Single phase motor not self-starting; DFRT

Why a single-phase induction motor is not self-starting

When a single-phase ac supply is connected to the stator winding, it produces a pulsating (alternating) magnetic field along a fixed axis, not a rotating field. This field induces currents in the stationary rotor, but the torque produced on one half of the rotor is equal and opposite to that on the other half, so the net starting torque is zero. The rotor stays at rest. However, if it is turned by hand in either direction, it accelerates in that direction.

Double field revolving theory

The single-phase winding carrying alternating current produces a pulsating (alternating) flux along a fixed axis: $\phi = \phi_m\cos\omega t$. According to the double field revolving theory, this pulsating flux is equivalent to two rotating fluxes, each of constant magnitude $\phi_m/2$, rotating at synchronous speed $N_s = \frac{120f}{P}$ in opposite directions.

$$\phi_m\cos\omega t = \frac{\phi_m}{2}e^{j\omega t} + \frac{\phi_m}{2}e^{-j\omega t}$$

• $\phi_f$: forward-rotating component (in the direction of the rotor).
• $\phi_b$: backward-rotating component (opposite).

 phi_f = phi_m/2 -->  (anticlockwise)
          \   /
   phi_b   \ /  resultant = phi_m cos(wt)
 = phi_m/2  X   along fixed axis (pulsating)
 (clockwise)

At every instant the vertical components cancel and the horizontal components add up, giving the pulsating flux $\phi_m\cos\omega t$.

Rotor behaviour

• The forward slip is $s_f = s$ and the backward slip is $s_b = 2 - s$, and the net torque is $T = T_f - T_b$.
• At standstill $T_f = T_b$, so the net torque is zero (not self-starting).
• Once the rotor is started in a direction, $T_f > T_b$ in that direction, and it accelerates to a speed slightly less than $N_s$.