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Vibration and Sound Radiation Analysis of Vehicle Powertrain

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Vibration and Sound Radiation Analysis of Vehicle Powertrain Vibration and Sound Radiation Analysis of Vehicle Powertrain Systems with Right-Angle Geared Drive A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mechanical Engineering, Department of Mechanical and Materials Engineering College of Engineering & Applied Science University of Cincinnati March 2017 By Yawen Wang M.S., Mechanical Engineering, University of Cincinnati, Cincinnati, USA, 2013 B.S., Mechanical Engineering, Chongqing University, Chongqing, P. R. China, 2010 Committee chair: Dr. Teik C. Lim Members: Dr. Jay Kim Dr. Manish Kumar Dr. Michael J. Alexander-Ramos 1 ABSTRACT Hypoid and bevel gears are widely used in the rear axle systems for transmitting torque at right angle. They are often subjected to harmful dynamic responses which cause gear whine noise and structural fatigue problems. In the past, researchers have focused on gear noise reduction through reducing the transmission error, which is considered as the primary excitation of the geared system. Effort on the dynamic modeling of the gear-shaft-bearing-housing system is still limited. Also, the noise generation mechanism through the vibration propagation in the geared system is not quite clear. Therefore, the primary goal of this thesis is to develop a system-level model to evaluate the vibratory and acoustic response of hypoid and bevel geared systems, with an emphasis on the application of practical vehicle powertrain system. The proposed modeling approach can be employed to assist engineers in quiet driveline system design and gear whine troubleshooting. Firstly, a series of comparative studies on hypoid geared rotor system dynamics applying different mesh formulations are performed. The purpose is to compare various hypoid gear mesh models based on pitch-cone method, unloaded and loaded tooth contact analysis. Consequently, some guidelines are given for choosing the most suitable mesh representation. Secondly, an integrated approach is proposed for the vibro-acoustic analysis of axle systems with right-angle geared drive. The approach consists of tooth contact analysis, lumped parameter gear dynamic model, finite element model and boundary element model. Then, a calculation method for tapered roller bearing stiffness matrix is introduced, which is based on the Finite Element/Contact Mechanics model of axle system with right-angle geared system. The effect of rigid bearing support and flexible bearing support is studied by comparing the flexible axle system model with rigid supported gear pair model. Other important system dynamic factors are also investigated, ii such as the gear-shaft interaction, rotordynamics effect and housing flexibility. Finally, some conclusions and recommendations for future studies are given. iii iv ACKNOWLEDGEMENTS “Trust in the Lord with all your heart, and do not lean on your own understanding. In all your ways acknowledge him, and he will make straight your paths.” Proverbs 3:5-6 First and above all, I would like to thank God for giving me strength and wisdom to write this dissertation. I would like to express my sincere gratitude to my advisor Dr. Teik C. Lim for his guidance and support in the preparation of this dissertation and throughout my graduate study. I am very thankful to Dr. Jay Kim, Dr. Manish Kumar and Dr. Michael J. Alexander-Ramos for serving as my committee members and giving me valuable instructions. My sincere appreciation also goes to Dr. Sandeep Vijayakar at Advanced Numerical Solutions for his help in developing the gear contact model. I am grateful for the financial support provided throughout my graduate work by the Hypoid and Bevel Gear Mesh and Dynamic Modeling Consortium, the Vibro-Acoustic and Sound Quality Research Laboratory, the Department of Mechanical Engineering and the Graduate school. I would also like to express my gratitude to all my colleagues at the Vibro-Acoustic and Sound Quality Research Laboratory in University of Cincinnati. I am greatly indebted to Dr. Junyi Yang, who gave me many academic suggestions and shared with me his insights. My special thanks also go to Dr. Mingfeng Li and Dr. Guohua Sun, for their support and review of this thesis. Finally, I would like to thank my parents Rongfu Wang and Qimei Zhang for their unconditional love and support. v TABLE OF CONTENTS ABSTRACT .................................................................................................................................... ii ACKNOWLEDGEMENTS ............................................................................................................ v TABLE OF CONTENTS ............................................................................................................... vi LIST OF PUBLICATIONS ........................................................................................................... xi LIST OF TABLES ....................................................................................................................... xiii LIST OF FIGURES ..................................................................................................................... xiv LIST OF ABBREVIATIONS ....................................................................................................... xx LIST OF SYMBOLS ................................................................................................................... xxi Chapter 1 Introduction .................................................................................................................... 1 1.1 Motivation .............................................................................................................................. 1 1.2 Literature Review ................................................................................................................... 2 1.3 Scope and Objectives ............................................................................................................. 5 1.4 Organization ........................................................................................................................... 6 Chapter 2 Comparative Analysis of the Hypoid Geared Rotor System Dynamics Applying Dissimilar Tooth Meshing Formulations ............................................................................ 9 2.1 Introduction ............................................................................................................................ 9 2.2 Gear Mesh Models ............................................................................................................... 10 2.2.1 Pitch Cone-based mesh model ..................................................................................... 10 2.2.2 Unloaded tooth contact analysis based mesh model .................................................... 12 vi 2.2.3 Loaded tooth contact analysis based mesh model ....................................................... 13 2.2.4 Mesh stiffness calculation in pitch cone and TCA based mesh models ...................... 16 2.3 Hypoid Geared Rotor System Dynamics ............................................................................. 18 2.3.1 Light Load Case ........................................................................................................... 19 2.3.2 Heavy Load Case ......................................................................................................... 20 2.3.3 Multi-point Mesh Case................................................................................................. 21 2.4 Conclusion ............................................................................................................................ 23 Chapter 3 Vibration and Sound Radiation Analysis of Vehicle Axle Systems Using an Integrated Approach ........................................................................................................................... 25 3.1 Introduction .......................................................................................................................... 25 3.2 Gear Mesh and Dynamic Model ........................................................................................... 26 3.2.1 Gear Mesh Model ........................................................................................................ 26 3.2.2 Gear Dynamics Model ................................................................................................. 29 3.3 Vibration and Sound Radiation Analysis ............................................................................. 32 3.3.1 Housing Vibration Analysis ......................................................................................... 32 3.3.2 Sound Radiation Analysis ............................................................................................ 33 3.4 Conclusions .......................................................................................................................... 35 Chapter 4 Tapered Roller Bearing Contact Analysis and Stiffness Calculation .......................... 36 4.1 Introduction .......................................................................................................................... 36 4.2 Finite Element/Contact Mechanics Model ........................................................................... 37 4.2.1 Gear Mesh Model ........................................................................................................ 37 4.2.2 Bearing Model ............................................................................................................
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