How to know if the bearing of induction motor is healthy or not?

I was rather impressed by a good quality acoustic (expensive!) analyser I used. Portable so can use on many items, as well as steam traps etc. We know the ball race frequency at certain speeds so it can detect inner or outer race failures etc. very comprehensive. I am not a specialist in this instrument, but my opinion is it can be earlier detection than other methods such as vibe or thermal, sometimes.

The simplest answer is actually two things.

1) Observe the bearing (and lubricant) temperatures. Are they starting to trend away from "normal" ... particularly upward? If so - there may be a problem.

2) Observe the acoustical sound of the bearing (using a very simple probe, like a wooden or steel dowel. or even a screwdriver). If it starts to sound different than normal, then things need to be examined more closely.

If it comes to having to take a more in-depth look at the bearings, the best thing is to use a vibration analyzer that will allow both waveform and harmonic amplitude/frequency measurement. You'll need to know the type of bearing, the bearing number (if not a sleeve bearing), and rotational speed of the shaft - as a minimum - to sort out what frequencies are of interest.