Beating occurs when two dynamic excitation sources (forces) are close together in frequency, and a pathway allows the two excitation forces to transfer to each other. The beating effect results because the frequencies are so close to each other that the waveforms alternately reinforce each other at some times and cancel each other at other times. When the vibration from each source adds constructively, the vibration increases. When the vibration adds destructively, the vibration decreases.
An example was found while diagnosing two condensate pumps (Figure 1) located side by side and running at almost exactly the same rotational speeds. With induction motors as the prime movers for the pumps, slight differences in speed were always present as a function of how much slip occurred under varying load conditions. The residual unbalance in the pumps caused fairly large excitation forces. The piping and mounting details provided the necessary mechanical transmission path for the vibration from each pump to affect the other.
Figure 2 shows the resulting vibration trend when both pumps were running simultaneously. Note that at the tail end of Figure 2, when the second pump had been stopped, the beat effect ceased and the vibration consequently assumed a stable trend.
Figure 2. Amplitude modulation on condensate pump of Figure 2, arising due to beating effect. Note that vibration trend becomes steady at the tail end of the plot, after the second pump has been turned off.
Another machine type in which beating can be common is the centrifuge (Figure 3), where the bowl and screw rotate with slightly different speeds.
Figure 3. Cross-sectional view of centrifuge machine showing two main rotating parts (bowl and screw) slightly different in speed (image courtesy of TEMA/Seibtechnik).
When sufficiently large excitation forces exist, which often occurs with centrifuges due to buildup of material and subsequent unbalance, beating can occur. The beat frequency may arise from either the differences in speed between the bowl and the screw, or between the rotating fluid and the bowl.
To ascertain whether beating frequencies are present, the simplest method is to use a high-resolution spectrum plot (see Figure 4). Clearly, the sampling frequency must be chosen to give sufficient resolution between spectral components and prevent so-called spectral smearing from occurring. For the example in Figure 4, the data was collected from a centrifuge and the two frequencies differed by 38 rpm, as can be noted by the amplitude/speed labels at the top of the two predominant spectral peaks.
Figure 4. Spectrum showing two frequencies very close to each other (38 rpm apart). The beat frequency is the difference between these two frequencies; in this case 38 rpm or 0.63 Hz.
Because the resolution has been set for 7.5 cpm (0.125 Hz), it can easily distinguish between these two spectral components, which are 38 rpm apart. However, had the frequencies been closer together (such as 1 or 2 rpm apart), a spectral resolution of 0.016 Hz or better would have been required.
When performing field or shop balancing on machines in which a beat effect is present, it is likewise important to configure instrumentation with suitably sharp filter roll-off so that only the spectral component of exact running speed (1X) will be present and all other frequencies will be filtered out. Otherwise, the phase and amplitude readings will be distorted by the adjacent beat frequency spectral component, making balance measurements and results erratic.
Pumps & Systems, December 2009