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Effect of Material Nonlinearity on Rubber Friction a Thesis Presented

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Effect of Material Nonlinearity on Rubber Friction a Thesis Presented Effect of Material Nonlinearity on Rubber Friction A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science Tejas N. Bhave December 2016 © 2016 Tejas N. Bhave. All Rights Reserved. 2 This thesis titled Effect of Material Nonlinearity on Rubber Friction by TEJAS N. BHAVE has been approved for the Department of Mechanical Engineering and the Russ College of Engineering and Technology by Alireza Sarvestani Assistant Professor of Mechanical Engineering Dennis Irwin Dean, Russ College of Engineering and Technology 3 ABSTRACT BHAVE, TEJAS N., M.S., December 2016, Mechanical Engineering Effect of Material Nonlinearity on Rubber Friction Director of thesis: Alireza Sarvestani With the increase in the importance of vehicular transportation, the study of contact patch parameters including the contact patch forces and the tire-road friction has become essential from the perspective of improving vehicle safety as well as vehicle performance. The current work aims at analyzing the effect of the nonlinear elastic and nonlinear viscoelastic nature of tire tread rubber by modifying two commonly used rubber friction models (Gim’s analytical model and Heinrich-Klüppel (HK) friction model) in order to implement the nonlinear elasticity and the nonlinear viscoelasticity of rubber. Gim’s analytical model is modified by changing the linear elastic constitutive equation used in the original model to a nonlinear elastic equation based on the strain energy density of rubber. Results are obtained for a test simulation using this modified model and an experimental method is proposed to validate the modified model’s force predictions. The HK friction model computes the hysteretic sliding friction coefficient of rubber based on the viscoelastic modulus. It however, does not consider the (experimentally proven) dependence of viscoelastic modulus of rubber on the applied strain amplitude and temperature. The current work thus aims at implementing this dependence and modifying the classical HK friction model. A test simulation run for a rubber block sliding on a rough surface using the modified HK friction model yielded friction results that are sensitive to the input strain amplitude and temperature. 4 DEDICATION Dedicated to my family 5 ACKNOWLEDGMENTS I am indebted to my thesis advisor Dr. Alireza Sarvestani for his able guidance, sound advice (both technical and worldly) and unwavering support during this two-year journey that was my thesis research. It was the balance that he struck between allowing me to work independently and monitoring and helping me whenever I was stranded, that helped me develop not only as a researcher, but also as an engineering professional. I was able to achieve more in my academic life here at Ohio University than I could have ever imagined thanks to his support and encouragement. I would also like to thank my thesis committee members Dr. John Cotton, Dr. Munir Nazzal and Dr. Ardalan Vahidi for their valuable advice regarding my research work. Their technical expertise, help, advice and suggestions has helped me shape my research work. Furthermore, I would like to thank my lab colleagues, Mohammad Jafari Tehrani and Mohammad Hossein Moshaei for their support, encouragement and help during the course of my research. Thanks are due to Mayur, Manish, Shantanu, Pratik, Amit, Ajinkya, Aditya, Aniruddha, Cody, John, Brian McCoy and the Petitt family for all their help and support. I would also like to thank everybody, who in any way, has offered their help, support, guidance or advice throughout this process. Most importantly, I would like to thank my family and especially my parents. The daily conversations with them helped me tide over some difficult times. If it were not for their endless affection and support, at all levels, I am sure I would not have progressed to where I stand on this day. 6 TABLE OF CONTENTS Page Abstract ............................................................................................................................... 3 Dedication ........................................................................................................................... 4 Acknowledgments............................................................................................................... 5 List of Tables ...................................................................................................................... 8 List of Figures ..................................................................................................................... 9 1 Research Background ............................................................................................... 11 2 Introduction ............................................................................................................... 14 2.1 The Tire ................................................................................................................... 14 2.2 Introduction to Tread Rubber.................................................................................. 15 2.3 Properties of Tread Rubber ..................................................................................... 16 2.4 Contact Patch in Tires ............................................................................................. 19 3 Tire Road Interaction Models ................................................................................... 22 3.1 Introduction and Classification ............................................................................... 22 3.2 Brush Model Method .............................................................................................. 24 3.3 Improvements in the Classical Brush Model .......................................................... 26 3.3.1 Combined Slips ................................................................................................ 26 3.3.2 Pressure Distribution in the Contact Patch ...................................................... 28 3.3.3 Velocity-Dependent Coefficient of Friction .................................................... 30 3.3.4 Pressure Dependent Coefficient of Friction ..................................................... 32 3.3.5 The TreadSim Model ....................................................................................... 33 3.3.6 Applications of the Brush Model Method ....................................................... 34 3.4 Thesis Objective...................................................................................................... 35 4 Non Linear Elasticity of Rubber ............................................................................... 37 4.1 Expression for Material Nonlinearity of Rubber .................................................... 37 4.2 Friction Force Predictions Using Modified Brush Model Method ......................... 42 4.2.1 Longitudinal Force Prediction Using the Modified Brush Model Method ...... 42 4.2.2 Implementing Nonlinearity into Lateral Force Calculations ........................... 48 4.3 Proposed Method to Validate Modified Brush Model ............................................ 53 5 Effect of Tread Rubber Viscoelasticity on Tire Friction .......................................... 55 5.1 Adhesive and Hysteretic Friction............................................................................ 55 7 5.2 Introduction to Viscoelasticity ................................................................................ 56 5.3 Rubber Viscoelasticity and Hysteresis Friction ...................................................... 59 5.4 Classical HK Friction Model .................................................................................. 61 5.5 The Payne Effect ..................................................................................................... 63 5.6 Modified HK Model with Payne Effect .................................................................. 65 5.7 Temperature Dependent Rubber Viscoelasticity .................................................... 70 5.8 Strain Amplitude and Flash Temperature Dependent Modified HK Model ........... 73 6 Summary and Conclusions ....................................................................................... 76 References ......................................................................................................................... 79 Appendix: Supplemental Files .......................................................................................... 85 8 LIST OF TABLES Page Table 1: Input Parameters for Prediction of Longitudinal Force Using the Modified Brush Model Method ................................................................................................................... 44 Table 2: Input Parameters for Calculating the Lateral Force Due To Slip Angle Using the Modified Brush Model Method ........................................................................................ 50 Table 3: Input Parameters for Calculating the Lateral Force Due To Camber Angle Using the Modified Brush Model Method .................................................................................. 51 9 LIST OF FIGURES Page Figure 2.1 Nonlinear Stress-Strain Curve for Rubber ...................................................... 17 Figure 2.2 Stress Strain Curve for Viscoelastic Material ................................................. 18 Figure 2.3 Tire Contact Patch ..........................................................................................
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