Brushless Permanent Magnet Motor Design, 2^nd ed. ISBN: 1-932133-63-1 www.eece.maine.edu/motor Table of Contents
Preface to the Second Edition	xiii
Preface to the First Edition	xv
Chapter 1 Basic Concepts	1
1.1 Scope	1
1.2 Shape	3
1.3 Torque	4
1.4 Motor Action	5
1.5 Magnet Poles and Motor Phases	9
1.6 Poles, Slots, Teeth, and Yokes	9
1.7 Mechanical and Electrical Measures	11
1.8 Motor Size	13
1.9 Units	13
1.10 Summary	14
Chapter 2 Magnetic Modeling	15
2.1 Magnetic Circuit Concepts	16
Basic Relationships	16
Magnetic Field Sources	19
Air Gap Modeling	21
Slot Modeling	24
Example	28
2.2 Magnetic Materials	30
Permeability	30
Ferromagnetic Materials	30
Core Loss	32
Permanent Magnets	34
Permanent Magnet Magnetic Circuit Model	38
2.3 Example	41
2.4 Summary	43
Chapter 3 Electrical and Mechanical Relationships	45
3.1 Flux Linkage and Inductance	45
Self Inductance	45
Mutual Inductance	46
Mutual Flux Due to a Permanent Magnet	49
3.2 Induced voltage	50
Faraday's Law	50
Example	51
3.3 Energy and Coenergy	53
Energy and Coenergy in Singly-Excited Systems	53
Energy and Coenergy in Doubly-Excited Systems	55
Coenergy in the Presence of a Permanent Magnet	56
3.4 Force, Torque and Power	56
Basic Relationships	56
Fundamental Implications	57
Torque From a Macroscopic Viewpoint	58
Force From a Microscopic Viewpoint	61
Reluctance and Mutual Torque	62
Example	63
3.5 Summary	64
Chapter 4 Brushless Motor Fundamentals	67
4.1 Assumptions	67
Rotational Motion	67
Surface-Mounted Magnets	67
4.2 Fundamental Concepts	68
Magnetic Circuit Model	68
Magnetic Circuit Solution	71
Flux Linkage	74
Back EMF and Torque	76
Multiple Coils	78
4.3 Multiple Phases	80
4.4 Design Variations	82
Fractional Pitch Coils	82
Fractional Pitch Magnets	84
Fractional Slot Motor	86
4.5 Coil Resistance	90
4.6 Coil Inductance	94
Air Gap Inductance	95
Slot Leakage Inductance	96
End Turn Inductance	98
4.7 Series and Parallel Connections	100
4.8 Armature Reaction	103
4.9 Slot Constraints	104
Slot Fill Factors	104
Slot Resistance	105
Wire Gage Relationships	106
Constancy of Ni	107
4.10 Torque Constant, Back EMF Constant, and Motor Constant	108
4.11 Torque per Unit Rotor Volume	110
4.12 Cogging Torque	111
4.13 Summary	115
Chapter 5 Motor Design Possibilities	117
5.1 Radial Flux Motors	117
Inner Rotor	117
Outer Rotor	120
5.2 Axial Flux Motors	121
5.3 Linear Motors	123
5.4 Summary	124
Chapter 6 Windings	125
6.1 Assumptions	125
6.2 Coil Span	126
6.3 Valid Pole and Slot Combinations	127
6.4 Winding Layout	129
Example	131
Example	134
Winding Layout Procedure	137
6.5 Coil Connections	139
6.6 Winding Factor	140
6.7 Inductance Revisited	143
Single Tooth Coil Equivalence	144
Air Gap Inductance	144
Slot Leakage Inductance	148
6.8 Summary	150
Chapter 7 Magnetic Design	151
7.1 Air Gap Magnetic Field Distribution	152
Air Gap Region Solution	153
Magnet Region Solution	153
Symmetry	154
7.2 Influence of Stator Slots	154
7.3 Tooth Flux	158
7.4 Stator Yoke Flux	162
7.5 Influence of Skew	165
7.6 Influence of Ferromagnetic Material	169
7.7 Back EMF	173
7.8 Slotless Motor Construction	176
Concentrated Winding	176
Sinusoidally-Distributed Winding	180
7.9 Summary	181
Chapter 8 Electrical Control	183
8.1 Fundamentals of Torque Production	183
8.2 Brushless DC Motor Drive	185
Ideal Torque Production	185
Motor Constant	187
Torque Ripple	187
8.3 AC Synchronous Motor Drive	188
Ideal Torque Production	188
Motor Constant	189
Torque Ripple	189
8.4 General Drive	193
Ideal Torque Production	193
Torque Ripple	195
Motor Constant	195
8.5 Motor Drive Topologies	196
Half Bridge	196
Full H-Bridge	196
Y-Connection	198
D-Connection	200
8.6 Summary	201
Chapter 9 Performance	203
9.1 Motor Constant	203
General Sizing	203
Motor Constant Maximization	206
9.2 Cogging Torque Relationships	209
9.3 Radial Force Relationships	214
9.4 Core Losses	217
Basic Concepts	217
Core Loss Modeling	219
Application to Motor Design	222
Conclusion	223
9.5 AC Winding Resistance	223
9.6 Summary	226
Chapter 10 Examples	229
Common Characteristics	229
Presented Results	230
Notes	231
Two Pole Motors	232
Four Pole Motors	234
Six Pole Motors	250
Eight Pole Motors	258
Ten Pole Motors	278
Twelve Pole Motors	294
Fourteen Pole Motors	300
Sixteen Pole Motors	312
Twenty Pole Motors	320
Twenty-Four Pole Motors	326
Thirty-Two Pole Motors	330
Appendix A Fourier Series	335
A.1 Definition	335
A.2 Coefficients	336
A.3 Symmetry Properties	337
A.4 Mathematical Operations	337
Addition	338
Scalar Multiplication	338
Function Product	338
Phase Shift	338
Differentiation	339
Mean Square Value and RMS	339
A.5 Computing Coefficients	339
Procedure	340
A.6 Summary	341
Appendix B Magnetic Field Distributions in Polar Coordinates	343
B.1 Problem Formulation	343
B.2 Polar Coordinate Application	345
B.3 Air Gap Region Solution	348
B.4 Magnet Region Solution	350
B.5 Summary	352
B.6 Magnetization Profiles	353
Radial Magnetization	354
Parallel Magnetization	355
Radial Sinusoidal Amplitude Magnetization	356
Sinusoidal Angle Magnetization	356
B.7 Examples	357
B.8 Summary	360
Appendix C Magnetic Field Distributions in Rectangular Coordinates	361
C.1 Rectangular Coordinate Application	362
Single Magnet and Single Air Gap Case	363
Two Magnet, Single Air Gap Case	364
One Magnet, Two Air Gap Case	365
C.2 Magnetization Profile	366
C.3 Summary	366
Appendix D Symbols, Units, and Abbreviations	367
Appendix E Glossary	373
Bibliography	381
Books	381
Articles	384
Index	387