FFT of Loose Gear in a Governor Pump

What's the question?

Along with a clear question, it would be nice to know what this FFT analysis came from. Is this from the motor electric power signals from a variable frequency drive, a hall sensor used for commutation of the brushless DC motor, a microphone picking up the acoustic signature of this pump or is this from a hydrophone upstream or downstream of this pump in the pumped media?

Number of teeth? RPM ? pump design? Bearings, type dimensions, number of rolling elements ? What was measured : accelerations? pressure ? sound ? speed?

If you want an answer then you have to give an input.

Or may be it is a picture to show that you obtained results and found explanations ?

If your sampling rate isn't an even multiple of the frequency you're trying to measure, your signal (GMF) will fall between frequency bins. I think that is what you are seeing where it looks like your lower sideband has more energy than the upper. Also, sidebands are caused by the discontinuities at the edge of the block of data you are feeding into your FFT. Windowing (hanning, hamming, etc.) is used to minimize this.

If you had an encoder wheel on the pump shaft that you could use to synchronise the sampling with the rotation with the number of samples per rotation the same as the FFT size, I think the results would be improved.