3 phase induction motor designs

For 3 phase motor designs, there is hardly any slot combination that will yield a perfectly smooth torque-speed curve. Keeping the following rules in mind will (mostly) avoid the combinations that tend to amplify magnetic noise, harmonics, and parasitic torques.

Let the number of stator slots be S, and the number of rotor slots be R, and the number of poles be P. Undesirable combinations occur when any of the following are true:

1. S - R = 0
2. S - R = +1 OR -1
3. S - R = +2 OR -2
4. S - R = +P or -P
5. S - R = +(P + 1) or -(P +1)
6. S - R = +(P + 2) or -(P + 2)
7. S - R = -(P * 2)
8. S - R = -(P * 5)
9. S - R = +(P * 3) or -(P * 3) .. or multiples of +/-(3 * P).

We know the stator should have an even number of slots to make winding easier - although for certain pole counts, it too can be an odd integer value. And except for a few cases, the number of rotor slots can be either even OR odd.

Then it comes down to the accuracy of the compound die or indexing die for the slot stamping.