Enveloping Spectra Plots:
How Does Impact Energy Affect The FFT ?
Let's review how the FFT process works by examining the following computer generated signal:

Figure 1 - Shows Approximately 9 Shaft Rotations (470 msecs)
The conventional FFT process focuses on sinusoids - namely, mathematically calculating what series of simple sinusoids (signals) were combined to generate the signal we see here. What can we see from the above plot ?
  • A low frequency sinusoid that shows about 9 cycles across Fig. 1. That is the 1x rpm signal.
  • Some frequency modulation of that signal (compare the positive going side of the wave to the negative going side of the wave).
  • A large number of spikes, or impacts, that occur across the plot and appear to vary somewhat in intensity (the size of the spike).
Figure 1 is a typical example of a plot that an analyst might collect - 9 rotations of a shaft. But although the 1x sinusoid is fairly clear, the impacts are not. Let's zoom in a bit.

Figure 2 - Shows Approximately 2 Shaft Rotations (115 msecs)
Cutting the displayed sample to just over 115 msecs (about 2 shaft rotations), we can now clearly see:
  • The frequency modulation of the 1x rpm signal.
  • The ringdown frequency of the impacts.
  • If we simply count the number of impacts in one cycle (from 30 - 80 msecs, for instance), we would find about 4-5 per shaft revolution (or "x RPM").
It should be clear to us as analysts that this is an impact occurring and investigation of the period involved (time between impacts) should lead us to a diagnosis. But more often than not, the analyst will not be using the time domain - they will be using FFT analysis. What does an FFT performed on this signal generate ?

Figure 3 - FFT Generated From Signal In Figure 1
  • 1x, 2x and 3x rpm peaks. These are probably due to the frequency modulation present.
  • A series of peaks at high frequencies that are spaced about 5400 cpm apart.
  • The absence of a peak at or near 5x rpm - the impact frequency. This is because there is no sinusoidal motion associated with the frequency of the impacts - only the ringdown frequency that results from the impacts.
But where do the peaks between 31,000 and 65,000 cpm come from ? How does the FFT process come to "see" them ?