Design and Optimization of a Passive Magnetic Thrust Bearing by Thomas Matthew Lasko Bachelor of Science in Mechanical Engineering California Institute of Technology June, 2005 A thesis submitted to the College of Engineering & Computing at Florida Institute of Technology in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Melbourne, Florida May, 2018 We, the undersigned committee, hereby approve the attached thesis, “Design and Optimization of a Passive Magnetic Thrust Bearing” by Thomas Matthew Lasko _________________________________________________ Razvan Rusovici, Ph.D. Associate Professor Department of Mechanical & Aerospace Engineering _________________________________________________ James Brenner, Ph.D. Associate Professor Department of Chemical Engineering _________________________________________________ David Fleming, Ph.D. Associate Professor Department of Mechanical & Aerospace Engineering _________________________________________________ Hamid Hefazi, Ph.D. Professor and Department Head Department of Mechanical & Aerospace Engineering Abstract Title: Design and Optimization of a Passive Magnetic Thrust Bearing Author: Thomas Matthew Lasko Advisor: Razvan Rusovici, Ph.D. High-speed turbomachines present a number of unique challenges and problems. Large centrifugal forces create high stresses in rotating components, friction leads to elevated temperatures and component failure, and rotordynamic instability makes control difficult. The weak link in these high-speed systems is often the bearings because they provide the interface between the rotating and stationary components. Traditional bearings often fail in these conditions, especially when relatively large force capacities are required. In miniature gas turbines for unmanned aerial vehicle (UAV) applications, traditional bearings exhibit a typical lifetime of only 25 hours due to excessive axial loading. This research presents a passive magnetic thrust bearing design that reduces the effect of axial loading, therefore dramatically increasing expected lifetime and reducing the required maintenance. A procedure for designing and optimizing the bearing is developed, including equations for quickly producing new geometries for various load capacities. A specific bearing design for a UAV gas turbine application is designed, fabricated, and tested at both static and dynamic conditions. The results validate the design concept as well as the finite element models and associated analyses. The research concludes with suggestions for future research as well as possible improvements to the design based on the results and lessons learned throughout the design, fabrication, assembly, and testing phases. iii Table of Contents Table of Contents ................................................................................................... iv List of Figures ......................................................................................................... vi List of Tables ........................................................................................................ viii List of Symbols ....................................................................................................... ix Acknowledgement .................................................................................................... x Dedication ............................................................................................................... xi Chapter 1 Background ............................................................................................ 1 Permanent Magnets ........................................................................................................ 1 Magnet Properties ........................................................................................................... 2 Bearings ............................................................................................................................ 6 Traditional Bearings ...................................................................................................... 7 Non-contact Bearings .................................................................................................... 7 Chapter 2 Design .................................................................................................... 10 Passive Magnetic Bearing Concept .............................................................................. 10 Bearing Geometry ......................................................................................................... 11 Design Tools ................................................................................................................... 13 Chapter 3 Optimization ......................................................................................... 17 Introduction ................................................................................................................... 17 Non-dimensional Offset ................................................................................................ 18 Sleeve Thickness Ratio .................................................................................................. 21 Air Gap Ratio ................................................................................................................ 27 Magnet Ratio ................................................................................................................. 29 Effective Number of Magnets ....................................................................................... 30 Magnet Thickness Ratio ............................................................................................... 33 Rotor Ratio ..................................................................................................................... 35 Aspect Ratio ................................................................................................................... 37 Optimization Procedure................................................................................................ 39 Chapter 4 Design and Testing for UAV Application .......................................... 41 System Constraints and Objectives ............................................................................. 41 Bearing Configuration .................................................................................................. 41 Expected Bearing Lifetime ........................................................................................... 43 UAV Bearing Design ..................................................................................................... 45 UAV Test Stand Design ................................................................................................ 49 Shaft Design ................................................................................................................ 51 iv Thermal Analysis ........................................................................................................ 51 Rotordynamics ............................................................................................................ 54 Solenoid Design .......................................................................................................... 59 UAV Bearing Fabrication ............................................................................................. 60 Static Testing ................................................................................................................. 65 Test Stand.................................................................................................................... 65 Test Results ................................................................................................................. 65 Dynamic Testing ............................................................................................................ 66 Test Configuration ...................................................................................................... 66 Load Cell ..................................................................................................................... 67 Laser Sensor ................................................................................................................ 68 Variable Frequency Drive ........................................................................................... 69 LabVIEW .................................................................................................................... 70 Test Results ................................................................................................................. 71 Chapter 6 Conclusions ........................................................................................... 75 References ............................................................................................................... 76 Appendix: Simulation Code ................................................................................. 78 v List of Figures Figure 1. Permanent magnet field lines showing polarity1 ....................................... 3 Figure 2. Ring magnetization directions: axial (left), diametric (center), and radial (right) ....................................................................................................... 3 Figure 3. Typical BH curve5 ...................................................................................... 5 Figure 4. Foil bearing schematic8..............................................................................