1 principle of operation equivalent circuit design formula
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Induction Machines: 2-phase Induction Motors
Principle of Operation Equivalent Circuit Design Formula and Torque speed characteristics Transfer Function
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
Balanced Operation
MM
CM
0mV V
90ocV V
mI I
90ocI I
mV
cV
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Induction Machines: 2-phase Induction Motors
Magnetic Field Production & Distribution
. enc
H dl I
.c
H dl Ni
g2g
NiH M
g gH H Ni
S N
2NiM
p
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
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.
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
Unbalanced Operation
0m mV V
c c cV V
m mI I
c c cI I
mV
cV
1mV
1cV2mV
2cV
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
Unbalanced Operation
1mV
1cV2mV
2cV
snn
snn
1s
s
n ns sn
2 2s
s
n ns sn
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Induction Machines: 2-phase Induction Motors
Unbalanced Operation
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
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Induction Machines: 2-phase Induction Motors
Unbalanced Operation
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
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Induction Machines: 2-phase Induction Motors
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.
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
AC servo motor2 2
1 21 2
m mnet B B
m m
V VT T TV V
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
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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Induction Machines: 2-phase Induction Motors
AC servo motor: Single Phasing Problem
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Induction Machines: 2-phase Induction Motors
AC servo motor: Drag-cup Rotor Design
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
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
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Induction Machines: 2-phase Induction Motors
AC servo motor
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Induction Machines: 2-phase Induction Motors
AC servo motor
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