Reasons: slot numbers and speed vs size

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.