---
title: "Reasons: slot numbers and speed vs size"
subject: "Electric Machine Design"
chapter: 4
key: "semester_5/electric_machine_design:slot-and-speed-reasons"
source: https://www.bctengineer.com/q/semester_5/electric_machine_design/slot-and-speed-reasons
site: BCT Engineering
---

# Reasons: slot numbers and speed vs size

Electric Machine Design · Chapter 4: Three phase induction motor design

- Asked in: 2075 Chaitra, 6 marks; 2070 Asar, 3x2 marks (asked 2 times)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machine_design/slot-and-speed-reasons
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machine_design/chapter-4

## Question

Give reasons for the followings: i) Stator slots should never be equal to the number of rotor slots ii) The size of induction machine will be small if it is designed with higher speed for the same output.

## Short answer

i) Equal stator and rotor slots cause magnetic locking (cogging), preventing starting and causing vibration and noise. ii) Higher speed reduces D2L for the same output because volume is inversely proportional to speed, yielding a smaller, lighter machine.

## Answer

#### i) Stator slots should never equal rotor slots
- If $S_s = S_r$, every rotor tooth lines up with a stator tooth at the same time. The reluctance of the magnetic path is then minimum at these positions and the rotor tends to stay there.
- This strong alignment torque is called **cogging** or **magnetic locking**. The locking torque can exceed the starting torque, so the motor may fail to start, especially at reduced voltage.
- Equal slot numbers also give strong slot-harmonic torques, which cause noise and vibration.
- Therefore $S_r$ is always made different from $S_s$ (and differences like $S_s - S_r = \pm P$, $\pm 2P$, $\pm 5P$ are also avoided).

#### ii) A higher-speed machine is smaller for the same output
From the output equation:
$$
Q = C_0 D^2 L n_s \;\Rightarrow\; D^2 L = \frac{Q}{C_0 n_s}
$$
- For the same output $Q$ and the same specific loadings ($C_0$ fixed), the active volume $D^2L$ is inversely proportional to the synchronous speed $n_s$.
- A higher speed means fewer poles. The same power is produced with less torque ($T = P/\omega$), and torque decides the size of the machine.
- Example: a 4-pole motor ($n_s = 25$ rps) needs only half the $D^2L$ of an 8-pole motor ($n_s = 12.5$ rps) of the same rating.
- Hence a high-speed machine is smaller, lighter and cheaper.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why should stator and rotor slots never be equal?
   A. Equal slots reduce the air gap flux
   B. Teeth align together, giving strong cogging or magnetic locking and slot-harmonic torques
   C. Equal slots increase the rotor resistance
   D. The rotor would run faster than synchronous speed
   Answer: B. With Ss = Sr, all teeth align at the same time, so reluctance is minimum there and the rotor tends to lock, possibly failing to start. (Key point: Equal slot numbers)

2. From Q = C0 D^2 L ns, why is a higher-speed machine smaller for the same output?
   A. D^2L is proportional to ns
   B. D^2L is independent of ns
   C. D^2L = Q/(C0 ns), so volume is inversely proportional to speed
   D. C0 falls as speed rises
   Answer: C. For fixed Q and loadings, the volume D^2L falls as ns rises; the torque (P/omega) is lower and torque decides size. (Key point: Speed and size)

3. A 4-pole motor (25 rps) compared with an 8-pole motor (12.5 rps) of the same rating needs what D^2L?
   A. Twice that of the 8-pole
   B. The same
   C. Four times
   D. Half that of the 8-pole
   Answer: D. D^2L is inversely proportional to ns, and 25 is twice 12.5, so the 4-pole needs half the volume. (Key point: Worked comparison)

## Related in Electric Machine Design

- [Unequal stator/rotor slots and output equation](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aslots-unequal-output-equation) — Electric Machine Design, chapter 4
- [Selection of number of stator slots](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Astator-slot-number-selection) — Electric Machine Design, chapter 4, asked 4×
- [Rotor slots and turns, 90 kW motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Arotor-design-90kw-slip-ring) — Electric Machine Design, chapter 4
- [2.2 kW cage motor designed for best power factor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adesign-2-2kw-best-power-factor) — Electric Machine Design, chapter 4, asked 2×
- [Choice of number of armature slots](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-armature-slots-selection) — Electric Machine Design, chapter 5

## Related in other subjects

- [Synchronous speed and why rotor lags stator field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Asynchronous-speed-rotor-direction-slip) — Electrical Machines I, chapter 5
- [Synchronous speed; rotor follows rotating field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Asynchronous-speed-rotor-direction) — Electrical Machines, chapter 5
- [3-phase induction machine at slip 0.05](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Ainduction-machine-3phase-numerical) — Basic Electrical and Electronics Engineering, chapter 2
- [Delta induction motor: slip, rotor emf, turns ratio](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aim-delta-440v-1440rpm-rotor-emf) — Electrical Machines, chapter 5, asked 2×