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I ACTIVELY CONTROLLABLE HYDRODYNAMIC JOURNAL BEARING DESIGN USING MAGNETORHEOLOGICAL FLUIDS a Dissertation Presented to The

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I ACTIVELY CONTROLLABLE HYDRODYNAMIC JOURNAL BEARING DESIGN USING MAGNETORHEOLOGICAL FLUIDS a Dissertation Presented to The ACTIVELY CONTROLLABLE HYDRODYNAMIC JOURNAL BEARING DESIGN USING MAGNETORHEOLOGICAL FLUIDS A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Nathaniel Moles December, 2015 i ACTIVELY CONTROLLABLE HYDRODYNAMIC JOURNAL BEARING DESIGN USING MAGNETORHEOLOGICAL FLUIDS Nathaniel Moles Dissertation Approved: Accepted: _______________________________ _______________________________ Advisor Department Chair Dr. Minel J. Braun Dr. Sergio Felicelli _______________________________ _______________________________ Committee Member Interim Dean of the College Dr. Alex Povitsky Dr. Mario Ricardo Garzia _______________________________ _______________________________ Committee Member Dean of the Graduate School Dr. Abhilash J. Chandy Dr. Chand Midha _______________________________ _______________________________ Committee Member Date Dr. Robert Veillette _______________________________ Committee Member Dr. Kevin Kreider ii ABSTRACT This research comprised a multi-stage effort to create a hydrodynamic journal bearing design that had capability to be actively controlled through the use of magnetorheological fluids. An arrangement of electromagnets was designed and a modified Reynolds equation was derived to evaluate the performance of the bearing design. The fluid was modeled as a Bingham plastic, whose yield strength is proportional to the strength of the applied magnetic field. Bench tests were then utilized to provide a proof of performance for the bearing design and to quantify the rheological properties of the magnetorheological fluids created for the study. The evaluation of the performance of the bearing design consisted of 15 steady state conditions with operational parameters of speed and applied magnetic field as the key variables. The bearing performance was analyzed by measuring eccentricity, torque and fluid pressure. The results of the experimental testing indicated that a decrease of 15% in the eccentricity ratio was achievable relative to the baseline eccentricity ratio for all speeds. Given that the applied load remained constant, a decrease in eccentricity correlates to an increase in load capacity when a magnetic field is applied. The analysis also showed that an increase of up to 4.5% in the bearing torque, which represents reduction in operating efficiency when a magnetic field is applied. These results validated the advantages and disadvantages of this bearing design. This proves the bearing design gives the ability iii to control the bearing performance with the expected consequence of increased heat generation and power consumption from the electromagnets as well as the bearing torque. iv ACKNOWLEDGMENTS I want to take this opportunity to thank all of the people who have helped me in getting this far in my career. First I would like to thank Dr. Minel Braun who gave me this great opportunity to work on this research project and who has helped me through every stage of this project and beyond. Also, I extend my thanks to the committee members Dr. Abhilash Chandy, Dr. Kevin Kreider, Dr. Alex Povitsky and Dr. Robert Veillette. I could not have successfully made it through without their professional expertise and direction. I also want to thank Bill Wenzel for his excellent work and expertise in machining the bearing assembly and operating the bench test. I would also like to thank my former co-workers John Feltman, Keith Bandi and Greg Sturm who supported me during the long days of work, followed by evening classes and late nights studying; and Dr. Bill Hannon, for his mentorship and guidance throughout this process. Last, but certainly not least, I would like to thank Jackie Mach for her love and support during the last few years. Knowing she was in my corner helped me finally reach the finish line. v TABLE OF CONTENTS Page LIST OF TABLES .............................................................................................................. x LIST OF FIGURES ........................................................................................................... xi ABBREVIATIONS ........................................................................................................ xvii LIST OF SYMBOLS ..................................................................................................... xviii CHAPTER I. INTRODUCTION ...................................................................................................... 1 II. REVIEW OF LITERATURE ................................................................................... 14 2.1 Introduction ....................................................................................................... 14 2.2 Hydrostatic Bearings ......................................................................................... 15 2.3 Hydrodynamic Bearings ................................................................................... 18 2.3.1 Squeeze Film Bearings with Magnetic Fluid Lubrication ............................ 19 2.3.2 Slider Bearings with Magnetic Fluid Lubrication ........................................ 21 2.3.3 Hydrodynamic Journal Bearings with Ferrofluid Lubrication ...................... 22 2.3.4 Hydrodynamic Journal Bearings with MR Fluid Lubrication ...................... 24 III. NUMERICAL SETUP & PROCEDURES .............................................................. 31 3.1 Introduction ....................................................................................................... 31 vi 3.2 Derivation Reynolds Equation for Steady State Conditions ............................. 32 3.2.1 Modified Reynolds Equation for Bingham Plastic Fluids ............................ 34 3.2.2 Modified Reynolds Equation with Lubrication Inlet Source Term .............. 37 3.3 Cavitation Model .............................................................................................. 39 3.3.1 The Elrod Cavitation Model ......................................................................... 42 3.3.2 Coupling of the Cavitation Model and Modified Reynolds Equation .......... 43 3.4 Electromagnetic Field Application ................................................................... 45 3.4.1 Calculating Magnetic Fields Due to Electric Currents ................................. 50 3.4.2 Design of Magnetic Field Application .......................................................... 52 3.5 Numerical Implementation ............................................................................... 61 3.5.1 Discretization of Modified Reynolds Equation ............................................ 62 3.5.2 Numerical Procedure for Steady State Pressure Distribution ....................... 67 3.5.3 Proof of Convergence ................................................................................... 68 3.6 Dynamic Loading Model .................................................................................. 70 3.6.1 Dynamic Response to Small Perturbation .................................................... 70 3.6.2 Implementation of the Small Perturbation Method ...................................... 72 3.6.3 Journal Bearing Stability Analysis................................................................ 78 3.6.4 Discretization of the Perturbation Equations ................................................ 80 3.6.5 Numerical Procedure for Dynamic Pressure Distribution ............................ 84 IV. EXPERIMENTAL SETUP & PROCEDURES ........................................................ 87 4.1 Introduction ....................................................................................................... 87 4.2 Magnetorheological Fluid Production and Qualification ................................. 89 vii 4.2.1 Magnetorheological Fluid Sample Compositions ......................................... 90 4.2.2 Magnetorheological Fluid Sample Property Measurements ......................... 93 4.3 Hydrodynamic Journal Bearing Assembly Design ........................................... 98 4.3.1 Journal and Bearing Design .......................................................................... 99 4.3.2 Electromagnet Design ................................................................................. 103 4.3.3 Bearing Assembly Method ......................................................................... 106 4.4 Bench Test Setup ............................................................................................ 107 4.4.1 Bearing Load Application System .............................................................. 108 4.4.2 Lubrication Circuit ...................................................................................... 109 4.4.3 Electromagnet Power Supply ...................................................................... 110 4.4.4 Data Acquisition ......................................................................................... 111 4.4.5 Testing Procedure ....................................................................................... 112 V. RESULTS ............................................................................................................... 115 5.1 Introduction ..................................................................................................... 115 5.2 Numerical Results ........................................................................................... 115 5.2.1 Baseline Journal Bearing Performance ....................................................... 116
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