Faraday’s Law Applications Motors: AC Motor. For . ω = 0 cos cos 4. o net fm f bm b. BA TI I II....
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Faraday’s Law Applications 1. Inductors. 2. Transformers. 3. Electrical Generators. 4. Electrical Motors. 5. Transmission Lines. 1
Transcript of Faraday’s Law Applications Motors: AC Motor. For . ω = 0 cos cos 4. o net fm f bm b. BA TI I II....
Faraday’s Law Applications
1. Inductors.2. Transformers.3. Electrical Generators.4. Electrical Motors.5. Transmission Lines.
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Motors: DC Motor2
Motors: DC Motor3
Motors: DC Motor
oB B
DC
NS
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Motors: DC Motor5
Motors: DC Motor
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121 0
( )h
x yoF I dx u B u
12 ( )zoF IB h u
mF I dl B
yoB B u
2
121
F I dl B 12F
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Motors: DC Motor
4
343 0
( )h
x yoF I dx u B u
12 ( )zoF IB h u
4
343
F I dl B
12F
34F
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Motors: DC Motor
34F
12F
w
T r F
T FL
L
sinL w
( )sinoT IB hw
oF IB h
( )sin( )oT IB hw t
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Motors: DC Motor9
Motors: DC Motor
T m B
m I S
( ) nm I hw a
mP T sinm oP IB A
A hw
(1)(1)sin ( )n y xa u u
( ) n yoT I hw a B u
sin ( )xoT IB A u
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Motors: DC Motor11
Motors: DC Motor
2
121 0
( )h
z roF I dz u B u
12 ( )oF IB h u
mF I dl B
roB B u
2
121
F I dl B
ru
u
zu
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Motors: DC Motor
4
343 0
( ) ( )h
z roF I dz u B u
34 ( )oF IB h u
( )roB B u
4
343
F I dl B
ru
u
zu
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Motors: DC Motor14
Motors: DC Motor
T r F
T FL
(2 ) oT r IB h
2 ( )oT IB rhUnder the pole faces
0T
2p oT A B I
2T I
Ф = Total flux under one
pole
Beyond the pole edges
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Motors: AC Motor
1sinoB B t
1 2 f
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Motors: AC Motor
.
.S
c
Be dSt
v B dl
1sin yoB B tu
1 .S
Be dSt
1 2e e e
1 1 1cos( ) .y noS hw
e B t u dS a
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Motors: AC Motor
1 1 1( ) cos( ) cos( )o oe B wh t t
1 1 1 1[cos(( ) ) cos(( ) )]2o o oAe B t t
1 1 1cos( ) .y noS wh
e B t u dS a
(1)(1)cosn ya u
1 1 1( ) cos( ) cos( )oe B wh t
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Motors: AC Motor
2 1( )sin( )sin( )o oe B wh t t
2 .c
e v B dl
2 1 1( ) [cos(( ) ) cos(( ) )]
2o o owhe B t t
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Motors: AC Motor
1 2e e e
1 1
1 1
[( ) cos(( ) )2
( ) cos(( ) )]
o o
o
Ae B t
t
1 1 1 1[cos(( ) ) cos(( ) )]2o o oAe B t t
2 1 1[cos(( ) ) cos(( ) )]2o o oAe B t t
f be e e
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Motors: AC Motor
fe
be
fi
bi
1 1[( ) cos(( ) )]2
of o f
f
B Ai tZ
fi
bi
f
f
eZ
b
b
eZ
1 1[( ) cos(( ) )]2
ob o b
b
B Ai tZ
1( )R j L
1( )R j L
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Motors: AC Motor
Torque
1cos(( ) )f fm o fi I t
1cos(( ) )b bm o bi I t
fT m B fm i S
1 1cos(( ) )( ) sinn yf fm o f oT I t Aa B tu
1sin yoB B tu
1 1cos(( ) )sin sin( )f fm o o f oT I B A t t t
1 1 11sin sin( ) [cos(( ) ) cos(( ) )]2o o ot t t t
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Motors: AC Motor
Torque
1
1 1
cos(( ) )2
*[cos(( ) ) cos(( ) )]
fm of o f
o o
I B AT t
t t
1 1
1
cos(( ) )*cos(( ) )1 cos cos[2(( ) ) )]2
o f o
f o f
t t
t
1 1
1
cos(( ) )*cos(( ) )
1 cos[2( ) )] cos(2 )2
o f o
o f f
t t
t t
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Motors: AC Motor
Torque
1
1
cos cos[2(( ) ) )]*
cos(2 ) cos[2( ) )]4f o ffm o
ff o f
tI B AT
t t
cos4
fm ofavg f
I B AT Similarly cos4
bm obavg b
I B AT
cos cos4o
net fm f bm bB AT I I
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Motors: AC Motor
For ω = 0
cos cos4o
net fm f bm bB AT I I
f b fm bmI I
netT zero
This motor cannot start from rest by its own developed torque
For any speed ω
fm bmI I f b
netT zero
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Motors: AC Motor
The motor needs an external method to start-upIt is called Induction Motor
Single PhaseInduction Motor
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