What is the condition for maximum torque in relation to slip (S) in a three phase induction motor?

Concept:

The expression for Torque produced in the induction motor is

Condition to get maximum torque:

The slip at maximum torque is, s = R₂ / X₂

Important Points

The torque slip characteristic curve is divided into three regions:

• Low slip region
• Medium slip region
• High slip region

Low slip region:

• At synchronous speed, slip = 0, therefore the torque is zero.
• When there is a light load, the speed is very near to synchronous speed.
• The slip is very low and (sX20)2 is negligible in comparison with R2. Therefore

i.e. T ∝ S

Medium slip region:

• As the slip increases, the speed of the motor decreases with the increase in load.
• The term (sX20)2 becomes large.
• The term R22 may be neglected in comparison with the term (sx20)2 and the torque equation becomes

i.e.  

Hence for heavy loads, torque is inversely proportional to slip.

High slip region:

• Beyond the maximum torque point, the value of torque starts decreasing. As a result, the motor slows down and stops.
• At this stage, the overload protection must immediately disconnect the motor from the supply to prevent damage due to the overheating of the motor.
   

Note: The motor operates for the values of the slip between s = 0 and s = sm, where sm in the value of slip corresponding to maximum torque.