Torque-Slip and Torque-Speed Characteristics

The Torque-slip curve of an induction motor shows the variation of torque with the slip.

We have

If R₂ and X₂₀ are kept constant, then the torque τ will depend upon the slip s. The torque-slip characteristic curve is divided into three regions:

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

(a) Low-slip region

At synchronous speed s = 0, the torque will be zero. When the speed is very near to synchronous speed, the slip is very low and (sX₂₀)² is negligible in comparison with R₂. Therefore,

When k₂ = k₁/R₂

From the above relation, we can see that the torque is proportional to the slip. Hence, when the slip is small, the torque-slip curve is a straight line.

(b) Medium-slip region

As slip increases, the term (sX₂₀)² becomes large, so that may be neglected in comparison with (sX₂₀)² and

Thus, the torque is inversely proportional to slip towards standstill conditions. We can represent the torque-slip characteristic by a rectangular hyperbola. For intermediate values of the slip, the graph changes from one form to another. In doing so, it passes through the point of maximum torque when R₂ = sX₂₀. The maximum torque developed in an induction motor is called the pull-out torque or breakdown torque. This developed torque is a measure of the short-time overloading capability of the motor.

(c) High-slip region

The torque decreases beyond the point of maximum torque, and the result is that the motor slows down and then stops. At this stage, we should immediately disconnect the motor from the supply to prevent the damage due to overloading.

The motor operates for the value of the slip between s=0 and s = s_M, where s_M is the value of the slip corresponding to maximum torque. For a typical induction motor, the pull-out torque is 2 to 3 times the rated full-load torque. Thus, the motor can handle short- time overload, without stalling. The starting torque is 1.5 times the rated full-load torque.

The figure drawn below shows the torque-slip curves and torque-speed curves:

Figure: Torque-slip Curves

Figure: Torque-speed Curves