--- title: "Single phase motor working; effect of air gap" subject: "Electrical Machines" chapter: 7 key: "semester_4/electrical_machines:spim-working-air-gap-effect" source: https://www.bctengineer.com/q/semester_4/electrical_machines/spim-working-air-gap-effect site: BCT Engineering --- # Single phase motor working; effect of air gap Electrical Machines · Chapter 7: Fractional Kilowatt Motors - Asked in: 2068 Magh, 5+3 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/spim-working-air-gap-effect - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-7 ## Question Explain the working principle of a single phase induction motor. What is the effect of air gap in the magnetic circuit? ## Short answer The pulsating field is equivalent to two counter-rotating fluxes; at start torques cancel, once running forward slip s, backward slip 2-s, forward torque dominates. Air-gap magnetizing current increases with gap, lowering power factor; gap is kept as small as mechanically possible. ## Answer #### 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. ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the starting torque of a plain single-phase induction motor, and why? A. Zero, since forward and backward torques cancel at standstill B. Maximum C. Positive, since only the forward field exists D. Negative Answer: A. Equal and opposite fields at s = 1 cancel. (Key point: Starting torque) 2. Why is the backward torque small once the motor runs? A. The backward field disappears B. Backward slip is 2 - s, so the rotor reactance is high and the current more reactive C. Backward slip is s D. The backward field is stronger Answer: B. The backward slip is near 2, so the rotor current is reactive and the torque small; T = Tf - Tb is positive. (Key point: Running torque) 3. How does the air gap length affect magnetising current? A. It decreases with a larger gap B. It does not depend on the gap C. It increases with the gap, since most mmf is spent on the air gap D. It is zero Answer: C. mmf = Hg lg, so a longer gap needs more magnetising current. (Key point: Air gap and magnetising current) 4. Why is the air gap kept as small as mechanically possible? A. To increase noise B. To reduce the speed C. To raise leakage reactance D. To get a low magnetising current and good power factor Answer: D. A large gap gives a high magnetising current and low pf, but too small a gap raises harmonic losses, noise and rubbing risk. 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