We can identify the problem at hand better by some analysis. There is a difference between
- Vibration detection
- Vibration measurement
Measuring can solve the problem of detection. But mere detection cannot solve measurement! We can define these two approaches like this-
Detection can be about a single anomaly of pulse or a set of frequencies, above the ideal (inherent) noise of a balanced shaft rotor.
Measurement is about so many other things. RMS amplitude, THD- total harmonic distortion, mean, mode, std/variance, Median frequency. Or PSD- power spectral density of balanced shaft vs. unbalanced shaft.
Assuming you have either a dedicated electronics setup to measure these (Like an analog section, ADCs, pulse counters, timers and a micro controller) or a NI hardware with LabVIEW etc., the following approach may work.
(Not touching the angular domain mathematics here. Your 1PPR tacho may not give angular position)
In your test setup /script, split the measurement setup into these parts-
Up-ramp rotation speed from 18000rmp (300Hz pulse) to 150,000rmp (2500Hz pulse). With an unbalanced shaft, the relation between input RPM command and Tachometer will not be aligned. There will be non linearity, drift and jitters. One would first measure this relationship.
The main parameter is Jitter. This is the amount of deviation from the ideal position. You should determine the distribution of this jitter next. If this falls into random distribution, find what kind. (Gaussian etc.). Also determine if there is a drift. This will be difference of slope between ideal Input-RMP against Output Tachometer graph, and what is measured. Also examine if there is a non-linearity and if that is repeatable.
Repeat the same step with down-ramp from 150,000rpm(2500Hz) to 18,000rmp(300Hz).
Also during the ramp, acquire the noise signal from the vibration transducer. Ideally few tens multiple higher bandwidth than the max rpm.
These two together may give some insights into the non-linear model.
Once you know the RMS jitter value, you may compensate it for the "Time window" of the vibration transducer to do an FFT, or any other spectral measurements.