Vibration : Time & Frequency Analysis

Accurate diagnosis of problems in rotating machines requires a thorough understanding of the time domain signal and the frequency domain spectra. Following are some of the reasons:

1. The time signal is a plot of amplitude versus time. This signal contains all frequencies, harmonics, and subharmonics. The phase relationships of these frequencies are also contained in the signal. Pulses, amplitude modulation, frequency modulation, truncation, and distortion are also present.

2. The frequency spectra are plots of amplitude versus frequency. These spectra contain frequency, harmonics, subharmonics, and sum and difference frequencies. The FFT produces the frequency spectrum from the time signal, based on electronic physics. However, during the process, some information is lost. For example, phase, true amplitude of pulses, nature of the pulses, bandwidth, and the various forms of modulation are not easily identified in the frequency spectrum.

3. A mechanical machine may not generate a fundamental plus harmonics in the same way as in the electronic world. However, a rotating machine does generate relatively linear signals when a linear problem exists, such as imbalance. A machine can generate a distorted signal as a result of a nonlinear problem. This distorted signal is a composite signal, as would be obtained after various frequencies and harmonics are combined.

4. For the above reasons, various time signals can produce the same frequency spectrum. This explains why the time signal must be considered. Costly errors in diagnostics and loss of credibility could occur if the time signal is not analyzed.

BASIC PHYSICS
 
All things in the universe obey the basic laws of physics. Vibration signals from rotating machinery must obey these same basic laws of physics. This is why we can take data from either side of a motor and receive the same results. (Some slight variations can occur in nonlinear systems because of transfer functions.) In a pure linear system, data taken in different directions around a motor should be the same, except for phase.
a sine wave is the plot of a circle against time. All complete circles contain 360 degrees and all complete sine waves contain 360 degrees. The phase of a signal can be anything from 0 to 360 degrees, depending on the reference point .
Before analyzing the time signal, an understanding of how frequencies add and subtract, and the effects of the phase relationships is required. It may be helpful to remember that multiplication is a series of additions, and division is a series of subtractions.

a signal taken from the horizontal direction with a signal taken from the vertical direction, one signal should lag the other signal by 90 degrees. This is because the positions from horizontal to vertical are 90 degrees apart on the machine. This phase relationship should also apply to other data taken at various points around the machine.

We can start taking data at any instant of time or location, and it does not make any difference. The reason for this is the phase relationship between the fundamental and other frequencies,or a once-per-revolution marker, will remain constant.

These frequencies will add and subtract, depending on the phase relationship. When the signals are in phase, the amplitudes will add. This is why positive side bands occur on some frequencies. When the signals are out of phase, they will subtract. This is why negative side bands occur. This also explains how and why truncation occurs.

In rotating machines, several different problems can generate the same frequency spectrum. For example, a machine that is loose can generate a fundamental and the second harmonic. A machine that has a bent shaft can also generate a fundamental and the second harmonic. The only way to determine which problem exists is to determine the phase relationship between the fundamental and the second harmonic. If these two signals are in phase, the shaft is bent. If the two signals are out of phase, the machine is loose. Currently, the only way to determine this phase relationship is with the time signal.