Design of Brushless Permanent-Magnet Machines
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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

    1. 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

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

  1. 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
  2. 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
    1. 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
    2. 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
    3. 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
  3. 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
  4. 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
  5. 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
  6. 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

  1. 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
    1. 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
    2. 91
      256
      250
      252
      265
      334
      333
      367
      94
    3. 335
      …. 5
      . 5. 19
      .. 156
  2. 70
    .. 107
    …91
    1.2. 16
    .. 155
    …71
    …82
    .. 561
    . . . 333, 369
    507
    … 326.367
    1. 505
      335
      …. 69.704
      … 273.371
      335
      68
      69.248
      193
      247
      309Index 787
    1. 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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