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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.

T

_{f}a FI_{2}^{’}Cos F_{2}^{’}
= KF [ SE

_{2}/ Z_{2}] [ R_{2}/ Z_{2}]
= KFSE

_{2}R_{2}/ Z_{2}^{2}
= KFSE

_{2}R_{2}/ [ R_{2}^{2 }+ ( SX_{2 })^{2}]……………… ( 1 )**Condition for Maximum Full load torque**

dT

_{f}/ dS = 0
= d { KFSE

_{2}R_{2}/ [ R_{2}^{2 }+ ( SX_{2 })^{2}] } / dS_{ }= 0
= [ R

_{2}^{2 }+ ( SX_{2 })^{2}] KFE_{2}R_{2}– KFSE_{2}R_{2}[2( SX_{2 })( X_{2 }) ] / [ R_{2}^{2 }+ X_{2}^{2}]^{2}= 0
= KFE

_{2}R_{2}{ R_{2}^{2 }+ ( SX_{2 })^{2}– 2( SX_{2 })^{2}} = 0
The rotor
induced emf should not be zero therefore

{ R

_{2}^{2 }+ ( SX_{2 })^{2}– 2( SX_{2 })^{2}} = 0
{ R

_{2}^{2 }– ( SX_{2 })^{2}} = 0
{ R

_{2 }^{ }– ( SX_{2 }) } = 0 OR { R_{2 }^{ }+ ( SX_{2 }) }= 0
Therefore R

_{2 }^{ }= ( SX_{2 }) or R_{2 }^{ }= – ( SX_{2 })
R

_{2 }^{ }= – ( SX_{2 }) is not possible therefore R_{2 }^{ }= ( SX_{2 })- 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 R

_{2 }^{ }= ( SX_{2 }) in the equation ( 1 )
T

_{f( MAX ) }= KFSE_{2}R_{2}/ [ R_{2}^{2 }+ ( SX_{2 })^{2}]
= KFS

^{2}X_{2}E_{2}/ [( SX_{2 })^{2}+ ( SX_{2 })^{2}] { As R_{2 }^{ }= ( SX_{2 }) }
T

_{f( MAX ) }= KFE_{2 }/ 2X_{2}**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 = R

_{2}/ X_{2}- The maximum full load torque is inversely proportional to rotor reactance.
- Higher the rotor reactance, lesser the maximum starting torque and vice versa.

T

_{f( MAX )}a ( 1 / X_{2})**Ratio of full load torque to maximum torque**

Full load T

_{f}= KFSE_{2}R_{2}/ [ R_{2}^{2 }+ ( SX_{2 })^{2}] and full load maximum torque
T

_{f( MAX ) }= KFE_{2 }/ 2X_{2}
The ratio of
full load torque to maximum torque

T

_{f}/ T_{f( MAX )}= { KFSE_{2}R_{2}/ [ R_{2}^{2 }+ ( SX_{2 })^{2}] / KFE_{2 }/ 2X_{2}
T

_{f}/ T_{f( MAX )}= { 2SR_{2}X_{2}/ [ R_{2}^{2 }+ ( SX_{2 })^{2}]…….. ( 2 )
Multiply and
dividing equation ( 2 ) by ( X

_{2 })^{2}
T

_{f}/ T_{f( MAX )}= { 2SR_{2 }/ X_{2}} / [ R_{2}^{2 }/ ( X_{2 })^{2}+ ( SX_{2 })^{2}/ ( X_{2 })^{2}]
Putting R

_{2 }/ X_{2}= a
T

_{f}/ T_{f( MAX )}= 2aS / [ ( a_{ })^{2}+ ( s_{ })^{2}]
If S = 1 or
standstill condition

T

_{f}/ T_{f ( MAX )}= 2a / [ ( a_{ })^{2}+ 1 ]………….( 3 )
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