Single phase motor working; effect of air gap

Working principle of a single-phase induction motor

A single-phase induction motor has a stator with a distributed single-phase main winding and a squirrel-cage rotor.

1. The ac supply in the stator winding produces an alternating (pulsating) flux $\phi_m\cos\omega t$ along a fixed axis. By the double field revolving theory, this is equivalent to two rotating fields of $\phi_m/2$, rotating at synchronous speed $N_s = \frac{120f}{P}$ in opposite directions.
2. The field induces emfs and currents in the closed rotor bars (transformer action). At standstill, the forward and backward fields produce equal and opposite torques, so the starting torque is zero. A starting aid (auxiliary winding, capacitor or shaded pole) provides a rotating field at starting.
3. Once the rotor rotates in some direction at slip $s$, the forward field has slip $s$ and the backward field has slip $2-s$. The rotor reactance to the backward field is high and its current is mostly reactive, so the backward torque is small. The net torque $T_f - T_b$ is positive in the direction of rotation.
4. The rotor accelerates to near synchronous speed (slip 3 to 8 %). An equivalent explanation (cross-field theory): the emf induced in the rotor by its rotation produces a quadrature flux that, together with the main flux, gives a rotating field.

 phi (pulsating)  =  phi_f (CCW) + phi_b (CW)
 Rotor at standstill: Tf = Tb -> T = 0
 Rotor running: Tf > Tb -> T > 0

Effect of air gap on the magnetic circuit

• The working flux of an induction motor is set up by the magnetising current drawn by the stator. Most of the mmf needed is spent on the air gap, so the magnetising current increases with air-gap length (mmf $= H_g l_g$ and $H_g = B/\mu_0$).
• A large gap therefore gives a large magnetising current, and so a low power factor, lower efficiency, and greater copper loss in the stator.
• A larger gap does have some benefits: lower leakage reactance (better overload capacity), less unbalanced magnetic pull, and lower tooth-pulsation losses and noise.
• On balance, the air gap is kept as small as mechanically possible (typically 0.3 to 0.5 mm in small motors) to get a low magnetising current and a good power factor. Very small gaps, however, increase the harmonic (tooth) losses, noise and the risk of rubbing.