Every analyst develops their own process for analyzing vibration data. This is generally learned from others, being around to observe or communicate with, or from training the individual receives. Often, the person collecting the data will be the same person that analyzes the data. The process could include that during the data collection the person not only uses the vibration data collector but also collects physical data from their senses such as sound and smell to see what is going on with the equipment. They ought to look for material under the coupling guard to see if an elastomer coupling is shedding pieces, which may indicate misalignment; look at the oil level if possible for signs of oil leakage; look at the mechanical seal area to identify other leakage. Once data is collected one would generally look for anything outside of established alarm levels, look at the spectrum to see where the highest amplitude peak is at, look for other high amplitude peaks or groups of peaks and harmonic families, and look for sidebands around peaks to help in identifying the source. You would also look for the direction of the highest vibration. Examine the historical data too: you would want to look at the rate of change to determine how quickly failure is approaching. Also never, never forget to look at the time waveform as all data comes from the time waveform. I try to look at the time waveform in the raw units of the sensor as that can verify what you may be seeing in the spectral and give you a greater understanding of just how bad a problem you may be facing.
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Condition Monitoring, Maintenance Tips, Vibration Analysis by Gary James CRL