Single phase IM principle, torque-slip and starting

A single-phase induction motor works on electromagnetic induction like a 3-phase induction motor, but its single stator winding produces a pulsating field, which by double field revolving theory is two equal fields rotating in opposite directions.

Working principle

1. AC supply to the stator winding produces a flux $\phi = \phi_m\cos\omega t$ that alternates along one axis.
2. This flux is equivalent to a forward field and a backward field, each $\phi_m/2$, rotating at $N_s$ in opposite directions.
3. At standstill both fields induce equal rotor currents and produce equal and opposite torques, so the motor has no starting torque.
4. If the rotor is started in one direction (by an auxiliary means), the slip for the forward field is $s$ and for the backward field is $2 - s$. The forward torque becomes much larger than the backward torque, and the motor accelerates to a speed slightly below $N_s$ and continues running in that direction.

Torque-slip characteristic

        T
        |            _
        |         .-' \   forward run
        |      .-'     |  (Tf > Tb)
 -Ns ---+----.'--------+---> speed
     |  |  .' 0        Ns
      \_|.'
 reverse run      net T = 0 at N = 0
 (mirror image)

• Net torque is zero at $s = 1$ (standstill).
• Net torque is positive for forward running ($0 < s < 1$) and becomes zero slightly before $s = 0$ because the backward torque is not zero at synchronous speed.
• The curve is symmetrical for reverse rotation ($1 < s < 2$).

One starting method: resistance split-phase

 AC o---+------------+
        |            |
   Main wdg     Aux wdg (high R)
        |            |
        |      centrifugal switch
 o------+------------+

• An auxiliary winding of high resistance and low reactance is placed $90^\circ$ electrical from the main winding.
• Its current lags $V$ less than the main winding current, giving a phase difference of $25-30^\circ$, which creates a rotating field and starting torque $T \propto I_mI_a\sin\alpha$.
• At about 75 % of $N_s$ a centrifugal switch disconnects the auxiliary winding.
• Used in fans, blowers, washing machines and small tools.