Machinery Diagnostic Plots Part 2 ORBIT Back-to-Basics: What does the data really tell us?

Transcription

1 Machinery Diagnostic Plots Part 2 ORBIT Back-to-Basics: What does the data really tell us? Gaston Desimone Latin America Technical Leader Bently Nevada* Machinery Diagnostic Services (MDS) Buenos Aires City, Argentina Gaston.Desimone@bhge.com OVERVIEW Analytic vibration data plots are widely used in rotating machinery diagnostics, but they are often not used effectively for displaying the most valuable information. Part 1 of this article introduced steady-state plots, for data from highly critical rotating machines with fluid film bearings and proximity probes. In Part 2 of this article, we will introduce dynamic (waveform) plots including orbit and spectrum plots. We will also introduce transient plots, including the Bode plot and transient versions of the average shaft centerline, polar and timebase plots that we already discussed in Part 1. INTRODUCTION In part one of this article, we introduced basic concepts of machinery vibration measurements, including amplitude, frequency and phase. We showed how average shaft centerline, polar, timebase and trend plots can be used effectively for monitoring during steady-state (constant speed) running conditions. In this article, we will discuss the importance of transient data. Although there are many kinds of transient, (temperature, pressure, loading, flow rate, etc.) we will be referring specifically to machine speed changes. These occur when starting up or shutting down a machine, and sometimes during load changes, especially for machines with Variable Frequency Drive (VFD) control. TRANSIENT PLOTS When analyzing machinery vibration data, it is important to consider how the machine rotor vibrates in response to the action of dynamic forces such as unbalance. These dynamic forces are highly dependent on rotating speed, so we need to differentiate between data recorded at constant speed (steady state operation), and data which has been collected when rotating speed is changing (transient mode operation). Transient data typically provides much more information about the vibration behavior of rotating equipment than steady state data does. As an example, Chart 1 shows typical information available from transient data, along with the specific type of plot from which that information can be extracted. We will discuss these concepts in more detail later in this article.

2 Chart 1: This chart lists diagnostic information available from different data plot formats during transient (changing speed) conditions. Diagnostic Information Slow Roll Speed Range Runout Signature Resonances Heavy Spot / High Spot Angle Rotor Mode Shape Rotor Average Position Frequency Relationships Plot Type Bode Bode, Overall Orbit Bode, Polar Polar Polar, Filtered Orbit Average Shaft Centerline Cascade Orbit Plot The overall (unfiltered) orbit is the most realistic representation of dynamic rotor vibration within its bearing clearance (ignoring runout effects, which we will discuss in more detail later). Before the digital age, the orbit was used in machinery diagnostics by viewing the signals from two orthogonal (perpendicular) displacement transducers in an analog oscilloscope. The resulting Lissajous figure represented each signal voltage level on a two-dimensional phosphor screen, as shown in Figure 1, below. Note: Runout is noise in the output signal of a proximity probe transducer system resulting from electrical and mechanical effects that are not caused by either a shaft centerline position change or shaft dynamic motion. Electrical runout results from non-uniform electrical conductivity and magnetic permeability properties of the observed rotor shaft material. It can also be caused by local (spot) magnetic fields on the circumference of the shaft surface. Electrical runout noise does not result from a probe gap change (caused by dynamic motion or change in average shaft position). The error repeats exactly with each shaft revolution. Mechanical runout is caused by a probe gap change which does not result from either a shaft centerline position change or shaft dynamic motion. Common sources include out-of-round shafts, scratches, chain marks, dents, rust or other conductive buildup on the shaft, stencil marks, flat spots, and engravings. Even when both probes are observing the rotor external surface, the fact that this surface moves rigidly with the rotor geometric center makes it possible to interpret both signals as measuring the vibratory behavior of this center. If the timing relationship between signal X and signal Y is known, and the angular location of these sensors is known (45 degrees left for Y, 45 degrees right for X in this example), the direction of precession (the direction in which the orbit is described) can be determined. In this example, signal X reaches a maximum before signal Y, so the precession of this orbit is counterclockwise (CCW) or from X to Y. If the precession direction corresponds with the direction of rotation (which are both CCW in this example), the precession of the orbit is said to be forward.

3 Figure 1: The orbit plot is created by combining signals from orthogonal X and Y proximity probes. In addition to displaying the instantaneous path of the rotor geometric center, the orbit can also show information about vibration that is not visible when looking at each probe s signal separately in a timebase plot. The following example illustrates this. Figure 2 shows an elliptical orbit, which happens to be oriented horizontally. However, as in many typical installations, the displacement transducers are located at 45 degrees left (Y) and 45 degrees right (X) from the vertical direction. In this configuration, each probe will detect the projection of the orbit major axis on its measurement axis, as indicated in the plot, resulting in peak to peak readings that are lower than the actual mechanical movement of the rotor within the bearing clearance. If this machine had a trip setpoint configured at 5 mils pp, it would still be running, since the highest reading is mils peak-to-peak (pp), as measured by the X probe. However, the real peak-to-peak oscillatory motion taking place at the location where the probes are installed, reaches 6.48 mils pp. But how is it possible that the orbit shows us maximum amplitudes not detected by either probe individually? The answer is that, in addition to the use of the waveform of each probe, timing information between both signals is also used, specifically, relative phase.

4 Figure 2: Orbit example showing higher overall displacement than either the X or Y individual readings. Spectrum Plot The spectrum is a representation of a dynamic (waveform) transducer signal that has been digitally sampled so that a special computational algorithm known as Fast Fourier Transform, or FFT, can be applied. The main purpose of this algorithm is to find all the pure sine waves, each one with a specific amplitude, frequency and relative phase, such that when added together, they reconstruct the original complex waveform. Note: As shown in Figure 3, in the process of representing amplitude of each component versus frequency, the relative phase information available in the time domain is discarded.

5 Figure 3: The FFT process allows us to view vibration waveform data in the frequency domain rather than the time domain. Before rushing into analyzing frequency spectrum plots, it is important to remember that finding all the pure sine waves that when added together generate the original overall signal doesn t necessarily mean that the vibratory motion is taking place at all those frequencies. Since this statement might be difficult to understand, Figure 4 shows three signals with different shapes, and the corresponding FFT results. Even though their shapes are quite different, it is evident that the three signals have the same dominant frequency, as calculated and shown on the plots, approximately Hz. We would expect to see a peak at Hz in each associated spectrum on the right hand. Figure 4A shows a clean sinusoidal signal which only contains a single frequency, and therefore, a single spectral peak. For the other two examples, a signal showing a pulse and a square wave signal, many multiples or harmonics of this component populate the spectrum in addition to the fundamental Hz peak This is a consequence of the algorithm itself. The more the overall waveform deviates from a clean sinusoid, the more sine functions are needed to reconstruct the overall waveform. Because of this, it is important to evaluate spectrum plots in conjunction with their corresponding timebase waveforms.

6 Figure 4A: An undistorted sinusoidal signal is represented by a single peak in the spectrum plot. Figure 4B: The added periodic impact results in many added harmonics of the fundamental frequency. Figure 4C: This square wave example also produces a series of harmonics. These examples show how the spectrum is affected by the distorted shape of the signal. However, in all of them, the signal was still periodic as it repeated over and over at the same interval. There is an even worse scenario, in which the signal exhibits random or non-periodic behavior. This is problematic, since the FFT algorithm requires a perfectly periodic signal to work. Figure 5 shows a comparison between a periodic signal

7 with a dominant 3000 cpm (50 Hz) component, and the same signal exhibiting random spikes. On the right hand, the FFT for each signal is shown. The random spikes cause the FFT to show broadband noise that partially hides the frequency of interest, which is still 3000 cpm. Figure 5: Effect of signal non-periodic activity on FFT. The random impact spikes produce noise across a broad frequency range. Full Spectrum Plot Another type of FFT, the Full Spectrum, is also available for rotating machinery diagnostics. This version of FFT is not known as widely as the traditional spectrum, but it provides much more information. For a full spectrum, the dynamic (waveform) signals from two orthogonal probes are required, as well as rotation direction information. Figure 6 shows the basic processing path that is used to create the full spectrum, in which the FFT algorithm is applied separately to the individual X and Y signals. The results of each FFT are then sent through a final process, which provides information about frequency and precession. In contrast with the traditional spectrum, the full spectrum includes two frequency axes; one positive or forward and the other negative or reverse. Although a negative frequency sounds strange at first, it makes sense when you realize that the vibratory motion of the rotor shaft is perceived as an orbital motion, instead of a pure linear motion. Since the orbit is a closed loop, there are two possible ways to describe it, clockwise or counterclockwise. But most importantly, these two ways can be referenced to machine rotation. Orbital motion that takes place in the same direction as shaft rotation is forward precession, while orbital motion that is opposite to rotor rotation is reverse precession. Note: Although not exactly correct, many people remember that a full spectrum is simply the spectrum of an orbit. This is helpful in remembering that the full spectrum can only be generated from simultaneous signals from an orthogonal (XY) pair of transducers, which are also required to generate an orbit plot.

8 Figure 6: Basic process for calculating the full spectrum plot. It is important to realize that none of the amplitude peaks that are displayed in the full spectrum indicate the real amplitude of that specific frequency measured by each transducer, as they do with the traditional spectrum. Instead, they are actually a combination of the frequency content of both signals. So, what is the point of a full spectrum? The following discussion will clarify what type of information can be extracted from this plot format. Figure 7 shows a full spectrum plot in which a dominant 1X (synchronous) component is observed. Because of the process used by the Full Spectrum Transform, the 1X forward (A) amplitude on the right side as well as the 1X reverse amplitude on the left side (B), are mathematically related to the amplitudes of two rotating vectors by a ratio of 2. The two rotating vectors (A is red, B is blue) are such that when added together they represent a point in the orbit, which in this example corresponds to a 1X filtered orbit. In this orbit, three instantaneous conditions are shown, representing three different points in the orbit. From those three points, two are particularly interesting: the orbit major and minor radius. In one of these two cases (lower left plot), for the major radius, the amplitudes of the two vectors are added as simple numbers. However, in the case of the minor radius, they are subtracted. One benefit of the full spectrum is that, for any frequency component being displayed, by adding the forward and reverse amplitudes, the major diameter for the orbital motion at that frequency can be determined and that by subtracting the amplitudes, the minor diameter is calculated.

9 Depending on how different the major and minor diameters are, it is easy to have a clear idea of how elliptical the orbit is. Also, by observing whether the forward or reverse component shows the highest amplitude, we can determine the precession of the orbital motion at any of the frequencies present in the full spectrum. Figure 7: Relationship between full spectrum and filtered orbit. Amplitudes of the forward and reverse components add to give the major axis of the orbit, while they subtract to give the minor axis. At this point, you might wonder why we should go through such a complicated analysis instead of just looking at the 1X-filtered orbit. The answer is simple. This can only be done if filtered orbits are available, which requires having correctly-configured nx tracking filters previously established in the data acquisition instrument. Even though nx filters such as 1X and 2X are typically available by default, there will be cases in which the frequency content in the signals is different from a simple integer multiple of rotation speed. Example: Figure 8 shows a full spectrum with a sub-synchronous frequency in addition to the expected 1X component. In this example, a sub-synchronous frequency of 0.41X is present, with a forward amplitude of 0.51 mils pp and a reverse amplitude of just 0.16 mils pp. Two observations can be easily done in this case: The significant different between the two amplitudes indicates a quite circular orbit for this frequency (major and minor diameters are similar). And the orbital motion is described in the same direction of rotation

10 (forward precession). This can be further confirmed by looking at the overall orbit shown in the right side of Figure 8. In this example, the machine was experiencing a fluid-induced instability. Figure 8: Full spectrum (left) and compensated overall orbit (right) for machine running at 5861 rpm. In this example, a dominant frequency of 0.41X was present, with amplitudes well above those of any other component. Because of this, the shape of the orbital motion at this frequency can be observed directly by just looking at the overall orbit. However, there will sometimes be cases in which this will not happen. The following example shows more than one dominant frequency. Figure 9 has two frequency components in the full spectrum, 0.5X and 1X. The overall orbit does not look as smooth as the one shown in the previous example, making it difficult to determine precession and shape of the two orbital motions combined. In this scenario, the full spectrum becomes especially useful to allow comparing the amplitudes on the left (reverse) and right (forward) frequency axis. For the case of the 0.5X component, it is evident that the amplitudes are similar, indicating a highly elliptical orbit with forward precession (the highest amplitude is found in the forward section of the full spectrum). In contrast, when looking at the 1X vibration, the most relevant observation is its reverse precession, as indicated by the highest amplitude locating on the left side. All these are symptoms of a partial rub between stationary and rotating components of the monitored machine. Figure 9: Full spectrum at (left) and overall orbit (right) for a machine running at 4580 rpm.

11 Although the full spectrum is powerful in providing information about the orbit shape at each frequency, there is a caveat. It does not allow determining the actual orientation of those orbits. It is still necessary to look at the overall orbit and verify whether the information displayed in the full spectrum makes sense. One common misinterpretation is to assume that the frequency content in the full spectrum belongs to the signals from both probes. But depending on the specific malfunction, the different frequency components may or may not originate from both transducers. The following example illustrates this concept. Figure 10 shows the full spectrum for a machine running at 4375 rpm. In addition to the synchronous (1X) component at 4375 cpm (72.9 Hz), which in this case indicates that the orbital motion at this frequency is predominantly circular, a suspicious component is observed at 3600 cpm (60 Hz). The fact that both amplitudes, reverse and forward, are similar indicates that the orbital motion at this component (60 Hz) is predominantly linear or highly elliptical. Since it is not possible to determine the orientation of the orbit major axis, the overall orbit must also be examined. At first sight, the major axis of this orbit seems to be aligned with the X transducer. Also, the waveform for the X transducer (circled in red) is the one looking more irregular. Figure 10: Full spectrum for a machine running at 4375 rpm. However, when we view the normal spectrum for each signal separately, it becomes clear that only the X transducer signal is showing the 3600 cpm component, as indicated in Figure 11. In this case, the origin of this additional component was damaged field wiring, which allowed electrical noise from the 60 Hz electrical distribution system to get into the vibration signal path.

12 Figure 11: Evaluating separate spectrums for Y (left) and X (right) transducers revealed that the X transducer signal was experiencing significant 60 Hz noise, while the Y transducer was not. Waterfall Plot While both the traditional and the full spectrum plots are used for displaying frequency information at a given moment in time, when more than one of these spectrums has been generated, they can be shown or plotted versus time in the waterfall plot. This plot is a trend of the frequency content of the complex vibration signal. It allows determining how the frequency content of a signal changes with time in other words, its history, something that would be quite difficult to see by just looking at one spectrum at a time. Figure 12 shows a case where a sub-synchronous component of 1500 cpm appeared (in both the forward and reverse direction) at about 21:20, and then slowly increased in amplitude over about a 7-minute time span. The monitored machine was running at 3000 rpm, so this component can be expressed as 0.5X. By comparing the relative amplitudes of forward and reverse peaks, it is possible to infer the orbit shape at this particular frequency. Since both amplitudes are similar, we can conclude that the orbit associated to this frequency component is predominantly elliptical. Since this anomaly was not expected, there was no preconfigured 0.5X filter, so no 0.5X-filtered orbit was available to view.

13 Figure 12: Full waterfall plot, showing sub-synchronous (0.5X) activity in both the forward and reverse directions. TRANSIENT CONDITION PLOTS In this section, we will introduce the Bode plot, which is specifically used with transient speed conditions such as machine startups and shutdowns. We will also revisit the polar and average shaft centerline plots, which we discussed in Part 1 for steady state operating conditions. It turns out that these plots are also extremely valuable for evaluation of machinery behavior during speed transients. Bode Plot The most widely used plot format for transient speed operating conditions is the Bode plot. This plot displays amplitude and phase information versus rotating speed, as shown in Figure 13. It is a combination of two plots included in one single format. Technically, this plot can be used to display any nx filtered data, with n being an integer number and X being the vibration frequency associated with running speed. However, the Bode plot is most commonly used with 1X-filtered (synchronous) data, which represents the rotor response to the unbalance force. According to rotor dynamics theory, any critical speed (mechanical resonance of the rotor-bearing-seal system) involves an amplitude peak and a significant phase change, such as the one shown in Figure 13. Since the Bode plot shows rpm on its horizontal axis, it becomes very easy to observe the rpm value for any critical speed, which in this example occurs at 1750 rpm. In contrast, the phase coordinate, which is on the upper half of the plot, is not quite as intuitive. Despite being an actual coordinate in the Bode plot, the way in which the physical magnitude of phase changes requires us to use an auto scale feature, which can cause it to be deceiving.

14 Figure 13: Bode plot for machine vibration over a speed range from 0 to 4000 rpm. The upper plot shows vibration phase, and the lower plot shows vibration amplitude. Typically, the plot will have a fairly similar shape for both startups and shutdowns. The apparent disadvantage of the Bode plot regarding how clearly phase information can be extracted from it is completely absent in another plot format that also displays vector data: the polar plot. This format, which we discussed for steady state conditions in Part 1 of this article, is shown in Figure 14, below. Even though the same information shown on the Bode plot can be represented in the polar diagram, there are some significant differences in the coordinate system used. Taking a closer look at the polar plot, observe that the main coordinates are amplitude, represented in the radial direction outward from the center, and phase, which is measured circumferentially. Since those are the only traditional coordinates in this plot, the missing one (rpm), is typically included as labels shown next to each vector sample. The curved trace is then made up by joining the tip of each nx vector that has been recorded during the machine speed change. In this example, the vector cursor is showing the 1X vector measured at 4052 rpm during a machine startup. As we mentioned in our steady-state description of the polar plot, its main advantage is that any phase change can be easily seen as a vector that rotates. In this example, an evident phase change of more than 160 degrees can be seen between slow roll conditions of 267 rpm and full speed conditions of 7561 rpm. This is a clear indication that a critical speed was located between 4000 rpm and 4200 rpm.

15 Note: Slow Roll is an operating condition for large steam turbines and heavy-duty gas turbines, in which the rotor is rotated slowly by a turning gear. At such a low rotative speed, dynamic motion effects from forces such as unbalance are negligible. At this speed, rotor bow and runout can be measured. Typically, slow roll speed should be below 10% of the first balance resonance. Also, the circular geometry of the polar plot makes it intuitive to work with when performing a balance operation on the machine rotor, where it is vital to understand the angular location of balance weights and phase of 1X vibration. As an example, the location of the heavy spot or mass unbalance is shown here by the red line. The heavy spot is indicated by the earliest response of the rotor to unbalance conditions as speed increases during the startup. It is important to understand that phase angle increases in the lagging direction (opposite to machine rotation) during a startup. Also, that the zero-degree reference for this coordinate corresponds to the angular location of the vibration transducer that measured the data (though this could vary depending on the software used, since it is just a convention). Figure 14: Polar diagram for 1X vibration collected during machine startup from slow roll at 267 rpm to full running speed of 7561 rpm. Both the Bode and the Polar plots show the same information but using different coordinate systems, with corresponding advantages and disadvantages. However, there is a concept called runout that impacts the Bode plot in a more significant way than it does the polar plot.

16 As we mentioned earlier, the existence of some unavoidable runout is the main disadvantage of using eddy current displacement transducers. Every displacement reading will be affected by electrical or mechanical runout to some extent. Although this runout may produce many frequency components depending on how complex the generated signal is, when dealing with Bode or polar plots the only runout to be considered is the one occurring at the frequency of the filtered data we are displaying. Most often, this is 1X vibration. Remembering that filtered data will have amplitude and phase, the specific 1X-filtered runout displayed in these plots is known as a slow roll vector when collected. Also, both the amplitude and phase of the slow roll vector will be independent of running speed (any imperfection will be always at the same angular location relative to the reference mark on the rotor). This concept allows the diagnostician to apply compensation to the data, which involves subtracting the slow roll vector, i.e. amplitude and phase readings recorded at low speeds to all the 1X vectors recorded in the whole speed range during the machine startup or shutdown event. The result will be a set of 1X vectors that result from real synchronous vibration. At this point, it is necessary to make a clear distinction between Bode and polar plots as far as compensation is concerned. Both plots are designed to display vector data, using different coordinate systems. However, only the polar plot properly represents vectors from the mathematical standpoint. To represent vectors in the Bode plot, amplitude and phase readings are treated as scalar quantities, so that they can be displayed on the lower and upper section of this plot vs. machine speed. So we are actually displaying vector data as if it were just scalar values. This is mathematically incorrect, but it is still done, since the Bode plot is so useful. The problem arises when the data needs to be compensated for runout. This operation requires vector subtraction. Both summation and subtraction of vectors produces displacement of the vector tip in a twodimensional plane such as the polar diagram. However, due to the representation of vectors as scalar values in the Bode diagram, there may be extreme changes in both amplitude and phase traces when comparing the compensated and uncompensated versions. The following three plots (Figures 15, 16, and 17) show examples with three different slow roll vectors. When looking at the polar plot on the right side of each example, it can be clearly seen that the shape of the trace does not change at all (the shape and dimensions of the trace are the same in each example). Only location of the trace in the plot is different, which is a consequence of having different slow roll vectors (indicated by the red ovals). However, the amplitude and phase traces in the corresponding Bode plots look completely different from each other. Only the third example (Figure 17) has been properly compensated, since at low speed, 1X vibration amplitude is almost zero. This is actually the most reliable way to verify whether a plot has been compensated correctly. At low speed, the dynamic forces acting on the rotor are so weak that they cannot cause any deflection of the rotor. Therefore, properly compensated amplitude readings should be zero which means that the slow roll data should be located at the center of the plot (as in Figure 17).

17 Figure 15: 1X vibration data displayed in Bode (left) and Polar (right) formats, with a slow roll vector of mils pp at 54 degrees. Figure 16: 1X vibration data displayed in Bode (left) and Polar (right) formats, with a slow roll vector of mils pp at 120 degrees.

18 Figure 17: 1X vibration data displayed in Bode (left) and Polar (right) formats, compensated with the correct slow roll vector (amplitudes are zero at low rotating speeds, so the vibration response trace starts at the origin of the polar plot). By now, it should be clear that slow roll data is extremely important when analyzing vibration data measured by displacement probes. It is vital to collect good quality vector data at low speeds. The following example shows a Bode plot in which extreme and apparently abnormal oscillation of both amplitude and phase is seen below 800 rpm (Figure 18). This could complicate the selection of the slow roll vector. This behavior is a consequence of using a wide tracking filter (large bandwidth). The data in this example was collected using a 120 cpm (2 Hz) filter. Without getting into too much detail, the problem with a wide filter is that, when the speed is low enough, 1X and 2X components get too close together, and they both fall within the bandwidth of the filter. Since the filter is filtering not only 1X vibration, but also 2X vibration, the output will be irregular, such as the one shown. As I explain in Reference 1, the wider the filter, the faster its response to tracking running speed during transient conditions. However, the wider filter is also more likely to produce this error, as seen in this example. For this reason, an effective balance should be made between fast response and runout quality when selecting filter bandwidth.

19 Figure 18: Example Bode diagram showing extreme amplitude and phase oscillation at low speeds, due to a too-large tracking filter bandwidth. Average Shaft Centerline Plot for Transient Conditions In Part 1 of this article, we discussed using this plot for steady state data, as well as the need to measure the reference DC voltages when the rotor is resting at the bottom of the bearing clearance. However, this type of representation is most useful when evaluating transient data, collected either during startup or shutdown. Under these conditions, as the rotating speed increases in a fluid film bearing machine, the fluid wedge develops, lifting the rotor to its final operating position within the bearing clearances at nominal speed. When the speed decreases during a shutdown, the fluid film thickness decreases, causing the rotor to descend until it gets very close to the bearing bottom section. When the rotor operates at very low speed, it is essentially resting on the bottom of the bearing with an extremely thin oil film. During these conditions, the DC voltages generated by the displacement transducers are called reference voltages and are used to indicate the starting point on the shaft centerline plot. The selection of these voltages is critical to the proper use of this plot format for machinery diagnostics. Cold vs. Hot Reference Conditions When analyzing rotor average position in machines subjected to elevated operating temperatures for example, steam or gas turbines a common misinterpretation occurs when looking at cold startup data and comparing it with hot shutdown information. Figure 19 shows a typical scenario, including data collected during a cold startup, followed by steady state operation and then hot shutdown. Three different colors are used to indicate each portion of the run.

20 The shaft centerline diagram shown on the left shows an example where reference DC voltages were selected for cold conditions before machine startup. The displacement trace starts at zero (at the bottom of the bearing clearance on the vertical displacement axis, and in the center of the clearance on the horizontal displacement axis). The black part of the trace shows the change in rotor position as the oil film forms and lifts the rotor as the unit starts rotating and comes up to running speed (3000 rpm). Then, as the machine warms up, the green part of the trace shows an apparent change in rotor position at steady-state speed conditions but changing temperature conditions. This is the tricky part of the plot, which many times gets misinterpreted, concluding that the rotor actually moves within the bearing clearance during the time that the machine warms up to equilibrium temperature conditions. However, a quick look at the red trace shows that during shut down from hot conditions, the rotor apparently moves to a different location in the plot when it reaches low rotating speed. This does not mean that the rotor now rests at a different location in the bearing. The difference between the starting and ending points of the plot is caused by a combination of changes in the relative position between the rotor and the sensors, produced by thermal growth of the casing, thermal changes in alignment and thermal growth of the structure in which the displacement probes are installed. To avoid this confusion, it is a recommended practice to collect hot shutdown data and use it as DC reference values whenever possible. When this was done for the machine in this example, a machine shutdown from hot full-speed conditions appeared as shown in the right-hand plot, where the rotor position returned to zero position on both the vertical and horizontal axes of the shaft centerline plot. Figure 19: Comparison between use of hot and cold references in shaft centerline plots.

21 Timebase Plot for Transient Conditions We already introduced this plot type in our steady state discussions of Part 1 of this article, and we will now consider using it for transient conditions and with slow roll compensation to subtract the effects of runout. As we discussed previously, when analyzing vibration data that has been measured by displacement transducers, it is vital to identify what part of the data is real vibration and what part is consequence of runout, so that the runout can be eliminated from the dataset. However, this runout is not a simple 1X vector as is the slow roll vector used to compensate Bode or Polar plots. Instead, it is a waveform. Figure 20 shows an example of how a Timebase plot is compensated. Figure 20A corresponds to an overall uncompensated waveform generated by a probe that observes a poor-quality rotor surface rotating at 1904 rpm. Since waveform data was also collected during a shutdown transient, a similar waveform collected at a slow roll speed of 236 rpm is available (Figure 20B). Assuming that the waveform recorded at 236 rpm will remain the same relative to the reference mark on the rotor, the low speed waveform can then be subtracted from the one recorded at 1904 rpm. The resulting waveform corresponds to actual rotor vibration, as shown in Figure 20C. Figure 20A: Overall uncompensated waveform signal sampled at 1904 rpm. Figure 20B: Slow roll waveform signal sampled at 236 rpm.

22 Figure 20C: Vibration signal for 1904 rpm compensated with slow roll signal at 236 rpm. Orbit Plot for Transient Conditions When observing an overall orbit recorded at nominal running speed, there is no way of determining how much of that orbit is due to real vibration and how much to is due to runout. However, when collecting vibration data during a machine shutdown, it is possible view the overall orbit at low rotating speeds, when there are no longer dynamic forces acting on the rotor. This makes runout effects clearly visible, like in the waveform example in Figure 20. Since an overall orbit simply consists of two waveforms that are measured by two orthogonal displacement transducers, the compensation process used for overall orbits is very similar to the one used for single waveform compensation. Figure 21 shows an example of an uncompensated orbit (Figure 21A), and then the same orbit after being compensated by subtracted the runout component of the two signals (Figure 21B). Figure 21A: Overall orbit and waveforms before runout compensation.

23 Figure 21B: Overall orbit and waveforms after runout compensation. Cascade Plot The cascade plot is similar to the waterfall already discussed, in the sense that it shows a group of spectrums together. But instead of displaying them versus time, the cascade shows several spectrums that are generated for different rotating speeds during transient conditions. Figure 22 shows an example of cascade for a startup event. In the horizontal axis, frequencies are measured in cycles per minute (cpm). However, frequency units such as Hz or orders (1X, 2X, etc.) can also be used. One of the main advantages of this format is that when either cpm or Hz are used as frequency units, the cascade can provide a quick overview of which components track rotating speed and which don t. In the example, the 1X line is easily identified, grouping the synchronous components recorded at different speeds. Also, a group of peaks organized in a vertical line are seen, at a constant frequency of 3600 cpm or 60 Hz. They evidently have no relationship with running speed. In this example, these peaks were caused by line frequency noise getting into the wiring. Figure 22: Spectrum cascade for shutdown event showing line frequency noise (3600 cpm).

24 Another benefit of the cascade is that it makes it easy to identify specific relationships between frequency components, which would go unnoticed when displayed in isolated spectrum plots. In Figure 23, an interesting vertical relationship can be seen. More specifically, it can be seen how some nx components, in this case 33X, 44X and 55X, excite a frequency of kcpm ( Hz), when rotating speed is such that each of those nx components reach that particular frequency. In this example, it was later concluded that the existing frequency components of 33X, 44X and 55X excited a natural frequency of one of the probe supports every time running speed was such that these nx components were equal to Hz, the natural resonant frequency of the probe support. This is a good example of how a relative reading can deceive the diagnostician, since the vibration signals were not resulting from the rotor moving relative to the sensor, but the sensor moving relative to the rotor. Figure 23: Spectrum cascade for machine shutdown, with probe support resonance at Hz. The excitation of a natural frequency of 16,275 cpm, which is so clearly visible in the previous cascade, is not as evident when looking at the same cascade using orders as frequency units, instead of cpm. Figure 24 shows an example of the same cascade with orders as frequency units. This is a straightforward example of how the same vibration data presented in a slightly different format can hide important information during the vibration analysis.

25 Figure 24: Cascade with the same data as Figure 23 but using orders instead of cpm for frequency units. Full Cascade Plot Like the full spectrum and full waterfall plots, the cascade plot has its own full version, showing both forward and reverse vibration components. The advantages (and disadvantages) are the same as for the single spectrum and waterfall, with the ability to determine orbit shape and precession of the different frequency components, though in this case during transient conditions. Figure 25 shows a full cascade for the same examples shown on Figures 23 and 24. Since one of the probe supports is resonating, only one of the sensors is moving back and forth relative to the rotor. This oscillatory motion in the direction of that particular probe causes the orbit to look highly elliptical, with its major axis aligned with the resonant support probe. The resulting full cascade exhibits similar amplitudes for the reverse and forward components at the dominant frequency of 33X, consistent with a highly elliptical orbit.

26 Figure 25: Full cascade for the machine shutdown event shown in Figures 23 and 24, during which the natural frequency of the Y transducer support is excited. Note: All the limitations that affect the spectrum plot also apply to the cascade, full cascade, waterfall and full waterfall plots, as they are basically groups of spectrum plots. CONCLUSIONS Graphical representation of vibration data can be extremely useful when trying to solve a problem with monitored machinery. Sometimes the key to finding the root cause of a vibration problem is right in front of the diagnostician, but because of not using the most appropriate plot format in an effective way, the diagnostic analysis is unsuccessful. When dealing with rotating equipment having fluid film bearings, it is vital to understand how the typical displacement transducer provides the data to be plotted. In this Part 2 article, we introduced examples where runout introduced noise into the signals, and how a resonating probe support caused a confusing instance of relative vibration between the probe tip and the observed machine rotor. We also showed examples of useful dynamic plots (orbit, spectrum, waveform), transient plots (Bode), and plots that are useful for transient as well as steady-state conditions (average shaft centerline and polar). NOMENCLATURE Hz Vibration frequency (cycles per second) cpm Cycles per minute ms millisecond

27 dc Direct current ac Alternating current FFT Fast Fourier Transform rpm = revolutions per minute heavy spot = Rotor mass unbalance References 1. Desimone, G., 2014, Fundamentals of Signal Processing applied to rotating machinery diagnostics, Proceedings of the 43rd Turbomachinery and 30th Pump Users Symposia. ORBIT Articles Sampling waveforms and computing spectra, by Don Southwick. ORBIT Vol. 14, No.3, pg. 12, September line spectrum when shouldn t you use it?, by Don Southwick. ORBIT Vol. 14 No. 3, June ADRE 408 DSPi Signal Processing, by Gaston Desimone. ORBIT Vol. 31, No. 3, pg. 40, October General Bibliography Richardson M., 1978, Fundamentals of the Discrete Fourier Transform, Sound and Vibration Magazine. Hatch, C., 2002, Fundamentals of Rotating Machinery Diagnostics, Bently Nevada Press. Hewlett Packard, Application Note 243, The Fundamentals of Signal Analysis Eisenmann R., 2005, Machinery Malfunction, Diagnosis and Correction, Hewlett Packard Professional Books. * Denotes a trademark of Bently Nevada, LLC, a wholly owned subsidiary of Baker Hughes, a GE company. Copyright 2018 Baker Hughes, a GE company, LLC ("BHGE") All rights reserved.