An Introduction to Time Waveform Analysis

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An Introduction to Time Waveform Analysis J.Alex Bradley General, Data Collector/Analyzer Vibration Not Classified

AN INTRODUCTION TO TIME WAVEFORM ANALYSIS PRESENTED BY J. Alex Bradley with COMPUTATIONAL SYSTEMS INCORPORATED

The time waveform shown above was taken from a simple rotor kit. A weight was added to the rotor to create an imbalance. This imbalance causes the time waveform to show a once per revolution peak. The time that the shaft takes to make one revolution is illustrated on the plot. A mark has been-set at about 137 milliseconds and the cursor has been moved to a position at about 158 milliseconds. (These times are relative only to when data collection began, not to any specific location on the shaft.) This represents a time span of 21.78 milliseconds, or .02178 seconds. If the amplitude of the waveform is assumed to be caused from the imbalance weight then it could be concluded that the time required for the shaft to make one revolution is 21.78 milliseconds or .02178 seconds. A simple equation links "event" times in seconds to frequencies in hertz. It is:

This spectrum was created from the time waveform on the previous page. Since the time waveform is very sinusoidal the amplitude of the spectral peak at 1 times the run speed of the shaft is nearly the same as the peak to peak (PK-PK) amplitude of the time waveform. The spectrum cursor shows a peak of 5.709 mils at 46 hertz or 2760 rpm. The peak marked on the time waveform on the previous page is 2.9 mils, or about half of the peak-to-peak value shown on the spectrum. A peak to peak (PK-PK) value of the waveform could be estimated to be about 5.8 mils. The frequency of the waveform was shown on the previous page to be 45.92 hertz. Very simple time waveforms have good amplitude correlation with their associated spectra. This is because the Fourier transform (FFT) can very accurately determine the amplitude and frequency of the components of the waveform as it converts them to the frequency domain, that is, into a spectrum. Time waveforms with random energy do not convert so cleanly to the frequency domain. TIME WAVEFORM TO SPECTRUM CONVERSION

This waveform should be considered a side view of the spectrum. The fast Fourier transform (FFT) could be considered to be able to rotate each frequency in the time waveform 90 degrees.

This spectrum should be considered a side view of the time waveform.

Every peak seen in the spectrum should be considered as a sine wave coming out of the paper. The amplitude of the sine wave may be seen as the height of the spectral peak. The location of the peak in the spectrum specifies the frequency of the sine wave. TIME WAVEFOPM DURATION The time length of a waveform depends upon the maximum frequency of the spectrum, Fmax, that is to be examined. In order to filter out unwanted high frequency spectral information, the data acquisition rate MUST be over 2 times the maximum frequency of the spectrum, Fmax. This is required to perform proper anti-aliasing. Virtually all modern digital spectrum analyzers sample raw vibration data at a rate equal to 2.56 times the maximum spectral frequency, Fmax, being examined. This means that the analyzer stores "samples" of the waveform data coming from the transducer at this "RATE". This is called the "SAMPLING RATE". SAMPLING RATE = 2.56 X MAXIMUM FREQUENCY (in hertz) The analyzer must "SAMPLE" enough points to perform any necessary Fourier calculations from these points. More importantly, after the data has been sampled, the maximum spectral frequency, Fmax, CANNOT be increased° To calculate a 400 line resolution spectrum, 1024 "SAMPLES" of incoming data must be collected. By knowing the "SAMPLING RATE" and number of "SAMPLES" that must be collected, the time length, in seconds, of the waveform can be calculated.

The following table may be computed from this equation:

This chart clearly shows that low maximum frequencies require long time periods of data collection. TURBINE IMBALANCE EXAMPLE

This turbine has thrown a blade and is out of balance. The speed of the turbine has been reduced from over 4000 RPM to its current speed of about 2600 RPM in order to keep vibration levels acceptable.

This order based plot shows horizontal, vertical, and axial measurements on both the outboard and inboard turbine bearings. The major peaks in the radial directions are all found at 1 order of run speed, i.e. 1 X run speed. SINGLE SPECTRAL PLOT OF IMBALANCE

The spectral plot above shows vibration in the horizontal direction on the turbine outboard bearing. Vertical lines note the locations of harmonics of run speed. Virtually all the vibration energy in this spectrum is caused by a single peak at 2609 RPM, which is the run speed of the turbine. The sides, or skirts, of this peak are also very narrow. The sharpness of this peak indicates that it is created from a time waveform dominated by a single frequency. TIME WAVEFORM PLOT OF IMBALANCE

The time waveform plot above shows instantaneous acceleration over 240 milliseconds of time in the horizontal direction on the turbine outboard bearing. Vertical lines note the time required for the turbine shaft to make I complete revolution. The waveform is in units of acceleration since the probe used to collect data was an accelerometer. A clear, repeatable, waveform can be seen occurring once per shaft revolution, 1 X RPM. The waveform is showing the acceleration created on the bearing housing by the shaft imbalance. High frequency energy can be seen riding on top of the dominant 1 X RPM sine wave. The high frequency energy is created by the gearbox that this turbine is driving. The repeatability of the waveform both in time (with respect to shaft turning speed) and amplitude mean that the vibration force is tied to the shaft run speed. This is particularly true of waveforms taken in acceleration, as they can be influenced greatly by high frequency energy bursts, such as impacts. These impacts make the time waveform non-repeatable. The absence of impacting helps to conclude that the problem is imbalance. GENERATOR TO EXCITER MISALIGNMENT EXAMPLE

This exciter has had a history of vibration problems0 and has recently been repaired. The foundation of the generator is much firmer than the exciter, and the generator is much more massive. This means the exciter tends to show more vibration activity than the generator. MULTI-SPECTRAL PLOT OF MISALIGNMENT

This multi-spectral plot shows inboard and outboard exciter points. At first glance the problem with the exciter might appear to be looseness. Many harmonics of run speed are present in the radial directions, which often indicates a looseness problem. This is a good time to examine the time waveform. SINGLE SPECTRAL PLOT OF MISALIGNMENT

A full screen spectral view of the exciter outboard horizontal position is shown above. Harmonics of run speed are denoted by dotted vertical lines on the spectrum. Many harmonics of run speed are visible, which can be an indication of looseness. The sides of the spectral peaks, or skirts, however, are very steep and the peaks are very sharp. This means that the frequencies are well defined and were transformed well by the FFT process from the time waveform. The sharpness of the peaks indicates that the waveform is repeatable and that there is little random, or non-repeatable, energy in the time waveform. The presence of a repeatable time waveform will indicate more of an alignment problem. TIME WAVEFORM PLOT OF MISALIGNMENT

The time waveform plot for the exciter outboard horizontal is shown above. Vertical lines denote the time required for 1 revolution of the shaft to occur. The trace of the waveform is very repetitive and repeatable for each revolution period. This indicates that the force causing the shaft to vibrate is related to the turning speed, or a multiple of the turning speed, of the shaft. If the problem had been looseness the waveform would not be repetitive. This waveform shows 2 upward peaks each revolution, at a spacing of 3 times the turning speed of the shaft. That is, the interval between the peaks is 1/3 of a shaft revolution, and two peaks can be seen each revolution. These peaks are very repetitive both in amplitude and spacing. It is this repeatable, repetitive pattern that confirms that this machine is misaligned, and does not have a primary looseness problem. MOTOR TO PUMP LOOSENESS EXAMPLE

This is a diagram of an overhung pump that has a worn out bushing in the coupling. The motor turns at about 1750 RPM° The worn bushing makes the pump-motor system very loose torsionally. As is typical of many looseness problems this problem has grown progressively worse over time.

MULTI-SPECTRAL PLOT OF LOOSENESS

A multi spectral plot of all 5 motor points is shown above. Inboard and outboard radial measurements as well as an outboard axial measurement were made. Many harmonics of run speed are visible on all measurement positions. Baseline, or floor, energy is also very visible. SINGLE SPECTRAL PLOT OF LOOSENESS

A full screen view the motor inboard horizontal position is shown above. A cursor is positioned at 1 times run speed, as well as on the first 10 harmonics of run speed. The peaks are broad and have wide skirts. Broad humps of energy may be seen in the 3 times run speed range, as well as in the 6 through 11 times run speed range. This indicates that the time waveform cannot be cleanly transformed into a spectrum. This means that the waveform must have random, non-periodic, energy present. TIME WAVEFORM PLOT OF LOOSENESS

The time waveform used to calculate the motor inboard horizontal position is shown above. Vertical lines note the time required for the shaft to complete 1 full revolution. This waveform is not repeatable and is non-periodic. There is no similarity in its pattern from revolution to revolution. This means that the vibration being created is not tied to the turning speed of the shaft. It makes sense that the waveform trace is not repeatable if the shaft does have a looseness problem, and that the pattern would not be tied to the turning speed of the shaft. Patterns that are non-periodic and random do not convert well in the FFT process. It is very difficult to assign specific frequencies and amplitudes to patterns to waveforms like this one. This difficulty leads to the broad band energy humps in the spectrum. Broader humps indicate more random energy. Higher humps indicate more impacting in the waveform. ROLLING ELEMENT BEARING EXAMPLE

The locations of the measurement points are shown in this diagram. The inboard end of the motor was not accessible due to the coupling guard. The motor was recently replaced in an attempt to lower vibration levels of the entire unit. The noise levels remained high even after replacing the motor. MULTI-SPECTRAL SLEEVE BEARING MOTOR PLOT

This is a multi-spectral plot of the motor point outboard points. All the levels appear very low in amplitude, but note where the dominant peaks are located. The 2 times run speed peaks are as high as or higher than other peaks in the spectra. This probably means that the motor is slightly misaligned to the pump. Since the vibration levels are so low in amplitude it is probably not necessary to immediately correct the misalignment. MULTI-SPECTRAL PUMP BEARING PLOT

All the measurements made on this pump show broad banded humps of energy, along with some low frequency peaks. The humps of energy are in the 200 to 400 hertz (12000 RPM to 24000 rpm) range. This is about 10 to 20 orders of run speed. The low frequency peaks should be examined more closely. The peaks might be harmonics of run speed, or they could be harmonics of some bearing frequency. The full scale range of all the plots is low at .1 inches/second, but quite a bit of energy is being produced by the broad humps of energy. SINGLE SPECTRAL PLOT OF A BAD PUMP BEARING

A full screen plot of the Pump Inboard Horizontal, PIH, is shown above. Many of the low frequency peaks appear to harmonics of run speed. They are marked with dotted vertical lines. Because of the shear number of peaks it is also possible to find harmonics of non synchronous peaks. One such set of peaks has been highlighted with a harmonic cursor at 4.763 time run speed. Once again note that no individual peak is very high in amplitude. The full scale range of the plot is only .1 inches/second, but the overall value of this point is almost .3 inches/second. Broad humps of energy are responsible for the relatively high overall value. Random impacts occurring in the time waveform tend to generate these broad humps. Since the impacts are random the calculations performed to create the spectrum from the time waveform cannot assign the impacts to a particular frequency, thus the humps are created. TIME WAVEFORM PLOT OF A BAD PUMP BEARING

The number and height of the "spikes" in the time waveform confirm the presence of severe impacting. Many exceed ± 2 g's in amplitude. Remember that this is a very large, massive pump, so large amounts of energy are being generated by these impact levels. This impact energy is being absorbed by the bearings, and damaging them rapidly. The waveform shape is random and complex. This shape is impossible to be transformed into a "clean" spectrum, so the spectrum on the previous page with broad humps of energy is created. SPECTRAL OVERALL VALUE COMPARISON This pump spectrum is a good example of the reason a single overall number cannot be used to determine the condition of a machine. The top spectrum is from the pump with the bad bearing. It has an overall value of just under .3 inches/second. No particular peaks are very high. Broad banded energy is dominant.

The bottom spectrum comes from a steam turbine with an imbalance problem. It also has an amplitude of about .3 inches/second. Virtually all of the energy of the spectrum comes from the single peak at 1X RPM. This may be seen by comparing the amplitude of the single peak in the spectrum to the overall value of the spectrum.

TIME WAVEFORM OVERALL VALUE COMPARISON The time waveforms from the spectra on the previous page should now be examined to determine which machine has the worst problem. The bad pump bearing time waveform is at the top of the page. It shows high levels of impacts. 0neimpact reached almost 5 g's. Most impacts are in the ± 2 g range. The RMS overall value of the waveform is about .80 g's.

The bottom waveform comes from the imbalanced turbine. It shows virtually no impacting. No peaks exceed ± 1 g's. A sinusoidal shaped pattern is also seen. This is the type of signal pattern that can be well transformed into a spectral value. The RMS value of the waveform is about .23 g's. Even though the pump waveform RMS value is more than 3.3 times larger than the turbine waveform, the ease of transform of the turbine waveform ends up giving the turbine a higher spectral value.

TIME WAVEFORM COMPARISONS Another reason that the pump waveforms might be examined could be to determine which of the pump bearings had degraded the most° Higher impacts would be indicative of a bearing with more and larger defects.

The three time waveforms on this page are from the inboard pump bearing housing. The RMS values of the three waveforms are found at the upper right of the plot. PIH = .80 g's PIV = .89 g's PIA = 1.4 g's

The axial point appears to be the most energetic.

TIME WAVEFORM COMPARISONS The pump outboard points are shown on this page. POH = .58 g's POV = .77 g's POA = .83 g's Once again it is seen that the axial point is the most energetic point.

The RMS levels for the outboard points are consistently lower than the levels for the inboard points. More importantly the level of the spikes or impacts is much higher on the inboard points. This can be seen by examining the scale of the plots.

In this manner it can be determined that the inboard bearing is likely to be the one with the most severe defects. If only one bearing were to be changed it should be the inboard one.

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Last Updated 05/08/03

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