Vibration Spectrum : Mixing Frequencies

When two frequencies are present in a machine and a cause and effect relationship is not present, the high frequency will be riding the low frequency and the Fast Fourier Transform (F’FT) will yield spectral lines at frequency one and frequency two. If there is a cause and effect relationship and the two frequencies can mix together, the result is amplitude modulation. Without getting mathematical, amplitude modulation is a time varying amplitude. Amplitude modulation is caused when the equipment has some form of non linearity. This non linearity permits the amplitude of the two signals to add together when the signals are in phase, or subtract when the signals are out of phase. With amplitude modulation, the carrier frequency will be the frequency with the highest amplitude. The envelope of the varying amplitude will be the difference between the two frequencies. An FFT of these signals can yield spectral lines at frequency one, and frequency one plus and/or minus frequency two.

For example, suppose gear mesh frequency is modulated by gear speed, gear mesh frequency is 1200 Hz, and gear speed is 20 Hz. An FFT of this signal would then yield spectral lines at 1200 Hz, 1200 + 20 = 1220 Hz, and/or 1200 – 20 = 1180 Hz.

Descriptions of these frequencies are:
1. 1200 Hz is gear mesh frequency.
2. 1220 Hz is gear mesh frequency plus gear speed. This is a sum frequency.
3. 1180Hz is gear mesh frequency minus gear speed. This is a difference frequency.
4. The difference between 1200and 1220Hz, or 1200and 1180Hz is 20 Hz, and this is also a difference frequency.
5. The source of excitation, or the problem shaft or gear is usually expressed as a difference frequency.