identification of torsional vibration features in electrical powered rotating equipment
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Identification of Torsional Vibration Features inElectrical Powered Rotating EquipmentTRANSCRIPT
Identification of Torsional Vibration Features in Electrical Powered Rotating Equipment
Martin W. Trethewey Department of Mechanical and Nuclear Engineering
Penn State University University Park, PA 16802
Mitchell S. Lebold Complex Systems Monitoring and Automation Department
Applied Research Laboratory Penn State University
University Park, PA 16802 USA
ABSTRACT A common torsional vibration sensing method in rotating equipment is the Time Interval Measurement System (TIMS). The method utilizes the time passage of discrete intervals on a rotating element from an incremental geometric encoder (i.e., gear, optical encoder). Ideal measurement conditions consist of a constant shaft running speed, an encoder with identical segments and no transverse motion between the sensor and shaft. In practice, these ideal conditions are rarely achieved resulting in measurement errors. Torsional vibration sensing in internal combustion engines benefits the large inherent responses which produces a high signal to noise ratio and tends to minimize the effects of some measurement issues. In electrical motor applications the torsional responses tend to be smaller and the measurement issues may become more pronounced. For health monitoring applications (i.e., shaft crack growth diagnostics) it is imperative to accurately identify and track the fault sensitive torsional features. Tracking torsional mechanical shaft line dynamics can become challenging because of the lower signal to noise ratio, high harmonic content induced from the motor speed controller and processing artifacts from the Time Interval Measurement System. This work will discuss a number of potential measurement and data processing issues in the application of TIMS for health monitoring applications. The work will focus on separating the desired shaft line health features from all apparent in the torsional response. Of particular interest will be practical items related to installation and analysis on large electrical driven equipment. Examples from laboratory and field tests will be used to describe the identification and compensatory methods that have been successfully used. INTRODUCTION Torsional vibration is important in analysis and diagnostics of rotating equipment. Applications are plentiful, including the automotive [1,2,3], and the electrical power industry [4,5,6]. As the measurement of torsional vibration on a rotating shaft is inherently more difficult than translational vibration, a significant body of work has focused on effective torsional measurement techniques. A variety of schemes have evolved including lasers [7,8], in line torque sensors [9], angular accelerometers [10] and time passage encoder based systems [11,12,13]. The time passage encoder based systems have gained popularity. The method uses a fixed angular encoding device that rotates with the shaft, such as a gear or optical rotary encoder. A transducer senses the passage of each encoder segment. Optical encoders use a light based system to sense the passage of a rotating grating whereas
Proceedings of the IMAC-XXVIIFebruary 9-12, 2009 Orlando, Florida USA
©2009 Society for Experimental Mechanics Inc.
gear type shaft encoder systems have used a number of transducers including, Hall Effect, fiber-optic reflective light intensity, inductive and capacitive sensors. The sensor output is a pulse train type signal in which the passage times vary as a function of the shaft rotation and the torsional oscillation. Either an analog [14], or a digital Time Interval Measurement (TIM) approach [15] can be used to determine the torsional vibration from the pulse train. The analog method uses a frequency to voltage converter to change the pulse train into an analog signal proportional to the vibration. The digital method uses a high-speed timer to record the passage of each encoder segment. The encoder passage times are then compared to a reference and the time difference between the encoder and the reference signal is used to compute the torsional vibration. Because of the involved processing TIM torsional vibration measurement is more susceptible to algorithmic artifacts and errors such as 1) reference signal corruption; 2) non uniform sampling intervals; 3) timer resolution, and 4) transverse shaft movement with respect to passage sensor. Torsional vibration sensing in internal combustion engine applications benefits from the large amplitude responses. The larger magnitude torsional responses result from the fluctuating torque created by the inherent design of the crank shaft and the forces transmitted through the connecting rods from the cylinders. The high fluctuating torque excites readily the elastic torsional vibration. This tends to minimize the effects of some measurement issues. Most electrical motors run under steadier operating conditions experiencing much smaller torque fluctuations than an internal combustion engine. The excitation torque may come from the speed control or the driven device (i.e., hydrodynamic forces from a pump). The torsional vibration in electrical motor driven equipment is much smaller compared to an internal combustion engine. As such, the torsional vibrational measurement is further compounded by a lower signal to noise ratio. For health monitoring applications (i.e., shaft crack growth diagnostics) it is imperative to accurately identify and track the fault sensitive torsional feature. In electric motor applications it can be difficult to extract low level natural frequency related signals because of the presence of high amplitude order content. A typically order spectrum is shown in Figure 1. The ratio of natural frequency to the order component amplitudes can be greater than 60 dB. The order content can easily mask the resonances in the spectra. Hence, the order content can be viewed a corrupting feature when attempting to identify torsional natural frequencies. Tracking torsional mechanical shaft line dynamics can become challenging because of the lower signal to noise ratio, high harmonic content induced from the motor speed controller and processing artifacts from the Time Interval Measurement System. This work will discuss a number of potential measurement and data processing
issues in the application of TIMS for health monitoring applications with electric motors. The work will focus on separating the desired shaft line health features from all apparent in the torsional response. Of particular interest will be practical items related to installation and analysis on large electrical driven equipment. TORSIONALTIME INTERVAL MEASUREMENT METHOD A time interval measurement system used for torsional vibration is seen in Figure 2. The transducer output is a high or low voltage depending on whether it detects “white” or “black” regions of the transducer segments. If
Figure 2. Digital Time Interval torsional vibration measurement schematic.
Angular encoder
Transducer
Conditioning amplifier
Timer/Counter
Figure 1. Typical torsional vibration spectrum via Digital Time Interval Measurement method with high order content.
the shaft rotates at a constant rate in the absence of torsional vibration a periodic carrier wave is produced. When torsional vibration occurs, it causes a fluctuation in the rotating shaft speed. The output signal is a carrier wave modulated by the torsional vibration. A time interval measurement approach is used to demodulate the torsional vibration from the carrier wave [15]. The technique is based on the encoder segments’ passage times with respect to a stationary transducer. A triggering sensor is used to a record the times when the reference signal has a zero value with either a positive or negative slope. Note, the term “zero crossing” is used for descriptive purposes. An array containing the zero crossing times (tref) may be computed by:
( ) .Nn1),s(
fNnntshaft
ref ≤≤= (1)
When negative slope zero crossing detection is applied to the encoder signal an array (tencoder) indicative of respective passage times is created. The difference between the encoder and reference zero crossing times are computed by equation (2). ( ) ( ) ( ) (seconds), ntntnt refencoder -=Δ (2) The angular variation due to the vibration, in degrees, can then be calculated from the time difference array: ( ) ( ) ( ).reesdeg360fntn shaftΔθ = (3) Equation 3 can be used to create a discrete array containing the torsional vibration amplitude at the respective time corresponding to passage of each encoder segment. Since the shaft is assumed to rotate at a constant speed and an equal segment encoder is employed, the array is sampled on uniform angular increment basis. With the assumption that the time interval associated with the torsional vibration is much smaller than that due to the shaft rotation, a constant time sampling interval corresponding to the angular increments is: .Nft shaftsample =Δ (4) By combining equations (3) and (4) the shaft torsional vibration sampled with a constant interval time basis over one revolution becomes: ( )( ) ( ),nnt θθ = (5) where: ( ) .ntnt sampleΔ= (6) Although theoretically feasible, this measurement procedure has several potential problems [11,12,16,17]. Reference signal corruption: The ideal encoder reference expressed in equation (1) assumes 1) an encoder with exactly equal geometric segments, and; 2) a constant rotational speed. In practice both these assumptions are usually violated causing errors in reference signal used to compute the torsional vibration. Non uniform sampling intervals: Any variations in encoder segment geometry cause the torsional vibration signal to be sampled on a non-uniform angular increment basis. Furthermore, equation (4) assumes the shaft speed is constant. During normal operation the shaft speed can change for two reasons 1) inherent operation of the drive motor, and; 2) torsional oscillations in the shaft. These conditions can combine to cause the torsional vibration to be sampled on a non-uniform interval basis (both angular and time). Therefore, spectral analysis using constant interval algorithms such as the Discrete Fourier Transform is problematic if not precluded depending on the severity. Timer resolution: The derivation of Equation (2) is based on the assumption that it is possible to resolve infinitesimally small time differences between the reference and encoder signals. However, the achievable time
resolution is governed by the clock rate used in the zero crossing detection circuit. The clock rate affects the angular resolution of the measurement system. Transverse shaft movement: If the transducer experiences any lateral movement with respect to rotating shaft the zero crossing times will be affected inducing errors in the torsional vibration. ORDER EFFECTS The source of the order content can be either the normal operation of the rotating equipment or artifacts of the torsional vibration instrumentation and processing. The torsional vibration computed via the Time Interval Method [15] requires an accurate reference signal. The reference signal is assumed to; 1) have equal encoder segments and 2) operate with a constant shaft rotational speed, sans any torsional vibration. Unless a high precision encoder such as an incremental optical encoder is used, assumption 1 is violated. Other than synchronous motors, the running speed does not remain constant, so assumption 2 is also questionable. These conditions create difficulties in establishing a suitable set of reference times to calculate the torsional vibration for a non uniform encoder (i.e., zebra tape). Furthermore, these deviations from the ideal conditions introduce computational artifacts in the form of extraneous order content as seen in Figure 1.
To compensate for the deviations from ideal encoder segments the time interval differences used to calculate the torsional vibration uses the measured circumference as the reference. The resulting torsional spectrum is shown in Figure 3 and there is a marked reduction in the order content.
However, some low level order components remain. The unequal encoder segments causes the angular based sampling to occur on a non uniform basis, even if the shaft running speed is constant. The non uniform angular sampling is further exacerbated by running speed changes. Hence, both the encoder segments and changing shaft speed leads to torsional vibration signals that are not sampled with a constant angular increment basis. Recall, a premise of the FFT algorithm is that the signal to be transformed has been discretized with a constant sampling interval. Hence, the use of a waveform sampled with non constant intervals will produce errors in the spectra. These errors manifest themselves as the order content apparent in Figure 3. Therefore, to eliminate the error the torsional signal is resampled to a constant time basis before application of the FFT. The resampling method directly uses the algorithm developed in [17]. The resampling method may be outlined as follows:
1. The shaft speed is calculated and cataloged once each revolution over the acquisition of the entire torsional vibration data array.
2. Using the shaft speed and the measured encoder angular increments the discrete torsional vibration array is converted to a variable increment time basis.
3. A time array is created with a constant interval.
Figure 3. Torsional vibration spectrum of high speed turbo-machine in using encoder interval correction via the Digital Time Interval Measurement method.
Figure 4. Torsional vibration spectrum of high speed turbo-machine using encoder interval correction, and constant time resampling via the Digital Time Interval Measurement method
4. The non constant time interval discrete torsional vibration array is interpolated to obtain signal values at the constant time intervals created in step 3.
The result is a torsional vibration array which is sampled on a constant time basis appropriate for application of a FFT algorithm. The resampling adjusts for the non constant angular sampling and variations in running speed. Figure 4 shows the frequency domain spectrum after application of the resampling algorithm. Note the further elimination of the low level corrupting order content that was apparent in Figure 3. The application of the order reduction process has now made the interpretation of the torsional spectrum much easier than the original in Figure 1.
ELECTRIC MOTOR DRIVEN OPERATIONAL EFFECTS
Torsional vibration measured from internal combustion engines and turbo-machinery tend to be dominated by the forced responses and mechanical resonances. In addition, electric motor driven rotating equipment often contains harmonics of the power mains frequency and speed control artifacts. The power and speed control torsional artifacts can be strong and obscure desired mechanical shaft line features. Two electrical driven laboratory test beds are shown is Figures 5A and 6A. Both are driven be variable speed motors. The corresponding torsional spectra are shown in Figures 5B and 6B. A mechanical resonance is readily apparent in Figure 5B as are many additional discrete line frequencies which are attributed to the electric drive. Figure 6B shows the corresponding spectra for the test bed driven at several different RPM. Again a torsional resonance is identified but is obscured by the higher amplitude speed controller related spectral components. As the spectrum from each different speed is presented by a different color, the speed related effects are readily apparent. The presence of the electric power harmonics and speed controller responses make it difficult to identify other desired features in the spectra.
The ability to vary a motor speed can be beneficial in separating controller artifact from mechanical related
Figure 5A. Variable speed electric motor driven test stand.
Figure 5B. Torsional spectrum from equipment in Figure 5A.
Figure 6A. Variable speed electric motor driven test stand.
Figure 6B. Torsional spectrum from equipment in Figure 6A at various rotational speeds.
torsional responses as evident in Figure 6B. For constant speed electrical driven equipment the separation and identification can become more difficult. Consider the torsional response in Figure 7 from a large nuclear reactor coolant pump. This spectrum was calculated using the algorithms previously mentioned to address encoder irregularities and non constant time sampling issues. The harmonic content induced from the power and controller is readily apparent. These results are typical and illustrate the added level of interpretation difficulty in evaluating torsional responses from electrical driven equipment.
EQUIPMENT INSTALLATION AND OPERATING EFFECTS
A premise of the incremental time sensing approach to measure torsional is that the 1) transducer is remains stationary, and 2) the shaft
rotates about its centerline without lateral movement. Violating either of these assumptions can cause errors in the incremental time passage sensing and subsequently the computed torsional vibration. In smaller equipment, as depicted in Figures 5 and 6, these are reasonable assumptions. However, in larger equipment the possibility of transducer or shaft movement is higher. A toothed gear encoder with Hall Effect transducers is shown in Figure 8. The transducer mounts are apparent and are designed to be adjustable, yet stiff in the tangential direction. In this application the mounting hardware was acceptable and no elastic mounting artifacts appeared in the torsional response. Figure 9 shows a transducer bracket constructed to hold a Hall Effect transducer on a nuclear reactor coolant pump. The attachment locations to the pump frame were very limited and dictated the cantilever type bracket. Although designed to be stiff as to minimize the tangential motion, during operation artifact of the bracket lateral resonance was observed in the computed torsional response. Elastic lateral motion of the rotating shaft can cause similar corrupting effects on the torsional data. Again, for the smaller table top size equipment seen in Figures 5 and 6 the shaft motion is not an issue. However, in larger industrial scale equipment in Figures 8 and 9
Figure 7. Torsional vibration from a constant speed driven electric motor.
0 50 100 150 200 250 300 350 400 450 50010-6
10-5
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4Mar05 20:36 (S17R1)9Mar05 1:09 (S25R1)14Mar05 6:51 (S35R1)19Mar05 12:33 (S45R1)22Mar05 3:24 (S50R1)
Figure 8. AREVA IRIS loop torsional vibration instrumentation used for seeded fault testing.
Figure 9. Bracket for torsional vibration sensor on large electric motor driven pump.
some magnitude of lateral shaft movement is natural. Consider the torsional sensing instrumentation shown in Figure 10. By measureing the encoder time passages at three locations around the circumference, the respective response computed from the time passage sequences can be related to the orthogonal elastic shaft motion and the pure torsional motion by Equation 7 [12].
(7)
v1(t) is the computed the response from transducer 1 as computed by the TIMS approach, likewise for v2(t) and v3(t) respectively. [T] is a transformation matrix that relates the sensor positions to the leading edge passage detection with lateral movement of movement of the shaft mounted encoder. To solve Equation (7) requires the following measurement and preprocessing steps:
1. The TIMS torsional vibration method is applied to time passage arrays acquired from each of the three transducers; (v1(ti), v2(tj), v3(tk). Note, the time arrays for each response are different.
2. Resample the v1(ti), v2(tj), v3(tk) arrays with a constant increment time sequence creating (v1(tn), v2(tn), v3(tn)).
3. Solve Equation (7) at each time increment resulting in time variant arrays for the torsional response,θ(t), translational response, x(t), in the x direction as defined in [T], translational response, y(t), in the y direction as defined in [T].
4. Estimate the spectra of the torsion and two translation responses.
Timer/Counter
Signal Amplifier & Analog/TTL
Hall Effect transducer
Hall Effect transducer
Toothed Encoder Wheel
Figure 10. Instrumentation for 3 three probe torsion and translational vibration measurement.
Figure 11. Torsional and translational spectra from three probe transformation method; A) Torsion; B) x–axis translation; C) y-axis translation.
0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 01 0 - 6
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0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 5 0 01 0
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A
B
C
The solution process is computational intensive. The spectra resulting from the processing is depicted in Figure 11. The coordinate separation process greatly enhances the respective vibration features associated with the respective motion measurement direction. By further combining with the following information:
1. Torsional finite element model analysis.
2. Bump tests on the transducer mounting brackets.
3. Operational vibration, including shaft proximity sensor spectral data during nominal operation.
4. Pump and frame natural frequencies.
additional insight into the dynamic response of the electric motor driven pump can be found.
Inspection of the torsional spectrum in Figure 11A in conjunction with a finite element model results allows modes to be identified. The responses of modes 1 (30 Hz) and mode 3 (134) Hz are strong and well defined. However, the response of mode 2 (46 Hz) is less obvious. Also apparent are some unidentified responses (e.g., around 80Hz), along with ever-present power mains components at 60 and 120 Hz.
Integration of this information with the intermediate spectral results (i.e., cross probe coherence functions, order spectra, etc.) allowed for a more comprehensive understanding of the captured vibration features. As an example, Figure 12 shows a typical lateral response, with the identification of several features marked resulting from the analysis. The effects of the transducer mount resonant motion can be more readily identified. Also the effects of both the shaft lateral movement and the pump frame motion are separated and identified. Without the multi channel processing these responses would be artifacts contained in the computed TIM torsional response. Obviously, their appearance in the torsional spectrum would cloud the ability to interpret the results.
SUMMARY
Torsional vibration is inherently more difficult to measure than translational motion, it is susceptible to a number of measurement and processing issues. High amplitude order content introduced from measurement and/or processing of torsional vibration signals can obscure the fixed frequency components. Corrupting order content can be produced in time interval measurement schemes from a variety of sources. Corrective algorithms have been implemented to alleviate transducer and speed related computational errors.
Figure 12. Translational spectra illustrating the identification of response features.
Line power mains harmonics and speed controller artifacts can make torsional vibration measurement with electrical motor drives difficult. The dynamic response of sensor mounting hardware, the shaft line and framework can add further corruption and artifacts. The measurement and processing of multi channel TIMS sensors can be used to separate two dimensional lateral movement and torsional responses. While the processing is computationally intensive, the results can significantly enhance the ability to separate the respective directional dependent features.
Although torsional vibration is more difficult from both an instrumentation and computational perspective, the data is very useful in understanding the dynamics and responses of rotating equipment. Continued improvements to instrumentation, installation methods and processing algorithms should improve the capabilities and implementation costs. ACKNOWLEDGEMENTS This work was supported by the Electric Power Research Institute (EPRI Contract EP-P9801/C4961). The content of the information does not necessarily reflect the position or policy of the EPRI, and no official endorsement should be inferred. REFERENCES 1. Citron, S.J., O’Higgins J.E., and Chen, L.Y, “Cylinder By Cylinder Engine Pressure And Pressure Torque
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