Synchronous speed; rotor follows rotating field

Synchronous speed

Synchronous speed is the speed of the rotating magnetic field produced by the stator winding of a three-phase induction motor:

$$N_s = \frac{120 f}{P}\ \text{rpm}$$

where $f$ is the supply frequency and $P$ the number of poles. For $f = 50$ Hz and $P=4$, $N_s = 1500$ rpm.

Why the rotor rotates in the direction of the field

1. The rotating field cuts the stationary rotor conductors and induces an emf (Faraday's law).
2. The closed rotor circuit carries a current, so each conductor in the field experiences a force.
3. By Lenz's law, the effect of the induced current opposes its cause, which is the relative motion between the field and the rotor conductors. The rotor can reduce this relative motion only by moving in the same direction as the field.
4. So the torque on the rotor acts in the direction of the field and the rotor follows it.

Why the rotor cannot reach synchronous speed

• If the rotor ran at $N_s$, the relative speed between field and rotor would be zero.
• No emf would be induced in the rotor, so no rotor current would flow.
• Without current there is no torque, and the rotor would slow down due to friction and windage losses and load.
• It therefore settles at a speed $N_r < N_s$ where the induced current gives the torque needed for the load. The difference $N_s - N_r$ is the slip speed, and slip $s = \frac{N_s - N_r}{N_s}$ is 2 to 5 % at full load.

For this reason the induction motor is also called an asynchronous motor.