When recently dealing with some vibration data from a runup of a pump, we observed some strange phenomena in the results.It turned out to be a classic case of amplitude modulation.
As shown in Figure 1 the original data looks a fairly standard run up time series. Figure 2 shows an associated tachometer signal and Figure 3 shows the speed curve calculated from the tachometer signal.
Waterfall analysis of the data, as shown in Figure 4, shows a number of interesting frequency components.
This shows a sharp central frequency with wider outer peaks. The presence of the outer peaks both above and below the central frequency suggests ‘side-bands’. The presence of side bands around a central frequency is a well-known phenomenon which we discussed further in – Bearing & Gearbox Vibration Analysis using Demodulation Techniques? (Part 1)
Figure 5 focuses on one particular frequency component in detail. The central, resonant frequency can be seen, with the side bands, and their harmonics, moving away from the central frequency on both the left and right-hand sides of the spectrum.
Sidebands are usually caused by amplitude modulation of a central carrier frequency. If the carrier frequency is A Hz and the frequency of the modulation is B Hz then the side bands will appear at frequencies (A+B) and (A-B) Hz.
In this case it is important to note that the carrier frequency is fixed whilst the sideband locations are changing with speed.
If we examine the frequency difference between the fixed frequency and the sidebands then we find that the difference is always a factor of eight of the rotational speed. For example, at 1000RPM (16.6Hz) the difference between the carrier and the side bands is around 132Hz (Figure 6) and at 1200RPM (20Hz) the difference between the carrier and the side bands is approximately 160Hz (Figure 7). Secondary sidebands are also visible at 16x rotational speed.
The observations show that a number of fixed frequency components are present in the vibration. These could well be due to resonances within the pump body or housing. The variable frequency components are no doubt caused by modulation which affects the signal on a cyclic basis. We know that the particular pump under test has 8 impeller blades, which matches the modulation frequency of 8 times the rotational speed.
As the impeller rotates around at speed, it can decelerate and then accelerates slightly around the revolution causing the modulation. The root cause may well be a blade fault on the impeller.
The modulation can be shown more clearly by band pass filtering the original pump vibration data. The result is a modulated sine wave.
Figure 8 shows a section of the original time signal. Figure 8 shows the same section of the original time signal, but band pass filtered around one of the phenomena, in this case 5000Hz to 6200Hz.
In Figure 9 it is hard to make any clear deductions, indeed there appears to be general a noise issue, however once band pass filtered, as shown in Figure 8, the amplitude modulation effect can clearly be seen.
This wave shape shows that the initial assumptions were indeed proven correct. A classical case of amplitude modulation causing sidebands in the frequency domain.
The presence of side bands around a central frequency is a well known phenomena and is discussed further in the following articles, written by Don Davies,
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