# Starting Torque of Squirrel Cage Induction Motor

#### Starting Torque in Induction Motor:

Starting torque means the torque developed by machine during starting. At the start of induction motor↗, rotor is initially at rest and slip S is 1 since speed of the rotor is zero w.r.t stator which is rotating at synchronous speed. Rotor frequency is given by the formula

Rotor frequency Fr = Slip Stator frequency.

Or               Fr =        S            Fs

At Starting, Slip S= 1 ,

Hence rotor frequency is equal to stator frequency at the start of motor ( i.e. Fr = Fs)

Rotor reactance Xr formula is written as :

Xr=                …. eq.2

Putting the value of rotor frequency in  eq. 2

Xr=

At starting , slip s=1.

So, the above eq. can be written as:

Xr=

From rotor reactance formula equation, we can say that the value of rotor reactance is very large as compared to rotor resistance during the start of motor. High reactance makes the rotor current lags the rotor emf by large scale such that the phase difference between current and voltage is very large. Large phase angle difference between current and voltage results in low power factor due to which starting torque of induction motor is small.

How we can increase the starting torque of Induction Motor?

The calculated mathematical expression of  induction motor starting torque↗ is as follows:

By analyzing the starting torque equation, we can say that starting torque of induction motor is directly proportional to the resistance of rotor circuit.  Hence, we can improve the starting torque of induction motor by increasing the rotor resistance. By adding resistance in the rotor circuit, power factor is improved which results in high starting torque. Although more resistance will reduce the value of rotor current and increases the rotor impedance but the effect of improve power factor is more predominant and starting torque of the motor is increased.

There are two main types of three phase induction motors which are termed as squirrel cage motor and slip ring induction motor↗ (also known as wound rotor motor). Let discuss the starting torque of squirrel cage induction motor.

Starting torque of Squirrel Cage Motor:

In case of squirrel cage induction motor↗, rotor consists of cylindrical laminated core on which aluminum bars are present inside the slots. These bars are joined at each end by large shorting rings known as end rings. Hence rotor of squirrel cage induction motor is permanently short circuited. Since the rotor bars of motor is permanently short circuited, it is not possible to add any external resistance in the rotor circuit during the start of squirrel cage induction motor in order to have high starting torque.

How we can increase the starting torque of Squirrel Cage Induction Motor?

The starting torque of squirrel cage induction motor can be increased by using double squirrel cage rotor. In this case, rotor has two sets of independent cages. Upper cage has high resistance and low reactance while lower cage has low resistance and high reactance.

Now, high starting torque can be obtained if the rotor circuit is less inductive and has high resistance. At the start of motor, rotor frequency is equal to stator frequency as the value of slip s=1. Lower cage having high reactance offers high impedance to high frequency stator current while upper cage offers low impedance. Hence most of the current tends to flow towards the upper cage which offers low impedance. Since upper cage offers high resistance which is require for high starting torque. Hence starting torque of the squirrel cage induction motor becomes high. In this way, we can achieve high starting torque in squirrel cage induction motor. The conductor arrangement in upper and lower cage of double squirrel cage rotor is shown in the below fig.

As the speed of motor increases, slip value decreases↗ which cause the rotor frequency to decrease. In that case, reactance of the lower cage also becomes less due to decrease in frequency current. Since lower cage of the rotor offers low impedance as compared to upper cage. Hence current will tend to flow towards lower cage as it has low impedance. In that way, starting torque of the motor gradually reduced as the motor attains its normal speed and it runs like a normal motor.