Torque in induction motor and relationship with rotor power factor.

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The torque in induction motor is proportional to the product of flux per stator pole and the rotor current one more term we will take in account is power factor of the rotor.


  T →  φ  *  I₂  * cos∅₂ 


Where φ  - flux per status pole

I₂ - rotor current

cos∅₂ - rotor power factor

∅₂ phase angle  rotor current and rotorEMF.


The induced rotor EMF E2 is proportional to flux per status φ.


Therefore T = K1 * E₂ *  I₂ * cos φ2 


Where K1 is another constant.


From the above equation it is clear that when φ2 increases cos φ2 decreases and vice versa.

Due to the revolving stator flux EMF is induced in rotor conductor, and this EMI is also sinusoidal.

When rotor is non inductive.



φ₂=0


in this case rotor current is in phase with rotor EMF. So the instantaneous value of torque is product of instantaneous value of flux and current. It is seen that torque is always positive.


When rotor is inductive load.

In inductive load I₂ lags behind E₂ bY an angle φ2.

φ2 = tan-¹(X₂/R₂ )

R2 = rotor  resistance per phase

X2 = rota reactance per phase at standstill.

Its clear from diagram that portion of torque is reverse direction and hence the total torque is difference of forward torque and reverse torque. When φ2 = 90 degree then reverse torque equals to forward torque and total torque is equals to zero so the motor will not run.






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