Spectrum from a belt-driven machineCepstrum Terminology
The term "cepstrum" is simply "spectrum" with the first four letters in reverse order. The various parameters of the cepstrum have been given somewhat whimsical names, summarized below:
|
Spectrum |
Cepstrum |
|
Frequency
|
Quefrency
|
|
Harmonic
|
Rahmonic
|
|
Magnitude
|
Gamnitude
|
|
Phase
|
Saphe
|
|
Filter
|
Lifter
|
|
High-Pass
|
Short-Pass
|
|
Low-Pass
|
Long-Pass
|
|
Fundamental
|
Mundafental
|
Quefrency is the horizontal axis of the cepstrum, and has the units of periodic time.
Rahmonics are cepstral components that are spaced at equal increments of time.
Following are the spectrum and cepstrum plots of the vibration signature of a belt-driven machine. In the spectrum, the harmonic cursor is set to 8.35 Hz, which is the fundamental belt frequency. Note that many harmonics are highlighted. The second figure is the cepstrum of this spectrum. The cursor is set at 0.119 seconds, which is the period of the 8.35 Hz component in the spectrum. Note how much simpler the cepstrum is compared to the spectrum. The peaks at 0.119 sec and rahmonics of 0.119 sec indicate a strong periodicity in the spectrum; i.e. a distinct harmonic series.
If this machine were to be monitored in a predictive maintenance program, its spectra would be collected and trended over time. To determine the belt condition, the levels of the various harmonics of belt frequency would need to be noted, for the level of the fundamental is not a good indicator of belt condition.
If the cepstrum were used for the same type of trending, only the component at 0.119 sec would need to be considered, since its level is dependent on the levels of all the harmonics of 8.35 Hz in the spectrum.
Spectrum from a belt-driven machine
Cepstrum from a belt-driven machine
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