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Machinery Diagnostic Plots – Part 1 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 Even though analytic vibration data plots such as trend, Bode, polar, cascade, etc. are widely used in rotating machinery diagnostics, they are often not used effectively for displaying the most valuable information. This two-part Orbit article describes the plot formats that are typically used for performing diagnostics on highly critical rotating machines with fluid film bearings and proximity probes, as well as the type of information that can be extracted from each plot type. Special emphasis is given to “transient” (changing machine speed) and “steady state” conditions, and to what plot type is most suitable for extracting diagnostic data during these operating modes. This article is intended for rotating machinery engineers who perform routine audits and diagnose machinery vibration problems. It is part one of a two-part series.

INTRODUCTION You have probably heard the old saying, “a picture is worth a thousand words,” meaning that complex written information can often be conveyed with a single visual image. Suppose you want to buy a car but are not sure about which color to select, and decide to ask for a second opinion from a friend who is not at the shop with you. You take photos of the different colors using your cell phone and send them to your friend for advice. However, he replies that something is wrong with the pictures, as he cannot see the colors properly (Figure 1). The problem is quite evident; the photos were captured as grayscale images!

Figure 1: Photos of cars for sale – same model, different colors. This analogy is a good example of how something as useful as a photo taken to provide data about colors can hide the most vital information if certain parameters – color settings in this case – are not properly configured. A similar situation can occur in machinery diagnostics. When this happens, critical data that could lead to the root cause of a problem could go unseen. Beyond the technical description of the different plot formats, this article will provide precautions for interpreting each plot type.

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VIBRATION MEASUREMENTS There is no point in analyzing vibration data if we don’t understand where it originates. Two processes are critical to ensure data quality – transforming the physical vibration into an electronic analog signal, and then converting the analog signal into digital data for further processing. The first process involves the vibration transducer. Vibration transducers can be divided into three groups, based on the physical measurement that they make: acceleration, velocity and displacement. Most of the plots discussed here relate to rotor displacement within the clearances of fluid film bearings, so we will concentrate on measurements made with eddy current displacement transducers. The displacement transducer is widely used in rotating equipment with fluid film bearings, and is recommended by industry standards. It outputs a voltage that is proportional to the distance between the probe and the machine rotor. The other two types of sensors, seismic (velocity) and accelerometer (acceleration) sensors, can only measure the periodic oscillation (vibration) of the surface on which they are mounted. But the eddy current proximity transducer has the unique capability of measuring not only the magnitude of the oscillating distance between the probe and the rotor shaft, but also static or average distance. This average distance measurement will be discussed in detail when reviewing a specific plot format: the average shaft centerline. The lowest frequency this transducer can detect is zero Hz, and it still measures the distance to the observed surface when the machine is stopped and the rotor is completely motionless. Two important factors can distort the data measured by a proximity transducer. The first is that most displacement transducers are sensitive to imperfections in the target area (section of the rotor being observed by the probes). This effect is commonly referred to as “runout”. The second is that it constitutes a “relative” measurement between the sensor and the rotor. This is why rotor displacement data is also known as relative data. It is generally assumed that the probe does not move or vibrate during machine operation, but this is not always true. For this reason, it is extremely important that the person analyzing relative displacement data is aware of this limitation. We will discuss both factors later in this article. A typical response curve for an eddy current proximity transducer system is shown in Figure 2. It is clear from the chart that the shorter the distance between the probe and the target, the smaller the negative output voltage, and vice-versa.

Figure 2: Typical response curve for an eddy current displacement transducer

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When observing the signal generated by displacement transducers, we need to be aware of what it represents physically. When the monitored machine is running, the transducer system output signal will include two components, the varying ac voltage (resulting from the mechanical vibration of the rotor), and the dc or average voltage (representing the average distance between the rotor and the probe). Figure 3 shows a voltage vs. time plot with these two signal components identified. Since a smaller distance is indicated by a smaller negative voltage, it is easy to see that a maximum “peak” in the signal indicate a minimum distance between the rotor and the probe. And a minimum “trough” in the signal indicates a maximum distance between the rotor and the probe.

Figure 3: Representation of AC and DC output voltages for a typical displacement transducer. Before we can use modern software tools to analyze the rotor vibration, the analog voltage signal must be converted to a digital format. If you are interested in learning about the process, the References at the end of this article describe the process in depth. Once the rotor vibration has been translated into an electronic analog signal, and this signal converted into digital format, several parameters can be obtained from the data, and plotted for analysis. The most common parameter associated with the vibration signal is the overall (unfiltered or “broadband”) amplitude, which for displacement measurements is typically expressed as a peak-to-peak (pp) value, as shown on Figure 4.

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Figure 4: Digitized overall vibration signal (amplitude vs time). In this example, displacement amplitude is shown in SI units of micrometres (“microns”). The jagged, irregular shape of the signal waveform indicates that multiple frequency components are present. Amplitude in this example is 49.25 microns pp. After determining the overall vibration amplitude, the digitized signal is typically filtered to the dominant frequency components of the signal. When performing rotating equipment diagnostics, it is common practice to evaluate synchronous (1X) vibration, which corresponds to the rotating speed of the machine rotor. This indicates how the rotor responds to the effect of the unbalance force present in the rotating machine. In some cases, other nX components (0.5X, 2X, etc.) are required to analyze specific malfunctions. A special type of digital filter called a “bandpass” filter is required to measure and record nX data. This filter removes all signal content located above and below a specific center frequency. When collecting filtered data during a machine speed transient, these bandpass filters are required to be able to adjust the center frequency as machine speed changes. These special filters are known as “tracking filters.” The peak-to-peak amplitude for a filtered signal can be extracted as shown on Figure 5.

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Figure 5: Peak-to-peak amplitude of a 1X filtered signal. Observe that frequencies outside of the bandpass filter have been removed, leaving a smooth sinusoidal waveform. Amplitude in this example is 41.55 microns pp. The frequency of a filtered signal can be easily calculated by measuring the period T (the time for one complete cycle), and then calculating its reciprocal, as shown on Figure 6.

Figure 6: Calculating the frequency of a filtered signal. In this example, T ≈ 0.042 s, so 1/T ≈ 23.8 Hz. Another important piece of information that can be extracted from a filtered signal is timing or phase measurement. Two types of phase can be measured: relative and absolute. Relative phase is measured as the offset in degrees (where 360 degrees is one full cycle) between two signals with the same frequency. Figure 7 shows two signals, A and B, both with the same frequency. Using the horizontal axis, the time delay T between similar points in both signals, for example, their maximum levels, can be measured, and then converted to degrees of relative phase difference between the signals. We can either measure the time delay

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between 1 and 2 or the time delay between points 2 and 3. Either way is allowable, but, by tradition, we normally select the time difference between the two points that are closest together in time. Since points 1 and 2 are closer together than points 2 and 3, the time delay between points 1 and 2 is chosen. Instead of using the original time units, 360 degrees are assigned to a whole cycle, so that T can be calculated proportionally and then expressed in degrees. Once the relative phase is calculated, it is also important to determine which of the two signals is “leading” or “lagging” the other. For the example shown on Figure 5, looking from left to right, it is easy to see that signal B reaches its maximum (point 1) level before signal A does (point 2). In other words, signal B leads signal A by 138 degrees. It is just as correct to say that signal A lags signal B by 138 degrees.

Figure 7: Example: Relative phase angle between two signals, which must have the same frequency. Even when this definition of relative phase implies that both signals are filtered to one single frequency, in certain real cases, it can be applied to overall signals to extract useful information. We will show such an example later in this article. To measure absolute phase, or simply “phase,” as it is usually known in the field, there is a special instrumentation requirement. A once-per-revolution pulse reference signal is necessary, which can be generated by various methods. One method that is convenient for temporary installations is to attach a piece of reflective tape on the rotor shaft, which is then observed by an optical sensor. Another method is to observe a notch or projection on the shaft, using either a magnetic sensor or a displacement probe. No matter which method is used, every time the “mark” on the rotor passes in front of the sensor, it triggers a pulse in the output signal, such as the one shown on the lower section of Figure 8. This reference pulse is then used to measure the time to the next positive pulse in the vibration signal being analyzed. In Figure 8, the upper section shows the filtered vibration signal. plot

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Note: In this example both the vibration signal and the once-per-turn signals have the same frequency (1X). However, absolute phase can also be measured for any (nX) frequency. For example, a 2X filtered vibration signal will be still compared to the once-per-turn reference signal. This is different from relative phase measurements, where both signals must have the same frequency.

Figure 8: Absolute phase measurement. From the reference pulse to the next positive peak in the vibration signal, ~16 ms have elapsed. Since one full cycle takes ~55 ms, the absolute phase lag of the vibration signal is (16/55)(360 degrees) ≈ 105 degrees. It is vital to understand what phase measurements mean physically when analyzing vibration data. When we do this, it is possible to analyze what happens in the machine when looking at waveforms and calculating their relative and absolute phase relationships. We can then have a more realistic understanding of absolute phase, and, more importantly, we can understand what a change in this number means. As defined previously, the absolute phase indicates the timing between the reference pulse and the closest maximum in the vibration signal, in other words, it measures the time delay between the reference pulse and the moment in which the rotor gets as close as possible to the vibration sensor. Since the reference mark on the rotor, the reference transducer looking at that mark and the vibration sensor are all at fixed locations, the only possible conclusion to explain a change in absolute phase is that the rotor is deflecting in a different direction relative to the mark. Figure 9 shows how a rotor bends at two different times during operation. The image on the left shows the rotor bowing in a direction that is lagging by 100 degrees from the reference mark. The image on the right shows the same rotor deflecting 180 degrees from that mark. This change would be detected by observing a change of 80 degrees in the absolute phase readings. In this example, the different colors used for the longitudinal section of the rotor subjected to the maximum bending indicate that when a vibration phase angle change occurs, a different part of the rotor is pointing in the direction of deflection.

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Figure 9: Dynamic rotor bending for two different absolute phase values. The red line indicates the part of the rotor that is closest to the probe when the phase lag is 100 degrees. The green line indicates the part of the rotor that is closest to the probe when the phase lag is 180 degrees. Typically, most rotating equipment is running most of the time, so it is usually easier to collect steady state data than transient data. Part 1 of this article focuses on steady state data analysis, while Part 2 will expand into a discussion of vibration analysis for transient conditions.

STEADY STATE PLOTS In any industrial control room, the plant operators have access to the most popular plot available, the trend plot. This plot is a representation of any numeric variable, such as vibration amplitude, temperature, flow, tank level, etc., versus time. The purpose of this plot is to show how these variables change with time, as well as how they correlate with other variables. The importance of displaying a certain variable versus time is that the way the variable changes can provide important initial clues about a specific machine malfunction. In vibration analysis, the first plot that is usually examined is the overall amplitude trend. The following three examples correspond to three different malfunction scenarios, all of them involving synchronous or 1X dominant vibration. Even when the root cause of each of them was determined using additional plots and other relevant information, these trend plots provided important initial clues on how to continue the analysis. Figure 10 shows an unpleasant screen for any control room operator – a progressive increase in vibration. In this case, the continuous increase in vibration was due to a gradual decrease in rotor stiffness, caused by the propagation of a crack over an interval of almost two days. The red and blue curves indicate measurements from two different probes.

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Figure 10: Overall amplitude trend for a cracked rotor. Figure 11 involves a case that often puzzles operators as vibration slowly increases, but after reaching some maximum amplitude it goes back to normal levels, with no apparent correlation with other process variables. In this example, the behavior was caused by carbonized oil deposits in the clearance between a shaft seal and the rotor, which caused a rub. When the rotor bowed due to the hot spot associated with the rub, it broke the hard oil deposits, allowing the hot spot to cool down and vibration to return to normal.

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Figure 11: Overall amplitude trend for a rub caused by carbonized oil in a shaft seal. Again, the red and blue curves represent measurements from two different probes. Finally, the third case, shown in Figure 12, corresponds to a step change in vibration, after which overall levels remained constant. In this example, a broken blade caused a sudden increase in mass unbalance of the rotor.

Figure 12: Overall amplitude for a sudden mass loss (caused by a broken blade).

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In cases where filtered vibration data is available (1X, 2X, etc.), not only amplitude but also phase can be plotted versus time. This type of plot is far richer in diagnostic information since it can help detect changes in phase even when the amplitude remains constant. Figure 13 shows a trend plot for 1X vibration, recorded at a constant running speed of 2280 rpm. The overall vibration amplitude trend wouldn´t draw much attention on its own. But the continuously changing phase trend was quite unusual. Basic rotor dynamic theory states that when rotating at constant speed, rotor synchronous response remains constant, both in amplitude and phase. Without getting into too much detail about machinery diagnostics, the occurrence of phase changes at constant speed could be caused by several different things, including rubs between stationary and rotating parts, angular shift of shrink fit components, a crack propagating through the rotor, etc.

Figure 13: 1X vibration and phase trend, during steady state operation for a period of a few minutes.

Polar Plot The polar plot displays the same information as the trend for amplitude and phase of filtered vibration, but in a different coordinate system. Since synchronous or 1X filtered vibration (as well as any other nX component) is defined by amplitude and phase, it can be treated as a vector. And, since the polar diagram has amplitude and phase as its main coordinates, it is well suited to represent vector magnitudes. When comparing it with the trend plot, it has a major advantage: any phase change is directly identified by observing any rotation of the vibration vector. In the trend plot, it is necessary to read the phase values on the vertical axis, which is a less intuitive process. In Figure 14, the same data from Figure 13 is displayed, this time using polar coordinates, where the “rotating” 1X vector is quite evident. An interesting fact about the polar plot is that no time or running speed coordinates are present. This allows the plot to be used to display both steady state and transient vibration data. We will revisit the polar plot in the Transient condition plot formats section in Part 2 of this article.

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Figure 14: Polar diagram showing changes in 1X vibration during steady state conditions.

Shaft Centerline Plot As mentioned earlier, proximity transducers have a major advantage over the traditional vibration sensors such as seismic or accelerometers: they provide an output voltage proportional not only to the rapid change in distance between the probe and the rotor (AC voltage) but also to the static or average distance between the two (DC voltage). This is particularly useful in fluid film bearing machines, where the rotor can move within the bearing clearance, as opposed to rolling element bearing machines, in which the rotor is essentially centered in the bearing. The normal operating position of the rotor within the clearance of a fluid film bearing depends on rotating speed, bearing design, oil characteristics, but most importantly, on the alignment between the driver and driven machines. When the DC output voltages of two orthogonal (perpendicular) proximity transducers are combined, the average position of the rotor can be measured. Since the probes are typically close to the bearings, the position of the rotor axis relative to the journal bearing axis can be determined, if we have specific reference voltages. On the left side of Figure 15, the rotor rests at the bottom of the bearing at very low speed, since the thickness of the oil wedge supporting the rotor against gravity is small. Under these conditions, the DC output voltages for both sensors are recorded as reference voltages. When the speed increases, the fluid wedge develops and the rotor moves upwards until it reaches normal operating position, changing also its distance to each probe. Then, by calculating the change in those DC voltages, and using the sensitivity or “scale factor” of these sensors, rotor displacement within the known clearance of the bearing can be calculated and plotted, as shown in the right side of Figure 15. Special attention is required when selecting the reference voltages, and we will discuss this topic in detail in the transient condition plots section in Part 2 of this article.

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Figure 15: Average shaft centerline position at low speed (left) and at normal running speed (right). Even though this plot is very easy to generate (it does not require complex signal processing other than simply recording DC voltages and plotting them in Cartesian coordinates), it is very important to consider that these are relative measurements between the probes and the rotor. A common error with the use of this plot type is the assumption that the sensors are always fixed, and that only the rotor is moving. While this is always desirable, it is not always true. The following example illustrates this concept. The drawing in Figure 16 shows a top view of the basic configuration of a steam turbine driving a generator. This machine train consists of a High-Pressure / Intermediate-Pressure (HP/IP) steam turbine, a Low-Pressure (LP) steam turbine and the generator. Each of the six bearings is equipped with orthogonal displacement probes, which allow generating the six corresponding shaft average centerline diagrams shown at the bottom. The plot for LP Bearing #4 shows a clear movement of the samples from right to left, indicated by the red arrow. On LP Bearing #3, a smaller horizontal displacement is also seen. However, no horizontal movement is measured on adjacent bearings. If these observations are combined with the fact that the three rotors are coupled together using rigid couplings, it must be concluded that the LP rotor is not moving from right to left in the bearing clearance, but that the LP casing (to which the probes are attached) is moving from left to right. In other words, the rotor is at a fixed location relative to the HP/IP and generator casings, but the LP casing, along with its bearing pedestals and orthogonal probes, is moving horizontally from left to right. In this example, this movement occurred due to a combination of machine configuration and foundation problems in the LP section. While this behavior is not common, the diagnostician must be aware of how the machine behaves before rushing into drawing conclusions from a shaft centerline plot.

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Figure 16: Example of how relative readings should be interpreted on a complex machine train. So far, we have discussed various plots associated with “static” variables. These variables are simple numbers that represent a parameter such as temperature, vibration amplitude, phase angle, etc. However, there is another type of data called “dynamic,” which is associated with physical magnitudes that can change rapidly with time, such as the vibratory motion of the rotor. This dynamic data is represented by the digitized signal coming from the transducer. This representation is usually referred to as a timebase plot.

Timebase Plot This plot is a simple representation of instantaneous signal levels versus time in a similar way to a trend plot for a static variable. The main difference is that the time interval between two consecutive samples is very small (Reference 1). When digitized dynamic data is stored for analysis, it is commonly referred to as a “waveform” sample, since the original analog waveform can be reproduced by the digital timebase display. Figure 17 shows an example of Timebase representation, corresponding to the output signals of two displacement transducers, recorded at a machine speed of 8435 rpm. Both sensors are installed at the same angular location (45 degrees left from vertical direction), but on different bearings, Inboard and Outboard. Even when these waveforms are based on “overall” (unfiltered) data, it is possible to detect a smooth sinusoidal shape with a period of 20.9 ms, which is equivalent to a frequency of 47,85 Hz (2871 cpm). Since the machine is running at 8435 rpm, this frequency sub synchronous (less than 1X) vibration. One of the advantages of this plot format is that, despite not being filtered signals, it is still possible to get an idea of the relative phase between both ends of the rotor deflection at this low frequency, especially in those cases where no filter has been previously set for this unexpected frequency component. By comparing maximum levels at both signals, it becomes obvious that they are in phase. Considering our previous discussions about relative and absolute phase, as well as the transducer response curve, these two signals indicate that at both bearings, the rotor reaches the minimum distance to the vibration transducer at the same time. In this example, the rotor is experiencing the excitation of its first natural frequency, associated to its first mode (shown on Figure 18), but at nominal speed.

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Figure 17: Timebase representation of two overall signals measured at Inboard and Outboard bearings.

Figure 18: First mode rotor deflection – indicated by in-phase vibration measured by two separate proximity transducers.

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CONCLUSIONS Graphical representation of data can be extremely useful when trying to solve a problem. This is particularly true in vibration analysis. 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 critical to understand how the typical displacement transducer provides the data to be plotted. Knowing where that data comes from eliminates or at least drastically reduces the possibility of misinterpreting it. In this article, we have used real-world examples to present a fundamental concept: there is no single plot that can be used alone to analyze a vibration problem. The information shown in one plot should be tested for consistency with other relevant plot formats.

NOMENCLATURE

• Hz Vibration Frequency (cycles per second)

• cpm Cycles per minute

• ms millisecond

• dc Direct current

• ac Alternating current

• 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 1993.

• 3200-line spectrum – when shouldn’t you use it?, by Don Southwick. ORBIT Vol. 14 No. 3, June 1998.

• ADRE 408 DSPi Signal Processing, by Gaston Desimone. ORBIT Vol. 31, No. 3, pg. 40, October 2011.

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

• 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.