The Relationship Between The Time Domain And The FFT: Amplitude Modulation (Sidebands)

Remember this plot from the first page in this section ? Well, Figure 2 shows a computer generated plot that is somewhat similar:

Figure 1 - Actual Time Domain Signal Figure 2 - Computer Generated Time Domain Signal

You can see the low frequency (usually 1x rpm) cycle still occurring but this shape looks somewhat like an Angel Fish. This shape is typical of an amplitude modulation. Let's zoom in on the computer generated signal to get a clearer picture of what is happening.

Figure 3

Figure 3 shows only a bit more than a single one of the low frequency cycles. It is clear that the high frequency signal (the gear mesh amplitude) is increasing and decreasing in amplitude at a rate of once per shaft revolution. Figure 4 shows the two signals involved separated:

Figure 4

This represents what we were discussing before - a modulation of gear mesh amplitude once per shaft revolution due to a gear problem. The amplitude varies significantly at a rate of once per revolution. How does the FFT handle amplitude modulation ? Figure 5 shows you:

Figure 5

Figure 5 shows a peak at 1x rpm and a peak at gear mesh frequency (GMF) with smaller peaks surrounding it. It you could measure the frequencies involved, you would see that the smaller peaks are equally spaced around the large peak - the separation is equal to the frequency of 1x rpm. There may be a series of these peaks called sidebands around the gear mesh frequency. This series of peaks are what would mathematically cause the amplitude to go up and down (modulate) as the peaks go in and out of phase with one another. The difference between sidebands and other noise around a peak is the equal spacing (1x rpm in this case). Peaks that are not equally spaced are most likely not sidebands.

Peaks on the higher frequency side of the large peak will be located at GMF + 1x rpm, GMF + 2x rpm, GMF + 3x rpm, etc. On the low frequency side of GMF, the peaks will be located at GMF - 1x rpm, GMF - 2x rpm, etc. The spacing of the peaks is the key indicator in where the problem lies. The spacing at 1x rpm indicates the gear running at that frequency (speed) is the source of the problem.

Although not nearly as common as harmonics, sidebands are critically important to learn to recognize for a couple of reasons: Sidebands always indicate a problem (amplitude modulation is never "normal"). Sidebands are only generated by three types of problems: Gear-related problems Bearing-related problems Electrically-related problems Sidebands can be significant at very low amplitudes (their mere presence can be significant).  Sidebands should be analyzed on a logarithmic scale (as opposed to a linear amplitude scale) so the low-amplitude peaks can be detected.

The Addition Of Sidebands Is The FFT's Explanation Of The Presence Of Amplitude Modulation