Permanent Magnet Spherical Motors (eBook)

Kun Bai: Professor Kun Bai received his B.S. degree from Zhejiang University, China in 2006 and earned his M. S. and Ph. D. degrees from the Woodruff School of Mechanical Engineering at Georgia Institute of Technology, Atlanta, US in 2009 and 2012 respectively. Currently, he is an Associate Professor with the State Key Laboratory of Digital Manufacturing Equipment and Technology and the School of Mechanical Science and Engineering at Huazhong University of Science and Technology, China. Prof. Bai's research areas include smart electromagnetic actuators/sensors and novel applications, in which he has published over 20 peer-viewed papers and held over 10 international and domestic patents. He has extensive expertise and experience in developing direct drive electromagnetic actuators. He has been PI for several funded projects regarding manufacturing and robotics where spherical motors has been developed for applications such as conformal printing, haptic device, desktop machining-stage. Kok-Meng Lee: Professor Kok-Meng Lee earned his B.S. degree from the University of Buffalo, the State University of New York, Buffalo, NY, USA, in 1980, and M. S. and Ph. D. degrees from Massachusetts Institute of Technology, Cambridge, MA, USA, in 1982 and 1985, respectively. He is currently Professor of Mechanical Engineering at Georgia Institute of Technology, Atlanta, GA, USA. He is also Distinguished Professor with the State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, China, under Thousand Talents Plan. Prof. Lee’s research interests include system dynamics/control, robotics, automation, and mechatronics. He is a world renowned researcher with more than 30 years of research experience in magnetic field modeling and design, optimization and implementation of electromagnetic actuators. He has published over 150 peer-reviewed papers and he holds eight patents in machine vision, three degrees of freedom (DOF) spherical motor/encoder, and live-bird handling system. He is IEEE/ASME Fellow and was the Editor-in-Chief for the IEEE/ASME Transactions on Mechatronics from 2008 to 2013. Recognitions of his research contributions include the National Science Foundation (NSF) Presidential Young Investigator, Sigma Xi Junior Faculty Research, International Hall of Fame New Technology, and Kayamori Best Paper awards. 

Preface 6
Contents 8
Nomenclature 11
1 Introduction 13
1.1 Background 13
1.2 The State of the Art 15
1.2.1 Magnetic Modeling and Analysis 18
1.2.2 Orientation Sensing 20
1.2.3 Control Methods 22
1.3 Book Outline 24
References 26
Modeling Methods 30
2 General Formulation of PMSMs 31
2.1 PMSM Electromagnetic System Modeling 31
2.1.1 Governing Equations of Electromagnetic Field 31
2.1.2 Boundary Conditions 34
2.1.3 Magnetic Flux Linkage and Energy 35
2.1.4 Magnetic Force/Torque 36
2.2 PMSM Rotor Dynamics 37
References 40
3 Distributed Multi-pole Models 41
3.1 Distributed Multi-pole Model for PMs 41
3.1.1 PM Field with DMP Model 42
3.1.2 Numerical Illustrative Examples 45
3.2 Distributed Multi-pole Model for EMs 53
3.2.1 Equivalent Magnetization of the ePM 55
3.2.2 Illustrations of Magnetic Field Computation 57
3.3 Dipole Force/Torque Model 57
3.3.1 Force and Torque on a Magnetic Dipole 57
3.3.2 Illustration of Magnetic Force Computation 59
3.4 Image Method with DMP Models 62
3.4.1 Image Method with Spherical Grounded Boundary 63
3.4.2 Illustrative Examples 66
3.4.3 Effects of Iron Boundary on the Torque 68
3.5 Illustrative Numerical Simulations for PMSM Design 72
3.5.1 Pole Pair Design 75
3.5.2 Static Loading Investigation 80
3.5.3 Weight-Compensating Regulator 81
Appendix 85
References 89
4 PMSM Force/Torque Model for Real-Time Control 91
4.1 Force/Torque Formulation 91
4.1.1 Magnetic Force/Torque Based on the Kernel Functions 92
4.1.2 Simplified Model: Axis-Symmetric EMs/PMs 95
4.1.3 Inverse Torque Model 96
4.2 Numerical Illustrations 96
4.2.1 Axis-Asymmetric EM/PMs 96
4.2.2 Axis-Symmetric EM/PM 100
4.3 Illustrative PMSM Torque Modelling 103
Sensing Methods 106
5 Field-Based Orientation Sensing 107
5.1 Coordinate Systems and Sensor Placement 107
5.2 Field Mapping and Segmentation 108
5.3 Artificial Neural Network Inverse Map 110
5.4 Experimental Investigation 111
5.4.1 2-DOF Concurrent Characterization 112
References 115
6 A Back-EMF Method for Multi-DOF Motion Detection 116
6.1 Back-EMF for Multi-DOF Motion Sensing 116
6.1.1 EMF Model in a Single EM-PM Pair 118
6.1.2 Back-EMF with Multiple EM-PM Pairs 119
6.2 Implementation of Back-EMF Method on a PMSM 121
6.2.1 Mechanical and Magnetic Structure of the PMSM 122
6.2.2 Numerical Solutions for the MFL Model 123
6.2.3 Experiment and Discussion 125
6.2.4 Parameter Estimation of the PMSM with Back-EMF Method 127
Appendix 129
References 129
Control Methods 130
7 Direct Field-Feedback Control 131
7.1 Traditional Orientation Control Method for Spherical Motors 131
7.1.1 PD Control Law and Stability Analysis 132
7.1.2 Comments on Implementation of Traditional Control Methods 133
7.2 Direct Field-Feedback Control 134
7.2.1 Determination of Bijective Domain 135
7.2.2 DFC Control Law and Control Parameter Determination 135
7.2.3 DFC with Multi-sensors 136
7.3 Numerical 1-DOF Illustrative Example 137
7.3.1 Sensor Design and Bijective Domain Identification 137
7.3.2 Field-Based Control Law 139
7.3.3 Numerical Illustrations of Multiple Bijective Domains 141
7.4 Experimental Investigation of DFC for 3-DOF PMSM 141
7.4.1 System Description 141
7.4.2 Sensor Design and Bijective Domains 144
7.4.3 Bijective Domain 145
7.4.4 TCV Computation Using Artificial Neural Network (ANN) 148
7.4.5 Experimental Investigation 148
Appendix 156
References 156
8 A Two-Mode PMSM for Haptic Applications 157
8.1 Description of the PMSM Haptic Device 157
8.1.1 Two-Mode Configuration Design for 6-DOF Manipulation 159
8.1.2 Numerical Model for Magnetic Field/Torque Computation 160
8.1.3 Field-Based TCV Estimation 161
8.2 Snap-Fit Simulation 162
8.2.1 Snap-Fit Performance Analyses 164
8.2.2 Snap-Fit Haptic Application 165
Appendix: PM/EM/Sensor Position Coordinates 169
References 170