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A Thesis Submitted for the Degree of PhD at the University of Warwick

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130972

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-1

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

(3)
(4)

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

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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 ... 69

3.6 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

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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

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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

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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

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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

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

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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

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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

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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. 2

and

3

C 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

. . . .

135

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X

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

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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

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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

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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

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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

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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

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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 density

B

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 voltages

emf 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

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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

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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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RO

TO

R

PO

SI

TI

O

N

S

EN

SO

R

□ — oo<_p < o c z ; < i — ^ c c l u z o i — o c c

PO

W

ER

R

EG

U

LA

TO

(24)

F

i

gu

r

e

I

2

A

n

e

x

p

l

o

d

e

d

view

o

(25)

<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

(26)

[

\

i \

!

magnets

__ L_

{

J

_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

^

- ^ r r . . . .V ,

■\

/

■N,

si

/

r

magneto

____ _

1

_

V

V

)

V

— m

J

F i jure 1 • 4 S i n ai«» sided f ield

(27)

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

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(29)

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

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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

n

w 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,

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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

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(33)

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

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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

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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.

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I

Figure 2.1 Axia l - f i e l d principle

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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.

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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

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1 «

(40)
(41)

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

(42)

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

(43)

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

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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

(45)

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.

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Figure

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
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  &lt;
Figure  2.1  Axia l - f i e l d   principle
Figure  2.4  P e r formance  c h a r a c t e r  1 at 1C3  of  the  l a w n -mow er  m o t o r   supply  volt a u e   •  12V
+7

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