A Thesis Submitted for the Degree of PhD at the University of Warwick
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DESIGN AND DEVELOPMENT OF
AXIAL-FIELD AIR-CORED BRUSHLESS DC MOTORS
by
C H Tam
B Sc (Hons)
A thesis submitted for the
degree of Doctor of Philosophy
to
The Department of Engineering
University of Warwick
T A B L E OF C O N T EErrS
Table of Co n t e n t s ... i
List of Figures ... v *
List of T a b l e s ... xiv
Acknowledgements ... xv
Summary ... x v * List of Principle S y m b o l s ... xvii
CHAPTER 1 INTRODUCTION ... ... 1
1.0 Axial-Field Br u s h l e s s DC Motor - An o v e r v i e w ... l 1.1 Motor Cons t r u c t i o n ... 4
1.1.1 T he rotor ... 4
1.1.2 The a r m a t u r e ... 6
1.2 Motor Design Parame t e r s ... 6
1.2.1 Active co n d u c t o r dimen s i o n s ... 6
1.2.2 Air-gap flux density ... io 1.2.3 Number of p oles ... 12
1.2.4 P o l e - a r c / pole-pitch ratio ... 12
CHAPTER 2 P R I N CIPLE OF ROTATING M A G N E T A X I A L - F I E L D M A C H I N E S ... 14
2.0 Introduction ... 14
2.1 T y p e s of P e r m anent Magnet A x i al-field M a c h i n e s ... 16
2.1.1 Stat i o n a r y - f i e l d axial ma c h i n e s ... 16
2.1.2 Rotati n g - f i e l d axial m a chines ... 17
2.2 The Magnetic Circ u i t ... 20
2.2.1 The p r o p e r t i e s of magnetic r a t e r i a l s ... 22
2 .2.2 Magnet circ u i t principle ... 26
2.2.3 Air-gap flux distribution ... 29
2.2.3. 1 EMF wav e f o r m and power i n v e r t e r ... 29
2.2.3.2 Pole-arc/p o l e - p i t c h ratio ... 30
2.2.3.3 Numb e r of poles ... 33
2.2.3.4 F ield system arrangement ... 33
2.2.3.5 C h o o s i n g the value of a ... 34
2.3 Th e Electric Circuit ... 34
2.3.1 Design a nd assum p t i o n s ... 38
2.3.2 Approxi m a t i o n of the flux d e n s i t y function ... 38
2.3.3 The EMF e q uation ... 44
i i
-CHAPTER 3 BR U S H L E S S DC M O T O R S ... *8
3.0 I n t r o d u c t i o n ... *8
3.1 In d u c t i o n Mach i n e Fed by v a riab frequency Inverter ... *9
3.2 I nvert.or- fed S y n c h r o n o u s Mach i n e w i t h Rotor P o s i t i o n s Fe e d b a c k ... 51
3.3 F / i tion of Br u s h l e s s DC Motor from C ommutator DC M o t o r ... 52
3.4 B r u s h l e s s DC Motor C o n f i g u r a t i o n s ... 54
3.4.1 T h e o n e - phase u n i - polar b r u s h l e s s dc m o t o r ... 57
3 .4.2 T h e o n e - phase bi - p o l a r b r u s h l e s s dc m otor ... 57
3 .4.3 T h e two-phase u n i - polar b r u s h l e s s dc m o t o r ... 57
3.4.4 T h e twO-phase bi - p o l a r b r u s h l e s s dc m otor ... 61
3.4.5 T h e three-phase u n i - p o l a r br u s h l e s s dc m o t o r ... 61
3.4.6 T h e four-phase u n i - polar b r u s h l e s s dc m o t o r ... 61
3.4.7 T h e three-phase bi-polar b r u s h l e s s dc m otor ... 61
3 . 4 . 8 Number of w i n d i n g s and e x c i t a t i o n current p u lses ... 62
3.5 B r u s h l e s s DC M otor C o n s t r u e t i o n s a nd O p e r a t i o n s ... 62
3.5.1 High power th y r i s t o r - s w i t c h e d brushless dc m o t o r s ... 62
3 . 5 . 2 M e dium power t r a n s i s t o r - s w i t c h e d brushless dc m o t o r s ... 68
3 . 5 . 3 Small b r u shless
dc
m o t o r s ... 693.6 R o t o r Position D e t e c t o r s ... 70
3.6.1 Reluc t a n c e s w i t c h e s ... 72
3 . 6 . 2 Optical sen s o r s ... 72
3 . 6 . 3 H a l l-effect ICs ... 74
C H A P T E R 4 MOTOR P E R F O R M A N C E A S S E S S M E N T ... 75
4.0 I n t r o d u c t i o n ... 75
4.1 T h e M otor S c h e m e ... 75
4 .2 M o t o r Parameter M o d e l l i n g ... 78
4.2.1 Power devi c e m o d e l l i n g ... 78
4 . 2 . 2 Machine equiv a l e n t circuit ... 79
4.3 C u r r e n t E quation ... 83
4.4 O u t p u t E q u ations ... 91
4.5 Digi t a l compu t a t i o n of the P e r f o r m a n c e C h a r a c t e r i s t i c s ... 93
C H A P T E R 5 U N D E R C O M M U .ATION A ND C O M M U T A T I O N AD V A N C I N G ... 98
5.0 O v e r v i e w ... 98
5.1 E f f e c t s of U n d e r c o m m u t a t i o n ... 98
5.2 C o m m u t a t i o n A d v a n c i n g ...100
5.3 O p t i m u m C o m m u t a t i o n A d v a n c i n g ... 101
C H A P T E R 6 B R U S H L E S S DC DISC- M O T O R PROTO T Y P E S ... 107
6.1 Design S p e c i f i c a t i o n s of P r o t o t y p e s ... 108
6.1.1 Motor 1 ... 108
6 . 1 . 2 Motor 2 ... 109
6 .1.3 Motor 3 ... i°9 6 .2 Magnetic C i r c u i t Design ... H O 6.2.1 P r o p e r t i e s of magn e t m a t e r i a l s ... 110
6 . 2 . 2 S e l e c t i n g a permanent magnet material for Motors 2 and 3 ... 112
6.2.3 The m a g n e t i c c i r c u i t s ... 113
6.3 Electric C i r c u i t D e sign ... 116
6.4 Mechanical Desi g n ... 122
6.5 Motor P a r a m e t e r s ... 128
6.6 Rotor Pos i t i o n D etector ... 132
6.7 o p e r ation of the P r o totype Motors ... 134
6.7.1 Motor 1 ... 134
6 .7.2 Motor 2 ... 136
6.7.2.1 U n i - p o l a r mode ... 136
6.7.2.2 B i-polar mode ...138
6 .7.3 Motor 3 ... I*6 C H A P T E R 7 T HE E L E C T R O N I C P OWER REGULATOR ... 158
7.0 Introduction ... 158
7.1 P u l se-width M o d u l a t i o n ... 158
7.1.1 S i n e - w a v e m o d u l a t i o n ...159
7.1.2 H a rmonic e l i m a t i o n ... 161
7 .2 Electronic Power R e g u lator C o n f i g uration ...162
7.2.1 Est a b l i s h i n g a m o d u l a t i o n strategy ... 162
7.2.2 p w m p u l s e - t r a i n g eneration ... 166
7.3 T h e Power C i r c u i t ... 169
7.3.1 Power t ransistor s w i t ching c h a r a c t e r i s t i c s ...169
7.3.2 S e l e c t i n g the p w m power devices ... 170
7.3.3 The p ower M O S F E T ... 173
7.3.3.1 C o n s t r u c t i o n an d properties ... 173
7.3.3.2 Driving the power MOSFET ... 174
7.3.4 The power circuit ... 175
7.3.5 Power circuit s w i t c h i n g efficiency ... 177
7.4 Current Tra n s f e r C h a r a c t e r i s t i c s of T he EPR ... 183
7.4.1 A s s u m p t i o n s ... 183
7.4.2 Mo t o r i n g mo d e ...184
7.4.2.1 T h e o n - p e r i o d e q u a tions ... 184
7.4.2.2 T he o f f - p e r i o d (free wheeling) e q u a t i o n s ... 187
7.4.2.3 C o n t i n u o u s and di s c o n t i n u o u s c o n d u c t i o n s ... 187
7.4.2.4 A v e r a g e a r m a t u r e current ... 190
1 9 1
7.4.2.5 Average d c - l i n e current
7.4.2.6 C o mputed r e sultes ... 192
7.4.3 R e g e n e r a t i v e bra k i n g mode ... 192
7.4.3.1 T he o n - p e r i o d e q u a tions ... 192
7 . 4 . 3 . 2 T he r e g e n -period e q u a t i o n s ...197
7.4.3.3 Average bra k i n g current ... 200
7.4.3.4 Average reg e n e r a t i v e current ... 201
7.4.3.5 C o mputed res u l t s ... 201
CHAPTER 8 M O T O R DRIVE C O N T R O L SUB-S Y S T E M ... 203
8.0 Introduction ... 203
8.1 Functional R e q u i r e m e n t s and Design Solution ... 204
8.1.1 C o m m u t a t i o n control ... 204
8 .1.2 PWM torque-control ... 205
8.2 Hardware S u b - s y s t e m D e s i g n and Implementation ... 207
8.2.1 O v e r v i e w ... 207
8 .2.2 T he M C U Module ... 208
8.2.3 P o s i t i o n Detection Modu l e ... 212
8.2.4 S p e e d Detector M o d u l e ... 216
8 .2.5 PWM G e n e r a t i o n M o d u l e ... 218
8 .2.6 O v e r - c u r r e n t Prote c t i o n Logic ... 221
8.3 S o ftware S u b - s y s t e m Desi g n and Implementation ... 221
8.3.1 O v e r v i e w ... 221
8 .3.2 S o f t w a r e design ... 222
8.3.3 Power Down ... 224
8 .3.4 P o s i t i o n Decoding ... 224
8 .3.5 PWM Control ... 226
8 .3.6 P o w e r - u p Initialisation and Demand Input ...229
8 .3.7 Data Base ...229
8.4 System Perf o r m a n c e ... 231
8.5 Discu s s i o n of Drive C h a r a c t e r i s t i c s ... 234
8.5.1 M o t o r i n g mode ... 234
8 . 5 . 2 Reg e n e r a t i o n mode ... 239
CHAPTER 9 C O N C L U S I O N S A N D S U G G E S T I O N S FOR FUR T H E R W O R K ... 240
9.0 Introduction ... 240
9.1 The B r u s h l e s s DC D i s c - m o t o r s ...240
9.2 The Elect r o n i c Power R e g u lator ... 241
9.3 The Motor C o n t r o l l e r S u b - s y s t e m ... 242
9.4 S u g g e s t i o n s for further w o r k ... 244
Appendix B D i s c r e t e Fourier Transform ...2 * 7
Appendix C D e s i g n Data a nd Performance of the W heelchair Motor ... 2 4 9
Appendix D M e a s u r e m e n t of Armature S e l f -1nductance ... 251
Appendix E MPU M e m o r y Ma p and Port Assi g n m e n t s ...2 5 2
LIST OF
Figure
F i gure Figure F i gure Figure F i gure F i gure F i gure Figure F i gure Fi gure Fi gure Fi gure F i gure Figure
F i gure F i gure F i gure F i gure
Figure Figure F i gure F i gure
F i gure F i gure Figure
VÍ
FIGURES
1.1 Functional block diagram of d r i v e system
1.2 An e x ploded vi e w of the mac h i n e
1.3 Double-sided field system
1.4 S i n g l e-sided field system
1.5 A preformed w i r e - w o u n d coil
1.6 Dimens i o n s of a c tive conduc t o r s
1.7 An extr e m e case of very small inner diameter
1.8 Po l e - a r c / p o l e - p i t c h ratio
2.1 Axial-field principle
2.2 a practicle axia l - f i e l d desi g n
2.3 DC d isc-motor
2.4 P e rformance of the lawn-mower motor
2.5 S t a t i o n a r y - f i e l d ac disc-motor
2.6 R o t a ting-field ac d isc-motor
2.7 B r u s hless dc d isc-motor
2.8 Air- g a p clearance
2.9 B-H h v s t e r e s i s - l o o p
2.10 Normal and intrinsic m a g n e t i s a t i o n curves
2.11 Demag n e t i s a t i o n curve wi t h cont o u r of constant BH-product. and BH-product curve
2. 12 R e c o i 1 1 i nes
2.13 C r o s s - s e c t i o n of the flux path
2.14 C e n t r e s of pole-faces
2.15 C o m p a r s i o n of power output between sinewave
and square w a v e inverters
2.16 Position of point Q related to magnet face
2.17 D o u b le-sided field-system flux distribution
F i gure 2.24 An example of d i s c - m o t o r w i n d i n g arrangement . 37
F i gure 2 _ 25 Position of the a c tive conductor in the
air- g a p of a d o u b l e - l a y e r armature . 39
Figure 2.26 Conduc t o r s are treated as w i t h zero thickness . 39
F i gure 2.27 Position of the ar e a dA related to the
field-system and an armature coil 40
Figure 2 . 2S Measured radial flux d i s t r ibution along three radial lines 40
F i gure 2.29 Rectangular image co-ordinates of the
polar c o - o r d i n a t e s of Figure 2.27 43
Figure 2.30 Distribution of the c onductors around r^ 43
Figure 3.1 Functional d i a g r a m of an induction-type br u s h l e s s dc motor 50
F i gure 3 .2 Tor q u e - s p e e d c h a r a c t e r i s t i c of a typical inverter-fed
squirrel cage induction motor 50
F i gure 3.3 Mechanical and electrical arrangement of a dc m o t o r
(coils 1-5. 5-1 a b o u t to enter commutation z o n e > 53
F i gure 3.4 Coils 1-5. 5-1 in c o m mutation zone 53
F i gure 3.5 C oils 2-6, 6-2 a b o u t to enter commutation zone 53
Fi gure 3.6 S y n t h e s i s of a 3 - p h a s e brushless dc motor from
a conventional dc motor 55
Figure 3.7 The 3-phase b r u s h l e s s dc motor with rotor p o s i t i o n detector 56
Figure 3.8 O n e - phase u n i - p o l a r motor 58
Figure 3.9 O n e - phase bi-polar motor 58
Figure 3 . lO T w o - phase un i - p o l a r motor 58
Figure 3.11 T w o -phase b i-polar motor 59
F i gure 3.12 T h ree-phase u n i -polar motor 59
Figure 3. 13 Four-phase u n i -polar motor 59
F i gure 3 . 14 T h r ee-phase bi- p o l a r motor 60
F i gure 3. 15 Voltage-fed th y r i s t o r - s w i t c h e d brushless dc m o t o r 64
a chopper regulator 65
i i
Figure 3.17 Figure 3.18 Figure 3.19 Figure 3.20 Figure 3.21
Figure 3.22 Figure 3.23 Figure 3.24 Figure 3.25 Figure 3.26 Figure 3.27 Figure 4. l F i gure 4.2 Figure 4.3 Figure 4.4
Figure 4.5 Figure 4.6 Figure 4.7
Figure 4.8 Figure 4.9 Figure 4.10
F i gure 4.11 Fi gure 4. 12 F i gure 4.13 F i gure 4.14 Figure 4.15 Figure 4.16 Fi gure 4. 17
Pulse-width m o d u l a t i o n
Principle c i r c u i t of c u r r e n t - f e d b r u s hless machine
Inverter w a v e f o r m s of c u r r e n t - f e d b r u s hless machine A b r u shless d c motor commu t a t e d by t r a nsistors and steered by Hall-effect sensors
a skew-pole lamination
Effect of a u x i l i a r y torque Reluctance s w i t c h
Tran s m i s s i v e optical d etector Reflective optical det e c t o r
An a r r a n g e m e n t of trigger m a g n e t s and H a l l-effect ICs Scheme of the brushless dc d isc-motor
Phasor d i a g r a m of the nth h a r m onics Connections of Darlington t r a nsistors
Circuit to m e a s u r e the forward c h a r a c t e r i s t i c s of a Darii n g t o n
Forward c h a r a c t e r i s t i c s of MJ1 1 0 1 5 and MJ11016 Equivalent c i r c u i t curcuit of a s w i t ching Darlington Relationship in time between the motor v o l t a g e s and the s w i t c h i n g sequence
C o n d u c t i o n - s t a t e diagram of the s t a r - c o n n e c t e d bi-polar motor Transistor r e p l a c e d by their circuit e q u i v a l e n t s
Voltage s o u r c e s of the t r a n s i s t o r s removed from the m a i n loop
Equivalent c i r c u i t of the star-c o n n e c t e d bi-polar motor The b r u s h l e s s motor being represented by cou p l e d circuits Simple e q u i v a l e n t circuit of the motor
Simulated c u r r e n t w a v e f o r m s of the brushless motor D i s c r e t e -time ap p r o x i m a t i o n of a c o n t i n u o u s -time function Flow-chart of the output p e r f o r m a n c e c a l c u l a t i o n process Calculated o u t p u t c h a r a c t e r i s t i c s of the
600W b r u s h l e s s dc d i s c - m o t o r
. 65
.
66.
6 6. 71 . 71 . 71 . 73 . 73 . 73 . 73 . 76 . 76 . 80
. 80 . 80 . 80
. 81 . 82 . 84
. 84 . 84 . 85 . 85 . 90 . 90 . 94
Fi gure 5. 1
Fi gure 5.2
F i gu r e 5.3
F i gure 5.4
F i gu r e 5.5
F i gure 5.6
F i gure 5.7
F i gure 6. 1
F i gure 6.2
F i gure 6.3
Figu r e 6.4
F i gure 6.5
F i gure 6.6
F i gure 6.7
F i gure 6.8
F i gure 6.9
Fi gure 6. 10
F i gure 6.11
F i gure 6. 1 2
F i gure 6.13
F i gure 6.14
F i gure 6.15
F i gure 6. 16
F i gure 6.17
F i gure 6 . 18 F i gure 6 . 19
F i gure 6.20
F i gure 6.21
Linear c o m m u t a t i o n -- a linear change of current with time in the commutated coil
C o m m u t a t i o n sequence, and the r e l a t ionship in time between the v o l t a g e and current of a coil of the b i-polar motor Effect of shifting the rotor position sensor by an angle Effect on the coil current a s a result of o v e r c o mmutation
Trapezoidal ap p r o x i m a t i o n of the coil emf e<t> R e l a t i o n s h i p in time between v. e and i w i t h i n g the rising e d g e of v as the zero reference
C a l c u l a t e d values of optimum angle of a d v a n c i n g for the 600W 3-phase bi-polar motor
Demagnetisation curves
D e m a g n etisation c h a r a c t e r i s t i c s of Feroba III and S u p e r m a g l o y B2
Proper t i e s of Su p e r m a g 1oies A pr e f o r m e d w i r e - w o u n d coil
Arrangement of the armature coils
wind i n g diag r a m of the 3-phase d i s c - w i n d i n g s C a l c u l a t e d voltage w a v e f o r m s of M o t o r s 1. 2 and 3 General a ssembly of Motors 1 and 2
Rotor a s s e m b l i e s of Motors 1. 2 and 3 *
Armatures
of Motors 1. 2and
3C a s i n g s of M o tors 1. 2 and 3
Phase emf w a v e f o r m s of M o t o r s 1. 2 and 3 Open circuit c h a r a c t e r i s t i c s
Measurements of winding resistances
Mea s u r e d phase inductance at d i f ferent rotor orientations Dynamic loss chara c t e r i s t i c s
P r i n ciple of the rotor position d etector
Physical a r r a n g e m e n t s of the rotor p o sition detector Segment of the rotor position coded disc
Eff e c t s of a l20<>elec voltage pulse on the a r m a t u r e current of Motor 1
Drive co n f i g u r a t i o n of Motor 2 in u n i - polar mode
.... 99 ....102
....102
....103
....103
. . . .
106 . . . . 1 1 1. . . . 1 1 5
. . . . 1 1 5
. . . . 1 1 7
. . . . 1 1 7
. . . . 1 1 9
. . . .
120. . . .
123. . . .
126. . . .
126. . . .
127. . . .
129. . . .
130. . . .
130. . . .
131__ _
131. . . .
133. . . .
133. . . .
135. . . .
135X
Figure 6.22
Figure 6.23 Figure 6.24
Figure 6.25 Figure 6.26 Figure 6.27
Figure 6.28 Figure 6.29 Figure 6.30 F i gure 6.31
Figure 6.32 Figure 6.33
Figure 6.34
Figure 6.35
Figure 6.36 Figure 6.37
Figure 6.38
Figure 6.39
F i gure 7. 1 F i gure 7.2
R e l a t i o n s h i p in time between the induced emfs. the phase currents, the applied v oltages and the base drive s i g n a l s of Motor 2 in uni-polar mode
Output c h a r a c t e r i s t i c s of Motor 2 in uni-polar mode
Current and terminal voltage w a v e f o r m s of Motor 2 in uni-polar mode
Output torque ripple of Motor 2 in uni-polar mode Drive co n f i g u r a t i o n of Motor 2 in bi-polar mode R e l a t i o n s h i p in time between the induced emfs. the a p p l i e d voltages and the base drive signals of Motor 2 in bi-polar mode
Output c h a r a c t e r i s t i c s of Motor 2 in bi-polar mode Phase current w a veform of Motor 2 in bi-polar mode A r r a n g e m e n t s of separate power circuit for each winding A r r a n g e m e n t s of Motor 2 in bi-polar mode wi t h triacs inserted in series to interrupt the delta loop
S c h e m a t i c of the triac t riggering circuit
R e l a t i o n s h i p in time between the phase emfs. the base d r i v e signals, and the triac triggering signals Current a nd terminal voltage w a v e f o r m s of Motor 2
in bi-polar mode with triacs inserted
Output c h a r acteristic of Motor 2 in bi-polar mode wi t h triacs inserted
A r r angement of Motor 3 in s t a r -connected bi-polar mode R e l a t i o n s h i p in time between the phase emfs. the phase currents, the line emfs. and the base drive signals of Motor 3 in star-connected b i -polar mode
Current a nd terminal phase vol t a g e waveform of Motor 3 in star-connected b i -polar mode
Output c h a r a c t e r i s t i c s of Motor 3 in star-connected bi-polar mode
a p u l se-width modulated wav e f o r m
A s y c h r o n o u s and s y n chronous s i n e-wave m odulation
Figure 7.3 Harmonic e l i mination PWM (m * 3>
F i gure 7.4 Equivalent conduction loop of the conduction - states
....137 -- - 139
.... 141
. . . . 142 . . . . 142
. . . . 143 . ... 144
....145 ....147
. . . . 147 . ... 148
....148
....149
....150 __ _ 153
. . . .
154. . . . 1 5 5
. . . .
156. . .
160. . . .
1 6 0. . . . 1 6 3 ....163
Figure 7.8
F i gure 7.9
F i gure 7.10
F i gure 7.11
F i gure 7.12
F i gure 7.13
F i gure 7.14
F i gure 7 . 15
Fi gure 7.16
F i gure 7.17
F i gure 7.18
F i gure 7.19
F i gure 7.20
Figure 7.21
Figure 7.22
Fi gure 7.23
F i gure 7.24
F i gure 7.25
F i gure 7.26
Figure 7.27
F i gure 7.28
F i gure 7.29
Fi gure 7.30
Figure 7.31
Rela t i o n s h i p in time b e t w e e n the induced emfs, the driving signals and t he PWMed arm a t u r e current
Functional block d i a g r a m of the PWM generator The timing of the PWM carr i e r signal
S w i tching times of t r a n s i s t o r s
R elative performance of switching power d e v i c e s D o uble-diffused s t r u c t u r e of a MOSF E T cell
Power M O SFET driven b y a CM O S gate
Power MOSFET driven b y an e m i tter-follower buffer Power M O SFET driven by a 74 TTL gate
Power MOSFET driven b y a h igh-speed c a p a c i t i v e driver The basic power c i r c u i t of the EPR
The col l e c t o r - e m i t t e r satur a t i o n c h a r a c t e r i s t i c s of the Darlington
Forward c h a r a c t e r i s t i c of the Sch o t t k y d i o d e Schematic circuit d i a g r a m of the power regulator
Static equivalent c i r c u i t of the power circ u i t o u t p u t - s t a t e s .. Block diagram of the test circuit for as s e s s i n g
the EPR * s switching e f f i c i e n c y
E fficiency c h a r a c t e r i s t i c of the d r i v e s y stem
under PWM control ••
S w i t ching e fficiency of the power circuit PWM terminal voltage a n d current w a v e f o r m s M otoring mode current flow paths
M otoring mode e q u i v a l e n t circuits
M otoring mode s t e a d y - s t a t e arm a t u r e cu r r e n t s
M otoring mode s t e a d y - s t a t e a r mature current transfer c haracteristics (ca r r i e r frequency - 20KHz>
M otoring mode s t e a d y - s t a t e a r mature current transfer c h a r a c teristics « c a r r i e r frequency » lOKHz>
. 167 . 167 . 168 . 168 . 171 . 171
. 176 . 176 . 176 . 176 . 176
. . 178 . . 178 . . 179 . . 180
. . 181
. . 181 . . 182 . . 182 . . 185 . . 186 . . 188
. 1 9 3
X i i
-Figure 7.32 M o t o r i n g mode steady-state dc-link ar m a t u r e current transfer
c h a r a c teristics (carrier frequency - 20KHz> ....194
Figure 7.33 R e l a t ionship in time between the induced emfs.
the driving signals, and the PWMed a r mature
current for regenerating mo d e .... 194
Figure 7.34 Regen. mode current flow paths .... 195
Figure 7.35 Regen. mode equivalent c ircuits . . . 1 9 6
Figure 7.36 Regen. mode steady-state armature cu r r e n t s ....198
Figure 7.37 Regen. mode steady-state armature current
transfer characteristics ....202
Figure 7.38 Regen. mode steady-state regen. current
transfer characteristics ....202
Figure 8.1 Block diagram of the commutation control logic ....206
Figure 8.2 Two-dimensional a rray of PWM on-times ....206
Figure 8.3 Block diagram of the PWM torque-control logic ....206
Figure 8.4 Equivalent system diagram of the c ontroller ...209
Figu r e 8.5 O u t l i n e of hte controller's hardware sub-system ....209
Figu r e 8.6 Pict u r e of the hardware sub-system ....210
Figu r e 8.7 Functional block diagram of the MPU Modu l e ....210
Figu r e 8.8 Sc h e m a t i c of the MCU logic ....211
Figure 8.9 Functional block diagram of the Position Detector M o dule ....213
Figure 8.10 Sc h m a t i c of the Position Detector logic ....214
Figure 8.11 T i m i n g relationship of the signal processing logic ....215
Figure 8.12 S c h e m a t i c and signal timings of the Speed Detector logic ....217
Figure 8.13 S c hmatic diagram of the PWM Generation Logic ....219
Figure 8.14 Signal timings of the PWM Generation Logic ....220
Figure 8.15 S c h e matic diagram of the Over-current Protection Logic ....220
Figure 8.16 T r a n s f e r c haracteristics of the Over-current
P rotection Logic ....220
Figure 8.17 Functional diag r a m of the software sub-system ....223
Figure 8.18 Flow-chart of the Power Down Module ....225
F i gure 8.19 Flow-chart of the Position Dector M o d u l e . . . 2 2 5
Figure 8.20 Flow-chart of the PWM Control Module ....227
Figure 8. 26
Figure 8. 27
Figure 8. 28
Figure 8. 29
F i gure 8. 30
Figure 9. 1
Figure A 1 (
Figure B 1
Figure D 1 1
F i gure D2 <
against rotor speed
Impulse approxi m a t i o n of function
Cir c u i t to mea s u r e ar m a t u r e sei f-inductance
D 2 Coil cur r e n t o s c illogram
. . 233
. . 235
. . 237
. . 238
. . 238
. . 2*3
. . 2*6
. .
2 * 8. . 251
a c k n o w l e d g e m e n t s
I w o u l d like to a c k n o w l e d g e the h e l p of those w ho have e ncouraged and a s sisted
me d u r i n g the p e r i o d of my research. First of all. I would like to extend my
s i n c e r e gratitude to my supervisor. Mr. A .E . Corbett, for his helpful advice,
s u g g e s t i o n s and comments.
I a l s o wish to t hank all the memb e r s of staff in the Engineering Department,
w i t h o u t whose h e l p much of the work described here would not have been possible. In particular. I w o u l d like to expr e s s my g r a titude to Peter Hunt for letting me use t h e Machines Lab. and for charging the batteries. To Dave Thom s o n and Graham
R o b i n s o n for bui l d i n g the prototype m o tors a nd grinding the magnets. To Dave
R o b e r t s and Phil C o p e for getting me those impossible-to-get components. To
B r u c e Cosh and Selami S o y l e m e z for doing the mechanical design a nd d r a w i n g s of
the motors. To Jo h n Corbett for m a k i n g the armatures. And to Alan Hume for his
p a t i e n c e and instruction in the use of the Prime computer.
S p e c i a l l y . I w o u l d like to thank my wife. Mary, for her patience, u n derstanding
and support, and for her lessons in * how to w r i t e in English*; my parents for
their moral and financial support; a nd Sunny for lending me his w o r d p r o c e s s o r .
F i n a l l y I record my gratitude to C a b l e f o r m Ltd. for their finanical support of
X V i
SUMMARY
T h i s thesis is concerned wi t h the principle and operation of axial-field
b r u s hless dc motors. It also de s c r i b e s the development of a brushless dc drive
syst e m which c o n s i s t s of three system elements: a disc-motor, an electronic
power regulator, and a micro p r o c e s s o r - b a s e d controller.
The principle of a x i al-field mac h i n e s is discussed, an d a t t e ntion is given to
the effect of the air - g a p flux d i s t r ibution on the emf waveform. By controlling
the flux distribution, the induced emf is optimised for inverter-fed operation.
T he aim of the o p t i m isation is to increase the m o t o r ' s power density, and to
s i mplify the interfacing between the control e l e c t r o n i c s and the motor. The
d e s i g n s and o p e r a t i o n s of three prototype m o t o r s a r e described, and certain
pr o b l e m s r e lating to b r u s hless dc motors, and to d i s c - m o t o r s in particular. are
discussed. T h e s e problems include undercommutation, a n d the effect of the drive
6 co n f i g u r a t i o n o n the a r mature current.
T he design of the electronic power regulator and the s e l ection of a suitable
puls e - w i d t h m o d u l a t i o n < r*WM) strategy for current control are presented. The
features of the 3-phase 4-quadrant regulator, w hich c a p i t a l i s e d on the special
c h a r a c t e r i s t i c s of the disc-motor, include the use of power MOSFETs as the PWM
devices, and the use of an inverter bridge of w h i c h o n l y the bottom-half is
PWMed. A model of the s w i t ching regulator is also presented.
Th e m i c r o p r o c e s s o r - b a s e d controller sub-sy s t e m c o n t r o l s the commutation sequence
an d the s w i t c h i n g p u l se-width of the power r e g u l a t o r to provide a constant
torque output from the drive system. Both the c o m m u t a t i o n and the pulse-width
c o n t r o l s are implemented by using the look-up table technique. The commutation
LIST OF P R I N C I P L E SYM B O L S
ac alternating current
*c specific electric loading
a pole-arc to pole-pitch ratio
Apn area of pole face
A PP area of pole area
B specific magnetic loading
Ba
air-gap flux densityB
m flux density of magnet
Bms maximum flux density allowable in
Be circumferential flux d i s t r i b u t i o n
c r reduction factor
d f d 2 inner, and outer active d i a m e t e r s
dc direct current
V
e b- e c- e induced phase voltagesemf electro motive force
f frequency
g number of turns per coil
H
g magnetising force of the a i r - g a p
H
m magnetising force of magnet
*•* ‘b- ‘c- 1 armature currents
Ken chord factor for the nth h a r m o n i c
Ksn skew factor for the nth h armonic
K
w wind i n g factor
‘» length of air-gap
l„ total thickness of magnet
La a " L b b ’ Lcc' L wind i n g s e 1f - inductances
Lab * L b a ... n mutal inductances
mi Id steel in the a i r - g a p
of d isc-motor
m a g n e t o m o t i v e force
number of poles total flux per pole
inner, and outer a c tive radii of d i s c - m o t o r
w i n d i n g resis t a n c e s number of slots space factor
t h i ckness of flux return ring
C H A P T E R l INTRODUCTION
1.0 A x i al-Field B r u s hless DC Motor - An Overview
Axia l - f i e l d machines, w h i c h have disc-shaped armatures a nd short axial lengths,
have long been an active research subject at the Unive r s i t y of War w i c k . The
deve l o p m e n t of such mac h i n e s at Warwick began in 1967 with an industrial
contract for research into * in w h e e l ’ traction-drive a p p l i c a t i o n s ill.
D e v e l opments since then have produced a number of m o t o r s for both d o m e s t i c and
industrial a p p l i cations (2.3.4). T h e s e were mostly of the dc commu t a t o r type.
A m ajor break from the e s tablished mode of dc
made w h e n the unive r s i t y received a new
br u s h l e s s dc d r i v e system in 1979. This
c ommutator 1 ess a x i al-field motor, a
m i c r o p r o c e s s o r - b a s e d power regulator. Figure d i a g r a m of the d r i v e system.
axial-field motor r e s e a r c h was
contract for the d e v e l o p m e n t of a
system w a s to consist of a
rotor p o s i t i o n - s e n s o r , and a
1.1 gives the functional block
The most interesting component of this system is the motor. T he m o t o r has a
topological lay-out w h i c h is similar to that of a typical dc disc motor; but its
c o n s t ruction d i f f e r s from the conventional dc disc machine in such a w a y that,
instead of havi n g a m o ving armature, its armature is stationary, and it is the
permanent magnet field system w h i c h rotates instead. Figure 1.2 s h o w s an
e xploded view of the machine; and its salient features ar e listed below:
<1> T h e topology of the motor gives rise to a short axial - length, a n d hence a
compact machine.
<2> T he armature is comple t e l y free of iron. <3) T h e r e is no dis c r e t e slot in the armature.
(4 > Field excitation is provided by permanent magnets. < 5 > Machine operation is c ompletely brushless.
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<1) T he c o m p a c t n e s s of the m otor g i v e s rise to high power - t o - w e i g h t . a n d p o w e r - t o - v o 1u m e , ratios.
(2) B e c a u s e of the i ronless armature, u n d e r normal op e r a t i n g conditions, the
a r m a t u r e r e a c t i o n flux is e x t r e m e l y small. so that it is p r a c t i c a l l y impossible, e i t h e r to sat u r a t e the m a gnetic circuit, or to d e m a g n e t i s e the
p e r m anent magnets.
< 3 > As there is no iron, iron-losses ( e d d y c u r r e n t s and hysteresis) are a l m o s t
c o m p l e t e l y eliminated.
<4> S i n c e there a r e no d e s c r e t e s l o t s in the armature, b r e a kaway f r iction
n o r m a l l y c a u s e d by hysteresis, and cogging, w h i c h usually results from the
i n t eraction b e t w e e n the dis c r e t e m a g n e t i c p o l e s and the a r m a t u r e slots, a r e
e l i m i n a t e d .
(5) The m a c h i n e ’s e f f i c i e n c y is i n h e r e n t l y gieater, because no field e x c i t a t i o n
is required.
< 6) T he m a i n t e n a n c e p r o b l e m s a s s o c i a t e d with the b r u s h e s and the c ommutator a r e
r e m o v e d .
(7) As t h e r e is no w e a r i n g of essential components, the mac h i n e has a longer
life-span and improved reliability.
<8) B r u s h l e s s o p e r a t i o n pro d u c e s low electrical a n d acoustic noise.
(9) B eing brushless, these m a c h i n e s are e x p l o s i o n - p r o o f and can oper a t e in
h o s t i l e and e x p l o s i v e enviroments; they are o p e r a t i v e even in hard vacuum. <10> T h e s e m a c h i n e s a re capa b l e of v e r y high speed operations. again d u e to
their brushlessness. f o l 1o w s :
i.
i Halar., construction
1.1.
The field e x c i t a t i o n of the motor is pro v i d e d by m u l t i - p o l a r s y s t e m of
[
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magnets__ L_
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_u
F l o u r « - 1 . 3 Dou hl i - s l c l i - d l n - l i | .hvmi e n
alrgap flux return rlnga
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- ^ r r . . . .V ,
■\
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magneto
____ _
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F i jure 1 • 4 S i n ai«» sided f ield
dep e n d s o n the type of permanent m a g n e t material used, the length of the airgap, and the r e q u i r e d flux-density. T he p o l e s a r e m a g n e t i s e d in a l t e r n a t i n g sequence, and a r e bond e d to a thin a n n u l a r mi l d steel p l a t e w h i c h n e v e r t h e l e s s has
suffic i e n t thickness to provide a m a g n e t i c path to a d j a c e n t m a g n e t s without
being saturated. T h e m a gnetic r e t u r n path on the remo t e s i d e of the a i r - g a p is
co m p l e t e d by an identical m a g n e t assembly, a s s hown in Figure 1.3; or
a l t e r n a t i v e l y , the m a gnetic r e t u r n path can be c o m p l e t e d by a s i n g l e steel plate, b ut the same total magnet v o l u m e is required to m a i n t a i n the a i r - g a p flux
density, a s shown in Figure 1.4.
1.1.2 T h e A r mature
Si t u a t e d in the a i r - g a p is a d i s c - s h a p e d armature. T h i s a r m a t u r e is c o n s t r u c t e d by n e s t i n g the individually f o rmed w i r e - w o u n d c o i l s (Figure 1.5) in a w i n d i n g
jig. a n d t he ends of the coils are c o n n e c t e d t ogether to form a t h r e e - p h a s e
win d i n g in the normal way. The w h o l e ar m a t u r e is e i t h e r e n c a p s u l a t e d in epoxy
resin or t a p e d with h e a t - c u r i n g , i m p r e g n a t e d glass tape, to prov i d e r i g i d i t y and s t r e n g t h .
1.2.1 A c t i v e Conductor D imensions
Among t he design p a r a m e t e r s of an a x i a l - f i e l d b r u s h l e s s motor, there a r e four p a r a m e t e r s that a re of p a r t i c u l a r importance in d e t e r m i n i n g the m o t o r ’s
character i s t i c s . T he first p a r a m e t e r is the radial d i m e n s i o n of the active
ar m a t u r e conductors. T h i s d i m e nsion is def i n e d by the inner diameter. d J# and
the o uter diameter. d 2 , of the m a g n e t pieces, as s h o w n in F i g u r e 1.6.
From F i g u r e 1.6, it is clear that t h e total number of c o n d u c t o r s is d i c t a t e d by the inner d i a m e t e r for a given a r m a t u r e thickness. In d e s i g n i n g the a r m a t u r e it is n e c e s s a r y to m a x i m i z e the u s e of the inner d i a m e t e r to a c c o m m o d a t e the l . 2
H
d i a m e t e r d t would leave no room
d i a m e t e r s less than d J . A space e n d - w i n d i n g space reguirement:
for the end-win d i n g s . which must exit at
factor is t h e r efore d e f i n e d to account for the
SF nTG
1 r , L ___ il. 1 >
w h e r e n * no. of p h a s e s T * t u r ns/phase L - no of layers
G = w i r e gauge
In de s i g n i n g an armature, one s h ould ensure that the s p a c e factor is not t oo
c l o s e to unity, so that the inner end w i n d i n g s can be stacked t o g e t h e r
comfortably. The e x a c t value of the space factor is d e p e n d e n t on the p a r t i c u l a r
a r m a t u r e construction. But as a general rule, the location of the end w i n d i n g s
mu s t be as close to d 1 as possible, whilst a l l o w i n g a suitable c l e a r a n c e
(normally of about lmm) between the end w i n d i n g s and the magnet edges.
If d A is fixed by the number of armature conductors, then the output power c a n
be increased by the lengthening of the acti v e conductors. Th i s is do n e by
en 1argi ng the o u t e r diameter
d 2 In doing s o . a s h o r t -comi ng of the d i s c
a r m a t u r e w i n d i n g arra n g e m e n t -- the usage of the a v a 1 i able arm a t u r e s p a c e
d e c r e a s e s wi th an increased
d 2 is reveall e d . An extreme case is shown i n
F i gure 1.7. Undoubtedly, this is wasteful in the s e n s e that it is not filled
w i t h c u r r e n t - c a r r y i n g c o n d u c t o r s to take a d v a n t a g e of the a v a i lable m a g n e t i c field to produce torque.
O n the other hand, if the rotor inertia is to be kept low, d 2 should be reduced.
But if d 2 is allowed to decrease the power output w o u l d be d e c r eased d ue to t he
d i m i n i s h e d active conductors. Of course the lost p o w e r output can be restored by
increasing the c o p p e r content in the armature thickness. But then the a i r - g a p
p o w e r -to-weight r a t i o and p o w e r - t o - v o l u m e ratio, w h i c h a re a f f e c t e d by the
choice of d 2 * It is therefore necessary to e s t a blish a r e l a t i o n s h i p betw e e n dj
and d 2# in w h i c h the opt i m u m perf o r m a n c e is obtained. However, it is impossible
to find a s i n g l e r e l a t i o n s h i p that relates all the p e r f o r m a n c e character i s t i c s . From the point of vi e w of the potential a p p l i c a t i o n of the motor, o n e feels that the r e l a t i o n s h i p betw e e n d^ and d 2 should be o p t i mised aga i n s t the output power.
Th i s is c o n f i r m e d by the finding of t h e Electrical R e v i e w s (51 that it is
important to r e d u c e the size and weight of the m o t o r s d e s i g n e d for traction
a p p l i c a t i o n s a s m u c h as possible.
I has been s h o w n by C a m p e l 1 (18) that the o u t p u t power c an be e x p r e s s e d in terms of the two d i a m e t e r s , u sing expr e s s i o n s for the sp e c i f i c magnetic, and ele c t r i c loadings of the machine:
p - 0 . 1 3 8 7 k B A n (di - d J ) d. ■ 10 3 <kw>
W c 2 1 1
w here k
w B
A
C
nw i n d i n g factor
s p e c i f i c mag n e t i c loading s p e c i f i c e lectric loading n u m b e r of poles
...(1.2)
In this equation. if w e a s sume that B. A are fixed and k is an e s t i m a t e d
c w
a a
value, then the p o w e r output is proportional to <d2 - d^) dj. Th e m a x i m u m power
for a given d 2 c an be found by e quating the d i f f e rential dP/dd^ to zero:
dd“- <0.1387 k < d 2 - 3d J ) - ....<1.3)
d 2 - /id,
i o
By s u b s t i t u t i n g <l.4) into (1.2). we have
-3
< kW) . . . < 1.3)
C o n s e q u e n t l y , one can c o n c l u d e that the power o u t p u t of an a x i a l - f i e l d machine
is a f u nction of the outer d i a m e t e r as well as the values of B a n d A . In
c
d e s i g n i n g an a x i a l - f i e l d machine, therefore, these v a l u e s must be chosen
c a r e f u l l y , so that the a r m a t u r e t h i c kness is m i n i m i s e d in order to mai n t a i n a
short air-gap, w h i l e at the same time a l l o w i n g t he armature to h a ndle the rated
curr e n t .
1.2.2 A i r - g a p Fl u x D e n sity
The s e c o n d important d e s i g n p a r a meter is the a i r - g a p flux density. This
p a r a m e t e r d i r e c t l y a f f e c t s the choi c e of the ty p e of magnet material used and
the a i r - g a p length; a nd ultimately, the mot o r ' s o p e r a t i n g efficiency. For a
s p e c i f i e d output power, a di s c m o t o r ' s electric loading is reduced by means of
i n c r e a s i n g the a i r - g a p flux d e n s i t y (proportional to the ma g n e t i c loading). This w o u l d lead to a r e d u c t i o n in the copper loss, and h e n c e to increased efficiency.
However, rais i n g the a i r - g a p flux d e n s i t y would involve the c h a n g i n g of the
magn e t material, or incre a s i n g the m agnetic volume, or both. But the exact
c o u r s e will d e p e n d on the n a t u r e of the m o t o r ' s application.
The m e a n i n g of 'air gap* in the a x i a l - f i e l d b r u s h l e s s machine d o e s not comply
w i t h that of the a i r - g a p of the conventional machine, w here it s i m p l y m e a n s the
gap b e t w e e n the stator a nd rotor cores. In the i r o n 1 ess axial -field machine, it
a c t u a l l y includes the a r m a t u r e t h i c kness and the r u n n i n g c l e a r a n c e on both sides
of the armature. S u p p o s i n g that this a i r - g a p has a length lg . and the reluctance
of the flux r e turn path Is negligible, then all o f the mm f s of the m a gnet must
d r o p a c r o s s the air-gap, thus.
H • H
w h e r e H m a g n e t i s i n g force of the magnet m
m = total length of the magnet
H * m a g n e t i s i n g force of the air - g a p g
T h i s eq u a t i o n shows the d e p e n d e n c e of both t h e magnet length. a n d the
m a g n e t i s i n g force, on the a i r - g a p length. One of t h e s e q u a n t i t i e s must t h e r e f o r e
w i t h i n the air-gap. Nowadays, it is taken for g r a n t e d that permanent m a g n e t s
wi t h high c o e r c i v i t i e s s h o u l d be chosen to pro v i d e t h e field. Invariably, this c h o i c e is influenced by the general a v a i l a b i l i t y of m o d e r n magnet m a t e r i a l s with
high c o e r c i v i t i e s and hi g h ener g y contents. Hriwpver, a higher prem i u m h a s to be
paid for this ‘obvious* choice, and one should bear in mind the fact that the
type of m a gnet material e v e n t u a l l y chosen is still deter m i n e d by the s p e c i f i c
a p p l i c a t i o n of the motor. Cha p t e r 2 w i 11 deal w i t h t h i s subject in more detail.
1.2.3 Num ber of poles
T h e third d e s i g n p a r a m e t e r is the c h oice of the p o l e number. S p e c i f y i n g too few p o l e s leads to e x c e s s i v e l y long end- w i n d i n g s t h e r e b y increasing the a s s o c i a t e d
I“ R loss. On the other hand, a large number of p o l e s can result in an e x c e s s i v e
number of coils, and c o n s e q u e n t l y m a k e s the d e s i g n impracticable. Also, m a g n e t i c
leakage i n c r eases with po l e number. Therefore, w h e n d e s i g n i n g w i t h axial field
motors, the p o l e number must be c h osen carefully.
l . 2. u P o l e - a r c / p o l e - p i t c h Ratio
T he forth important p a r a m e t e r of the motor is the p o l e arc / p o l e pitch ratio, a .
of the magnet po l e pieces. Re f e r r i n g to Figure l.fi. this ratio is d e f i n e d as. increase to a c c o m m o d a t e a larger 1^, w h i l e m a i n t a i n i n g a sp e c i f i e d flux d e n s i t y
pole-arc po I e pi tch
9,
or ■ pa
PP
. . .<1.7)
A pa A
PP
where A pa * a r e a of pole face (area of abed)
A p p * e f f e c t i v e pole area (area of efgh)
From e quation <1.8), it can be seen that for a g iven o p e r a t i n g flux density, B , m
the total a i r - g a p flux, *pa» * * become grea t e r as a increases. However, the
percentage of t h e useful flux (which is the flux cutting the a r m a t u r e c o n d u c t o r s
in p e r p e n d i c u l a r to their d i r e c t i o n of travel) will a l s o be reduced, due to a greater l e a k a g e of flux bet w e e n a d j a c e n t poles. This m e a n s that t he c a pacity of
the magnet m a t e r i a l is not u t i l i s e d to its fullness For th e b r u s hless
C H A P T E R
PRINCIPLE QF ROTATINQ MAGNET AXIAL-FIELP MACHINES
T h e essential d i f f e r e n c e b e t w e e n an a x i a l - f i e l d machine a nd its conventional c o u n t e r p a r t lies in the d i s p o s i t i o n s of the a c tive conduc t o r s and the wor k i n g
mag n e t i c flux. In a n a x i a l - f i e l d machine, the m a gnetic flux flows in parallel
with, w h i l e the acti v e c o n d u c t o r s run p e r p e n d i c u l a r to. the s haft of the
machine. T h i s c o n s t r u c t i o n lends itself to a m o t o r design w hich is slimmer and
lighter than the conventional type, a lthough it h as a slightly larger diameter.
D e s p i t e the d i f f e r e n c e s in their field and w i n d i n g arrangements, the operating
pr i n c i p l e of the axial field m a c h i n e s is exactly the same as that of all
conventional electrical machines. In other words, in order to pro d u c e optimum
e n e r g y conversion, the d i r e ction of the m a gnetic field and the acti v e c onductors
must be perpendicular. T he a x i a l - f i e l d p r i n ciple is best illustrated by the
sing l e c o n d u c t o r machine. w h i c h is shown in Figure 2.1. Figure 2 .2 s hows a
practical a x i a l - f i e l d desi g n w h i c h is based on the same principle. However. in
o r d e r for this m a c h i n e to prod u c e rotary motion, the d i r e c t i o n of the coil
curr e n t must be r eversed as the polarity of the flux influencing the c oils is
c h a n g e d -- this is done by rotating either the field system, or the coil
winding, through one pole-pitch. T h e proc e s s of current reversal is called
commutation. C o m m u t a t i o n can be a chieved by various means; the meth o d will
d e p e n d on the a r r a n g e m e n t of the field-system and of the windings. T h e various
m e t h o d s will be d i s c u s s e d in sect i o n 2.1. An o v e r v i e w of the d i f f e r e n t types of permanent magnet a x i a l - f i e l d m a c h i n e s is al s o g i v e n in that section.
S e c t i o n 2.2 of this chapter exp l a i n s the p r i nciple of- tne magnetic circuit of
b r u s h l e s s a x i a l - f i e l d machines. Firstly, the proper t i e s of permanent magnets
will be described; this is then followed by an explanation of the design
principle. Th e effect of the p o l e - a r c / p o l e - p i t c h ratio on the flux d i s t ribution
will also be discussed.
I
Figure 2.1 Axia l - f i e l d principle
lb
Firstly, the c o n s t r u c t i o n of the arm a t u r e w i n d i n g is described; and this is
followed by the d e r i v a t i o n of the emf equation.
2.1 Types.of Permanent Magnet Axia)-field Machines
There are two t y p e s of a x i a l - f i e l d machines. T h e s e are: s t a t 1o n a r y - f 1 eld
machines, and r o t a t 1n g - f 1 eld machines. In a s t a t 1o n a r y - f t e l d machine, mechanical energy Is transformed Into electrical energy, a nd vice versa, by the r o tation of
the windings. In a r o t a t i n g - f 1 eld machine. the t r a n s f o r m a t i o n of ener g y is
achieved by the r o t a t i o n of the field system. Almost with o u t exception, all of
the commutator dc a x i a l - f i e l d m o t o r s belong to the first type, and most of the
s y n chronous a x i a l - f i e l d ma c h i n e s belong to the second type.
The mach i n e w hich is to be d e s c r i b e d In detail In this thesis is in fact a
rotating-field m a chine.
2 . 1 . 1 s t a t i o n a r y - f i e l d a x i a l ma c h i ne s
A stationary-field a x i a l mac h i n e has a r o tating a r m a t u r e - w l n d i n g into which
current is fed. a n d as a result, e l e c t r o - mechanical e n ergy c o n v e r s i o n takes
place. The armature o f such a m a c h i n e Is built In the shape of a flat disc. and
can be of either th e p r 1n t e d - c 1rcult type (6) or the w i r e - w o u n d type (71. The
armature can be of e i t h e r the dc or ac design.
In a dc armature. c o m m u t a t i o n Is a c h i e v e d firstly by c o n n e c t i n g the win d i n g
terminations to c o p p e r seg m e n t s (the commutator), a nd s econdly by a p p l y i n g the
current to the c o m m u t a t o r thro u g h a set of s t a t i o n a r y c a rbon brushes. T h e fixed
relationship between the p osition of the b r u s h e s and the field s y stem Invariably
causes the current to reverse at the right moment. and this g u a r a n t e e s a
uni-dlrectIonal t o r q u e output.
shows the a r r a n g e m e n t s of such a machine: it has 2 coils, 4 poles and 4 c ommutator copper segments. But in order to reduce torque ripples, and to obtain
better c o m m u t a t i o n c h a racteristics, motors of this type usually have more than
two c o i l s a nd ma n y mo r e c o m m u t a t o r segments. T he work on axial-field machines at
War w i c k U n i v e r s i t y s i n c e 1967 has mainly concentrated on this type. The first
pr o t o t y p e to be built at W a r w i c k w a s a motor for an electric lawn-mower (8); its
p e r f o r m a n c e c u rves a r e shown in Figure 2.4. When delivering a rated output of
1.25 HP, the m a c h i n e ' s effici e n c y of 76% is extremely good, bearing in mind that
the s u p p l y volt a g e is only 12V (the batt e r y voltage). Encouraged by the
p e r f o r m a n c e of the lawn-mower motor, further developments were pursued.
Subse q u e n t research into practical a p p l ications include a radiator fan motor for a u t o m o t i v e a p p l i c a t i o n (9). several 'wh e e l - c h a i r ' motors (10.11), and a 10 kw traction m otor (12).
By m a k i n g a slight m o d i f i c a t i o n to the c o n nections of the dc armature, and by
replacing the c o m m u t a t o r se g m e n t s with a pair of slip rings, the motor can also
be d r i v e n by an ac current, as s hown in F i g u r e 2.5. Commutation is .now achieved
by the ac s u pply itself. But to produce uni-directional torque output. the
frequency of the ac supply a nd that of the armature rotation must be
synchronised, i.e. there is no relative m o t i o n between the stator and rotor
mmfs; an d the r e s u lting ac mach i n e is a s y n chronous disc-motor. Prior to the
project d e s c r i b e d here no w o r k on this kind of machine had been done at Warwick.
2 . 1 . 2 B Q t a U n f l - f i e l d a x i a l mac h l u e a
The a r m a t u r e of a r o t a t i n g - f i e 1d axial m a c h i n e is stationary. It is also built
in the s h a p e of a flat disc such a s that of the dc disc-motor. The basic
d i f f e r e n c e between a s t a t i o n a r y - a r m a t u r e m a c h i n e and a stationary- field machine
is that the former d o e s not require the commutator and slip rings used in the
l a t t e r .
When an ac current is a p p l i e d to the armature. as shown in Figure 2.6. the
1 «
g i v e n by Leung and C h a n (13). (Note: in their motor, elec t r o magnets w e r e used i n s t e a d of permanent m a g n e t s . > When the mach i n e is d r iven by a prime mover, it
b e c o m e s an alternator. An example of this can be found in S o y l e m e z ' s thesis
(14.), where an axial a l t e r n a t o r w as de v e l o p e d for w e l d i n g applications.
But, by e m p loying a pa i r of electronic sw i t c h e s and a rotor position detector,
as s h o w n in Figure 2.7, dc supply can also be used. T he arm a t u r e current of the
m o t o r is now commut a t e d by the electronic switches, w h i c h are in turn c ontrolled
by the rotor position. This kind of e l e c t r o n i c a l l y commutated axia l - f i e l d
m a c h i n e has output c h a r a c t e r i s t i c s similar to those of a c o m m u t a t o r dc
d i s c - m o t o r and is often referred to a s a b r u s hless dc disc-motor. T he brushless
dc d i s c - m o t o r forms the main subject of this thesis, a nd its basic princi p l e s
will be discussed.
2.2
The naaneUç circuit
As m e n t i o n e d in C h a p t e r 1, there are two p o ssible m e a n s of c o m p l e t i n g the
m a g n e t i c circuit of a permanent magnet d i sc -1motor One i s by using the
si n g l e - s i d e d a r r a n g e m e n t (Figure 1.4). and the other i s by u s i n g the
doubl e-sided a r r angement (Figure 1.3). In both of these arrangements. the
a i r - g a p is large enough to a c commodate the total ar m a t u r e thickness and to allow
s u f f i c i e n t running c l e a r a n c e on either side of the armature, as shown in Figure
2
.
8.
In a closed magnetic circuit, the integral f Hdl is equal to zero. Based on this
p r emise, and a ssuming infinite permeability in the remainder of the magnetic
c i rcuit, the mmf in the air- g a p H g can be related to that of the magnet H m by
H 1 . .(2.1>
o
F i g u r e 2.7 p ru «h i e.s.s de d i s c - m o t g r
«
clearance
99
seen that in order to accommodate the large air-gap whilst m a i n t a i n i n g a given
flux d e n s i t y in it, requires a long magnet or one with a high coe r c i v e force. In
normal circumstances, the latter course is always followed in order to avoid
excessive mach i n e weight. Suitable magnet materials include the inexpensive
ferrites, the very expensive rare-earth cobalts, and t h e less expensive
p o l y m e r - b o n d e d rare-earth cobalts. But the choice of material us e d will always
depend on the particular appli c a t i o n in question.
Before proceeding any further w i t h the discussion of the d e s i g n of the magnetic
circuit, it is useful at this s t a g e to consider some of the b a s i c properties of
magnetic materials.
2 . 2 . 1 The p r o p e r t i e s p f mag n e t i c m a t e r i a l s
The reaction of a specimen of m a gnetic material to a m a g n e t i c field depe n d s on
the nature a n d the history of the specimen, and the magnitude a n d direction of
the field. T he m a t e r i a l ’s b e h a viour can be described in t e r m s of the applied
field H and the resulting flux-density B. and is summed up in Figure 2.9. The
B-H h y s t e r esis-loop represents the complete cycle of the m a gnetisation and
d e m a g n e t i s a t i o n of the m a t e r i a l . This B-H loop. known as the normal
ma g n e t i s a t i o n curve. is the s u m of the magnetic p o l a r i s a t i o n J and the
flux-density B resulting from the applied field, i.e.
B ■ J ♦ B^ ■ J ♦ |i H -- .(2.2)
O O
In this equation. J is also known a s the intrinsic flux-density. If J is plotted
against H. the effect of B is excluded, and the resultant loop, which represents
the intrinsic magnetisation curve, is shown in Figure 2.10 (t h e heavy lines).
The point H c j represents the polarisation coercivity and is greater than the
normal coerci v i t y H . c
When de s i g n i n g with permanent magnets. which normally operate in a
d e n s ity
F i g u r e 2 .9 B-H h v s t e r e a l 3-1 p o p
however, for the p u r p o s e of machine design, it is only ne c e s s a r y to c o nsider the
normal curve w i t h i n that quadrant. Th i s part of the normal curve is often
referred to as the d e m a g n e t i s a t i o n curve.
Figure 2.11 shows a typical demag n e t i s a t i o n curve of a permanent magnet
material. T he circle m a r k e d on the curve r epresents the ideal work i n g point
BH max of the material. T h i s BH __ max point c o r r e s p o n d s to the maxi m u m energy
a v a ilable from the material and thus to opt i m u m utilisation. H is the coercive
c
force of the material a nd it is an indication of the m a t e r i a l ' s r esistance to
demagnetisation. is the remanence and it is the flux-density of a magn e t in a
closed magnetic cir c u i t a f t e r saturation. If the point (B . H ) is the wor k i n g
m m
point of the m a g n e t . t h e n the line intersecting the demagn e t i s a t i o n curve of the
material at the w o r k i n g point is known as the load line. T h e slope of this line
B_/H_ (or cota> is the p e r m e a n c e of the m agnetic circuit,
m m
The d e m a g n e t i s a t i o n c urve s hown in Figure 2.11 r epresents the steady d e c r e a s e in
flux-density with increa s i n g d e m a g n e t i s a t i o n of the material. If a magnet is
saturated. and then s u b j e c t e d to a c e r t a i n d e m a g n e t i s i n g field less powerful
than the coercivity. then the flux-density in the magnet will be given by the
d emagnetisation curve. U nder normal conditions, however, the d emagnetisation
field applied to the magnet is rarely constant; a n d the w o r k i n g point will not
n e c essarily follow the normal d e m a g n e t i s a t i o n curve. Th i s is most a p parent when
a magnet is subjected to a given v a l u e of d e m a g n e t i s i n g field which is
s u b s e quently reduced. T h i s situation is s h o w n in Figure 2.12.
A s a t u rated magnet is s u b jected to a d e m a g n e t i s i n g field H ^ . When this field is
reduced, the w o r k i n g point of the material do e s not follow the d e m a g n etisation
curve back towards the remanence. but moves along the curve C. If the
demagne t i s i n g field is reduced to zero, the w o r k i n g point follows the curve C to
B Q ; restoring the original value of d e m a g n e t i s i n g field thus causing the wor k i n g
point to fall back to A ^ . in doing this the wor k i n g point follows the curve D.