Maximum Torque Condition of Induction Motor


Condition for Maximum Torque : 


We know the equation for torque from Torque equation of induction motor.


     The condition for maximum torque can be obtained by differentiating toque with respect to slip and equating it to zero.


Therefore,


Therefore,

S  =  R/ X

The slip at which the torque is maximum is denoted as Sm

Sm  =  R2 / X2

     The slip at which the torque is maximum when rotor resistance is equal to rotor reactance under running condition.


At starting ( or ) standstill

       At start, Slip,   s = 1


The condition for maximum torque at starting can be obtained by substituting s = 1 in equation (1), we get

R2  =  X2

     Therefore starting torque is maximum, when rotor resistance is equal to rotor reactance at stand still.



Expression for Maximum Torque :


The expression for the torque is,


The maximum torque can be obtained substituting  R2   =   s Xin the torque equation. 



From the expression of  Tmax, it can be observed that :

(i) Maximum torque is independent of rotor resistance.

(ii) But the slip (or speed) at which the maximum torque occurs depends upon the rotor resistance.

(iii) It is inversely proportional to the stand still rotor reactance.

(iv) It is directly proportional to the square of the stand still rotor induced e.m.f.



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