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Fault detection of a planetary gear under variable speed conditions

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PER method for Fault detection of a planetary gear under variable speed conditions

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Fault detection of a planetary gear under variable speed conditions

  1. 1. Seoul National University Positive Energy Residual (PER) Based Planetary Gears Fault Detection Method Under Variable Speed Conditions Presenter: Jungho Park PhD Candidate in Seoul National University Visiting Researcher in University of Alberta System Health & Risk Management Laboratory Department of Mechanical & Aerospace Engineering Seoul National University
  2. 2. Seoul National University2018/7/31 - 2 - Seoul National University Edmonton Seoul Location Mechanical engineering department
  3. 3. Seoul National University2018/7/31 - 3 - Seoul National University Professor Associate professor Assistant professor Endowed professor Total 1,535 413 153 977 3,078 Under- graduate M.A Ph.D. Total 16,511 7,882 3,709 28,102 Under-graduate Graduate Professional Graduate 16 Colleges with 82 Departments 74 Departments and 30 Interdisciplinary 10 Professional Graduate Schools College & School (As of April, 2017 ) Full-time faculty (As of April, 2018; Unit: Persons) Students (As of April, 2018; Unit: Persons)
  4. 4. Seoul National University2018/7/31 - 4 - Biography Education  B.S. Seoul National University, Aug. 12’  Ph. D. Seoul National University, Aug. 19’ (Expected) Experience  Korean Army, Apr. 2009 – Feb. 2011  Intern at Samsung Heavy Industries, Dec. 11’ – Feb. 12’ Research interest  Model-based fault diagnosis of a planetary gear  Fault detection of a planetary gear under variable speed conditions Publication  8 Journal papers (2 first author), 1 in revision  Research assistant at PARC, Jul. 17’ – Nov. 17’
  5. 5. Seoul National University CONTENTS 2018/7/31 - 5 - Introduction1 PER (Positive Energy Residual) method2 Case study: Simulation & Experiment3 Conclusion4
  6. 6. Seoul National University2018/7/31 - 6 - Introduction http://www.youtube.com/watch?v=u8QEqtvt_IA Sun gearCarrier Ring gear Planet gear  Planetary gear: Ring, sun, planet and carrier  Multiple planets could share the heavy loads  Applications : wind turbine, helicopters, etc.  Economic loss and casualties from unexpected failures Fault Detection of a Planetary Gear Various methods have been developed for fault detection of the planetary gears
  7. 7. Seoul National University2018/7/31 - 7 - Introduction *Randall, R. B. "A new method of modeling gear faults." Journal of mechanical design 104.2 (1982): 259-267. Normal Fault Distributed  Usually based on vibration (acceleration) signals  Time-domain signals could be covered with noise  Fault detection by side-band behaviors in frequency domain Previous Methods for Gear Fault Detection* Many fault detection methods have been developed based on frequency-domain Local
  8. 8. Seoul National University2018/7/31 - 8 - Limitation of the Previous Methods Introduction Distributed Local *Randall, R. B. "A new method of modeling gear faults." Journal of mechanical design 104.2 (1982): 259-267.  Variable speed conditions in real-world applications  Frequency-domain based methods are not available Normal in Variable speed Fault in Variable speed Need for fault detection methods which can also be applied to variable speed conditions
  9. 9. Seoul National University PER (Positive Energy Residual) method 2018/7/31 - 9 -
  10. 10. Seoul National University2018/7/31 - 10 - PER (Positive Energy Residual) method Review of the Techniques – (1) Wavelet Transform  Wavelet transform (WT): Represent transient signals in the time-frequency domain  Adaptive in resolution: High time resolution in high frequency & Low time resolution in low frequency  Good performance in extracting transient signals from contraction of wavelet  Widely used for fault detection in combination with machine learning (ML) Limitations of WT in fault detection under variable speeds : Need stationary conditions used with the machine learning (ML) 𝑊𝑇 𝑎, 𝑏 = 𝑥 𝑡 𝜓( 𝑡 − 𝑏 𝑎 )𝑑𝑡 ∞ −∞ Time-domain signals Wavelet TransformTime-domain Wavelet
  11. 11. Seoul National University2018/7/31 - 11 - PER (Positive Energy Residual) method Review of the Techniques – (2) Gaussian Process  Gaussian process (GP): Represent statistical properties of the non-linear signals in the continuous domain using Gaussian distribution  Could be used for regression using observed signals  Prediction results will be based on mean and standard deviation Could statistically represent non-linear behaviors of wavelet coefficients from variable speed conditions Gaussian process regression model 𝑌 𝑡 ~ 𝐺𝑃(𝑚 𝑡 , 𝑘 𝑡, 𝑡′ ) Observation 𝒟 = (𝑡, 𝑓 𝑡 ) Prediction 𝒚 𝐧𝐞𝐰|𝒟 ~ 𝒩(𝑚 𝒕 𝒏𝒆𝒘|𝒟 , 𝜎new 2 𝒕 𝒏𝒆𝒘|𝒟 ) 𝒕 𝒏𝒆𝒘 Mean Std. Obs.
  12. 12. Seoul National University - 12 - Procedures for the PER Method – (1) PER (Positive Energy Residual) method Normal Fault Normal Fault Wavelet Coeff. ① Measurement of vibration signals ② Wavelet coefficients Wavelet transform  Could represent time-varying behaviors of vibration signals  Could extract transient behaviors from peaks in the signals
  13. 13. Seoul National University - 13 - Procedures for the PER Method – (1) PER (Positive Energy Residual) method Normal Fault Normal Fault Wavelet Coeff. ③ Marginalized wavelet coefficients ② Wavelet coefficients Marginalize  Transformation of 3-D data to 2-D data  More efficient for signal processing
  14. 14. Seoul National University - 14 - Procedures for the PER Method – (2) PER (Positive Energy Residual) method  Could represent statistical behaviors of non- linear wavelet coefficients  Predicted mean values represent the effects of variable speed condition ③ Marginalized wavelet coefficients GP regression ④ Predicted statistical properties Gaussian process regression Normal Fault Normal Fault
  15. 15. Seoul National University - 15 - Procedures for the PER Method – (2) PER (Positive Energy Residual) method GP regression ④ Predicted statistical properties ⑤ Energy residual (ER) = Wavelet coeff. - mean Normal Fault Normal Fault  The effects of variable speed conditions could be minimized while leaving faulty information Subtract mean values
  16. 16. Seoul National University - 16 - Procedures for the PER Method – (3) PER (Positive Energy Residual) method  Faulty behaviors exist only in a positive direction  Take the positive portions of ER to enhance fault sensitivity ⑤ Energy residual (ER) = Wavelet coeff. - mean Normal Fault ⑥ Positive energy residual (PER) Take positive portions Normal Fault Calculate kurtosis
  17. 17. Seoul National University Flowchart PER (Positive Energy Residual) method >Threshold Yes No Faulty state Normal state Step 1: Wavelet transform & Marginalize Step 2: Gaussian process (GP) regression Marginalized wavelet coefficients, 𝑤𝑡 Step 3: Calculate energy residual (ER) Predicted mean, m Step 5: Calculate kurtosis of PER ER = 𝑤𝑡 − 𝑚 Step 4: Calculate positive portions in ER (PER) PER Testing vibration signals Calculate ratio of kurtosis between training normal and testing data Kurtosis of PER from training normal data Kurtosis of PER from training fault data
  18. 18. Seoul National University Case study: Simulation & Experiment 2018/7/31 - 18 -
  19. 19. Seoul National University2018/7/31 - 19 - Case Study: Simulation Accelerometer *Inalpolat, Murat, and A. Kahraman. "A theoretical and experimental investigation of modulation sidebands of planetary gear sets." Journal of Sound and Vibration 323.3 (2009): 677-696. A Simulation Model of the Planetary Gear*  Acceleration signals considering vibration modulation  Variable speed condition : -300(t-3)2+2800 RPM  Different amplitudes according to rotating speed  Assumption of planet gear fault (4 levels)
  20. 20. Seoul National University2018/7/31 - 20 - Case Study: Simulation Simulated Vibration Signal Normal Fault 1 Fault 2 Fault 3 Fault 4
  21. 21. Seoul National University2018/7/31 - 21 - Case Study: Simulation Demonstration of the proposed method using kurtosis at each step
  22. 22. Seoul National University2018/7/31 - 22 - Case Study: Simulation Result Ratios of Kurtosis btw. Normal and Faults F1/N F2/N F3/N F4/N WT 1.0132 1.1010 1.2622 1.4640 ER 1.0341 1.1232 1.3099 1.6046 PER 1.5186 3.6843 6.0268 7.6211 Fault/Normal
  23. 23. Seoul National University2018/7/31 - 23 - Case Study: Experiment 20 sec. A Planetary Gear in a 2kW Wind Turbine Simulator  5 levels of fault in a planet gear (M=1.5) (Semi-circle shapes with D=0.25, 0.75, 1.25mm)  Variable speed: Sinusoidal curve (T=20 sec.)  Torque: 2Nm, Temp: 60°C D=0.25 D=0.75 D=1.25
  24. 24. Seoul National University2018/7/31 - 24 - Case Study: Experiment Experimental Vibration Signal 2018/7/31 Measured vibration signals of planetary gears at each fault level Normal Fault 1 Fault 2 Fault 3
  25. 25. Seoul National University2018/7/31 - 25 - Case Study: Experiment Demonstration of the proposed method using kurtosis at each step
  26. 26. Seoul National University2018/7/31 - 26 - Case Study: Simulation Model Ratios of Kurtosis btw. Normal and Faults (5 times of 20 seconds data averaged) F1/N F2/N F3/N WT 1.0464 1.0627 3.5783 ER 1.0915 1.0806 3.7216 PER 1.2106 1.1177 4.3372
  27. 27. Seoul National University Conclusion 2018/7/31 - 27 -
  28. 28. Seoul National University2018/7/31 - 28 -  Development of a PER method for a planetary gear fault detection under variable speed conditions  Employment of wavelet transform (WT) and a Gaussian process (GP)  Derivation of energy residual (ER) by subtracting predicted mean values of GP from marginalized wavelet coefficients  Kurtosis from positive portions of energy residual, ER (PER)  We demonstrated the performance using simulation and experiment Conclusions  Application of the proposed method to various variable speed conditions  Application of the proposed method to various rotating machinery (bearing, motor, etc.) Future Works Conclusion
  29. 29. Seoul National University THANK YOU FOR LISTENING 2018/7/31 - 29 -
  30. 30. Seoul National University2018/7/31 - 30 - Back-up F1/N F2/N F3/N F4/N F5/N PER (Variable) 1.13 1.43 1.25 1.91 5.89 Kurtosis (Const.) 1.06 1.11 1.05 1.24 1.87 Constant speed: Kurtosis Variable speed: PER D=0.25 D=0.5 D=0.75 D=1 D=1.25

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