## Do Missing Tachometer Pulses Mean The End Of The Road For Your Test?

Creating a good quality tachometer signal is one of the hardest parts of analyzing rotating machinery. So what happens if we have missing tachometer pulses? The data looked great until we tried to perform some in-depth torsional vibration analysis. And now we no longer have the component or vehicle to retest it.  Do we have to scrap the whole test? Was all that time wasted? Not necessarily…

The essential method of determining angular vibration is to initially determine the instantaneous speed, shown as a blue curve in the graph below (Figure 1), and the average speed over several revolutions, shown on the overlayed green curve below. The particular example here was based upon a tachometer signal with 90 pulses per revolution. Typically 15 revolutions is sufficient to form a good estimate of the local average speed; this corresponds to 1350 tachometer pulses.

Figure 1: Instantaneous speed with average speed

The detail speeds are clearly erroneous around the 30 and 50 seconds times. If we were to use the existing tachometer for vibration analysis then clearly any angular vibration would be wrong around those times. It is interesting to note that the ‘poor tacho’ problem occurs in a particular narrow speed band, which could be indicative of a mounting problem.

Looking at the tachometer signal in detail shows that there are several missing tachometer pulses in these regions. One such example is shown below in Figure 2.

Figure 2: Example tacho with missing pulses

It is necessary to clean up the tachometer and insert the missing tachometer pulses appropriately. To do this using DATS we use the Tacho Ideal Equivalent Module in Rotating Machinery ? Tacho Analysis (as shown in Figure 3). What this module does is to create a very clean “ideal” tachometer whose edges coincide as far as possible with those of the acquired signal.

Figure 4: Analysis parameters for “Tacho Ideal Equivalent”

The module parameters are as shown in Figure 4 so let us explain these. The first parameter, Tacho Pulses per Rev, is actually redundant (it is present for historical reasons) so we set it to unity. The second parameter, Threshold Level, is set to the crossing level we wish to use on the tacho. The special case of NVN, which in DATS speak means a Non Valid Number, is telling the software to choose the optimum level. The Threshold Tolerance and % Hold Off Time parameters allow working with noisy tachos, but as we have a clean input tacho then these parameters are set to zero, which essentially turns them off. The Use Tacho Repair Function is obviously what we want to do, so it is turned on (True). The Mark Space Ratio simply says how wide should the output pulses be as a fraction of the current period. Typically 0.5 is fine. The final parameter, Output Sample Rate, is very useful. First if it is set to zero, as shown above, then the constructed Ideal Equivalent Tacho will have the same sample rate as the input tachometer.

Figure 5: Fragment of tacho signal

Figure 6: Tacho fragment expanded further

Now the accuracy of a crossing in time is ultimately specified by the sample rate as that gives the step between successive values. So consider the fragment of tacho shown in Figure 5, which was sampled at 1000 samples per second. That is successive samples, as indicated by the + symbol, are 1 millisecond apart. Expanding even further (Figure 6) shows the tachometer edge is somewhere between 2.000 and 2.001 seconds. A reasonable choice for the threshold level would be zero which would estimate the tachometer crossing at 2.0005, definitely not at 2,000 or out 2001 seconds. But if we stay at 1000 samples per second that is the only time points available in the digitised signal. Setting to say 10000 samples/second will give much better accuracy as illustrated in Figure 7. The software uses a bandlimited resampling algorithm to better determine the waveform. We would also note that when it comes to estimating the crossing time a further increase in accuracy is achieved by linearly interpolating between the two points which straddle the crossing level.

Figure 7: Interpolated tacho signal

The result is a tachometer which matches the edge crossing of the pulses and with the aid of further sophisticated software fills in the missing pulses as illustrated below.

Figure 8: Repaired tacho signal

The proof of the pudding, however, is in the eating, or in our case, in usage. So we now use this modified tachometer to determine the angular vibration of the entire signal. The DATS worksheet to do this is shown in Figure 9. The worksheet also analyses the first 27 seconds of the original signal prior to the part where tacho pulses were missing.

Figure 9: A DATS worksheet to perform analysis

The angular vibration found for the entire signal is shown in Figure 10.

Figure 10: Angular vibration of entire signal

The angular vibration of the first 27 seconds of the original signal is also calculated by the work sheet and provides a comparison between using the original tachometer and the ideal equivalent one. This is shown in Figure 11.

Figure 11: Angular vibration of first 27 seconds of original signal

Overlaying the two sets of angular displacement indicates very good agreement as can be seen in figure 12.

Figure 12: Comparison of results from original and reconstructed tacho

Expanding to look in detail (Figure 13) shows the two results are, for all practical purposes, identical.

Figure 13: Expanded view of comparison

The matching is not exact everywhere due to the presence of very low frequency trends as shown in Figure 14. But note that the amplitudes of the individual ‘waves’ are still very, very similar. Order extraction will therefore be reliable.

Figure 14: Small discrepancies due to low frequency trends

Figure 15: Angular displacement calculated with reformulated tacho

There were missing pulses in the original tachometer signal at 30.469 seconds, and these were reformulated in the Ideal Equivalent version. Looking at the calculated angular displacement around this time (Figure 15) shows no unusual characteristics.

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#### Dr Colin Mercer

Chief Signal Processing Analyst at Prosig
Dr Colin Mercer was formerly at the Institute of Sound and Vibration Research (ISVR), University of Southampton where he founded the Data Analysis Centre. He then went on to found Prosig in 1977. Colin retired as Chief Signal Processing Analyst at Prosig in December 2016. He is a Chartered Engineer and a Fellow of the British Computer Society.

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