Full
load torque
- The torque in
the DC Motor is related by the product of field flux and armature current
whereas the torque in the induction motor is product of rotor flux, rotor
current and rotor power factor.
Tf a
FI2’Cos
F2’
= KF [ SE2
/ Z2 ] [ R2 / Z2 ]
= KFSE2
R2 / Z22
= KFSE2 R2
/ [ R22 + ( SX2 )2 ]……………… ( 1 )
Condition
for Maximum Full load torque
dTf /
dS = 0
= d { KFSE2
R2 / [ R22 + ( SX2 )2 ] }
/ dS = 0
= [ R22 + (
SX2 )2 ] KFE2 R2
– KFSE2R2
[2( SX2 )( X2 ) ] / [ R22 + X22
]2 = 0
= KFE2 R2
{ R22 + ( SX2 )2 – 2( SX2 )2
} = 0
The rotor
induced emf should not be zero therefore
{ R22
+ ( SX2 )2 – 2( SX2 )2 } = 0
{ R22
– ( SX2 )2 } = 0
{ R2 – ( SX2 ) } = 0 OR { R2 + ( SX2 ) }= 0
Therefore R2
= ( SX2 ) or
R2 = – ( SX2 )
R2 = – ( SX2 ) is not possible
therefore R2 = (
SX2 )
- When the rotor resistance is slip times the rotor reactance, the maximum torque occurs in the three phase induction motor at full load condition.
Maximum Full load torque
Putting R2 = ( SX2 ) in the equation ( 1 )
Tf( MAX ) =
KFSE2
R2 / [ R22 + ( SX2 )2 ]
= KFS2X2E2
/ [( SX2 )2 + ( SX2 )2 ] { As R2 = ( SX2 ) }
Tf( MAX ) =
KFE2
/ 2X2
Parameters
affecting full load torque
- The maximum full load torque does not depend upon rotor resistance.
- As the rotor resistance increases, the maximum full load torque does not change but speed or slip at which maximum torque occur change.
S = R2
/ X2
- The maximum full load torque is inversely proportional to rotor reactance.
- Higher the rotor reactance, lesser the maximum starting torque and vice versa.
Tf( MAX )
a
( 1 / X2 )
Ratio
of full load torque to maximum torque
Full load Tf
= KFSE2
R2 / [ R22 + ( SX2 )2 ]
and full load maximum torque
Tf( MAX ) =
KFE2
/ 2X2
The ratio of
full load torque to maximum torque
Tf /
Tf( MAX ) = { KFSE2 R2 / [ R22
+ ( SX2 )2 ]
/ KFE2
/ 2X2
Tf /
Tf( MAX ) = { 2SR2X2 / [ R22 +
( SX2 )2 ]…….. ( 2 )
Multiply and
dividing equation ( 2 ) by ( X2 )2
Tf /
Tf( MAX ) = { 2SR2 / X2 } / [ R22
/ ( X2 )2 + ( SX2 )2 / ( X2
)2 ]
Putting R2 /
X2 = a
Tf /
Tf( MAX ) = 2aS / [ ( a )2 + ( s )2
]
If S = 1 or
standstill condition
Tf /
Tf ( MAX ) = 2a / [ ( a )2 + 1 ]………….( 3 )
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