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 |  موضوع: كتاب Brushless Permanent Magnet Motor Design - Second Edition الخميس 12 سبتمبر 2024, 6:19 pm | |
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Brushless Permanent Magnet Motor Design - Second Edition
Dr. Duane Hanselman
Electrical and Computer Engineering
University of Maine
Orono, ME 04469 USA
و المحتوى كما يلي :
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
viiviii Contents
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 96Contents ix
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
Chapters 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
Chapters 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 152X Contents
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 203Contents xi
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.l 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 339xii Contents
A.5 Computing Coefficients 339
Procedure 340
A.6 Summary 341
Appendix B Magnetic Field Distributions in Polar Coordinates 343
B.l 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.l 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 387Index
A
AC synchronous motor 185
AC Synchronous Motor Drive 188
AC Winding Resistance 223
airgap 5,21,373
air gap flux density 109
air gap inductance 95, 96, 144, 146, 148,
373
Air Gap Magnetic Field Distribution 152
Air Gap Modeling 21
Air Gap Region Solution 153
air gap shear stress 110
alignment torque 7, 60, 62, 373, 376
allowable current density 92
alnico magnet 34
American Wire Gage 92
Ampere's law 19, 373
anomalous loss 219
armature reaction 62, 103, 104, 373
armature reaction flux density 103
AWG 92
axial flux motor 3, 121
B
B-H curve 30, 373
back EMF 51, 173, 373
Back EMF and Torque 76
back EMF constant 77, 108, 185, 187, 373
back EMF shape 184, 187
back iron 9, 10, 378,379
balanced winding 125, 127-129, 137, 373
bare wire slot fill factor 104
(BH)max 37
BLi law 62, 63, 373
BLv law 52, 53, 373
bonded magnet 34
bonding material 91
breadloaf 373
breadloaf magnet motor 117
brushless DC motor 184-186
brushless DC motor drive 185, 187
buried magnet motor 118
Carter's coefficient 25, 77, 374
chorded 127, 374
circular-arc straight-line modeling 23
circulating current 100, 101, 139, 140, 200
coenergy 54,59
Coenergy in the Presence of a Permanent
Magnet 56
coercive force 35, 374
coercivity 35, 374
cogging torque 7, 60, 62, 111-113, 209,
210, 213, 374
Cogging Torque Relationships 209
Coil Connections 139
coil inductance 94
coil pitch 74, 126, 374
coil pitch factor 82, 374
Coil Resistance 90
coil span 126
coil throw 74
commutation 9,374
commutation points 187
commutation torque ripple 188, 374
concentrated winding 9, 176, 374
conservation of energy 58, 184
Constancy of Ni 107
copper motor 207, 374
core ' 374
core loss 32, 217, 374
Core Loss Modeling 219
Epstein Square Test 218
387388 Index
proximity effect 223
rotational loss 218
skin depth 225
skin effect 223
covered wire diameter 91
covered wire slot fill factor 105
4-Connection 200
demagnetization curve 35, 36, 374
Design Variations 82
detent position 6,374
distributed winding 9, 374
distribution factor 141
double layer lap winding 130
double layer winding 125, 374
dg transformation matrix 192
eddy current 32, 33, 374
eddy current loss
proximity effect 223
skin effect 223
eddy current losses 374
electrical degrees 11
electrical position 11
electrical radians 11
electrical steel 30
electrical time constant 103, 106
electromagnet 7,59
electromotive force 1,374
end turn inductance 98, 99, 374
end turns 209, 374
energy 59
Energy and Coenergy 53
Energy and Coenergy in Doubly-Excited
Systems 55
Energy and Coenergy in Singly-Excited
Systems 53
Epstein Square Test 218
excess loss 218, 219
factor
bare wire slot fill 104
coil pitch 82
covered wire slot fill 105
flux concentration 72, 375
leakage 70, 376
reluctance 71, 169, 171, 172, 378
skew 167, 168
slot correction 155-158, 160, 161
slot fill 104, 106
stacking 33, 379
winding 129, 140, 141, 176
Faraday's law 50, 76, 173, 375
ferrite magnet 34
ferromagnetic material 30, 375
B-H curve 373
electrical steel 30
laminations 33
magnetic material 30
powdered 34
saturation 31, 378
field excitation 185
field intensity 16, 375
finite element analysis 15, 375
flux 17, 375
flux concentration 117
flux concentration factor 42, 72, 375
flux density 16, 375
flux linkage 45, 50, 74, 375
Flux Linkage and Inductance 45
Force From a Microscopic Viewpoint 61
Force, Torque and Power 56
Fourier series 335
Fractional Pitch Coils 82
fractional pitch magnet 84, 85, 375
fractional pitch winding 82, 87, 375
fractional slot motor 86, 87, 130, 375
fringing flux 22
Full H-Bridge 196
full pitch winding 74, 375
fundamental cogging frequency 210
fundamental electrical frequency 12, 375Index 389
fundamental radial force frequency 214
Fundamentals of Torque Production 183
G
General Drive 193
General Sizing 203
Glossary 373
H
Half Bridge 196
Hall effect device 187
hysteresis 30, 375
hysteresis loops 375
hysteresis loss 32, 375
I
I2R loss 92, 100, 106, 109, 376
Induced voltage 50
inductance 45, 94, 143
air gap 95, 96, 144, 146, 148, 373
coil 94
end turn 98, 99, 374
mutual 7, 46, 48, 94
phase winding 100
self 45, 48, 94
slot leakage 96-98, 113, 148, 149, 378
Inductance Revisited 143
inertia 58
Influence of Ferromagnetic Material 169
Influence of Skew 165
Influence of Stator Slots 154
inner rotor 117
inside-out motor 120, 375
integral slot motor 87, 375
International System of Units 13, 17
intrinsic demagnetization curve 37, 375
ironless 124,376
K
knee 36, 37, 376
L
lamination thickness 219
laminations 33
Laplace's equation 343, 346
law
Ampere's 19, 373
Faraday's 50, 173,375
Lenz's 50, 52, 376
Lorentz force 61, 376
leakage factor 70, 376
Lenz's law 50, 52, 376
Linear Motors 123
Lorentz force equation 61, 376
loss
anomalous 219
core 217
core loss 32, 374
eddy current 32, 33, 374
excess 218
hysteresis 30, 32, 375
7
I R 92, 100, 106, 109, 376
ohmic 376
macroscopic viewpoint 58
magnet leakage flux 69, 376
magnet leakage permeance 40, 376
magnet motor 207, 376
Magnet Poles and Motor Phases 9
Magnet Region Solution 153
magnet reluctance 69
magnetic circuit analysis 15, 29, 151, 376
Magnetic Circuit Concepts 16
magnetic field distribution 151, 152, 155
Magnetic Field Distributions
in Polar Coordinates 343
Magnetic Field Distributions
in Rectangular Coordinates 361
Magnetic Field Sources 19
magnetic material 30
magnetization 344
Magnetization Profiles 353
magnetomotive force 18
maximum energy product 37
mean coil pitch 99
Mechanical and Electrical Measures 11
mechanical degrees 11390 Index
mechanical output power 64 demagnetization curve 35, 36, 374
mechanical position 11 ferrite 34
mechanical radians 11 intrinsic demagnetization curve 37,
minimum skew 212 375
MMF 18, 376 knee 36, 376
Motor Action 5 maximum energy product 37
motor constant 108,187/189, 195, 203, NdFeB 34
209, 376 neodymium-iron-boron 34, 377
Motor Constant Maximization 206 normal demagnetization curve 37, 376
Motor Drive Topologies 196 rare earth 34
Motor Size 13 recoil 35
moving coil 123, 376 remanence 35, 378
moving magnet 123, 376 residual induction 35, 378
Multiple Coils 78 reversible temperature coefficient 37
Multiple Phases 80 samarium-cobalt 34, 377
Mutual Flux Due to a Permanent Magnet sintered 34
49 permanent magnet 34
mutual inductance 7, 46, 48, 94 Permanent Magnet Magnetic Circuit
mutual torque 60, 62, 64, 111 373, 376 Model 38
mutual torque ripple 111 permanent magnet synchronous motor
185
NdFeB 34, 377 permeability 16, 30, 377
neodymium-iron-boron 34 relative 30, 377
nominal coil span 126, 138 relative recoil 36, 378
normal demagnetization curve 37, 376 permeability of free space 22,30
number of parallel paths 102 permeance 19, 377
permeance coefficient 36, 43, 72, 109, 377
ohmic loss phase 79, 377
I2 R loss 376 phase offset 127-129, 377
outer rotor 120 phase winding 9, 79, 377
phase winding inductance 100
pancake motor 121, 376 pitch 377
Parallel Magnetization 355 pole 5, 377
permanent magnet pole pair 11, 377
(BH)max 37 pole pitch 377
alnico 34 Poles, Slots, Teeth, and Yokes 9
B-H curve 30 position
bonded 34 detent 6,374
breadloaf 373 electrical 11
coercive force 374 mechanical 11
coercivity 374 Mechanical and Electrical Measures11Index 391
Q R S
position encoder 189 saturation 31, 378
powdered ferromagnetic materials 34 self inductance 15, 48, 94
principle angle 377 Series and Parallel Connections 100
printed circuit board motor 123, 377 shoe 378
proximity effect 223, 377 shoe design 112
psi 110 SI units 13, 77
single tooth coil 144
quadrature 192 single tooth coil equivalence 144
quasi-Poisson partial differential equa- sintered magnet 34
tion 344 Sinusoidal Angle Magnetization 356
sinusoidal back EMF 188
radial flux motor 3, 117 sinusoidal currents 188
radial force 214 sinusoidal winding distribution 180
Radial Force Relationships 214 Sinusoidally-Distributed Winding 180
Radial Magnetization 354 six step drive 186, 378
Radial Sinusoidal Amplitude Magnetiza- skew 114,210
tion 356 skew factor 167, 168
rare earth 377 skin depth 225, 378
rare earth magnet 34 skin effect 223, 378
recoil 35,377 slot 9,378
relative permeability 30, 377 Slot Constraints 104
relative permeance 155, 377 slot correction factor 155-158, 160, 161
relative recoil permeability 36, 378 slot fill factor 104, 106
reluctance 19, 46, 378 slot fraction 27, 378
Reluctance and Mutual Torque 62 slot heat density 106
reluctance factor 71, 169, 171, 172,378 slot leakage inductance 96-98, 113, 148,
reluctance torque 7, 60, 62, 378 149, 378
remanence 35, 378 slot liner 105, 379
residual induction 35, 378 slot measure 161
resistance 90 slot modeling 24
resistivity 91 slot permeance coefficient 98, 379
resolver 189 slot pitch 26, 379
reversible temperature coefficient 37 Slot Resistance 105
right hand rule 61, 378»- slotless 119
right hand screw rule 19, 378* slotless motor 176
rotational loss 218 Slotless Motor Construction 176
rotor 378 slotless stator 120
rotor yoke 10, 378 slotted <■ 119
rotor yoke width 205 slotted stator 120
solenoidal winding 9,374
samarium-cobalt magnet 34,377 speed voltage 51, 379392 Index
spindle motor 122
spoke 117
squarewave currents 185
stacking factor 33, 379
stator 379
stator yoke 9, 379
stator yoke flux 162, 164, 165
stator yoke width 205
structural periodicity 213
Surface-Mounted Magnets 67
Symbols 367
T
teeth 9, 379
thermal resistivity coefficient 91
tooth body 162
tooth body flux density 162
tooth body width 162, 204
tooth flux 158-160
torque 4, 379
alignment 7, 60, 62, 373, 376
cogging 7,60,62,111-113,210,213,
374
cogging torque 209
commutation torque ripple 188, 374
mutual 60, 62, 64, 111, 376
mutual torque ripple 111
reluctance 7, 60, 62, 378
Reluctance and Mutual Torque 62
torque ripple 184, 187, 189-191, 195
torque constant 77, 108, 185, 379
Torque Constant, Back EMF Constant,
and Motor Constant 108
torque efficiency 109
Torque From a Macroscopic Viewpoint
58
torque per unit rotor volume 110
torque ripple 184, 187, 189-191, 195, 379
transformer voltage 51,379
trapezoidal back EMF 184, 185, 201
triple-H 194, 379
triplen 194, 200, 201, 379
V w
Valid Pole and Slot Combin,Jtions 127
vector 379
vector control 191
winding 379
balanced 125, 127--129, 137, 373
concentrated 9, 176, 374
distributed 9,374
double layer 125
double layer lap 130
end turns 374
fractional pitch 82, 87, 375
full pitch 74, 375
phase 9, 79, 377
sinusoidal distribution 180
solenoidal 9, 374
winding factor 129, 140, 141, 176
Winding Layout 129
Winding Layout Procedure 137
wire gage relationships 106
wire insulation 91
work 56
Y-Connection 198
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