Any vibration signal may be analyzed into amplitude and phase as a function of frequency. The phase represents fifty percent of the information so it is most important to measure phase for vibration monitoring. Most vibrations on a rotating machine are related to the rotational speed so it is clearly important to have a measure of the speed, either directly or as a once per revolution tacho pulse. A question sometimes arises as to whether a once per revolution tacho reference signal is needed to measure phase. Is it possible to get phase if we only have a speed signal? This note gives some insight into those questions.
Actually the question that should be asked is – “Can we measure a meaningful phase, for use in vibration monitoring, if we only have a speed signal as well as the vibration signals?”
Suppose we have a vibration monitoring system that provides shaft speed, but does not have a tacho pulse. Knowing the shaft speed means that we know the duration of each revolution. Thus we can ensure we can accurately acquire data over a complete number of revolutions. If we were acquiring hundreds of revolutions any end effects of including only part of a revolution would be very small. But if acquiring only a few revolutions then it is important to acquire an exact number of revolutions for best accuracy.
Often the available speed signal is an average speed over a period of time as it is used for instrument readout and perhaps in the main system speed control loop. That is, we do not know the exact speed corresponding to a short segment of data covering, say, eight complete revolutions. In principle, knowing only the average speed is not a problem. What we know is the approximate frequency so we can Fourier analyze the signal and search for the peak of the modulus versus frequency curve closest to the approximate frequency to identify the actual speed. Hence, we can select an exact number of revolutions. In this way, knowing only the speed, albeit only approximately, still allows one to avoid end effect problems.
If we have a segment from the continuous time signal, then of course it may be Fourier analyzed and this will give both an amplitude curve versus frequency and a phase curve versus frequency. But are these amplitude and phase curves obtained using a speed curve rather than a tacho useful for vibration monitoring? For the amplitudes the answer is “Yes”. For the phase the answer is “No”.
A ‘perfect’ vibration signal
Consider the example vibration signal (Figure 1) from a near perfect turbine running at 3000 rpm. In this case the entire vibration is at 50Hz only. As this is an unchanging ‘perfect’ system then both the amplitude and the phase will remain constant. We need to track the variations of amplitude and phase with time or speed. In either case, segments of the data would be taken at appropriate times. In the simpler case of constant speed operation then data is taken at regular time intervals. The results for the amplitude are shown in Figure 2.
As expected the amplitude for each segment is identical and we only have a response at one frequency. That is the amplitude (modulus) at each frequency is independent of the starting point in time from where the segment was taken. Now looking at the phase part (Figure 3) whilst there is a clear change occurring at 50 Hz, the three dimensional representation is more difficult to interpret. To simplify the situation the first order, which is at 50 Hz in this example, was extracted and is shown in Figure 4. It is clear that the phase is varying with time over a full ±180°. That is, the phase value is dependent on which point in the revolution is the start point. This then makes the phase, obtained with only a knowledge of the speed, unsuitable for vibration monitoring. Basically, one cannot tell if any phase change over time is due to a change in the turbine or just due to the arbitrary start point in the cycle.
It may be thought that another approach could be to narrow band filter (or use a tracking filter) to get the first order time history. One could then think of using one of the zero crossings of that signal as a consistent start point. However, if there has been a phase change in the first order we would never see it! Changes in phase at other orders tend to be sympathetic with each other. So when a fault is developing we are unlikely to see a phase change in the higher orders until the problem is so severe it causes significant changes in the makeup of the vibration signatures. This defeats the primary objective of a vibration monitoring system. In order to obtain a useful phase signal it needs to be related to a physically fixed reference point rotating with the shaft. This is provided by a once per revolution tacho pulse.
To illustrate this, the same analysis as above was carried out except that now the vibration signal was analyzed using the leading edge of the tacho signal as the start point.
In Figure 5 a section of the tacho signal is shown on its own and then overlaid on the vibration signal. The tacho signal in this example crosses the vibration signal at exactly the same point on each cycle. If the phase of the vibration signal were to change then its position relative to the tacho pulse would also change.
Extracting the first order modulus and phase, as before, gives the curves shown in Figure 6. The phase is now constant as it should be for such a signal. We can now observe the change in phase of each frequency or order with time or speed. The answer to the question “Can we measure a meaningful phase for use in vibration monitoring if we only have a speed signal as well as the vibration signals?” is “No”. Does this mean that the phase we measure without a tacho in other circumstances is worthless? Clearly the answer to this question is also “No”. What it can tell us is the relative phase of one frequency component with respect to the phase at another frequency at that time. This can be useful in structural vibration and occasionally in rotor dynamics, where it will indicate a change in shape of the waveform. If we do have a tacho with the rotating shaft then we can observe the absolute phase change at a frequency as well as the relative phase changes between frequencies.