Wind Turbine Gearbox Condition - Mecânica dos Fluidos (2025)

Prévia do material em texto

<p>NREL is a national laboratory of the U.S. Department of Energy, Office of Energy</p><p>Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.</p><p>Contract No. DE-AC36-08GO28308</p><p>Wind Turbine Gearbox Condition</p><p>Monitoring Round Robin Study –</p><p>Vibration Analysis</p><p>S. Sheng, Editor</p><p>National Renewable Energy Laboratory</p><p>Technical Report</p><p>NREL/TP-5000-54530</p><p>July 2012</p><p>NREL is a national laboratory of the U.S. Department of Energy, Office of Energy</p><p>Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.</p><p>National Renewable Energy Laboratory</p><p>15013 Denver West Parkway</p><p>Golden, Colorado 80401</p><p>303-275-3000 • www.nrel.gov</p><p>Contract No. DE-AC36-08GO28308</p><p>Wind Turbine Gearbox Condition</p><p>Monitoring Round Robin Study –</p><p>Vibration Analysis</p><p>S. Sheng, Editor</p><p>National Renewable Energy Laboratory</p><p>Prepared under Task No. WE11.0305</p><p>Technical Report</p><p>NREL/TP-5000-54530</p><p>July 2012</p><p>NOTICE</p><p>This report was prepared as an account of work sponsored by an agency of the United States government.</p><p>Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty,</p><p>express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of</p><p>any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately</p><p>owned rights. Reference herein to any specific commercial product, process, or service by trade name,</p><p>trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation,</p><p>or favoring by the United States government or any agency thereof. The views and opinions of authors</p><p>expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.</p><p>Available electronically at http://www.osti.gov/bridge</p><p>Available for a processing fee to U.S. Department of Energy</p><p>and its contractors, in paper, from:</p><p>U.S. Department of Energy</p><p>Office of Scientific and Technical Information</p><p>P.O. Box 62</p><p>Oak Ridge, TN 37831-0062</p><p>phone: 865.576.8401</p><p>fax: 865.576.5728</p><p>email: mailto:reports@adonis.osti.gov</p><p>Available for sale to the public, in paper, from:</p><p>U.S. Department of Commerce</p><p>National Technical Information Service</p><p>5285 Port Royal Road</p><p>Springfield, VA 22161</p><p>phone: 800.553.6847</p><p>fax: 703.605.6900</p><p>email: orders@ntis.fedworld.gov</p><p>online ordering: http://www.ntis.gov/help/ordermethods.aspx</p><p>Cover Photos: (left to right) PIX 16416, PIX 17423, PIX 16560, PIX 17613, PIX 17436, PIX 17721</p><p>Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.</p><p>http://www.osti.gov/bridge</p><p>mailto:reports@adonis.osti.gov</p><p>mailto:orders@ntis.fedworld.gov</p><p>http://www.ntis.gov/help/ordermethods.aspx</p><p>i</p><p>Acknowledgements</p><p>The National Renewable Energy Laboratory’s (NREL) contributions to this report were funded</p><p>by the Wind and Water Power Program, Office of Energy Efficiency and Renewable Energy of</p><p>the U.S. Department of Energy, under contract No. DE-AC02-05CH11231. The authors are</p><p>solely responsible for any omission or errors contained herein. NREL wishes to acknowledge</p><p>and thank the Office of Energy Efficiency and Renewable Energy and its staff who have</p><p>supported this work from its inception. Specifically, NREL would like to thank Mark Higgins</p><p>and Michael Derby for their support and guidance.</p><p>NREL deeply appreciates the voluntarily support from all sixteen partners of the Wind Turbine</p><p>Gearbox Condition Monitoring Round Robin project. One project partner estimates that the</p><p>value of the voluntary support from all partners would be worth $2 to $3 million.</p><p>ii</p><p>Nomenclature</p><p>Acronym Definition</p><p>A/D analog to digital</p><p>AM amplitude modulation</p><p>BPFI ball-passing frequency inner race</p><p>BPFO ball-passing frequency outer race</p><p>BSF ball-spinning frequency</p><p>CF crest factor</p><p>CI condition indicator</p><p>CM condition monitoring</p><p>COE cost of energy</p><p>CRB cylindrical roller bearing</p><p>DAS data acquisition system</p><p>DOD Department of Defense</p><p>DOE Department Of Energy</p><p>DSTO Defence Science and Technology Organisation (Australia)</p><p>DTF Dynamometer Test Facility</p><p>EO energy operator</p><p>fcCRB full complement cylindrical roller bearing</p><p>FFT Fast Fourier Transform</p><p>FTF fundamental train frequency</p><p>FM frequency modulation</p><p>GE General Electric</p><p>GL Germanischer Lloyd</p><p>GRC Gearbox Reliability Collaborative</p><p>GMF gear meshing frequency</p><p>HS High speed</p><p>HSGM high-speed gear meshing stage</p><p>HSIS high-speed intermediate shaft</p><p>HSS high-speed shaft</p><p>ISGM intermediate speed gear meshing stage</p><p>IMS intermediate-speed shaft</p><p>IMS Intelligent Maintenance Systems</p><p>INT intermediate</p><p>JTFA joint time frequency analysis</p><p>iii</p><p>Acronym Definition</p><p>LS low speed</p><p>LSIS low-speed intermediate shaft</p><p>LSS low-speed shaft</p><p>MS main shaft</p><p>NASA National Aeronautics and Space Administration</p><p>NREL National Renewable Energy Laboratory</p><p>NWTC National Wind Technology Center</p><p>O&M operation and maintenance</p><p>PGSF spin frequency of the planetary gear</p><p>PLC planet carrier</p><p>PLTGM planetary gear meshing stage</p><p>RMS root mean square</p><p>RPM revolutions per minute</p><p>SER sideband energy ratio</p><p>SF severity factor</p><p>SH shaft</p><p>SK spectral kurtosis</p><p>SO shaft order</p><p>TRB tapered roller bearing</p><p>TSA time synchronous averaging</p><p>iv</p><p>Executive Summary</p><p>Utility-scale wind turbines have historically experienced premature component failures, which</p><p>subsequently increase the cost of energy. The majority of these failures are caused by faults in</p><p>the drivetrain, led by the main gearbox. To understand the possible causes for gearbox failures</p><p>and recommend practices for improvement, the National Wind Technology Center (NWTC), at</p><p>the National Renewable Energy Laboratory (NREL), started a project called the Gearbox</p><p>Reliability Collaborative (GRC). Condition Monitoring (CM) is one research area under the</p><p>GRC. It is a method to assess a system’s health, which enables proactive maintenance planning,</p><p>reduces downtime and operations and maintenance costs, and, to some extent, increases safety.</p><p>To understand the dynamic responses of wind turbine gearboxes under different loading</p><p>conditions, the GRC tested two identical gearboxes. One was tested on the NWTC’s 2.5 MW</p><p>dynamometer and the other was first tested in the dynamometer, and then field tested in a turbine</p><p>in a nearby wind plant. In the field, the test gearbox experienced two oil loss events that resulted</p><p>in damage to its internal bearings and gears. Since the damage was not catastrophic, the test</p><p>gearbox was removed from the field and retested in the NWTC’s dynamometer before it was</p><p>disassembled. During the dynamometer retest, various condition monitoring systems, e.g.,</p><p>vibration and oil debris, collected data along with testing condition information. The vibration-</p><p>based condition monitoring system and the test condition data enabled NREL to launch a Wind</p><p>Turbine Gearbox Condition Monitoring Round Robin project, as described in this report. The</p><p>main objective of this project is to evaluate different vibration analysis algorithms used in wind</p><p>turbine CM and determine whether typical practices are effective. With the involvement of both</p><p>academic researchers and industrial partners, the Round Robin provides cutting edge research</p><p>results to industry stakeholders.</p><p>Under this project, the collected vibration and testing condition data, along with the test gearbox</p><p>configuration information, were shared with partners who signed memoranda of understanding</p><p>documents with NREL. The partners were given a time window of two months to analyze the</p><p>shared data using whichever algorithms they had or could develop. Partners did not have prior</p><p>knowledge of the extent or location of the damage in the test gearbox. After their diagnostic</p><p>results were submitted to NREL, the actual damage information on the test gearbox was</p><p>disclosed to them so they could further fine tune</p><p>sensors.</p><p>In the early days, this enveloping detection process was performed using several analog devices.</p><p>As shown in Figure 3.5, the conditioned vibration sensor signal is first passed through an analog</p><p>filter to isolate the impulse response excited by the bearing damage. The filtered response is</p><p>then passed through a rectifier to flip the negative half of the oscillation signal to the positive</p><p>side. The rectified signal is fed into an envelope detector to identify the envelope of the signal.</p><p>The envelope signal is then used to identify bearing damage signature through a signal analyzer.</p><p>If necessary, a low-pass filter can be added before the analyzer.</p><p>18</p><p>The process shown in Figure 3.5 works well, if all the analog devices are appropriately designed</p><p>for a particular application. However, a different application may require different parameter</p><p>settings of the analog devices. For example, the bearing support system may have a different</p><p>resonant structure; thus, it requires a different cut-off frequency design for the band-pass filter to</p><p>isolate the damage impulse response. For different structural damping, the envelope detector</p><p>needs a different time constant design to match the impulse response decay rate, so that the</p><p>bearing damage-related high frequency and low amplitude vibration signals can be maximized.</p><p>More importantly, the bearing damage detection is usually conducted in a harsh environment.</p><p>An increased number of electronic components involved in the bearing defect detection process</p><p>will usually decrease the overall system reliability.</p><p>Figure 3.5. Analog devices-based approach</p><p>With the improvement of computer technology and the development of high dynamic range A/D</p><p>converters, the acceleration enveloping-based bearing damage detection becomes much easier to</p><p>implement. Many of the analog devices, as shown in Figure 3.5, can now be replaced by digital</p><p>signal processing techniques, thus improving detection accuracy and system reliability. One</p><p>possible digital signal processing-based realization of acceleration enveloping is shown in Figure</p><p>3.6. The conditioned acceleration signal is first digitized with high speed and high dynamic range</p><p>A/D converter. The high speed and high dynamic range A/D is especially important because it</p><p>ensures that the digitized vibration data contain low amplitude high frequency resonant responses</p><p>excited by the bearing damage impulse. The digitized data are then passed through a digital</p><p>band pass filter to isolate the resonant response excited by the bearing damage. Next, the</p><p>enveloping detection algorithm is used to detect the envelope of the filtered data. In the digital</p><p>domain, this process can be achieved by the Hilbert transform. The digital Hilbert transform is</p><p>related to the FFT and can be easily achieved [12]. If accurate enveloping detection is required,</p><p>a local maximum interpolation technique can provide better results [13]. The bearing damage</p><p>detection is then accomplished by spectrum analysis on the enveloped data.</p><p>19</p><p>Figure 3.6. Digital processing-based approach</p><p>3.2 Round Robin Analysis Results</p><p>3.2.1 Bearing and Gear Damage Features</p><p>Based on the gear configuration data given by NREL, the gear damage features were calculated</p><p>and listed in Table 3.1. Similarly, the bearing damage features were calculated and listed in</p><p>Table 3.2. In both tables, MS stands for Main Shaft. The bearing notations used in Table 3.2 is</p><p>the same as those used in the test gearbox failure analysis report [4] and illustrated in Figure 3.7.</p><p>The numbers of gear mesh teeth count are also marked in Figure 3.7.</p><p>Figure 3.7. Gearbox power flow</p><p>20</p><p>Table 3.1. Gear damage features</p><p>Shaft frequencies</p><p>Relative freq at 1800 rpm at 1200 rpm</p><p>MS HSS [rpm] [Hz] [rpm] [Hz]</p><p>Rotor/carrier 1.00 0.012 22.1 0.37 14.7 0.25</p><p>Planets (minus carrier rotation) 2.54 0.031 56.1 0.93 37.4 0.62</p><p>Planets 3.54 0.043 78.2 1.30 52.1 0.87</p><p>Sun shaft (minus carrier rotation) 4.71 0.058 104.1 1.74 69.4 1.16</p><p>Sun shaft 5.71 0.070 126.2 2.10 84.1 1.40</p><p>Intermediate shaft 20.37 0.250 450.0 7.50 300.0 5.00</p><p>Generator shaft 81.49 1.000 1800.0 30.00 1200.0 20.00</p><p>Gear mesh tooth passing freqs</p><p>Gear mesh - Planet > Ring 99.00 1.215 3048.2 36.45 2032.1 33.87</p><p>Gear mesh - Sun > Planet 99.00 1.215 3048.2 36.45 2032.1 33.87</p><p>Gear mesh - Sun shaft > Intermediate 468.57 5.750 10350.0 172.50 6900.0 115.00</p><p>Gear mesh - Intermediate > HSS 1792.80 22.000 39600.0 660.00 26400.0 440.00</p><p>Single gear tooth fault freqs</p><p>HSS gear set pinion (HSS) 81.49 1.000 1800.0 30.00 1200.0 20.00</p><p>HSS gear set wheel (intermediate shaft) 20.37 0.250 450.0 7.50 300.0 5.00</p><p>Intermediate gear set pinion (intermediate shaft) 20.37 0.250 450.0 7.50 300.0 5.00</p><p>Intermediate gear set wheel (sun shaft) 5.71 0.070 126.2 2.10 84.1 1.40</p><p>Sun gear 14.14 0.174 312.4 5.21 208.3 3.47</p><p>Planet gear 7.08 0.087 156.3 2.61 104.2 1.74</p><p>Ring gear 3.00 0.037 66.3 1.10 44.2 0.74</p><p>21</p><p>Table 3.2. Bearing damage features</p><p>Bearings Relative Freq</p><p>Main Bearing MS HSS</p><p>Main bearing (INP-A) - roller rotation freq 5.22 0.064</p><p>Main bearing (INP-A) - cage freq 0.45 0.006</p><p>Main bearing (INP-A) - roller defect freq (= 2 x roller rotation freq) 10.44 0.128</p><p>Main bearing (INP-A) - outer race defect freq 12.70 0.156</p><p>Main bearing (INP-A) - inner race defect freq 15.30 0.188</p><p>HSS A1 & A2 Relative freq</p><p>HSS-A1 and A2 - roller rotation freq 253.99 3.117</p><p>HSS-A1 and A2 - cage freq 34.63 0.425</p><p>HSS-A1 and A2 - roller defect freq (= 2 x roller) 507.98 6.234</p><p>HSS-A1 and A2 - outer race defect freq 691.89 8.490</p><p>HSS-A1 and A2 - inner race defect freq 937.93 11.510</p><p>HSS B Relative freq</p><p>HSS-B - roller rotation freq 254.78 3.127</p><p>HSS-B - cage freq 47.10 0.578</p><p>HSS-B- roller defect freq (= 2 x roller) 509.56 6.253</p><p>HSS-B- outer race defect freq 584.60 7.174</p><p>HSS-B - inner race defect freq 800.74 9.826</p><p>ISS C1 &C2 Relative freq</p><p>ISS-C1&C2 - roller rotation freq 106.14 1.303</p><p>ISS-C1&C2 - cage freq 9.25 0.114</p><p>ISS-C1&C2 - roller defect freq (= 2 x roller) 211.88 2.600</p><p>ISS-C1&C2 - outer race defect freq 287.25 3.525</p><p>ISS-C1&C2 - inner race defect freq 344.30 4.225</p><p>ISS D Relative freq</p><p>ISS-D - roller rotation freq 63.70 0.782</p><p>ISS-D - cage freq 11.78 0.145</p><p>ISS-D- roller defect freq (= 2 x roller) 127.39 1.563</p><p>ISS-D- outer race defect freq 146.15 1.793</p><p>ISS-D - inner race defect freq 200.19 2.457</p><p>22</p><p>Table 3.2. Bearing damage features (continued)</p><p>Bearings Relative Freq</p><p>LSS E1&E2 Relative freq</p><p>LSS-E1&E2 - roller rotation freq 41.37 0.508</p><p>LSS-E1&E2 - cage freq 2.67 0.033</p><p>LSS-E1&E2 - roller defect freq (= 2 x roller) 82.86 1.017</p><p>LSS-E1&E2 - outer race defect freq 109.71 1.346</p><p>LSS-E1&E2 - inner race defect freq 124.57 1.529</p><p>Hollow Shaft F Relative freq</p><p>HS-F - roller rotation freq 47.20 0.579</p><p>HS-F - cage freq 3.03 0.037</p><p>HS-F - roller defect freq (= 2 x roller) 94.39 1.158</p><p>HS-F - outer race defect freq 139.61 1.713</p><p>HS-F - inner race defect freq 157.53 1.933</p><p>Carrier G Relative freq</p><p>Carrier-G - roller rotation freq 8.59 0.105</p><p>Carrier-G - cage freq 0.53 0.006</p><p>Carrier-G - roller defect freq (= 2 x roller) 17.17 0.211</p><p>Carrier-G - outer race defect freq 25.43 0.312</p><p>Carrier-G - inner race defect freq 28.57 0.351</p><p>Carrier H Relative freq</p><p>Carrier-H - roller rotation freq 8.11 0.100</p><p>Carrier-H - cage freq 0.53 0.007</p><p>Carrier-H - roller defect freq (= 2 x roller) 16.22 0.199</p><p>Carrier-H - outer race defect freq 23.93 0.294</p><p>Carrier-H - inner race defect freq 27.07 0.332</p><p>Planet 1G&1R Relative freq</p><p>Planet-1G&1R - roller rotation freq 8.28 0.102</p><p>Planet-1G&1R - cage freq 1.46 0.018</p><p>Planet-1G&1R - roller defect freq (= 2 x roller) 16.57 0.203</p><p>Planet-1G&1R - outer race defect freq 19.42 0.238</p><p>Planet-1G&1R - inner race defect freq 26.27 0.322</p><p>23</p><p>3.2.2 Tool Development</p><p>A MATLAB-based tool was developed for easy data processing operations.</p><p>The tool</p><p>incorporated regular FFT spectrum analysis, acceleration enveloping analysis, synthesized</p><p>synchronous sampling, and order analysis.</p><p>3.2.3 Damaged Gearbox Data analysis</p><p>The main goal of the Round Robin project was to identify the gear and bearing damage</p><p>associated with the gearbox. In our analysis, we categorized the gear damage according to the</p><p>gearbox meshing stages: the high speed gear meshing stage (HSGM), the intermediate gear</p><p>meshing stage (ISGM), and the planetary gear meshing stage (PLTGM). For bearings, we</p><p>categorize the damage according to the shaft, which the bearing is associated with, i.e., the High</p><p>Speed Shaft (HSS), the High Speed Intermediate Shaft (HSIS), the Low Speed Intermediate</p><p>Shaft (LSIS), and the Low Speed Shaft (LSS) or the Main Shaft (MS).</p><p>3.2.3.1 HSGM</p><p>The sensor AN7 was used to evaluate the HSGM stage health condition. From the order</p><p>spectrum, it can be clearly seen that the fundamental gear meshing order is heavily modulated by</p><p>the HSS speed, as seen in Figure 3.8.The sideband energy ratio (SER) is over three, which</p><p>indicates severe gear damage in the HSGM pinion. The sideband contents in the higher order</p><p>harmonics of HSGM also indicate the pinion damage, as seen in Figure 3.9 and Figure 3.10.</p><p>Post-test examination indicated that the HSP had severe scuffing [4].</p><p>Figure 3.8. HSGM (22) modulated by HSS (1)</p><p>24</p><p>Figure 3.9. HSGM X2 (44) modulated by HSS (1)</p><p>Figure 3.10. HSGM X3 (66) modulated by HSS (1)</p><p>Similar order analyses also indicated that the HSGM order was modulated by the HSIS shaft</p><p>(Figure 3.11). This kind of modulation is visible in the HSGMX2 and HSGMX3 as well (refer</p><p>to Figure 3.12 and Figure 3.13 respectively). Post-test examination indicated that the HSG also</p><p>had severe scuffing [4].</p><p>25</p><p>Figure 3.11. HSGM (22) modulated by HSIS (0.25)</p><p>Figure 3.12. HSGM X2 (44) modulated by HSIS (0.25)</p><p>26</p><p>Figure 3.13. HSGM X2 (66) modulated by HSIS (0.25)</p><p>3.2.3.2 ISGM</p><p>Damage signatures related to the ISGM were not shown in the vibration analysis. As seen in</p><p>Figure 3.14 though, the ISGM and higher order harmonics do exist. However, the shaft</p><p>modulations are too small to draw any conclusion regarding the gear damage. The post-test</p><p>examinations revealed fretting corrosion, polishing wear, and scuffing damage in the ISGM</p><p>pinion; however, the damage was imprinted on all teeth because the gear-set had a hunting tooth</p><p>gear ratio, which has potentially smoothed out the damages and reduced vibration responses</p><p>incurred by the damage.</p><p>Figure 3.14. ISGM and higher order harmonics</p><p>27</p><p>3.2.3.3 PLTGM</p><p>For planetary gear stage damage detection, sensors AN3 and AN4 were used (refer to Table 2.3</p><p>for more information on sensors). The planetary gear set arrangement in this gearbox is a</p><p>simultaneous mesh; thus, there was no cancellation/enhancement around the gear mesh</p><p>frequency and harmonics, as seen in the sequential mesh design. Detailed order spectrum</p><p>analysis indicated that the planetary gear mesh order and its harmonics are present Figure 3.15</p><p>for sensor AN4). Sidebands of planet passing are visible around the PLTGM and its harmonics.</p><p>The modulation is significant at the third harmonic of the PLTGM (Figure 3.16). Similar</p><p>information can be extracted from the sensor AN3 and the corresponding order spectra are</p><p>shown in Figure 3.17 and Figure 3.18, respectively.</p><p>The acceleration enveloping analysis of the sensor AN3 (Figure 3.19) indicated that the damage</p><p>is likely associated with the ring gear (0.037 Order), instead of planet gear (0.087 Order) or sun</p><p>gear (0.174 Order). Post-test examination confirmed the ring gear scuffing and polishing</p><p>damage [4].</p><p>The post-test also indicated severe fretting corrosion on the sun pinion. Though the sun/plant</p><p>gear meshing is evident in the data analysis, as shown in Figure 3.15 and Figure 3.17, the LSIS</p><p>shaft modulation (0.07 Order) is very small (Figure 3.20); thus, the sun pinion damage is</p><p>inconclusive using current vibration-based analysis.</p><p>Figure 3.15. Planetary gear stage meshing order and harmonics from AN4</p><p>28</p><p>Figure 3.16. PLTGM X3 modulated by planet passing order (0.037)</p><p>Figure 3.17. Planetary gear stage meshing order and harmonics from AN3</p><p>29</p><p>Figure 3.18. PLTGM X3 and X4 modulated by planet passing order (0.037)</p><p>Figure 3.19. Sensor AN3 acceleration enveloping order spectrum</p><p>30</p><p>Figure 3.20. Modulation by LSIS in PLTGM is very small</p><p>3.2.3.4 HSS Bearings</p><p>An acceleration enveloping analysis (AEA) on the high speed shaft sensor, AN7, indicated</p><p>possible damage initiation of the HSS downwind bearing inner race. As seen in Figure 3.21,</p><p>there was a fundamental order of 11.48 and its harmonics (22.95 and 34.42) in the envelope</p><p>order spectrum. These orders re modulated by the HSS shaft speed. By referring to Table 3.2,</p><p>we can identify that the order 11.48 is very close to the 11.51, the HSS-A1 and/or HSS-A2 inner</p><p>race defect frequency. These two bearings are identical; therefore, further differentiation is not</p><p>feasible.</p><p>The post-test examination revealed that the HSS-A1 bearing had mild overheating, which created</p><p>straw-yellow temper colors near each end of the IR raceway [4]. However, it is not likely the</p><p>overheating caused the BPFI response in the envelope spectrum. Acceleration enveloping</p><p>analysis can be very sensitive to bearing mechanical damage. It is likely that the damage</p><p>response was caused by the minor scratches on the race edge or the small indentations in the</p><p>middle of the raceway.</p><p>An acceleration enveloping analysis on the high speed shaft sensor AN7 also indicated possible</p><p>HSS-A1 cage damage. In the envelope spectrum (Figure 3.22), there is a minor but clear tone at</p><p>0.4261 Order and its harmonics at 0.8522 and 1.278 Order. By referring to Table 3.2, we can see</p><p>that this fundamental tone of 0.4261 Order is very close to HSS-A1 cage damage tone of 0.425</p><p>Order. However, HSS-A1 cage damage was not reported in the post-test inspection.</p><p>31</p><p>Figure 3.21. Envelope spectrum of AN7</p><p>Figure 3.22. Zoomed envelope spectrum of AN7</p><p>3.2.3.5 HSIS Bearings</p><p>Initial data analysis did not reveal any damage signatures of the bearings on the HSIS shaft.</p><p>However, the post-test examinations indicated moderate assembly damage and mild contact</p><p>corrosions on the bearing D inner race [4].</p><p>By careful re-examination of the order spectrum Figure 3.23, we saw that there was a small peak</p><p>at 2.43 Order, which is very close to bearing D BPFI 2.457 Order; however, it was also the</p><p>second harmonic of the planet gear mesh between the ring gear and the planets. Therefore, it</p><p>32</p><p>was very difficult to draw a conclusion about the bearing D BPFI damage signature at the current</p><p>stage.</p><p>Figure 3.23. Possible bearing D BPFI</p><p>3.2.3.6 LSIS Bearings</p><p>No damage signatures were identified from post-test inspection or from data analysis.</p><p>3.2.3.7 Carrier/ Main Shaft Bearing</p><p>Post-test inspection found severe fretting corrosion on the bearing H outer race [4]. However, no</p><p>damage signature was identified from data analysis, because, even though the corrosion was</p><p>severe in this bearing, the outer race surface was still smooth. Thus, it does not incur any</p><p>additional vibrations. In conclusion, this kind of bearing damage cannot be detected by a</p><p>vibration-based condition monitoring system.</p><p>3.3 Discussions</p><p>This Round Robin project provided a platform for commercial wind turbine condition</p><p>monitoring system suppliers, as well as, academic institutions to exercise different</p><p>methodologies. The GE Bently Nevada team provided a unique set of solutions based on the</p><p>techniques developed and implemented into its commercially available wind turbine drivetrain</p><p>condition monitoring system, ADAPT.wind.</p><p>Compared to the condition monitoring systems for other rotating machinery, condition</p><p>monitoring systems for wind</p><p>turbines face a few unique challenges including constantly variable</p><p>operating speeds and a high gear-up ratio from the rotor to the high-speed shaft. To overcome</p><p>the inaccuracy incurred by speed variations, synchronous sampling is the preferred data</p><p>acquisition technique. Subsequently, a synchronous analysis technique can be used to extract the</p><p>bearing and gear damage signatures. To accommodate high gear ratios in wind turbine</p><p>gearboxes, a digital domain synchronous re-sampling is very useful for signature extraction. The</p><p>digital synchronous re-sampling utilizes a low count mechanically- or electrically- based</p><p>33</p><p>encoder, or a key phaser, and interpolates the data between the pulses, with linear or more</p><p>sophisticated speed variation assumptions.</p><p>The data provided by NREL for the Round Robin analysis included accelerometer data and</p><p>speed profile data. To carry out the digital synchronous sampling, without shaft encoder or key</p><p>phaser data, the GE team developed and implemented a so-called synthesized synchronous</p><p>sampling technique. Although the phase information cannot be recovered, the technique</p><p>successfully carried out the synchronous analysis using the shaft speed profile.</p><p>The vibration sensing-based method is believed to be the cost effective approach for wind</p><p>turbine condition monitoring. However, any gearbox anomalies that do not incur additional</p><p>vibrations, such as overheating, minor fretting, and smoothed polishing will not be effectively</p><p>detected by vibration sensors.</p><p>Generally speaking, vibration-based wind turbine condition monitoring systems can detect</p><p>damage in the high speed side with higher confidence than that from the low speed side,</p><p>especially planetary gear set-related component damage. This is because accelerometers are</p><p>inherently more sensitive to high frequency vibrations. In addition, the mechanical</p><p>transmissibility from planetary gear components is usually low. Damage detection and condition</p><p>monitoring related to the gearbox low speed side is an area that needs more research attention in</p><p>the future.</p><p>34</p><p>4 Combining Novel Approaches with Proven Algorithms for</p><p>Robust Wind Turbine Gearbox Fault Detection</p><p>Jeremy Sheldon*, Matthew Watson, Genna Mott and Hyungdae Lee</p><p>Impact Technologies, A Sikorsky Innovations Company</p><p>*Corresponding Author Email: jeremy.sheldon@impact-tek.com</p><p>4.1 Introduction</p><p>Impact Technologies’ analysis efforts focused on applying a number of novel vibration</p><p>diagnostic algorithms to the GRC data set. They have been developed and matured by the team</p><p>in Department of Defense (DOD) applications for more than 10 years. The algorithms and results</p><p>are summarized herein. Generally, the methods employed by the team worked well, once the</p><p>challenges and peculiarities of the data set were realized. In particular, the absence of raw, time-</p><p>domain data from a healthy system (only FFT plots were provided) made it difficult to baseline</p><p>the system for comparison purposes. Regardless, the results of the automated algorithms were</p><p>corroborated with visual spectral analysis and are provided herein.</p><p>4.2 Algorithm Overview</p><p>Impact applied several component-specific analysis modules to the GRC data set. Each</p><p>algorithm is briefly introduced below.</p><p>4.2.1 FirstCheck: Sensor Validation</p><p>Having accurate and validated data is critical to performing effective condition monitoring. Even</p><p>the most durable sensors often become loose, disconnected, or damaged providing corrupted</p><p>system information. Consequently, changes in the dynamics of a vibration signal that are</p><p>characteristic of various sensor faults can be deceptively similar to those of mechanical failures,</p><p>or vice versa, inevitably resulting in false alarms.</p><p>For example, Figure 4.1 shows the result of the authors’ previous analysis of a gear pinion failure</p><p>that occurred on the test stand of a high-speed (thousands of RPMs), high-power (tens of</p><p>thousands of horsepower) military fighter aircraft drive train. As seen, several vibration features</p><p>react simultaneously, indicating that a potential fault is present in the system. Information</p><p>gathered solely from this sensor would confidently indicate a fault. However, upon further</p><p>investigation of the raw sensor data (shown in the top plot of the figure), one can see that this</p><p>reaction was caused by faulty (intermittent) data and, therefore, should not be trusted.</p><p>35</p><p>Figure 4.1. False alarm caused by faulty sensor</p><p>In addition, because many diagnostic feature algorithms are based on higher order statistics and</p><p>energy measures; it is possible for a corrupt signal to generate feature values that are within an</p><p>acceptable range despite the signal containing no periodic frequency content. Rigorous and</p><p>automated analysis of the integrity of accelerometer data is, therefore, critical to providing</p><p>accurate health assessments. To address this potential source of false alarms, the validity of the</p><p>high frequency vibration sensors is first evaluated as an initial step in the analysis, using an</p><p>approach termed FirstCheck. This module looks at a number of signal characteristics (including</p><p>the range, bias, and other proprietary characteristics) to verify the integrity of the vibration signal</p><p>before it is analyzed by the other algorithms.</p><p>4.2.2 ImpactEnergy: Bearing Fault Detection and Isolation</p><p>Bearing fault detection and isolation was performed using a set of algorithms termed</p><p>ImpactEnergy. Although bearing characteristic frequencies are easily calculated, they are not</p><p>always easily detected by conventional frequency domain techniques. Incipient bearing damage</p><p>is most often characterized as short-burst impulses in the vibration signature. Vibration</p><p>amplitudes at these frequencies, due to incipient faults (and sometimes more developed faults),</p><p>are often indistinguishable from background noise or obscured by much higher amplitude</p><p>vibration from other sources in a running machine, including rotors, blade passing, and gear</p><p>meshes. Similarly, time domain energy features, such as root mean square (RMS) or kurtosis, are</p><p>not significantly affected by such short burst of low intensity vibrations. Traditional time domain</p><p>or frequency domain analyses, therefore, encounter problems in detecting early stages of bearing</p><p>failure.</p><p>The ImpactEnergy module (Figure 4.2) integrates traditional spectral analysis techniques with</p><p>high-frequency demodulation and advanced feature extraction algorithms, providing a more</p><p>effective solution. The advantages of using the high frequency response to identify and track</p><p>36</p><p>bearing damage is well documented [14,15] and proven to be an effective method.</p><p>Demodulation, or enveloping, allows the broadband energy caused by failure effects to be</p><p>differentiated from the energy due to normal system noise. This approach provides the ability to</p><p>detect defect impulse events much easier than traditional analysis techniques allow. A key</p><p>consideration is selecting the band-pass filter that is centered on the expected carrier frequencies.</p><p>Through proprietary knowledge and field-application experience, the authors have developed a</p><p>process to identify key carrier frequencies.</p><p>Figure 4.2. ImpactEnergy overview</p><p>For complete characterization of bearing health from incipient fault to failure, the ImpactEnergy</p><p>module includes algorithms to extract an extensive set of time and frequency domain features</p><p>from both the raw, unprocessed, and demodulated vibration signals. Some time domain features</p><p>include traditional statistical measures, such as RMS, kurtosis, and Crest Factor. Frequency</p><p>domain features include the power levels of specific bearing defect frequencies compared against</p><p>known, health baseline thresholds, which can be very useful in diagnosing a fault [16].</p><p>4.2.3 GearMod and GearMod-Shaft: Gear and Shaft Fault Detection and Isolation</p><p>The GearMod module (Figure 4.3) is used to extract diagnostic features that are used for gear</p><p>fault detection</p><p>and isolation. This module contains a broad range of statistical methods based on</p><p>the time synchronous averaged (TSA) signal and other processed signals. The time synchronous</p><p>averaging technique is a useful technique to reduce the random noise level, as well as</p><p>disturbances from events unrelated to the gear of interest, and it has been extensively used to pre-</p><p>process gear vibration signals [17,18]. The fundamental principle of the TSA is that the vibration</p><p>components related to a shaft rotation and the gears on that shaft repeat periodically with the</p><p>shaft rotation. By dividing the vibration signal into contiguous segments, of exactly one shaft</p><p>rotation, and averaging a sufficiently large number of segments, the vibration components that</p><p>are synchronous to the shaft rotation, are reinforced. Non-synchronous vibrations are cancelled</p><p>out because they are out of phase in consecutive rotations.</p><p>37</p><p>Figure 4.3. GearMod overview</p><p>GearMod calculates time-domain features, such as RMS, skewness, kurtosis, and Crest Factor, as</p><p>well as features from the spectrum of the averaged signal, including FM0 (the peak-to-peak</p><p>amplitude compared to summation of GMF & harmonic magnitudes), Sideband Index (the</p><p>average spectral magnitude from sidebands on the 1st GMF), and Sideband Level Factor (the</p><p>spectral magnitude of sidebands on the 1st GMF, normalized by TSA RMS). The equations for</p><p>some of these features are included in Table 4.1 [19-21].</p><p>Table 4.1. Select gear diagnostic feature definitions</p><p>Feature Name Equation Symbols</p><p>FM0 ∑</p><p>=</p><p>= n</p><p>i</p><p>ifA</p><p>PPAFM</p><p>1</p><p>)(</p><p>0 PPA = peak-to-peak amplitude</p><p>A(fi) = GMF & harmonic amplitudes</p><p>Sideband Index</p><p>2</p><p>)()( 1,11,1 minmin</p><p>sRMCsRMC</p><p>SI</p><p>sb</p><p>n</p><p>sb</p><p>n antdoantdo +− +</p><p>=</p><p>sb</p><p>n antdo</p><p>RMC 1,1 min − and sb</p><p>n antdo</p><p>RMC 1,1 min +</p><p>= 1st order sideband amplitudes about</p><p>fundamental GMF</p><p>Sideband Level</p><p>Factor σ</p><p>)()( 1,11,1 minmin</p><p>sRMCsRMC</p><p>SIL</p><p>sb</p><p>n</p><p>sb</p><p>n antdoantdo +− +</p><p>= σ = standard deviation</p><p>Additional features are also calculated using proprietary methods. In addition, GearMod contains</p><p>built-in functionality to extract the TSA signal without a tachometer signal, making it appropriate</p><p>for situations when an accurate or useable tachometer signal does not exist.</p><p>4.2.4 Joint Time Frequency Analysis (JTFA) Overview</p><p>Gearbox vibration diagnostics are often based on frequency domain analysis, which assumes the</p><p>monitored signal is “stationary” during the analysis period. However, because operating</p><p>conditions are often non-stationary and evolving, this assumption leads to spectral smearing and</p><p>erroneous analysis that creates uncertainty in the health assessment.</p><p>38</p><p>Spectral smearing, in which energy from an evolving characteristic frequency (i.e., shaft</p><p>frequency, bearing fault frequency, gear mesh frequency) is spread across multiple frequency</p><p>bins, can reduce the efficacy of traditional frequency domain analysis, including Fourier</p><p>transforms. Typically, this is avoided by defining steady-state operating conditions in which to</p><p>perform the analysis. Although this may be acceptable for some systems, most wind turbines</p><p>have constantly varying shaft speeds and loads. In addition, certain component faults and their</p><p>progressions can also lead to non-stationary signals that could be missed by traditional</p><p>techniques. As a result, the authors have developed a novel vibration diagnostics methodology</p><p>that is applicable during non-steady operation through application of joint time-frequency</p><p>analysis (JTFA)[22]. These methods use various techniques to transform the two dimensional</p><p>time domain signal into a three dimensional, time-frequency domain signal to increase feature</p><p>extraction accuracy. An example is shown in Figure 4.4. Various features are then extracted from</p><p>the three dimensional signals for fault detection.</p><p>Figure 4.4. Example JTFA approach (short time Fourier transform)</p><p>4.3 Results Summary</p><p>The results of the analysis performed by Impact are briefly discussed in the following sections.</p><p>Both the blind results, obtained without knowing details on actual gearbox condition, and the</p><p>conclusions that were drawn after learning the actual damage, are discussed separately. It is</p><p>worth noting that FirstCheck was applied to all vibration data and no sensor faults were detected.</p><p>4.3.1 “Blind” Results</p><p>The results obtained without knowing the actual gearbox faults are summarized in Table 4.2. The</p><p>table includes the suspected damage, location, or component, severity, and the suspected damage</p><p>mode, as identified by Impact’s “blind” analysis. As shown, Impact correctly identified three of</p><p>the seven damage instances and had one false alarm (planet gear fault was called out but not</p><p>correct). Some specific evidence and results are shown in the following sections.</p><p>Segment 2</p><p>Segment 1</p><p>Segment n</p><p>M</p><p>ag</p><p>M</p><p>ag</p><p>Time</p><p>Extract</p><p>Spectrum</p><p>Extract</p><p>Spectrum</p><p>Extract</p><p>Spectrum</p><p>39</p><p>Table 4.2. Initial blind results summary</p><p>4.3.1.1 High Speed Shaft Gears</p><p>Figures 4.5 and 4.6 show the results of Impact’s GearMod analysis of data sets 2b and 2c for the</p><p>high speed gear/pinion pair. As seen, the analysis showed typical gear fault indicators, especially</p><p>on accelerometers AN6 and AN7. The distinct harmonics (1-4 and some higher) of the high</p><p>speed gear mesh frequency (GMF) combined with the numerous sidebands around each GMF</p><p>indicated teeth scuffing or other distributed wear (Figure 4.5). In addition, the high second order</p><p>GMF, clearly visible in Figure 4.6, indicated potentially misaligned gears/shafts.</p><p>40</p><p>Figure 4.5. High speed gear fault evidence, blind results (AN6)</p><p>Figure 4.6. High speed gear fault evidence, blind results (AN7)</p><p>41</p><p>4.3.1.2 Intermediate Shaft Bearings</p><p>Impact’s ImpactEnergy analysis of the bearings on the intermediate shaft is summarized by the</p><p>spectral plots in Figure 4.7 and Figure 4.8. For the downwind bearings (IMS-SH B&C, which are</p><p>indistinguishable since they are the same model bearing running at the same speed), the clear</p><p>peaks in the conventional, non-demodulated spectrum (Figure 4.7) at the outer raceway fault</p><p>frequency indicated substantial localize defects. Notice, too, the clear spectral peak at the IMS-</p><p>SH-A inner raceway defect frequency, in both the faulted and baseline (supposed healthy) FFT.</p><p>Because the bearing fault frequency was visible in the baseline FFT data that was provided,</p><p>Impact was not confident in the evidence enough to call out the fault. As such, this fault was not</p><p>called out in the blind analysis (see Section 4.3.2.1 for more details). .</p><p>Figure 4.7. Intermediate speed downwind bearing fault evidence, blind results (AN6, Data 2b)</p><p>Damage in the IMS-SH B component was also evident by the elevated levels of multiple</p><p>harmonics of the inner raceway fault frequency seen in the demodulated spectrum (Figure 4.8).</p><p>42</p><p>Figure 4.8. Intermediate speed downwind bearing fault evidence, blind results</p><p>4.3.1.3 Sun Pinion Gear</p><p>Focusing on the planetary gear analysis, Impact found evidence of heavy distributed or uniform</p><p>wear on the Sun Pinion Gear, specifically using the AN3 Ring Gear Radial 180° accelerometer.</p><p>In addition to the relatively low GMF harmonics and high sidebands, as shown in Figure 4.9,</p><p>Impact’s analysis showed higher than normal statistical features, including Energy Ratio (ER,</p><p>ratio of spectral energies between Difference and Regular signals), NB4 (time averaged kurtosis</p><p>of the envelope of the TSA signal band-pass filtered around dominant meshing frequency), FM0,</p><p>and RMS.</p><p>43</p><p>Figure 4.9. Sun pinion gear fault evidence, blind results</p><p>4.3.1.4 Intermediate and High Speed Gear JTFA Results</p><p>As mentioned above, Impact applied a set of JTFA algorithms to this data set. Since these</p><p>algorithms are still under development, the results summarized in Figure 4.10 were enough to</p><p>raise suspicion, but were not enough alone to call out a fault for the intermediate speed gear pairs</p><p>(and</p><p>were thus missed). However, when combined with the above gear analysis, Impact’s JTFA</p><p>results further confirmed distributed faults in the high speed gear pairs. Interestingly, several of</p><p>the JTFA features exhibited upward trends, normally indicating fault progression, but there was</p><p>no evidence of fault progression provided to Impact to confirm this behavior. Although the</p><p>torque load increased from 2a to 2c in Figure 4.10, the change was a step change and torque</p><p>levels were fairly steady during each segment. Therefore the upward trends of the features within</p><p>each segment (most noticeably 2b and 2c) seem to indicate some other evolving/influencing</p><p>phenomena.</p><p>44</p><p>Figure 4.10. JTFA speed gear fault evidence, blind results</p><p>4.3.2 Revisited Results</p><p>After providing NREL with the above results from the blind analysis, the gearbox inspection</p><p>results were provided to the Round Robin team. Knowing what to look for, Impact revisited the</p><p>analysis to determine if any additional fault/damage signatures were present in the data. The</p><p>results of the subsequent analysis are described below and in Table 4.3. As seen, most of the</p><p>faults not called out in the blind analysis were detected in hindsight, resulting in the detection of</p><p>six of the seven damage instances. Specifically the intermediate speed shaft upwind bearings and</p><p>the high speed shaft downwind bearing damages were detected. These are described in more</p><p>detail in the following sections. Note that Impact didn’t reevaluate the planet carrier bearing fault</p><p>since it was our opinion that this type of fault is not detectable with vibration analysis due to the</p><p>fact that the damage appears on the outside bore of the outer raceway, not in the contact zone of</p><p>the bearing.</p><p>45</p><p>Table 4.3. Post-inspection results summary</p><p>4.3.2.1 Intermediate Shaft Upwind Bearings</p><p>As briefly mentioned previously, Impact’s analysis during the blind portion of this effort</p><p>revealed a high inner race defect frequency magnitude for both the test data and the provided</p><p>baseline data, as shown in Figure 4.11. Initially this decreased the confidence in diagnosing a</p><p>fault in the IMS Upwind bearing (IMS-SH-A). However, the inspection report revealed that the</p><p>damage was due to an assembly error and, therefore, it was also present during the baseline</p><p>testing.</p><p>Figure 4.11. Intermediate speed upwind bearing damage evidence</p><p>46</p><p>With this information and the results exemplified by Figure 4.12, Impact could correctly identify</p><p>the fault as a progressed or distributed inner raceway fault because there was little modulation</p><p>and clear inner raceway frequency vibration.</p><p>Figure 4.12. Intermediate speed upwind bearing fault evidence, post-inspection results</p><p>4.3.2.2 High Speed Shaft Downwind Bearings</p><p>During the blind portion of this effort, Impact did not diagnose the defect present on the high</p><p>speed shaft downwind bearings (HSS-SH-B/C). Based on the information contained in the</p><p>inspection report, a discrepancy in the bearing part numbers was found. The initially provided</p><p>documentation listed the HSS-SH-B/C bearings as 32222J2 SKF, but the inspection report</p><p>visually confirmed them as 32222A FAG. Although similar in size, these bearings have different</p><p>fault frequencies.</p><p>Using the correct fault frequencies, Impact’s analysis clearly showed small, early stage inner</p><p>raceway defects, as evident by the multiple BPFI harmonics (1x-4x) that are dominant in the</p><p>demodulated FFT (for data sets 2a and 2c). Example demodulated spectra and fault frequency</p><p>peaks are shown in Figures 4.13 and 4.14. Although Impact did detect a defect in the bearing, the</p><p>diagnosed fault signature seems unlikely to have been caused by only the cited overheating</p><p>event. Instead, Impact believes the evidence points to some additional defect, which may have</p><p>resulted from the overheating.</p><p>47</p><p>Figure 4.13. High speed downwind bearing fault evidence, revisited (Data 2a)</p><p>Figure 4.14. High speed downwind bearing fault evidence, revisited (Data 2c)</p><p>48</p><p>4.4 Lessons Learned and Conclusions</p><p>Impact’s blind analysis successfully detected three of the seven damaged components that were</p><p>present in the gearbox, with a fourth component detected but not called out due to the relative</p><p>immaturity of the approach that detected the damage. Of the remaining three, two were detected</p><p>during the secondary analysis that was performed after the inspection report was provided. These</p><p>two were originally missed due to: 1) the use of incorrect bearing design information that was</p><p>provided in the original analysis, and 2) the presence of the damage during assembly, which</p><p>caused the baseline results that were used for comparison to be higher. It is Impact’s opinion that</p><p>the seventh damaged component is not detectable with vibration analysis since the damage</p><p>appears on the outside bore of the outer raceway, not in the contact zone of the bearing.</p><p>In general, this analysis was confounded by the number and severity of the defects, especially the</p><p>obfuscation of bearing and other faults by the widespread gear damage. Impact believes that in</p><p>actual practice the expected diagnostic performance will be better since a smaller and less severe</p><p>set of faults will be present during the early stages of fault evolution. To clarify, this data set</p><p>contains multiple progressed faults that would be better detected as they individually occur over</p><p>time versus diagnosing each one once they have all occurred. Additionally, assessing the fault</p><p>severity was more difficult due to the lack of time-domain baseline data. Although this was</p><p>overcome by using our experience of previous analysis of different machinery, higher fidelity</p><p>results may be produced by comparing like data to like data and allowing the algorithms to be</p><p>baselined against typical, healthy vibration levels and trended over time. Regardless of these</p><p>minor issues, this analysis and effort should enable a good assessment on the state of wind</p><p>turbine diagnostics, as well as an indication of what work remains.</p><p>49</p><p>5 Analysis Algorithms and Diagnostics Results from NRG</p><p>Systems</p><p>Eric Bechhoefer</p><p>NRG Systems</p><p>Email: erb@nrgsystems.com</p><p>5.1 Introduction</p><p>NRG Systems, as a participant of this Round Robin study, wished to validate the effectiveness of</p><p>analysis algorithms used in the aerospace community, for the wind industry. The aerospace</p><p>industry, specifically vertical flight, developed an extensive toolset for gearbox fault detection as</p><p>a result of helicopter gearbox failures. These algorithms were specifically developed for shaft,</p><p>gear, and bearing fault detection. This is counter to most installed condition monitoring systems,</p><p>which have matured out of industrial monitoring of large turbo-machinery (turbo-machinery</p><p>have no gearbox, focusing extensively on shaft misalignment, out of balance, or rub conditions).</p><p>NRG implemented two analysis methodologies: synchronous analysis of shaft/gear components</p><p>and non-synchronous analysis of bearings. Synchronous methods were based on the work of</p><p>McFadden [23], while the bearing analysis was based on the work of Randall [24].</p><p>The data set consisted of 10 samples each under three operating conditions, for a total of 30 files.</p><p>The samples were separated by a short time interval. Because these industrial gearboxes are</p><p>designed to run for years versus minutes, we assumed that the analysis would consist of taking a</p><p>snap shot of the current gearbox condition. No attempt was made to trend component condition</p><p>indicators or look at statistical differences between early and late files. It was assumed that over</p><p>the period of the test, there was no appreciable degradation of the gearbox. The analysis</p><p>consisted of viewing the output of various analysis algorithms for each component, and based on</p><p>some nominal experience with aerospace gearboxes, defining the wind turbine gearbox as good,</p><p>bad, or indifferent.</p><p>5.2 Analysis Algorithms</p><p>5.2.1 Condition</p><p>Analysis Algorithms - Feature Extraction to Improve Signal to</p><p>Noise</p><p>Vibration signatures for machinery faults tend to be small relative to other vibration signatures.</p><p>For example, in the typical gearbox, the energy associated with gear mesh and shaft vibrations</p><p>will be orders of magnitude larger than a fault feature. Spectral analysis or root mean squares</p><p>(RMS) of vibration are not powerful enough analyses to find early faults or defects. Techniques</p><p>to improve the signal to noise are needed to remove frequencies associated with nominal</p><p>components, while preserving the fault signatures.</p><p>Gear analysis was based on operations of the time synchronous average [23]. Time synchronous</p><p>averaging (TSA) is a signal processing technique that extracts periodic waveforms from noisy</p><p>data. The TSA is well suited for gearbox analysis, where it allows the vibration signature of the</p><p>gear under analysis to be separated from other gears and noise sources in the gearbox that are not</p><p>synchronous with that gear. Additionally, variations in shaft speed can be corrected, which</p><p>would otherwise result in spreading of spectral energy into adjacent gear mesh bins. To do this, a</p><p>signal is phased-locked with the angular position of a shaft under analysis.</p><p>50</p><p>This phase information can be provided through an n per revolution tachometer signal (such as a</p><p>Hall sensor or an optical encoder, where the time at which the tachometer signal crosses from</p><p>low to high is called the zero crossing) or though demodulation of gear mesh signatures [25]. In</p><p>the case of the GRC data set, the phase information was extracted from the generator signal itself</p><p>(e.g., voltage signal capacitively coupled onto the RPM signal).</p><p>The model for vibration in a shaft in a gear box was given in [23] as:</p><p>x(t) = Σi=1:K Xi(1+ ai(t))cos(2πi fm(t)+ Φi)+b(t)</p><p>where:</p><p>Xi is the amplitude of the kth mesh harmonic</p><p>fm(t) is the average mesh frequency</p><p>ai(t) is the amplitude modulation function of the kth mesh harmonic.</p><p>φi(t) is the phase modulation function of the kth mesh harmonic.</p><p>Φi is the initial phase of harmonic k, and</p><p>b(t) is additive background noise.</p><p>The mesh frequency is a function of the shaft rotational speed: fm = Nf, where N is the number of</p><p>teeth on the gear and f is the shaft speed, with no reduction in the analysis performance. This</p><p>vibration model assumes that f is constant. In most systems, there is some wander in the shaft</p><p>speed due to changes in load or feedback delay in the control system. This change in speed will</p><p>result in smearing of amplitude energy in the frequency domain. The smearing effect, and non-</p><p>synchronous noise, is reduced by re-sampling the time domain signal into the angular domain:</p><p>mx(θ) = E[x(θ)] = mx(θ+Θ). The variable Θ is the period of the cycle that the gearbox operation</p><p>is periodic, and E[] is the expectation (e.g., ensemble mean). This results in the assumption that</p><p>mx(θ) is stationary and ergodic. If this assumption is true, then non-synchronous noise is reduced</p><p>by 1/sqrt(rev), where rev is the number of cycles measured for the TSA.</p><p>5.2.2 TSA Techniques for Condition Indicators</p><p>The TSA is an example of angular resampling [23], [25], where the number of data points in one</p><p>shaft revolution (rn) is interpolated into m number of data points, such that:</p><p>• For all shaft revolutions n, m is larger than r,</p><p>• And m = 2ceiling (log2 (r)) (typical for radix 2 Fast Fourier Transform).</p><p>The TSA itself can be used for Condition Indicators (CIs). Typically, a CI is a statistic of a</p><p>waveform (in the case the TSA). Common statistics are RMS, peak to peak, Crest Factor,</p><p>kurtosis and skewness. For the shaft, a shaft order (SO) of 1, 2, and 3 (first, second and third</p><p>shaft rate harmonic) can be used to determine shaft out of balance, bent shaft, and/or shaft</p><p>coupling damage, respectively. Figure 5.1 outlines the process of generating the TSA, and shaft</p><p>CIs.</p><p>51</p><p>Figure 5.1. Generation of the TSA and selected CIs</p><p>5.2.3 Gear Fault Indicators</p><p>There are at least six failure modes for gears: surface disturbances, scuffing, deformations,</p><p>surface fatigue, fissures/cracks, and tooth breakage. Each type of failure mode, potentially, can</p><p>generate a different fault signature. Additionally, relative to the energy associated with gear</p><p>mesh tone and other noise sources, the fault signatures are typically small. A number of</p><p>researchers have proposed analysis techniques to identify these different faults [25,26].</p><p>Typically, these analyses are based on the operation of the TSA. Examples of analysis are:</p><p>• Residual Analysis. Shaft order 1, 2, and 3 frequencies, and the gear mesh harmonics, of</p><p>the TSA are removed. Faults such as a soft/broken tooth generate a 1 per rev impact in</p><p>the TSA. In the frequency domain of the TSA, impacts are expressed as multiple</p><p>harmonics of the 1 per rev. The residual analysis removes the shaft order 1, 2, and 3</p><p>frequencies and gear mesh harmonics in the frequency domain, and then the inverse FFT</p><p>is performed. This allows the impact signature to become prominent in the time domain.</p><p>CIs are statistics of this waveform (RMS, peak to peak, Crest Factor, and kurtosis).</p><p>• Energy Operator (EO), which is a type of residual of the autocorrelation function. For a</p><p>nominal gear, the predominant vibration is gear mesh. Surface disturbances and scuffing</p><p>generate small higher frequency values, which are not removed by autocorrelation.</p><p>Formally, the EO is: TSA2:n-1 x TSA2:n-1 – TSA1:n-2 x TSA3:n . The bold indicates a vector</p><p>of TSA values. The CIs of the EO are the standard statistics of the EO vector.</p><p>• Narrowband Analysis operates the TSA by filtering out all tones except that of the gear</p><p>mesh and with a given bandwidth. It is calculated by zeroing bins in the Fourier</p><p>transform of the TSA, except the gear mesh. The bandwidth is typically 10% of the</p><p>number of teeth on the gear under analysis. For example, a 23-tooth gear analysis would</p><p>retain bins 21, 22, 23, 24, and 25, and their conjugates in the Fourier domain. Then, the</p><p>inverse FFT is taken, and statistics of the waveform are taken. Narrowband analysis can</p><p>capture sideband modulation of the gear mesh tone due to misalignment, or detect a</p><p>cracked/broken tooth.</p><p>52</p><p>• Amplitude Modulation (AM) analysis is the absolute value of the Hilbert transform of the</p><p>Narrowband signal. For a gear with minimum transmission error, the AM analysis feature</p><p>should be a constant value. Faults will greatly increase the kurtosis of the signal.</p><p>• Frequency Modulation (FM) analysis is the derivative of the angle of the Hilbert</p><p>transform of the narrowband signal. It is a powerful tool capable of detecting changes of</p><p>phase due to uneven tooth loading, a characteristic of a number of fault types.</p><p>For a more complete description of these analyses, see [25] or [26]. Figure 5.2 is an example of</p><p>the processing to generate the gear CIs for a spiral bevel gear with surface pitting and scuffing.</p><p>Figure 5.2. Process for generating gear CIs</p><p>The cepstrum was also evaluated, although it is difficult to implement in an automated system.</p><p>For bearing analysis, the envelope analysis was used.</p><p>5.3 Analysis Results</p><p>5.3.1 Synthetic Tachometer Signal</p><p>All shaft and gear analysis is based on the TSA, which requires a tachometer signal for a key-</p><p>phasor. The data set contained an RPM signal, but not a raw tachometer signal. It was noticed</p><p>that the RPM signal carried modulated noise. It was conjectured that this was the convolution of</p><p>60 Hz power, with the 20/30 Hz output of the generator onto the RPM signal (indicating a poor</p><p>ground). By removing the DC value of the RPM signal, then low pass filtering, the generator 20</p><p>Hz signal was isolated and used as a tachometer zero crossing index. This is possible because the</p><p>20 Hz generator signal is synchronous with the high speed shaft, see Figure 5.3.</p><p>53</p><p>Figure 5.3. Synthetic tachometer</p><p>5.3.2 High Speed Shaft/High Speed Pinion</p><p>The HSS/HSP</p><p>showed a large shaft order 1 in the TSA Figure 5.4a (spectrum in G’s) and a large</p><p>vibration in the AM signal (units of G’s) of Figure 5.4b coupled with a large phase change in the</p><p>FM signal (units of radian). This indicates a large eccentricity (the gear was not centered on the</p><p>shaft). Additionally, the energy operator was large and periodic, indicating severe</p><p>scuffing/pitting. There was limited evidence of a soft/broken tooth (a broken or soft tooth result</p><p>in a 1/rev impact, which is visible in the residual analysis, the EO signal (units of G’s), and the</p><p>AM and FM analysis).</p><p>Figure 5.4a. HSS TSA/spectrum</p><p>Figure 5.4b. HSS gear analysis</p><p>54</p><p>5.3.3 Intermediate Speed Shaft/High Speed Gear and Intermediate Speed Pinion</p><p>The ISS/HSG/ISP showed a large shaft order 4 in the TSA (Figures 5.5a and 5.5b). Since there is</p><p>a 4:1 relationship with the HSS, this further confirms the eccentricity of the HSP. Both the HSG</p><p>and ISP showed large (e.g., .05 G’s) energy operator, indicative of sever pitting/scuffing. The</p><p>AM and FM signals did not indicate any missing teeth/soft teeth, but did reflect a high variation</p><p>in loading due to the HSP (Figure 5.5b).</p><p>Figure 5.5a. TSA intermediate shaft</p><p>Figure 5.5b. Intermediate speed pinion, where</p><p>the units for the Energy Operator,</p><p>Narrowband and Amplitude Modulation</p><p>analysis are in G’s, and the Frequency</p><p>Modulation analysis is in radians.</p><p>5.3.4 Sun/Planet Gear Analysis</p><p>The Sun Gear showed no soft/broken teeth. However the EO values are large. Similarly, the</p><p>planet gears showed large EO values. This suggests that there is pitting/scuffing on these gears</p><p>(Figures 5.6a and 5.6b). Because the accelerometer is in a fixed frame relative to the planet, the</p><p>planet AM analysis should show a sinusoid of three cycles (corresponding to the number of</p><p>plants passing the sensor. Because this is not present, it could indicate that one of the planet</p><p>bearings is worn and the planet is not sharing the load evenly with its two neighboring planets</p><p>(Figure 5.6b AM and FM plots). The bearing analysis could not confirm the presence of a planet</p><p>bearing fault, although this may be due to poor window selection. The units for the Energy</p><p>Operator, Narrowband and Amplitude Modulation analysis is in G’s, and the Frequency</p><p>Modulation analysis is in radians.</p><p>55</p><p>Figure 5.6a. Sun gear</p><p>Figure 5.6b. Planet gears</p><p>5.3.5 Annulus/Ring Gear</p><p>The ring gear shows no cracked tooth/soft tooth. The carrier is not cracked. The large EO</p><p>indicates scuffing/pitting. There is some suggestion that the pitting is larger on the ring gear than</p><p>the planet (Figure 5.7). Note that in the AM analysis, the variation in load is a function of the</p><p>planets passing the fixed sensor. As suggested earlier, because the load is not even across all</p><p>three planets, this may indicate planet bearing error. The units for the Energy Operator,</p><p>Narrowband and Amplitude Modulation analysis is in G’s, and the Frequency Modulation</p><p>analysis is in radians.</p><p>Figure 5.7. Ring gear</p><p>5.3.6 Bearing Analysis</p><p>Bearing analysis was based on the envelop algorithm. The raw data was heterodyned to the base</p><p>band; the carrier frequency is based on the resonance of the bearing structure. The energy</p><p>spectrum (units of G’s) is taken on the base band signal, where the modulation rate is taken as</p><p>the bearing fault frequency [28].</p><p>56</p><p>Figure 5.8a. High speed shaft, downwind side</p><p>Figure 5.8b. Intermediate speed shaft</p><p>downwind side</p><p>It was found (Figures 5.8a, 5.8b, and 5.9) that most bearings had some level of damage. The</p><p>analysis could not find direct evidence of a fault on the planet bearing. While some attempt was</p><p>made in optimizing the window frequency using spectral kurtosis, it’s likely that the lack of</p><p>performance was due to poor window selection in the envelope analysis.</p><p>Figure 5.9. Low speed shaft downwind side</p><p>5.4 Discussion</p><p>The lack of fleet data forces one into an analysis of individual algorithm waveforms. It is</p><p>desirable to have vibration analysis off of a fleet of gearboxes to compare the test gearbox</p><p>against. Additionally, it is desirable to have at least six months of condition indicator data on a</p><p>gearbox to observe (or capture) degradation. Because of the lack of fleet data or any appreciable</p><p>history, analysis was based on a “by eye” analysis. It is likely that better performance could be</p><p>gained with more experience on this gearbox, or in comparison of waveforms with a known,</p><p>good gearbox. The algorithms, based on the TSA, appear to find faults that were consistent with</p><p>[26]. In fact, most analysis did show a response indicative of a wear/fault. Because there seemed</p><p>to be no broken/soft tooth, the residual analysis was nominal on all gears. It was noted that</p><p>0 50 100 150</p><p>2</p><p>3</p><p>4</p><p>5</p><p>6</p><p>7</p><p>8</p><p>x 10</p><p>-3</p><p>G</p><p>s</p><p>Freq (Hz)</p><p>Cage: 2</p><p>Ball: 50</p><p>Outer: 85</p><p>Inner: 70Gear: 5 Hz</p><p>AN6 ISSRadial Bearing: Int Speed Shaft: Downwind</p><p>57</p><p>cepstrum analysis showed numerous harmonics (indicative of fault), but because the cepstrum is</p><p>not a synchronous analysis, it was difficult to assign a particular frequency with a component.</p><p>In general, the analysis methodology seemed appropriate for wind turbines, and has the</p><p>advantage of being relatively simple to implement in an autonomous manner, e.g., the generation</p><p>of statistics from the analysis waveforms, which could be trended or a threshold set to indicate</p><p>when a maintenance action needs to be performed. This lends credence that aerospace gearbox</p><p>analysis techniques are appropriate for wind turbine gearbox analysis.</p><p>58</p><p>6 Review and Application of Methods and Algorithms in Wind</p><p>Turbine Gearbox Fault Detection</p><p>David Siegel*, Wenyu Zhao, Edzel Lapira, Mohammed AbuAli, and Jay Lee</p><p>Center for Intelligent Maintenance Systems, University of Cincinnati</p><p>*Corresponding Author Email: siegeldn@mail.uc.edu</p><p>6.1 Introduction</p><p>This chapter contains a description of the method and algorithms used by the research team at the</p><p>University of Cincinnati – Center for Intelligent Maintenance Systems (IMS) for the Round</p><p>Robin study. The outline of this chapter is as follows: Section 6.2 provides an overview of the</p><p>signal processing and feature extraction methods evaluated in the study by the IMS research</p><p>team, followed by more specific details for each method. Section 6.3 provides a summary of the</p><p>results for each evaluated method along with some additional discussion. The final summary</p><p>table in Section 6.3 also provides an indication of which analysis methods were considered prior</p><p>to and after the failure report was released. Lastly, conclusions and suggestions for future work</p><p>are provided in Section 6.4.</p><p>6.2 Signal Processing and Feature Extraction Methods</p><p>An overview of the signal processing methods evaluated during this study is provided in Table</p><p>6.1, along with the advantages and disadvantages of each method. Despite its simplicity, the use</p><p>of analyzing the vibration data in the frequency domain does have its merits for detecting gear</p><p>related problems. Gear mesh frequencies and associated sidebands can be identified in the</p><p>vibration spectrum and various vibration indicators or features can be calculated in the frequency</p><p>domain [27]. The real cepstrum is particularly useful for analyzing a family of harmonics, which</p><p>has application for gear related faults [24]. A series of sidebands can be analyzed by calculating</p><p>the cepstrum and comparing them to the baseline condition; the magnitude of the peaks</p><p>compared to that baseline can be used to diagnose the health condition for each gear. The</p><p>calculation of the real cepstrum can also be performed from the frequency spectrum; this was a</p><p>useful asset for this analysis since only a baseline frequency spectrum was provided.</p><p>For bearing condition monitoring, the most established method in the literature is bearing</p><p>envelope analysis, also called the high frequency resonance technique [24]. The general concept</p><p>is that a spall or damage on the bearing race or rolling element causes a series of impacts that</p><p>excite the structural resonances of the mechanical system; this causes an amplitude modulation</p><p>effect in which the carrier frequency is the resonance frequency and the bearing fault frequency</p><p>is the modulation frequency. By filtering around the excited resonance and performing the</p><p>demodulation, the envelope spectrum, along with the calculated fault frequencies, can be used to</p><p>diagnose the bearing condition. A more detailed description of bearing faults, the bearing</p><p>envelope analysis method, and methods for selecting the band-pass filter frequency range are</p><p>provided in [24]. Despite bearing envelope analysis being a very effective technique; the method</p><p>usually requires a high sampling rate since the excited resonance can occur at frequencies above</p><p>10 KHz for many applications. The selection of the band-pass filter is also a crucial aspect in the</p><p>method and a current area of research [24]. The use of spectral kurtosis filtering can be used to</p><p>select the filter band for the bearing envelope analysis method, as well as for calculating</p><p>indicators for the overall health condition of the monitored gearbox [28].</p><p>59</p><p>Time synchronous averaging represents one of the most established signal processing techniques</p><p>for gear condition monitoring. The method is ideally suited for the processing of gear vibration,</p><p>since the synchronous averaging method enhances and separates the periodic gear vibration from</p><p>the cyclostationary vibration of rolling element bearings. Additional processing methods can be</p><p>performed on the time synchronous average signal, including the gear residual signal and the</p><p>amplitude and phase modulation functions [18]. For planetary gearboxes, due to the relative</p><p>motion of the planet gears and the multiple contact points between each planet gear meshing</p><p>with the sun and ring gear, the traditional synchronous averaging algorithm is not able to isolate</p><p>the individual vibration for each planet gear or the sun gear. Specific algorithms for performing</p><p>synchronous averaging for planetary gears are also evaluated in this work; the method suggested</p><p>by McFadden [29] is used in this study. This specific algorithm for planetary gearboxes does</p><p>have some potential drawbacks; in particular, the long data acquisition period needed to perform</p><p>the calculation procedure is a major challenge for implementing this method.</p><p>60</p><p>Table 6.1. Summary of evaluated methods – advantages and disadvantages</p><p># Technique Advantages Disadvantages</p><p>1 Frequency Domain</p><p>Sidebands around gear mesh frequencies</p><p>can be identified and provide a relatively</p><p>simple method for extracting gear</p><p>condition indicators without a tachometer</p><p>signal [27].</p><p>Signal to noise ratio is not enhanced by using</p><p>a tachometer signal, which can help reduce the</p><p>vibration from other sources not synchronous</p><p>with the shaft and gear components.</p><p>2 Cepstrum</p><p>Convenient method for extracting</p><p>information from a family of harmonics;</p><p>ideally suited for extracting gear condition</p><p>indicators due to sidebands and amplitude</p><p>modulation [24].</p><p>Family of harmonics could be related to shaft</p><p>problems such as imbalance or misalignment</p><p>and may not be due to a gear related fault;</p><p>requires a baseline for comparing the</p><p>cepstrum and determining whether there is a</p><p>significant change.</p><p>3 Bearing Envelope</p><p>Analysis</p><p>Most established method for bearing</p><p>diagnosis in the literature [28]; is more</p><p>suited for detecting incipient bearing</p><p>spalls.</p><p>Selection of the demodulation band is not</p><p>trivial and still an area of active research [28],</p><p>also could require a higher sampling rate</p><p>depending on the excited system resonance.</p><p>4 Spectral Kurtosis</p><p>Filtering</p><p>Filters signal based on the frequency band</p><p>that is most impulsive [30]; can be used to</p><p>calculate features on the filtered signal and</p><p>to select an appropriate filter in envelope</p><p>analysis.</p><p>Extended spalls or faults might not be</p><p>impulsive, and hence, this affects the ability of</p><p>this method to detect these types of faults.</p><p>5 Time Synchronous</p><p>Averaging</p><p>Enhances vibration synchronous with the</p><p>shaft, residual signal can look for</p><p>abnormalities in the regular meshing</p><p>pattern, demodulation around gear mesh</p><p>frequency can detect a soft tooth by</p><p>analyzing amplitude and phase modulation</p><p>signals [18].</p><p>Requires accurate tachometer signal for</p><p>performing the synchronous averaging, might</p><p>require a long acquisition time for low speed</p><p>shafts due to the low rotational speed and</p><p>collecting an ensemble of readings for</p><p>averaging.</p><p>6 Planet Separation</p><p>Method</p><p>Specific algorithm designed for</p><p>performing synchronous averaging for</p><p>planetary gearboxes [29], provides a way</p><p>to individually analyze the health condition</p><p>of the multiple planet gears and the sun</p><p>gear.</p><p>Requires very long acquisition time, collecting</p><p>enough rotations to perform the averaging;</p><p>also requires a tachometer for aligning the</p><p>data with respect to the carrier rotation.</p><p>6.2.1 Frequency Domain Methods</p><p>For rotating machinery, gaining an understanding of the time domain and frequency domain</p><p>signature is a typical first approach prior to applying more advanced processing methods. For</p><p>meshing gears in particular, there are signature frequencies related to the gear mesh frequencies</p><p>and sidebands; the use of the Fast Fourier Transform (FFT) and an analysis of the gear mesh</p><p>frequency peaks and sidebands can provide an initial evaluation of the gear wheel health</p><p>condition. Gears in a nominal healthy or degraded condition typically have a similar gear mesh</p><p>frequency peak; however, the magnitude of the sidebands is more useful for assessing the gear</p><p>health condition. In addition, the spacing of the sidebands can indicate which particular shaft</p><p>and associated gear wheel is degraded [27]. An example vibration spectrum from this study is</p><p>provided in Figure 6.1, in this example one can clearly identify the gear mesh frequency peak</p><p>(for the high speed shaft gear and pinion) at 662 Hz in the vibration spectrum for the gearbox in</p><p>the nominal baseline condition. The gear mesh frequency peak is also present in the vibration</p><p>spectrum of the degraded gearbox; however, there are very large sidebands at 631 Hz and 691</p><p>Hz for the degraded gearbox. The sidebands are spaced at 30 Hz, which is the high speed shaft</p><p>61</p><p>rotational speed; this initial example provides some evidence that the high speed pinion is</p><p>degraded due to the sidebands observed in the vibration spectrum.</p><p>Figure 6.1. Vibration spectrum - Case C: top plot - AN7 baseline;</p><p>bottom plot - AN7 degraded gearbox</p><p>To further quantify these observations from the vibration spectrum; a set of gear wheel vibration</p><p>features was extracted using the baseline spectrum and the spectrum from the degraded gearbox.</p><p>To quantify the magnitude of the sidebands, the sideband level was calculated using Equation</p><p>(6). In this calculation, SBLa stands for the sideband level, Sba1 is the magnitude of the lower</p><p>sideband and SBa2 is the magnitude of the upper sideband. In addition, a sideband ratio was also</p><p>calculated using Equation (7); this normalizes the sideband ratio by the gear mesh frequency</p><p>peak. Prior work by Combet et al. [31] has shown this sideband ratio feature to be an effective</p><p>metric to quantify gear health since it is less susceptible to load fluctuations due to the sideband</p><p>magnitude being divided by the gear mesh frequency peak [31]. Table 6.2 provides a listing of</p><p>the frequency domain gear features; a total of 16 were calculated. For each respective gear, four</p><p>features were calculated. The sideband ratio and sideband level were calculated for the gear</p><p>mesh frequency and the first harmonic of the gear mesh frequency. Also, the frequency domain</p><p>gear features were only calculated for the four gears on the parallel gearbox stage; the analysis of</p><p>the sideband patterns for the planetary gearbox is quite</p><p>complicated and more advanced</p><p>techniques were evaluated for the planetary gearbox.</p><p>62</p><p>Table 6.2. Frequency domain gear features</p><p>Signal Feature Name # of Features</p><p>AN5 Side Band Ratio and Sideband level for Intermediate</p><p>Speed Shaft Gear 4</p><p>AN6 Side Band Ratio and Sideband level for Intermediate</p><p>Speed Shaft Pinion and High Speed Shaft Gear 8</p><p>AN7 Side Band Ratio and Sideband level for High Speed Shaft</p><p>Pinion 4</p><p>2a1aa SBSBSBL +=</p><p>(6)</p><p>peak</p><p>aa</p><p>a GMF</p><p>SBSBSBR 21 +=</p><p>(7)</p><p>Example results using the frequency domain gear features are provided in Figure 6.2. In this</p><p>example, the sideband ratio for the intermediate speed shaft pinion and the high speed shaft</p><p>pinion are much larger in magnitude for the degraded gearbox when compared to the gearbox at</p><p>the baseline condition. The sideband ratio for the high speed shaft gear is very similar to the</p><p>baseline level and would imply that this particular gear is normal using this frequency domain</p><p>feature. It should be noted in the failure report that the high speed shaft gear set was observed to</p><p>have severe scuffing on both gears. In addition, the failure study reported that the intermediate</p><p>speed shaft gear set had severe fretting corrosion and scuffing for both gears as well. From the</p><p>frequency domain method, there is a strong indication that there is damage on the high speed</p><p>shaft pinion. There also is an indication, but with lower confidence, of damage on the</p><p>intermediate speed shaft pinion. However, there is little evidence from the frequency domain</p><p>gear features of damage on the high speed shaft gear or the intermediate speed shaft gear despite</p><p>the reported damage in the failure report. Other processing algorithms were used to further</p><p>investigate the health condition of the parallel stage gear wheels, as well as the other bearing and</p><p>gear components. If several processing methods provide evidence of a degraded component, this</p><p>can provide an increased level of confidence that the component is damaged.</p><p>63</p><p>Figure 6.2. Sideband ratio gear features – Case C: (a) Low speed shaft pinion;</p><p>(b) High speed shaft gear; (c) High speed shaft pinion</p><p>6.2.2 Cepstrum Processing Method</p><p>The real cepstrum provides a processing method that is ideally suited for analyzing a family of</p><p>harmonics, in a much more consolidated way than the frequency domain representation. For</p><p>calculating the real cepstrum, the inverse Fourier Transform is applied to the logarithm of the</p><p>power spectrum, as shown in Equation (8), where Cxx(t) is the real cepstrum and A(f) is the</p><p>frequency spectrum [24]. For mechanical systems and gears in particular, the cepstrum provides</p><p>a convenient way of analyzing a series of sidebands that are spaced at a given shaft speed;</p><p>comparing the cepstrum from a baseline and current state can be used to infer the health</p><p>condition of each gear. The example cepstrum result in Figure 6.3 further illustrates this aspect,</p><p>in which the cepstrum from the baseline gearbox is compared to the degraded gearbox. In both</p><p>instances, one can observe a peak in the cepstrum at 0.133s, which corresponds to 7.5 Hz and the</p><p>intermediate speed shaft. This implies that a family of harmonics spaced at 7.5 Hz was always</p><p>present in this gearbox. However, an additional peak at 0.0325s, which corresponds to 30 Hz</p><p>and the high speed shaft, can be seen in the cepstrum of the degraded gearbox. This additional</p><p>set of harmonics spaced at 30 Hz for the degraded gearbox provides evidence that the gear wheel</p><p>on the high speed shaft (high speed shaft pinion) is degraded and is responsible for this</p><p>noticeable change in the cepstrum.</p><p>[ ])](ln(2)( 1 fACxx</p><p>−ℑ=τ (8)</p><p>64</p><p>Figure 6.3. Real cepstrum - Case C: top plot - AN7 baseline; bottom plot - AN7 degraded gearbox</p><p>Figure 6.4. Cepstrum peak features from Case C: blue – baseline; red - degraded gearbox</p><p>65</p><p>Additional vibration features were extracted from the cepstrum at the corresponding shafts, using</p><p>data from both the baseline gearbox and the degraded gearbox. Example results from the</p><p>cepstrum features are provided in Figure 6.4, in which several peaks in the cepstrum are</p><p>noticeably larger in magnitude when comparing the degraded gearbox to the baseline gearbox.</p><p>The cepstrum peak related to the high speed shaft pinion is highlighted, since this feature was</p><p>dramatically larger in magnitude for the degraded gearbox. This provides an additional set of</p><p>evidence that the high speed shaft pinion is damaged. To further quantify the difference in the</p><p>cepstrum features from the baseline state, and diagnose which gear in a meshing pair had the</p><p>most severe condition, a cepstrum based health indicator using Equation (9) was calculated [32].</p><p>In this calculation, d(t) is the cepstrum health indicator, Ap(t) is the cepstrum peak for the input</p><p>gear at time t, Ar(t) is the cepstrum peak for the output gear at time t, Ap(0) is the cepstrum</p><p>baseline peak for the input gear, and Ar(0) is the cepstrum baseline peak for the output gear. For</p><p>a monitored system, this health indicator would be zero in the baseline condition, close to -1, if</p><p>the output gear is degraded, and close to 1 if the input gear is degraded. Figure 6.5 provides a</p><p>result from this health indicator calculation, for the high speed shaft gear and pinion meshing</p><p>pair. The health indicator is near -1 for all 10 data samples, which indicates that the high speed</p><p>pinion is the gear with the more severe level of damage, according to this metric. This agrees</p><p>with the previous result from the sideband features in the vibration spectrum, in which there was</p><p>evidence of damage on the high speed shaft pinion, but little evidence of damage on the high</p><p>speed shaft gear.</p><p>)0(/)()0(/)(</p><p>)0(/)()0(/)(</p><p>)(</p><p>rrpp</p><p>rrpp</p><p>AtAAtA</p><p>AtAAtA</p><p>td</p><p>+</p><p>−</p><p>=</p><p>(9)</p><p>Figure 6.5. Cepstrum health Indicator for Case C calculated for high speed shaft gear and pinion</p><p>1 2 3 4 5 6 7 8 9 10</p><p>-1</p><p>-0.8</p><p>-0.6</p><p>-0.4</p><p>-0.2</p><p>0</p><p>0.2</p><p>0.4</p><p>0.6</p><p>0.8</p><p>1</p><p>Sample #</p><p>C</p><p>ep</p><p>st</p><p>ru</p><p>m</p><p>P</p><p>ea</p><p>k</p><p>/ R</p><p>at</p><p>io</p><p>Cepstrum Peak Ratio Plot (HSS/ISS) - Case C</p><p>ratio index (d21)</p><p>Sum Index</p><p>ISS CepPeak</p><p>HSS CepPeak</p><p>66</p><p>6.2.3 Bearing Envelope Analysis</p><p>Although the area of bearing condition monitoring has been an area of research for quite some</p><p>time, with new algorithms and methods proposed each year; the bearing envelope analysis</p><p>method remains one of the more effective techniques for bearing condition monitoring [28]. A</p><p>more detailed description of bearing envelope analysis can be found in prior work [28, 33],</p><p>therefore, this study simply provides a brief review of the method and highlights the results for</p><p>this study. A flow chart that shows the steps in this algorithm is provided in Figure 6.6, in which</p><p>the initial step is to band pass filter around an excited natural frequency. The selection of the</p><p>band-pass filter center frequency and bandwidth is an important step and also a current area of</p><p>research [28]. In this study, the filter parameters were selected by inspection of the frequency</p><p>domain spectrum for the respective accelerometers, but alternative methods could also be</p><p>considered. After filtering the signal, the Hilbert Transform is used to extract the envelope</p><p>signal, which is further analyzed in the frequency domain. For a bearing with damage on the</p><p>rolling element or bearing races, the bearing fault frequency peaks are usually much easier to</p><p>distinguish in the envelope spectrum when compared to the frequency spectrum.</p><p>Figure 6.6. Bearing envelope analysis flow chart</p><p>For performing envelope analysis in this Round Robin study, a band pass filter centered at</p><p>10,000 Hz, with a bandwidth of 1000 Hz was used, with the exception of accelerometer AN10 in</p><p>which two different frequency bands were evaluated. Sample results from this method are</p><p>provided in Figure 6.7, in which the envelope spectrum is shown for accelerometer AN6 and</p><p>AN7. The envelope spectrum for AN6 shows noticeable peaks</p><p>at 73 Hz and 345 Hz. The peak</p><p>at 73 Hz corresponds to the ball pass frequency inner race (BPFI) for the intermediate shaft</p><p>upwind bearing. The failure report confirms the inner race damage for this particular</p><p>intermediate shaft bearing. The peak at 345 Hz is very close to the calculated BPFI frequency</p><p>(336 Hz) for the high speed shaft downwind bearing; the failure report confirms that this bearing</p><p>had inner race damage, with overheating as the mode. The envelope spectrum for AN7 also</p><p>clearly shows a peak at the BPFI frequency (345 Hz) for the high speed shaft downwind bearing.</p><p>The envelope spectrum for accelerometer AN10 in Figure 6.8 is provided using two different</p><p>band pass filter ranges; the first one is at a high frequency from 9,500 Hz - 10,500 Hz and the</p><p>later is from a frequency range of 4,000 Hz – 6,000 Hz. The results shown in Figure 6.8 (a)</p><p>clearly show a peak at the BPFO and its first harmonic for the intermediate speed shaft</p><p>downwind bearing; the failure report confirms that there was an outer race damage on this</p><p>Vibration Signal</p><p>Band pass filter around excited natural</p><p>frequency</p><p>Take Hilbert Transform of band</p><p>pass signal</p><p>Take magnitude of analytical signal</p><p>to obtain envelope signal</p><p>Take Fast Fourier Transform (FFT)</p><p>of envelope signal</p><p>Analyze envelope spectrum at</p><p>bearing fault frequencies</p><p>67</p><p>bearing. The envelope spectrum in Figure 6.8 (b) shows a peak at the BPFO for the planet</p><p>carrier upwind bearing; this bearing also had outer race damage according to the failure report.</p><p>Using a filter from 9,500 Hz-10,500 Hz would have resulted in a missed detection for the planet</p><p>carrier upwind bearing. Using the frequency band from 4000 Hz - 6000 Hz resulted in a</p><p>detection of an outer race fault on the planet carrier bearing; however, it provided a less clear</p><p>detection for the ISS downwind bearing, in which only the first harmonic of the BPFO could be</p><p>identified.</p><p>Figure 6.7. Envelope spectrum - Case C: (a) AN6 - peaks at BPFI for ISS upwind bearing and HSS</p><p>downwind bearing; (b) AN7 - BPFI peak for HSS downwind bearing</p><p>Figure 6.8. Envelope spectrum accelerometer AN10 - Case C: (a) band-pass filter from 9500 Hz -</p><p>10,500 Hz, peaks at BPFO and 2X BPFO for ISS downwind bearing; (b) band pass filter from 4000</p><p>Hz - 6000 Hz, peak at BPFO for planet carrier upwind bearing and also peak at 2X BPFO for ISS</p><p>downwind bearing</p><p>68</p><p>6.2.4 Spectral Kurtosis Filtering</p><p>For condition monitoring of mechanical systems, the vibration signals for damaged gear and</p><p>bearing components typically display an impulsive signature. Detecting that impulsive signature</p><p>is not a trivial task since the signature could be masked by other sources of vibration.</p><p>Techniques and filtering methods based on spectral kurtosis are aimed at finding the optimal</p><p>frequency band for recovering the impulsive fault signature that could be hidden in the raw</p><p>vibration waveform. A brief review of the calculation procedure and the results of this study are</p><p>provided, and the interested reader is referred to the work by Antoni et al [30] and Combet et al</p><p>[34] for a more detailed discussion on the use of spectral kurtosis for filtering vibration signals.</p><p>The initial step in this algorithm is to calculate the short time Fourier Transform of the vibration</p><p>signal, denoted by H(t,f). Equation (10) indicates that the average value of the fourth power of</p><p>H(t,f) is divided by the mean square value of H(t,f), which provides a kurtosis value as a function</p><p>of frequency. The Wiener filter is constructed using the kurtosis values for each frequency bin,</p><p>as shown in Equation (11); the frequency bin is only included if the kurtosis value is above a</p><p>statistical threshold at a given confidence level [30]. The Wiener filter is then multiplied by the</p><p>frequency domain representation of the original signal, X(f), and the result is transformed back to</p><p>the time domain as indicated in Equation (12). The advantage of this method is that the signal is</p><p>filtered without any a priori knowledge of which frequency band to filter in, and instead is based</p><p>on which frequency band is most impulsive.</p><p>2</p><p>),(</p><p>),(</p><p>)( 22</p><p>4</p><p>−=</p><p>ftH</p><p>ftH</p><p>fKr</p><p>(10)</p><p></p><p></p><p></p><p> ></p><p>=</p><p>Otherwise 0</p><p>)(Kfor )(</p><p>)(ˆ r αsffK</p><p>fW r</p><p>(11)</p><p>{ })()(ˆ)( 1 fXfWty −ℑ= (12)</p><p>In this study, the filtering algorithm was used to process data for all 12 accelerometers using a</p><p>block size of 256 data samples and an overlap of 80% when performing the short time Fourier</p><p>Transform calculation. When applying this processing method, only high kurtosis values were</p><p>observed for accelerometers AN3 and AN4; thus, the example results do not include the other</p><p>accelerometers. An example result from the filtering method is provided in Figure 6.9 from</p><p>accelerometer AN4, in which one can observe that the Wiener filter is focused on the high</p><p>frequency content of the signal from approximately 8 KHz - 18 KHz. This implies that although</p><p>the rotational frequencies of the carrier are quite low; structural resonances at a high frequency</p><p>appear to be excited by defects and damage from the internal components within the planetary</p><p>gearbox. Figure 6.9 illustrates how the impulsive signature is masked in the raw time signal, but</p><p>is quite clear in the filtered signal; the raw signal has a kurtosis value of only 3.39 compared to a</p><p>kurtosis value of 169 for the filtered signal. Further examination of the filtered signal shows a</p><p>pattern that repeats for every 2 revolutions of the carrier. This periodic pattern in the filtered</p><p>signal from accelerometer AN4 is shown in Figure 6.10. The high kurtosis value of the filtered</p><p>signal, along with the periodic pattern that is related to the carrier rotation, and the location of the</p><p>accelerometer each point to a problem with the internal components in the planetary gearbox.</p><p>However, it was difficult to determine which gear or bearing component was the cause of this</p><p>problem from the filtered signal and the envelope spectrum; a potential reason is that multiple</p><p>69</p><p>faults occurred in the planetary gearbox. The results from the failure report indicate that the ring</p><p>gear and sun pinion both had scuffing and corrosion damage and the planet carrier's upwind</p><p>bearing had damage on the outer race.</p><p>Figure 6.9. (a) Wiener filter based on spectral kurtosis; (b) raw and filtered AN4 accelerometer</p><p>signal – Case A</p><p>Figure 6.10. Filtered AN4 signal showing the periodic repetition based on 2 revolutions of the</p><p>carrier – Case A</p><p>0 1 2 3 4 5 6 7 8</p><p>-100</p><p>0</p><p>100</p><p>Time (s)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Filtered AN4 Signal (First 2 Rotations)</p><p>0 1 2 3 4 5 6 7 8</p><p>-100</p><p>0</p><p>100</p><p>Time (s)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Filtered AN4 Signal (Third and Fourth Rotations)</p><p>0 1 2 3 4 5 6 7 8</p><p>-100</p><p>0</p><p>100</p><p>Time (s)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Filtered AN4 Signal (Fifth and Sixth Rotations)</p><p>70</p><p>The results in Figures 6.9 and 6.10 and were from an example data file from Case A. The same</p><p>filtering method was also applied to the remaining data files and the kurtosis feature from the</p><p>filtered signal was stored. The results of the filtered kurtosis value are provided in Figure 6.11</p><p>and provide an interesting point for discussion. The kurtosis values were very large for files</p><p>from Case A, with values above 50. It is also worth noting that the kurtosis values show a</p><p>decreasing trend for the data files in Case A, in which each file was collected in sequential order.</p><p>For Case B and Case C, the kurtosis values are quite low and in a normal range between 2 and 4.</p><p>This implies that the fault signature was not present for accelerometer AN3 and AN4 for the</p><p>operating conditions in Case B and Case C. This could imply that the operating conditions for</p><p>Case A are more conducive for detecting this type of problem in the planetary gearbox.</p><p>However, it is also worth noting that the data was collected in sequential order from Case A to</p><p>Case C; this could imply that the vibration signature</p><p>their results. The project had sixteen partners,</p><p>including seven universities and nine from the private sector. The main body of this report</p><p>discusses detailed analysis algorithms and diagnostic results from eight of the sixteen partners.</p><p>Below is a brief synopsis for this report:</p><p>• In Chapter 1, the background and objectives of this Round Robin project are presented,</p><p>along with the summary of blind study stage diagnostics results from all sixteen project</p><p>partners.</p><p>• In Chapter 2, the test gearbox, dynamometer test facility, one customized vibration data</p><p>acquisition system, test conditions, and actual damage found on the test gearbox through</p><p>its disassembly are presented.</p><p>v</p><p>• In Chapter 3, to overcome the inaccuracy incurred by speed variations, a synchronous</p><p>sampling technique is introduced. To accommodate high gear ratios in wind turbine</p><p>gearboxes, a digital domain synchronous re-sampling technique is presented.</p><p>• In Chapter 4, an evaluation is conducted of analysis algorithms originally developed for</p><p>Department of Defense applications, including the results of these algorithms when</p><p>applied to the GRC wind turbine dataset. The algorithms consist of sensor validation,</p><p>bearing fault detection/isolation, and gear fault detection/isolation modules. A joint time</p><p>frequency analysis is also discussed.</p><p>• In Chapter 5, a validation is presented of analysis algorithms that are used in the</p><p>aerospace community for the wind industry. The focus is on two methodologies:</p><p>synchronous analysis of shaft/gear components and non-synchronous analysis of</p><p>bearings.</p><p>• In Chapter 6, various vibration signal processing and feature extraction algorithms are</p><p>evaluated. It details the evaluated methods including frequency domain, cepstrum,</p><p>bearing envelope analysis, spectral kurtosis filtering, time synchronous averaging, and a</p><p>planet separation method.</p><p>• In Chapter 7, sideband pattern analysis is performed on all gears for gear fault diagnosis.</p><p>Data from torque measurements have also been analyzed to facilitate annulus gear</p><p>diagnosis. For the bearing diagnosis, a multi-scale enveloping spectra technique is</p><p>investigated.</p><p>• In Chapter 8, analysis of “jerk” data derived from vibration acceleration data of the test</p><p>wind turbine gearbox are discussed. For component failure identification, the correlation</p><p>coefficient analysis and clustering analysis are applied to identify the failure stage of the</p><p>gearbox in the time domain.</p><p>• In Chapter 9, the algorithms for bearing diagnostics are presented. They consist of several</p><p>different stages to separate and enhance the bearing signals, and then envelope analysis is</p><p>applied. For parallel stage gear diagnostics, classic synchronously-averaged signatures</p><p>are studied and comparisons are made of spectra and cepstra from the healthy and faulty</p><p>conditions. For individual planet and sun gear diagnostics, the premium current method is</p><p>investigated.</p><p>• In Chapter 10, a two stage fault detection framework, with analytical and graphical</p><p>analysis for wind turbine gearbox CM, is proposed. The analytical diagnostics and</p><p>graphical analysis are performed for fault detection and defect severity level evaluation of</p><p>different damage modes based on sideband and kurtosis analyses.</p><p>• In Chapter 11, some recommended practices for data acquisition and data analysis are</p><p>described for use in conducting vibration-based wind turbine drivetrain condition</p><p>monitoring.</p><p>It is worth noting that the synopses detailed for Chapters 3-10 were based on the analysis</p><p>algorithms of the project's partners. Detailed diagnostic results obtained by each partner are</p><p>listed in this report.</p><p>vi</p><p>The study has demonstrated that the wind industry can improve vibration analysis algorithms for</p><p>drivetrain condition monitoring. Both the presented algorithms and the recommended practices</p><p>can be considered by CM equipment suppliers in their future product releases for the benefit of</p><p>the wind industry.</p><p>vii</p><p>Table of Contents</p><p>Acknowledgements ..................................................................................................................................... i</p><p>Nomenclature .............................................................................................................................................. ii</p><p>Executive Summary ................................................................................................................................... iv</p><p>1 Introduction ............................................................................................................................................ 1</p><p>2 Tests and Actual Gearbox Damage ..................................................................................................... 3</p><p>2.1 Test Article ............................................................................................................................... 3</p><p>2.2 Dynamometer Test Facility ...................................................................................................... 6</p><p>2.3 One Customized Vibration Data Acquisition System ............................................................... 7</p><p>2.4 Test Conditions ........................................................................................................................ 9</p><p>2.5 Actual Gearbox Damage ........................................................................................................ 10</p><p>3 Analysis Algorithms and Diagnostics Results from General Electric ........................................... 12</p><p>3.1 Fundamentals ......................................................................................................................... 12</p><p>3.2 Round Robin Analysis Results ............................................................................................... 19</p><p>3.3 Discussions ............................................................................................................................ 32</p><p>4 Combining Novel Approaches with Proven Algorithms for Robust Wind Turbine Gearbox Fault</p><p>Detection .................................................................................................................................... 34</p><p>4.1 Introduction ............................................................................................................................. 34</p><p>4.2 Algorithm Overview ................................................................................................................ 34</p><p>4.3 Results Summary ................................................................................................................... 38</p><p>4.4 Lessons Learned and Conclusions ........................................................................................ 48</p><p>5 Analysis Algorithms and Diagnostics Results from NRG Systems ............................................... 49</p><p>5.1 Introduction ............................................................................................................................. 49</p><p>5.2 Analysis Algorithms ................................................................................................................ 49</p><p>5.3 Analysis Results ..................................................................................................................... 52</p><p>5.4 Discussion .............................................................................................................................. 56</p><p>6 Review and Application of Methods and Algorithms in Wind Turbine Gearbox Fault Detection 58</p><p>6.1 Introduction ............................................................................................................................. 58</p><p>6.2 Signal Processing and Feature Extraction Methods .............................................................. 58</p><p>6.3 Summary of Results ............................................................................................................... 80</p><p>6.4 Conclusions</p><p>became less impulsive with the running</p><p>time of the gearbox. Despite these discussion points for potential reasons as to why the signature</p><p>was not present in all three operating conditions, the spectral kurtosis filtering method provided a</p><p>very clear detection of a problem in the planetary gearbox for Case A, based on the very high</p><p>kurtosis values. This provided enough confidence and evidence to believe that the internal</p><p>components in the planetary gearbox stage were degraded.</p><p>Figure 6.11. Kurtosis of filtered signal - shown for all 3 cases</p><p>6.2.5 Time Synchronous Averaging</p><p>This section discusses the results using time synchronous averaging for the parallel stage gears</p><p>and the ring gear. The rationale for excluding the results for the planet and sun gears in this</p><p>section is that a specific algorithm is needed for extracting the synchronous average signals for</p><p>the individual planet and sun gears. The synchronous averaging algorithm and results for the</p><p>plant and sun gears are provided in section 6.2.6. For all gears, the results from the residual</p><p>signal, amplitude modulation signal, and the phase modulation signal are extracted and analyzed</p><p>for determining the health condition of each gear.</p><p>0 5 10 15 20 25 30</p><p>0</p><p>50</p><p>100</p><p>150</p><p>200</p><p>250</p><p>Sample #</p><p>K</p><p>ur</p><p>to</p><p>si</p><p>s</p><p>of</p><p>F</p><p>ilt</p><p>er</p><p>ed</p><p>S</p><p>ig</p><p>na</p><p>l -</p><p>A</p><p>N</p><p>4</p><p>Kurtosis of Filtered Signal - AN4 - All Cases</p><p>Case A</p><p>Case B</p><p>Case C</p><p>71</p><p>The additional processing methods for the residual signal (section 6.2.5.1) and the amplitude and</p><p>phase modulation signals (section 6.2.5.2), first require the extraction of the time synchronous</p><p>average signal for each shaft. The time synchronous averaging algorithm requires a reference</p><p>pulse train for aligning the data with respect to a given shaft, and ensemble averaging the signal</p><p>over several rotations. In this study, a tachometer signal was not provided, but an alternative</p><p>method was used for extracting a reference signal. The provided speed signal had a clear tone at</p><p>the generator shaft speed (20 Hz or 30 Hz); band pass filtering in a range between 15 Hz – 35 Hz</p><p>provided a way of extracting a pulse train from the speed signal. The filtered speed signal was</p><p>used as a surrogate for the tachometer signal; alternative methods that use the gear mesh</p><p>frequency peak for estimating a synthetic tachometer signal could also have been used [35].</p><p>With the necessary reference signal, the vibration signals could be aligned and ensemble</p><p>averaged with respect to the carrier, low speed shaft, intermediate speed shaft, and the high speed</p><p>shaft, using the established synchronous averaging methods. More specific details on the</p><p>synchronous averaging method including the different interpolation methods; the frequency</p><p>domain implementation can be found in [36]. In this study, a time domain interpolation method</p><p>was used. From the provided vibration signals, accelerometer AN3 was used for calculating the</p><p>time synchronous average signal for the carrier shaft, AN5 was used for the low speed shaft,</p><p>AN6 was used for the intermediate speed shaft, and AN7 was used for the high speed shaft.</p><p>6.2.5.1 Gear Residual Signal</p><p>The extraction of the periodic vibration waveform using time synchronous averaging allows one</p><p>to further analyze the vibration signature and meshing pattern for each gear. Departures of the</p><p>regular meshing pattern could be indicative of a fault in the gear; the residual signal aims to</p><p>remove the regular meshing pattern from the synchronous signal to further examine this aspect.</p><p>The residual signal for a gear can be calculated by removing the shaft harmonics and the gear</p><p>mesh frequency and harmonics from the time synchronous average signal [18]. Considering that</p><p>the time synchronous average signal of the gear is aligned with the shaft, the signal is periodic</p><p>and the filtering can be conveniently performed in the frequency domain and transformed back to</p><p>the time domain. It is common to remove the first five shaft harmonics, the gear mesh</p><p>frequency, and all of the gear mesh frequency harmonics when calculating the residual signal.</p><p>Prior works from seeded fault studies have also shown the residual signal to be effective for</p><p>detecting gear tooth pitting faults [37].</p><p>The time synchronous average signal and the residual signal are shown in Figure 6.12 for the</p><p>high speed shaft pinion. The kurtosis value of the residual signal for this gear is quite low (2.34),</p><p>and there appear to be no abnormalities that can be seen in the time averaged signal or the</p><p>residual signal. However, previous results from the cepstrum and frequency domain methods</p><p>indicated large sidebands and a significant problem with this high speed shaft pinion; these were</p><p>also confirmed in the failure report study. Large sidebands are noticed in the frequency domain</p><p>representation of the time synchronous average signal for the high speed shaft, which is provided</p><p>in Figure 6.13. The gear mesh frequency peak (order 22) is lower in magnitude then a peak at</p><p>one of the sidebands (order 23). The inability for the residual signal to detect this fault on the</p><p>high speed shaft pinion highlights the importance of extracting multiple gear vibration features to</p><p>have better coverage for the different failure modes.</p><p>72</p><p>Figure 6.12. TSA signal and residual signal from accelerometer AN7 - Case C: top plot - TSA signal</p><p>for high speed shaft pinion; bottom plot - residual signal for high speed shaft pinion</p><p>Figure 6.13. TSA vibration spectrum for accelerometer AN7 and high speed shaft – Case C</p><p>Another example residual signal is shown for the ring gear in Figure 6.14. The kurtosis value of</p><p>the ring gear is also in a normal range (3.36), and there appears to be no abnormal patterns or an</p><p>0 50 100 150 200 250 300 350 400</p><p>-4</p><p>-2</p><p>0</p><p>2</p><p>4</p><p>High Speed Shaft Angle (degree)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Time Synchronous Signal HSS Pinion</p><p>0 50 100 150 200 250 300 350 400</p><p>-4</p><p>-2</p><p>0</p><p>2</p><p>4</p><p>High Speed Shaft Angle (degree)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Residual Signal HSS Pinion</p><p>Kurtosis Value of 2.3433</p><p>0 50 100 150</p><p>0</p><p>0.2</p><p>0.4</p><p>0.6</p><p>0.8</p><p>1</p><p>1.2</p><p>X= 23</p><p>Y= 0.35919</p><p>Orders of High Speed Shaft</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>TSA Spectrum High Speed Shaft AN7</p><p>73</p><p>indication of a fault in the time synchronous average signal or the residual signal for the ring</p><p>gear. This is in sharp contrast to the results from the phase modulation function provided in the</p><p>subsequent section, in which there is a clear indication of damage on the ring gear. The residual</p><p>signal for the other parallel shaft gears also offers no indication of damage. This highlights that</p><p>the residual signal was not the most appropriate algorithm for detecting the failure modes that</p><p>were occurring on the parallel shaft gears and the ring gear.</p><p>Figure 6.14. TSA signal and residual signal from accelerometer AN3 - Case C: top plot - TSA signal</p><p>for ring gear; bottom plot - residual signal for ring gear</p><p>6.2.5.2 Amplitude and Phase Modulation</p><p>For detecting local defects, such as a fatigue crack in a gear wheel, the prior work done by</p><p>McFadden [38] suggested an analysis of the amplitude and phase modulation function of the</p><p>gear vibration. For performing this analysis, the synchronous average signal for a given shaft is</p><p>performed. A band pass filter around a dominant gear mesh frequency is used and typically</p><p>includes a number of sidebands around the gear mesh frequency peak. The Hilbert Transform is</p><p>then performed on the filtered signal. The modulus and phase of the analytical signal provide the</p><p>envelope and phase modulation functions, respectively. The amplitude and phase modulation</p><p>functions were calculated for each gear wheel in this study. In addition, the kurtosis of the</p><p>amplitude modulation function and the kurtosis of the derivative of the phase modulation</p><p>function were also calculated to quantify the health condition of each gear. For the parallel shaft</p><p>gears, the band pass filter</p><p>included four sidebands, while the band pass filter for the ring gear</p><p>included six sidebands. The accelerometer AN3 was also effectively down sampled to 200 Hz</p><p>prior to extracting the synchronous average for the ring gear. Sample results for this method are</p><p>provided in Figure 6.15, in which the amplitude and phase modulation functions are plotted for</p><p>0 50 100 150 200 250 300 350 400</p><p>-0.15</p><p>-0.1</p><p>-0.05</p><p>0</p><p>0.05</p><p>Carrier Angle (degree)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Time Synchronous Signal Ring Gear</p><p>0 50 100 150 200 250 300 350 400</p><p>-0.1</p><p>-0.05</p><p>0</p><p>0.05</p><p>0.1</p><p>Carrier Angle (degree)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Residual Signal Ring Gear</p><p>Kurtosis Value of 3.3604</p><p>74</p><p>the high speed shaft pinion. As one can observe, there are significant jumps in the phase</p><p>modulation function for this gear and a high kurtosis value at 12.8. This would be an indication</p><p>of a damage on the high speed shaft pinion. In addition, the amplitude modulation function is</p><p>close to zero when these significant changes in phase occur. The phase modulation function for</p><p>the high speed shaft gear had a moderate indication of a gear problem, with a kurtosis value of</p><p>5.2. However, there was no indication of a problem for the intermediate speed shaft gear or</p><p>pinion. Another example is provided in Figure 6.16, in which the amplitude and phase</p><p>modulation for the ring gear is provided. There appears to be a clear indication of a problem</p><p>with the ring gear through visual observation of the amplitude and phase modulation signals.</p><p>The phase modulation function, in particular, has a high kurtosis value and two noticeable shifts</p><p>in phase, which indicate a damaged gear. In summary, the amplitude and phase modulation</p><p>functions provide a strong indication of a problem with the ring gear and high speed shaft pinion,</p><p>and a moderate indication for the high speed shaft gear; however, there was no indication of a</p><p>problem for the other gear wheels.</p><p>Figure 6.15. High speed pinion amplitude and phase modulation signal from accelerometer AN7 -</p><p>Case C: top plot - Time Synchronous Average; middle plot - amplitude modulation signal;</p><p>bottom plot - phase modulation signal</p><p>0 50 100 150 200 250 300 350 400</p><p>-5</p><p>0</p><p>5</p><p>High Speed Shaft Angle (degree)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Time Synchronous Signal HSS Pinion</p><p>Kurtosis Value of 2.8923</p><p>0 50 100 150 200 250 300 350 400</p><p>0</p><p>0.5</p><p>1</p><p>1.5</p><p>High Speed Shaft Angle (degree)</p><p>E</p><p>nv</p><p>le</p><p>op</p><p>e</p><p>(A</p><p>M</p><p>) (</p><p>m</p><p>/s</p><p>2 )</p><p>AM and PM Modulation Signal HSS Pinion</p><p>Kurtosis Value of 2.5465</p><p>0 50 100 150 200 250 300 350 400</p><p>-20</p><p>-10</p><p>0</p><p>10</p><p>High Speed Shaft Angle (degree)</p><p>P</p><p>ha</p><p>se</p><p>M</p><p>od</p><p>ul</p><p>at</p><p>io</p><p>n</p><p>(R</p><p>ad</p><p>)</p><p>Kurtosis Value of 12.8058</p><p>75</p><p>Figure 6.16. Ring gear amplitude and phase modulation signal from accelerometer AN3 - Case C:</p><p>top plot – TSA; middle plot - amplitude modulation signal; bottom plot - phase modulation signal</p><p>6.2.6 Planet Separation Algorithm – Time Synchronous Averaging</p><p>Considering the relative motion of the planet gears and the multiple mesh points that occur</p><p>because the planet gears mesh with the ring gear and sun gear simultaneously, it is necessary to</p><p>use a specific algorithm for extracting the time synchronous average signal for the individual</p><p>planet and sun gears. The algorithm considered in this study follows the algorithm proposed by</p><p>McFadden et al [29]. There are variations of this algorithm, including the method proposed by</p><p>researchers at the Defence Science and Technology Organisation (Australia) (DSTO) [39], as</p><p>well as a version that uses multiple accelerometers on the planetary gearbox housing [40]. A</p><p>flow chart of the algorithm is provided in Figure 6.17 and highlights the algorithm processing</p><p>steps. The initial step is to calculate the time synchronous average signal with respect to the</p><p>carrier rotation. The central idea in this method is to capture a meshing period of each tooth</p><p>when the planet gear is in very close proximity to the fixed accelerometer on the gearbox</p><p>housing. To accomplish this, it is necessary to know when the planet gear is passing by the fixed</p><p>accelerometer. Considering the amplitude modulation effect from the increased vibration level,</p><p>as each planet passes the fixed accelerometer; the narrow band envelope signal can be used to</p><p>determine the number of planet passing instances. A window function is applied to the</p><p>synchronous average signal when each planet gear passes for a short period of time; the short</p><p>period of time is typically one to three gear mesh periods. Based on the number of teeth for each</p><p>respective gear, a lookup table can be used to determine which tooth was meshing during that</p><p>captured time signal. Then, it is stored in the proper location in the array. This capture of the</p><p>windowed data is repeated for each tooth and requires several rotations of the carrier; the number</p><p>0 50 100 150 200 250 300 350 400</p><p>-0.1</p><p>0</p><p>0.1</p><p>Carrier Angle (degree)</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Time Synchronous Signal Ring Gear</p><p>Kurtosis Value of 3.3138</p><p>0 50 100 150 200 250 300 350 400</p><p>0</p><p>0.005</p><p>0.01</p><p>Carrier Angle (degree)</p><p>E</p><p>nv</p><p>le</p><p>op</p><p>e</p><p>(A</p><p>M</p><p>) (</p><p>m</p><p>/s</p><p>2 )</p><p>AM and PM Modulation Signal Ring Gear</p><p>Kurtosis Value of 4.1418</p><p>0 50 100 150 200 250 300 350 400</p><p>-10</p><p>-5</p><p>0</p><p>5</p><p>Carrier Angle (degree)</p><p>P</p><p>ha</p><p>se</p><p>M</p><p>od</p><p>ul</p><p>at</p><p>io</p><p>n</p><p>(R</p><p>ad</p><p>)</p><p>Kurtosis Value of 33.0163</p><p>76</p><p>of rotations is equal to the reset time for the planet or sun gear. The result is an assembled</p><p>vibration signal for each gear tooth. This process is repeated until several assembled signals can</p><p>be constructed. Lastly, the constructed waveforms are ensemble averaged and this completes the</p><p>process for extracting the time synchronous average</p><p>Figure 6.17. Flow chart for planet separation algorithm</p><p>For implementing this method, accelerometer AN3 was initially down sampled to a 200 Hz</p><p>sampling rate. Considering the number of carrier rotations and time period needed by this</p><p>algorithm, five files from Case C were concatenated and combined prior to applying the</p><p>algorithm. A narrow band filter that included four sidebands around the gear mesh frequency</p><p>was applied to the time synchronous average signal for the carrier. The envelope signal of the</p><p>filtered signal is provided in Figure 6.18 and one can clearly observe noticeable peaks that are</p><p>related to the planet passing the fixed accelerometer. The angular spacing of the peaks is</p><p>approximately 120 degrees, which again confirms that these peaks correspond to the passing of</p><p>the three planet gears. For capturing the meshing vibration during the planet passing, a Tukey</p><p>window is used. An example Tukey window is shown in Figure 6.19, in which Nv was set to</p><p>three to capture the vibration for three mesh periods. Using these parameters for the planet</p><p>separation algorithm, the synchronous average signal was extracted for each planet gear and the</p><p>sun gear; the number of averages was eight for the planet gears and 15 for the sun gear. The</p><p>residual signals and amplitude and phase modulation signals were also calculated to further</p><p>analyze the health condition of the gear wheels. For the amplitude and phase modulation signals,</p><p>a band pass filter that included three sidebands was used.</p><p>Vibration Signal</p><p>Perform TSA with respect to carrier</p><p>Determine planet passing by narrow</p><p>band demodulation</p><p>Apply window function for a tooth mesh</p><p>period during planet passing</p><p>Store windowed data according to tooth</p><p>number</p><p>Assemble signal from each tooth</p><p>Repeat Steps 1-6 and take the average</p><p>of the ensemble</p><p>1.</p><p>2.</p><p>3.</p><p>4.</p><p>5.</p><p>6.</p><p>7.</p><p>77</p><p>Figure 6.18. Narrow band amplitude modulation signal for determining planet passing - Case C</p><p>Figure 6.19. Example Tukey window used for planet separation algorithm - in this study,</p><p>Nv was set to 3 to include 3 mesh periods</p><p>Sample results from the synchronous averaging signal and the residual signal are provided in</p><p>Figure 6.20, in which the result is shown for one of the planet</p><p>gears. In this example, the time</p><p>synchronous average signal and the residual signal show no abnormal behavior for the planet</p><p>gear; the failure report found no defects on any of the planet gears. The spectrum for the time</p><p>0 0.5 1 1.5 2 2.5 3 3.5 4</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6</p><p>0.7</p><p>0.8</p><p>0.9</p><p>1</p><p>Tooth Mesh Period</p><p>W</p><p>in</p><p>do</p><p>w</p><p>M</p><p>ag</p><p>ni</p><p>tu</p><p>de</p><p>Example Tukey Window</p><p>Tv=NvTm</p><p>78</p><p>synchronous average signal for this planet gear is shown in Figure 6.21, and one can observe a</p><p>clear gear mesh frequency peak at the 39th order. The sidebands are not large in magnitude in the</p><p>spectrum and the planet gear appears to be in a health state from these data processing results.</p><p>The other two planet gears were also considered to be in a normal condition based on similar</p><p>results that were observed in their time synchronous average signal and residual signal.</p><p>Figure 6.20. Top - TSA signal for Planet 2; bottom - residual signal for Planet 2 – Case C</p><p>Figure 6.21. TSA vibration spectrum for Planet 2 – Case C</p><p>0 5 10 15 20 25 30 35 40</p><p>-0.2</p><p>-0.1</p><p>0</p><p>0.1</p><p>0.2</p><p>Planet Tooth</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Time Synchronous Signal Planet 2</p><p>0 5 10 15 20 25 30 35 40</p><p>-0.1</p><p>-0.05</p><p>0</p><p>0.05</p><p>0.1</p><p>Planet Tooth</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Residual Signal Planet 2</p><p>Kurtosis Value of 3.287</p><p>0 50 100 150</p><p>0</p><p>0.005</p><p>0.01</p><p>0.015</p><p>0.02</p><p>0.025</p><p>0.03</p><p>X= 39</p><p>Y= 0.028945</p><p>Orders for Planet 2</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>TSA Planet 2 Spectrum</p><p>79</p><p>The time synchronous average signal and the residual signal analysis were also performed for the</p><p>sun gear, with the results provided in Figure 6.22. In this example, the residual signal is</p><p>providing a moderate indication of damage on the sun gear, with a kurtosis value of 5.36. The</p><p>failure report confirms scuffing and fretting corrosion on the sun pinion. Additional narrowband</p><p>amplitude modulation and phase modulation analysis was also performed on the time</p><p>synchronous average signals for the planet gears and the sun gear. Although the residual signal</p><p>provided an indication of damage on the sun gear, the amplitude and phase modulation signals</p><p>did not provide any indication of damage on the sun gear. A sample result from one of the planet</p><p>gears is provided in Figure 6.23. Both the amplitude and phase modulation signals do not</p><p>indicate damage on this particular planet gear. The other two planet gears also did not have any</p><p>indication of damage from the narrowband amplitude and phase modulation analysis; this is</p><p>encouraging since the failure report did not find any damage on any of the three planet gears.</p><p>For the sun gear, the residual signal provided a moderate indication of damage, but no damage</p><p>was indicated from the amplitude and phase modulation signals.</p><p>Figure 6.22. Top - TSA signal for sun gear; bottom - residual signal for sun gear – Case C</p><p>0 2 4 6 8 10 12 14 16 18 20</p><p>-0.15</p><p>-0.1</p><p>-0.05</p><p>0</p><p>0.05</p><p>Planet Tooth</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Time Synchronous Signal Sun Gear</p><p>0 2 4 6 8 10 12 14 16 18 20</p><p>-0.1</p><p>-0.05</p><p>0</p><p>0.05</p><p>0.1</p><p>Planet Tooth</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Residual Signal Sun Gear</p><p>Kurtosis Value of 5.3562</p><p>80</p><p>Figure 6.23. Planet Gear 2 amplitude and phase modulation signal from accelerometer AN3 –</p><p>Case C: top plot – TSA; middle plot - amplitude modulation signal;</p><p>bottom plot - phase modulation signal</p><p>6.3 Summary of Results</p><p>For each data processing method, a qualitative metric was assigned based on its ability to detect</p><p>each failed component in the gearbox used in this study; the results are provided in Table 6.3.</p><p>For each failed component and algorithm, a ranking of three levels is assigned for low, medium,</p><p>and high confidence; the rankings are based on examining the output plots and the calculated</p><p>features. An example of a high confidence rating is the amplitude and phase modulation results</p><p>for the high speed pinion, in which the output plots and large kurtosis values are clear indications</p><p>of damage. In certain instances, an algorithm was not evaluated for detecting a failed component</p><p>or the algorithm is not designed or suited for that task. In this case, the label of NA (not</p><p>applicable) was assigned. An example of the NA ranking is a bearing envelope analysis for</p><p>detecting damage on any of the gear wheels. The spectral kurtosis method was only applied to</p><p>the planetary gearbox (signals AN3 and AN4) and could only provide an indication of</p><p>degradation to the planetary stage, but not which specific gear was degraded. This is reflected in</p><p>the table with the additional notation of “stage” for the spectral kurtosis technique. Lastly, the</p><p>rankings are given a black color if the method was applied prior to the release of the failure</p><p>report and a blue color if the method was applied after the failure report was provided. Bearing</p><p>envelope analysis, time synchronous averaging, and the planet separation algorithm were all</p><p>performed after the failure report was released.</p><p>From the tabular results in Table 6.3, one can observe that the high speed pinion had high</p><p>indications of damage from several techniques, including the vibration spectrum, cepstrum</p><p>processing, and narrowband analysis from the phase modulation signal. Only the residual signal</p><p>0 5 10 15 20 25 30 35 40</p><p>-0.2</p><p>0</p><p>0.2</p><p>Planet 2 Tooth</p><p>V</p><p>ib</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>/s</p><p>2 )</p><p>Time Synchronous Signal Planet Gear</p><p>Kurtosis Value of 3.3138</p><p>0 5 10 15 20 25 30 35 40</p><p>0.02</p><p>0.03</p><p>0.04</p><p>Planet2 Tooth</p><p>E</p><p>nv</p><p>le</p><p>op</p><p>e</p><p>(A</p><p>M</p><p>) (</p><p>m</p><p>/s</p><p>2 ) AM and PM Modulation Signal Planet2 Gear</p><p>Kurtosis Value of 2.8756</p><p>0 5 10 15 20 25 30 35 40</p><p>-4</p><p>-3</p><p>-2</p><p>Planet2 Tooth</p><p>P</p><p>ha</p><p>se</p><p>M</p><p>od</p><p>ul</p><p>at</p><p>io</p><p>n</p><p>(R</p><p>ad</p><p>)</p><p>Kurtosis Value of 2.1986</p><p>81</p><p>did not provide an indication of a fault for the high speed pinion. The residual signal in general</p><p>did not detect damage on the gear wheels for this study, with only a moderate indication of</p><p>damage on the sun gear. The intermediate speed shaft pinion had a moderate indication of</p><p>damage from both frequency domain analysis and the cepstrum features; however, there was no</p><p>indication of damage by the narrow band analysis. Bearing envelope analysis provided high</p><p>confident indications for three of the bearing failures that were on the intermediate and high</p><p>speed shafts. The bearing damage on the planet carrier upwind bearing had only a moderate</p><p>detection; the peak was less noticeable and a different band pass filter range had to be used to</p><p>detect this fault. For the planetary gearbox, the ring gear appeared to be the easiest to detect,</p><p>with a high confidence indication of damage from the narrowband phase modulation signal. It</p><p>should be noted that none of the planet gears had damage according to the failure report; this</p><p>agrees with the results from the data processing, in which none of the algorithms detected any</p><p>abnormality or damage with the planet gears. In summary, many of the failed components could</p><p>be detected using the evaluated algorithms. However, for gear components, in particular,</p><p>multiple algorithms appear necessary since many of the algorithms are only tuned to one failure</p><p>mode.</p><p>Table 6.3. Summary of results for each algorithm with the following notation: L-low confidence, M-medium</p><p>confidence, H-high confidence, NA –not applicable or evaluated; black - indicates a method that was</p><p>evaluated before the failure report, blue - indicates a method that was evaluated after the failure report</p><p>Failed Component Frequency</p><p>Domain Cepstrum Spectral</p><p>Kurtosis</p><p>Bearing</p><p>Envelope</p><p>Analysis</p><p>TSA –</p><p>Residua</p><p>l Signal</p><p>TSA –</p><p>Amplitude /</p><p>Phase</p><p>Modulation</p><p>HSS Pinion H H NA NA L H</p><p>HSS Gear L L NA NA L M</p><p>ISS Pinion M M NA NA L L</p><p>ISS Gear L M NA NA L L</p><p>Ring Gear NA NA H - stage NA L H</p><p>Sun Pinion NA NA H - stage NA M L</p><p>ISS Upwind</p><p>Bearing NA NA NA H NA NA</p><p>ISS Downwind</p><p>Bearings NA NA NA H NA NA</p><p>HSS Downwind</p><p>Bearings NA NA NA H NA NA</p><p>Planet Carrier</p><p>Upwind Bearing NA NA NA M NA NA</p><p>82</p><p>6.4 Conclusions and Future Work</p><p>This chapter</p><p>provides an evaluation of vibration signal processing and feature extraction</p><p>algorithms used by the research team at the Center for Intelligent Maintenance Systems (IMS)</p><p>for the Condition Monitoring Round Robin study. As one can observe from the summary results</p><p>table, most of the failed components could be detected by one or more of the processing</p><p>methods. This is encouraging and highlights that vibration-based condition monitoring can be</p><p>used to assess and diagnose which components are in a failed condition. For gear wheels in</p><p>particular, the use of multiple algorithms appears necessary, considering the different number of</p><p>gear failure modes that are possible. The residual signal, in particular, did not seem suited for</p><p>the failure modes exhibited by the damaged gear wheels on the parallel stage shaft, while the</p><p>other algorithms provided more confident detections. The detection results for each algorithm do</p><p>not account for the additional hardware or on-board processing requirements. The planet</p><p>separation algorithm, in particular, is difficult to implement given the time period required to</p><p>accumulate enough rotations of the carrier shaft.</p><p>Although the results from this study were encouraging, there are some aspects that could have</p><p>aided the study or should be considered for future work. This study could have been aided by</p><p>time domain waveforms instead of frequency spectrums provided for the baseline data. Many of</p><p>the more advanced algorithms require the raw time waveform and they could not be evaluated</p><p>based on the baseline data set. In addition, alternative methods were used for acquiring a</p><p>reference signal for performing synchronous averaging. Further experimental studies should</p><p>acquire and save a tachometer pulse train to avoid this issue. Considering that the gearbox was</p><p>already in a severely damaged condition, the algorithms were evaluated on the basis of their</p><p>ability to detect the health state of the various bearing and gear components. Unfortunately, this</p><p>does not allow one to evaluate the algorithms ability to provide an early detection of a problem</p><p>or whether the extracted vibration features are monotonic with the damage level. Both early</p><p>detection and severity estimation are additional aspects worth evaluating for vibration-based</p><p>condition monitoring techniques for wind turbine drivetrains. Continuous monitoring of a wind</p><p>turbine drivetrain from a baseline condition until failure could provide a way to further evaluate</p><p>the merits of the vibration-based condition monitoring algorithms.</p><p>83</p><p>7 Defect Diagnosis in Wind Turbine Gearbox based on Sideband</p><p>Energy and Enveloping Spectral Analysis</p><p>Robert X. Gao*1, Jinjiang Wang1, and Ruqiang Yan2</p><p>1Department of Mechanical Engineering, University of Connecticut, Storrs, CT, USA</p><p>2School of Instrument Science and Engineering, Southeast University, Nanjing, China</p><p>*Corresponding Author Email: rgao@engr.uconn.edu</p><p>7.1 Introduction</p><p>To improve cost-effectiveness of wind energy, wind turbines must operate in a highly reliable</p><p>fashion, given the significant cost associated with system repair, maintenance, and unexpected</p><p>failure. Accordingly, techniques for the condition monitoring and fault diagnosis of wind turbine</p><p>structures and components have been gaining increasing attention [41].</p><p>Of the various components in a wind turbine, the gearbox is a major component that is costly and</p><p>vulnerable to failure. Accordingly, signal processing for gearbox defect identification and</p><p>diagnosis has been an active research area. There are two major components in a gearbox: gears</p><p>and bearings. For gear diagnosis, sideband analysis, amplitude, and phase modulation [42],</p><p>wavelet transform [43], and spectral kurtosis [44] have been investigated. Typically, diagnosis is</p><p>achieved through comparisons between a defective gear and a healthy gear. As for the bearing</p><p>diagnosis, a band pass resonant signal processing technique has been reported. Choosing an</p><p>appropriate bandwidth remains an important issue, given its effect on the diagnosis result.</p><p>As part of the CM Round Robin study, three sets of vibration data measured by NREL on a wind</p><p>turbine gearbox (of unknown damaged condition) were analyzed at three different operating</p><p>speeds. For gear fault diagnosis, sideband pattern analysis was performed on all gears. Data from</p><p>torque measurements were also analyzed to facilitate annulus gear diagnosis; whereas for bearing</p><p>diagnosis, the multi-scale enveloping spectra technique [45] has been investigated. The result of</p><p>the analysis was compared with that of a spectral analysis of a healthy gearbox that was provided</p><p>by NREL as a reference base.</p><p>7.2 Algorithms</p><p>Vibration of a gearbox can be caused by various sources, such as gear meshing, interaction</p><p>between the rolling elements and raceways in bearings, and shaft rotation. Structural defects on</p><p>gear’s surface also constitute a source of vibrations that are carried by gear meshing frequencies.</p><p>Research reported in the literature has shown that the energy associated with frequency</p><p>components at the sidebands around the gear meshing frequency will increase as the health</p><p>condition of the gear deteriorates, in comparison to a healthy gear. Accordingly, sideband</p><p>analysis has been performed for gear analysis in this study.</p><p>For bearing defect diagnosis, the multi-scale enveloping spectra technique has been investigated</p><p>[45], which makes use of the time, scale, and frequency information contained in the bearing</p><p>vibration signal. The algorithm first decomposes the bearing vibration signal into a series of</p><p>wavelet basis functions, through variations of the scales and time shifts of the wavelet function.</p><p>The envelope of each decomposed wavelet function is then extracted from the modulus of the</p><p>wavelet coefficients. Next, spectral analysis is performed repeatedly on the envelope signal,</p><p>resulting in an envelope spectrum of the original signal at the various scales. The integration of</p><p>84</p><p>the wavelet transform, using post-spectral analysis, reveals the defect characteristic more clearly,</p><p>enhancing its effectiveness in bearing defect diagnosis.</p><p>7.3 Results</p><p>Vibration data measured by NREL on a wind turbine gearbox was analyzed for gear and bearing</p><p>defect diagnosis, respectively. Figure 7.1 illustrates the physical system analyzed for this study,</p><p>with the locations of the specific bearings, shaft, and gears identified.</p><p>Bearing H HS_Shaft</p><p>INT_PinionAnnulus Gear</p><p>HS PinionSun Gear Bearing A1</p><p>Bearing C1/C2Bearing D</p><p>Figure 7.1. Locations of defective components in the gearbox assembly</p><p>7.3.1 Gear Diagnosis Results</p><p>Gear test data at 1,800 rpm measured by vibration sensor AN7, was analyzed by means of</p><p>sideband analysis, and the result is presented in this chapter. Figure 7.2 (a) and Figure 7.2 (b)</p><p>show the spectra of gear vibrations under healthy and deteriorated (at the end of service life)</p><p>conditions, at the locations of HS_Pinion and INT_Pinion, respectively. From the figures, the</p><p>gear meshing frequencies of the HS_Pinion and INT_Pinion can be clearly seen. A zoom-in view</p><p>around the INT_Pinion and HS_Pinion gear meshing frequencies are shown in Figure 7.2 (c) to</p><p>Figure 7.2 (f). Comparing the result of the gearbox under healthy and deteriorated conditions, the</p><p>increase in energy content of the sideband frequencies can be identified, for both the HS_Pinion</p><p>and INT_Pinion. This indicates that the tested gear is defective. The same trend is observed from</p><p>the sideband analysis of Annulus_Gear and Sun_Gear, in Figure 7.3, which indicates that the</p><p>Annulus_Gear and Sun_Gear are also defective. In Table 7.1, the sideband energy ratios</p><p>(defined as the first order sideband energy over the energy at the gear meshing frequency) of</p><p>these four gears are summarized. It is seen that for all the four gears, there is a consistent</p><p>increase in the sideband energy ratio (e.g., from 29.4% to 107.7% for the INT_Pinion).</p><p>85</p><p>120</p><p>130 140 150 160 170 180 190 200 210 220</p><p>0</p><p>0.02</p><p>0.04</p><p>0.06</p><p>0.08</p><p>0.1</p><p>0.12</p><p>0.14</p><p>AN7__HSSRadial</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>0 200 400 600 800 1000 1200 1400 1600 1800 2000</p><p>0</p><p>0.05</p><p>0.1</p><p>0.15</p><p>0.2</p><p>0.25</p><p>0.3</p><p>0.35</p><p>0.4</p><p>AN7__HSSRadial</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>120 130 140 150 160 170 180 190 200 210 220</p><p>0</p><p>0.002</p><p>0.004</p><p>0.006</p><p>0.008</p><p>0.01</p><p>0.012</p><p>0.014</p><p>0.016</p><p>0.018</p><p>0.02</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>AN7</p><p>0 200 400 600 800 1000 1200 1400 1600 1800 2000</p><p>0</p><p>0.01</p><p>0.02</p><p>0.03</p><p>0.04</p><p>0.05</p><p>0.06</p><p>0.07</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>AN7</p><p>600 650 700 750</p><p>0</p><p>0.01</p><p>0.02</p><p>0.03</p><p>0.04</p><p>0.05</p><p>0.06</p><p>0.07</p><p>0.08</p><p>AN7__HSSRadial</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>fHS_Mesh</p><p>fHS_Mesh</p><p>fHS_Mesh</p><p>fHS_Mesh+f2</p><p>fHS_Mesh-f2</p><p>fHS_Mesh-f1</p><p>fHS_Mesh+f1</p><p>fHS_Mesh</p><p>fHS_Mesh+f2</p><p>fHS_Mesh+f1</p><p>fHS_Mesh-f2</p><p>2*fHS_Mesh</p><p>2*fHS_Mesh</p><p>fINT_Mesh</p><p>fINT_Mesh fINT_Mesh+f2fINT_Mesh</p><p>fINT_Mesh+f2</p><p>fINT_Mesh</p><p>600 650 700 750</p><p>0</p><p>0.01</p><p>0.02</p><p>0.03</p><p>0.04</p><p>0.05</p><p>0.06</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>AN7</p><p>(a) (b)</p><p>(c) (d)</p><p>(e) (f)</p><p>fHS_Mesh</p><p>fHS_Mesh-f2</p><p>fHS_Mesh+f2</p><p>fINT_Mesh-f2</p><p>AN7_DefectiveAN7_New</p><p>AN7_DefectiveAN7_New</p><p>AN7_DefectiveAN7_New</p><p>Figure 7.2. Comparison analysis between test data and reference data for HS_Pinion and</p><p>INT_Pinion</p><p>86</p><p>0 10 20 30 40 50 60 70 80 90 100</p><p>0</p><p>0.005</p><p>0.01</p><p>0.015</p><p>0.02</p><p>0.025</p><p>0.03</p><p>0.035</p><p>0.04</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>AN7</p><p>0 10 20 30 40 50 60 70 80 90 100</p><p>0</p><p>0.05</p><p>0.1</p><p>0.15</p><p>0.2</p><p>0.25</p><p>AN7__HSSRadial</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>15 20 25 30 35 40 45 50 55</p><p>0</p><p>0.02</p><p>0.04</p><p>0.06</p><p>0.08</p><p>0.1</p><p>0.12</p><p>0.14</p><p>AN7__HSSRadial</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>32 34 36 38 40 42 44 46 48 50 52</p><p>0</p><p>0.005</p><p>0.01</p><p>0.015</p><p>0.02</p><p>0.025</p><p>0.03</p><p>0.035</p><p>0.04</p><p>AN7__HSSRadial</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>32 34 36 38 40 42 44 46 48 50 52</p><p>0</p><p>0.005</p><p>0.01</p><p>0.015</p><p>0.02</p><p>0.025</p><p>0.03</p><p>0.035</p><p>0.04</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>AN7</p><p>15 20 25 30 35 40 45 50 55</p><p>0</p><p>0.005</p><p>0.01</p><p>0.015</p><p>0.02</p><p>0.025</p><p>0.03</p><p>0.035</p><p>0.04</p><p>Frequency (Hz)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>(m</p><p>W</p><p>)</p><p>AN7</p><p>fAnnulus_Mesh</p><p>fSun_Mesh+f3</p><p>fSun_Mesh-f3</p><p>fAnnulus_Mesh</p><p>2*fAnnulus_Mesh</p><p>fAnnulus_Mesh</p><p>fAnnulus_Mesh-f4</p><p>fAnnulus_Mesh</p><p>fSun_Mesh</p><p>fAnnulus_Mesh+f4</p><p>fSun_Mesh</p><p>(a) (b)</p><p>(c) (d)</p><p>(e) (f)</p><p>AN7_DefectiveAN7_New</p><p>AN7_New AN7_Defective</p><p>AN7_DefectiveAN7_New</p><p>Figure 7.3. Comparison analysis between test data and reference data for Annulus_Gear and</p><p>Sun_Gear</p><p>87</p><p>Table 7.1. Sideband energy comparison between new gearbox and gearbox at the end of service life</p><p>Components Healthy Gearbox Gearbox at End of Service Life</p><p>Meshing</p><p>energy</p><p>(mw)</p><p>1st sideband</p><p>energy (mw)</p><p>Sideband</p><p>Energy ratio</p><p>Meshing</p><p>energy</p><p>(mw)</p><p>1st sideband</p><p>energy (mw)</p><p>Sideband</p><p>Energy ratio</p><p>HS_Pinion 0.051 0.016 31.4% 0.051 0.114 223.5%</p><p>INT_Pinion 0.017 0.005 29.4% 0.13 0.14 107.7%</p><p>Sun_Gear 0.0002 0.0004 200% 0.008 0.019 237.5%</p><p>Annulus_Gear 0.035 0.014 40% 0.135 0.059 43.7%</p><p>The increase in the sideband energy ratio related to the annulus gear is not as significant as that</p><p>of the other three gears (relative increase is 9.3%). Considering that the annulus gear runs at low</p><p>speed under high torque conditions resulting from the gearbox transmission mechanism, the</p><p>torque measurement may be more effective for low speed gear diagnosis, due to its sensitivity to</p><p>angular vibrations of the gear. Based on this consideration, data obtained from torque</p><p>measurements of the gearbox have been analyzed. Figure 7.4 shows the waveform of the torque</p><p>data under 1,200 RPM. The interval between the peaks is approximately 4.03s, corresponding to</p><p>the rolling-over period of the annulus gear. Figure 7.5 shows the result of envelope spectrum</p><p>analysis of torque data. A peak at frequency of 0.248 Hz, which corresponds to the roll-over</p><p>period of the annulus gear, is identified. This indicates a structural defect on the annulus gear.</p><p>0 10 20 30 40 50 60</p><p>95</p><p>100</p><p>105</p><p>110</p><p>115</p><p>120</p><p>125</p><p>Time (Sec)</p><p>A</p><p>m</p><p>pl</p><p>itu</p><p>de</p><p>1200RPM</p><p>Peaks corresponding to defect in annulus gear</p><p>Figure 7.4. Time series of torque data under 1200 rpm</p><p>88</p><p>0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2</p><p>0</p><p>0.5</p><p>1</p><p>Frequency (Hz)</p><p>E</p><p>nv</p><p>el</p><p>op</p><p>in</p><p>g</p><p>S</p><p>pe</p><p>ct</p><p>ru</p><p>m</p><p>(m</p><p>W</p><p>)</p><p>0.248 Hz</p><p>0.496 Hz</p><p>Figure 7.5. The envelope spectrum of torque data under 1200 rpm</p><p>7.3.2 Bearing Diagnosis Results</p><p>Using the wavelet enveloping technique [45], vibration data of the tested gearbox was analyzed.</p><p>In Figure 7.6, wavelet enveloping spectrum of data measured by sensor AN3 (close to bearing H)</p><p>under rotational speed 1,800 rpm is presented. Given the high peak related to the frequency</p><p>component fBPFO , bearing H is considered defective. Furthermore, from the energy concentration</p><p>at the HSS_Shaft rotating frequency (1,000 mw) and its harmonics, it can be concluded that the</p><p>HSS_Shaft has imbalance or misalignment.</p><p>0 10 20 30 40 50 60 70 80 90 100</p><p>0</p><p>500</p><p>1000</p><p>1500</p><p>2000</p><p>2500</p><p>3000</p><p>Frequency (Hz)</p><p>S</p><p>pe</p><p>ct</p><p>ru</p><p>m</p><p>(m</p><p>W</p><p>)</p><p>Bearing H</p><p>fBPFO</p><p>HSS_Shaft</p><p>imbalance fu</p><p>HSS_Shaft</p><p>2*fu</p><p>HSS_Shaft</p><p>3*fu</p><p>Figure 7.6. Wavelet enveloping spectrum of sensor AN3 at 1,800 rpm</p><p>89</p><p>Figure 7.7 shows the wavelet enveloping spectrum of data measured by sensor AN6 (adjacent to</p><p>bearing D) at the running speed of 1,800 rpm. Defect frequency, fBPFI, of bearing D can be</p><p>identified, although its amplitude is not as significant due to masking from the high energy</p><p>component, fu, which is related to imbalance of the HSS_Shaft.</p><p>Bearing D fBPFI</p><p>HSS_Shaft imbalance fu</p><p>HSS_Shaft 2*fu HSS_Shaft 6*fu</p><p>Figure 7.7. Wavelet enveloping spectrum of sensor AN6 at 1,800 rpm</p><p>7.3.3 Comparison with Inspection Result</p><p>The analyses results have been compared with physical damages identified in the gearbox when</p><p>it was disassembled for visual inspection. As shown in Table 7.2, all gear defects were</p><p>successfully identified. Also, two of the four bearings were identified as defective.</p><p>Table 7.2. Comparison between the analysis result and the actual damage of a tested gearbox</p><p>Damage Component Damage mode Severity Rationale</p><p>1 HS gear set Scuffing Severe Sideband</p><p>2 Intermediate gear set Fretting corrosion and scuffing Severe Sideband</p><p>3 Annulus gear Scuffing/polishing Moderate Sideband</p><p>4 Sun pinion Fretting corrosion Severe Sideband</p><p>5 Bearing H Fretting corrosion Severe Wavelet envelope</p><p>6 Bearing D Assembly damage Moderate Wavelet envelope</p><p>7 Bearing C1/C2 Assembly damage on spacer Severe Not identified</p><p>8 Bearing A1 Overheating Severe Not identified</p><p>90</p><p>7.4 Lessons Learned</p><p>The diagnosis results have demonstrated that sideband analysis provides an effective and</p><p>computationally efficient approach to gear defect diagnosis. Considering that the energy content</p><p>associated with a structural defect may not be significant at the defect incipient stage,</p><p>complementing sideband analysis with other advanced techniques should be considered.</p><p>As for the bearing diagnosis, defects in bearing H and D have been identified by means of</p><p>wavelet enveloping. Because of the low signal-to-noise ratio and interference caused by gear</p><p>meshing frequencies, diagnosis of bearing D was more challenging than that of bearing H. This</p><p>indicates the need for separating the signal related to gear meshing from that of the bearing</p><p>vibration before performing the bearing diagnosis. Because the nature of the damage to Bearing</p><p>A1 is related to overheating, instead of a surface defect, and damage on bearing C1/C2 is not on</p><p>the roller raceway, but on the spacer, defects from bearings C1/C2 and A1 could not be identified</p><p>by the vibration data analysis conducted herein. This leads to the consideration that, besides</p><p>vibration sensing, other sensing techniques (e.g., temperature sensing) should be considered as</p><p>well to enable fusion of diverse sensing modalities for improved gearbox diagnosis. Research is</p><p>needed to address this issue.</p><p>91</p><p>8 Fault Analysis of a Wind Turbine Gearbox: A Data Driven</p><p>Approach</p><p>Zijun Zhang*, Anoop Verma, Andrew Kusiak</p><p>Department of Mechanical and Industrial Engineering, The University of Iowa</p><p>*Corresponding Author Email: zijun-zhang@uiowa.edu</p><p>8.1 Introduction</p><p>The wind industry has been affected by failures of wind turbine components, such as main</p><p>bearings, gearboxes, and generators. The high cost of replacing failed components impacts the</p><p>energy cost. Therefore, research in fault identification and condition monitoring is warranted.</p><p>Fault identification is concerned with a fault that has occurred and its labeling. In condition</p><p>monitoring, parameters reflecting the component conditions are identified and their changes are</p><p>analyzed to detect an emerging failure. In this chapter, the fault identification analysis is studied</p><p>in the time domain based on the vibration data of an impaired gearbox tested by NREL, which is</p><p>different from the traditional fault analysis from the frequency domain [46-51].</p><p>8.2 Methodologies</p><p>This section describes the data processing and analysis methods applied to the detection of the</p><p>gearbox faults.</p><p>8.2.1 Change Rate of Vibration Acceleration</p><p>To analyze the gearbox vibration in the time domain, jerk is utilized. Jerk describes the rate of</p><p>acceleration change, and it is often used to indicate the excitement of vibration. For the high-</p><p>frequency vibration acceleration data in Section 2.4, the jerk is approximated in Equation (13).</p><p>t t Ta aJ</p><p>T</p><p>−−</p><p>≈</p><p> </p><p>(13)</p><p>The expression in Equation (13) is derived in Equation (14).</p><p>0</p><p>lim , and ( )</p><p>( )</p><p>t t T t t T</p><p>t t Tt</p><p>a a a ada aJ a a a t t t T</p><p>dt t t t T T</p><p>− −</p><p>−∆ →</p><p>− −∆</p><p>= = ≈ = ∆ = − ∆ = − −</p><p>∆ − −</p><p>        (14)</p><p>where J</p><p></p><p>is jerk, a is acceleration, t is the time index, and T represents the sampling interval,</p><p>1/40000 s.</p><p>8.2.2 Root Mean Square, Crest Factor and Kurtosis</p><p>Besides jerk, the root mean square (RMS), crest factor (CF), and kurtosis are estimated based on</p><p>the acceleration data and utilized in time domain analysis.</p><p>RMS is the simplest method for measuring abnormalities in the time domain. The RMS value</p><p>can be used to detect unbalanced rotating elements. It is a statistical measure of the magnitude</p><p>with varying quantity, and it is expressed in Equation (15).</p><p>( )2</p><p>1</p><p>1 N</p><p>i</p><p>i</p><p>RMS s</p><p>N =</p><p>= ∑ (15)</p><p>The crest factor (CF) is a measure used to detecting changes in the signal pattern due to</p><p>impulsive vibration sources, such as tooth breakage. It can be useful in detecting high peaks in</p><p>the signal at higher magnitudes of the peak and for smaller numbers of peaks. A small value of</p><p>92</p><p>RMS and high peak value implies a higher crest factor. A CF with values in the range 2-6</p><p>represents normal operations; whereas, a value higher than six represents a defective component.</p><p>The crest factor is computed by dividing the peak level of the signal average by the standard</p><p>deviation (RMS) of the signal average, as shown in Equation (16).</p><p>Peak levelCF</p><p>RMS</p><p>= (16)</p><p>Kurtosis is defined as the fourth statistical moment of an array of values about the mean. It</p><p>indicates the existence of major peaks. A kurtosis value of less than three represents a component</p><p>in a normal health condition; whereas, a value greater than three represents abnormality. The</p><p>greater the number of peaks in the signal, the larger is the kurtosis. The kurtosis is expressed in</p><p>Equation (17).</p><p>( )</p><p>( )</p><p>4</p><p>1</p><p>2</p><p>2</p><p>1</p><p>.</p><p>N</p><p>i</p><p>i</p><p>N</p><p>i</p><p>i</p><p>N s s</p><p>K</p><p>s s</p><p>=</p><p>=</p><p>−</p><p>=</p><p> − </p><p> </p><p>∑</p><p>∑</p><p>(17)</p><p>8.2.3 Correlation Coefficient</p><p>The correlation coefficient is a quantity that measures the linear relationship between two</p><p>parameters ranges from -1 to 1. The value of the correlation coefficient equal to 1 (-1) indicates a</p><p>strong positive (negative) relationship between two parameters. A value of the correlation</p><p>coefficient close to zero means there is a weak linear relationship. The formulation of correlation</p><p>coefficient can be written as Equation (18).</p><p>2 2 2 2</p><p>( )( )</p><p>( ) ( ) ( ) ( )</p><p>n xy x y</p><p>r</p><p>n x x n y y</p><p>−</p><p>=</p><p>− −</p><p>∑ ∑ ∑</p><p>∑ ∑ ∑ ∑</p><p>(18)</p><p>where r is the correlation coefficient, and x and y are two different parameters.</p><p>8.2.4 Clustering</p><p>Clustering analysis is an unsupervised method of data analysis. Clustering algorithms group</p><p>observations into clusters by evaluating similarities among the observed data. A k-means</p><p>algorithm [52] is modified in this study to establish clusters. In the original version of the k-</p><p>means algorithm, the number of clusters, k, should be arbitrarily set by the analyst. In this study,</p><p>a clustering cost function is introduced to evaluate the cluster quality with k. The clustering cost</p><p>function is formulated as Equation (19) and used in a 10-fold, cross-validation scheme [53,54].</p><p>2</p><p>1</p><p>1</p><p>1( , , )</p><p>j i</p><p>k</p><p>j ik</p><p>i C</p><p>i</p><p>i</p><p>d k</p><p>m = ∈</p><p>=</p><p> </p><p>= −  </p><p> </p><p>∑ ∑</p><p>∑ x</p><p>x c x c</p><p>(19)</p><p>where d is the clustering cost, k is the number of clusters, m is the number of observations</p><p>(sensors) contained in each cluster, x is a vector of parameters used in this research, c presents</p><p>the centroid of each cluster, j is the index of each data point, and Ci represents cluster i.</p><p>The modified k-means algorithm involves the following steps:</p><p>93</p><p>Step 1. Set the initial value of k to 2</p><p>Step 2. Divide the data set into 10 subsets of equal size.</p><p>Step 3. Repeat 10 times.</p><p>Step 3.1. Randomly select nine subsets for training and use the 10th subset for testing.</p><p>Step 3.2. Initialize k centroids.</p><p>Step 3.3. Repeat the following two steps until the centroids do not change.</p><p>Step 3.3.1. Assign data point to the closest cluster by *</p><p>*{ : , 1,2, , }t t t</p><p>i j j i j i</p><p>C i k= − ≤ − =x x c x c  .</p><p>Step 3.3.2. Update the values of the centroids by</p><p>/</p><p>j i</p><p>i j</p><p>C</p><p>n</p><p>∈</p><p>= ∑</p><p>x</p><p>c x</p><p>, where n is the total number of</p><p>observations.</p><p>Step 3.4. Compute the clustering cost, d.</p><p>Step 4. Estimate the average of clustering cost d in 10-fold cross-validation.</p><p>Step 5. Stop the algorithm if d(k,x,c) – d(k – 1,x,c) ≤ ξ or k = 12; otherwise, go back to Step 1.</p><p>To implement the modified k-means algorithm, the parameter, ξ, is set to 0.05.</p><p>8.3 Results</p><p>8.3.1 Data Process and Description</p><p>Acceleration data are sampled at 40,000 Hz and recorded for 10 minute intervals. The data set is</p><p>large. As the sensors are used to recording acceleration, the data is transformed based on (1) to</p><p>obtain the jerk values. Acceleration data for all three test cases (2a, 2b, and 2c) at 10 minute</p><p>intervals are transformed. Each data set is divided into 40 data subsets of equal size (or equal</p><p>length, 15 seconds) for the further investigation.</p><p>Since the sampling frequency of the acceleration data is high, 40,000 Hz, viewing and data</p><p>analysis of the high frequency data directly in the run-chart form is not feasible. Therefore, four</p><p>statistical metrics, the mean, standard deviation, maximum, and minimum, are utilized to</p><p>compute the Jerk value for each data subset discussed in Section 8.2.1. The values of the mean,</p><p>standard deviation, maximum, and the jerk for all 40 data subsets are used to develop three new</p><p>data sets for analysis discussed in Section 8.3.2, 8.3.3, and 8.3.4. The minimum Jerk value is</p><p>always zero and, therefore, it is excluded from this research.</p><p>8.3.2 Detection of Ring Gear Fault</p><p>Figure 8.1 displays the time series speed data for 10 minutes. As shown, it is obvious that the</p><p>speed experiences significant change at the third minute. The maximum rate of change is about</p><p>500 rpm/15s and at the same time the change of LSS Torque suddenly increases to 15 kNm/15 s.</p><p>These two phenomena point to a fault. To analyze the faulty component and its location, the</p><p>maximum jerk data from 12 accelerometers, at each 15 second interval, is utilized. The</p><p>94</p><p>maximum and minimum of the maximum jerk data of each accelerometer are estimated. Then,</p><p>the ratio, R, is estimated based on the maximum and minimum values of the maximal jerk based</p><p>on Equation (20).</p><p>R = (Max{maximum jerk} – Min{maximum jerk}) / Max{maximum jerk} (20)</p><p>Figure 8.2 shows the R for each accelerometer.</p><p>As shown, the Ratio 1 of sensors AN3 and AN4</p><p>is much higher than the R of other sensors. Therefore, the location and component that AN3 and</p><p>AN4 monitored are considered as the possible location where the fault occurred. From the</p><p>specification provided by NREL, the component monitored by AN3 and AN4 is a ring gear and</p><p>the location is in the low speed stage (LSS-T) of the gearbox.</p><p>Figure 8.1. Run chart of maximum rate of speed</p><p>Figure 8.2. Bar char of R</p><p>8.3.3 Detection of Faults in Intermediate and High Speed Stages</p><p>The suspected faults in intermediate and high speed stages manifest themselves by significant</p><p>vibration observed at the high speed stage (HS-ST) and intermediate speed stage (IS-ST) of</p><p>gearbox in testing case 2b and 2c. As HS-ST is connected with IS-ST, there are three possible</p><p>causes: HS-ST damaged, IS-ST damaged, or both are damaged. One possible root cause of high</p><p>vibration in HS-ST and IS-ST is the oil leakage and gear wear at the two stages.</p><p>In this section, a correlation coefficient analysis is performed based on a data set containing the</p><p>mean jerk described in Section 8.3.1. Table 8.1 and Table 8.2 present the results of correlation</p><p>coefficient analysis based on cases 2b and 2c. As shown in Table 8.1 and Table 8.2, sensors,</p><p>0</p><p>100</p><p>200</p><p>300</p><p>400</p><p>500</p><p>600</p><p>1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39</p><p>M</p><p>ax</p><p>im</p><p>al</p><p>ra</p><p>te</p><p>o</p><p>f s</p><p>pe</p><p>ed</p><p>(r</p><p>pm</p><p>/1</p><p>5-</p><p>s)</p><p>Time (15 s intervals)</p><p>Speed of encoder on HSS</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0.6</p><p>0.7</p><p>0.8</p><p>0.9</p><p>1</p><p>AN1 AN2 AN3 AN4 AN5 AN6 AN7 AN8 AN9 AN10AN11AN12</p><p>Pe</p><p>rc</p><p>en</p><p>ta</p><p>ge</p><p>Index of sensors</p><p>Ratio 1</p><p>95</p><p>AN5, AN6, AN7, AN8, AN9, AN11, and AN12, are highly correlated. Since the component</p><p>monitored by AN1 and AN2 is considered healthy, results in Table 8.1 and Table 8.2 indicate</p><p>that significant vibration originates at one of the areas AN5, AN6, AN7, AN8, and AN9</p><p>monitored (HS-ST and IS-ST), and it impacts the generator monitored by AN11 and AN12.</p><p>Table 8.1. Correlation coefficient analysis of the mean of jerk data: Case 2b</p><p>Sensor AN1 AN2 AN3 AN4 AN5 AN6 AN7 AN8 AN9 AN10 AN11 AN12</p><p>AN1 1.00 0.98 0.53 0.20 0.02 0.14 0.00 -0.11 0.16 0.16 0.16 0.03</p><p>AN2 0.98 1.00 0.59 0.06 0.18 0.30 0.17 0.05 0.32 0.25 0.33 0.19</p><p>AN3 0.53 0.59 1.00 0.09 0.31 0.53 0.41 0.19 0.62 0.77 0.48 0.32</p><p>AN4 0.20 0.06 0.09 1.00 -0.88 -0.78 -0.85 -0.94 -0.70 -0.11 -0.76 -0.89</p><p>AN5 0.02 0.18 0.31 -0.88 1.00 0.94 0.97 0.97 0.90 0.50 0.92 0.97</p><p>AN6 0.14 0.30 0.53 -0.78 0.94 1.00 0.98 0.93 0.99 0.60 0.95 0.96</p><p>AN7 0.00 0.17 0.41 -0.85 0.97 0.98 1.00 0.97 0.96 0.56 0.94 0.97</p><p>AN8 -0.11 0.05 0.19 -0.94 0.97 0.93 0.97 1.00 0.88 0.39 0.90 0.98</p><p>AN9 0.16 0.32 0.62 -0.70 0.90 0.99 0.96 0.88 1.00 0.67 0.92 0.93</p><p>AN10 0.16 0.25 0.77 -0.11 0.50 0.60 0.56 0.39 0.67 1.00 0.59 0.42</p><p>AN11 0.16 0.33 0.48 -0.76 0.92 0.95 0.94 0.90 0.92 0.59 1.00 0.92</p><p>AN12 0.03 0.19 0.32 -0.89 0.97 0.96 0.97 0.98 0.93 0.42 0.92 1.00</p><p>Table 8.2. Correlation coefficient analysis of the mean of jerk data: Case 2c</p><p>Sensor AN1 AN2 AN3 AN4 AN5 AN6 AN7 AN8 AN9 AN10 AN11 AN12</p><p>AN1 1.00 0.83 0.32 -0.73 0.50 0.56 0.49 0.67 0.49 0.48 0.64 0.56</p><p>AN2 0.83 1.00 0.76 -0.91 0.88 0.90 0.87 0.92 0.87 0.86 0.91 0.91</p><p>AN3 0.32 0.76 1.00 -0.67 0.94 0.92 0.95 0.78 0.96 0.95 0.80 0.90</p><p>AN4 -0.73 -0.91 -0.67 1.00 -0.85 -0.90 -0.84 -0.97 -0.83 -0.80 -0.94 -0.91</p><p>AN5 0.50 0.88 0.94 -0.85 1.00 0.99 0.99 0.92 0.99 0.98 0.92 0.98</p><p>AN6 0.56 0.90 0.92 -0.90 0.99 1.00 0.99 0.95 0.98 0.97 0.95 0.99</p><p>AN7 0.49 0.87 0.95 -0.84 0.99 0.99 1.00 0.91 0.99 0.98 0.92 0.98</p><p>AN8 0.67 0.92 0.78 -0.97 0.92 0.95 0.91 1.00 0.91 0.88 0.96 0.96</p><p>AN9 0.49 0.87 0.96 -0.83 0.99 0.98 0.99 0.91 1.00 0.98 0.90 0.98</p><p>AN10 0.48 0.86 0.95 -0.80 0.98 0.97 0.98 0.88 0.98 1.00 0.88 0.96</p><p>AN11 0.64 0.91 0.80 -0.94 0.92 0.95 0.92 0.96 0.90 0.88 1.00 0.96</p><p>AN12 0.56 0.91 0.90 -0.91 0.98 0.99 0.98 0.96 0.98 0.96 0.96 1.00</p><p>Besides correlation coefficient analysis, the k-means clustering algorithm is utilized to examine</p><p>the relationship among sensors. Since the k-means algorithm groups parameters into clusters by</p><p>examining their similarity, it is capable of evaluating the relationship among sensors. Table 8.3</p><p>shows the clustering result of both case 2b and 2c. In Table 8.3, AN6, AN7, AN8, AN9 and</p><p>AN12 are grouped into one cluster while other sensors are grouped into another cluster. This</p><p>96</p><p>result points to the same pattern as the correlation coefficient analysis, which indicates the faulty</p><p>location of HS-ST and IS-ST.</p><p>Table 8.3. Clustering based classification</p><p>Case 2b Case 2c</p><p>Index of AN Final classification Index of AN Final classification</p><p>1 2 1 2</p><p>2 2 2 2</p><p>3 2 3 2</p><p>4 2 4 2</p><p>5 2 5 2</p><p>6 1 6 1</p><p>7 1 7 1</p><p>8 1 8 1</p><p>9 1 9 1</p><p>10 2 10 2</p><p>11 2 11 2</p><p>12 1 12 1</p><p>The results of RMS, CF, and kurtosis also show an agreement with the correlation and clustering</p><p>analysis. Figure 8.3 presents the RMS values of 2b, averaged over a 1 minute interval. The case</p><p>2b reveals a pattern; whereas, the low RMS values of sensors AN1 and AN2 cause a high crest</p><p>factor. The increase in RMS of AN8 may indicate that a fault is in progress in the gearbox. It</p><p>could be due to the oil leakage.</p><p>Figure 8.3. RMS across 12 sensors - Case 2b</p><p>Figure 8.4 displays the crest factor of 2b across 12 sensors. In Figure 8.4, it can be observed that</p><p>the main bearing is affected in test case 2b. It can be assumed that the significant amount of crest</p><p>factor near AN1 is contributed by the vibrations of other components.</p><p>97</p><p>Figure 8.4. Crest factor across 12 sensors - Case 2b</p><p>Figure 8.5 represents the kurtosis of three test cases across 12 sensors. In case of CM_2b,</p><p>kurtosis across all 12 sensors shows increasing patterns. This could indicate a gradual wear.</p><p>Figure 8.5. Kurtosis across 12 sensors - Case 2b</p><p>8.4 Conclusion and Discussion</p><p>Analysis of jerk data derived from vibration acceleration data of the test wind turbine gearbox</p><p>was discussed in this chapter. In the analysis of the component failure identification, the</p><p>correlation coefficient analysis and clustering analysis were applied to identify the failure stage</p><p>of the gearbox in the time domain. Some faults of the intermediate and high-speed stages of the</p><p>gearbox were correctly identified by the approaches discussed in this chapter. Some root causes</p><p>could be inferred based on the data patterns of some specific sensors. Since the drivetrain was</p><p>fixed to the floor, other factors (e.g., force from the wind and tower) that could impact the</p><p>vibration excitement were not presented. In the future research, gearbox vibration acceleration</p><p>data collected from field operated wind turbines, as well as data such as wind speed, generator</p><p>torque and tower vibration, is needed to validate applicability of the proposed approach in fault</p><p>identification.</p><p>98</p><p>9 Techniques for Separation and Enhancement of Various</p><p>Components in the Analysis of Wind Turbine Vibration Signals</p><p>Nader Sawalhi1, Robert B. Randall2*, and David Forrester3</p><p>1College of Engineering, Prince Mohammad Bin Fahd University, The Kingdom of Saudi</p><p>Arabia.</p><p>2School of Mechanical and Manufacturing Engineering, The University of New South Wales,</p><p>Australia</p><p>3Defence Science and Technology Organisation, Australia</p><p>*Corresponding Author Email: b.randall@unsw.edu.au</p><p>9.1 Introduction</p><p>This chapter provides a summary of the handling and processing of wind turbine data provided</p><p>by NREL for the CM Round Robin study. The University of New South Wales took an active</p><p>role in this study through Dr. Nader Sawalhi and Professor Bob Randall.</p><p>NREL provided three sets of data (taken from a number of accelerometers on the planetary</p><p>gearbox) at different speeds and load conditions. The data was for a faulty condition only. The</p><p>data was first analyzed blindly, in the sense that there was originally no information given as to</p><p>the type and location of faults in the gearbox. Our group concentrated on the search for bearing</p><p>faults, because it is our opinion that to be sure of detecting gear</p><p>faults, it is necessary to make</p><p>comparisons with signals from the gears in healthy condition. We did, however, look for</p><p>indications of local faults on the gears, as these might show up clearly as local impulsive</p><p>responses in the gear signatures.</p><p>Later, after receiving the inspection report, and spectra from the gearbox in good condition, we</p><p>made a further analysis, in particular of the gear signals, and were able to detect other indicators</p><p>of the actual faults. Most of these could have been detected in the original blind analysis, if we</p><p>had had the signals for good condition.</p><p>Our group had already had a certain amount of experience in analyzing signals from wind</p><p>turbine transmissions, and was aware that the main differences, with respect to other similar</p><p>gearboxes, were because the load can vary considerably over relatively short periods, at least</p><p>with respect to the low speed input sections of the transmission. The vibration signal from gears</p><p>is affected greatly by the load, and so some means has to be found to distinguish such variations</p><p>from changes in condition. We have considerable experience with the diagnoses of helicopter</p><p>gearboxes, which are somewhat similar. However, these operate at perhaps ten times higher</p><p>speeds, and it is possible to obtain reasonably long signals with an approximately constant load.</p><p>In contrast to gear fault signals, bearing signals are not so sensitive to torque load (although in</p><p>gearboxes, radial load depends on torque load), and there is usually a dramatic difference in the</p><p>signals in the presence of faults, which often allows them to be diagnosed without necessarily</p><p>having access to historical data. This is because of the development of spectral kurtosis (SK)</p><p>techniques in recent years by our group and colleagues, in particular Professor Jerome Antoni,</p><p>now of INSA Lyon, in France [55]. The techniques we have used for analyzing the signals for</p><p>gear and bearing faults are described in more detail below. Those bearing diagnosis are primarily</p><p>based on a semi-automated procedure, with several different stages to separate and enhance the</p><p>mailto:b.randall@unsw.edu.au</p><p>99</p><p>bearing signals. Then envelope analysis is applied (spectrum analysis of squared envelope</p><p>signals) to diagnose the fault repetition frequencies and their modulations by lower frequencies</p><p>[56]. We also applied a recently developed cepstral pre-whitening technique, which can</p><p>circumvent some of the stages in the earlier procedure [57]. For gear diagnosis we applied</p><p>classic techniques based on obtaining a synchronously averaged signature for each gear, and then</p><p>looking for localized impulses characteristic of local faults. This requires the signals to be “order</p><p>tracked,” or re-sampled in the angular domain, with equal numbers of samples in each</p><p>revolution. This normally requires a tachometer or shaft encoder signal for synchronization. The</p><p>supplied speed signal was not suitable for this so we extracted a “pseudo-encoder” signal from</p><p>the vibration signal to use for order tracking. For obtaining signatures of the individual planet</p><p>gears and sun gear in the planetary part of the gearbox, the premium current method is one</p><p>patented by DSTO (Defence Science and Technology Organisation), of the Australian Defence</p><p>Department. We engaged Dr. David Forrester of DSTO, the inventor of the technique, to obtain</p><p>these signatures for us for the latest results presented at the Wind Turbine Condition Monitoring</p><p>Workshop in Broomfield, CO, in September 2011. Those results are included here. It should be</p><p>mentioned that Dr. Forrester was surprised by the design of the planetary section of the gearbox,</p><p>as the choice of tooth numbers was far from a hunting tooth design, normally considered good</p><p>practice, and as a result of this, groups of teeth always mesh in the same way and repeat</p><p>frequently. The effects of this are discussed below. It is also somewhat unusual that the ratio of</p><p>the high speed section was exactly 4:1 (88:22) meaning that the 22 teeth on the pinion always</p><p>mesh in exactly the same way with four groups of 22 teeth on the intermediate shaft wheel.</p><p>Therefore, a fault on one tooth transfers to individual teeth on the mating gear, and is not</p><p>smeared out as it is in a hunting tooth design.</p><p>After receiving spectra for the gearbox in good condition, we were also able to make spectrum</p><p>comparisons to detect changes in modulation sideband patterns, often indicative of faults, and</p><p>also cepstrum analysis to concentrate the information in the sideband patterns.</p><p>9.2 Algorithms</p><p>Our general approach is to separate the signals, into the components coming from the gears and</p><p>bearings, and analyze them separately. The separation is based on the assumption that the gear</p><p>signals are deterministic (with respect to rotation angle), and the bearing signals are stochastic,</p><p>because of the minor random slip between the components and the random positioning of the</p><p>rolling elements in the clearance of the cage. These two effects give an approximately 1-2%</p><p>deviation of the mean value of the actual bearing fault frequencies, with the same order of</p><p>random variation around the mean from those frequencies and calculated on the basis of no slip</p><p>and perfectly uniform spacing. The signals can then be classified as approximately second order</p><p>cyclostationary, which allows their separation from the deterministic gear components [58].</p><p>There are a number of methods for achieving this separation [28], but the one initially used in</p><p>this research was to first isolate and then remove the deterministic components corresponding to</p><p>each gear in the system, by synchronous averaging, leaving a residual stochastic signal, which</p><p>should be dominated by bearing faults in some frequency bands. The optimum frequency bands</p><p>are found using some sort of kurtogram to find the frequency band with maximum SK. In this</p><p>case, a wavelet kurtogram [59] was used. An alternative preprocessing technique used in this</p><p>case was cepstrum pre-whitening [57]. By this means, the signal spectrum amplitude is set to a</p><p>constant value (whitened) and the original phase used to generate a time signal. This</p><p>simultaneously nullifies the effect of both discrete frequencies and resonances, so that a</p><p>100</p><p>frequency band containing an impulsive signal will tend to dominate the time signal. SK can be</p><p>used to further isolate the impulsive band.</p><p>9.2.1 Summary of Processing Algorithm</p><p>The five basic steps in the processing algorithm used during the first stage of analysis are listed</p><p>in Figure 9.1.</p><p>Figure 9.1. Signal processing approach pre release of inspection report</p><p>The first stage involves extracting a pseudo tachometer/encoder (tacho) signal from the measured</p><p>vibration signal; it was found that the speed signal provided by NREL was only useful for giving</p><p>an arithmetic mean estimate of the speed of the high speed shaft (generator rotor) and could not</p><p>be used for re-sampling purposes. The extracted tacho signal was used to resample the signal of</p><p>interest and extract the synchronous average for the intermediate shaft. The residual signal was</p><p>pre-whitened as a first step. The squared envelope spectrum was then obtained using the Hilbert</p><p>transform and scanned for bearing defect frequencies, which had been calculated for each</p><p>bearing in the gearbox. Pre-whitening was achieved using the newly proposed approach based on</p><p>the cepstrum (Cepstrum-pre-whitening). This squared enveloped signal was extracted and</p><p>inspected for bearing faults.</p><p>9.2.2 Pseudo Encoder Extraction and Speed Estimate</p><p>The process of extracting a reference speed signal is described schematically in Figure 9.2 [60].</p><p>In the first step, Figure 9.2 (a), the spectrum of the signal is visually examined to identify a</p><p>proper HSS (high speed shaft) gear mesh harmonic (and a suitable band around it). Highest</p><p>separable harmonics are preferable due to the more evident effect of smearing and will give more</p><p>accurate results. In the second</p><p>step, Figure 9.2 (b), a buffer (filled with zeros) of a size equal to</p><p>the FFT size is created. The complex spectrum of interest (band) is transferred to this buffer</p><p>(placed in the same lines as in the original spectrum). Note that the presentation in Figure 9.2 (b)</p><p>only shows the amplitude of the spectrum; however, it is the complex spectrum that has been</p><p>transferred to this buffer and the phase information is thus preserved. Finally the buffer is inverse</p><p>transformed to the time domain to obtain the reference signal, Figure 9.2 (c). As the buffer is</p><p>1. Tacho signal extraction</p><p>2. Successive signal re-sampling to obtain a synchronously averaged</p><p>signal for each shaft in the gearbox</p><p>3. Synchronously averaged signals are examined for gear faults.</p><p>4. Synchronously averaged signals subtracted from re-sampled signal</p><p>(at each stage) to find a residual signal.</p><p>5. Residual signal examined for bearing faults:</p><p>Pre-whitened (AR)- MED- Squared Envelope spectrum</p><p>Basic Processing Algorithm</p><p>101</p><p>filled with zeros up to the sampling frequency - negative frequencies were set to zero - the</p><p>inverse transform signal is analytic (complex), and it is the real part that will then represent the</p><p>reference signal. Note that zero crossings represent 180° increments in rotation phase, and this is</p><p>unaffected by amplitude modulation by any positive modulating function.</p><p>Figure 9.2. Reference (speed) signal extraction stages: (a) identifying a separable band; (b)</p><p>extracting the band into a new buffer; (c) inversing the transform signal b into the time domain</p><p>[60]</p><p>The signal obtained in 2.c is a sinusoidal-type signal whose periods represent the speed for each</p><p>shaft rotation. The speed variation in this signal (a reflection of the speed variation of the shaft</p><p>under investigation) can be traced using the zero crossings of the consecutive periods, which can</p><p>be achieved by detecting the zero crossings (an interpolation between the samples on either side).</p><p>This signal can also be used to order track the signal. Note, however, that this process may have</p><p>to be repeated progressively to order track the signal to higher harmonics and achieve better</p><p>results. This means that after each stage, a higher harmonic will be made available due to the</p><p>reduction of speed fluctuations and the analyst can select bands around the gear mesh harmonics</p><p>to improve the quality of order tracking and gain more accuracy.</p><p>The approach illustrated in Figure 9.2 was used to extract a tachometer and speed signal for the</p><p>High Speed shaft (HSS) of the gearbox. The speed extraction was based on the gear mesh</p><p>frequency of the high speed stage (22 × HSS). For this purpose, sensor 7 was selected for</p><p>extracting the gear mesh signal for the HSS, although this can also be achieved using other</p><p>650 700 750 800 850 900 950 1000 1050 1100</p><p>-200</p><p>0</p><p>200</p><p>400</p><p>600</p><p>800</p><p>1000</p><p>1200</p><p>(a) Step 1: Identifying the band</p><p>of interest. The plot shows the</p><p>amplitude of the spectrum.</p><p>Frequency axis scaled in lines</p><p>rather than Hz</p><p>0</p><p>100</p><p>200</p><p>300</p><p>400</p><p>500</p><p>600</p><p>700</p><p>800</p><p>NFFT</p><p>(b) Step 2: Band of interest</p><p>moved into a buffer filled with</p><p>zeros</p><p>0 1 2 3 4 5 6 7 8</p><p>x 105</p><p>-8</p><p>-6</p><p>-4</p><p>-2</p><p>0</p><p>2</p><p>4</p><p>6</p><p>8</p><p>x 10-3</p><p>(c) Step 3: real part of the</p><p>IFFT (Inverse Fast Fourier</p><p>Transform) of the buffer</p><p>obtained in step 2.</p><p>700 Frequency (line no.) 1000</p><p>0 Frequency (line no.)</p><p>800</p><p>Amp</p><p>0</p><p>800</p><p>Amp</p><p>0</p><p>0 Time (sample no.) NFFT</p><p>Zoom spectrum</p><p>102</p><p>sensors in close proximity to the high speed shaft. The zero crossings for the signal in Figure 9.2</p><p>(c) were used to estimate the speed of the HSS. Examples of estimates at two speeds based on</p><p>this procedure (scaled in rpm) from data set a and data set c are presented in Figure 9.3. It is</p><p>noted that the speed is relatively constant.</p><p>Figure 9.3. HSS estimates: Top - data 2a:5; Bottom - data 2c:5</p><p>9.2.3 Successive Re-sampling and Synchronous Average Extraction</p><p>A separation algorithm (gear/bearing signal separation) [61,62], which is based on successive re-</p><p>sampling of the signal under analysis has been adopted to obtain synchronously averaged signals</p><p>for each shaft and to completely remove the shaft harmonics, without much disruption of the</p><p>vibration signal.</p><p>The algorithm works by re-sampling the order-tracked signal to obtain an integer number of</p><p>samples per revolution for a specific shaft. The removal of the harmonics of that specific shaft</p><p>can be achieved by one of two methods. The first is by finding the synchronous average and</p><p>subtracting it (repeated periodically) from the signal. The second is by truncating the signal to an</p><p>integer number of revolutions (preferably a power of 2) and setting the lines corresponding to the</p><p>harmonics of that shaft (after FFT analysis) to √2 times the mean (complex) value of the adjacent</p><p>frequencies (the multiplication by √2 is to make the amplitude statistically the mean of the two</p><p>amplitudes). To avoid treating the negative frequency components, it is recommended that they</p><p>be set to zero after the FFT step, and double the positive frequency components, then take the</p><p>real part of the resulting analytic signal in the time domain. Both methods arrive at the same</p><p>result, as was presented in [62].</p><p>The extracted tacho signal was used to resample the signal of interest and extract the</p><p>synchronous average for the intermediate shaft. As the HSS and the intermediate speed shaft</p><p>(ISS) have a ratio of four, the removal of the harmonics of HSS was included at this stage. The</p><p>end result of this stage was four synchronously averaged signals for the ISS, Low Speed shaft</p><p>0 0.5 1 1.5 2 2.5 3 3.5 4</p><p>x 104</p><p>1802</p><p>1802.5</p><p>1803</p><p>1803.5</p><p>1804</p><p>2c: 5</p><p>R</p><p>ot</p><p>ai</p><p>on</p><p>al</p><p>s</p><p>pe</p><p>ed</p><p>o</p><p>f h</p><p>ig</p><p>h</p><p>sp</p><p>ee</p><p>d</p><p>sh</p><p>af</p><p>t (</p><p>rp</p><p>m</p><p>)</p><p>0 0.5 1 1.5 2 2.5</p><p>x 104</p><p>1205</p><p>1205.5</p><p>1206</p><p>1206.5</p><p>2a: 5</p><p>Gear mesh Periods</p><p>103</p><p>(LSS), the planet carrier shaft, and the planetary gears (a composite of all the planetary gears;</p><p>this was later updated to extract an average for each planetary gear). Typical results for the four</p><p>synchronously averaged signals are presented in Figure 9.4 and Figure 9.5 for sensor three</p><p>(planetary stage and low speed shaft) for both data set a and data set c.</p><p>Figure 9.4. Synchronously averaged signals from sensor 3, data 2a:5</p><p>0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2</p><p>-5</p><p>0</p><p>5</p><p>2a:5 sensor 3</p><p>Intermediate Shaft</p><p>0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8</p><p>-0.5</p><p>0</p><p>0.5</p><p>Low Speed Shaft</p><p>A</p><p>c</p><p>c</p><p>e</p><p>le</p><p>ra</p><p>ti</p><p>o</p><p>n</p><p>(</p><p>m</p><p>.s</p><p>2</p><p>)</p><p>0 0.5 1 1.5 2 2.5 3 3.5 4 4.5</p><p>-1</p><p>0</p><p>1</p><p>Planet carrier</p><p>0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6</p><p>-0.5</p><p>0</p><p>0.5</p><p>Planet gear</p><p>Time (s)</p><p>104</p><p>Figure 9.5. Synchronously averaged signals from sensor 3, Data 2c:5</p><p>9.2.4 Residual Signal Processing for Bearing Fault Detection</p><p>After the removal of the synchronously averaged signals, a residual signal is obtained. This</p><p>should contain non-stationary and second order cyclostationary components. As a first step to</p><p>enhance the residual signal and maximize the impulsiveness, the residual signal was pre-</p><p>whitened. Pre-whitening was attempted using a newly proposed approach based on the cepstrum</p><p>(cepstrum-editing). The approach is described in Figure 9.6. The extreme case of this approach is</p><p>where the real cepstrum is set to zero (spectrum amplitude set to one, i.e. whitened). Both</p><p>discrete frequencies and resonances are thus removed. Uniform spectrum weighting means that</p><p>impulsive frequency bands dominate the time signals.</p><p>The whitening stage can, in fact, be used on the raw signals giving an enhancement of the</p><p>bearing related signature. The advantage of pre-whitening is that all frequency components in</p><p>this signal are equally weighted and, thus, the potential to detect faults is enhanced.</p><p>0 0.02 0.04 0.06 0.08 0.1 0.12 0.14</p><p>-0.5</p><p>0</p><p>0.5</p><p>Intermediate Shaft</p><p>0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5</p><p>-0.5</p><p>0</p><p>0.5</p><p>Low Speed Shaft</p><p>A</p><p>cc</p><p>el</p><p>er</p><p>at</p><p>io</p><p>n</p><p>(m</p><p>.s</p><p>2 )</p><p>0 0.5 1 1.5</p><p>2 2.5 3</p><p>-1</p><p>-0.5</p><p>0</p><p>0.5</p><p>Planet carrier</p><p>0 0.2 0.4 0.6 0.8 1 1.2 1.4</p><p>-0.5</p><p>0</p><p>0.5</p><p>Planet gear</p><p>Time (s)</p><p>105</p><p>Figure 9.6. Schematic diagram of the cepstral method for removing selected families of harmonics</p><p>and/or sidebands from time signals [57]</p><p>The squared envelope spectra for the pre-whitened residual signals were obtained using Hilbert</p><p>Transform techniques (simply by inverse transforming one-sided spectra, shifted to zero</p><p>frequency, and taking the modulus of the resulting complex numbers).</p><p>9.3 Results</p><p>9.3.1 Bearings</p><p>9.3.1.1 Initial Bearing Diagnosis Results</p><p>Through the inspection of the squared envelope spectra of the residual signals obtained from</p><p>section 9.2.4, two defective bearings were identified. These are FAG 3222 and NU 2220 ECM.</p><p>The diagnosis indicated an inner race fault on bearing FAG 3222 and an inner race fault and</p><p>roller/cage defect on the NU 2220 bearing.</p><p>The inner race fault (localized spalling) of the FAG thrust bearing (3222) was mainly detected</p><p>through signals from sensors seven and nine. The envelope spectra from these sensors contained</p><p>the ball pass frequency of the inner race (BPFI), and its harmonics were clearly modulated by the</p><p>high speed shaft speed. An example from the low speed data (set a) and the high speed data (set</p><p>c) is shown in Figure 9.7 and Figure 9.8 respectively. In Figure 9.7, the high speed shaft</p><p>frequency (20.1 Hz) and its second harmonic are clearly visible. The 230.7 Hz component</p><p>(suspected BPFI) and its second harmonic are modulated by the frequency of the high speed</p><p>shaft. The calculated BPFI for the FAG bearing (3222) at an inner race shaft speed of 20.1 Hz is</p><p>around 218.5 Hz. The difference between the observed BPFI in the figure and the calculated one</p><p>is around 5.5%, which can be due to slippage and an incorrect estimation of load angle. This rate</p><p>of slippage is also observed for the high speed data (set c) in Figure 9.8, where the BPFI of 345.3</p><p>Hz and its second harmonic are observed. The 345.3 Hz component has around a 5% difference</p><p>from the calculated BPFI, which is in agreement with the low speed data observation of Figure</p><p>9.7.</p><p>106</p><p>Figure 9.7. Squared envelope spectrum for data 2_a_10 sensor 7</p><p>Figure 9.8. Squared envelope spectrum for data 2_c_10 sensor 7</p><p>0 100 200 300 400 500 600</p><p>0</p><p>0.5</p><p>1</p><p>1.5</p><p>2</p><p>2.5</p><p>3</p><p>3.5</p><p>4</p><p>x 10-7</p><p>X: 461.4</p><p>Y: 2.537e-008</p><p>X: 20.1</p><p>Y: 3.364e-007</p><p>X: 230.7</p><p>Y: 1.697e-007</p><p>Carrier Frequency at : 230.987 Hz, Sideband Spacing at : 20.0878 Hz</p><p>0 100 200 300 400 500 600 700 800 900 1000</p><p>0</p><p>0.01</p><p>0.02</p><p>0.03</p><p>0.04</p><p>0.05</p><p>0.06</p><p>0.07</p><p>0.08</p><p>0.09</p><p>Harmonic Spacing at : 345.3 Hz</p><p>Frequency (Hz)</p><p>Frequency (Hz)</p><p>107</p><p>Figure 9.9 shows that the suspected BPFI of 345.3 Hz is close to one of the harmonics of the</p><p>intermediate shaft (46th harmonic), but is not in fact a harmonic of the intermediate shaft.</p><p>Figure 9.9. Zoom-in around the BPFI. Harmonic cursors for the ISS</p><p>The second bearing fault diagnosis indicated the presence of an inner race fault and possible</p><p>roller/cage pitting in the SKF HSS upwind bearing (NU 2220 ECM). This was detected mainly</p><p>through sensor eight and was confirmed by testing data from set a through the presence of the</p><p>BPFI, its harmonics, and the modulation of these harmonics by the high speed shaft speed. There</p><p>are also indications of modulations by the fundamental train frequency (FTF), which can come</p><p>from variations between rollers.</p><p>In Figure 9.10, the BPFI at 198.08 Hz modulated by a shaft speed of 20.091 Hz is observed. This</p><p>matches very closely the calculated BPFI of bearing NU 2220 ECM at a shaft speed of about</p><p>20.1 Hz. The FTF harmonics (12.8 Hz) are at the same speed for the NU 2220 bearing, as shown</p><p>in Figure 9.11.</p><p>330 335 340 345 350 355</p><p>0</p><p>0.01</p><p>0.02</p><p>0.03</p><p>0.04</p><p>0.05</p><p>0.06</p><p>Harmonic Spacing at : 7.51772 Hz</p><p>X: 345.3</p><p>Y: 0.06</p><p>Frequency (Hz)</p><p>108</p><p>Figure 9.10. Squared envelope spectrum for data 2_a_5 sensor 8 showing the BPFI of bearing</p><p>NU2220</p><p>Figure 9.11. Squared envelope spectrum for data 2_a_5 sensor 8 showing the FTF harmonics of</p><p>bearing NU2220</p><p>140 160 180 200 220 240 260</p><p>-2</p><p>0</p><p>2</p><p>4</p><p>6</p><p>8</p><p>10</p><p>12</p><p>14</p><p>x 10-4 Carrier Frequency at : 198.082 Hz, Sideband Spacing at : 20.0906 Hz</p><p>0 10 20 30 40 50 60 70 80 90 100</p><p>0</p><p>0.01</p><p>0.02</p><p>0.03</p><p>0.04</p><p>0.05</p><p>0.06</p><p>X: 22.54</p><p>Y: 0.01013</p><p>Harmonic Spacing at : 12.8097 Hz</p><p>Frequency (Hz)</p><p>Frequency (Hz)</p><p>109</p><p>9.3.1.2 Actual Findings and Missed Detection</p><p>In the test gearbox failure analysis report [4], it was shown that the IR raceway and rollers of</p><p>bearing 3222 had straw-yellow temper colors. The color implies that the temperature reached</p><p>about 400°F. The root cause of the overheating was probably lubricant starvation. Even though</p><p>no spalls were detected, it is likely there was geometric distortion from the overheating. The IR</p><p>of bearing NU 2220 ECM had assembly damage at the roller spacing caused by cocking of the</p><p>rollers during blind assembly. Debris dents and lines of false brinelling were also observed. The</p><p>IR of bearing NU 2220 ECM had corrosion at roller spacing.</p><p>The spacer for bearing 32032X outer race had assembly damage at the roller spacing caused by</p><p>interference with the bearing rollers during assembly. This damage was missed in our initial (and</p><p>later) diagnosis. The ball-pass frequency of the outer race (BPFO), when the HSS speed is 30</p><p>Hz is estimated at 105. 9 Hz. Figure 9.12 shows the squared envelope analysis for data c_5,</p><p>sensor 6, where the HSS is 30.06 Hz and is present. A frequency at 210.4 Hz appears clearly in</p><p>this figure. This is close to 7×HSS, but it is also close to 2×BPFO. This main evidence seems to</p><p>indicate the presence of the fault in the 32032X, but it was not considered strong enough for us</p><p>to call the fault. Note also the presence of the 345.1 Hz, which is the BPFI of the NU 2220</p><p>bearing. Also, upon inspection of the spectrum comparison of sensor five (Figure 9.13), there is a</p><p>strong presence of 210 Hz and a change around this frequency, in particular.</p><p>Figure 9.12. Squared envelope spectrum of data 2c_5 sensor 6 showing the shaft speed (30.06</p><p>Hz), what appears as 2×BPFO for bearing 32032X and the BPFI for bearing NU 2220</p><p>0 100 200 300 400 500 600 700 800 900 1000</p><p>0</p><p>0.2</p><p>0.4</p><p>0.6</p><p>0.8</p><p>1</p><p>1.2</p><p>1.4</p><p>1.6</p><p>x 10</p><p>-4</p><p>X: 210.4</p><p>Y: 7.143e-005</p><p>X: 30.06</p><p>Y: 0.0001195</p><p>X: 345.1</p><p>Y: 4.035e-005</p><p>Frequency (Hz)</p><p>110</p><p>Figure 9.13. Power spectrum density comparison of the high speed data through sensor 5</p><p>9.3.2 Gears</p><p>9.3.2.1 Initial Diagnosis</p><p>Initial diagnosis indicated the possibility of severe damage in the planetary stage of the gearbox.</p><p>The main indications came through sensors three and four and were observed more in the low</p><p>speed data (set a). It was noticed that the impact pattern came in pairs (roughly separated by 10-</p><p>12 teeth on the planetary gear). This was clearly observed in data 2_a, but not very clearly in</p><p>2_c. The residual signal from sensor five for data 2a_5 is shown in Figure 9.14, where the</p><p>impacts are seen clearly. The analysis of the squared envelope spectrum of the signal, Figure</p><p>9.14, is shown in Figure 9.15. The carrier speed (around 0.25 Hz), the spin frequency of the</p><p>planetary gear (PGSF) at around 0.625 Hz, and 3×PGSF are very clear in Figure 9.15. It was</p><p>indicated at the time of this diagnosis that to confirm this, further analysis would be required to</p><p>obtain the synchronous average with respect to each planet.</p><p>Frequency (Hz)</p><p>Frequency (Hz)</p><p>111</p><p>Figure 9.14. Residual of signal 2a_5 sensor 5</p><p>Figure 9.15. Squared envelope spectrum of the residual signal shown in Figure 9.14</p><p>1 2 3 4 5 6 7</p><p>x 10</p><p>5</p><p>-6</p><p>-4</p><p>-2</p><p>0</p><p>2</p><p>4</p><p>6</p><p>Time (Samples)</p><p>0 2 4 6 8 10 12 14 16 18 20</p><p>0.5</p><p>1</p><p>1.5</p><p>2</p><p>2.5</p><p>3</p><p>3.5</p><p>x 10</p><p>-5</p><p>X: 0.2504</p><p>Y: 9.977e-006</p><p>Frequency (Hz)</p><p>X: 0.626</p><p>Y: 1.351e-005</p><p>X: 1.878</p><p>Y: 1.747e-005</p><p>112</p><p>9.3.2.2 Revised Diagnosis</p><p>The revised diagnoses included using the healthy set of data and comparing it with the</p><p>and Future Work ................................................................................................ 82</p><p>7 Defect Diagnosis in Wind Turbine Gearbox basd on Sideband Energy and Enveloping Spectral</p><p>Analysis ...................................................................................................................................... 83</p><p>7.1 Introduction ............................................................................................................................. 83</p><p>7.2 Algorithms .............................................................................................................................. 83</p><p>7.3 Results ................................................................................................................................... 84</p><p>7.4 Lessons Learned .................................................................................................................... 90</p><p>8 Fault Analysis of a Wind Turbine Gearbox: A Data Driven Approach ........................................... 91</p><p>8.1 Introduction ............................................................................................................................. 91</p><p>8.2 Methodologies ........................................................................................................................ 91</p><p>8.3 Results ................................................................................................................................... 93</p><p>8.4 Conclusion and Discussion .................................................................................................... 97</p><p>9 Techniques for Separation and Enhancement of Various Components in the Analysis of Wind</p><p>Turbine Vibration Signals ......................................................................................................... 98</p><p>9.1 Introduction ............................................................................................................................. 98</p><p>9.2 Algorithms .............................................................................................................................. 99</p><p>9.3 Results ................................................................................................................................. 105</p><p>9.4 Discussion, Conclusions, Lessons Learned ........................................................................ 122</p><p>10 A Two Stage Fault Detection Framework for Wind Turbine Gearbox Condition Monitoring ..... 124</p><p>10.1 Introduction ........................................................................................................................... 124</p><p>10.2 Vibration Based Condition Monitoring Framework ............................................................... 124</p><p>10.3 Analytical Diagnostics .......................................................................................................... 126</p><p>10.4 Graphical Diagnostics .......................................................................................................... 129</p><p>10.5 Results ................................................................................................................................. 130</p><p>viii</p><p>11 Recommended Practices .................................................................................................................. 132</p><p>11.1 Data Acquisition ................................................................................................................... 132</p><p>11.2 Data Analysis ....................................................................................................................... 133</p><p>Appendix A – Project Partners .............................................................................................................. 135</p><p>References ............................................................................................................................................... 136</p><p>List of Figures</p><p>Figure 1.1. Blind study stage diagnostics results comparison ........................................................ 2</p><p>Figure 2.1. GRC test turbine ........................................................................................................... 3</p><p>Figure 2.2. GRC gearbox internal components view ...................................................................... 4</p><p>Figure 2.3. GRC gearbox internal nomenclature and abbreviations ............................................... 4</p><p>Figure 2.4. GRC gearbox layout and bearing nomenclature .......................................................... 5</p><p>Figure 2.5. Diagram of NREL 2.5 MW dynamometer test facility ................................................ 7</p><p>Figure 2.6. NREL dynamometer test stand with the test article installed ....................................... 7</p><p>Figure 2.7. Vibration data acquisition system sensor locations ...................................................... 8</p><p>Figure 2.8. Physical sensor installation ........................................................................................... 9</p><p>Figure 2.9. Test gearbox high speed stage gear damage ............................................................... 11</p><p>Figure 3.1. Synchronous sampling – analog approach ................................................................. 13</p><p>Figure 3.2. Synchronous sampling– digital approach ................................................................... 14</p><p>Figure 3.3. Time synchronous averaging ...................................................................................... 14</p><p>Figure 3.4. Synthesized tachometer generation from speed function ........................................... 16</p><p>Figure 3.5. Analog devices-based approach ................................................................................. 18</p><p>Figure 3.6. Digital processing-based approach ............................................................................. 19</p><p>Figure 3.7. Gearbox power flow ................................................................................................... 19</p><p>Figure 3.8. HSGM (22) modulated by HSS (1) ............................................................................ 23</p><p>Figure 3.9. HSGM X2 (44) modulated by HSS (1) ...................................................................... 24</p><p>Figure 3.10. HSGM X3 (66) modulated by HSS (1) .................................................................... 24</p><p>Figure 3.11. HSGM (22) modulated by HSIS (0.25) .................................................................... 25</p><p>Figure 3.12. HSGM X2 (44) modulated by HSIS (0.25) .............................................................. 25</p><p>Figure 3.13. HSGM X2 (66) modulated by HSIS (0.25) .............................................................. 26</p><p>Figure 3.14. ISGM and higher order harmonics ........................................................................... 26</p><p>Figure 3.15. Planetary gear stage meshing order and harmonics from AN4 ................................ 27</p><p>Figure 3.16. PLTGM X3 modulated by planet passing order (0.037) .......................................... 28</p><p>Figure 3.17. Planetary gear stage meshing order and harmonics from AN3 ................................ 28</p><p>Figure 3.18. PLTGM X3 and X4 modulated by planet passing order (0.037) ............................. 29</p><p>Figure 3.19. Sensor AN3 acceleration enveloping order spectrum .............................................. 29</p><p>Figure 3.20. Modulation by LSIS in PLTGM is very small ......................................................... 30</p><p>Figure 3.21. Envelope spectrum of AN7 ...................................................................................... 31</p><p>Figure 3.22. Zoomed envelope spectrum of AN7 ......................................................................... 31</p><p>Figure 3.23. Possible bearing D BPFI .......................................................................................... 32</p><p>Figure 4.1. False alarm caused by faulty sensor ...........................................................................</p><p>faulty</p><p>one, in both the frequency domain (using power spectrum density) and the cepstrum domain. The</p><p>revised analysis also included the removal of shaft related components from the synchronously</p><p>averaged signals through pre-whitening. Finally synchronous averages were extracted for the sun</p><p>gear and each planet using an algorithm earlier developed by DSTO.</p><p>9.3.2.2.1 Power spectrum and cepstrum comparisons (healthy and faulty signals)</p><p>The scaling for the healthy spectra was given in g's, while the time domain was reported in ms-2.</p><p>The resolution of the healthy spectra was determined and used to find the equivalent FFT</p><p>transform size to use with the faulty data. When scaling both in dB, reference level 1e-6 was used</p><p>for the faulty data and 1e-7 for the healthy data to compensate for the units. Comparisons show</p><p>increases at the gear mesh frequencies and sideband families. This is shown clearly for all</p><p>sensors (AN3, AN5, AN6 and AN7). Harmonic and sideband cursors show dominant</p><p>components and modulations.</p><p>Cepstra were generated from the corresponding spectra to give more information on sideband</p><p>patterns. The cepstra represent the amplitude of the analytic cepstrum (from the one-sided log</p><p>spectrum). This version can also be used on zoom spectra [24].</p><p>Figure 9.16 shows the spectrum comparison using the data from sensor three, in the low speed</p><p>section of the gearbox. There is a noticeable increase (more than 20 dB) in the HSS, the epicyclic</p><p>mesh frequency, and its sidebands. Most noticeable are the sidebands at the planet pass</p><p>frequency around the epicyclic mesh frequency in the fault case. This is evident in the cepstrum</p><p>comparison presented in Figure 9.17. Note the second rahmonic in the healthy case,</p><p>corresponding to 1½ times the carrier speed, which is unexplained. It is possible that it has</p><p>something to do with the “far from hunting tooth” design of the planetary section and means that</p><p>the particular tooth combinations occur much more frequently than usual.</p><p>In Figure 9.18 and Figure 9.19, the spectrum and cepstrum comparisons based on the data from</p><p>sensor five, with generator speed 30 Hz, are presented. The fact that the cepstrum does not</p><p>change appreciably shows that modulation at ISS (which would come from local faults) did not</p><p>occur, and the corresponding lack of sidebands in the faulty spectrum confirms that the faults are</p><p>distributed.</p><p>The distributed wear of the intermediate shaft pinion, ascribed in the inspection report to the</p><p>hunting tooth ratio, is shown in Figure 9.20 in the growth of the harmonics of the IS gear mesh.</p><p>Figure 9.21 shows the same spectra, but concentrates on the growth of sidebands around the HS</p><p>gear mesh harmonics, and they are spaced at the HS shaft speed. The corresponding cepstra of</p><p>Figure 9.22 shows that the local faults causing the sideband generation have grown from nothing</p><p>in the healthy condition; whereas, the increased peak corresponding to the ISS probably indicates</p><p>some growth of harmonics at this shaft speed since the sidebands were not in evidence. Both the</p><p>high speed pinion and gear had localized scuffing, which would explain the strong modulation at</p><p>HSS speed.</p><p>Data from sensor seven in Figure 9.23 shows the same story as Figure 9.21.</p><p>113</p><p>Figure 9.16. Spectrum comparison using the data from sensor 3</p><p>Figure 9.17. Cepstrum comparison using the data from sensor 3</p><p>0 0.5 1 1.5 2 2.5 3 3.5 4</p><p>0</p><p>0.2</p><p>0.4</p><p>0.6</p><p>0.8</p><p>1</p><p>0 0.5 1 1.5 2 2.5 3 3.5 4</p><p>0</p><p>0.2</p><p>0.4</p><p>0.6</p><p>0.8</p><p>1</p><p>Rahmonics of planet pass quefrency</p><p>Quefrency (seconds)</p><p>0 10 20 30 40 50 60 70 80 90 100</p><p>20</p><p>30</p><p>40</p><p>50</p><p>60</p><p>70</p><p>80</p><p>90</p><p>100</p><p>0 10 20 30 40 50 60 70 80 90 100</p><p>20</p><p>30</p><p>40</p><p>50</p><p>60</p><p>70</p><p>80</p><p>90</p><p>100</p><p>Harmonics at epicyclic gear mesh, sidebands at</p><p>planet pass frequency (3X carrier)</p><p>HSS</p><p>Frequency (Hz)</p><p>Frequency (Hz)</p><p>Carrier</p><p>2</p><p>nd</p><p>rahmonic unexplained (1½ × carrier speed)</p><p>114</p><p>Figure 9.18. Spectrum comparison using the data from sensor 5</p><p>Figure 9.19. Cepstrum comparison using the data from sensor 5</p><p>0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1</p><p>0</p><p>0.1</p><p>0.2</p><p>0.3</p><p>0.4</p><p>0.5</p><p>0 50 100 150 200 250 300 350 400 450 500</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>0 50 100 150 200 250 300 350 400 450 500</p><p>20</p><p>40</p><p>60</p><p>80</p><p>100</p><p>Harmonics at HSS</p><p>Frequency (Hz)</p><p>Frequency (Hz)</p><p>Rahmonics of ISS</p><p>Quefrency (seconds)</p><p>115</p><p>Figure 9.20. Spectrum comparison using the data from sensor 6</p><p>Figure 9.21. Spectrum comparison using the data from sensor 6</p><p>0 200 400 600 800 1000 1200 1400 1600 1800 2000</p><p>40</p><p>50</p><p>60</p><p>70</p><p>80</p><p>90</p><p>100</p><p>110</p><p>120</p><p>0 200 400 600 800 1000 1200 1400 1600 1800 2000</p><p>40</p><p>50</p><p>60</p><p>70</p><p>80</p><p>90</p><p>100</p><p>110</p><p>120</p><p>Harmonics at IS gearmesh</p><p>Faulty</p><p>Healthy</p><p>Frequency (Hz)</p><p>Frequency (Hz)</p><p>116</p><p>Figure 9.22. Cepstrum comparison using the data from sensor 6</p><p>0 0.05 0.1 0.15 0.2 0.25</p><p>0</p><p>0.2</p><p>0.4</p><p>0.6</p><p>0.8</p><p>1</p><p>0 0.05 0.1 0.15 0.2 0.25</p><p>0</p><p>0.2</p><p>0.4</p><p>0.6</p><p>0.8</p><p>1</p><p>HSS ISS</p><p>Quefrency (seconds)</p><p>117</p><p>Figure 9.23. Spectrum comparison using the data from sensor 7</p><p>9.3.2.2.2 AN6 ISS signal processed to remove effects of HSS</p><p>Because the ratio is exactly 4:1, the ISS record was divided into four sections, which were</p><p>averaged, recombined, and subtracted. The residual record should contain only information from</p><p>the ISS, for example, the shaft harmonics that are not divisible by four and the IS gear mesh</p><p>frequency (23X). Time signals and spectra are shown in Figures 9.24 and 9.25.</p><p>The HS gear mesh is strongly modulated by the HSS, because damage is more localized. The IS</p><p>gear mesh is much distorted, with many harmonics, but it is not modulated. This is compatible</p><p>with the distributed damage attributed to the hunting tooth design.</p><p>118</p><p>Figure 9.24. Time records from the averaged ISS signals: (a) original, including four rotations of</p><p>the HSS; (b) Residual after removal of the HSS average.</p><p>Figure 9.25. Spectra of signals of Figure 9.24: (a) original including four rotations of the HSS;</p><p>(b) residual after removal of the HSS average.</p><p>9.3.2.2.3 Synchronously averaged signals pre-whitened</p><p>The pre-whitened synchronous averages presented in Figure 9.26 show impact events of the</p><p>damaged gears (not just a single impact). Such impacts appear clearly in all stages (AN3). Note</p><p>that the denomination “Planet Carrier” really refers to an average over the annulus gear, since</p><p>one revolution of the planet carrier corresponds to meshing with all teeth on the annulus. Local</p><p>faults were found on the HS gear of the intermediate shaft, on the sun gear (and spline) of the</p><p>0 1000 2000 3000 4000 5000 6000 7000 8000</p><p>-10</p><p>-5</p><p>0</p><p>5</p><p>10</p><p>0 1000 2000 3000 4000 5000 6000 7000 8000</p><p>-10</p><p>-5</p><p>0</p><p>5</p><p>10</p><p>0 20 40 60 80 100 120 140 160 180 200</p><p>10</p><p>0</p><p>10</p><p>2</p><p>10</p><p>4</p><p>0 20 40 60 80 100 120 140 160 180 200</p><p>10</p><p>0</p><p>10</p><p>2</p><p>10</p><p>4</p><p>(a)</p><p>(b)</p><p>(a)</p><p>(b)</p><p>Time (sample no.). One rotation of IS</p><p>Time (sample no.). One rotation of IS</p><p>Harmonics of ISS</p><p>Harmonics of ISS</p><p>119</p><p>low speed shaft, and on the annulus gear. No faults were reported on the planet gears, but this is</p><p>discussed in the next section.</p><p>Figure 9.26. Whitened synchronously averaged signals corresponding to the periods of all major</p><p>gear components in the gearbox, which enhance local faults</p><p>Note that the “Planet gear” result is a composite of all planets, and shows a similar result to the</p><p>individual planets in the next section.</p><p>9.3.2.2.4 Planet, sun, and annulus gear signatures extracted by Dr. David Forrester using</p><p>patented DSTO software#</p><p>Signatures for each planet and the sun gear were extracted by shifted and weighted averages of</p><p>signals taken as the various planets pass the measurement point [63]. Note that the signature for</p><p>each planet tooth is actually a composite of the two teeth meshing simultaneously with the</p><p>annulus and sun gears (opposite flanks). This is an important observation since no faults were</p><p>reported on the planet gears, even though virtually</p><p>all Round Robin partners detected apparent</p><p>faults corresponding to the planet gear rotation period. This is discussed further below.</p><p>The DSTO patented method described in [63] and illustrated below produces average time</p><p>signals for each individual planet gear and the sun gear using shifted weighted signals from</p><p>passage of each planet past the transducer, with correction for the phase offset of individual teeth</p><p>0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2</p><p>-0.2</p><p>0</p><p>0.2</p><p>Intermediate Shaft</p><p>0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8</p><p>-0.2</p><p>0</p><p>0.2</p><p>Low Speed Shaft</p><p>Ac</p><p>ce</p><p>le</p><p>ra</p><p>tio</p><p>n</p><p>(m</p><p>.s</p><p>2 )</p><p>0 0.5 1 1.5 2 2.5 3 3.5 4 4.5</p><p>-1</p><p>-0.5</p><p>0</p><p>0.5</p><p>1</p><p>Planet carrier</p><p>0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6</p><p>-0.4</p><p>-0.2</p><p>0</p><p>0.2</p><p>0.4</p><p>Planet gear</p><p>Time (s)</p><p>120</p><p>for each passage. Note that the average for the sun gear can include the contact of individual</p><p>teeth with all planet gears.</p><p>Figure 9.27. Phase shifts for separated sun gear averages</p><p>The residual mentioned in some figures is the result of removing the regular tooth mesh signal so</p><p>as to highlight local faults on a gear.</p><p>Figure 9.28. Sun Gear – residual of DSTO average data set 2c (high speed, high load)</p><p>Figure 9.28 shows the residual signal for the sun gear at high speed and load. This result is</p><p>compatible with the observation of the inspection report that the sun gear had localized fretting</p><p>corrosion.</p><p>121</p><p>Figure 9.29. Sun Gear – residual of DSTO average data set 2a (low speed, low load)</p><p>Even at a very different speed and load, in Figure 9.29, the sun gear signature is almost identical</p><p>(though displaced because there is no common phase reference). The same was found for the</p><p>individual planet gear signatures discussed below, in Figure 9.30.</p><p>Figure 9.30. Residual signals for the three planet gears</p><p>Several Round Robin partners found evidence of faults on the planet gears, even though none</p><p>were reported in the inspection report, but the above figure implies that the fault patterns are the</p><p>same on all three planets. This could be caused by the “far from hunting tooth” design of the</p><p>planetary section. Individual pairs of teeth on the annulus and sun gears, both of which had</p><p>Planet 1</p><p>Planet 2</p><p>Planet 3</p><p>Revolutions</p><p>122</p><p>faults, could mesh simultaneously on opposite sides of a given planet gear relatively frequently.</p><p>It would be natural for this to occur identically for all three planets, since all tooth numbers are</p><p>divisible by three. This potential explanation should be confirmed by more detailed analysis of</p><p>the kinematics of this particular configuration.</p><p>Figure 9.31. Average for the annulus gear</p><p>Figure 9.31 shows a typical average signal for the annulus gear. The residual in this case did not</p><p>clarify the local faults to any great extent. However, the visible variations are compatible with</p><p>the results of the inspection report, which found a distributed fault pattern from a local area of</p><p>scuffing. Because of the numbers of teeth of all planetary components being divisible by three,</p><p>the damage tended to imprint on every third tooth, and many examples this pattern over groups</p><p>of three teeth can be seen in the above figure.</p><p>9.4 Discussion, Conclusions, Lessons Learned</p><p>This research showed that our methods for analyzing gear and bearing faults in wind turbine</p><p>transmissions are basically sound, and picked up most faults that could be expected to change the</p><p>vibration patterns. In the initial blind analysis, we correctly detected faults in two of the three</p><p>bearings with faults, usually in data from both low and high speed operation. We did, however,</p><p>miss a fault in the ISS bearing, which should have been detectable, and are at a loss to explain</p><p>why. There is a possibility that there was not good transmission to any of the measurement</p><p>points. We did find indications of local faults on a gear on the IS shaft (initially not separated</p><p>from the HS shaft because of the exact 4:1 ratio), the sun gear, and the annulus gear. There was</p><p>also an indication of local faults on one or more of the planet gears.</p><p>When spectra were received for the gearbox in healthy condition, at about the same time as</p><p>receiving the inspection report, considerably more detailed analysis could be done as to the</p><p>details of the faults on each gear. An exception was the indication of faults on the planet gears,</p><p>which were not found on inspection. Much of this analysis could have been done blind, with the</p><p>availability of a healthy data for comparison from the outset.</p><p>123</p><p>Much more detailed analysis was later performed by Dr David Forrester, of DSTO in Australia,</p><p>using patented algorithms that allowed for the production of separate averages for the individual</p><p>planet gears and sun gear. These corresponded well with the detected faults on most gears, but</p><p>once again indicated faults on the planet gears. Other Round Robin partners found the same. It</p><p>now seems likely that the misdiagnosis was due to the “far from hunting tooth” design of the</p><p>planetary section, which could mean that faulty teeth on the sun and annulus gears could mesh</p><p>simultaneously with a healthy planet gear relatively frequently, and thus give an indication of a</p><p>fault on the planet gear. The fact that the three planets had the same fault pattern lends credence</p><p>to this interpretation, as the meshing patterns would likely be the same for all three planets (with</p><p>all tooth numbers divisible by three). This hypothesis needs to be further investigated before it</p><p>can be confirmed.</p><p>This highlighted the fact that gear diagnostics is made easier by the adoption of designs as close</p><p>as possible to “hunting tooth” designs, considered good design practice in any case. The exact</p><p>4:1 ratio between the IS and HS shafts also made it difficult to separate the faults on gears on</p><p>these two shafts, although luckily the second mesh on the ISS was a hunting tooth design.</p><p>For the relatively modest speed variations in the test data, it was possible to extract information</p><p>on instantaneous speed from the signals themselves in the form of a “pseudo-encoder” signal.</p><p>The signal, typically based on a high speed gear mesh component, can be used for order tracking</p><p>and, thus, synchronous averaging of gear signals throughout the gear train. For larger speed</p><p>variations, which are not uncommon with pitch controlled wind turbines, it would be necessary</p><p>to start with a lower order harmonic of the shaft speed; however, in principle, the process can be</p><p>done iteratively to improve the speed correction. This should be tested in the future.</p><p>124</p><p>10 A Two Stage Fault Detection Framework for Wind Turbine</p><p>Gearbox Condition Monitoring</p><p>Pingfeng Wang* and Prasanna Tamilselvan</p><p>Department of Industrial and Manufacturing Engineering, Wichita State University</p><p>*Corresponding Author Email: pingfeng.wang@wichita.edu</p><p>10.1 Introduction</p><p>Maintaining wind turbines in top operating condition ensures not only a continuous revenue</p><p>generation but a reduction in electric power drawn from non-renewable and more polluting</p><p>sources. Despite the large capital for establishing a wind farm, the maintenance activities of wind</p><p>turbines are the primary contributors for the wind energy costs [64-66]. The need for reduction in</p><p>O&M costs are likely to increase due to the rising competition in today’s global economy.</p><p>Effective health diagnosis of wind turbines provides various benefits, such as improved</p><p>reliability and reduced costs for operation and maintenance (O&M). Research on real-time</p><p>diagnostics and prognostics, which interpret data acquired by smart sensors and distributed</p><p>sensor networks, and utilization of these data streams to make critical O&M decisions offers</p><p>significant advancements in creating early awareness of wind turbine health condition before</p><p>unexpected failures. The unexpected breakdowns can be prohibitively expensive since they</p><p>immediately result in lost production [67-70]. To reduce, and possibly eliminate such</p><p>problems,</p><p>real time condition monitoring is required to avoid sudden catastrophic system failures.</p><p>Vibration analysis is the most vastly used mechanism of condition monitoring in wind turbines.</p><p>It is mainly applied to identify the current condition of rotating components, such as gearbox,</p><p>generator, and main bearing, by installing mechanical sensors on the components. The defects of</p><p>the components are estimated based on the vibrations produced by these components during</p><p>operation. This chapter presents the vibration based condition monitoring framework with</p><p>analytical defect detection method and graphical analysis developed for the CM Round Robin</p><p>study.</p><p>10.2 Vibration Based Condition Monitoring Framework</p><p>The framework for the proposed vibration-based condition monitoring is shown in Figure 10.1.</p><p>The two major stages included in the vibration based condition monitoring framework are</p><p>analytical diagnostics and graphical analysis of frequency domain signals. The raw time domain</p><p>vibration data is pre-processed and converted into frequency domain data. The sideband and</p><p>kurtosis-based online defect detection method is employed to process the frequency data</p><p>analytically. The results from the analytical diagnosis are used as inputs to the graphical</p><p>verification process. The failure modes and their severity levels are determined by graphical</p><p>verification from the multi-dimensional vibration-based sensory signals.</p><p>125</p><p>Figure 10.1. Vibration based condition monitoring approach</p><p>The pre-processing of vibration data involves three steps, as shown in Table 10.1. The primary</p><p>step of the vibration analysis is the calculation of gear and bearing frequencies. The gear</p><p>meshing frequencies of all the gears, bearing frequencies such as Ball Passing Frequency Outer</p><p>(BPFO), Ball Passing Frequency Inner (BPFI), and Ball Spinning Frequency (BSF) of all the</p><p>bearings were determined for both speeds 1200 rpm and 1800 rpm. The next step involves the</p><p>identification of the relationship between the sensor and the components. The final step in the</p><p>pre-processing is to develop the frequency spectrum from the raw time domain vibration signal</p><p>using the fast Fourier transformation (FFT) process for the desired sensors.</p><p>Table 10.1. Procedure for vibration data preprocessing</p><p>Step 1 Calculate Gear Meshing Frequency (GMF) for gears and bearing frequencies</p><p>Step 2 Determine relationship between sensors and components</p><p>Step 3 Develop FFT plot for desired sensors in each case</p><p>The Round Robin study involves three speed stages: low speed (LS), intermediate speed (IS) and</p><p>high speed (HS). In this research, the high frequency rotating components such as intermediate</p><p>and high speed stages of the gearbox are only considered for damage detection. Among the total</p><p>of 10 sensor values from the Round Robin gearbox, the desired sensors for the IS and HS are AN</p><p>5 to AN 9. The relationships between these sensors and the components are determined based on</p><p>the location and proximity to the rotating components, as listed in Table 10.2.</p><p>126</p><p>Table 10.2. Sensor and component relationship</p><p>Sensor Sensor</p><p>Name GMF SRF Bearing Damage</p><p>AN5 LSS radial IS gear LSS LSS upwind and</p><p>downwind bearing</p><p>LSS bearings defect and ISS</p><p>gear defect</p><p>AN6 ISS radial IS pinion and</p><p>HS gear ISS ISS ISS bearings defect, IS pinion</p><p>defect, HS gear defect</p><p>AN7 HSS radial HS pinion HSS HSS HSS bearings defect, HS pinion</p><p>defect</p><p>AN8 HSS front</p><p>radial HS pinion HSS HSS upwind</p><p>bearing</p><p>HS pinion defect, HSS upwind</p><p>bearing defect</p><p>AN9 HSS rear</p><p>radial HS pinion HSS HSS downwind</p><p>bearing</p><p>HS pinion defect, HSS</p><p>downwind bearing defect</p><p>The raw vibration signals from the sensors are time domain signals. The defects from the</p><p>bearings and gears can be identified from their corresponding desired frequency amplitudes in</p><p>the frequency spectrum. The FFT converts the time domain signal into a frequency domain</p><p>signal and helps in analyzing each desired frequency based on its amplitude and its harmonics.</p><p>10.3 Analytical Diagnostics</p><p>The sideband and kurtosis based online defect detection method is employed to process the</p><p>frequency data analytically and the stepwise procedure is shown in Table 10.3. The maximum</p><p>amplitude of the desired frequency, the sidebands, and the kurtosis values for the sidebands are</p><p>determined to calculate the severity factors to formulate the defect severity matrix. The failure</p><p>modes and their severity levels are determined by the defect severity matrix from the vibration-</p><p>based sensory signals.</p><p>Table 10.3. Procedure for analytical diagnostics</p><p>Step 1 Determine maximum amplitude values for sidebands and desired frequency</p><p>Step 2 Determine kurtosis values for sidebands</p><p>Step 3 Calculate severity factor 1, 2 and 3</p><p>Step 4 Formulate defect severity matrix</p><p>10.3.1 Sideband and Kurtosis Analysis</p><p>The sidebands are indicators of the failure modes in the frequency spectrum of the rotating</p><p>components based on their spread on both the sides of the desired frequency. The rising and</p><p>inequality of the sidebands correspond to component defects, and moreover, the severity of the</p><p>defect can be identified based on the frequency sideband features, as listed in Table 10.4 [71].</p><p>The height and sharpness of the peak amplitudes in the frequency spectrum are measured by</p><p>kurtosis. The spread of the sidebands on either side of the desired frequency can be analyzed</p><p>127</p><p>using the kurtosis values. The differences in the kurtosis values of both sidebands denote the</p><p>inequality in the sidebands. The kurtosis ratio KR, is the ratio of the left side of jth, the desired</p><p>frequency is KLj , to the right side of jth, the desired frequency KRj is as shown in Equation (21).</p><p>Similarly, the ratio of maximum amplitude of the sideband on left and right sides of the jth</p><p>frequency is determined as AR shown in Equation (21).</p><p>; Lj Lj</p><p>Rj Rj</p><p>K A</p><p>KR AR</p><p>K A</p><p>= = (21)</p><p>Table 10.4. Sideband-based severity definition</p><p>Frequency Sideband Feature Severity Level</p><p>Rising of sidebands around desired frequency Low</p><p>Unequal sidebands on both sides Medium</p><p>High sideband amplitude than frequency amplitude High</p><p>10.3.2 Severity Factors</p><p>The different failure modes and their severity levels are determined from the converted</p><p>frequency domain signal through analytical sideband and kurtosis analysis.</p><p>Table 10.4 shows the different severity levels based on the frequency sideband features. The</p><p>severity factor analysis resulted in three severity factor metrics for online defect detection. The</p><p>severity factor 1 (SF1) ensures equal spread of the sidebands using the kurtosis ratio metric, as</p><p>shown in Equation (22). The threshold kurtosis ratio, KRT, is considered to be 0.6. The value of</p><p>SF1<1 denotes the unequal spread of sidebands and vice versa. The severity factor 2 (SF2)</p><p>ensures equal maximum amplitude of sidebands on both sides of the desired frequency, as shown</p><p>in Equation (23). The threshold amplitude ratio, AT, is considered to be 0.9. The value of SF2< 1</p><p>denotes the unequal frequency amplitudes on both sides of the sidebands and vice versa.</p><p>1</p><p>1</p><p>Min ( , )j j</p><p>T</p><p>KR KR</p><p>SF</p><p>KR</p><p>−</p><p>= (22)</p><p>1</p><p>2</p><p>Min ( , )j j</p><p>T</p><p>AR AR</p><p>SF</p><p>A</p><p>−</p><p>= (23)</p><p>The severity factor 3 (SF3) ensures that the maximum desired frequency amplitude is higher than</p><p>the maximum amplitude of the sideband Amax, as shown in Equation (24), where AF is the</p><p>maximum amplitude at the desired frequency. The value of SF3< 1 denotes the frequency</p><p>amplitude of the sideband, Amax, which is higher compared to the desired frequency, Amax.</p><p>3 Max ( , )</p><p>F</p><p>Lj Rj</p><p>ASF</p><p>A A</p><p>= (24)</p><p>128</p><p>Table 10.5. Severity factor analysis of sensor AN 6 for Case 2a</p><p>Component Desired</p><p>Frequency SF1 SF2 SF3 Low Medium High</p><p>ISS gear and ISS</p><p>pinion GMF 0.49 0.97 0.46 0 0 1</p><p>ISS upwind</p><p>bearing BPFI 0.98 0.73 2.85 0 1 0</p><p>ISS downwind</p><p>bearing BPFO 0.86 0.42 2.94 0 1 0</p><p>HSS upwind</p><p>bearing BPFO 0.58 1.06 0.23 0 0 1</p><p>HSS downwind</p><p>bearing BPFI 0.72 0.58 1.67 0 1 0</p><p>The conditions SF1 ≤ 1, SF2> 1, and SF3> 1 show that the component has a low severity defect.</p><p>The severity factor characteristics of the medium severity defect are SF1 ≤ 1, SF2 ≤ 1, and SF3></p><p>1 and SF1> 1, SF2 ≤ 1, and SF3> 1. Similarly, the high severity defect conditions are SF1 ≤ 1,</p><p>SF2 ≤ 1, and SF3 ≤ 1; SF1> 1, SF2 ≤ 1, and SF3 ≤ 1; SF1 ≤ 1, SF2> 1, SF3 ≤ 1, and SF1> 1,</p><p>SF2> 1, SF3≤ 1. Based on these rules, the severity levels and the failure modes of the</p><p>components are identified based on the each sensor. The severity factor analysis of sensor AN 6</p><p>for 2a case is listed in Table 10.5.</p><p>10.3.3 Severity Defect Matrix</p><p>The failure modes and their severity levels of the rotating components based on the each sensor</p><p>are identified with different severity metrics. However, the same defect of the rotating</p><p>components can be identified by different sensors in and around the component location.</p><p>Therefore, there is a need for developing a unified metric to make decisions on the failure mode</p><p>and its severity level. This, in turn, will lead to the development of a defect severity matrix,</p><p>combining the results of all the components from the different sensors. The desired component</p><p>matrix U is shown in the Equation (25).</p><p>ISS Gear and ISS Pinion</p><p>HSS Gear and HSS Pinion</p><p>LSS upwind bearing</p><p>LSS downwind bearing</p><p>ISS upwind bearing</p><p>ISS downwind bearing</p><p>HSS upwind bearing</p><p>HSS downwind bearing</p><p>U</p><p> </p><p> </p><p> </p><p> </p><p> </p><p> =  </p><p> </p><p> </p><p> </p><p>  </p><p> </p><p>(25)</p><p>129</p><p>The desired component matrix and the severity factor levels of all the components are utilized</p><p>for developing a defect severity matrix. The severity ratio of component u at severity level g, Sug</p><p>is represented as Equation (26), where g represents the different severity levels, such as low,</p><p>medium, and high, and Sugm represents the severity level of component u at level g through</p><p>sensor m.</p><p>1</p><p>3</p><p>1 1</p><p>M</p><p>ugm</p><p>m</p><p>Mug</p><p>ugm</p><p>g m</p><p>S</p><p>S</p><p>S</p><p>=</p><p>= =</p><p>=</p><p>∑</p><p>∑∑</p><p>(26)</p><p>The defect severity matrix, DS, represents the defect component and its severity level in the</p><p>matrix format as shown in Equation (27), where rows of the matrix represent each desired</p><p>component and columns represent the severity level of the components, such as low, medium</p><p>and high.</p><p>11 12 13</p><p>1 2 3U U U</p><p>S S S</p><p>DS</p><p>S S S</p><p> </p><p> =  </p><p> </p><p> </p><p>  </p><p>(27)</p><p>The unified DS matrix of the Round Robin study is determined and shown in the Equation (28).</p><p>The analytical diagnostics results indicated that there is no defect in the LSS upwind and</p><p>downwind bearings. The IS gear and pinion each have a high severity defect and the HS gear and</p><p>pinion each have a medium severity defect. The analytical results are further fine-tuned using the</p><p>graphical verification process.</p><p>0.33 0.50 0 0 0.67 0.50 0.50 0.60</p><p>0.34 0.50 0 0 0.33 0.50 0.33 0.40</p><p>0.33 0.00 0 0 0.00 0.00 0.17 0.00</p><p>T</p><p>DS</p><p> </p><p> =  </p><p> </p><p> </p><p>(28)</p><p>10.4 Graphical Diagnostics</p><p>The unified defect severity matrix results provide the initial insights about the component defects</p><p>and their severity levels. There is the possibility of false identifications in the analytical</p><p>methodology due to the overlap of different frequencies and their harmonic levels. Therefore,</p><p>there is a need for verification of identified component defects graphically. The frequency</p><p>spectrum of the predetermined component defects are verified graphically based on the sideband</p><p>amplitudes and their spread. The second harmonic of the BPFO (172 Hz) of HSS downwind</p><p>bearing at (344 Hz) in AN 6 ISS is the radial sensor value shown in Figure 10.2. The Amax of</p><p>right sideband is almost two times the Amax of left sideband and moreover, the high amplitude of</p><p>the right sideband is almost eight times the high amplitude of the desired frequency. These</p><p>inferences from the figure prove that there is a high severity failure in the outer raceway. Since</p><p>the sideband amplitudes are found in the second harmonic, there is a chance of misalignment of</p><p>the bearing. Similarly, component defects are identified graphically and the results are discussed</p><p>in the next section.</p><p>130</p><p>Figure 10.2. HSS downwind bearing BPFO – graphical analysis</p><p>10.5 Results</p><p>The results from the online analytical defect detection method are used as inputs to the graphical</p><p>verification. The failure modes and their severity levels from the multi-dimensional vibration-</p><p>based sensory signals are verified graphically, and the results are unified to the component level,</p><p>with their corresponding severity levels, as shown in Table 10.6.</p><p>Table 10.6. Vibration-based condition monitoring results</p><p>Damage Component Mode Severity</p><p>1 HSS pinion Gear tooth failure of HSS pinion High</p><p>2 HSS downwind bearing OR failure and bearing misalignment High</p><p>3 ISS gear Early stages of gear failure Low</p><p>4 ISS upwind bearing IR failure and bearing misalignment Medium</p><p>5 ISS downwind bearing OR failure High</p><p>The tabulated results were identified before the receiving knowledge of the actual failure modes.</p><p>The possible number of failures that can be identified from the vibration analysis for this Round</p><p>Robin study is about seven. The proposed condition monitoring approach identified five failures</p><p>and their severity levels. Moreover, the failures identified by the proposed vibration analysis</p><p>approach do not have any false identification. The accuracy of the condition monitoring</p><p>approach is due to its two fold analysis process, i.e. the analytical identification and the graphical</p><p>verification. The preliminary results from the analytical identification are further fine-tuned</p><p>using the graphical verification to avoid false identifications.</p><p>330 335 340 345 350 355 360</p><p>0</p><p>0.02</p><p>0.04</p><p>0.06</p><p>0.08</p><p>0.1</p><p>0.12</p><p>0.14</p><p>0.16</p><p>Frequency (Hz)</p><p>|Y</p><p>(f)</p><p>|</p><p>2a 10 AN6 ISS Radial</p><p>131</p><p>As a summary, this research showed that the developed vibration based two stage fault detection</p><p>framework that integrates both analytical diagnostics and graphical diagnostics is quite effective</p><p>for analyzing gear and bearing faults in wind turbine transmissions, as proved by the CM Round</p><p>Robin study results. With successful studies and lessons learned on the drivetrain CM, the</p><p>research can be extended to a probabilistic complex system design framework that potentially</p><p>can quantify the functionality, reliability, uncertainty, and cost/benefits of condition monitoring</p><p>techniques. It can integrate them into a system-level wind turbine design practice, as a</p><p>fundamental solution of enhancing reliability and reducing life cycle cost.</p><p>132</p><p>11 Recommended Practices</p><p>Based on the comparison of diagnostics results provided by sixteen partners during the blind</p><p>study stage, as presented in Chapter 1, and the detailed results from eight of the sixteen partners,</p><p>as presented in Chapters 3-10, it is clear that there is still room for the industry to improve</p><p>vibration analysis algorithms. Some algorithms presented in this report have not been widely</p><p>adopted in commercialized vibration-based condition monitoring (CM) systems. If adopted, they</p><p>can lead to increased accuracy of vibration-based wind turbine drivetrain condition monitoring.</p><p>They may potentially help increase the cost effectiveness of wind turbine condition monitoring</p><p>techniques. In addition, based on the lessons learned in this study, some recommended practices</p><p>were provided by several partners, especially Impact Technologies, National Instruments, and</p><p>STC Consultants. They will be discussed in this chapter. It is hoped that these recommended</p><p>practices can be considered in future research and development efforts within the wind turbine</p><p>condition monitoring community.</p><p>11.1 Data Acquisition</p><p>To meet the dynamometer retest schedule of the damaged GRC gearbox, the vibration CM data</p><p>acquisition system used in this study was put together within an extremely tight time window.</p><p>However, efforts were made, as much as possible, to represent a typical commercialized</p><p>vibration CM system</p><p>and meet the guidelines recommended by Germanischer Lloyd (GL) [72].</p><p>For example, anti-aliasing filters and 24 bit ADC were adopted for all sensor channels.</p><p>This study, however, was challenged by poor speed measurements. As pointed out by almost all</p><p>of the project partners, there was no once per revolution signal, which is valuable for time</p><p>synchronous averaging for gear health condition diagnostics. The measured high speed shaft rpm</p><p>also showed oscillations, which could be worked around but was a challenge. A once per</p><p>revolution signal could have been generated based on the raw encoder readings throughout the</p><p>test and provided to all Round Robin project partners. It was not attempted so the project</p><p>partners could have enough time to conduct the blind stage data analysis. However, it is</p><p>recommended that a once per revolution signal be provided in gear health monitoring since</p><p>tachometer signal acquisition requires converting pulse trains into a series of timestamps and</p><p>speeds. In general, to isolate mechanical vibration frequencies from one another, accurate speeds</p><p>and angular positions of the shaft's rotation are critical. The GL guidelines [72] call for high</p><p>resolution speed measurements as part of an instrumentation system in the field. Further, to track</p><p>vibration frequencies with respect to speed, both vibration and speed measurements should be</p><p>made simultaneously or clocked from the same base clock. In the Round Robin project, speed</p><p>information came from the high speed shaft. Adding a tachometer to monitor the input rotor shaft</p><p>might provide a more accurate result for the lower speed components.</p><p>This Round Robin study focuses on the gearbox, as it is the only component with disassembled</p><p>information. If the main bearing is considered for study, accelerometers, with a measurement</p><p>frequency range down to 0.1 Hz, are recommended. Alternatively, new sensing techniques, such</p><p>as acoustic emission [73], can be investigated. This recommendation may also be applicable to</p><p>the ring gear. In addition, for some bearing locations and types inside the gearbox, it may be</p><p>worth evaluating axial-mounted accelerometers.</p><p>133</p><p>In this study, only the frequency domain baseline data was provided. Also, the test data was</p><p>collected from one test gearbox for a short period of time. Diagnostics results could have been</p><p>further improved by providing the baseline data in the time domain from a bigger population of</p><p>gearboxes of the same model, and a longer data acquisition window of months or years.</p><p>The data acquisition system developed for this study was put together to facilitate the Round</p><p>Robin research. Its main emphasis was to collect high resolution raw time series data, which can</p><p>be provided to vibration analysts for diagnosis of the monitored gearbox condition. When</p><p>deploying a condition monitoring system in the field, it is important to balance the amount of</p><p>data, communications, and timing of the data acquisition. Communications may be expensive</p><p>when using a cellular modem, or slow using a 900 MHz radio. The amount of data storage on-</p><p>board an embedded data acquisition system may be limited. For this balancing task, a machine</p><p>with a check trigger state containing continuous acquisition and analysis of incoming sensory</p><p>data can be investigated. When the monitored wind turbine is operating, and measured values</p><p>have changed by a specific percentage or delta, then both pre-trigger and post-trigger sensory</p><p>data is stored to a binary file with a complete descriptive set including enterprise, wind farm, and</p><p>wind turbine. By combining both periodic data recordings with data change driver recordings, a</p><p>complete picture of the wind turbine is possible, using just the right amount of data.</p><p>11.2 Data Analysis</p><p>Once data is collected, the challenge lies in how to interpret the data and derive useful</p><p>information. The diagnostic tasks in the Round Robin project are more challenging because the</p><p>drivetrain damage was more complex than in a typical operational wind turbine. Therefore, the</p><p>diagnostics techniques presented in this report could potentially perform better when deployed in</p><p>the field. For this project, NREL is fortunate to have the support from vibration analysts across</p><p>the world. Main recommended practices mentioned by the project partners for vibration data</p><p>analysis are discussed below.</p><p>Though no sensor faults were present in the test data sets shared by NREL for this study, it is</p><p>generally recommended to perform sensor validation before using vibration data for condition</p><p>monitoring of rotating components. GL uses a similar guideline. [72] This will help reduce</p><p>ambiguity between sensor and mechanical faults and reduce false alarms.</p><p>The GRC test turbine operates at two relatively constant speeds. For variable speed wind</p><p>turbines, the GL guidelines call for order tracking using measured speed [72].</p><p>Due to the complexity in gearbox design and the dynamic operating conditions, an integrated</p><p>approach must be taken that uses diagnostic information from all components (gears, bearings,</p><p>and shafts) as a whole. In other words, the analysis needs to integrate all available diagnostic</p><p>information to confidently detect and isolate problems via a high level reasoning / classifier</p><p>method. In addition, vast differences in speed/torque could cause dramatic differences in results</p><p>of vibration analysis. The accuracy can be increased by comparing results from similar steady</p><p>state operating conditions, e.g., the operational-category concept [74], by applying techniques</p><p>that are less sensitive to the effects, or by normalizing results. Conventional gear diagnostic</p><p>features are limited for planetary gear component fault detection because of the changing</p><p>transmission path, moving fault location, and modulation. As such, special consideration should</p><p>be given to fault detection of these components. For example, multiple cycles of the hunting</p><p>134</p><p>tooth ratio should be recorded for each planetary component. In addition, diagnostic approaches</p><p>that are specifically designed for planetary gear fault detection should be used.</p><p>Enveloping or demodulation has proven to be an effective approach for bearing diagnostics.</p><p>However, proper selection of various filters used by this approach is critical to diagnostic</p><p>performance, in particular for the incipient fault detection capabilities. These filters should also</p><p>be optimized for each sensor location [75]. Note, too, that these resonant frequencies may likely</p><p>change with operating conditions as well. Enveloping or demodulation at higher frequencies is</p><p>desirable to avoid higher order gear mesh harmonics that obfuscate bearing fault frequencies.</p><p>Ideally, both the sensor and data acquisition system would provide data above 20 kHz. However,</p><p>an increase in only the sampling rate has been shown to increase diagnostic performance.</p><p>Another factor to consider is how much additional cost is needed for collecting data above 20</p><p>kHz.</p><p>Fusing vibration results with those from other sensors would help complete the diagnostic</p><p>coverage. In particular, oil debris, oil temperature, and casing temperature [72,76] would provide</p><p>additional evidence of impending failures. Modeling/simulation of expected vibration at different</p><p>operating and fault conditions is useful and a good compliment to seeded fault and accelerated</p><p>life testing.</p><p>135</p><p>Appendix A – Project Partners</p><p>Brüel & Kjær Vibro A/S</p><p>Colorado School of Mines</p><p>GE Bently Nevada</p><p>Impact Technologies</p><p>IVC Technologies</p><p>National Instruments</p><p>NRG Systems Inc.</p><p>Purdue University</p><p>Schenck Corporation</p><p>Sentient Corporation</p><p>STC Consultants (SKF)</p><p>University of Cincinnati</p><p>University of Connecticut</p><p>University of Iowa</p><p>University of New South Wales in Australia</p><p>Wichita State University</p><p>136</p><p>References</p><p>1. Motavalli, J. (2004). “Catching the Wind.” The Environmental Magazine; Dec 31, 2004.</p><p>http://www.emagazine.com/archive/2176</p><p>2. Link, L.; LaCava, W.; van Dam, Jeroen.; McNiff, B.; Sheng, S.; Wallen, R.; McDade, M.;</p><p>Lambert, S.; Butterfield, S.; Oyague, Francisco. Gearbox Reliability Collaborative Project</p><p>Report: Findings from Phase 1 and Phase 2 Testing. NREL/TP-5000-51885. Golden, CO:</p><p>National Renewable Energy Laboratory, June 2011.</p><p>http://www.nrel.gov/docs/fy11osti/51885.pdf.</p><p>3. Sheng, S.; Link, L.; LaCava, W.; van Dam, J.; McNiff, B.; Veers, P.; Keller, J.; Butterfield, S.;</p><p>Oyague, Francisco. Wind Turbine Drivetrain Condition Monitoring During GRC Phase 1 and</p><p>Phase 2 Testing. NREL/TP-5000-52748. Golden, CO: National Renewable Energy Laboratory,</p><p>October, 2011. http://www.nrel.gov/docs/fy12osti/52748.pdf</p><p>4. Errichello, R.; Muller, J. (2012) Gearbox Reliability Collaborative Gearbox 1 Failure</p><p>Analysis Report. NREL/SR-5000-530262. Work performed by Geartech, Townsend, Montana.</p><p>Golden, CO: National Renewable Energy Laboratory, February 2012.</p><p>http://www.nrel.gov/docs/fy12osti/53062.pdf</p><p>5. Musial,W.; McNiff, B. “Wind Turbine Testing in the NREL Dynamometer Test Bed.”</p><p>American Wind Energy Association’s WindPower 2000 Conference; April 30-May 4, 2000, Palm</p><p>Springs, CA. NREL/CP-500-28411. Golden, CO: National Renewable Energy Laboratory, June</p><p>2000 . http://www.nrel.gov/docs/fy00osti/28411.pdf</p><p>6. National Renewable Energy Laboratory. Dynamometer Testing (Fact Sheet). NREL/FS-5000-</p><p>45649. Golden, CO. http://www.nrel.gov/docs/fy11osti/45649.pdf.</p><p>7. Frarey, J.L. “The History and Application of the Envelope Detector.” Technology Showcase:</p><p>Integrated Monitoring, Diagnostics and Failure Prevention, Proceeding of a Joint Conference,</p><p>Mobile, Alabama, and April 22-26, 1996. Haymarket, VA: Society for Machinery Failure</p><p>Prevention Technology. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADP010154</p><p>8. Broderick, J.J.; Burchill, R.F.; Clark, H.L. Design and Fabrication of Prototype System for</p><p>Early Warning of Impending Bearing Failure. NASA-CR-123717, MTI-71TR1. Hunstville, AL:</p><p>National Aeronautics and Space Administration (NASA), January 1972.</p><p>http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720020851_1972020851.pdf</p><p>9. Luo, H.; Qiu, H.; Ghanime, G.; Hirz, M.; van der Merwe, G. “Synthesized Synchronous</p><p>Sampling Technique for Differential Bearing Damage Detection.” Journal of Engineering for</p><p>Gas Turbines and Power; Vol.132, Issue 7, 2010. http://dx.doi.org/10.1115/1.4000092</p><p>10. Hochmann, D.; Sadok, M. “Theory of Synchronous Averaging.” Proceedings of the 2004</p><p>IEEE Aerospace Conference; March 6-13, 2004, Big Sky, Montana. Washington, DC: IEEE,</p><p>2004; pp. 3636-3653. http://dx.doi.org/10.1109/AERO.2004.1368181</p><p>http://www.emagazine.com/archive/2176</p><p>http://www.nrel.gov/docs/fy11osti/51885.pdf</p><p>http://www.nrel.gov/docs/fy12osti/52748.pdf</p><p>http://www.nrel.gov/docs/fy12osti/53062.pdf</p><p>http://www.nrel.gov/docs/fy00osti/28411.pdf</p><p>http://www.nrel.gov/docs/fy11osti/45649.pdf</p><p>http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADP010154</p><p>http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720020851_1972020851.pdf</p><p>http://dx.doi.org/10.1115/1.4000092</p><p>http://dx.doi.org/10.1109/AERO.2004.1368181</p><p>137</p><p>11. Hanna, J.; Hatch, C.; Kalb, M.; Weiss, A.; Luo, H. “Detection of Wind Turbine Gear Tooth</p><p>Defects Using Sideband Energy Ratio™.” China Wind Power 2011;October, 19-21, 2011,</p><p>Beijing, China. http://www.ge-mcs.com/download/monitoring/SER-Technical-Paper.pdf</p><p>12. Marple, L. Jr., “Computing the Discrete-Time Analytic Signal via FFT.” IEEE Transactions</p><p>on Signal Processing, Vol. 47, No. 9, 1999; pp.2600-2603. http://dx.doi.org/10.1109/78.782222</p><p>13. Luo, H.; Fang, X.; Ertas, B. “Hilbert transform and its engineering applications.” AIAA</p><p>Journal, Vol. 47, No. 4, 2009’ pp. 923-932. http://dx.doi.org/10.2514/1.37649</p><p>14. Bagnoli, S.; Capitani, R.; Citti, P. “Comparison of Accelerometer and Acoustic Emission</p><p>signals as Diagnostic Tools in Assessing Bearing Damage,” Proceedings of the 2nd International</p><p>Conference: Condition Monitoring; 24-25 May 1988, London, UK. Cranfield, England: BHRA,</p><p>1988.</p><p>15. Braun, S.; Datner, B. “Analysis of Roller/Ball Bearing Vibrations.” Transactions of the</p><p>ASME, Vol. 101, 1979; pp. 118-125.</p><p>16. Harris, T.A. Rolling Bearing Analysis. 4th edition. New York, NY: John Wiley & Sons, York,</p><p>2001; pp. 993-1000.</p><p>17. Braun, S.G.; Seth. B.B. “On the Extraction and Filtering of Signals Acquired from Rotating</p><p>Machines.” Journal of Sound and Vibration, Vol. 65, No. 1, 1979; pp. 37-50.</p><p>18. Lebold, M.; McClintic, K.; Campbell, R.; Byington, C.; Maynard, K. “Review of Vibration</p><p>Analysis Methods for Gearbox Diagnostics and Prognostics.” Proceedings of the 54th Meeting of</p><p>the Society for Machinery Failure Prevention Technology; May 1-4, 2000,Virginia Beach, VA.</p><p>Haymarket, VA: Society for Machinery Failure Prevention Technology, 1985.</p><p>http://php.scripts.psu.edu/users/k/p/kpm128/pubs/FeatureTutorialBody18.PDF</p><p>19. Szczepanik, A. "Time Synchronous Averaging of Ball Mill Vibrations." Mechanical Systems</p><p>and Signal Processing; Vol. 3, No. 1, 1989, pp. 99-107. http://dx.doi.org/10.1016/0888-</p><p>3270(89)90025-3</p><p>20. Ma, J. "Energy Operator and Other Demodulation Approaches to Gear Defect Detection."</p><p>Proceedings of the 49th Meeting of the Society of Mechanical Failures Prevention Technology;</p><p>April 18-20, Virginia Beach, VA. Haymarket, VA: Society for Machinery Failure Prevention</p><p>Technology, 1995; pp. 127-140.</p><p>21. Favaloro, S.C. A Preliminary Evaluation of Some Gear Diagnostics Using Vibration</p><p>Analysis. ARL-AERO-RPOP-TM-427. Melbourne, Australia: Aeronautical Research</p><p>Laboratory, 1985.</p><p>22. Watson, M. J.; Sheldon, J.S.; Lee, H. “Novel Joint Time Frequency Vibration Diagnostics of</p><p>Turbine Engine Accessories.” ASME Turbo Expo 2010: Power for Land, sea, and Air; June 14-</p><p>18, 2010, Glasgow, UK. New York, NY: ASME, 2010; pp. 353-363.</p><p>http://dx.doi.org/10.1115/GT2010-23539</p><p>http://www.ge-mcs.com/download/monitoring/SER-Technical-Paper.pdf</p><p>http://dx.doi.org/10.1109/78.782222</p><p>http://dx.doi.org/10.2514/1.37649</p><p>http://php.scripts.psu.edu/users/k/p/kpm128/pubs/FeatureTutorialBody18.PDF</p><p>http://dx.doi.org/10.1016/0888-3270(89)90025-3</p><p>http://dx.doi.org/10.1016/0888-3270(89)90025-3</p><p>http://dx.doi.org/10.1115/GT2010-23539</p><p>138</p><p>23. McFadden, P. “A Revised Model for the Extraction of Periodic Waveforms by Time Domain</p><p>Averaging.” Mechanical Systems and Signal Processing; Vol. 1, No. 1, 1999; pp. 83-95.</p><p>http://dx.doi.org/10.1016/0888-3270(87)90085-9</p><p>24. Randall, R.B. Vibration-based Condition Monitoring. Hoboken, NJ: Wiley, 2011.</p><p>25. McFadden, P.; Smith, J. “A Signal Processing Technique for Detecting Local Defects in a</p><p>Gear from a Signal Average of the Vibration.” Proceedings of the Institution of Mechanical</p><p>Engineers, Part C: Journal of Mechanical Engineering Science; Vol. 199, No. 4, 1985; pp. 287-</p><p>292.</p><p>26. Zakrajsek, J.J.; Townsend, D.P.; Decker, H.J. “An Analysis of Gear Fault Detection Method</p><p>as Applied to Pitting Fatigue Failure Damage.” 47th Mechanical Failure Prevention Group; April</p><p>13-15, 1993, Virginia Beach, VA. NASA Technical Memorandum 105950. Cleveland, OH:</p><p>National Aeronautics and Space Administration (NASA), Lewis Research Center, 1993.</p><p>http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA263115.</p><p>27. Mark, W.D.; Lee, H.; Patrick, R.; Coker, J.D. “A Simple Frequency-Domain Algorithm for</p><p>Early Detection of Damage Gear Teeth.” Mechanical Systems and Signal Processing; Vol. 24,</p><p>No. 8, 2010; pp. 2807-2823. http://dx.doi.org/10.1016/j.ymssp.2010.04.004</p><p>28. Randall, R.B.; Antoni, J. “Rolling Element Bearing Diagnostics-A Tutorial.” Mechanical</p><p>Systems and Signal Processing; Vol. 25, No. 2, 2011; pp. 485-520.</p><p>http://dx.doi.org/10.1016/j.ymssp.2010.07.017.</p><p>29. McFadden, P.D. “Window Functions for the Calculation of the Time Domain Averages of</p><p>the Vibration of the Individual Planet Gears and Sun Gear in an Epicyclic Gearbox.” Journal of</p><p>Vibration and Acoustics; Vol. 116, No. 2, 1994. http://dx.doi.org/10.1115/1.2930410</p><p>30. Antoni, J.; Randall, R.B. “The Spectral Kurtosis: Application</p><p>to the Vibratory Surveillance</p><p>and Diagnostics of Rotating Machines.” Mechanical Systems and Signal Processing; Vol. 20,</p><p>No. 2, 2006; pp. 308-331. http://dx.doi.org/10.1016/j.ymssp.2004.09.002.</p><p>31. Combet, F.; Gelman, L. “Novel Adaptation of the Demodulation Technology for Gear</p><p>Damage Detection to Variable Amplitudes for Mesh Harmonics.” Mechanical Systems and</p><p>Signal Processing; Vol. 25, No. 3, 2011; pp. 839-845.</p><p>http://dx.doi.org/10.1016/j.ymssp.2010.07.008</p><p>32. El Badaoui, M.; Guillet, F.; Daniere, J. “New Applications of the Real Cepstrum to Gear</p><p>Signals, Including Definition of a Robust Fault Indicator.” Mechanical Systems and Signal</p><p>Processing; Vol. 18, No. 5, 2004; pp. 1031-1046. http://dx.doi.org/10.1016/j.ymssp.2004.01.005</p><p>33. McFadden, P.D.; Smith, J.D. “Vibration Monitoring of Rolling Element Bearings by the</p><p>High-Frequency Resonance Technique-A Review.” Tribology International; Vol. 17, No. 1,</p><p>1984; pp. 3-10. http://dx.doi.org/10.1016/0301-679X(84)90076-8</p><p>http://dx.doi.org/10.1016/0888-3270(87)90085-9</p><p>http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA263115</p><p>http://dx.doi.org/10.1016/j.ymssp.2010.04.004</p><p>http://dx.doi.org/10.1016/j.ymssp.2010.07.017</p><p>http://dx.doi.org/10.1115/1.2930410</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.09.002</p><p>http://dx.doi.org/10.1016/j.ymssp.2010.07.008</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.01.005</p><p>http://dx.doi.org/10.1016/0301-679X(84)90076-8</p><p>139</p><p>34. Combet, F.; Gelman, L. “Optimal Filtering of Gear Signals for Early Damage Detection</p><p>Based on the Spectral Kurtosis.” Mechanical Systems and Signal Processing; Vol. 23, No. 3,</p><p>2009; pp. 652-668. http://dx.doi.org/10.1016/j.ymssp.2008.08.002</p><p>35. Bonnardot, F.; El Badaoui, M.; Randall, R.B.; Daniere, J.; Guillet, F. “Use of the</p><p>Acceleration Signal of a Paradox in Order to Perform Angular Resampling (with Limited Speed</p><p>Fluctuation).” Mechanical Systems and Signal Processing; Vol. 19, No. 4, 2005; pp. 766-785.</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.05.001</p><p>36. Bechhoefer, E.; Kingsley, M. “A Review of Time Synchronous Average Algorithms.”</p><p>Annual Conference of the Prognostics and Health Management Society; September 27-October</p><p>1, 2009, San Diego, CA. New York, NY: PHM Society, 2009.</p><p>http://www.phmsociety.org/sites/phmsociety.org/files/phm_submission/2009/phmc_09_5.pdf</p><p>37. Dempsey, P.J. “A Comparison of Vibration and Oil Debris Gear Damage Detection Methods</p><p>Applied to Pitting Damage.” 13th International Congress on Condition Monitoring and</p><p>Diagnostic Engineering Management; December 3-8, 2000, Houston, Texas. NASA/TM-2000-</p><p>210371. Cleveland, OH: National Aeronautics and Space Administration (NASA), Glenn</p><p>Research Center, 2000; 18 pp.</p><p>http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20000120403_2000175883.pdf</p><p>38. McFadden, P.D. “Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation</p><p>of the Meshing Vibration.” Journal of Vibration, Acoustics, Stress, and Reliability in Design;</p><p>Vol. 108, No. 2, 1986; pp. 165-170. http://dx.doi.org/10.1115/1.3269317</p><p>39. Forrester, D. “A Method for the Separation of Epicyclic Planet Gear Vibration Signatures.”</p><p>Proceedings of the Acoustical and Vibratory Surveillance Methods and Diagnostic Techniques;</p><p>Senlis, France. 1998; pp. 539-548.</p><p>40. Samuel, P.D.; Conroy, J.K.; Pines, D.J. Planetary Transmission Diagnostics. NASA/CR-</p><p>2004-213068. Cleveland, OH: National Aeronautics and Space Administration (NASA), Glenn</p><p>Research Center, May 2004.</p><p>http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20040073522_2004069093.pdf</p><p>41. Ciang, C.C.; Lee, J.-R.; Bang, H.-J. “Structural Health Monitoring for a Wind Turbine</p><p>System: A Review of Damage Detection Methods.” Measurement Science and Technology; Vol.</p><p>19, No. 12, 2008. http://dx.doi.org/10.1088/0957-0233/19/12/122001</p><p>42. McFadden, P.D. “Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation</p><p>of the Meshing Vibration.” Journal of Vibration, Acoustics, Stress, and Reliability in Design;</p><p>Vol. 108, No. 2, 1986; pp. 165-170. http://dx.doi.org/10.1115/1.3269317</p><p>43. Lin, J.; Zuo, M.J. “Gearbox Fault Diagnosis Using Adaptive Wavelet Filter.” Mechanical</p><p>Systems and Signal Processing; Vol. 17, No. 6, 2003; pp. 1259-1269.</p><p>http://dx.doi.org/10.1006/mssp.2002.1507</p><p>http://dx.doi.org/10.1016/j.ymssp.2008.08.002</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.05.001</p><p>http://www.phmsociety.org/sites/phmsociety.org/files/phm_submission/2009/phmc_09_5.pdf</p><p>http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20000120403_2000175883.pdf</p><p>http://dx.doi.org/10.1115/1.3269317</p><p>http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20040073522_2004069093.pdf</p><p>http://dx.doi.org/10.1088/0957-0233/19/12/122001</p><p>http://dx.doi.org/10.1115/1.3269317</p><p>http://dx.doi.org/10.1006/mssp.2002.1507</p><p>140</p><p>44. Barszcz, T.; Randall, R.B. “Application of Spectral Kurtosis for Detection of a Tooth Crack</p><p>in the Planetary Gear of a Wind Turbine.” Mechanical Systems and Signal Processing; Vol. 23,</p><p>No. 4, 2009; pp. 1352-1365. http://dx.doi.org/10.1016/j.ymssp.2008.07.019</p><p>45. Yan, R.; Gao, R.X. “Multi-Scale Enveloping Spectrogram for Vibration Analysis in Bearing</p><p>Defect Diagnosis.” Tribology International; Vol. 42, No. 2, 2009; pp. 293-302.</p><p>http://dx.doi.org/10.1016/j.triboint.2008.06.013.</p><p>46. Tsai, C.-S.; Hsieh, C.-T.; Huang, S.-J. “Enhancement of Damage-Detection of Wind Turbine</p><p>Blades via CWT-Based Approaches.” IEEE Transactions on Energy Conversion; Vol. 21, No. 3,</p><p>2006; pp. 776-781. http://dx.doi.org/10.1109/TEC.2006.875436</p><p>47. Watson, S.J.; Xiang, B.J.; Yang, W.; Tavner, P.J.; Crabtree, C.J. “Condition Monitoring of</p><p>the Power Output of Wind Turbine Generators Using Wavelets.” IEEE Transactions on Energy</p><p>Conversion; Vol. 25, No. 3, 2010; pp. 715-721. http://dx.doi.org/10.1109/TEC.2010.2040083</p><p>48. Mohanty, A.R.; Kar, C. “Fault Detection in a Multistage Gearbox by Demodulation of Motor</p><p>Current Waveform.” IEEE Transactions on Industrial Electronics; Vol. 53, No. 4, 2006; pp.</p><p>1285-1297. http://dx.doi.org/10.1109/TIE.2006.878303.</p><p>49. Wang, W.J.; McFadden, P.D. “Application of Wavelets to Gearbox Vibration Signals for</p><p>Fault Detection.” Journal of Sound and Vibration; Vol. 192, No, 5, 1996; pp. 927-939.</p><p>http://dx.doi.org/10.1006/jsvi.1996.0226</p><p>50. Yuan, X.; Cai, L. “Variable Amplitude Fourier Series with its Applicationh in Gearbox</p><p>Diagnosis-Part I: Principle and Simulation.” Mechanical Systems and Signal Processing; Vol.</p><p>19, No. 5, 2005; pp. 1055-1066. http://dx.doi.org/10.1016/j.ymssp.2004.10.011</p><p>51. Yuan, X.; Cai, L. “Variable Amplitude Fourier Series with its Applicationh in Gearbox</p><p>Diagnosis-Part I: Principle and Simulation.” Mechanical Systems and Signal Processing; Vol.</p><p>19, No. 5, 2005; pp. 1067-1081. http://dx.doi.org/10.1016/j.ymssp.2004.10.012</p><p>52. Tan, P.-N.; Steinbach, M.; Kumar, V. Introduction to Data Mining. Boston, MA: Pearson</p><p>Addison Wesley, 2006.</p><p>53. Devijver, P.A.; Kittler, J. Pattern Recognition: A Statistical Approach. Englewood Cliffs, NJ:</p><p>Prentice-Hall, 1982.</p><p>54. Mosteller, F. “A k-Sample Slippage Test for an Extreme Population.” The Annals of</p><p>Mathematical Statistics; Vol. 19, No. 1, 1948; pp. 58-65. http://www.jstor.org/stable/2236056</p><p>55. Antoni, J. “The Spectral Kurtosis: A Useful Tool for Characterising Non-Stationary Signals.”</p><p>Mechanical Systems and Signal Processing; Vol. 20, No. 2, 2006; pp. 282-307.</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.09.001</p><p>http://dx.doi.org/10.1016/j.ymssp.2008.07.019</p><p>http://dx.doi.org/10.1016/j.triboint.2008.06.013</p><p>http://dx.doi.org/10.1109/TEC.2006.875436</p><p>http://dx.doi.org/10.1109/TEC.2010.2040083</p><p>http://dx.doi.org/10.1109/TIE.2006.878303</p><p>http://dx.doi.org/10.1006/jsvi.1996.0226</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.10.011</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.10.012</p><p>http://www.jstor.org/stable/2236056</p><p>http://dx.doi.org/10.1016/j.ymssp.2004.09.001</p><p>141</p><p>56. Sawalhi, N.; Randall, R.B. “Semi-Automated Bearing Diagnostics-Three Case Studies.”</p><p>Comadem Conference;June 13-15, 2007, Faro, Portugal. Coimbra : Inst. de Telecomunicações,</p><p>2007.</p><p>57. Sawalhi, N.; Randall, R. B. “Signal Pre-Whitening for Fault Detection Enhancement and</p><p>Surveillance in Rolling Element Bearings.” Eighth International Conference on Condition</p><p>Monitoring and Machinery Failure Prevention Technologies; June 20-22,2011, St David's Hotel,</p><p>Cardiff, UK, 20-22 June.</p><p>58. Antoni, J. “Differential Diagnosis of Gear and Bearing Faults.” Journal of Vibration and</p><p>Acoustics; Vol. 124, No. 2, 2002; pp. 165-171. http://dx.doi.org/10.1115/1.1456906</p><p>59. Sawalhi, N.; Randall, R.B. “Spectral Kurtosis Optimization for Rolling Element Bearings.”</p><p>ISSPA 2005: The 8th International Symposium on Signal Processing and its Applications; August</p><p>28-31, 2005, Sydney, Australia. Piscataway, NJ: IEEE, 2005; pp. 839-842.</p><p>http://dx.doi.org/10.1109/ISSPA.2005.1581069</p><p>60. Urbanek, J.; Barszcz, T.; Sawalhi, N.; Randall, R.B. “Comparison of Amplitude Based and</p><p>Phase Based Methods for Speed Tracking in Application to Wind Turbines.” IMEKO TC 10,</p><p>11th Workshop on Smart Diagnostics of Structures; October 18-20, Krakow, Poland.</p><p>61. Sawalhi, N.; Randall, R.B. “Localised Fault Diagnosis in Rolling Element Bearings in</p><p>Gearboxes.” The Fifth International Conference on Condition Monitoring and Machinery Failure</p><p>Prevention Technologies; July 15-18, Edinburgh, UK, 2008. Oxford, UK: Coxmoor Publishing</p><p>Company, 2008.</p><p>62. Randall, R.B.; Sawalhi, N.; Coats, M. “A Comparison of Methods for Separation of</p><p>Deterministic and Random Signals.” International Journal of Condition Monitoring; Vol. 1, No.</p><p>1; 2011; pp. 11-19. http://dx.doi.org/10.1784/204764211798089048</p><p>63. Forrester, D.; Blunt, D. “Analysis of Epicyclic Gearbox Vibration.” DSTO HUMS;</p><p>Conference, Melbourne. 2003.</p><p>64. Tamilselvan, P.; Wang, P.; and Twomey, J. “Quantification of Economic and Environmental</p><p>Benefits for Prognosis Informed Wind Farm Operation and Maintenance.” ISERC 2012, 62nd</p><p>Annual IIE Industrial Systems and Engineering Research Conference; May 19-23, 2012,</p><p>Orlando, FL, USA.</p><p>65. Tamilselvan, P.; Wang, Y.; and Wang, P. “Optimization of Wind Turbines Operation and</p><p>Maintenance Using Failure Prognosis.” PHM 2012, IEEE 2012 Prognostics and Health</p><p>Management; June 18-21, 2012, Denver, CO, USA.</p><p>66. Tamilselvan, P.; Wang, P.; and Twomey, J. “Prognosis Informed Stochastic Decision</p><p>Making Framework for Operation and Maintenance of Wind Turbines.” ISFA 2012, ASME 2012</p><p>International Symposium on Flexible Automation; June 18-20, 2012, St. Louis, MO, USA.</p><p>http://dx.doi.org/10.1115/1.1456906</p><p>http://dx.doi.org/10.1109/ISSPA.2005.1581069</p><p>http://dx.doi.org/10.1784/204764211798089048</p><p>142</p><p>67. Tamilselvan, P.; Wang , P.; and Jayaraman, R. “Diagnostics with Unexampled Faulty States</p><p>Using a Two-Fold Classification Method.” PHM 2012, 2012 IEEE International Conference on</p><p>Prognostics and Health Management; June 18-21, 2012, Denver, CO, USA.</p><p>68. Tamilselvan, P.; and Wang P. “A Hybrid Inference Approach for Health Diagnostics with</p><p>Unexampled Faulty States.” AIAA 2012-1784, 53th AIAA/ASME/ASCE /AHS/ASC Structures,</p><p>Structural Dynamics, and Materials Conference; April 23-26, 2012, Honolulu, Hawaii, USA.</p><p>69. Tamilselvan, P.; and Wang, P. “Structural Health Diagnosis Using Deep Belief Network</p><p>Based State Classification.” AIAA 2012-1783, 53th AIAA/ASME/ASCE /AHS/ASC Structures,</p><p>Structural Dynamics, and Materials Conference; April 23-26, 2012, Honolulu, Hawaii, USA.</p><p>70. Tamilselvan, P.; Wang, P.; and Youn, B. “Multi-Sensor Health Diagnosis Using Deep Belief</p><p>Network Based State Classification.” ASME 2011 International Design Engineering Technical</p><p>Conference; August 29-31, 2011, Washington DC, USA.</p><p>71. Spectra Quest Tech Note. “Analyzing Gearbox Degradation Using Time-Frequency</p><p>Signature Analysis.” March, 2006.</p><p>72. Germanischer Lloyd. “Guidelines for the Certification of Condition Monitoring Systems for</p><p>Wind Turbines.” Hamburg, Germany, 2007.</p><p>73. Smulders, A. “Challenges of Condition Monitoring for Wind Turbines and Successful</p><p>Techniques.” Wind Turbine Condition Monitoring; October 8-9, 2009, Omni Interlocken Resort,</p><p>Broomfield, CO. Golden, CO: National Renewable Energy Laboratory, 2009.</p><p>http://wind.nrel.gov/public/Wind_Turbine_Condition_Monitoring_Workshop_2009/3.2.Smulder</p><p>s.Challenges_of_CM_for_WT_and_Successful_Techniques.pdf</p><p>74. Gellermann, T.; Walter, G. Requirements for Condition Monitoring Systems for Wind</p><p>Turbine. AZT Report No. 03.01.068, 2003.</p><p>75. Wade, D. and Larsen Christopher. "Measurement of Gearbox Surface Frequency Repsonse</p><p>Functions for HUMS Algorithm Improvement. Presented at the American Helicopter Society</p><p>68th Annual Forum, Fort Worth, TX. May 1-3, 2012.</p><p>76. Sheng, S. “Investigation of Various Condition Monitoring Techniques Based on a Damaged</p><p>Wind Turbine Gearbox.” 8th International Workshop on Structural Health Monitoring; 13-15</p><p>September 2011, Stanford, CA. NREL/CP-5000-51753. Golden, CO: National Renewable</p><p>Energy Laboratory, 2011; 10 pp.</p><p>http://wind.nrel.gov/public/Wind_Turbine_Condition_Monitoring_Workshop_2009/3.2.Smulders.Challenges_of_CM_for_WT_and_Successful_Techniques.pdf</p><p>http://wind.nrel.gov/public/Wind_Turbine_Condition_Monitoring_Workshop_2009/3.2.Smulders.Challenges_of_CM_for_WT_and_Successful_Techniques.pdf</p><p>Acknowledgements</p><p>Nomenclature</p><p>Executive Summary</p><p>Table of Contents</p><p>List of Figures</p><p>List of Tables</p><p>1 Introduction</p><p>2 Tests and Actual Gearbox Damage</p><p>2.1 Test Article</p><p>2.2 Dynamometer Test Facility</p><p>2.3 One Customized Vibration Data Acquisition System</p><p>2.4 Test Conditions</p><p>2.5 Actual Gearbox Damage</p><p>3 Analysis Algorithms and Diagnostics Results from General Electric</p><p>3.1 Fundamentals</p><p>3.2 Round Robin Analysis Results</p><p>3.3 Discussions</p><p>4 Combining Novel Approaches with Proven Algorithms for Robust Wind Turbine Gearbox Fault Detection</p><p>4.1 Introduction</p><p>4.2 Algorithm Overview</p><p>4.3 Results Summary</p><p>4.4 Lessons Learned and Conclusions</p><p>5 Analysis Algorithms and Diagnostics Results from NRG Systems</p><p>5.1 Introduction</p><p>5.2 Analysis Algorithms</p><p>5.3 Analysis Results</p><p>5.4 Discussion</p><p>6 Review and Application of Methods and Algorithms in Wind Turbine Gearbox Fault Detection</p><p>6.1 Introduction</p><p>6.2 Signal Processing and Feature Extraction Methods</p><p>6.3 Summary of Results</p><p>6.4 Conclusions and Future Work</p><p>7 Defect Diagnosis in Wind Turbine Gearbox based on Sideband Energy and Enveloping Spectral Analysis</p><p>7.1 Introduction</p><p>7.2 Algorithms</p><p>7.3 Results</p><p>7.4 Lessons Learned</p><p>8 Fault Analysis of a Wind Turbine Gearbox: A Data Driven Approach</p><p>8.1 Introduction</p><p>8.2 Methodologies</p><p>8.3 Results</p><p>8.4 Conclusion and Discussion</p><p>9 Techniques for Separation and Enhancement of Various Components in the Analysis of Wind Turbine Vibration Signals</p><p>9.1 Introduction</p><p>9.2 Algorithms</p><p>9.3 Results</p><p>9.4 Discussion, Conclusions, Lessons Learned</p><p>10 A Two Stage Fault Detection Framework for Wind Turbine Gearbox Condition Monitoring</p><p>10.1 Introduction</p><p>10.2 Vibration Based Condition Monitoring Framework</p><p>10.3 Analytical Diagnostics</p><p>10.4 Graphical Diagnostics</p><p>10.5 Results</p><p>11 Recommended Practices</p><p>11.1 Data Acquisition</p><p>11.2 Data Analysis</p><p>Appendix A – Project Partners</p><p>References</p><p>35</p><p>Figure 4.2. ImpactEnergy overview .............................................................................................. 36</p><p>Figure 4.3. GearMod overview ..................................................................................................... 37</p><p>Figure 4.4. Example JTFA approach (short time Fourier transform) ........................................... 38</p><p>Figure 4.5. High speed gear fault evidence, blind results (AN6) ................................................. 40</p><p>ix</p><p>Figure 4.6. High speed gear fault evidence, blind results (AN7) ................................................. 40</p><p>Figure 4.7. Intermediate speed downwind bearing fault evidence, blind results (AN6,</p><p>Data 2b) ............................................................................................................................. 41</p><p>Figure 4.8. Intermediate speed downwind bearing fault evidence, blind results .......................... 42</p><p>Figure 4.9. Sun pinion gear fault evidence, blind results .............................................................. 43</p><p>Figure 4.10. JTFA speed gear fault evidence, blind results .......................................................... 44</p><p>Figure 4.11. Intermediate speed upwind bearing damage evidence ............................................. 45</p><p>Figure 4.12. Intermediate speed upwind bearing fault evidence, post-inspection results ............ 46</p><p>Figure 4.13. High speed downwind bearing fault evidence, revisited (Data 2a) .......................... 47</p><p>Figure 4.14. High speed downwind bearing fault evidence, revisited (Data 2c) .......................... 47</p><p>Figure 5.1. Generation of the TSA and selected CIs .................................................................... 51</p><p>Figure 5.2. Process for generating gear CIs .................................................................................. 52</p><p>Figure 5.3. Synthetic tachometer .................................................................................................. 53</p><p>Figure 5.4a. HSS TSA/spectrum ................................................................................................... 53</p><p>Figure 5.4b. HSS gear analysis ..................................................................................................... 53</p><p>Figure 5.5a. TSA intermediate shaft ............................................................................................. 54</p><p>Figure 5.5b. Intermediate speed pinion, where the units for the Energy Operator, Narrowband</p><p>and Amplitude Modulation analysis are in G’s, and the Frequency Modulation analysis</p><p>is in radians. ...................................................................................................................... 54</p><p>Figure 5.6a. Sun gear .................................................................................................................... 55</p><p>Figure 5.6b. Planet gears ............................................................................................................... 55</p><p>Figure 5.7. Ring gear .................................................................................................................... 55</p><p>Figure 5.8a. High speed shaft, downwind side ............................................................................. 56</p><p>Figure 5.8b. Intermediate speed shaft downwind side .................................................................. 56</p><p>Figure 5.9. Low speed shaft downwind side ................................................................................. 56</p><p>Figure 6.1. Vibration spectrum - Case C: top plot - AN7 baseline; bottom plot - AN7 degraded</p><p>gearbox .............................................................................................................................. 61</p><p>Figure 6.2. Sideband ratio gear features - Case C: (a) Low speed shaft pinion; (b) High speed</p><p>shaft gear; (c) High speed shaft pinion ............................................................................. 63</p><p>Figure 6.3. Real cepstrum - Case C: top plot - AN7 baseline; bottom plot - AN7 degraded</p><p>gearbox .............................................................................................................................. 64</p><p>Figure 6.4. Cepstrum peak features from Case C: blue – baseline; red - degraded gearbox ........ 64</p><p>Figure 6.5. Cepstrum health Indicator for Case C calculated for high speed shaft gear and</p><p>pinion ................................................................................................................................ 65</p><p>Figure 6.6. Bearing envelope analysis flow chart ......................................................................... 66</p><p>Figure 6.7. Envelope spectrum - Case C: (a) AN6 - peaks at BPFI for ISS upwind bearing and</p><p>HSS downwind bearing; (b) AN7 - BPFI peak for HSS downwind bearing.................... 67</p><p>Figure 6.8. Envelope spectrum accelerometer AN10 - Case C: (a) band-pass filter from 9500</p><p>Hz - 10,500 Hz, peaks at BPFO and 2X BPFO for ISS downwind bearing; (b) band pass</p><p>filter from 4000 Hz - 6000 Hz, peak at BPFO for planet carrier upwind bearing and also</p><p>peak at 2X BPFO for ISS downwind bearing ................................................................... 67</p><p>Figure 6.9. (a) Wiener filter based on spectral kurtosis; (b) raw and filtered AN4 accelerometer</p><p>signal – Case A ................................................................................................................. 69</p><p>Figure 6.10. Filtered AN4 signal showing the periodic repetition based on 2 revolutions of the</p><p>carrier – Case A ................................................................................................................ 69</p><p>Figure 6.11. Kurtosis of filtered signal - shown for all 3 cases .................................................... 70</p><p>x</p><p>Figure 6.12. TSA signal and residual signal from accelerometer AN7 - Case C: top plot - TSA</p><p>signal for high speed shaft pinion; bottom plot - residual signal for high speed shaft</p><p>pinion ................................................................................................................................ 72</p><p>Figure 6.13. TSA vibration spectrum for accelerometer AN7 and high speed shaft - Case C ..... 72</p><p>Figure 6.14. TSA signal and residual signal from accelerometer AN3 - Case C: top plot - TSA</p><p>signal for ring gear; bottom plot - residual signal for ring gear ........................................ 73</p><p>Figure 6.15. High speed pinion amplitude and phase modulation signal from accelerometer</p><p>AN7 - Case C: top plot - Time Synchronous Average; middle plot - amplitude</p><p>modulation signal; bottom plot - phase modulation signal .............................................. 74</p><p>Figure 6.16. Ring gear amplitude and phase modulation signal from accelerometer AN3 - Case</p><p>C: top plot - TSA; middle plot - amplitude modulation signal; bottom plot - phase</p><p>modulation signal .............................................................................................................. 75</p><p>Figure 6.17. Flow chart for planet separation algorithm .............................................................. 76</p><p>Figure 6.18. Narrow band amplitude modulation signal for determining planet passing –</p><p>Case C ............................................................................................................................... 77</p><p>Figure 6.19. Example Tukey window used for planet separation algorithm - in this study, Nv</p><p>was set to 3 to include 3 mesh periods .............................................................................. 77</p><p>Figure 6.20. Top - TSA signal for Planet 2; bottom - residual signal for Planet 2 – Case C ....... 78</p><p>Figure 6.21. TSA vibration spectrum for Planet 2 – Case C ........................................................ 78</p><p>Figure 6.22. Top - TSA signal for sun gear; bottom - residual signal for sun gear – Case C ....... 79</p><p>Figure 6.23. Planet Gear 2 amplitude and phase modulation signal from accelerometer</p><p>AN3 –</p><p>Case C: top plot – TSA; middle plot - amplitude modulation signal; bottom plot -</p><p>phase modulation signal .................................................................................................... 80</p><p>Figure 7.1. Locations of defective components in the gearbox assembly .................................... 84</p><p>Figure 7.2. Comparison analysis between test data and reference data for HS_Pinion and</p><p>INT_Pinion ....................................................................................................................... 85</p><p>Figure 7.3. Comparison analysis between test data and reference data for Annulus_Gear and</p><p>Sun_Gear........................................................................................................................... 86</p><p>Figure 7.4. Time series of torque data under 1200 rpm ................................................................ 87</p><p>Figure 7.5. The envelope spectrum of torque data under 1200 rpm ............................................. 88</p><p>Figure 7.6. Wavelet enveloping spectrum of sensor AN3 at 1,800 rpm ....................................... 88</p><p>Figure 7.7. Wavelet enveloping spectrum of sensor AN6 at 1,800 rpm ....................................... 89</p><p>Figure 8.1. Run chart of maximum rate of speed ......................................................................... 94</p><p>Figure 8.2. Bar char of R .............................................................................................................. 94</p><p>Figure 8.3. RMS across 12 sensors - Case 2b ............................................................................... 96</p><p>Figure 8.4. Crest factor across 12 sensors - Case 2b .................................................................... 97</p><p>Figure 8.5. Kurtosis across 12 sensors - Case 2b .......................................................................... 97</p><p>Figure 9.1. Signal processing approach pre release of inspection report .................................... 100</p><p>Figure 9.2. Reference (speed) signal extraction stages: (a) identifying a separable band; (b)</p><p>extracting the band into a new buffer; (c) inversing the transform signal b into the time</p><p>domain [60] ..................................................................................................................... 101</p><p>Figure 9.3. HSS estimates: Top - data 2a:5; Bottom - data 2c:5 ................................................ 102</p><p>Figure 9.4. Synchronously averaged signals from sensor 3, data 2a:5 ....................................... 103</p><p>Figure 9.5. Synchronously averaged signals from sensor 3, Data 2c:5 ...................................... 104</p><p>Figure 9.6. Schematic diagram of the cepstral method for removing selected families of</p><p>harmonics and/or sidebands from time signals [57] ....................................................... 105</p><p>xi</p><p>Figure 9.7. Squared envelope spectrum for data 2_a_10 sensor 7 .............................................. 106</p><p>Figure 9.8. Squared envelope spectrum for data 2_c_10 sensor 7 .............................................. 106</p><p>Figure 9.9. Zoom-in around the BPFI. Harmonic cursors for the ISS ........................................ 107</p><p>Figure 9.10. Squared envelope spectrum for data 2_a_5 sensor 8 showing the BPFI of bearing</p><p>NU2220 ........................................................................................................................... 108</p><p>Figure 9.11. Squared envelope spectrum for data 2_a_5 sensor 8 showing the FTF harmonics</p><p>of bearing NU2220 ......................................................................................................... 108</p><p>Figure 9.12. Squared envelope spectrum of data 2c_5 sensor 6 showing the shaft speed (30.06</p><p>Hz), what appears as 2×BPFO for bearing 32032X and the BPFI for bearing NU2220 109</p><p>Figure 9.13. Power spectrum density comparison of the high speed data through sensor 5 ...... 110</p><p>Figure 9.14. Residual of signal 2a_5 sensor 5 ............................................................................ 111</p><p>Figure 9.15. Squared envelope spectrum of the residual signal shown in Figure 9.14 .............. 111</p><p>Figure 9.16. Spectrum comparison using the data from sensor 3 ............................................... 113</p><p>Figure 9.17. Cepstrum comparison using the data from sensor 3 ............................................... 113</p><p>Figure 9.18. Spectrum comparison using the data from sensor 5 ............................................... 114</p><p>Figure 9.19. Cepstrum comparison using the data from sensor 5 ............................................... 114</p><p>Figure 9.20. Spectrum comparison using the data from sensor 6 ............................................... 115</p><p>Figure 9.21. Spectrum comparison using the data from sensor 6 ............................................... 115</p><p>Figure 9.22. Cepstrum comparison using the data from sensor 6 ............................................... 116</p><p>Figure 9.23. Spectrum comparison using the data from sensor 7 ............................................... 117</p><p>Figure 9.24. Time records from the averaged ISS signals: (a) original, including four rotations of</p><p>the HSS; (b) Residual after removal of the HSS average. .............................................. 118</p><p>Figure 9.25. Spectra of signals of Figure 9.24: (a) original including four rotations of the HSS;</p><p>(b) residual after removal of the HSS average. ............................................................... 118</p><p>Figure 9.26. Whitened synchronously averaged signals corresponding to the periods of all major</p><p>gear components in the gearbox, which enhance local faults ......................................... 119</p><p>Figure 9.27. Phase shifts for separated sun gear averages .......................................................... 120</p><p>Figure 9.28. Sun Gear – residual of DSTO average data set 2c (high speed, high load) ........... 120</p><p>Figure 9.29. Sun Gear – residual of DSTO average data set 2a (low speed, low load) .............. 121</p><p>Figure 9.30. Residual signals for the three planet gears ............................................................. 121</p><p>Figure 9.31. Average for the annulus gear .................................................................................. 122</p><p>Figure 10.1. Vibration based condition monitoring approach .................................................... 125</p><p>Figure 10.2. HSS downwind bearing BPFO – graphical analysis .............................................. 130</p><p>List of Tables</p><p>Table 2.1. Gear element dimensions and detail .............................................................................. 5</p><p>Table 2.2. Bearing type, number, and location ............................................................................... 6</p><p>Table 2.3. Sensor notations and descriptions .................................................................................. 8</p><p>Table 2.4. Test conditions ............................................................................................................. 10</p><p>Table 2.5. Actual damage on the test gearbox .............................................................................. 10</p><p>Table 3.1. Gear damage features ................................................................................................... 20</p><p>Table 3.2. Bearing damage features .............................................................................................. 21</p><p>Table 3.2. Bearing damage features (continued) .......................................................................... 22</p><p>Table 4.1. Select gear diagnostic feature definitions .................................................................... 37</p><p>Table 4.2. Initial blind results summary ....................................................................................... 39</p><p>xii</p><p>Table 4.3. Post-inspection results summary ................................................................................. 45</p><p>Table 6.1. Summary of evaluated methods</p><p>– advantages and disadvantages ............................... 60</p><p>Table 6.2. Frequency domain gear features .................................................................................. 62</p><p>Table 6.3. Summary of results for each algorithm with the following notation: L-low</p><p>confidence, M-medium confidence, H-high confidence, NA –not applicable or</p><p>evaluated; black - indicates a method that was evaluated before the failure report,</p><p>blue - indicates a method that was evaluated after the failure report .......................... 81</p><p>Table 7.1. Sideband energy comparison between new gearbox and gearbox at the end of service</p><p>life ............................................................................................................................... 87</p><p>Table 7.2. Comparison between the analysis result and the actual damage of a tested gearbox .. 89</p><p>Table 8.1. Correlation coefficient analysis of the mean of jerk data: Case 2b ............................. 95</p><p>Table 8.2. Correlation coefficient analysis of the mean of jerk data: Case 2c ............................. 95</p><p>Table 8.3. Clustering based classification ..................................................................................... 96</p><p>Table 10.1. Procedure for vibration data preprocessing ............................................................. 125</p><p>Table 10.2. Sensor and component relationship ......................................................................... 126</p><p>Table 10.3. Procedure for analytical diagnostics ........................................................................ 126</p><p>Table 10.4. Sideband-based severity definition .......................................................................... 127</p><p>Table 10.5. Severity factor analysis of sensor AN 6 for Case 2a ............................................... 128</p><p>Table 10.6. Vibration-based condition monitoring results ......................................................... 130</p><p>1</p><p>1 Introduction</p><p>Wind energy is currently the fastest growing type of renewable energy resource in the world [1].</p><p>However, the industry still experiences premature component failures, which increase operation</p><p>and maintenance (O&M) costs, and subsequently, the cost of energy (COE) for wind power. As</p><p>turbines increase in size and are installed offshore, these failures will become even more costly.</p><p>To make wind power more competitive, there is a need for the industry to improve turbine</p><p>reliability and availability.</p><p>Given that the gearbox is the most costly drivetrain component to maintain throughout the</p><p>expected 20-year design life of a wind turbine, the National Renewable Energy Laboratory</p><p>(NREL) organized a consortium called the Gearbox Reliability Collaborative (GRC) to address</p><p>the gearbox reliability and availability challenges. The GRC engages key representatives in the</p><p>wind turbine gearbox supply chain, including turbine owners, operators, gearbox manufacturers,</p><p>bearing manufacturers, lubricant companies, and wind turbine manufacturers. The GRC's goals</p><p>are to conduct research that improves gearbox reliability and increases turbine availability. The</p><p>GRC engages a multi-track approach, which includes modeling and analysis, dynamometer</p><p>testing, field testing, condition monitoring (CM), and developing a gearbox failure database [2].</p><p>CM is a method to assess a system’s health, which enables proactive maintenance planning,</p><p>reduces downtime and operations and maintenance costs, and, to some extent, increases safety</p><p>[3]. It will be the main focus of this report.</p><p>The GRC uses two identical test gearboxes: one was tested on NREL’s 2.5 MW dynamometer;</p><p>the other was first tested in the dynamometer, and then field tested in a turbine in a nearby wind</p><p>plant. In the field, the test gearbox experienced two oil loss events that resulted in damage to its</p><p>internal bearings and gears. Additional field tests of this gearbox were terminated to prevent</p><p>further damage to the gearbox. From the CM point of view, however, it provided a unique</p><p>opportunity to evaluate different monitoring techniques by retesting the gearbox in NREL’s</p><p>dynamometer under controlled testing conditions. The gearbox was removed from the field and</p><p>retested in the NREL’s 2.5 MW dynamometer before it was disassembled. During the</p><p>dynamometer retest, various condition monitoring systems data were collected, e.g., vibration</p><p>and oil debris, along with testing condition information. The vibration-based condition</p><p>monitoring system and the test condition data enabled NREL to launch the Wind Turbine</p><p>Gearbox Condition Monitoring Round Robin (Round Robin) project that involves the analysis of</p><p>the collected vibration data by several independent research partners and then draws</p><p>conclusions from the comparison of their analysis results.</p><p>The main objective of the CM Round Robin project was to evaluate different vibration analysis</p><p>algorithms used in wind turbine CM and to determine whether typical practices are effective.</p><p>Another project objective was to assess the capability of vibration-based CM and to establish a</p><p>baseline from which future improvements can be measured. With the involvement of both</p><p>academic researchers and industrial partners, the Round Robin provides cutting edge research</p><p>results to industry stakeholders.</p><p>In the project, the collected vibration and testing condition data, along with the test gearbox</p><p>configuration information, were shared with partners who signed memorandum of understanding</p><p>2</p><p>documents with NREL. The partners were given a time window of two months to analyze the</p><p>shared data using whichever algorithms they had or could develop. Partners did not have prior</p><p>knowledge of the actual damage within the test gearbox. After their diagnostics results were</p><p>submitted to NREL, the actual damage information within the test gearbox was disclosed to</p><p>them, so they could further fine tune their results. The project had sixteen partners, including</p><p>seven universities and nine from the private sector. The main body of this report discusses</p><p>detailed analysis algorithms and diagnostics results from eight of the sixteen partners. (For a list</p><p>of partners, see Appendix A.)</p><p>The project is unique since the initial diagnostic results from the partners were obtained during a</p><p>blind study. Also, the test gearbox did not begin with seeded faults, as have been investigated in</p><p>many other studies. Based on the particulars of the actual damage found after the test gearbox</p><p>was disassembled [4], all of the partners agreed that seven damage instances could be detected</p><p>through vibration analysis. These damage instances were chosen as the reference for the partners'</p><p>diagnostics performance evaluation. The evaluation criteria included successful identifications,</p><p>false alarms, and missed detections. A comparison of the results, without the partners' names is</p><p>illustrated in Figure 1.1. The chart depicts the highest ratio of successful identification as five of</p><p>the seven damage instances. Most partners had more missed detections than false alarms. Thus,</p><p>there is room for the industry to improve vibration-based diagnostic algorithms. Most of the</p><p>Round Robin study partners agreed that this project was a valuable effort.</p><p>Figure 1.1. Blind study stage diagnostics results comparison</p><p>The next chapter of this report describes the test gearbox configuration, its customized data</p><p>acquisition system, test conditions, and actual damage information obtained during the test</p><p>gearbox disassembly. The main body of the report contains a detailed presentation of the analysis</p><p>algorithms and diagnostic results from eight out of the sixteen research partners. Finally, the</p><p>report concludes with some recommended practices for conducting vibration-based wind turbine</p><p>drivetrain CM.</p><p>3</p><p>2 Tests and Actual Gearbox Damage</p><p>The test gearbox, dynamometer test facility, one customized vibration data acquisition system,</p><p>test conditions, and actual damage</p><p>found on the test gearbox through its disassembly are</p><p>presented in this chapter.</p><p>2.1 Test Article</p><p>The GRC test turbine drivetrain (Figure 2.1) is designed for a stall-controlled, three-bladed,</p><p>upwind turbine, with a rated power of 750kW. The turbine generator operates at 1800 rpm and</p><p>1200 rpm nominal, on two different sets of windings, depending on the wind conditions.</p><p>The gearbox under test was one of two units, which were originally taken from the field and</p><p>redesigned, rebuilt and instrumented with more than 125 sensors. The gearbox first finished its</p><p>run-in in the NREL dynamometer test facility and later was sent to a wind plant located near to</p><p>NREL for field tests, where two oil loss events occurred while the turbine was being tested. The</p><p>gearbox has an overall ratio of 1:81.491. It is composed of one low speed (LS) planetary stage</p><p>and two parallel stages, as shown in the expanded view in Figure 2.2. Nomenclature for the</p><p>internal elements is described in Figure 2.3, and the gear dimensions, teeth number, and helix</p><p>angles are listed in Table 2.1.</p><p>Figure 2.1. GRC test turbine</p><p>Generator</p><p>Hub</p><p>Main</p><p>Bearing</p><p>Main</p><p>Shaft</p><p>Brake</p><p>Generator</p><p>Shaft</p><p>Gearbox</p><p>Bed Plate</p><p>4</p><p>Figure 2.2. GRC gearbox internal components view</p><p>Figure 2.3. GRC gearbox internal nomenclature and abbreviations</p><p>Annulus</p><p>Planet</p><p>Sun</p><p>Gear</p><p>Gear Pinion</p><p>Pinion</p><p>PLC</p><p>Low Speed Stage</p><p>LS-ST</p><p>High Speed Stage</p><p>HS-ST</p><p>Intermediate Speed Stage</p><p>IMS-ST</p><p>Low Speed Shaft</p><p>LS-SH</p><p>Intermediate Speed</p><p>Shaft</p><p>IMS-SH</p><p>High Speed Shaft</p><p>HS-SH</p><p>5</p><p>Table 2.1. Gear element dimensions and detail</p><p>Gear Element No. of</p><p>Teeth</p><p>Mate</p><p>teeth</p><p>Root</p><p>diameter</p><p>(mm)</p><p>Helix</p><p>angle</p><p>Face</p><p>width</p><p>(mm)</p><p>Ratio</p><p>Ring gear 99 39 1047 7.5L 230</p><p>Planet gear 39 99 372 7.5L 227.5</p><p>Sun pinion 21 39 186 7.5R 220 5.71</p><p>Intermediate gear 82 23 678 14R 170</p><p>Intermediate pinion 23 82 174 14L 186 3.57</p><p>HSS gear 88 22 440 14L 110</p><p>HSS pinion 22 88 100 14R 120 4.0</p><p>Overall: 81.49</p><p>Several bearing types are employed in the gearbox, according to the loading conditions and</p><p>gearbox life requirements. The planet carrier is supported by two full-complement cylindrical</p><p>roller bearings (fcCRB) and each planet gear is supported by two identical cylindrical roller</p><p>bearings (CRB). Each parallel shaft in the gearbox is supported by a CRB on the upwind side of</p><p>the assembly, and by two back-to-back mounted, tapered roller bearings (TRB) on the downwind</p><p>side. Table 2.2 provides the location and bearing manufacturer part number of all bearings in the</p><p>gearbox. Location and shaft designations are as noted in Figure 2.4. The letter following the</p><p>abbreviation indicates the position of the bearing according to the component from upwind (A)</p><p>to downwind (B, C). Lubrication oil is another important component in the test gearbox,</p><p>although it is not shown in either Table 2.2 or Figure 2.4.</p><p>Figure 2.4. GRC gearbox layout and bearing nomenclature</p><p>PLC-A PLC-B</p><p>LSS-A</p><p>LSS-B LSS-C</p><p>PL-A PL-B</p><p>ISS-A ISS-B ISS-C</p><p>HSS-A HSS-B HSS-C Annulus</p><p>Planet</p><p>Sun</p><p>Gear</p><p>Gear Pinion</p><p>Pinion</p><p>6</p><p>Table 2.2. Bearing type, number, and location</p><p>Location Location</p><p>Designation Type Provider Part Number</p><p>Planet carrier PLC-A fcCRB INA SL 18 1892 E</p><p>PLC-B fcCRB INA SL 18 1880 E</p><p>Planet PL-A CRB FAG NJ 2232 E.M1.C3</p><p>PL-B CRB FAG NJ 2232 E.M1.C3</p><p>Low Speed Shaft</p><p>LS-SH-A fcCRB INA SL 18 1856E</p><p>LS-SH-B TRB SKF 32948</p><p>LS-SH-C TRB SKF 32948</p><p>Intermediate Speed Shaft</p><p>IMS-SH-A CRB FAG NU 2220 E.M1.C3</p><p>IMS-SH-B TRB SKF 32032 X</p><p>IMS-SH-C TRB SKF 32032 X</p><p>High Speed Shaft</p><p>HS-SH-A CRB FAG NU 2220 E.M1.C3</p><p>HS-SH-B TRB SKF 32222 J2</p><p>HS-SH-C TRB SKF 32222 J2</p><p>The operating gear mesh and bearing characteristic frequencies can be determined by the project</p><p>partners, based on the data shown in Tables 2.1 and 2.2, along with catalogue information from</p><p>bearing suppliers.</p><p>2.2 Dynamometer Test Facility</p><p>The retest of the damaged gearbox was conducted in the NREL 2.5 MW dynamometer test</p><p>facility (DTF), which conducts performance and reliability tests on wind turbine drivetrain</p><p>prototypes and commercial machines [5,6]. The facility is capable of providing static, highly</p><p>accelerated life and model-in-the-loop tests. The prime movers of the dynamometer are a 2.5</p><p>MW induction motor, a three-stage epicyclical reducer, and a variable-frequency drive, with full</p><p>regeneration capacity. The rated torque provided by the dynamometer to a test article can be up</p><p>to 1.4 meganewton meters (MNm), with speeds varying from 0 rpm to 16.7 rpm. Non-torque</p><p>loading actuators, rated up to 440 kilonewtons (kN) for radial load and 156kN for thrust load,</p><p>also can be utilized in the dynamometer to apply thrust, bending, and shear loads similar to those</p><p>typically generated by a wind turbine rotor. Figure 2.5 provides a diagram of the test facility.</p><p>Figure 2.6 is a photo of the test implementation, with the test gearbox installed. The complete</p><p>nacelle and drivetrain was installed in the NREL DTF and hard fixed to the floor, without the</p><p>hub, rotor, yaw bearing, or yaw drives. The actual field controller was used to provide start-up</p><p>and system safety response.</p><p>7</p><p>Figure 2.5. Diagram of NREL 2.5 MW dynamometer test facility</p><p>Figure 2.6. NREL dynamometer test stand with the test article installed. NREL/PIX #16913.</p><p>2.3 One Customized Vibration Data Acquisition System</p><p>During the dynamometer retest of the damaged gearbox, the data for this Round Robin project</p><p>was collected by a vibration data acquisition system (DAS) customized by NREL. It is composed</p><p>of twelve accelerometers. Low speed shaft torque and generator speed were recorded, in addition</p><p>to the accelerometer data. The HSS speed measurement was obtained by an optical encoder. For</p><p>8</p><p>simplicity of implementation, data was collected at 40 kHz per channel using a National</p><p>Instruments PXI -4472B high speed DAS.</p><p>The accelerometers mounting locations are illustrated in Figure 2.7, with sensor labels and</p><p>descriptions given in Table 2.3. The mounting locations were chosen to reflect typical sensor</p><p>placement practices seen in commercial wind turbine drivetrain vibration-based condition</p><p>monitoring systems. The physical installation of these accelerometers is shown in Figure 2.8.</p><p>Figure 2.7. Vibration data acquisition system sensor locations</p><p>Table 2.3. Sensor notations and descriptions</p><p>Sensor Label Description</p><p>AN1 Main bearing radial</p><p>AN2 Main bearing axial</p><p>AN3 Ring gear radial 6 o’clock</p><p>AN4 Ring gear radial 12 o’clock</p><p>AN5 LSS radial</p><p>AN6 ISS radial</p><p>AN7 HSS radial</p><p>AN8 HSS upwind bearing radial</p><p>AN9 HSS downwind bearing radial</p><p>AN10 Carrier downwind radial</p><p>AN11 Generator drive end radial</p><p>AN12 Generator non-drive end axial</p><p>9</p><p>a) AN1, AN2, AN3, and AN4 (From left to right, NREL/PIX #19589, 19590, 19588, 19587)</p><p>b) AN5, AN6, AN7, and AN8 (From left to right, NREL/PIX #19591, 19592, 19594, 19593)</p><p>c) AN9, AN10, AN11, and AN12 (From left to right, NREL/PIX #19595, 19598, 19597, 19596)</p><p>Figure 2.8. Physical sensor installation</p><p>2.4 Test Conditions</p><p>The vibration data was collected under the test conditions shown in Table 2.4. The highest test</p><p>load applied was 50% of rated power to reduce the chances of a catastrophic gearbox failure.</p><p>Under each test condition, ten minutes of data was collected and broken into 10 separate files,</p><p>each containing one minute of test data. In total, thirty data files from three test conditions were</p><p>shared with the project partners.</p><p>10</p><p>Table 2.4. Test conditions</p><p>Test Case LSS Speed</p><p>(rpm)</p><p>Nominal HSS Speed</p><p>(rpm)</p><p>Electric Power</p><p>(% of rated)</p><p>Duration</p><p>(min)</p><p>CM_2a 14.72 1200 25% 10</p><p>CM_2b 22.09 1800 25% 10</p><p>CM_2c 22.09 1800 50% 10</p><p>2.5 Actual Gearbox Damage</p><p>After the dynamometer retest, the gearbox was sent to a rebuild shop, where it was disassembled</p><p>and a detailed failure</p><p>analysis [4] was conducted. A complete list of actual damage found</p><p>through the failure analysis is given in Table 2.5. For example, the high speed stage gear damage</p><p>in Figure 2.9 shows clear scuffing marks.</p><p>Table 2.5. Actual damage on the test gearbox</p><p>Damage # Instances Mode</p><p>1 HSS Gear Set Scuffing</p><p>2 HSS Downwind Bearings Overheating</p><p>3 ISS Gear Set Fretting Corrosion</p><p>Scuffing</p><p>Polishing Wear</p><p>4 ISS Upwind Bearing Assembly damage</p><p>Plastic deformation</p><p>Scuffing</p><p>False brinelling</p><p>Debris dents</p><p>Contact Corrosion</p><p>5 ISS Downwind Bearings Assembly damage</p><p>Plastic deformation</p><p>Dents</p><p>6 Annulus/Ring Gear, or Sun Pinion Scuffing and polishing</p><p>Fretting Corrosion</p><p>7 Planet Carrier Upwind Bearing Fretting Corrosion</p><p>8 Sun Pinion Thrust Rings Fretting Corrosion</p><p>Adhesive Wear</p><p>9 Oil Transfer Ring for Planet Carrier Polishing</p><p>10 LSS Seal Plate Scuffing</p><p>11 LSS Downwind Bearings Abrasion</p><p>12 HSS Shaft Misalignment</p><p>11</p><p>Figure 2.9. Test gearbox high speed stage gear damage. NREL/PIX #19599.</p><p>The root cause of the faults was assembly damage and oil starvation resulting from the two oil</p><p>loss events in the field test. Among the 12 damaged items listed in Table 2.5, the consensus</p><p>reached among the sixteen Round Robin partners was that the first seven should be detectable by</p><p>vibration analysis. Damage 12 could potentially be detected by vibration analysis as well, but</p><p>most partners considered it to be an operational condition and not damage. Therefore, the first</p><p>seven damage instances were used as references for performance evaluations of the partner's</p><p>diagnostic results, as discussed in the introduction chapter of this report. The task for the partners</p><p>was to diagnose possible internal component damage of the test gearbox based on the shared</p><p>vibration, rpm, and torque data. As the project progressed, each of the partners recognized that</p><p>some baseline data collected from a healthy test gearbox would be beneficial. Therefore,</p><p>vibration spectrum data collected by several accelerometers mounted on the test gearbox, when it</p><p>was considered healthy, were later shared with the project partners. The following report sections</p><p>were submitted by eight out of the sixteen partners who took part in the CM study.</p><p>12</p><p>3 Analysis Algorithms and Diagnostics Results from General</p><p>Electric</p><p>Huageng Luo*, Charles Hatch, Matthew Kalb, Jesse Hanna, Adam Weiss</p><p>General Electric Energy</p><p>*Corresponding Author Email: luoh@ge.com</p><p>3.1 Fundamentals</p><p>Solutions provided by the General Electric (GE) Energy Team are mainly based on order</p><p>analysis to accommodate the constant speed variations in a wind farm. For gear damage</p><p>detection, the sideband distributions were used to estimate the gear meshing condition and a</p><p>sideband energy ratio was used to qualitatively evaluate the gear damage. For early bearing</p><p>damage detection, the acceleration enveloping detection technique was used.</p><p>In the wind farm, the wind speed is not predictable, thus many wind turbines are operated at</p><p>variable speed. As a result, the gearbox operational speed is constantly changing. Due to this</p><p>kind of speed variation, a direct application of the conventional Fast Fourier Transform (FFT)</p><p>will not result in accurate gearbox condition features, especially those features extracted from</p><p>high frequency response, such as acceleration enveloping analysis techniques [7,8]. On the other</p><p>hand, to improve the energy extraction efficiency, the wind turbine rotor speed has to be geared</p><p>up about two orders of magnitude before being used to drive the generator shaft. Because of the</p><p>high gear ratio, a very high-count encoder is needed. For example, in a 1.5 MW wind turbine,</p><p>the ratio between the high-speed gear meshing frequency and the rotor frequency can easily be</p><p>greater than 1500.</p><p>To overcome these difficulties, the GE team utilized a series of signal processing techniques,</p><p>such as synchronous sampling, synchronous analysis, digital domain encoder synthesizing,</p><p>acceleration enveloping analysis, and sideband energy ratio (SER), in the data processing and</p><p>damage feature extractions.</p><p>3.1.1 Synchronous Sampling</p><p>For rotating machinery, vibrations may occur at multiples and submultiples of the shaft speed.</p><p>For example, if the shaft is rotating at 3600 rpm, which is 60 Hz, then the vibration response at</p><p>multiples of this frequency, and sometimes fractions of this frequency, can be seen. These</p><p>multiples are called orders (or harmonics in musical terms). The general relationship between the</p><p>order (O), the shaft speed (RPM), and the frequency (f) in Hz is</p><p>60</p><p>RPMOf ×</p><p>= (1)</p><p>If the rotating speed is fixed, a regular FFT analysis can have the desired results. However, if the</p><p>rotor speed changes within the time window of data acquisition, the variation of the rotor speed</p><p>will cause the fundamental order and harmonics in the frequency domain to be smeared into</p><p>multiple frequency bins. On the other hand, the frequency of interest may not always be right at</p><p>a bin, depending on the resolution of the frequency analysis. The signal energy has to be split</p><p>into neighboring bins, in such a case. That is why in rotor dynamics, order analysis is preferred</p><p>over the frequency spectrum analysis. In the order domain, the values of the fundamental order</p><p>13</p><p>and the harmonics remain constant with respect to the shaft speed; the first order is always at the</p><p>shaft speed and the second order is always twice the shaft speed, and so on.</p><p>To achieve order analysis in rotating machinery applications with variable running speeds,</p><p>instead of sampling at equal increments of time, a different sampling technique has to be used.</p><p>Sampling is conducted at equal increments of shaft rotation position, thus reducing the effect of</p><p>the shaft speed variations. This is called synchronous sampling. The synchronous sampling</p><p>technique is very useful for rotating machinery-related data processing, especially in instances of</p><p>varying shaft speed.</p><p>Generally, there are two approaches to achieving synchronous sampling - analog and digital</p><p>approaches. One of the analog approaches uses an Analog to Digital (A/D) sampling clock to</p><p>achieve the synchronous sampling. The key to this approach is generating an appropriate</p><p>sampling clock based on shaft rotation conditions. As shown in Figure 3.1, the sampling clock is</p><p>derived from the shaft encoder by an analog ratio generator to meet the desired order analysis</p><p>requirements (such as order resolution and maximum order). In cases where only lower order</p><p>components are of interest, the encoder output can be used as a sampling clock directly.</p><p>In the digital approach, or synthesized synchronous sampling [9], both vibration and encoder</p><p>signals are discretized simultaneously, preferably at high speed. Different signal processing</p><p>techniques can be used to resample the data and convert time domain data into shaft cycle</p><p>domain data, with the help of an encoder signal from the shaft (refer to Figure 3.2). In this</p><p>approach, both the encoder and key phaser can be used as a shaft speed reference. Regardless,</p><p>the availability of the shaft encoder/key phaser is crucial to both analog and digital synchronous</p><p>sampling approaches.</p><p>Figure 3.1. Synchronous sampling – analog approach</p><p>14</p><p>Figure 3.2. Synchronous sampling– digital approach</p><p>With the synchronously sampled data, a common way to enhance the signal components of</p><p>interest is through time synchronous averaging [10]. With a shaft encoder/key phaser, the</p><p>vibration signal detected contains three major components: the synchronous coherent signal</p><p>component, the synchronous, non-coherent component, and random noise. Conventional time</p><p>synchronous averaging can only enhance the synchronous coherent signal component. The</p><p>synchronous, non-coherent component and the random noise will be averaged out with a</p><p>sufficient</p><p>number of averages.</p><p>Figure 3.3 (a) shows a simulation result with a combination of the shaft response, ( )tfa 02sin π ; its</p><p>second harmonic, ( )tfb 04sin π ; a nonsynchronous coherent signal, ( )tfc 03.12sin ⋅⋅π ; and a uniform</p><p>random noise. After 250 times of synchronous averaging, the results are shown in Figure 3.3 (b);</p><p>the random noise and the nonsynchronous coherent component have been successfully removed.</p><p>Figure 3.3. Time synchronous averaging</p><p>15</p><p>When applying the synchronous sampling technique to diagnose bearing/gear damage, there are</p><p>two issues that need to be resolved. The first is that the bearing damage signatures are usually</p><p>nonsynchronous to the shaft order. In complicated gear sets, such as in the planetary gear, not all</p><p>gear meshing frequencies are integer multipliers of a shaft frequency. So, if the regular time</p><p>domain synchronous averaging technique is applied to the vibration response, the bearing</p><p>damage signatures will be averaged out. Thus, instead of averaging in the time domain, order</p><p>domain averaging should be used in gearbox health feature extractions. The second problem is</p><p>unique to a wind turbine gearbox. For example, in a typical 1.5 MW wind turbine, the order</p><p>span between the main shaft and the third stage gear meshing (the high speed shaft gear meshing</p><p>frequency) can be above 1500. Care must be taken on the order resolution and on the maximum</p><p>order applied during the data acquisition.</p><p>3.1.2 Synthesized Synchronous Sampling</p><p>With the help of a tachometer, the equal time sampled data can be converted into equal shaft</p><p>angular space data as shown in Figure 3.2.</p><p>In the event that the direct shaft tachometer signal is not available, traditional synchronized</p><p>sampling becomes difficult, if not infeasible. For example, in this Round Robin project, only the</p><p>speed profile is provided. If a synthesized tachometer signal can be generated from the speed</p><p>signal, then the equal circumferential space sampling (synchronous sampling) can be carried out</p><p>following well-established routines.</p><p>The following describes a procedure to synthesize a tachometer from the shaft speed profiles. In</p><p>Figure 3.4, assume we have determined that the synthesized tachometer generated a pulse at time</p><p>it . We need to find out the location of the next pulse timing 1+it . The time elapsed, from it to</p><p>1+it , i.e., ii ttt −= +11∆ , is the instantaneous shaft rotation period. On the other hand, if we have</p><p>determined the 1+it , since we know the shaft speed as a function of time, the average speed, n ,</p><p>between it and 1+it can be calculated numerically. Therefore, the shaft instantaneous period can</p><p>also be approximated by the averaged instantaneous shaft speed, i.e., nt /602 =∆ . In theory, by</p><p>equalizing 1t∆ and 2t∆ , we can determine 1+it ; thus, calculating the next pulse location. In</p><p>practice, due to time resolution and speed accuracy, an approximation procedure is used instead</p><p>of solving for an exact solution. The following steps further explain the procedure of the</p><p>synthesized synchrophaser:</p><p>1. Assume a synchrophaser pulse at time zero.</p><p>2. Once the ith synchrophaser pulse is located, at it , assume the (i+1)th pulse be located at</p><p>1+it .</p><p>3. Calculate the average shaft speed, n in RPM, which is a function of 1+it , from it to 1+it</p><p>( ) ( )∫ +</p><p>−</p><p>=</p><p>+</p><p>+</p><p>1</p><p>1</p><p>1</p><p>1 i</p><p>i</p><p>t</p><p>t</p><p>ii</p><p>i dttShaftSpeed</p><p>tt</p><p>tn (2)</p><p>4. Formulate the time elapsed from it to 1+it</p><p>16</p><p>ii ttt −= +11∆ (3)</p><p>and the time elapsed by one instantaneous rotation</p><p>nt /602 =∆ (4)</p><p>5. Find 1+it such that 21 tt ∆∆ − is minimized.</p><p>The 1+it then is the approximate location of the ( )thi 1+ synchrophaser pulse. The tachometer</p><p>can be generated from the synchrophaser, say, by equal spacing between the consecutive</p><p>synchrophaser pulses.</p><p>With this method, one of the major error sources is the discretization resolution. The maximum</p><p>error in the shaft period is</p><p>2</p><p>T , where T the sampling period is. Fortunately, for bearing and gear</p><p>dynamic response analysis, especially acceleration enveloping analysis, the frequency of interest</p><p>is usually much higher than the shaft speed. In other words, the digitization rate is usually</p><p>several orders of magnitude higher than the shaft speed. Thus, the synthesizing error from the</p><p>digitization error is expected to be negligibly small.</p><p>Figure 3.4. Synthesized tachometer generation from speed function</p><p>3.1.3 Sideband Energy Ratio</p><p>Sideband Energy Ratio (SER) [11] is calculated from high resolution spectrum data. Each</p><p>spectrum is created from time-based waveform data generated by an accelerometer sensor and</p><p>collected by the monitoring system. Several accelerometer sensors were mounted in strategic</p><p>locations on the wind turbine gearbox to monitor each gear mesh. The waveforms from each</p><p>sensor were synchronously sampled so that the sampling frequency tracks change in speed. This</p><p>technique produces narrow spectral lines of speed-dependent frequencies, like gear mesh</p><p>frequencies and associated sidebands, for variable speed machines; they are essential to</p><p>17</p><p>accurately calculate SER. Once the spectrum is generated the SER algorithm sums the</p><p>amplitudes of the first six sideband peaks on each side of the center mesh frequency and divides</p><p>by the amplitude of the center mesh frequency.</p><p>SER= ∑ Sideband Amplitude𝑖 6</p><p>i=1</p><p>Center mesh frequency amplitude</p><p>(5)</p><p>SER is sensitive to the sideband amplitudes relative to the center mesh frequency. In a healthy</p><p>gear mesh, any sidebands have small amplitude compared to the center mesh frequency, or they</p><p>may be missing altogether resulting in a low SER. SER is typically less than one for a healthy</p><p>gear mesh. As damage develops on a gear tooth that passes through the gear mesh, the sidebands</p><p>increase in amplitude, as well as in number, and SER will go up. In GE Bently Nevada’s wind</p><p>turbine condition monitoring system, ADAPT.wind, SER is calculated for the fundamental mesh</p><p>frequency and the first two harmonics of each gear mesh.</p><p>3.1.4 Acceleration Enveloping</p><p>The acceleration enveloping technique was originally called the high frequency resonance</p><p>technique. It was discovered, almost accidentally, from an oscilloscope display [7] in the early</p><p>1970s, through a National Aeronautics and Space Administration (NASA) funded project [8].</p><p>The acceleration enveloping technique is based on the following assumptions. When a defect</p><p>occurs in a bearing, repetitive impacts occur during rotation. These kinds of impacts are a</p><p>broadband excitation. This broadband excitation stimulates the resonant response of the</p><p>bearing's support system. However, the resonant response levels from the defect impacts, such</p><p>as unbalance, are usually very low compared to the shaft excitation; though, the frequency</p><p>contents of the resonant response are usually much higher. If the dynamic range of the vibration</p><p>sensor and the consequent analyzer is low, the resonant response signals are down in the noise</p><p>level. The key to detecting bearing faults is to capture the low amplitude response caused by</p><p>bearing defect excitation, without including the high amplitude rotational vibration signals and</p><p>system fundamental resonant frequency responses. To accomplish this, a band pass filter is used</p><p>to isolate the signal. Once the high frequency damage response is captured, the signal goes</p><p>through a rectification device and the envelope of the signal is detected from the rectified signal.</p><p>Applying FFT to the envelope signal will reveal the frequency and amplitude, which is uniquely</p><p>associated with the damaged bearing component.</p><p>In theory, any vibration sensor can achieve bearing/gear damage detection through the</p><p>enveloping or demodulation processes, as long as the sensor has the frequency range required.</p><p>Since the bearing/gear damage excited response is known to have high frequency content, the</p><p>accelerometer has an advantage over velocity and displacement</p>