Torque in Three Phase Induction Motor

 

To study the torque in three phase induction motor, it is necessary to have the  understanding of the basics of torque. So before moving forward to the concept of torque in induction machine, let us revise some basics of torque.

 

Torque is nothing but the force that is applied to an object around a circular axis. This force or torque tends to move an object around the circumference of the circular axis. It is also known as rotational force.

Torque in three phase induction motor

 

Similarly, torque in an induction machine is the force which tends the rotor to rotate in a circular axis.

 

In three phase induction motor torque is produced by the interaction of magnetic field produced by stator winding and magnetic field produced by rotor winding. These two magnetic fields are sinusoidal distributed along the air gap and also they both rotate at synchronous speed with respect to the stator. 

 

These two fields produce north pole and south pole on both the stator and the rotor shown in the figure.

Initially the stator magnetic field axes and the rotor magnetic field axes are at some angle that is delta. 

 

These two field axes tend to align due to the magnetic force between poles on the rotor and the stator.

 

For the torque development it is necessary that the both stator field and rotor field have the same number of poles and these two are stationary with respect to each other. 

 

When there is no angle between these two magnetic field axes then no torque is produced. For the torque development this condition is also necessary that these two field axes initially have some angle.

So, we can say torque produced in induction motor depends on the Fs (stator magnetic field) and Fr (rotor magnetic field) and δ.

 

So,  

 

                      T    α    Fs. Fr. Sin&

 

In three phase induction motor Fs produced by the supply voltage V and it induced the voltage Er in the rotor conductor.

 

So, we can say that,

 

                     V   α   Fs   α   Er

 

And the rotor magnetic field Fr is produced due to rotor current and this rotor current is produced because the rotor is short circuited.

 

So, we can say that

 

                        Fr   α   Ir

 

And the & is the angle between Fr and Fs. From equation (1) and (2) it is assumed that & is the angle between Er and Ir.

 

So, the angle between Er and Ir is ɸr

 

So, we can say that 

 

                      T   α   Er . Ir.  cosɸr

 

where cosɸr is the rotor power factor 

where k Is the proportionality constant.

Equation (3) represents the torque equation of three phase induction motor.

 

Maximum Torque of Three Phase Induction Motor

 

To get the maximum torque, differentiate equation (3) with respect to Rr because Rr can be varied by adding external resistance to the rotor circuit.

 

After differentiating we get the condition for maximum torque i.e. 

 

                     Rr   =   s.Xr 

 

Slip at which maximum torque occurs is

 

                    s (max)     =     Rr  /  Xr

Starting Torque of Three Phase Induction Motor 

 

At starting slip = 1

 

So, the torque equation at starting of three phase induction motor

For getting maximum torque at starting, Rr must be equal to Xr at starting. It is achieved by adding external resistance to the rotor circuit. It is only possible in the case of slip ring induction motors.

 

Torque Under Running Condition

 

Under running condition equation (3) represents the torque in three phase induction motor.

 

The slip under running condition is very low. So sXr is also very low and it can be neglected.

Under running condition, Torque is inversely proportional to the rotor resistance and directly proportional to the induced emf in the rotor circuit and slip.

 

As,

 

                                Er   α   Fs   α   V

 

So, we can say,

 

                               T     α     V2

 

Under running conditions torque has a direct relation to slip in induction motor. This relation between torque and slip is studied with the help of torque slip characteristics of three phase induction motor.

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