Synchronous speed and why rotor lags stator field

Synchronous speed

Synchronous speed is the speed at which the rotating magnetic field produced by the 3-phase stator winding rotates. It depends only on supply frequency and number of poles:

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

Example: $f = 50$ Hz, $P = 4$: $N_s = 1500$ rpm; $P = 6$: $N_s = 1000$ rpm.

Why the rotor turns in the direction of the rotating field

1. The stator field rotates at $N_s$ and cuts the stationary rotor conductors, inducing emf and current in them.
2. By Lenz's law, the induced current opposes the cause producing it. The cause is the relative motion between the field and the rotor conductors.
3. The rotor cannot stop the field, so it reduces the relative speed by chasing the field, i.e. rotating in the same direction.
4. In force terms, the rotor current in the field gives a force $F = BIl$ on each conductor in the direction that drags the rotor along with the field.

To reverse the motor, the field direction is reversed by interchanging any two supply leads.

Why the rotor can never reach synchronous speed

1. If the rotor ran at $N_s$, there would be no relative motion between rotor conductors and the field.
2. Then no flux is cut, so rotor emf $= 0$, rotor current $= 0$ and torque $= 0$.
3. But the rotor always needs some torque to overcome friction, windage and load. So it slows down until enough relative speed exists to induce the required current.
4. Hence the rotor always runs slightly below $N_s$. The difference is expressed as slip:

$$s = \frac{N_s - N}{N_s}$$

Typical full-load slip is 2–5% (about 0.5% at no load). This is why the machine is called an asynchronous motor. Running exactly at $N_s$ is possible only if an external prime mover drives it; above $N_s$ it becomes a generator.