Why Number of Stator and Rotor Poles must be Equal for Production of Electromagnetic Torque?

This is very basic but important concept to understand Electrical Machine. It is well known fact that, the number of stator and rotor poles must be equal for the production of net Electromagnetic Torque. In this post we will discuss the reason behind this.

Let us consider an Electrical machine having 2 Stator Poles and 4 Rotor Poles as shown in figure below.

As shown in figure above, the rotor poles are equally paced i.e. the alternate north and south pole are displaced by 90° mechanical or 180° electrical.

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Let us consider rotor pole N1 and stator pole N. The angle between rotor pole N1 and stator pole N is equal to the angle between the rotor pole N2 and stator pole S1. Mind that this angle between the rotor pole axis and stator pole axis is called the Torque Angle. Also Electromagnetic Torque in an Electrical Machine is given as

Torque = K x Stator Field Strength x Rotor Field Strength x Torque Angle

Where K is some constant.

Thus the force of repulsion (in clockwise direction) between the rotor pole N1 and stator pole N will be equal in magnitude to the force of attraction (in anticlockwise direction) between the rotor pole N2 and stator pole S. Thus the net torque due to the interaction of rotor poles N1 & N2 and stator poles N & S will be zero.

Similarly, if we consider rotor pole S1 & S2 and stator poles N & S, then the force of attraction (in clockwise direction) between the rotor pole S2 and stator pole N will be equal in magnitude with the force of repulsion (in anticlockwise direction) between the rotor pole S1 and stator pole S. Thus the net torque because of the this will be zero.

Therefore, from the above discussion we observe that for an Electrical Machine having 2 stator poles and 4 rotor poles, the net electromagnetic torque is zero. In view of this, it is essential that in all rotating electrical machines, the number of rotor poles must be equal to the number of stator poles for the production of net electromagnetic torque.