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Angular resampling for vibration analysis in windturbines under non-linear speed fluctuation

Luisa F. Villa, Aníbal Reñones, Jose R. Perán, LuisJ. de Miguel

PII: S0888-3270(11)00067-7DOI: doi:10.1016/j.ymssp.2011.01.022Reference: YMSSP2747

To appear in: Mechanical Systems and Signal

Received date: 29 April 2010Revised date: 25 January 2011Accepted date: 30 January 2011

Cite this article as: Luisa F. Villa, Aníbal Reñones, Jose R. Perán and Luis J. deMiguel, An-gular resampling for vibration analysis in wind turbines under non-linear speed fluctuation,Mechanical Systems and Signal, doi:10.1016/j.ymssp.2011.01.022

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Angular resampling for vibration analysis in wind turbines under non-linear speed fluctuation.

Luisa F. Villa a, Aníbal Reñones a,* Jose R. Perán a, Luis J. de Miguel b

a CARTIF Foundation, Parque Tecnológico de Boecillo, 47151 Boecillo, Valladolid, Spain

b University of Valladolid, Spain Abstract: This work presents the development of an angular resampling algorithm for applying in conditions of high speed variability, as occurs in wind turbines, and the results obtained when applied to simulated signals, bearings diagnostic test-beds and wind turbines. The results improve the accuracy of similar resampling algorithms offered by the consulted bibliography. This algorithm is part of the wind turbine diagnostic system developed by the authors. Keywords: Angular resampling, vibration analysis, wind turbines

1. Introduction Predictive maintenance in wind turbines is being used to reduce costs and maintenance time. Such maintenance is based on monitoring the status and condition of the machinery throughout the life of the equipment [1]. The simple adaptation of existing systems is often not sufficient to make them suitable for wind turbines [2]. The most commonly used monitoring techniques for wind turbines are vibration analysis, oil analysis, thermography and acoustic monitoring. These techniques are applied to the rotor, power train and generator, which is where the most common faults arise [3, 4, 5]. Vibration analysis is the technique that provides the most information on the state of the gearbox and the generator. First of all, it is necessary to identify the operating frequencies [1, 2], and when calculating the frequency of component failure, the actual speed at any time must be taken into account for a proper vibration analysis [4]. Two types of frequency data are registered; a low-frequency field, with an associated long sampling time, in which the behavior of the structure and the low-speed rotating elements of the wind turbine are measured; and a high * Corresponding author. Tel.: +34983546504; fax:+34983546521. E-mail addresses: [email protected] (L. Villa), [email protected] (A. Reñones), [email protected] (L.J. de Miguel), [email protected] (J.R. Perán).

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frequency field, including analysis of high speed rotating elements [1] that present a lot of speed variation over long sampling times (smearing). It is, therefore, necessary to resort to angular resampling [6]. The main features that differentiate a wind turbine from a conventional rotary machine are the operating conditions under parameters of speed and variable load. For this reason, conventional techniques of signal processing must be modified to make them suitable for use in the monitoring of wind turbines.

2. Variable speed wind turbines One way of diminishing the load generated by the rotor, given the variability of wind speed over time, is to vary the speed of the turbine. When the turbine speed is constant, changes in wind speed result in abrupt changes in the torque transmitted, however, when the turbine speed varies, the rotor acts as a flywheel capable of storing part of the transitional mechanical energy introduced in the kinetic energy system of rotation. This softens the torque transmitted and the electric power generated [7]. The frequency of the grid controls the speed of the generator and, through the gearbox, the rotor speed. For this reason, the wind turbine rotor should turn at a relatively constant speed [8]. As for its rotational speed, two operating modes can be developed for the rotor of a wind turbine: fixed or variable speed. Wind turbines of variable speed and constant power coefficient are characterized by the fact that rotor speed varies with wind speed, so the rotor turns faster when the wind speed increases and slower otherwise. As the rotor turns at varying speeds, the electric wave frequency is also variable and therefore cannot send it directly to the grid. This grid interconnection is carried out through a rectifier-inverter system. The rectifier converts alternating current of variable frequency into a direct current and then the inverter converts the direct current into alternating current, but with a constant frequency equal to the grid (see figure 1) [8].

3. Angular resampling Vibration analysis has been implemented and studied in rotating machinery for many years. With the advance of technology, more complex systems that operate under more severe conditions have been developed; an example of this is wind turbines, which, as explained above, are subject to varying speeds and loads. The initial research in the area of transmission damage detection was focused on vibration signal analysis. At first, as discussed in [9], the statistical characteristics of the signal in the time domain were the primary focus of study. However, the field quickly expanded to include spectral analysis, time-frequency analysis, wavelet analysis, neural networks and mathematical modeling. This

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field is continuing to grow. As new signal processing techniques emerge, they are applied to the transmission damage detection problem and must be accommodated to the needs and specificities of each mechanical system. As for the analysis of systems operating under variable speed conditions, work has long been under way to find techniques that allow a better processing and analysis of the signals emitted by this type of systems. A theory of interpolation applied to time domain averaging was presented in [10] as an alternative to averaging when there is no rotational reference signal. The experiments shown in the work were performed in the gearbox of a helicopter. Later, in [11], a technique was developed which makes it possible to calculate the time domain averages of the tooth meshing vibration, of both the individual planet gears and the sun gear, in an epicyclic gearbox from information obtained by viewing the vibration through a small window in time as each of the planet gears passes a transducer mounted on the annulus gear. Each of the steps that comprise the order tracking method are explained in [12], where comparisons are made at each step and the best alternatives for each are given. Later, [13] presented a hybrid, computed order tracking method to perform angular resampling which was compared with two previously proposed methods by comparing the results. Simulation results showed that the accuracy of the traditional approach can be matched by asynchronously resampling sampled vibration signals in software. A method to perform angular resampling was presented in [6] using the acceleration signals directly without the need for an encoder signal, but this method has the limitation that it can only be used when speed variations are small and it requires a sufficient number of harmonics. This algorithm estimates the angular position of the shaft through a demodulation of a harmonic of the sampling frequency. An extension to the algorithm proposed by Bonnardot, the previously proposed algorithm, was presented in [14]. The harmonic used to estimate the angular position of the axis was chosen by trial and error. This article proposes a solution to automatically select this harmonic. The proposed methodology only requires the knowledge of an approximate value of the running speed and the number of teeth in the gears. The limitations of this method are: that it is not appropriate for ramp speed and that it is suitable for one stage of the gearbox only. In 2009, Combet extended a method previously proposed by Bonnardot and another by himself. An original method for the estimation of the instantaneous speed relative fluctuation (ISRF) in a vibration signal, measured on a system submitted to relatively heavy load and speed fluctuations and without speed measurement available, was proposed in [15]. Contrary to conventional methods based on the instantaneous frequency estimation of one spectral component, the proposed method for ISRF estimation does not depend on the

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choice of one particular component. However, it is not advisable for use in the case of very large speed variations, such as during acceleration.

4. Algorithm development The works that have been developed previously on the issue of angular resampling are applicable to cases in which the speed fluctuations are small [6, 10, 12, 13]. The method proposed by [12] includes the following steps; first records the data at constant t� increments, and them resamples this signal to provide the desired data at constant �� increments, based on a keyphasor signal. To determine the resample times, it is assumed that the shaft is undergoing constant angular acceleration, the shaft angle; � is described by the following quadratic equation:

2210)( tbtbbt ���� (1)

The unknown coefficients 0b , 1b and 2b are found by fitting three successive keyphasor arrival times ( 1t , 2t and 3t ), which occur at known shaft angle increments. Once the resample times are calculated, the corresponding amplitudes of the signal are calculated by interpolating between the sampled data. After the amplitudes are determined, the resampled data are transformed from the angle domain to the order domain by means of an FFT. The application of this kind of signal processing to the vibration analysis of wind turbines is limited, because the angular speed and hence acceleration variations experienced in a wind turbine are high and are not predictable as they depend on the wind. This paper presents an evolution of the angular resampling algorithm proposed by [12] and applies it to the speed variation that usually occurs in a variable speed wind turbine. For the implementation of this algorithm, speed signals are available so that eliminate the need for a speed estimation that is performed in other works [14, 15]. Different speed profiles, measured in a variable speed wind turbine of 850 kW, are presented in figure 2. The graphs show the evolution of rotational speed in the rotor during 85 seconds (the equivalent frequency precision of this sampling time is marked with a square bracket). Such a variation is caused by the variation in wind speed, as explained before. In order to know whether this variation could influence the subsequent frequency analysis, it is necessary to know the minimum frequency that must be analyzed, and then to fix a desired frequency precision. This precision can be expressed as the minimum measuring time, and the variation of the speed during this time must then be analyzed in order to see if the angular resampling has to be performed, so as to avoid the so-called smearing of the different frequencies in a FFT analysis. Usually, the minimum frequency to be analyzed is the frequency associated to the speed of the rotor. The minimum speed of the analyzed wind turbine is around 15 rpm (0.25 Hz). Then, with a minimum desired precision between 10

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and 20 lines for this frequency (0.025-0.0125 Hz), the measuring time should be between 40 s and 80 s. An increase in precision to 50 lines would lead to 200 s of measuring time. With a precision of 0.0125 Hz (0.75 rpm and 80 s of measuring time), the allowed variation in rotor speed before smearing should be less than 5% for the minimum speed of 0.25 Hz (15 rpm). It is clear from the analysis of figure 2 that the angular resampling is necessary if the analysis of the rotor is required, due to the fact that the variation in speed is around 5 to 10 times the frequency precision (0.0125 Hz). Moreover, the fact that the speed variation increases in line with the increase in the analyzed order must be taken into account. Due to the fact that the speed varies considerably between consecutive rotations, the decision taken was to use more than one pulse per revolution, and to use the full profile of the speed instead the analysis of three consecutive samples like the algorithm presented in [12]. The rotor of the wind turbine has 24 holes at its blade side for use by speed control system, and these keyphasor were used to perform the following algorithm (see figure 3): � Estimation of the resampled times � ���kt * , for which there is a constant

angular increment: perform an spline interpolation using the keyphasor angular positions � �k��� ,,, 21 � and their arrival times � �kttt ,,, 21 � , see figure 3(a).

� Spline interpolation of the original sampled vibration signal � �tV at the resampled time instants � ���kt * .The angular increment is taken to have the original number of samples at the final angular position k� .

It must be said that the proposed algorithm was not intended for use in real time conditions.

5. Simulated tests First, simulation tests were performed using simulated signals in order to build the algorithm under controlled conditions. These simulations allow different algorithm conditions, such as the interpolation method, number of pulses per revolution and non uniform keyphasor angles, to be tested. The interest of simulating non-uniform separation of pulses is to study the effect of a failure in the speed measurement as will be explained below. The simulated signals consist of a carrier sinusoidal signal with sidebands. The signal is similar to the modulation generated by a gearbox. Both carrier and sidebands are modulated in frequency by the speed variation. The test also shows this modulation generated using an additional sinusoidal speed variation. The equation generated is presented in (2) [6]:

� � � � mM

mmm nnTfmnaXnx �� ���

�1

02cos1)( (2)

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Where 1f could be seen as the frequency of one of the gears, T is the number of teeth, 1Tf is the meshing frequency, m is the number associated with harmonic of the meshing frequency, mX is the amplitude of the � �thm harmonic,

m� is the original phase and � �nam are the amplitude modulation function. � � 2/2sin* tfAa vmm �� (3)

Where mA is the average speed and vf is the speed variation frequency. The number of terms in the previous formula, for simplicity, takes 1�m and the term of the sine function � �nam has the same frequency modulation of the carrier cosine term [6]. The aim is to simulate a speed signal, with speed variation and amplitude similar to measurements in the wind turbine. As a result, and having as a reference the profile speed of figure 2c, a speed signal is simulated with a frequency of 0.03 Hz, amplitude 0.25 Hz, mean value 0.4 Hz and keyphasor sampling resolution = 2 kHz for a capture time of 85 s. Figure 4 (a) presents the spectrum of the generated signal, expressed in orders (carrier order = 10 and sideband order =1), while in figure 4 (b), the corresponding angular resampling spectrum uses 1 pulse per revolution with the algorithm presented in this work. With the increase in speed variation (speed signal of frequency 0.09 Hz), the angular resampling starts to create spurious sidebands that can only be avoided by increasing the number of pulses per revolution, as is shown in figure 5. Another interesting aspect is to test the non-uniform separation of pulses. The interest of this experiment is to simulate the effect of a fault in the speed measurement due to the discrepancy between the physical location of the keyphasors and the uniform angle configuration of the algorithm. We take this into account in our algorithm producing a discrepancy in the angular distance between pulses. Figure 6 shows that, with a deviation of 1% in the angular location of every pulse, the resampled spectrum shows sidebands of order 1 throughout the spectrum. This is due to the discrepancy in the angular distance between pulses, which is not accurate. On the other hand, it must be said that this is only noticeable with a logarithmic scale for the spectrum or with higher deviations (10% and above). These sidebands are more noticeable with higher orders of the carrier (100 and above). Another effect of this non-uniform separation of keyphasors is that the height of the resulting sidebands is not exactly the same. It must be said that similar effect (order 1 sidebands) is obtained if the number of keyphasors configured in the algorithm is different from the reality, due to an error. That kind of errors could lead to an incorrect diagnosis of the mechanical system under monitoring.

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The algorithm developed in this work has also been compared with the algorithm presented in [12], which was developed for a constant angular acceleration. Figure 7 shows the comparison of both algorithms for the signal generated above. The constant acceleration algorithm generates a spectrum with spurious orders, because that algorithm is only valid for constant acceleration signals and that is not the case of the signal analyzed in figure 7. This behavior can be improved by increasing the number of pulses, but still, when it comes to reconstructing high orders, supposing a constant acceleration also means the resampling will be problematic. As seen in Figure 8, which compares the algorithms for a carrier signal of order 100 and 10 pulses per revolution, it is possible to verify the spurious patterns generated symmetrically in the orders 90 and 110 when the algorithm is based on constant acceleration. These spurious sidebands could lead also to an incorrect diagnosis. The algorithm developed in the current work solves this problem as can be seen in Figure 8.

6. Test bed tests In order to test the algorithm under real conditions, the proposed algorithm was tested in a test bed (figure 9). The PT 500.12 rolling elements bearings faults kit, designed by Gunt Hamburg [16], allows the simulation of five different types of bearing damage. The system has a three-phase cage induction asynchronous motor mounted on a base that can be adjusted to cause misalignment. To simulate vibration and develop exercises related to imbalance and alignment, the system has bearings in good condition and others with different types of defect, weight plates, shafts of different lengths and various types of joints. It also has a brake that allows studies of vibration in load conditions [16]. The tests were carried out using a bearing with damage to the inner ring and different accelerations. The results presented below are two measurements with different values of acceleration, but with equal average speed value 0.787352 Hz (figure 10). In the first case, where the acceleration is 1 rpm/s (0.0166 Hz/s), the accuracy in frequency is 0.0394 Hz (25s of measuring time), in the case of 20 lines of frequency (for the first harmonic at a speed of 47 rpm). Due to the fact that the speed difference is less than this precision, angular resampling is not required for the fundamental harmonic. In the case of the sixth harmonic and later, angular resampling is necessary, as this relationship is no longer fulfilled (figure 11).

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In the second case, where the acceleration is 10 rpm/s (0.1667 Hz/s), the accuracy in frequency is 0.0394 Hz (25s of measuring time), in the case of 20 lines of frequency (for the first harmonic at a speed of 47 rpm). Due to the fact that the speed difference is greater than this precision, angular resampling is required for the fundamental harmonic and therefore for the rest of harmonics (figure 12).

7. Wind turbines tests This section shows the results of the angular resampling algorithm applied to vibration and speed signals measured in various wind turbines. The speed measurement was done taking advantage of 24 present orifices in the main shaft of the turbine, which are used for the control of the machine. Similarly, in the generator shaft, the measurement of the instantaneous speed was carried out for 10 bolts used for the assembly of the flexible coupling that connects the gearbox and generator. Examples of speed profiles measured in the main shaft are shown in Figure 2 and the need to carry out an angular resampling is obvious. Using the same reasoning as in section 4, the conclusion is that the angular resampling of the vibration of the generator is not necessary, at least for the first speed harmonics. In the gearbox, however, due to the speeds of the different stages, this resampling will be necessary. Figures 13 and 14 show the result of applying the angular resampling algorithm to the vibration measured in the carrier of the gearbox on the side of the slow shaft (Fig. 13), and the slow shaft of the entrance to the gearbox (Figure 14). Applying the algorithm of the current work, the improvement in the precision with respect to the algorithm presented in [12], which carried out a linear approximation of the acceleration, is obvious.

8. Conclusions The present work shows an angular resampling algorithm suitable for use in wind turbines where the speed variability makes the resampling essential, especially in the main shaft. The algorithms of the literature are based on the assumption that the acceleration is constant which is not true for a real case like wind turbines. The main improvement of the proposed algorithm is to take full advantage of the whole measured speed to obtain an accurate angular resampled vibration. The developed algorithm was tested with simulated signals, on test-bed and with real signals of vibration and speed of wind turbines. The simulated and test-bed experiments have allowed the fine-tunning of the algorithm, the study of the influence of the different parameters and the simulation of different situations like the influence of a non-uniform separation of keyphasors. The algorithm developed has also been tested with real wind turbine signals, where the improvement has been verified with regard to the algorithm in [12].

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Acknowledgments: The authors wish to thank Iberdrola for finance and support in this project. The research work developed in this paper was partially supported by the funded projects: CICYT reference DPI2006-09866 “Failure detection and automatic diagnosis of wind turbines” and CICYT reference DPI2009-14608-C02-02 “Diagnosis of wind turbines based on analytical redundancy”. Special thanks to Roberto Arnanz for his work in the project and Mario Ruiz for his aid with the simulated tests. Figure Captions Figure 1. Variable speed wind turbine [8]. Figure 2. Different speed profiles in the rotor of a wind turbine measured over 85 s. Figure 3. Angular resampling algorithm implemented. Figure 4. (a) Spectrum before angular resampling, (b) Spectrum after angular resampling. Figure 5. (a) Spectrum before angular resampling, (b) Spectrum after angular resampling with 1 pulse per revolution, (c) Spectrum after angular resampling with 24 pulses per revolution. Figure 6. Non uniform location of pulses (a) Log scale, (b) Linear scale. Figure 7. Comparison of resampling algorithm developed in the current article and the algorithm presented in [12]. Figure 8. Comparison of resampling algorithm to a carrier of order 100 and 10 pulses per revolution. Figure 9. Bearings test bed. Figure 10. Speed per revolution (a) Acceleration of 1 rpm/s, (b) Acceleration of 10 rpm/s. Figure 11. Spectrum before and after angular resampling for a signal with acceleration of 1 rpm/s. Figure 12. Spectrum before and after angular resampling for a signal with acceleration of 10 rpm/s.

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Figure 13. (a) Speed profile, (b) Spectrum before and after angular resampling. Measuring time 55s, 24 pulses per revolution. Figure 14. (a) Speed profile, (b) Spectrum before and after angular resampling. Measuring time 180s, 24 pulses per revolution.

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References:

[1] A. Creus, Aerogeneradores. 2008.

[2] T. W. Verbruggen, Wind turbine operation and maintenance based on condition monitoring. Final report, 2003.

[3] UpWind, “state of the art” report condition monitoring for wind turbines, 2006.

[4] V. Giao, A. Ordóñez, Implantación de un sistema de mantenimiento predictivo de averías en el tren de potencia de un aerogenerador. Universidad de Sevilla, 2006.

[5] Z. Hameed, Y. S. Hong, Y. M. Cho, S. H. Ahn, C. K. Song, Condition monitoring and fault detection of wind turbines and related algorithms: a review . Renewable and Sustainable Energy Reviews 13 (1) (2009) 1-39.

[6] F. Bonnardot, M. El Badaoui, R. B. Randall, J. Danière, F. Guillet, Use of the acceleration signal of a gearbox in order to perform angular resampling (with limited speed fluctuation), Mechanical Systems and Signal Processing 19 (2005) 766–785.

[7] J. L. Rodríguez, J. C. Burgos, S. Arnalte, Sistemas eólicos de producción de energía eléctrica, Madrid, 2003.

[8] M. Villarrubia, Energía eólica, 2004.

[9] P. D. Samuel, D. J. Pines, A review of vibration-based techniques for helicopter transmission diagnostics, Journal of Sound and Vibration 282 (2005) 475-508.

[10] P.D. McFadden, Interpolation techniques for time domain averaging of gear vibration, Mechanical Systems and Signal Processing 3 (1) (1989) 87–97.

[11] P.D. McFadden, A technique for calculating the time domain averages of the vibration of the individual planet gears and the sun gear in an epicyclic gearbox, Journal of Sound and Vibration 144 (1) (1991) 163–172.

[12] K.R. Fyfe, D.S. Munck, Analysis of computed order tracking, Mechanical Systems and Signal Processing 11 (2) (1997) 187–205.

[13] K.M. Bossley, R.J. Mckendrick, C.J. Harris, C. Mercer, Hybrid computed order tracking, Mechanical Systems and Signal Processing 13 (4) (1999) 627–641.

[14] F. Combet, L. Gelman, An automated methodology for performing time synchronous averaging of a gearbox signal without speed sensor, Mechanical Systems and Signal Processing 21 (2007) 2590–2606.

Bibliography

[15] F. Combet, R. Zimroz, A new method for the estimation of the instantaneous speed relative fluctuation in a vibration signal based on the short time scale transform, Mechanical Systems and Signal Processing 23 (2009) 1382-1397. [16] Gunt Hamburg. G.U.N.T. Gerätebau GmbH, Experiment instructions Equipment for engineering education, Barsbüttel, Germany, 2004.