ABSTRACT SHAH, JAY AMIT. Design, Fabrication, and Experimental Demonstration of a Permanent Magnet Synchronous Spherical Motor (PMSSM) for High-Mobility Servomechanisms. (Under the direction of Dr. Gregory Buckner). Over the past two decades there have been significant advancements in the field of robotics. We live in a multi degree-of-freedom (DOF) world where electro-mechanical systems are capable of complex movements, with their benefits spread across many industries. In-spite of these advancements we are still heavily reliant on single DOF technology. Traditionally multi DOF motion has been achieved by combining single DOF actuators in series or parallel configurations. These arrangements are often accompanied by computationally expensive inverse kinematics, singularities in the workspace and reduced power densities since each link bears the added weight of the actuators of the succeeding links. Multi DOF actuators can provide a potential solution with enabling rotations about any arbitrary axis. This research aims at developing a multi DOF actuator, a permanent magnet synchronous spherical motor. © Copyright 2020 by Jay Amit Shah All Rights Reserved Design, Fabrication, and Experimental Demonstration of a Permanent Magnet Synchronous Spherical Motor by Jay Amit Shah A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Master of Science Mechanical Engineering Raleigh, North Carolina 2020 APPROVED BY: _______________________________ ______________________________ Dr. Gregory Buckner Dr. Larry Silverberg Committee Chair _______________________________ Dr. Matthew Bryant BIOGRAPHY Jay Shah pursued a master’s degree with the Mechanical and Aerospace Engineering Department at the North Carolina State University. He received his bachelor’s degree in Mechanical Engineering from the University of Mumbai. He spent a year and half of his master’s program working at the Electro-mechanics Research Lab. His research under the guidance of Dr. Gregory Buckner, focused on the development of a multi degree-of-freedom actuator with potential applications in the field of robotics. He currently works as a Mechatronic Systems Integration Engineer at Auris Health Inc. ii ACKNOWLEDGMENTS The author would like to thank several researchers and staff in the Mechanical and Aerospace Engineering Department at North Carolina State University for their key contributions to the work described here. Dr. Gregory Buckner (Director, Electro-Mechanics Research Laboratory) advised the author throughout the course of this work and supported the research. John Cameron (Research Fabrication Facility Supervisor) and Vincent Chicarelli (Specialty Trades Technician) provided expert design guidance, tireless efforts, and quality workmanship on machining the stator poles and rotor. Samuel Miller (doctoral student, Electro-Mechanics Research Laboratory) designed, built and implemented the control hardware (Fig. 18), designed and implemented the control algorithm (Eqns. 6-16), conducted the experimental work (Figs. 21-24), and authored the associated subsections in this manuscript. Shaphan Jernigan (Lab Manager, Electro-Mechanics Research Laboratory) co-authored the Introduction of this manuscript. iii TABLE OF CONTENTS LIST OF TABLES ......................................................................................................................... v LIST OF FIGURES ...................................................................................................................... vi Chapter 1: Introduction .............................................................................................................. 1 1.1 Overview ............................................................................................................................. 1 1.2 Rotor Support ...................................................................................................................... 1 1.3 Actuation ............................................................................................................................. 2 1.4 Bearing Selection ................................................................................................................ 3 1.5 Orientation Sensing ............................................................................................................. 4 Chapter 2: Methods ..................................................................................................................... 5 2.1 Stator Design ...................................................................................................................... 5 2.2 Stator Fabrication ............................................................................................................... 9 2.3 Rotor Design .................................................................................................................... 12 2.4 Rotor Fabrication ............................................................................................................. 20 2.5 Control Theory ................................................................................................................. 22 2.6 Control Electronics .......................................................................................................... 25 Chapter 3: Results...................................................................................................................... 30 3.1 Step Response .................................................................................................................. 30 3.2 Time Varying Trajectory ................................................................................................ 32 Chapter 4: Discussion ................................................................................................................ 34 References ................................................................................................................................... 36 iv LIST OF TABLES Table 1 Optimized Stator Pole Dimensions ............................................................................ 9 Table 2 Normalized Permanent Magnet Location ................................................................. 19 v LIST OF FIGURES Figure 1 Goldberg Polyhedron (3,0) used for the stator design ............................................... 5 Figure 2 Stator pole geometry .................................................................................................. 6 Figure 3 FEA simulations for flux density ............................................................................... 8 Figure 4 FEA simulations for field lines of magnetic field ...................................................... 8 Figure 5 Regular hexagonal pole assembly ............................................................................ 10 Figure 6 Stator pole winding process ..................................................................................... 11 Figure 7 Complete stator assembly ......................................................................................... 11 Figure 8 Cross-sectional view of the PMSSM ........................................................................ 12 Figure 9 Bearing load as a function of magnet size ................................................................ 13 Figure 10 Example implementation of the Nearest Neighbor Method ..................................... 15 Figure 11 Workspace representation of 0.38 Steradians .......................................................... 17 Figure 12 Genetic Algorithm overview .................................................................................... 18 Figure 13 Determining permanent magnet polarities ............................................................... 19 Figure 14 Rotor fabrication process .......................................................................................... 20 Figure 15 Rotor assembly ......................................................................................................... 21 Figure 16 Complete PMSSM assembly .................................................................................... 21 Figure 17 Euler angle representation ........................................................................................ 22 Figure 18 Electronic system diagram ....................................................................................... 26 Figure 19 Geometric patterns used for grouping stator poles ................................................... 27 Figure 20 Phase groupings with stator pole polarities .............................................................. 29 Figure 21 Experiment results: current tracking of the 1st phase ............................................... 30 Figure 22 Experiment results: step response ............................................................................ 31 vi Figure 23 Snapshots of the reference trajectory ....................................................................... 32 Figure 24 Experiment results: time-varying trajectory tracking ............................................... 32 Figure 25 Experiment results: phase currents during trajectory tracking ................................. 33 vii CHAPTER 1: INTRODUCTION 1.1 Overview As robotic technologies and applications continue to advance, there is a growing need for innovative actuators with increased kinematic mobility and power density. Most robotic systems have