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Lee Adviser Professor Chia-Hsiang Menq Department of Mechanical Engineering T3MI Number; 9813272 UMI Microform 9813272 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Copyright by David Hochmann 1997 ABSTRACT Current thought is that the main sources of dynamic excitation in spur and helical gearing occurs along the line-of-action and are due to time varying tooth stiffness and static transmission. This study examines friction forces as a potential dynamic excitation source in the gear mesh of involute parallel axis spur and helical gearing. The friction forces act in a direction perpendicular to the line-of-action and occur at the tooth pair contact point. To support the claim that friction force is a potential dynamic excitation source, experimental evidence in the form of shaft motions measured near the support bearings in the line-of-action and off line-of-action directions is presented. These experimental results show that the off line-of-action motion is of the same order of magnitude as the line-of-action motion and at times the off line-of-action motion at gear mesh frequency is several times larger than the line-of-action motion. The shaft motion data is gathered from the published literature and performed experiments. The motions are converted to forces through the support bearing stiffness matrix. Other potential causes of the large off line-of-action shaft motion such as bearing cross coupling phenomena, reduced bearing stiffness, and bearing clearances are examined. The measurement of the shaft motion in the off line-of-action direction is related to the net friction force. The net friction force is the sum of all friction forces on the individual tooth pairs in contact at each instant. A methodology to m easure the individual friction forces for spur gears with a contact ratio less than or equal to two is introduced. The measurement scheme is based on the measurement of the net friction force and of the instantaneous power lost at the gear mesh. A general dynamic model incorporating off line-of-action friction force is introduced. The developed model typically forms nonlinear and linear time varying equations dependent upon the assumed friction force model. From the general model, a gear system supported on rigid bearings is examined in detail both under static and dynamic operating conditions. Under dynamic operating conditions, friction force models based on both a Dry friction and elastohydrodynamic fluid film theory are studied. The only extemal input function examined is a time invariant input torque. A constant input torque highlights the effect of the off line-of-action friction force on the output torque and the normal mesh force. The linear time varying and non-linear equations developed typically are solved using numerical techniques. For a certain class of linear time varying problems incorporating an off line-of-action friction force, an exact analytical solution is presented. Ill ACKNOWLEDGMENTS I would like to express my appreciation to my adviser, Dr. Donald R. Houser for his advice, guidance, and patience throughout the course of this research. I thank the other members of my dissertation committee, Dr. Gary L. Kinzel, Dr. Si C. Lee and Chia-Hsiang Menq for there suggestions and comments. I would like to thank the sponsors of the Gear Dynamics and Gear Noise Research Laboratory. I would also like to thank Fred Oswald for his assistance in the experiments performed at NASA Lewis Research Center, Cleveland Ohio. I would further like to thank the Army Research Office (URI Grant DAA03-92-G-0120), Project Monitor; Dr. T.L. Doligalski for the funding support for this research. I am grateful to the many students of the Gear Lab over the years. I also thank Jim Sorenson for his assistance with the test rigs. Finally, I would like to thank my Mom, Dad, and my Sister. IV VITA April 5, 1967 Bom - Prague, Czechoslovakia. May, 1990 Bachelor of Science in Mechanical Engineering, The University of Texas at San Antonio, San Antonio, Texas. September, 1990-Present Graduate Research Associate, Gear Dynamics and Gear Noise Research Lab, The Ohio State University, Columbus, Ohio. August, 1992 Master of Science in Mechanical Engineering, The Ohio State University, Columbus Ohio. PUBLICATIONS 1. D. Hochmann, D.R. Houser and J. Thomas, "Transmission Error and Load Distribution Analysis of a Spur and Double Helical Gear Pair Used in a Split Path Helicopter Transmission Design", Proceedings of the American Helicopter Society, 1991. 2. D. Hochmann and D.R. Houser, "An Experimental Test Stand for Measurements on Loaded Parallel Axis Gears", Proceedings of the Intemational Gearing Conference, 1994. FIELDS OF STUDY Major Field: Mechanical Engineering Studies in Vibrations, Signal Processing and Measurements VI TABLE OF CONTENTS Abstract...................................................................................................................... ii Acknowledgments .....................................................................................................iv Vita...............................................................................................................................V List of Tables .............................................................................................................xi List of Figures ..........................................................................................................xiii Nomenclature ........................................................................................................ xxiii Chapters: 1. Introduction .......................................................................................................... 1 1.1 Introduction .....................................................................................................1 1.2 Scope and Objective .....................................................................................4 1.3 Organization ................................................................................................... 5 2. Experimental and Analytical Evidence of Off Line-of-Action Friction Force as a Potential Dynamic Excitation Source ................................................ 8 2.1 Introduction .....................................................................................................8 2.2 Literature Review........................................................................................ 10 2.3 Experimental Evidence ............................................................................... 10 2.3.1 Experimental Results of Umezawa ............................................... 10 2.3.2 NASA Gearbox Test Rig ..................................................................14 2.3.2.1 NASA Gearbox Test Rig Description ...............................14 2.3.2.2 NASA Experiment Description ..........................................17 2.3.2.S NASA Experimental Results ............................................. 19 2.3.2.4 NASA Result Summary .....................................................22 2.3.3 Back-to-Back Gearbox Test Rig .....................................................25 2.3.3.1 Back-to-Back Gearbox Test Rig Description ..................25 2.3.3.2 Back-to-Back Experiment Description ............................. 27 2.3.3.3 Back-to-Back Experimental Results.................................29 2.3.5.4 Back-to-Back Results Summary ....................................... 34 2.3.4 Experimental Results Conclusion .................................................