES .......................................................................................................... xi 1. Introduction.................................................................................................................. 1 1.1 Preliminary Overview: The big picture.............................................................. 1 1.2 Research Objectives........................................................................................... 4 1.3 Research Approach ............................................................................................ 4 1.4 Research Contribution........................................................................................ 5 1.5 Dissertation Outline........................................................................................... 7 2. Background and Review of Literature......................................................................... 9 2.1 Background: Basic Tire and Vehicle Dynamics Terminology .......................... 9 2.2 Review of Literature: Terramechanics............................................................. 11 2.2.1 Empirical Methods for Traction Modeling .......................................... 13 2.2.2 Analytical Methods for Traction Modeling ......................................... 19 2.2.3 Finite Element/Discrete Element/Lumped Parameter Models for Traction Modeling................................................................................ 23 2.3 Review of Literature: Tire modeling................................................................ 26 2.3.1 Off-road Tire Model: Grecenko Slip and Drift Model......................... 26 2.3.2 Off-road Tire Model: Modified STI Tire Model.................................. 28 2.4 Review of Literature: Summary....................................................................... 28 3. Tire Model Mechanics: On-Road .............................................................................. 30 3.1 Tire Forces and the Contact Patch ................................................................... 30 3.2 Tire Model Development: Brief Overview...................................................... 32 3.3 Vertical Pressure Distribution and Normal Force............................................ 33 3.4 Longitudinal and Lateral Force: Tread and Belt Mechanics............................ 40 vi 3.5 Longitudinal and Lateral Force: Adhesion and Force Limit............................ 46 3.6 Aligning and Overturning Moment: Formulation............................................ 52 3.7 Transient Steering Properties: Relaxation and Time-delay ............................. 54 3.8 Rolling resistance: Steady State Handling ....................................................... 57 3.9 Conicity and Plysteer: Steady State Handling ................................................. 57 3.10 Summary .......................................................................................................... 58 4. Tire Model Mechanics: Off-road............................................................................... 60 4.1 Tire Model: Rigid Wheel Model...................................................................... 60 4.1.1 Rigid Wheel Model: Stationary Vertical Loading ............................... 62 4.1.2 Rigid Wheel Model: Slip and Shear Displacement.............................. 64 4.1.3 Rigid Wheel Model: Stresses and Forces............................................