University of Windsor Scholarship at UWindsor Electronic Theses and Dissertations Theses, Dissertations, and Major Papers 2017 A Multibody Dynamics Model of a Motorcycle with a Multi-link Front Suspension Changdong Liu University of Windsor Follow this and additional works at: https://scholar.uwindsor.ca/etd Recommended Citation Liu, Changdong, "A Multibody Dynamics Model of a Motorcycle with a Multi-link Front Suspension" (2017). Electronic Theses and Dissertations. 7376. https://scholar.uwindsor.ca/etd/7376 This online database contains the full-text of PhD dissertations and Masters’ theses of University of Windsor students from 1954 forward. These documents are made available for personal study and research purposes only, in accordance with the Canadian Copyright Act and the Creative Commons license—CC BY-NC-ND (Attribution, Non-Commercial, No Derivative Works). Under this license, works must always be attributed to the copyright holder (original author), cannot be used for any commercial purposes, and may not be altered. Any other use would require the permission of the copyright holder. Students may inquire about withdrawing their dissertation and/or thesis from this database. For additional inquiries, please contact the repository administrator via email ([email protected]) or by telephone at 519-253-3000ext. 3208. A Multibody Dynamics Model of a Motorcycle with a Multi-Link Front Suspension by Changdong Liu A esis Submied to the Faculty of Graduate Studies through Mechanical Engineering in Partial Fullment of the Requirements for the Degree of Master of Applied Science at the University of Windsor Windsor, Ontario, Canada ©2017 Changdong Liu A Multibody Dynamics Model of a Motorcycle with a Multi-link Front Suspension by Changdong Liu APPROVED BY S. Cheng Department of Civil and Environmental Engineering J. Johrendt Department of Mechanical, Automotive, & Materials Engineering B. Minaker, Advisor Department of Mechanical, Automotive, & Materials Engineering November 3, 2017 iii Author’s Declaration of Originality I hereby certify that I am the sole author of this thesis and that no part of this thesis has been published or submied for publication. I certify that, to the best of my knowledge, my thesis does not infringe upon anyone’s copyright nor violate any proprietary rights and that any ideas, techniques, quotations, or any other material from the work of other people included in my thesis, published or otherwise, are fully acknowledged in accordance with the standard referencing practices. Furthermore, to the extent that I have included copyrighted material that surpasses the bounds of fair dealing within the meaning of the Canada Copyright Act, I certify that I have obtained a wrien permission from the copyright owner(s) to include such material(s) in my thesis and have included copies of such copyright clearances to my appendix. I declare that this is a true copy of my thesis, including any nal revisions, as approved by my thesis commiee and the Graduate Studies oce, and that this thesis has not been submied for a higher degree to any other University or Institution. iv Abstract e development of motorcycles has been around for over a century. Nowadays, it has become one of the most popular means of transportation in the world. It is well known that the telescopic fork is the most widely used front suspension for motorcycles, because the rst motorcycle was a bicycle with a small engine aached to the frame. However, there are a number of shortcomings inherent in this design. erefore, a novel multi-link suspension has been designed for the front assembly of the motorcycle in this research. In order to compare the performance between telescopic fork and multi-link front suspension motorcycles, linear and nonlinear models were built and simulated under a variety of dierent conditions. Furthermore, an appropriate method of comparison between conventional and multi-link models was developed, and the assessment standard of performance for conventional and multi-link models was explored in this research. v To my mother, for her marvelous love and support. vi Anowledgements is thesis writing is nearing its end. Looking back over the past two years, many people have given me support and made this work possible, it is hard to thank all those people enough for their contributions and advice. I am always grateful for their help. First and foremost, my deepest gratitude to my advisor Dr. B.P. Minaker, for his excellent erudition, altruism and patience. Under his instruction and help, the last two years of my MASc career is the best experience I have ever had. I am very honored to have an advisor who gave me the freedom to explore and has inspired me to be positive and condent during my demanding MASc student life. His patience and guidance helped me to complete a number of research projects. I am oen aracted by his easy to understand and interesting teaching method, which also expanded my knowledge and is very helpful in nishing my thesis. I will never be able to adequately express my gratitude. I would like to thank my mother, and my family. With their support and encouragement, I can go further along the way of my choice. ey give me seless love; home is always my strongest shield and source of strength. I would also like to express my appreciation to all my friends; it was always a pleasure coming to work every day with such lovely and engaging people. Moreover, I would like to express my sincere gratitude to my thesis commiee members who have oered very valuable opinions and suggestions. vii Contents Declaration of Originality iii Abstract iv Dedication v Anowledgements vi List of Tables x List of Figures xii List of Abbreviations xvi Nomenclature xvii 1 Introduction 1 1.1 Background.............................................3 1.1.1 Development of the Bicycle................................3 1.1.2 Development of the Motorcycle..............................7 1.1.3 Motorcycle Front Suspension............................... 12 1.1.4 Patent Search........................................ 16 2 Motivation, Objectives, and esis Structure 20 2.1 Motivation.............................................. 20 2.2 Research Objectives......................................... 21 2.2.1 Comparisons of Simulations and Experiment...................... 22 2.3 esis Structure........................................... 24 3 Motorcycle Dynamics and Modeling 26 3.1 Kinematics of Motorcycles..................................... 26 CONTENTS viii 3.1.1 e Geometry of Motorcycles............................... 28 3.1.2 Kinematics of the Steering Mechanism.......................... 30 3.1.3 Roll Motion and Steering.................................. 32 3.2 Out-of-plane Modes......................................... 33 3.3 In-plane Modes........................................... 35 3.3.1 In-plane Dynamics Model................................. 35 3.4 Front Suspension Structure and Characteristics.......................... 38 3.5 Motorcycle Tires........................................... 43 3.6 Multibody Dynamics........................................ 47 3.6.1 Model in EoM Soware.................................. 48 3.6.2 Model in Altair MotionView® ............................... 51 3.7 Generation of a Random Road................................... 53 4 Simulation Results 55 4.1 Kinematics Simulation....................................... 55 4.2 Tire Test............................................... 57 4.3 Out-of-plane Simulation...................................... 59 4.3.1 Unforced Straight Running Simulation.......................... 59 4.3.2 Forced Straight Running Simulation........................... 66 4.4 In-plane Simulation......................................... 69 4.4.1 Braking Simulation..................................... 70 4.4.2 Plank Road Simulation................................... 78 4.4.3 Random Road Simulation................................. 80 5 Discussion of Results 96 5.1 Model Assesment.......................................... 96 5.1.1 Caster Angle and Trail................................... 97 5.1.2 Motorcycle Tire....................................... 97 5.2 Out-of-plane Simulation Analysis................................. 97 5.2.1 Unforced Straight Running Simulation Analysis..................... 98 5.2.2 Forced Straight Running Simulation Analysis...................... 102 5.3 In-plane Simulation Analysis.................................... 106 5.3.1 Braking Simulation Analysis................................ 106 5.3.2 Plank Road Simulation Analysis.............................. 112 5.3.3 Random Road Simulation Analysis............................ 113 CONTENTS ix 6 Conclusions, Recommendations, and Contributions 122 6.1 Conclusions............................................. 122 6.2 Recommendations.......................................... 123 6.3 Contributions............................................ 124 References 127 Appendix A 131 A.1 Matlab® Codes of Random Road................................. 131 A.2 Matlab® Codes of Power Spectral Density............................ 133 Appendix B 134 B.1 Eigenvalues, Natural Frequency, Damping Ratio of Telescopic Front Suspension at 5 m/s.. 134 B.2 Eigenvalues, Natural Frequency, Damping Ratio of Telescopic Front Suspension at 10 m/s.. 135 B.3 Eigenvalues, Natural Frequency, Damping Ratio of Telescopic Front Suspension at 40 m/s.. 137 B.4 Eigenvalues, Natural Frequency, Damping Ratio of Multi-link Front Suspension at 5 m/s.. 138 B.5 Eigenvalues, Natural Frequency,