I have recently obtained data from a Turbo Fan.
The motor is directly coupled to the overhung fan, which is supported on one side by a double sleeve bearing set.
The motor runs at 2900 rpm and multiple sidebands "appeared" or increased their amplitude around the first 6 motor orders, being the fundamental speed the one with the least of them. If I center frequency one of these orders (2896 x 1,2,3,..6), sidebands of 41 rpm surround these orders in a "christmas tree" type of shape and with amplitudes ranging from 0.005 to 0.03 in/s.There is minimum amp fluctuation and most likely due to the process flow.The digital display accusses a change in current from 563 to 567 at 80% load. The VFD output display shows 2915 output rpm and the actual speed measured by a strobe light and a second digital display by the motor show 2896 rpm. The spectrum also shows the speed to be 2896 rpm.
Is it 2915 minus 2896 the motor slip or the VFD output is not properly calibrated? There's no detectable pole pass frequency in the spectrum, but a audible humming noise is perceived mainly on the motor. Analog amp meter shows little to no change or deflection. How do I determine the motor slip on a VFD application wich is never running at 60 HZ without disturbing the operations? Please comment.

I don't know for sure but isn't it possible that your vfd output is showing the syncronous speed associated with the output frequency.

Then assuming this is a 2-pole, your pole pass frequency would be (2915-2896)*2=38 rpm - not too far from the 41 rpm sidebands you mentioned.

For severity, I always like to look at current spectrum instead of vibration.

To rule out process oscillations, that may be a challenge. I think process oscillations are more likely to show up as sidebands in current than vib, but I guess not unheard of in vib. Observing parameters during a change in load may help give a clue. Also look for oscillation at that frequency in the system flows and pressures and valves.