Design of Brushless Permanent-Magnet Machines
Design of Brushless Permanent-Magnet Machines
Contents
1 GENERAL INTRODUCTION 1
1.1 Definitions and types of brushless motor 1
1.2 Commutation 4
1.3 Operation of 3-phase brushless DC motor 5
1.3.1 EMF waveform
1.3.2 Torque and EMF constants 10
1.3.3 Speed/torque characteristic 11
1.4 Sinewave motors and generators 16
1.4.1 Phasor representation 19
1.4.2 Voltage 22
1.5 Practical considerations 23
2 MACHINE TYPES and APPLICATIONS 25
2.1 Machine configuration 25
2.1.1 Reasons for variety 25
2.1.2 Classification 27
2.2 Radial-flux machines 30
2.2.1 Interior-rotor surface-magnet machines 30
2.2.2 Interior-rotor interior-magnet machines (IPM) 32
2.2.3 Exterior-rotor machines 35
2.3 Axial-flux, linear and other machines
2.4 Gallery 43xiv Contents
3 BASIC DESIGN CHOICES 65
3.1 Machine and drive configuration 67
3.1.1 Squarewave and sinewave drives 67
3.1.1.1 Squarewave drive 67
3.1.1.2 Sinewave drive 68
3.1.2 Salient-pole and nonsalient-pole machines
3.1.2.1 Nonsalient-pole machines
3.1.2.2 Salient-pole machines
3.2 Number of phases, poles and slots
3.2.1 Number of phases
3.2.1.1 Practical considerations
3.2.1.2 Number of phases in electrical systems
3.2.1.3 Number of phases in electrical machines
3.2.1.4 Distribution of coils between phases
3.2.1.5 Number of phases in inverters and rectifiers
3.2.2 Numbers of slots and poles
3.3 Sizing — the ABC of electric machine design
3.3.1 The output equation
3.4 Rotor design
3.4.1 Lengthdiameter ratio
3.4.2 Airgap length
3.4.3 First estimate of magnet dimensions
3.4.4 Exploratory selection of magnet grade
3.4.5 Magnet overhang
3.4.6 Rotor yoke dimensions
3.5 Stator design
3.5.1 Cutting the laminations
3.5.2 Choice of core plate
3.5.3 Stacking
3.5.4 Insulating the slots
3.5.5 Slot-fill factor
3.5.6 Winding and inserting the phase coils
3.5.7 Varnishing
3.5.8 Winding with multiple-strand conductors 228288233
8828833
S3
88^83^
888Contents v 3.5.9 Number of stator slots 105 3.5.10 Stator core dimensions 105 3.5.11 Stator tooth-tips 106 3.5.12 Cogging and skew 10‘ 3.5.13 Management of end-turns 109 3.6 Electrical design of windings 110 3.6.1 Definitions H° 3.6.2 Integral-slot windings Hl 3.6.3 Windings for squarewave drive 115 3.6.4 Fractional-slot windings 1 18 3.6.4.1 A rule and two examples 118 S.6.4.2 The 12/10 motor; alternative windings 124 3.6.4.3 Pitch factor 128 3.6.4.4 Sinewave and squarewave motors 130 3.6.5 Irregular slotting 3.6.6 Systematic analysis of slot pole ratio and windings 133 3.6.7 Winding resistance 3.6.7.1 Resistance calculation 139 3.6.7.2 Relationship between resistance and copper weight 140 3.6.7.3 Variation of resistance with temperature 140 3.6.7.4 AC resistance 143 3.7 Magnet retention 153 4 FLUX, EMF, AND TORQUE 157 4.1 Permanent magnets and magnetic circuits 157 4.1.1 Magnetic equivalent circuits 158 4.1.1.1 Airgap flux distribution 184 4.1.1.2 Clearance gap and equivalent magnet 165 4.1.1.3 Magnet divided by thin bracing bridges 167 4.1.2 Direct solution of Laplace Poisson equations 169 4.1.3 Finite-element method 174 4.2 EMF 178 4.2.1 Formula 1’^ 4.2.1.1 EMF constant of squarewave motors 1 •9 4.2.1.2 EMF constant of sinewave motors 180xvi Contents 4.2.2 BLV waveform method 181 4.2.3 Toothflux waveform method 183 4.3 Torque 185 4.3.1 Torque constants 186 4.3.1.1 Three-phase squarewave motor 186 4.3.1.2 Sinewave motors 187 4.4 Torque and inductance 190 4.4.1 Salient-pole machines in phase variables 190 4.4.2 Salient-pole machines in dq axes 193 4.5 i-psi loop 197 4.6 Properties of the elliptical i-psi loop 203 5 INDUCTANCE 209 5.1 Definition of inductance and flux-linkage 210 5.1.1 Alternative definitions 211 5.1.1.1 di/dt 211 5.1.1.2 Flux times turns 211 5.1.2 Other necessary laws of electromagnetism 211 5.1.3 Turns squared 212 5.2 Important practical effects of inductance 213 5.3 Inductance components 214 5.4 Airgap inductance of surface-magnet machines 215 5.4.1 Airgap Self 215 5.4.2 Airgap mutual 217 5.4.3 Examples of airgap inductance calculation 217 5.4.4 General case of airgap inductance 5.5 Slot-leakage inductance 226 5.6 End-winding leakage inductanceContents xvii 5.7 Inductances of slotless (airgap) windings 238 5.7.1 Helical windings 241 5.7.2 Lawrensons method 241 5.8 Equivalent sine-distributed windings 242 5.9 Synchronous inductance 243 5.9.1 Static measurement of synchronous inductance 246 5.10 Inductances of salient-pole machines 247 5.10.1 dq-axis inductances from Park’s transform 248 5.10.2 Synchronous inductance coefficients 252 5.10.3 Direct calculation of synchronous inductance 253 5.10.4 Differential leakage inductance 258 5.10.5 Static measurement again 260 5.11 Inductance from finite-element calculations 262 5.12 Magnetization curves — beyond inductance 263 5.12.1 Magnetization curves in dq-axes 266 5.13 Saturation in the dq-axis model 267 5.14 Demagnetization 268 6 SQUAREWAVE DRIVE 273 Introduction 273 6.1 Three-phase bipolar drives 274 6.1.1 Waveforms and commutation sequences 274 6.1.2 Current regulation 279 6.1.3 Commutation 282 6.1.4 3-phase squarewave control strategies 286 6.1.5 Accumulations for mean and RMS currents 288 6.1.6 Selection of appropriate switching strategy 289xviii Contents 6.2 Transient analysis of 3-phase drives 291 6.2.0.1 Wye connection 293 6.2.0.2 Delta connection 296 6.2.0.3 Regeneration (over-running); no-load speed 301 6.2.0.4 Phase advance 304 6.2.0.5 Dwell control 306 6.2.1 Salient-pole machines with squarewave drive 309 6.2.2 Back-EMF sensing 312 6.3 1- and 2-phase unipolar drives 315 6.4 Controller architecture 321 7 SINEWAVE DRIVE 325 Introduction 325 7.1 The phasor diagram — motor operation 327 7.1.1 Torque angle curves 332 7.1.2 The voltage locus diagram 336 7.1.3 The circle and ellipse diagrams 338 7.1.4 Calculation of the torque speed characteristic 349 7.1.5 The synchronous reluctance motor 361 7.1.6 Summary — calculated characteristics 367 7.2 Electronic control 368 7.2.1 The need for current regulation 369 7.2.2 Historical development 371 7.2.3 Overview of controllers 373 7.2.4 Switching representation by voltage vectors 374 7.2.5 Six-step 375 7.2.6 Hysteresis-band current regulator 377 7.2.7 dq_W_CR 381 7.2.8 Sine/triangle ramp comparison 383 7.2.9 Voltage PWM (sine/triangle) 385 7.2.10 The synchronous regulator 389 7.2.11 Space-vector controller 391 7.2.12 Direct torque control (DTC) 396 7.2.13 Summary of voltage capabilities 404Contents 8 kT AND kE, AND FICURES-OF-MERIT 8.1 Introduction 8.2 kT & kE of squarewave and sinewave motor/drives 8.2.1 DC commutator motor and drive 8.2.2 3-phase squarewave motor and drive 8.2.3 3-phase sinewave motor and drive 8.2.4 3-phase sinewave motor with squarewave drive 8.2.5 3-phase squarewave motor with sinewave drive 8.2.6 3-phase squarewave & sinewave systems compared 8.2.7 Example calculations (3-phase) 8.2.8 2-phase squarewave motor and drive 8.2.9 2-phase sinewave motor and drive 8.2.10 2-phase sinewave motor with squarewave drive 8.2.11 2-phase squarewave motor with sinewave drive 8.2.12 2-phase squarewave & sinewave systems compared 8.3 Figures of merit 8.3.1 kT and kE 8.3.2 Efficiency and power factor 8.3.3 Torque Inertia ratio 8.3.4 Power rate 8.3.5 Speed rate and mechanical time-constant 8.3.6 Motor constant 8.4 The brushless PM motor in control systems 8.4.1 Classical transfer function betw-een voltage & speed 8.4.2 Brushless DC motor model including inductance 8.4.3 Closed-loop feedback system 8.4.4 Response of generic second-order system 8.4.5 Dynamic braking xix 405 405 407 407 411 415 417 419 422 424 426 428 430 432 435 436 436 436 437 437 439 440 442 443 445 446 448 449xx Contents 9 GENERATING 451 9.1 Introduction 451 9.2 Configurations and loads 454 9.2.1 No-load (open-circuit) 455 9.2.2 Steady-state short-circuit 456 9.2.3 Passive impedance load 457 9.2.4 Voltage regulation curves 459 9.2.5 Connection to an infinite bus 462 9.2.6 Diode rectifier load 464 9.2.7 Active rectification 467 9.3 Short-circuit faults 468 9.3.1 Classical analysis 468 9.3.2 Transient Magnetic Field by Fourier Transform 472 10 MULTIPLE-PHASE MACHINES 475 Introduction 475 10.1 Polyphase machines 475 10.2 Multiplex windings 478 10.2.1 Reasons for using multiplex windings 479 10.2.2 Fault-tolerant machines 480 10.3 Analysis of multiplex windings 481 10.3.1 Balance 484 10.4 Matrix analysis of the inductances 485 10.5 Torque 491 10.6 Steady-state operation : phasor diagram 493 10.7 Solution method — transient 495 10.8 Finite-element analysis 496Contents xxi 1 1 LINE-START MOTORS 497 11.1 Introduction 497 11.2 History 500 11.3 Analysis of polyphase line-start motors 503 11.3.1 Steady state 503 11.3.2 Asynchronous operation and starting 506 11.3.3 Analysis of synchronization 510 1 1.4 Analysis of single-phase line-start motors 517 11.4.1 Steady state: no rotor cage 517 11.4.2 Symmetrical components 519 11.4.3 Asynchronous and starting performance 537 11.5 Advanced topics 542 11.5.1 Winding harmonics 542 11.5.2 Bar-pair-by-bar-pair model of the rotor cage 543 11.5.3 Connection circuits 550 12 LOSSES and COOLING 553 12.1 Introduction 553 12.2 Joule losses in stator conductors 554 12.3 Core losses 555 12.3.1 The nature of core losses 555 12.3.2 Core loss properties of practical materials 556 12.3.3 Calculation of core losses 559 12.4 Rotor eddy-current losses 561 12.4.1 Causes of rotor loss 561 12.4.1.1 Loss mechanisms in the magnets themselves 563 12.4.1.2 Resistance- or inductance-limited eddy-currents? 564 12.4. 1.3 Hysteresis loss in magnets 566 12.4.2 Harmonic losses in surface-magnet machines 568 12.4.2.1 Solution of the Complex Diffusion Equation 570xxii Contents 12.4.2.2 Exterior-rotor machine; 2-region model 574 12.4.2.3 Evaluation of the Exciting Harmonic Current Sheets 580 12.4.2.4 Balanced operation of 3-phase machines 586 12.4.2.5 Unbalanced operation of 3-phase machines 589 12.4.3 Segmented magnets and finite-length effects 602 12.4.3.1 Circumferential segmentation 604 12.4.3.2 Simplified analysis of double segmentation 610 12.4.3.3 End-effect; segmentation in the axial direction 611 12.4.3.4 Russell and Norsworthy’s method 616 12.4.3.5 Alternative analysis of segmented magnets 618 12.4.4 Slot ripple 620 12.4.4.1 Flux-dip-sweeping analysis of losses in thin can 624 12.4.4.2 Rotor can losses 626 12.4.5 Harmonic losses in the IPM 628 12.4.5.1 Losses caused by time-harmonics in the current 628 12.4.5.2 Losses caused by flux-pulsations (slotting! 629 12.4.6 Subtransient inductance and time-constant 631 12.4.6.1 Effect of segmentation on subtransient reactance 635 12.4.6.2 Coupling coefficient of the IPM 638 12.4.6.3 Rotor time-constant 642 12.4.7 Finite-element calculation of losses 644 12.5 Windage, friction and bearing losses 647 12.6 Thermal analysis and cooling 648 12.6.1 The need for cooling 648 12.6.2 Cooling and efficiency 649 12.6.3 Responsibility for temperature rise 650 12.6.4 Heat removal 650 12.6.5 Detailed analysis of cooling 652 12.6.5.1 Conduction 652 12.6.5.2 Radiation 653 12.6.5.3 Convection 654 12.6.5.4 Some rules of thumb 655 12.6.5.5 Internal temperature distribution 656 12.6.5.6 Thermal equivalent circuit 657 12.6.5.7 Some useful tables 658 12.6.6 Intermittentoperation 660Contents xxiii 13 TESTING 667 13.1 Introduction 667 13.2 Objectives of testing 667 13.3 Basic tests and measurements 668 13.3.1 Inertia 668 13.4 Resistance 669 13.5 EMF Testing 670 13.6 Generator load testing 671 13.7 Motor load testing 672 13.8 Torque Testing 672 13.8.1 Torque constant kT 672 13.8.2 Cogging torque 673 13.8.3 On-line estimation of torque using the i-psi loop 674 13.9 Thermal Testing 675 13.9.1 Thermal equivalent-circuit parameters 675 13.10 Inductance Testing 676 14 APPENDIX 681 14.1 Frequently asked questions 681 14.1.1 Machine Design Questions 681 14.1.1.1 How do 1 decide the shape and size of the machine’.’ 681
14.1.1.2 How do I choose the number of slots and poles? 682
14.1.1.3 How do I design the stator teethand slots? 682
14.1.1.4 How do I decide the number of turns? 684
14.1.1.5 How do I decide the type of stator winding? 685
14.1.1.6 How can I gel a fractional number of turns coil? 685
14.1.1.7 How can I reduce the wire size? 685
14.1.1.8 How can I reduce the inductance? 686
14.1.1.9 How can I increase the inductance? 686
1 4. 1. 1.10 How do 1choose Iwtween SPM and IPM? 68614.1.1.11 How do I choose between exterior or interior rotor? 688
14.1.1.12 When should I consider an axial-flux machine? 688
14.1.1.13 How do I decide the rotor geometry? 689
14.1.1.14 How can I reduce the inertia? 691
14.1.1.15 How can I improve the torque linearity? 692
14.1.1.16 How can I reduce torque ripple? 692
14.1.1.17 How do I design a PM synchronous generator? 692
14.1.1.18 How do I test a PM synchronous machine? 692
14.1.1.19 Why isn’t my measured kE equal to kT? 692
14.1.1.20 How do I calculate the machine temperature? 692
14 . 1.1.21 What are the main effects of temperature? 693
14.1.1.22 How can I prevent demagnetization? 694
14.1.1.23 How can I reduce the noise level? 695
14.1.1.24 How can I reduce the motor cost? 695
14.1.1.25 How about EMF ripple? 696
14.1.1.26 How about a sine-EMF motor with squarewave drive? 696
14.1.2 Performance and Control Questions 697
14.1.2.1 How can I increase efficiency? 697
14.1.2.2 How can I increase power-factor? 698
14.1.2.3 How can I get smooth rotation at low speed? 698
14.1.2.4 How can I make the motor go faster? 699
14.1.2.5 How can I get a more sinusoidal EMF waveform? 700
14.1.2.6 How can I get a more sinusoidal current waveform? 700
14.1.2.7 How do I avoid first-turn insulation failure? 700
14.1.2.8 How do I avoid bearing currents? 702
14.1.2.9 What causes machines to fail? 702
14.2 Saliency 703
14.3 Half turns
14.4 Series and parallel inductances 709
14.5 Gearing
14.6 Units of inertia
14.7 Calculation of inertia
Symbols. Abbreviations, and Explanatory Notes
u 737
Bibliography
755
IndexINDEX
Index 755
1.5 slot* pole ….. &,86. |35 136 685
Croft 1924
136
1- and 2-phasc unipolar drives 315
12-10 motor
alternative windings 124
1*5 slot& pole 138
Abandon inductance!
214
ABB 502
AC resistance 554
and deep slots 683
and stranded conductors 144
example 150
practical considerations 151
proximity effect 102, 143
redistribution of current in a slot 146
Roebel transposition 102
AC synchronous
see Brushless AC 28
Acceleration of pure inertia load 716
Accumulations for mean and RMS currents 288
Active rectification 467
ADC (analog digital converted 323
Adhesives 156
Adkins B 468.500
Airgap
tapered 316
Airgap fiux distribution 157, 164
Airgap flux-density 161
Airgap inductance 215
calculation examples 217
general case 221
mutual between phases 217
Airgap length 92.115
182, 252, 257. 622
Ampere-conductor distribution …. 18. 19. 69. 77. 82. 169. 239. 250. 255. 476. 482. 510.
107
116
226
and Carter’s coefficient
and cogging
and EMF waveform
and inductance
effective (synchronous inductance! .. .
relative to magnet length
88.89
108.686
238
70, 190. 309. 329, 335. 347. 367. 492. 501
190.332.335
-
- 534
451.453.455.501
208
695
.. 256
…93
Airgap shear stress
Airgap winding
inductance
Alignment torque
and reluctance torque . . . .
in line-start motor
Alnico
Alstom high-speed train (AGVl
Aluminium conductors756 Design of Brushless Permanent-Magnet Machines
and six-step
balanced operation
in squarewave motor
rotating
sinewave motor
space harmonics
AO Smith
APPLICATIONS
aerospace
checklist of requirements
for brushless permanent-magnet machines
general-purpose
high torque
high-precision motion-control
high-speed
high-volume
light-duty fan
low-powered fans or blowers
of permanent-magnet generators
single-phase line-start
with intermittent duty
Arc magnets
effective dimensions
Ar^lik Turkey
Armadillo < Panasonic!
525, 528, 580, 582-584, 601, 635
375
586
273
- 534
n KME 93. 108, 113. 131, 315, 387. 456. 561, 620. 621. 689, 700
in flux-density waveform 558
in line-start motor 542. 543
in power measurement 671,672
in rotor llux 131
in squarewave current (effect on RMS) 419, 421
in squarewave motors 79, 116
inductance components not available from finite-element method 263
inverter 386,394.419
one of the nasty things that goes on in machines 326
permeance/slot*modulation 108, 131,456,561
series representation of magnetization 169.171.172.225
slot-order 700
space 131.217.250
space harmonics used to start single-phase motor 71
third harmonic and zero-sequence 599. 600, 700
third-harmonic injection 387. 404
triple-n 116. 117. 278. 593. 599, 600
variation of inductance with rotor position . 191. 249. 251. 259. 261. 314. 489.
490
Head-scratching
caused by failure to measure things 668
Heat removal 650
Heat transfer
see Cooling 648
Helical windings 241
Heller B and Hamata V 628
Hermetic compressors 648
Hexagon tracking 394
and Third-harmonic injection 387
High-speed machines 92. 96. 105. 151. 156. 366, 554. 620. 647, 682. 690
Historical development of sinewave drive
Hitachi 502
26
Holes (to reduce inertia) 691
Holtz 374,394
Space-vector controller 391
Honeywell 43
Honsinger 499,51X1.507
Hoop stress
in retaining sleeve
569
Hughes A
Hybrid vehicles 451
Hysteresis loss 555772 Design of Brushless Permanent-Magnet Machines
197
43
700
561
593
100
26
209
214
IEC
IGBT transistors
Imbalance
single-parameter
Impedance protection ….
Inconel®
INDUCTANCE
abandon!
566
377
377
372
. . 192. 196
200
. . 268.496
203
. . . 200-202
. . . 203-207
. . . 197-200
206
207
Hysteresis loss in magnets
Hysteresis-band current regulator
leakage outside the hysteresis band
l-y controller
i-f loop
and cogging torque
calculation of saturated synchronous inductance . . . .
elliptical
examples
properties
theory of average torque production
torque per ampere
with six-step drive
i-psi loop
see i-i|« loop
airgap component 214,215
and airgap length 226
and ceramic or bonded NdFeB magnets 36
and closed slots 229
and current regulation 33
and current ripple 33. 213, 280
anddi dt 213
and finite-element calculations 262
and flux-linkage 210
and flux-weakening ….
and Hague’s method . ..
and parallel paths
and phase shift
and power factor
and short-circuit faults .
and skew
and speed range
and switching frequency
and type of magnet ….
chopping frequency . . . .
components
definition
di/dt
differential
effect of slot shape
effect of tooth overhangs
end-turn component . . .
Faraday’s law
flux times turns
33,344
225
216
213
213
213
250
213
213
212
213
214
209
211
- 134, 214, 225, 226. 258. 482, 487, 490, 686
231
231
214
210
211773
.. 221
131, 134. 214, 225. 226. 25«, 482. 487, 490.686
716
721
668
36
691
716
462
341
harmonic
in salient-pole machines
in torque calculations ,
incremental
link between static and dynamic calculations
magnetizing
measurement
mutual
of end-winding
of slotless (airgap) windings
per-unit
phase
position of conductors in slot
practical effects
Prescott and El-Karashi inductance bridge . ,
self
. 648
. 447
. Ill
. 45
3.688
Index
general case of airgap inductance ….
… 247
… 190
… 263
… 209
… 225- 676
… 210
… 233
… 238
… 212
… 214
… 230
… 213
… 677
… 210
…709
… 226
…682
… 214
… 631
… 243
…686
…686
… 212
191, 249. 251. 259. 261. 314. 489. 490
713
213
series and parallel
slot-leakage
slot-leakage and magnetic slot-wedges
slot-leakage component
subtransient
synchronous
how to increase
how to reduce
turns squared
variation with rotor position
wye and delta connections
Inductive voltage drop
Inertia
acceleration of
calculation
measurement
of exterior-rotor machine
how to reduce
units
Infinite bus
Infinite maximum speed
Insulation life
related to temperature
Integral gain compensation
Integral-slot windings
Integrated frequency converter
Interior rotor
Interior-rotor machine
split ratio
Interlocking laminations
Intermittent operation
Inverse saliency 349. 251. 505
Inverter
available current 338
oversized required for llux-weakening 345771 Design of Brushless Permanent-Magnet Machines
sinewave : Bee Chapter 7 325
squarewave :see Chapter 6 273
Inverter circuit
bridge; inverter circuit 8
Inverter-grade magnet-wire 26,701
Ionel DM 558
I PM 28.32
airgap comparable to that of an induction motor 33
and demagnetization 33
and torque linearity 33
control complexity 33
control mode diagram 348
essential features 32
multiple-layer 690
reasons to use 687
reluctance torque 32
saturation in 34
speed range 33
V-shaped magnets 53
with squarewave drive 309
Iron losses
see (‘ore losses 555
Irregular slotting 131.132
Irreversible loss of magnetization 694
Isosyn motor 371, 501, 509
j
rotate phasor by 90 19
Jack A
fault-tolerant machine 100
powdered-iron core 100
prepressed windings 100
Jahns IM
373
John Deere
H
Jones bridge
see Prescott and El-Karashi inductance bridge
Jones CV
Joule losses
Kalluf
kE
… 677
… 677
143.554
…542
see EME constant kE
Keeper
Kelvin functions
Knee point
157
455
572
on magnet demagnetization curve
Koch Th
kT
161,693. 694
131
sec Torque constant kT
kT & kE 157
2-phase sinewave motor and drive
2 phase sinewave motor with squarewave drive
2 pha.M- squarewave and sinewave systems compared
2 phase squarewave motor and drive
428
430
435
426Index
2-phiw squarewave motor with sinewave drive
J-phaw sinewave motor and drive
3-phase sinewave motor with squarewave drive
; phas<. squarewave and sinewave systems compared’ .'
J-pnasesquarewave motor and drive
3-phasc squarewave motor with sinewave drive
as Figures of merit……
775
432
415
417
422
411
419
DC commutator motor and drive .. ..” /
detailed analysis: see Chapter 8
Tables; 2-phase
Tables; 3-phase
when are they equal and when are they not equal?
traced end-turns
436
407
405
434
422
- 692
Lqjoie-Mazenc M
Laminations
62
.. 371.372
choice of steel
custom designs
improvements in electrical steels .
insulating coatings
insulation
punching
self-cleating
skewing
stacking
suppliers
thickness and eddy-current core loss
thin
Lammeraner and .Stall
Langhorst
l-ap winding
inductance calculation .. . .
Lapiace/Poisson equations
Laronze J
Lateral deflection and whirling
Lawrenson PJ
97
683
26
97
26
97
99
99
98
683
556
97
146.563.642,643
702- 100, 104. 109-113, 120, 685
157.169
473, 662. 568. 569
end-winding inductance calculation
pull-in criterion
synchronous reluctance motor
Layers
in winding 77. 110 Hi l.P
LCM
least common multiple of slots and poles
Ixi
we Synchronous inductance
Ldiff
see harmonic or differential inductance ….
leakage factor
Leakage flux (in rotor bridges)
Leakage flux (pole-to-pole or ‘rotor leakage”) …. 113. 116. 153-160 167. 183. -1- 689
Length/diameter ratio
Libert F776 Design of Brushless Permanent-Magnet Machines
Line-start motor
advantages
analysis of polyphase
analysis of synchronization
d starting 5
of the rotor cage
Chapter 11
connection circuits
asynchronous operation an
bar-pair-by-bar-pair model
history
magnet braking torque ..
non-orthogonal windings .
phasor diagram
pull-up torque
saliency braking torque . . .
single-phase
torque reversals
winding harmonics
Linear motor
Linear power amplifier
Linearity
from a control viewpoint . .
see Torque linearity
Liquid coolant
Litz wire
Ixiad
speed, torque characteristic
Load angle
power angle
Load-line
out-of-stator
Locked-rotor stall 13. 14, 270, 436, 439-441,
Loctite 98.
Losses
AC resistance
and cooling
and finite-length effects
and multiple phases
bearing loss
core losses
due to imbalance
due to MME Space-harmonics
due to permeance harmonics
due to time-harmonics
effect of temperature on resistance
finite-element calculation
in Segmented magnets
in the IPM rotor
in thin can
Joule (copper!
proximity effect ’
rotor eddy-current
slot ripple- 509, 516,
144, 151,Index 777
windage and friction
563 647
M
see Synchronous inductance
243
Lubrication ‘
Machine configuration
chart
variety of
Machine Design Questions
Machine temperature
How to calculate
MAGNA circulator pump
Grundfos
Magnet
alignment torque
«rc 93
effect of temperature 23
effect on inductance 212
energy product 94
ferrite 26
flux calculation 162
full-ring 107. 607
grade of 94
initial dimensioning 93
knee-point 161
knee-point and its variation with temperature 693. 694
length 93
load-line calculation 162
Neodymium-lron-Boron 26
operating point calculation 162
overhang 95
permeance coefficient calculation 162
polymer-bonded 45
profiling 689
retention 31. 153, 690
rotating 1
Samarium-Cobalt 26
segmented 93
thickness 93
width 93
Magnet braking torque 507. 509. 516, 543
Magnet flux-linkage . . 5
Magnet-wire
inverter-grade 26
Magnetic equivalent-circuit method 157, 158
Magnetic frequency’ 82.681.697
Magnetic loading B 87
Magneticslot-wedge 682
Magnetization curves 263-267
in dq-axes 266
Magnetizing fixture
with skewed poles 107778 Design < >f Brushless Permanent-Magnet Machines
Magnetizing inductance
Magnussen F
Manual winding
Maximum speed
and inductive voltage drop –
attainable with a given supply voltage
infinite *”‘
of nonsalienl-pole motor ••••••
Maximum torque
Current-limited
Voltage-limited •••
Maxon
slotless motor ……
McLachlan NW
Mean rectified EMF 407′
Measurement
airgap length
cogging torque •••••
EMF
EMF constant
(lux-linkage …….
inductance 260.
inertia
mutual inductance ……….
on-line estimation of torque using the i-psi loop
resistance
synchronous inductance y.-
thermal resistance
torque
torque constant ;
Mechanical time-constant
as a Figureof merit ……..
MelfiM
Merrill FW
Mhango I
Miller TJE
Rotor eddy-currents …
MIN ASH servo-motor
Panasonic 99.
Misalignment
Miyashita ”
.
MMF distribution
see Ampere-conductor distribution
Modi- diagram
I PM control
synchronous reluctance motor . .
Modular winding
Modulation index
Morley A
Motor constant
Figure of merit
Motor load testing SI
Hill
§
§82
a
$83l
ss
2£§Index 779
Motorcycle alternator
Triumph Bonneville 57
Moulded plastic insulator 100
Mounting flange 43
MS-TECH Japan 53.63
MTS Systems Inc 48
Multi-level converter 80
Multiple phases
used to increase efficiency 475
Multiple-layer 1PM 690
MULTIPLE-PHASE MACHINES 475
Multiple-strand conductor
see Conductor; stranded 104.685
Multiplex windings 478
reasons for using 479
Mutual inductance
airgap component 217-225
and differential inductance 258
between phases … 191. 198. 209. 214. 225, 232. 243-250. 258. 259. 265, 280.
291,313,314.319
214
210
234
316
… 529.543-548- 481-491.495
… 6X5,638.641
709-714
238-240
679
705
229-231
212
156
448
530
43
152
569
13
646
440
458
…. 15,443
23
… 424.425
455
… 157,455
… . 301-303
455
401
components
definition
end-winding component
in bifilar winding
in line-start rotor
in multi-phase winding
in rotor loss calculation
in series parallel connections
in slotless machine
measurement
saliency and torque-production . ..
slot-leakage component
turns-square rule modified
Mylar
Natural frequency
Natural symmetrical components
NEMA
Neutral connection
insulated
Ng K
No-load speed
and losses
and Motor Constant
and regulation
and voltage
effect of temperature
example calculation
generator on open-circuit
open-circuit condition
precise determination
No-load test
Noguchi780 Design of Brushless Permanent-Magnet Machines
Noise causes
Non-orthogonal windings
in line-start motor 520.536
Non-overlapping winding
mm* Concentrated winding 86
Non-uniqueness of reluctance torque 335
Nonsalient-pole machines 68
Number of phases
in electrical machines 75
in electrical systems 72
in inverters and rectifiers 80
multiple phase’s used to increase efficiency 698
practical considerations 71
Number of poles 82, 682
Number of stator slots 82,105,682
Offset
winding 127
ohms per 1000ft 140
ohms km or ohms’1000ft 140
On-line estimation of torque using the i-psi loop 674
Open slots 100, 105
and form-wound coils 105. 682
slot-fill factor 102
Open-circuit test 456, 670
Operating point
of the magnets 157
Operation of salient-pole motor generator (IPMI 347,348
Optimization tools 681
Optimum gamma 333 347 343
Oriental Motor Co Ltd 52
planetary gearmotor 52
Output equation 37
Outside rotor
see Exterior rotor 688
Overcurrent circuit-breaker 213
Overcurrents during commutation ’ ” ” ’ 289
Overexcited generator 339
Overmodulation
3^ 3$^
Oversized inverter ‘345
Overview Ltd UK
Overview of controllers
Sinewave drive
Pacific Scientific
Pan-and-tilt mechanism
Overview Ltd
Panasonic Japan
Pancake coils
Parallel paths
and biHlar winding
and circulating currents …
and Litz wire
and turns in aeries per phase JIndex 781
248
… 108
453
467
451
469
453
462
464
671
455
456
301
330
457
461
458
453
468
456
456
461
469
469
454
331
459
5(H)
289
341
212
343
343
697
154
.. 93. 161
230
sw open slots .
Park’s equations
Park’s transform
and inductance
105.682
195- 194, 247-249. 326. 485
Peak, mean and RMS currents
versus duty-cycle (squarewave)
Per-unit EMF
Per-unit inductance
Per-unit short-circuit current
Per-unit synchronous reactance
Performance and Control Questions
Peripheral velocity
Permanent-magnet generator
sign conventions
active rectification
applications
armature time-constant
asa motor with the direction of power How reversed
connected to infinite bus
diode rectifier load
load testing
no-load (open-circuit)
open-circuit test
over-running of squarewave drive
overexcited
passive impedance load
pull-out torque
regulation
self-regulating
short-circuit fault
short-circuit ratio
steady-state short-circuit
steady-state stability limit
subtransient reactance
subtransient time-constant
types of load
underexcited
voltage regulation curves
Permasyn motor
Permeance coefficient
of magnetic circuit
of slot
Permeance harmonics
and cogging torque
defining conductor current
effect on EMF constant kE ’ / ‘
effect on inductance
effect on resistance
not balanced
used to adjust wire size
used to get correct turns/coil or turns in series per phase .
Parallel-sided slots
110
180- 232,712
139
151
685… 152.685
_782 Design of Brushless Permanent-Magnet Machines
Pitch (coin
see coil span
Pitch factor
definition
for a general winding
harmonic
and KMF ripple
and rotor losses
Phase advance
and flux-weakening
effect on torque constant
in squarewave drive
increase in torque ripple
uncontrolled rectification
Phaseseparator
Phase shift
and inductance
Phasor diagram
definition
does not apply to squarewave drive
duplex winding
flux-linkages
generating
including space phasor diagram of flux-linkages
motor operation
of split-phase line-start PM motor
- 126
113, 122. 126. 128, 129. 134. 136
129
130
240
108.456.696
. 561. 562. 620-630
18.70
304,344
333
304
305.696
304
101
371
213
22, 203, 327, 329, 332
19
273
494
328
330
203,329
327
533
PM alignment torque
see Alignment torque 70
PM generator
see permanent-magnet generator 451
PM synchronous AC
see Brushless AC 28
PM-assisted synchronous reluctance motor 64, 364
Pole-group 111-113
Pole-pairs
and frequency 1
and speed 1
Poles
number of 82. 682
Polifibra 156
Position of the neutral 708
Powdered-metal materials 26
Power factor
and double-frequency pulsating component of power 187
and llux-weakening 358 364
and inductance 213.314
and phase advance 67
and volt -ampere requirement 213.698
us a Figure of merit 436
auxiliary capacitor as a power-factor correction capacitor 534
•xample 342
how to increaseIndex 783
importance a performance criterion 367
in line-start motor 503 534
in testing 650
internal 205
4 497,503
maximization as a control strategy 366
of generator 330,331, 459-463
variation with speed 341, 359, 365
zero-power-factor load 650
Power per volt-ampere 213
Power rate
Figure of merit 437
Premature failure 702
Prescott and El-Karashi inductance bridge . . 677
Presscd-core
see powdered-metal materials 26
Printed-circuit board 100
Prius
Toyota Prius 34
Prolibus
see Fieldbus 66
Proximity effect 102, 109, 143, 144, 150,554,646
Pull-out torque
of permanent-magnet generator 461
Pull-up torque
in line-start motor 506. 507
Punching
see Lamination 683
Punching die 683
PWM <pulse-width modulation)
see Chopping 370
q-axis synchronous inductance
see synchronous inductance 247
q-axis web
effect on inductance 258
Quadrants of operation 24
Quadrature control 329. 353
Rabi novici R 164. 559
Radial-flux machines 30,31
Ramp comparison 383
Rasmussen KF 169
Ratio of reluctance torque to alignment torque 335
REA Magnet Wire Co USA 102
Recoil permeability
and saliency 94
generally of little significance 94
Rectangular conductors 100. 102. 109. 145.685
Rectifier 80
12- or 24-pulse 79.80
action of transistor bridge diodes in over-running 301
as load on a PM generator 2. 18. 22. 453, 454. 458, 464-467, 671
in l.qjoie-Mazenc’8 1-y controller 372784 Design of Brushless Permanent-Magnet Machines
370
Reliance Electric . 68. 190-192. 329. 332. 335. 346. 347. 350. 351, 361. 705
Reluctance torque
520
193
701
301
… 458.459
371.497.502
mean rectified
phase-controlled SCR
precision • • •
transistor inverter operating as active rectifier
waveforms
Reference current
see Set-point current
Reference-fra me t ransformations
of single-phase line-start motor
see Park’s transform
Reflection of voltage wave
Regeneration
Regulation
of permanent-magnet generator
and saliency
and squarewave drive
and torque linearity
and torque ripple
cogging as a form of reluctance torque
concept undermined by saturation
in IPM
in line-start motor
in multi-phase machine
included in i-<» loop
1PM
maximizing using multiple-layer IPM
non-uniqueness
small effect due to recoil permeability
Remanence
variation with temperature
Renewable energy
Resistance
AC resistance
and copper weight
and Figures of merit
and Joule loss
and Litz wire
and locked-rotor current
and magnet braking torque
and ohms/km or ohms/1000ft
and parallel paths
and saliency braking torque
and short end-windings
and slot-fill factor
calculation of winding resistance
effect on measurement of inductance
equivalent DC impedance and commutating inductance
in armature time-constant
in complex synchronous inductance
in electrical and mechanical time-constants
407,410
… 13.372,454
456,670
453, 454, 458, 467
410
. 68-70.256.703
. . . 273.310.371
423
191, 192, 309.310
107.703
335.367
32.92.687
501-504.514.515
492
197, 198
32
689
335
94
. . . 158, 160, 161
693.694
451
12
…. 104,143-151
140
405, 406, 439, 441
554,693
144
13,14
507
140
139
507
133
101
139
677,678
464
471
632
443-445Index 785
712
556
470
104
142
140
323
26
49
155
63
561
156
153
241
28
31.68.83. 107, 607,687
increased using bifilar winding. .
load on generator
measurement
must be known in DTC controller
of eddy-current paths .
of laminations
712
457
669.670
402
- 618, 619, 629, 630, 632, 644
Resistivity
of copper
temperature coefficient …
Resolver
Retaining sleeve
carbon fibre
effect of thermal expansion
fitting
loss calculations
material
tangential or hoop stress . .
Rhombic windings
Richter
Ring magnet
Rise-time
of magnets in subtransient time-constant
of multi-strand conductor
of rotor cage in line-start motor 5l6t 524. 543. 548, 549
per-unit, and scaling laws 509
ratio formula for temperature variation 142
temperature rise by resistance 658 675
thermal:see Thermal resistance ‘ L ‘ . / . 99
variation with temperature ” 140-142, 554. 693
X’R ratio of split-phase line-start motor
. 712
Resistance thermometer
559
Resistance-limited eddy-currents 563-566, 569, 602, 603, 618, 620, 625 633 646
Resistance-start line-start motor
of voltage pulse from the inverter 700
Roebel transposition 102. 145
Roll up stator (Panasonic Armadillo) 57
Rosa and Grover 234
Rotating field
forward and backward components 75
production with two phases 75
Rotor
can loss 561. 626
diameter 87
eccentricity 137
eddy-current loss 107. 561.62b
exterior 15
inertia 668.717
interior 3, 30
interpolar axis (q-axis)
I PM
line-start 499-503
nonsalient-pole786 Deskin <» Brushless Permanent-Magnet Machines
and 2-pole rotor •
and double-frequency inductance variation . .
and effective airgap
and magnetization curves
and optimum delta
and optimum gamma
and power factor
and recoil permeability
and saturation
and torque linearity
braking torque in line-start motor
in IPM
inverse
ratio of reluctance torque to alignment torque
test for
undesirable with squarewave drive
Saliency ratio
Salient-pole and nonsalient-pole machines
Salient-pole machines
dq transformation
inductance
with squarewave drive
of DC motor
permanent-magnet
reference axis (d-axis)
retaining sleeve
salient-pole
skew
split-ratio • ••
switching of transistors in synchronism
thermal expansion
torque at rest position
yoke
Rotor can losses
Rotor cup
flux-density
Rotor design
Rotor frequencies
rotor leakage
in IPM
permeance
see Leakage flux (pole-to-pole)
Rotor time-constant
Rotor volume
Rotor yoke
dimensions
solid steel
Rowan and Kerkman
RS232
RS485
96
.. . 92-96
. 588-592
96
96
384, 386, 389
66
66
Russell and Norsworthy •’ 51?
Saliency 68-70, 190. 248, 249, 350, 458, 509, 517, 518, 542. 543, 641. 703-705
…. 160
…. 159
…. 113
…. 642- 91
256
250
252
265
334
333
367
94- 335
…. 5
. 5. 19
.. 156- 70
.. 107
…91
1.2. 16
.. 155
…71
…82
.. 561
. . . 333, 369
507
… 326.367
- 505
335
…. 69.704
… 273.371
335
68
69.248
193
247
309Index 787
- 89.662
312
370
709
Servomotor
Set-point current
Shaft position transducer
Shaft-mounted fan
Shear stress in airgap .. .
Sampling
Sampling frequency
Saturable bridges .
Saturation
378.381
378.387.401
.. . . 167. 168, 254-256. 268, 270, 503, 544, 546, 639,689
and energy partition
and Finite-element analysis
and i-f diagram
and inductance
and losses
and magnet operating point
and magnetization curves
and narrow airgap
andq-axisweb
and reluctance torque
and short-circuit ratio
and speed’torque curve
and torque linearity
cross-saturation
finite-element method
in dq-axis model
in IPM
in salient-pole machines
in single-phase bifilar motor
in stator teeth and yoke
in the dq-axis model
local
non-uniqueness of reluctance torque .
of bridges
of current-regulator
of Ld and Lq
of rotor yoke
of stator tooth-tips
on open-circuit
Schiferl
Schofield N
Second-order system
Segmented magnets
Segmented rotor sleeve
Segmented stator
Self-cleating lamination stack
Seif-commutated
Self-inductance
Self-synchronous
Sensorless control
hack-EME sensing
sinewave drive
Senes and parallel inductances
‘ 281-284’ 296.300. 304. 305. 308, 370. 372.379.381. 467
323
- ’7′ .. 2.371Designof BrushlessPermanent-MagnetMachines
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