Induction Motor Torque-Slip (speed) Characteristics

     The curve obtained by plotting torque against slip is called torque-slip characteristics of the induction motor.

The expression for the torque is,

Induction Motor Torque-Slip (speed) Characteristics

     We can evaluate value of torque at different values of slip in the range from 0 to 1. 

(i) When slip s = 0, N = Ns and hence torque, T =  0. Motor can not run at synchronous speed.

(ii) When slip ' s ' is very low i.e., the speed is very near to synchronous speed, then the term ( sX2 )2 is very small and can be neglected in comparison with R22.


T  α  s / Rs

T  α  s  if  R2 is constant

     Hence for low values of slip, the torque-slip curve is a straight line. 

(iii) When slip increases i.e., the speed decreases ( with increase load ), the torque increases and becomes maximum when

s  =  sm  =  R2 / X2

i.e., T  =  Tm   when s  =  sm

   The maximum torque is called as pull-out or breakdown torque 

(iv) When slip is further increases beyond s  =  sm, then the term R22 is very small as compared to ( sX2 )2 and may be neglected. 

T  α  sR2 / (sX2)2

T  α  1 / s    if R2 & X2 are constants 

   Hence the torque values of slip, the torque-slip curve is a rectangular hyperbola.

(v) If slip s = 1, then motor is stationary hence corresponding torque is nothing but starting torque.

i.e., T  =  Tst when s = 1

     Figure below shows the Torque-slip Characteristics.

Induction Motor Torque-Slip (speed) Characteristics

     The region from s = 0 to s  =  sm  is called as operating region for the induction motor because if load is increased beyond s  =  sm, them torque decreases and motor will stop. The Torque-speed Characteristic is shown below.

Induction Motor Torque-Slip (speed) Characteristics

Effect of Rotor Resistance on Torque-slip Curve :

     In slip ring induction motor it is possible to add external resistance in series with the rotor through slip rings. This is used to control starting torque developed by the motor. 

Let   R2  =  rotor resistance / phase, then torque

Induction Motor Torque-Slip (speed) Characteristics

    The stand still rotor reactance phase, X2 will remain constant, since it is fixed by the design of the rotor.

Let us Consider   

(i) When no external resistance is inserted in the rotor circuit. Maximum torque is developed at

sm  =  R2 / X2

(ii) Now if rotor resistance is increased ( inserting external resistance in the rotor circuit) from
R2 to R'2.           

     The magnitude of the maximum torque, Tmax remains unchanged but the slip for maximum torque  is

s'm  =  R'2 / X2

(iii) As rotor resistance is increased from R'2 to R''2,  and so on, as shown in figure that Tmax  remains same but starting torque increases. 

(iv) At sm = 1 i.e., when R2  =  X2, motor will develop maximum torque at the instant of starting. This is represented by point ' A ' in the figure.

Induction Motor Torque-Slip (speed) Characteristics

From the torque-slip curves shown above the following points are noticed : 

(i) Maximum torque Tmax remains same and is independent of the rotor resistance.

(ii) The slip for maximum torque increases with increase in rotor resistance.

(iii) Starting torque increases with increase in rotor resistance.

(iv) When R2  =  X2, motor will develop maximum torque at the instant of starting.

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