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AN EXPERIMENTAL STUDY on the INFLUENCE of MISALIGNMENTS on the STATIC TRANSMISSION ERROR of HYPOID GEAR PAIRS THESIS Presented I

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AN EXPERIMENTAL STUDY on the INFLUENCE of MISALIGNMENTS on the STATIC TRANSMISSION ERROR of HYPOID GEAR PAIRS THESIS Presented I AN EXPERIMENTAL STUDY ON THE INFLUENCE OF MISALIGNMENTS ON THE STATIC TRANSMISSION ERROR OF HYPOID GEAR PAIRS THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Sandeep Makam, B.Tech Graduate Program in Mechanical Engineering The Ohio State University 2010 Master's Examination Committee: Professor Ahmet Kahraman, Advisor Dr. Sandeep Vijayakar Copyright by Sandeep Makam 2010 ABSTRACT An experimental investigation was performed in this study to quantify the influence of gear position errors and misalignments on the loaded static transmission error of a hypoid gear pair. A test machine was designed and procured for this purpose to allow operation of a hypoid gear pair under a given constant torque and at a very low rotational speed. The test set-up incorporated a capability to induce any type of misalignment at any user defined magnitude, including pinion (H), gear (G), shaft off-set (V) and shaft angle () errors, independent of each other in a tightly controlled manner. An encoder-based transmission error measurement system incorporated with the test machine consisted of two high-precision angular optical encoders and a special-purpose analyzer to obtain the transmission error in both time and frequency domains. The test matrix considered in this study included all four types of misalignments at various magnitudes, drive and coast side conditions as well as a typical range of input torque. A 4.1 ratio hypoid gear pair from an automotive axle application was used as the example system. The test results were presented in the form of the variation of the first three harmonic amplitudes of the transmission error as a function of torque and error magnitudes. It was shown the each misalignment impacts the transmission error in different levels. The drive and coast side transmission error measurements were shown ii to differ as well. A nearly “V-shaped” dependence of the first harmonic amplitude of the transmission error to the torque transmitted was also documented regardless of the error type and magnitude applied to the gear pair. iii DEDICATION This document is dedicated to my mom, dad and a friend whose memories I cherish. iv ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor, Prof. Ahmet Kahraman, for this great research opportunity, his guidance throughout my research and his effort in reviewing this dissertation. I am really grateful for his support and advise at various stages of my program. I would also like to express my appreciation to Dr. Sandeep Vijayakar for his patience and effort in being a part of my Masters examination committee. I would like to thank the sponsors of the Gear and Power Transmission Research Laboratory, especially Mazda, Japan and American Axle and Company, Michigan for their financial support throughout my study. I would like to specially thank Samuel Shon for his help, patience and guidance throughout my experiments. I would also like to thank Jonny Harianto and all my lab mates for their help and friendship throughout my study at OSU and beyond. Finally, I deeply appreciate the love and trust shown toward me by my parents, and grandparents, for all of their support and encouragement. A special mention to Sudeeksha for her unfailing encouragement and patience all through. I would also like to thank all my friends here at Columbus for making my life here very memorable. v VITA June 2004 .......................................................National Public School, Bangalore, India 2008................................................................B.Tech. Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India 2008 to present ..............................................Graduate Research Associate, Gear and Power Transmission Research Laboratory, Department of Mechanical Engineering, The Ohio State University FIELDS OF STUDY Major Field: Mechanical Engineering vi TABLE OF CONTENTS Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iv Acknowledgments............................................................................................................... v Vita ................................................................................................................................. vi List of Tables ...................................................................................................................... x List of Figures .................................................................................................................... xi Nomenclature .................................................................................................................... xv 1 Introduction .................................................................................................................... 1 1.1 Background, Literature Survey and Motivation .................................................... 1 1.2 Scope and Objective .............................................................................................. 4 1.3 Thesis Outline ........................................................................................................ 5 2 Hypoid Gear Test Methodology .................................................................................... 7 2.1 Introduction ........................................................................................................... 7 2.2 Description of the Hypoid Gear Pair Test Machine.............................................. 8 vii 2.3 Instrumentation and Measurement Systems ....................................................... 13 2.4 Application of Intentional Misalignments to the Hypoid Gear Pair ................... 16 2.4.1 Application of the H Error ....................................................................... 19 2.4.2 Application of the V error ........................................................................ 22 2.4.3 Application of the G error ........................................................................ 22 2.4.4 Application of the γ error ......................................................................... 26 2.5 Test Procedure ..................................................................................................... 29 2.6 Test Specimens and Test Matrix .......................................................................... 31 3 Experimental Results ................................................................................................... 34 3.1 Introduction .......................................................................................................... 34 3.2 Analysis of an Example Measurement. ............................................................... 35 3.3 Repeatability of the Experiments ......................................................................... 41 3.4 Gear Pair Backlash Measurements ...................................................................... 41 3.5 Transmission Error Test Results .......................................................................... 45 3.5.1 Influence of Torque on the Transmission Error ........................................ 45 3.5.2 Influence of the H error on the Transmission Error .................................. 49 3.5.3 Influence of the V error on the Transmission Error ................................... 52 3.5.4 Influence of the G error on the Transmission Error .................................. 55 viii 3.5.5 Influence of the γ error on the Transmission Error ................................... 57 4 Summary and Conclusions ......................................................................................... 62 4.1 Summary ............................................................................................................. 62 4.2 Conclusions ......................................................................................................... 63 4.3 Recommendations for Future Work.................................................................... 65 References ......................................................................................................................... 67 ix LIST OF TABLES 1 Basic gear geometry parameters of the test specimens. ............................................. 32 2 Test matrix for the loaded static transmission error tests on the hypoid gear pair. ... 33 x LIST OF FIGURES 1 Picture of the hypoid gear test machine used in this study. ....................................... 9 2 Top view schematic layout of the hypoid gear test machine showing its main components . ............................................................................................................ 10 3 Mounting details of Rear Axle gear pair.................................................................. 12 4 Schematic showing the control-setup and the data acquisition system in the hypoid test rig. .................................................................................................................... 15 5 Definition of pinion and gear position errors of a hypoid gear pair. ....................... 18 6 The H error setup mechanism. ................................................................................. 20 7 Calibrated H blocks.................................................................................................
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