THEORETICAL ANALYSES OF ROLL-AND PITCH-COUPLED HYDRO- PNEUMATIC STRUT SUSPENSIONS Dongpu Cao A Thesis in The Department of Mechanical and Industrial Engineering Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Mechanical Engineering) at Concordia University Montreal, Quebec, Canada March 2008 © Dongpu Cao, 2008 Library and Bibliotheque et 1*1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A0N4 Ottawa ON K1A0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-37763-5 Our file Notre reference ISBN: 978-0-494-37763-5 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par Plntemet, prefer, telecommunication or on the Internet, distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, electronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. 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Canada ABSTRACT Dongpu Cao, Ph.D. Concordia University, 2008 Vehicle suspension design and dynamics analysis play a key role in enhancement of automotive system performance. Despite extensive developments in actively-controlled suspensions, their commercial applications have been limited due to the associated high cost and weight. Alternative designs in either passive or semi-active suspensions are highly desirable to achieve competitive vehicle performance with relatively lower cost and greater reliability. This dissertation research proposes two hydro-pneumatic suspension strut designs, including a twin-gas-chamber strut, and systematically investigates various concepts in roll- and pitch-coupled suspensions employing hydraulic, pneumatic and hybrid fluidic interconnections between the wheel struts. The proposed strut designs, including single- and twin-gas-chamber struts, offer larger working area and thus lower operating pressure, and integrate damping valves. Nonlinear mathematical models of the strut forces due to various interconnected and unconnected suspension configurations are formulated incorporating fluid compressibility, floating piston dynamics, and variable symmetric and asymmetric damping valves, which clearly show the feedback damping effects of the interconnections between different wheel struts. The properties and dynamic responses of the proposed concepts in roll- and pitch- coupled suspension struts are evaluated in conjunction with in-plane and three- dimensional nonlinear vehicle models. The validity of the vehicle models is demonstrated iii by comparing their responses with the available measured data. The analyses of the proposed coupled suspensions are performed to derive their bounce-mode, anti-roll, anti- pitch and warp-mode properties, and vehicle dynamic responses to external excitations. These include road roughness, steering and braking, and crosswinds. The results suggest that the fluidically-coupled passive suspension could yield considerable benefits in enhancing vehicle ride and handing performance. Furthermore these offer superior design flexibility. The suspension struts offer a large number of coupling possibilities in the three- dimensions, some of which however would not be feasible, particularly for commercial vehicles where suspension loads may vary considerably. A generalized analytical model for a range of interconnected suspensions is thus developed, and a performance criterion is formulated to assess the feasibility of a particular interconnection in a highly efficient manner. The handling and directional responses of a three-dimensional vehicle model employing X-coupled hydro-pneumatic suspension are evaluated under split-p. straight- line braking and braking-in-a-turn maneuvers. The results clearly show that the X- coupled suspension offers enhanced anti-roll and anti-pitch properties while retaining the soft vertical ride and warp properties. Fundamental pitch and vertical dynamics of a road vehicle are also considered to derive a set of essential design rules for suspension design and tuning for realizing desirable pitch performance. IV ACKNOWLEDGEMENTS The author is sincerely grateful to his supervisors, Dr. S. Rakheja and Dr. C.-Y. Su, for their initiation of the research project and their guidance and efforts throughout the thesis work. The author also wishes to acknowledge Quebec Government, Concordia University and CONCAVE Center for their financial support: International Tuition Fee Remission, Graduate Fellowship and Research Assistantship, respectively. The author also thanks the colleagues, faculty and staff at the Department of Mechanical and Industrial Engineering, and CONCAVE Center, for their contributions to this thesis work. Finally, the author would like to express his special thanks to his wife and members of his family, for their encouragement and supports. The author would like to dedicate this thesis to his wife, Jing Lang. v TABLE OF CONTENTS TABLE OF CONTENTS vi LIST OF FIGURES x LIST OF TABLES xvii NOMENCLATURE xviii CHAPTER 1 1 INTRODUCTION AND LITERATURE REVIEW 1 1.1 Introduction 1 1.2 Literature Review 4 1.2.1 Heavy Vehicle Suspension Design 4 1.2.2 Roll and Pitch Dynamics of Heavy Vehicles 8 1.2.3 Handling and Directional Stability of Heavy Vehicles 15 1.2.4 Ride Dynamics of Heavy Vehicles 26 1.2.5 Vehicle-Road Interactions 30 1.2.6 Passive Interconnected Suspension 32 1.2.7 Semi-Active and Active Interconnected Suspension 40 1.3 Scope and Objectives of the Dissertation 44 CHAPTER 2 50 MODEL DEVELOPMENT OF IN-PLNAE INTERCONNECTED SUSPENSION50 2.1 Introduction 50 2.2 Hydro-Pneumatic Suspension Struts 51 2.3 Formulations of Strut Forces in the Roll Plane 53 2.3.1 Roll Plane Model of a Heavy Vehicle 53 2.3.2 Interconnected and Unconnected Strut forces 55 2.3.3 Twin-Gas-Chamber Strut Forces 66 2.4 Modeling of Roll Plane Properties of Suspension Systems 68 2.4.1 Properties of Interconnected and Unconnected Suspensions 69 2.4.2 Properties of Twin-Gas-Chamber Suspension 76 2.5 Pitch Plane Modeling of a Heavy Vehicle and Model Validation 81 2.6 Development of a Generalized Model of Suspension Forces 86 vi 2.6.1 A Generalized Model of Suspension Forces 89 2.6.2 Forces due to Pneumatic Configuration (AIP) 93 2.6.3 Forces due to Hydraulic Configuration (BJP) 96 2.6.4 Forces due to Hybrid Configuration (Hjp) 96 2.6.5 Forces due to Unconnected Configuration (Bup) 97 2.6.6 Forces due to Twin-Gas-Chamber Suspension (Aup) 97 2.7 Modeling of Pitch Plane Properties of Different Suspension Systems 98 2.7.1 Suspension Rate Property 98 2.7.2 Pitch Stiffness Property 100 2.7.3 Bounce and Pitch Mode Damping Properties 106 2.8 Summary 109 CHAPTER 3 110 PERFORMANCE ANALYSIS OF ROLL-INTERCONNECTED SUSPENSIONS 110 3.1 Introduction 110 3.2 Simulation Parameters and Excitations... Ill 3.2.1 Excitations 111 3.3 Relative Roll Plane Properties of Different Suspension Configurations ... 117 3.3.1 Suspension Rate 118 3.3.2 Roll Stiffness 119 3.3.3 Bounce and Roll Mode Damping Properties 122 3.3.4 Design Flexibility of Roll-Interconnected Suspensions 124 3.4 Roll Dynamic Responses of the Vehicle Model with Roll-Connected Suspensions 129 3.4.1 Performance Measures 130 3.4.2 Dynamic Responses 131 3.5 Summary 139 CHAPTER 4 141 PERFORMANCE ANALYSIS OF PITCH-INTERCONNECTED SUSPENSIONS 141 4.1 Introduction 141 vii 4.2 Simulation Parameters and Static Properties 142 4.3 Pitch Plane Suspension Properties 144 4.4 Design Flexibility of Pitch Interconnected Suspensions and Discussions.. 150 4.5 Pitch Dynamic Responses of the Vehicle Model with Different Suspension Configurations 154 4.5.1 Excitations and Performance Measures 155 4.5.2 Responses to Braking Inputs 158 4.5.3 Responses to Random Road Inputs 161 4.6 Ride Height Leveling 163 4.6.1 Effects of Load Variations on Suspension Properties and Vehicle Responses 164 4.7 Summary 172 CHAPTER 5 174 ROLL AND PITCH DYNAMIC ANALYSIS OF TWIN-GAS-CHAMBER STRUT SUSPENSION 174 5.1 Introduction 174 5.2 Roll Plane Analysis of Twin-Gas-Chamber Strut Suspension 176 5.2.1 Roll-Plane Property Analysis 177 5.2.2 Design Flexibility of the Twin-Gas-Chamber Strut Suspension 179 5.2.3 Dynamic Responses in the Roll Plane 182 5.3 Pitch Plane Analysis of Twin-Gas-Chamber Strut Suspension 189 5.3.1 Pitch Plane