How to detect uneven air gap around a motor rotor? Will spectrum analysis be helpful and does it occur at any particular frequency?

Uneven air gap will show up at two times line frequency. Where I see it mostly is on two pole motors, 3600 RPM if it is 60 Hz. You might have to take high resolution to separate 120 Hz from two times turning speed. The higher the speed the smaller the air gap and the more sensitive a motor is to uneven air gap. Hence two pole motors are the most sensitive. It is not uncommon for two pole motors to have some two times turning speed and some two times line frequency. When this occurs, you will hear a pulsing or beat sound when the two frequencies come in and out of phase with each other.

Ronnie