1 Principle of Operation Equivalent Circuit Design Formula ...

Induction Machines: 2-phase Induction Motors

Principle of Operation Equivalent Circuit Design Formula and Torque speed characteristics Transfer Function

1


ConstructionSimilar to 3-phase inductionmotor, have two identical statorwindings (main & control) whichare shifted in space 90 electricaldegrees. The rotor is a squirrel cage rotor. The aim of this motor is to obtain speed and position proportional to the voltage applied on the control winding

2


Balanced Operation

MM

CM

0mV V

90ocV V

mI I

90ocI I

mV

cV

3


Magnetic Field Production & Distribution

. enc

H dl I

.c

H dl Ni

g2g

NiH M

g gH H Ni

S N

2NiM

p

4


Magnetic Field Production & Distribution

MM

CM

cos( )m m ei I t

4 cos2NM Ip

4 cos( )cos2m m eNM I t pp

4 cos( )2t m eNM I t pp

cos( 90 )oc m ei I t sin( )c m ei I t

4 sin( )sin2c m eNM I t pp

5


Rotating Field and its speed

For a particular point:

4 cos( )2t m eNM I t pp

M

0t

2t

edp zerodt

eddt p

60s

fnp

2e fSpeedp p

e t p const.

6


Equivalent Circuit

s

s

n nsn

2 cosinP VI

21 1 12cuP I R

'2 '2 2 22cuP I R

''2 22 12g in cu

RP I P Ps

'2 '2 2 2

(1 )2d g cusP I R P P

s

2: :

1 : : (1 )g cu dP P P

s s

7


Unbalanced Operation

0m mV V

c c cV V

m mI I

c c cI I

mV

cV

1mV

1cV2mV

2cV

8


Unbalanced Operation mV

cV

1mV

1cV2mV

2cV

1 2c c cV V V

1 1c mV jV 2 2c mV jV

1

2

1 1m m

c m

V VV Vj j

1

2

1112

mm

cm

VV jVV j

1 2m m mV V V

9



1mV

1cV2mV

2cV

snn

snn

1s

s

n ns sn

2 2s

s

n ns sn

10



11

1 1

mm

f

VIR jX Z

21 12g m fP I R

f f fZ R jX b b bZ R jX

22

1 1

mm

b

VIR jX Z

22 22g m bP I R

1 21 1: :

1 : : (1 )g cu dP P P

s s

2 22 2: :

1 : 2 : (1 (2 ))g cu dP P P

s s

1 2 1 2(1 )( )d d d g gP P P s P P 1 2

g dnet

s

P PT T T

11

g

s

PT

2

2g

s

PT

' '2 2

' '2 2

( / )/f

jX R s jXZ

R s jX jX

' '2 2

' '2 2

( / (2 ) )/ (2 )b

jX R s jXZ

R s jX jX

11



fZ bZ

1

2

1 1m m

c m

I II Ij j

1 11 12cu cu cuP P P

2 21 22cu cu cuP P P

211 1 12cu mP I R

212 2 12cu mP I R

in m cP P P cos( )

m mm m m V IP V I

cos( )c cc c c V IP V I

12


Application: AC servo motorA servo motor is typically part of a feedback loop containing electronic, mechanical, and electrical components. The servo loop is a means of controlling the motion of an object via the motor. A requirement of many such systems is fast response. One phase is connected to the single phase line; the other winding is driven by a variable amplitude sine wave to control motor speed.

13


AC servo motor

1 2netT T T 11

g

s

PT

2

2g

s

PT

21 12g m fP I R 2

2 22g m bP I R11

1

mm

VIZ

22

2

mm

VIZ

1 2m m m ratedV V V V

11

mm B

VIZ

22

mm B

VIZ

11

g BB

s

PT

2

2g B

Bs

PT

2

1 1

1

m

B m

T VT V

2

2 2

2

m

B m

T VT V

2 2

1 21 2

m mnet B B

m m

V VT T TV V

14


AC servo motor2 2

1 21 2

m mnet B B

m m

V VT T TV V

15


AC servo motorTypically, the two voltages are made90o shifted.

0mV V

2 2

1 21 1

2 2net B BT T T

90ocV V j V

mV

cV

1

2

1112

m

m

V j VV j j V

11( )

2mV V 2

1( )2mV V

16


AC servo motor: Single Phasing Problem

Supposedly, when Vc = zero (ρ = zero) the motor should stop (i.e. Tnet= zero or negative). But this will only happen if T2B ≥ T1B. To avoid this problem, the design is adjusted to achieve R2

’ ≥ X2’ + Xm sm ≥ 1

2 2

1 21 1

2 2net B BT T T

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AC servo motor: Single Phasing Problem

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AC servo motor: Drag-cup Rotor Design

19


AC servo motor: Torque-speed characteristicsAt starting (s=1)

1 2B B stBT T T stT

m st mT T B

cm stB m

m

VT T BV

m m c mT k V B

2 21 12 2st stB stB stBT T T T

20


AC servo motor: Transfer Function

m LdT T Jdt

m m c mT k V B L LT B

L mJ J J

m c m LdJ k V B Bdt

T m cdJ B k Vdt

( ) ( ) ( )T m cJs s B s k V s

( )( ) 1

m

m T

c TT

kk Bs

JV s Js B sB

( )( ) 1

m

m T

c T m

kk Bs

V s Js B s

m

T

JB

21


AC servo motor

22


AC servo motor

23

1 Principle of Operation Equivalent Circuit Design Formula ...

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