--- title: "1-phase IM principle; air gap effect" subject: "Electrical Machine" chapter: 7 key: "semester_4/electrical_machine:single-phase-im-principle-air-gap" source: https://www.bctengineer.com/q/semester_4/electrical_machine/single-phase-im-principle-air-gap site: BCT Engineering --- # 1-phase IM principle; air gap effect Electrical Machine · 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_machine/single-phase-im-principle-air-gap - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/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 A single-phase winding produces a pulsating field, equivalent to two counter-rotating fields. At standstill net torque is zero, so a starting winding creates a rotating field; once running, forward torque dominates. The air gap is made small to limit magnetising current and improve power factor, but not too small to avoid rubbing and noise. ## Answer #### Working principle (5 marks) A single-phase induction motor has a stator with a single (main) winding on a laminated core, and a squirrel-cage rotor. 1. When the winding is connected to a single-phase a.c. supply, it produces a pulsating field along a fixed axis, φ = φ_m cos ωt. This field alternates but does not rotate. 2. By the double revolving field theory, this pulsating field is equal to two fields of magnitude φ_m/2 rotating in opposite directions at N_s = 120f/P. 3. **At standstill** the two fields give equal and opposite torques on the rotor, so the net starting torque is zero. The motor is not self-starting. 4. **With a starting arrangement** (an auxiliary winding in series with a capacitor or a resistance, or a shading coil) a rotating field is produced at starting, and the rotor accelerates. 5. **Once running** in one direction, say forward, the slip with respect to the forward field is s and with respect to the backward field is 2 − s. The forward torque is larger than the backward torque, and the net torque is T = T_f − T_b. The rotor accelerates toward N_s but stays below it. The auxiliary winding is then cut out by a centrifugal switch, and the motor runs on its main winding alone. 6. Compared with a three-phase motor of the same size, the output is lower (about 60 %), because the backward field reduces the torque, and the efficiency and power factor are also lower. #### Effect of air gap (3 marks) The air gap of an induction motor is the non-magnetic part of its magnetic circuit. - Nearly all the magnetising current is needed to set up flux across the air gap, whose reluctance is far larger than that of the iron. So a **large air gap** needs a **large magnetising current**, which lowers the power factor, increases the copper loss and so lowers the efficiency. - The single-phase motor already has a low pf because of the backward field, so the air gap is made as **small as mechanically possible** (about 0.3 to 0.8 mm for small motors) to keep the magnetising current low and the pf high. - A very small air gap increases noise, tooth (harmonic) flux pulsations and mechanical problems (rotor rubbing, effect of bearing wear). A larger gap reduces the zig-zag leakage reactance (improving the overload capacity) and allows greater mechanical tolerance. - The air gap is therefore a compromise: small to improve the pf, but large enough for mechanical safety and lower noise and harmonics. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A single main winding on a.c. produces which kind of field? A. A rotating field of constant magnitude B. A pulsating field along a fixed axis that alternates but does not rotate C. A constant d.c. field D. A field rotating at 2 N_s Answer: B. phi = phi_m cos(wt) stays on a fixed axis and only alternates in magnitude and direction. (Key point: Nature of the single-phase field) 2. Once running forward with slip s, how are the slips and torque related? A. The slips are s and 2 - s, T_f > T_b and T = T_f - T_b B. Both slips are s and T = T_f + T_b C. The slips are s and 1 - s and T = 0 D. The slips are 2 - s and 2 - s and T_b > T_f Answer: A. The backward field has slip 2 - s, so its torque is smaller, and the net torque is T_f - T_b. (Key point: Running torque) 3. Why does a large air gap lower the power factor of an induction motor? A. It needs a large magnetising current because the air gap reluctance is far larger than that of iron B. It reduces the rotor resistance C. It increases the iron loss only D. It reduces the supply voltage Answer: A. Almost all the magnetising current sets up flux across the air gap, so a larger gap needs more of it, which lowers pf and efficiency. (Key point: Air gap and magnetising current) 4. Why is the air gap not made extremely small? A. It would lower the power factor B. It would raise noise, tooth harmonics and risk rotor rubbing and bearing wear C. It would increase the leakage of the rotating field greatly D. It would make the motor self-starting Answer: B. A very small gap causes noise, harmonic flux pulsation and mechanical problems, so the gap is a compromise. (Key point: Air gap compromise) ## Related in Electrical Machine - [Single phase motor working; effect of air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aspim-working-air-gap-effect) — Electrical Machines, chapter 7 - [Construction and working of 3-phase induction motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-motor-construction-working) — Electrical Machines I, chapter 5 - [Operating principle of 3-phase induction motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-motor-operating-principle) — Electrical Machines I, chapter 5 - [Current for flux in cast steel series circuit with air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Acast-steel-series-circuit-airgap-200turns) — Electrical Machines I, chapter 1 - [3-phase IM principle; speed less than sync](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Athree-phase-im-principle-slip) — Electrical Machine, chapter 5 ## Related in other subjects - [Single phase IM principle, torque-slip and starting](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asingle-phase-principle-torque-slip) — Electric Machines II, chapter 3 - [Effect of too wide air gap in induction machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Awide-air-gap-effects) — Electric Machine Design, chapter 4 - [Factors for air gap length in induction motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aair-gap-length-factors) — Electric Machine Design, chapter 4, asked 4× - [DFRT and equivalent circuit of single phase IM](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Adfrt-equivalent-circuit) — Electric Machines II, chapter 3