Chapter 28 SYNCHRONOUS TIME AVERAGING

The signal to be measured and analyzed can sometimes be corrupted by unwanted contributions from noise, line hum, or other machines running nearby. When this occurs, spectrum averaging can be used to smooth out the total signal, but the tech- nique does not necessarily help with analyzing a particular machine.

Other techniques are required to extract only the signal harmonics related to the desired rotating element from a composite measured signal.

SEPARATING SIGNAL FROM NOISE

Several techniques are available for cleaning up a signal surrounded by noise. With most techniques, some type of spectrum averaging is used. However, for the most part, the enhancement provided by standard averaging is limited. If the level of the periodic component is below that of the surrounding noise, increasing the number of spectrum averages will not reveal the buried signal. It will only make the adjacent noise smoother.

Figure 28.1 illustrates a periodic signal that has been buried in noise. The display on the left is the unaltered waveform. The periodic signal also was available as a refer- ence waveform, but was not used in this first measurement. The display on the right is that of a standard averaged spectrum. In this case, 1000 averages were used and the total signal power was averaged. In the standard averaged display, only the fundamen- tal spectrum component at 350 Hz is visible. From this display, it is not clear if there are any harmonics or their distribution.

With synchronous time averaging, blocks of time records are triggered from the desired reference signal and averaging takes place in the time domain. Waveforms

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260 Vibration Fundamentals

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Figure 28.1 Unaltered time waveform (lef) and standard averaged spectrum (right) afer 1000 averages.

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Figure 28.2 Sync averaged time waveform (kft) and sync spectrum (right) after 10,000 averages.

that are synchronous with the reference tend to be reinforced frame after frame, whereas those that are random or synchronous at a different rate are not reinforced and average to zero. After sufficient averaging in the time domain, a single FFT is per- formed and the result is referred to as a sync spectrum.

With this method, the signal-to-noise ratio (S/N) improves proportional to the square root of the number of averages taken. Theoretically, all noise components could be eliminated by averaging for a long period of time. The result of synchronous spectrum averaging should be only a periodic spectrum or nothing at all. Because the reference signal is available for the waveform shown in Figure 28.1, it can be used as an exter- nal trigger input to the real-time analyzer and a Synchronous Average performed (see Figure 28.2).

Two important factors should be remembered when performing a synchronous time average:

1. A reference signal is crucial and must be mechanically linked to the physi- cal shaft or other rotating element to be isolated. An external signal gener- ator set, for example, at approximately the same frequency as the desired rotating element turning speed may appear to momentarily offer some sig-

Synchronous Time Averaging 261

nal cleanup. However, since it is not phase locked with the machine, aver- aging enhancement soon ceases and no long-term improvement results.

2. Averaging is done in the time domain and must be followed by a single FFT. This is important because the FFT typically performs a power average, including all coefficients that are present. However, with syn- chronous averaging, we care only about terms that are phase locked with the reference signal. Thus, we need to average in the time domain by creating blocks of data that always begin (or end) when the tachome- ter triggers. In this way, nonsynchronous, or random, events average to zero due to bipolar cancellation. In nonsynchronous or standard spec- trum averaging, all components (both synchronous and other periodic and random data) are averaged. This smooths the spectrum, but does not enhance the S/N.

APPLICATIONS

There are many applications of synchronous time averaging, but the more common uses include (1) obtaining multiple-order reference, (2) eliminating beating responses, and (3) recovering signals below the noise level.

Multiple-Order Reference

In some cases, the primary signal of interest may not be at the fundamental shaft- speed frequency, but rather at some multiple of that frequency. For example, the ana- lyst may want to focus on the condition of a rotating element by removing all vibra- tion except for specific passing frequencies, such as the number of blades on a turbine wheel, the number of impellers in a pump, gear ratio, etc.

If a multiple tachometer signal of the desired rate is available, it can be used as the reference trigger input. By using multiples of the tachometer input, only the trigger multiple and its harmonics will be preserved. An example of this is seen in Figure 28.3 below, where a 3x running speed signal was used as the trigger input to the time synchronous averaging process. With this trigger, the time waveform and resulting

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262 Vibration Fundamentals

Figure 28.4 Long-term (top) and expanded (bottom) time recording of beat.

spectrum will contain only the third order of running speed and each of its harmonics (3x, 6x, 9x, etc.).

If the contribution of a particular component (e.g., 35-tooth gear) is of interest, it also is feasible to multiply a known tachometer signal by a phase-locked ratio to recover just that signal from a composite waveform. In this case, the higher harmonics may not be of interest and, if they are, there may be a conflict between spectrum resolution and waveform stability. Remember that time synchronous averaging depends on the stability of the systems generating the multiple signals, especially on the stability of the recovered waveform. The more this waveform wanders in frequency or speed, the more difficult the synchronous averaging process will be.

Eliminating Beating Responses

In some cases, two machines or elements operating near the same running speed can create a phenomenon referred to as “beating,” which can confuse an otherwise straightforward measurement. This is another case where having the tachometer refer- ence for the specific rolling element can accurately separate out the desired compo- nent. An example of this is seen in Figure 28.4, which shows long-term and expanded time recordings of beat.

Synchronous Time Averaging 263

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X:2.4Wk Y4.174 OA3.141 ma I Figure 28.6 Sync spectrum using 2400-cpm reference, 200 averages; beating component at 2376 cpm.

Figure 28.5 illustrates a 3-D waterfall and 2400-cpm, 40-Hz track over a 1-min inter- val. Note that beating causes the spectrum level of the 2400-cpm, 40-Hz component to vary from nearly 0 to more than 8.6 V.

However, as shown in Figure 28.6, the actual level of the 2400-cpm component, as derived through sync averaging with respect to the actual 2400-cpm reference, is 4.174 V peak.

Recovering Signals Below the Noise Level

A benefit of synchronous time averaging is that no theoretical limit exists for the amount of signal “cleanup” that can be performed. It is one of the few signal-process- ing techniques available where the S/N enhancement is proportional to the square root of the number of time-averaged blocks processed. Thus, the longer the averaging

264 Vibration Fundamentals

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Figure 28.7 Standard free-run spectrum analysis performed with 1000 spectrum averages.

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Figure 28.8 Sync averaged spectrum of same signal shown in Figure 28.7.

takes place, theoretically, the cleaner the signal gets until the only signal left is the trigger, or synchronizing frequency, and its harmonics.

The spectrum shown in Figure 28.7 is the result of 1000 averages of a free-running signal input. The only apparent signal is a peak at 40 Hz. However, it is suspected that there might be a signal contributing at approximately 37 times the nominal 40-Hz component. To verify this, a synchronous time average was performed with a refer- ence signal of 1466 Hz.

The time synchronous spectrum shown in Figure 28.8 was performed with 3400 time averages followed by a single FFT. This technique makes it apparent that a clear sig- nal exists at 1466 Hz. Also note that the amplitude of this 1466 Hz component is less than half that of the amplitude of the 1466 Hz component in Figure 28.7. This indi- cates that the desired signal is at least 6 dB below the level of the surrounding noise in the original broadband spectrum.