46 Estimation of Instantaneous Speed for Rotating Systems: New Processing Techniques 529 Combined RPM estimate skipping 40 pulses Combined RPM estimate skipping 40 pulses Instantaneous speed (rpm) Instantaneous speed (rpm) 2.75 2.54 2.52 2.5 2.48 2.46 2.44 2.42 15.24 15.245 15.25 15.255 15.26 15.265 15.27 2.7 2.65 2.55 2.45 15 15.5 16 16.5 17 17.5 18 2.4 2.5 2.6 Time(sec) Time(sec) x 10 4 x 10 4 x: 15.25 Y: 2.482e+04 x: 15.26 Y: 2.481e+04 Amplitude Time a b c Fig. 46.10 (a) Combination technique for the nth pulse estimates, (b) combined instantaneous RPM curve and (c) reduction in fluctuations with combination curve. Vertical bars denote the time instances to which the RPM has been assigned and the small explosions denote the time instances of zero crossings; Different colors represent different initiating pulses Fig. 46.10 has a superior signal to noise ratio as compared to the raw estimate as shown in Fig. 46.7. Fitting a spline through this curve would be numerically much easier and physically more compatible than through the raw estimate. For averaging the different estimates, the RPM values have to correspond to the same time instances. This can be achieved by simply taking the time points associated with one estimate as a reference (for convenience the estimate starting from the 1st pulse) and then interpolating all other curves to the RPM values at the time instances corresponding to this reference vector. This is shown in Fig. 46.11. The function ‘spline’ can be used to do this in MATLAB. Once this is done, all the curves can be averaged. The obtained curve did not require curve fitting to eliminate noise. Though the nth pulse approach gives superior signal to noise characteristics to that of the spline fit, there is an underlying assumption that during the period of every ‘n’ pulses throughout the span of the data, the speed remains fairly constant. This might not be the case throughout the data and for all data sets. For example, at low speeds and high slew rates, though the conventional estimate generates a smooth enough curve, a number of pulses would be skipped unnecessarily. This causes varying time resolution throughout the curve. Any smooth inflections might be missed as a result of the skipping. Figure 46.12 demonstrates the effect of varying time resolution. Almost 1 s worth of data is skipped in a total data record of 30 s with 40 pulses skipped when the speed is below 5000 RPM. At about 26,000 RPM, this time interval is 0.1 s. Thus, there is a need for an adaptive algorithm which takes this time resolution issue into account while skipping pulses. If the time resolution of the curve is maintained fairly constant throughout, the instantaneous RPM curve can be transformed from a function of angle of rotation of the shaft (pulses and corresponding times) into a function of absolute time with a defined resolution. This would also provide an optimization for the number of pulses to be skipped. Consider a system rotating at ‘R’RPM. Number of pulses recorded by tachometer per secondDR/60 Therefore, time period for each pulseD60/R Time interval between ‘ n’ pulsesD60 n=R
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