Table Of ContentModern Permanent
Magnet Electric Machines
The late 1980s saw the beginning of the PM brushless machine era, with the
invention of high-energy density permanent magnets (PM) and the development
of power electronics. Although induction motors are now the most popular
electric motors, the impact of PM brushless machines on electromechanical
drives is significant. Today, PM machines come second to induction machines.
Replacement of electromagnetic field excitation systems by PMs brings the
following benefits:
• No electrical energy is absorbed by the field excitation system and thus
there are no excitation losses, causing substantial increase in efficiency
• Higher power density (kW/kg) and/or torque density (Nm/kg) than
electromagnetic excitation
• Better dynamic performance than motors with electromagnetic excita-
tion (higher magnetic flux density in the air gap)
• Simplification of construction and maintenance
• Less expensive for some types of machines
Modern Permanent Magnet Electric Machines: Theory and Control serves as a
textbook for undergraduate power engineering students who want to supplement
and expand their knowledge in the fundamentals of magnetism, soft magnetic
materials, permanent magnets (PMs), calculation of magnetic circuits with PMs,
modern PM brushed DC machines and their controls, modern PM brushless
DC motors and drive control, and modern PM generators. The book can help
students learn more about electrical machines and can serve as a prescribed text
for teaching elective undergraduate courses such as modern permanent magnet
electrical machines. Since the book is written in a simple scientific language and
without redundant mathematics, it can also be used by practicing engineers and
managers employed in electrical machinery or electromagnetic device industries.
Modern Permanent
Magnet Electric Machines
Theory and Control
Jacek F. Gieras
PBS University of Science and Technology, Bydgoszcz, Poland
Jian-Xin Shen
Zhejiang University, Hangzhou, China
First edition published 2023
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2023 Jacek F. Gieras and Jian-Xin Shen
Reasonable efforts have been made to publish reliable data and information, but the author and
publisher cannot assume responsibility for the validity of all materials or the consequences of their use.
The authors and publishers have attempted to trace the copyright holders of all material reproduced
in this publication and apologize to copyright holders if permission to publish in this form has not
been obtained. If any copyright material has not been acknowledged please write and let us know so
we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information
storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.com
or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400. For works that are not available on CCC please contact mpkbookspermissions@tandf.
co.uk
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are
used only for identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Gieras, Jacek F., author. | Shen, Jian-Xin, author.
Title: Modern permanent magnet electric machines : theory and control /
Jacek F. Gieras, Jian-Xin Shen.
Description: First edition. | Boca Raton : CRC Press, 2023. | Includes
bibliographical references and index.
Identifiers: LCCN 2022022229 (print) | LCCN 2022022230 (ebook) | ISBN
9780367610586 (hardback) | ISBN 9780367610616 (paperback) | ISBN
9781003103073 (ebook)
Subjects: LCSH: Permanent magnet motors. | Electric motors,
Brushless--Design and construction.
Classification: LCC TK2537 .S4544 2023 (print) | LCC TK2537 (ebook) | DDC
621.46--dc23/eng/20220916
LC record available at https://lccn.loc.gov/2022022229
LC ebook record available at https://lccn.loc.gov/2022022230
ISBN: 978-0-367-61058-6 (hbk)
ISBN: 978-0-367-61061-6 (pbk)
ISBN: 978-1-003-10307-3 (ebk)
DOI: 10.1201/9781003103073
Typeset in CMR10 font
by KnowledgeWorks Global Ltd.
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
Contents
Preface ........................................................ xi
1 FUNDAMENTALS OF MAGNETISM .................... 1
1.1 Atom, spin, magnetic dipole moment ..................... 1
1.2 Magnetic permeability, magnetization vector, magnetic
susceptibility .......................................... 3
1.3 Classification of materials according to magnetic permeability 4
1.4 Hysteresis loop of ferromagnetic materials ................. 8
1.5 Comparison of soft and hard magnetic materials............ 9
1.6 Analogies in electric and magnetic circuits................. 11
1.7 Effect of ferromagnetic core inside a coil................... 12
1.8 Applications of magnetism............................... 13
1.8.1 Electric motors and generators.................... 13
1.8.2 Magnetic storage of data ......................... 13
1.8.3 Loudspeakers ................................... 14
1.8.4 Lift electromagnet............................... 14
1.8.5 Magnetic core memory........................... 16
1.8.6 Magnetoresistive random-access memory (MRAM) .. 16
1.8.7 Cathode ray tube (CRT)......................... 17
1.8.8 Nuclear magnetic resonance (NMR) spectroscopy.... 18
1.8.9 Magnetic resonance imaging (MRI)................ 19
1.8.10 Magnetic levitation.............................. 20
1.8.11 Cyclotrons ..................................... 21
1.8.12 Tokamak....................................... 22
1.8.13 MHD generators ................................ 22
1.9 Biot-Savart law, Faraday’s law and Gauss’s law ............ 23
1.9.1 Biot–Savart law................................. 23
1.9.2 Faraday’s law................................... 24
1.9.3 Gauss’s law .................................... 25
1.10 Maxwell’s equations .................................... 26
1.10.1 Maxwell’s first equation.......................... 26
vi Contents
1.10.2 Maxwell’s second equation ....................... 27
1.10.3 Maxwell’s third equation ......................... 28
1.10.4 Maxwell’s fourth equation........................ 29
1.11 Magnetic vector potential ............................... 29
1.12 Speed of electromagnetic wave and theory of relativity ...... 30
1.13 Maxwell’s equations in application to electrical machines .... 33
1.14 Force in electromagnetic field ............................ 34
Summary ................................................... 35
2 SOFT MAGNETIC MATERIALS ......................... 39
2.1 Classification of soft ferromagnetic materials ............... 39
2.1.1 Laminated silicon steels.......................... 40
2.1.2 High-saturation cobalt alloys ..................... 42
2.1.3 Amorphous ferromagnetic alloys .................. 44
2.1.4 Soft magnetic composites (SMC).................. 45
2.1.5 Permalloys ..................................... 47
2.1.6 Nanocrystalline composites ....................... 47
2.1.7 Solid ferromagnetic steels ........................ 49
2.2 Losses in ferromagnetic materials......................... 51
2.2.1 Hysteresis losses ................................ 51
2.2.2 Eddy-current losses.............................. 53
2.2.3 Excess eddy-current losses........................ 53
2.2.4 Additional losses ................................ 54
2.3 Engineering approach to calculation of core losses .......... 54
2.4 Ferromagnetic cores .................................... 54
2.4.1 Transformers ................................... 55
2.4.2 Electronic devices ............................... 55
2.4.3 DC machines ................................... 56
2.4.4 Switched reluctance machines (SRM) .............. 57
2.4.5 Induction machines.............................. 57
2.4.6 Synchronous turbogenerators ..................... 58
2.4.7 Synchronous hydrogenerators ..................... 59
2.4.8 Permanent magnet (PM) brushless motors ......... 60
2.4.9 Segmented stator and rotor cores.................. 60
2.4.10 3D cores made of soft magnetic composites (SMC)
for special electric machines ...................... 60
2.4.11 Solid ferromagnetic rotors ........................ 61
2.5 Magnetic circuits of electrical machines for recycling ........ 61
Summary ................................................... 63
3 PERMANENT MAGNETS ............................... 65
3.1 Early history of permanent magnets (PM)................. 65
3.2 Earth’s magnetic field................................... 67
3.3 What is a permanent magnet (PM)?...................... 69
Contents vii
3.4 Hysteresis loop, demagnetizationcurve, recoilline, magnetic
energy density and intrinsic magnetization................. 69
3.5 Temperature coefficients and Curie temperature............ 72
3.6 PM materials used in construction of electrical machines .... 74
3.6.1 Alnico ......................................... 74
3.6.2 Ferrites ........................................ 76
3.6.3 Rare-earth magnets SmCo and NdFeB ............. 77
3.7 Nanocomposite magnets................................. 81
3.8 Shape of demagnetization curves of ferrite and rare
earth PMs............................................. 82
3.9 Simplified method of finding the operating point of a PM.... 84
3.10 Main flux and leakage flux............................... 85
3.11 B–H and Φ–F coordinate systems........................ 86
3.12 Operating point for PM magnetized outside the machine .... 87
3.12.1 PM without pole shoes in open space .............. 87
3.12.2 PM with pole shoes in open space................. 88
3.12.3 PM inside an external magnetic circuit............. 88
3.12.4 PM with a complete external armature system...... 89
3.13 Operating point for magnetization without armature........ 91
3.14 Mallinson–Halbach array ................................ 93
Summary ................................................... 95
4 CALCULATION OF MAGNETIC CIRCUITS
WITH PMs ............................................... 97
4.1 Methods of calculation of magnetic circuits with PMs ....... 97
4.2 Permeance evaluation by dividing the magnetic field into
simple solids........................................... 98
4.3 Graphical methods .....................................102
4.4 Analytical approach to calculation of magnetic circuits with
PMs ..................................................102
4.5 Calculation of magnetic circuits with PMs using an
equivalent reluctance network ............................104
4.6 Calculation of magnetic circuits with PMs using the FEM ...107
Summary ...................................................111
5 PM BRUSH DC MACHINES AND THEIR CONTROL ..113
5.1 Why PM machines? ....................................113
5.2 Construction of a brush-type PM DC machine .............114
5.3 Principle of operation of a PM brush DC machine ..........115
5.4 Windings of a slotted rotor (armature) of a brush-type DC
machine...............................................118
5.5 Construction of a coreless rotor winding with an inner PM ..120
5.6 Coreless rotor windings: Maxon versus Faulhaber winding ...122
5.7 PM brush DC motor with cylindrical rotor and foil winding .124
5.8 Disk-type PM brush DC motors with printed rotor winding..126
viii Contents
5.9 Fundamentals of transient analysis of PM brush DC motors .128
5.10 Speed control of a brush-type PM DC motor...............130
5.10.1 Three-phase fully controlled rectifier...............131
5.10.2 Chopper .......................................132
5.10.3 H-bridge .......................................133
5.11 PM brush DC servomotors ..............................135
5.12 Applications of brush-type PM DC motors ................136
5.12.1 Toys...........................................137
5.12.2 Auxiliary motors for automobiles..................139
5.12.3 Vibration motors for mobile phones ...............141
5.12.4 Robotic vehicles for Mars missions ................144
Summary ...................................................147
6 PM BRUSHLESS DC MOTORS AND DRIVE
CONTROL ................................................149
6.1 From PM DC brushed to PM DC brushless motors .........149
6.2 Construction of rotors ..................................151
6.3 Sinusoidally excited and square wave motors...............152
6.4 Method of changing DC bus voltage and speed control ......156
6.5 Unipolar and bipolar operating mode .....................158
6.6 Six-step commutation: two phases on .....................159
6.7 Three phases on: 180-degree conduction ...................161
6.8 Rotor position sensing ..................................163
6.8.1 Hall sensors ....................................163
6.8.2 Encoders.......................................164
6.8.3 Resolvers.......................................167
6.8.4 Sensorless control ...............................168
6.9 Mathematical model ....................................169
6.10 Cogging torque.........................................171
6.11 The smallest and the biggest PM brushless motors in the
world .................................................172
6.12 Wiring diagram for a solid-state converter-fed PM brushless
motor.................................................174
6.13 Integrated circuits (IC) for control of PM brushless motors ..175
6.14 Practical electromechanical drive system ..................177
6.15 Selected applications....................................177
6.15.1 Computer hard disk drives (HDD) ................177
6.15.2 Two-phase PM brushless motors for computer
cooling fans ....................................178
6.15.3 PM brushless motors integrated with an electronic
control circuit ..................................184
6.15.4 Hybrid electric vehicles ..........................185
Summary ...................................................189
Contents ix
7 PM SYNCHRONOUS MOTORS AND DRIVE
CONTROL ................................................193
7.1 Fundamental equations for synchronous machines ..........193
7.1.1 Speed..........................................193
7.1.2 Air gap magnetic flux density.....................193
7.1.3 Electromotive force (EMF) .......................194
7.1.4 Armature line current density and current density...195
7.1.5 Electromagnetic power...........................195
7.1.6 Synchronous reactance...........................196
7.2 Location of the armature current in the d-q coordinate
system ................................................196
7.3 Armature reaction......................................196
7.4 Phasor diagram ........................................201
7.5 Input and electromagnetic power .........................204
7.6 How to obtain zero d-axis current I =0 .................206
ad
7.7 Influence of d-axis current on the power factor .............206
7.8 Vector control of PM synchronous motors .................208
7.9 Starting...............................................211
7.9.1 Asynchronous starting ...........................211
7.9.2 Starting by means of an auxiliary motor ...........212
7.9.3 Frequency-change starting........................213
7.10 Comparison of PM synchronous motors with induction
motors ................................................214
Summary ...................................................214
8 AXIAL AND TRANSVERSE FLUX MOTORS ...........217
8.1 Axial flux disk motors ..................................218
8.1.1 Force and torque of axial flux motors ..............218
8.1.2 Double-sided motor with internal PM disk rotor ....220
8.1.3 Stator cores of axial flux motors ..................220
8.1.4 Main dimensions of axial flux motors ..............221
8.1.5 Double-sided axial-flux motors with a single stator ..223
8.1.6 Single-sided motors..............................227
8.1.7 Ironless double-sided motors......................229
8.1.8 Multidisk motors................................232
8.2 Transverse flux motors ..................................236
8.2.1 Principle of operation............................236
8.2.2 EMF and electromagnetic torque..................239
8.2.3 Armature winding resistance .....................241
8.2.4 Armature reaction and leakage reactance...........241
8.2.5 Magnetic circuit ................................243
8.2.6 Advantages and disadvantages ....................244
Summary ...................................................245
x Contents
9 HIGH-SPEED PM BRUSHLESS MACHINES ............247
9.1 Requirements ..........................................247
9.2 Main dimensions .......................................248
9.3 Mechanical requirements ................................250
9.4 Fundamental problems in design .........................252
9.5 Stator design ..........................................253
9.6 Rotor design...........................................256
9.7 Mechanical design ......................................259
9.8 Thermal issues and cooling technologies ...................260
9.9 Directed energy weapon (DEW)..........................263
Summary ...................................................265
AppendixA Conversion of units...............................267
A.1 Conversion of units .....................................267
A.1.1 Definitions .....................................267
A.1.2 Conversion .....................................268
A.1.3 Some physical constants .........................268
AppendixB Lenz’s law........................................269
AppendixC Right-handed cork-screw rule ....................271
AppendixD The right-hand grip rule .........................273
AppendixE Left-hand and right-hand rules ...................275
Symbols and Abbreviations....................................277
References.....................................................283
Index..........................................................289
