MC-C2 · Induction principle & slip

The Principle of the Induction Machine and Slip

The rotor chases the rotating field but can never catch it. Raise the rotor speed, watch how the induced current and torque change, and pin down why the synchronous speed can never be reached.

What happens to the torque if the rotor reaches synchronous speed?

There must be relative motion — the rotating field sweeping past the rotor bars — for current to be induced and torque to arise. Push the rotor-speed slider toward synchronous. As the relative motion shrinks, so does the induction. The instant the rotor reaches synchronous speed exactly, what happens to the torque?

Rotor speed NN = 900 rpm

Slide for continuous rotor speed. Gold is the rotating field, blue is the rotor.

Slip and rotor frequency

s = 0.50 · f2 = 30.0 Hz

The torque does not grow as it nears synchronous. Just the opposite: the relative motion vanishes and the induction stops. If the rotor moves at the same speed as the field, the bars cut no flux, so the EMF and current are zero.

At N = Ns, torque is?

Misaligned

Induction needs relative motion

When the rotating field sweeps past the stationary (or slower) rotor bars, the bars cut flux and have an EMF induced (Faraday). Current flows in the short-circuited rotor bars, and this current feels a force in the rotating field (F = BIl) that drags the rotor in the direction the field turns. By Lenz’s law the induced current opposes its cause, the relative motion, so the rotor accelerates to chase the field.

Observeslip speed = Ns - N

What drives induction is the speed difference between field and rotor.

Synchronous speed is the hare it cannot catch

As the rotor speeds up, its relative motion with the field shrinks, the bars cut flux less often, and the induced current and torque fall together. If the rotor reached synchronous speed the relative motion would be zero and the EMF, current and torque would all be zero. At that instant friction and load win, the rotor slows again, the relative motion revives, and torque returns. So the rotor never catches synchronous speed and settles a little behind it. For this reason the induction machine is called asynchronous.

Chooses = (Ns - N) / ?

Slip is that speed difference over the synchronous speed.

Slip measures everything

How far the rotor lags is measured by the slip s = (Ns - N)/Ns. At standstill s = 1; at synchronous speed s = 0. The frequency of the flux the rotor bars feel, the slip frequency, is f2 = s·f. The rotor’s induced EMF and reactance are also proportional to slip. At the instant of starting s = 1, so the rotor frequency equals the supply frequency; in normal running the slip is usually a few percent, so the rotor frequency is only a few hertz. Slip alone sets the electrical state of the induction machine.

Fill inf2 = s ?

The rotor frequency is slip times the supply frequency.

On your owns = 1 - ?

Slip is also one minus the speed ratio.

Back to the first screen

When the rotor reaches synchronous speed the torque becomes zero. Induction comes from the relative motion of the rotating field sweeping past the rotor bars, and at synchronous speed that relative motion vanishes. If the bars cut no flux there is no EMF, no current and no torque. With no torque the rotor cannot even overcome friction and slows again, which revives the relative motion and brings the torque back. Because of this self-contradiction the rotor forever only chases synchronous speed, settling always a slip s = (Ns - N)/Ns behind it. Slip is the very price the induction machine pays to make torque.

The induction machine: the relative motion of the rotating field sweeping past the rotor bars induces current and makes torque. At synchronous speed the relative motion is zero so the torque is zero, hence the rotor always runs a slip s = (Ns - N)/Ns behind (asynchronous). The rotor frequency is f2 = s·f, with s = 1 at standstill and s = 0 at synchronous.

Once you hold this slip

Slip is the handle for analysing the induction machine. Since the rotor circuit’s EMF and reactance both carry slip, treating slip as the variable lets you fold the rotor, seen from the stator, into a single equivalent circuit. The key is writing the rotor resistance as R2/s — this one term holds both the real electrical loss and the mechanical output the rotor delivers. The next unit builds that equivalent circuit (MC-C3).