Alan's article is correct in how it relates the frequencies generated by the bearing defects to the "orders of rotation" of the shaft. Is that the kind of information you are seeking? There is a signal processing method known as "order tracking" which incorporates a reference signal into the processing of the vibration data. This is typically a 1XRPM pulse that is used to create a "phase locked loop". The instrument then generates a sample clock based on this pulse train. The spacing of the pulses vary with the changing speed of the shaft and so does the sample rate used for sampling and digitizing the signal from the vibration sensor. The machine's variation in speed also results in vibration that varies in frequency. A time block of digitized data, that is acquired conventionally, with a fixed sample clock controlling the rate at which the data is sampled, is fine when the machine is operating at a fixed speed, but when the speed varies and this digitized data is transformed to the spectrum, the energy from each spectral peak may be "smeared" over several lines of resolution. This has the effect of lowering the amplitude of the peak beacuse the energy is spread into several FFT "lines" or bins. When the sample rate is varied over time with the shaft speed actually controlling the sample rate the resulting Fourier Transform has the energy from each frequency contained within a single FFT line, so all the amplitude is represented. This is true of the frequencies that are between the orders of rotation, as well, such as bearing defect frequencies. If you can see the true amplitude generated by the defect you have a much better idea of the severity of the defect.
We used to use this technique on Navy shipboard turbine driven pumps and blowers because their governors often did not control speed very precisely. Rolling element bearings did not always create a lot of energy when they have defects and if the speed variations during data acquisition created "smearing" the bearing defects were sometimes lost in the noise. This was in the days when all the data was tape recorded before being "processed" so we needed all the help we could get. Even though our real time analyzers had 72 db dynamic range, the analog tape recorders only had about 40 dB dynamic range, so it was important to preserve any of the amplitude near the noise floor that we had, and "Order Tracking" helped us do that. The data was used for planning an overhaul period that was 6-12 months in the future so detecting a developing bearing fault was important.
When using this technique and setting up for data acquisition you define the FFT range in number of "orders" rather than a frequncy range like 0-1000 Hz or 0-60,000 CPM. Typically, you would define an FFT range as 0 - 20 orders and maybe a second higher frequency range such as 0 - 60 orders, depending on the characteristics of the machine. The problem was that you need to have the tach signal, so setup time to get the data was longer. Sometimes when we could not record a tach signal we could generate one from the vibration signal if the 1X RPM vibration signal was strong enough and we band-pass filtered it so that the 1XRPM signal actually appeared to the instrument to be a pulse train that it could track in the tach input channel.
I hope this helps for your application.
Skip Hartman