Table Of ContentDESIGN AND DEVELOPMENT OF A HIGH-SPEED
AXIAL-FLUX PERMANENT-MAGNET MACHINE
DESIGN AND DEVELOPMENT OF A HIGH-SPEED
AXIAL-FLUX PERMANENT-MAGNET MACHINE
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
Rector Magnificus, prof.dr. M. Rem, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen
op woensdag 16 mei 2001 om 16.00 uur
door
Funda Sahin
geboren te Van, Turkije
Dit proefschrift is goedgekeurd door de promotoren:
prof.dr.ir. A.J.A. Vandenput
en
prof.dr.ir. J.C. Compter
CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN
Sahin, Funda
Design and development of a high-speed axial-flux permanent
machine / by Funda Sahin. - Eindhoven :
Technische Universiteit Eindhoven, 2001.
Proefschrift. - ISBN 90-386-1380-1
NUGI 832
Trefw: elektrische machines ; permanente magneten / electrische
machines ; verliezen / hybride voertuigen / elektrische machines ;
warmte.
Subject headings: permanent magnet machines / losses / electric
vehicles / thermal analysis.
Contents
1 Introduction 1
1.1 Rationale and approach . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Hybrid electric vehicle application 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Energy storage devices . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 Flywheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Hybrid electric vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 The particular HEV application . . . . . . . . . . . . . . . . . . . . . 12
2.5 Required electrical machine . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Axial-flux permanent-magnet machines 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Applications and types of AFPM machines . . . . . . . . . . . . . . . 24
3.2.1 Existing applications . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Some common features of AFPM machines . . . . . . . . . . . 25
3.2.3 AFPM machine types . . . . . . . . . . . . . . . . . . . . . . 26
3.2.4 Design variations . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Derivation of the sizing equations . . . . . . . . . . . . . . . . . . . . 33
3.3.1 Dimensional design parameters . . . . . . . . . . . . . . . . . 33
3.3.2 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.3 EMF and power . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4 Basic magnetic design . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.1 Rotor with surface-mounted permanent magnets . . . . . . . . 40
3.4.2 Rotor with interior permanent magnets . . . . . . . . . . . . . 43
3.4.3 Stator yoke . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 ComparisonofAFPMmachineswithsinewaveandsquarewavecurrent
excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
iv CONTENTS
3.5.1 Sizing equations for squarewave-current driven AFPM machine 45
3.5.2 Torque comparison . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.3 Efficiency comparison . . . . . . . . . . . . . . . . . . . . . . . 48
3.5.4 Comparison in terms of drive system requirements . . . . . . . 48
3.5.5 Choice of excitation . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Comparison of axial and radial-flux permanent-magnet machines . . . 50
3.7 Towards an initial design . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Design variations 57
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Slotted stator design . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3 Winding factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4 Synchronous reactance . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4.1 Armature reaction reactance . . . . . . . . . . . . . . . . . . . 63
4.4.2 Slot leakage reactance . . . . . . . . . . . . . . . . . . . . . . 65
4.4.3 End-turn leakage reactance . . . . . . . . . . . . . . . . . . . 67
4.4.4 Differential leakage reactance . . . . . . . . . . . . . . . . . . 69
4.5 Magnet span . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.6 EMF waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.7 Number of stator slots . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.8 Maximum coil span-short pitching . . . . . . . . . . . . . . . . . . . . 72
4.9 Distribution of the coils . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.10 Winding configurations . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.11 Comparison of winding schemes in terms of machine efficiency . . . . 74
4.12 Percentage harmonic contents of the emf waveforms . . . . . . . . . . 74
4.13 Pulsating torque components due to space harmonics of windings and
PMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.14 Effect of magnet skewing . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.15 Effect of the stator offset . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.16 Results of space harmonics analysis . . . . . . . . . . . . . . . . . . . 86
4.17 Design procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.18 The machine data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.19 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5 Finite element analysis 93
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Relevant theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.4.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 97
5.4.2 Finite element mesh and accuracy . . . . . . . . . . . . . . . . 98
CONTENTS v
5.4.3 Modelling rotation . . . . . . . . . . . . . . . . . . . . . . . . 99
5.5 Flux density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.5.1 Airgap flux density . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5.2 Stator flux density . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5.3 Magnet flux density oscillations . . . . . . . . . . . . . . . . . 107
5.5.4 Rotor flux density oscillations . . . . . . . . . . . . . . . . . . 109
5.5.5 Magnet leakage flux . . . . . . . . . . . . . . . . . . . . . . . . 109
5.6 EMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.7 Torque ripple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.7.1 Pulsating torque . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.7.2 Cogging torque . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.7.3 Torque-angle characteristics . . . . . . . . . . . . . . . . . . . 113
5.8 Inductances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.8.1 Armature reaction inductance . . . . . . . . . . . . . . . . . . 114
5.8.2 Slot leakage inductance . . . . . . . . . . . . . . . . . . . . . . 115
5.9 Eddy current loss analysis . . . . . . . . . . . . . . . . . . . . . . . . 117
5.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Losses 121
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 Copper losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3 Core losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.4 Rotor losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.5 Mechanical losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.5.1 Windage losses . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.5.2 Bearing Losses . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.6 Efficiency map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.7 Effect of the design parameters on efficiency . . . . . . . . . . . . . . 135
6.7.1 Stator outside diameter. . . . . . . . . . . . . . . . . . . . . . 135
6.7.2 Inside-to-outside diameter ratio . . . . . . . . . . . . . . . . . 139
6.7.3 Airgap flux density . . . . . . . . . . . . . . . . . . . . . . . . 139
6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7 Thermal analysis 143
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 Magnet temperature and demagnetization constraint . . . . . . . . . 145
7.3 Heating of an electrical machine . . . . . . . . . . . . . . . . . . . . . 146
7.4 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.4.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.5 The diffusion equation . . . . . . . . . . . . . . . . . . . . . . . . . . 149
vi CONTENTS
7.6 The thermal equivalent circuit . . . . . . . . . . . . . . . . . . . . . . 149
7.7 Method of calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7.8 Thermal parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.9 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8 Manufacturing and mechanical aspects 165
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.2 Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.2.1 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.2.2 Dynamical analysis of the rotor . . . . . . . . . . . . . . . . . 168
8.2.3 Mechanical analysis of the housing . . . . . . . . . . . . . . . 169
8.2.4 Stress analysis of the rotor . . . . . . . . . . . . . . . . . . . . 169
8.2.5 Technical drawings . . . . . . . . . . . . . . . . . . . . . . . . 172
8.3 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
8.4 Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
8.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
9 Measurements 181
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
9.2 Test bench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
9.3 Performance measurements . . . . . . . . . . . . . . . . . . . . . . . . 185
9.3.1 Resistance and inductance measurements . . . . . . . . . . . . 185
9.3.2 Back-emf measurement . . . . . . . . . . . . . . . . . . . . . . 186
9.3.3 No-load losses . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
9.3.4 Measurement of efficiency and current . . . . . . . . . . . . . 188
9.3.5 Temperature measurements . . . . . . . . . . . . . . . . . . . 189
9.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
10 Conclusions and recommendations 195
10.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
10.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
APPENDICES 199
A List of symbols and abbreviations 201
A.1 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
A.2 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
B Percentage higher order harmonic contents of various structures 207
C Standard deviations of torque for various structures 209
CONTENTS vii
D Simulation of the PWM inverter 213
Bibliography 215
Summary 225
Samenvatting 227
Curriculum vitae 229
Foreword
Manypeoplehavecontributedtothecompletionofthisdissertation, bothdirectly, by
providing me with useful comments, thoughts and suggestions, as well as indirectly,
by creating a stimulating and pleasant working environment. I would therefore like
to express my gratitude to all my friends and my (ex-)colleagues that I have been
working with over the last four years. I am not giving a full list of names here, but I
am sure that all the people to whom these acknowledgments are addressed are aware
of their inclusion.
A number of people deserve special attention here, though. First of all I would
like to thank Andre Vandenput for his fascinating supervision over the whole Ph.D.
period in all aspects, which can be listed with pages from the technical problems
to funding. I would also like to express my appreciation to his management skills
and character, which led to a friendly and almost stress-free working environment
independent of the work load.
I would also like to thank John Compter, for his supervision and especially for
his guidance by his industry experience. For any mind boggling issue, he always had
a real life example ready in mind.
During the four years of this project, Jaques van Rooij has been contributing to
this project first by supplying the application and then sparing the time to solve
mechanical problems, finding suppliers for materials, and giving ideas voluntarily.
It was a treat to have him as an advisor with his always kind and refined attitude
during the whole period of the project.
Almost two years I shared an office with Andrew Tuckey, who was a post-doc
researcher at that time, working on the development of the test bench in which the
measurementsofthemachinedesignedforthisprojectarecarriedout. Iwouldliketo
thankhimnotonlyforhisadvicesanddirecthelpinmanufacturingandtestingofthe
machine, but also for his existence that created extra stimuli and a nice friendship.
We had hours of conversations even for tiny technical aspects, and his ambition was
reallycontagious. Iwillneverforgethisoptimismandhiseverydaysentencesstarting
with a : “Hey Funda, we can also do ...”.
I would also like to express my gratitude to Jorge Duarte, for his helps in many
aspectssuchaspowerelectronicsandprogrammingDSPs,whicharenotmystrongest
points, for letting me use and manipulate his old Assembler codes, his latest advices
