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Crack propagation assessment for spur gears using model-based analysis and simulation

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Abstract

Model-based gear dynamic analysis and simulation has been a promising way for developing effective gearbox vibration monitoring approaches. In this paper, based on the dynamic model of a one-stage gearbox with spur gears and one tooth crack, statistical indicators and the discrete wavelet transform (DWT) technique are investigated to identify effective and sensitive health indicators for reflecting the crack propagation level. The results suggest that the root mean square (RMS) indicator is a better statistical indicator than the Kurtosis indicator to reflect the crack propagation in the early stage; the RMS indicator based on the residual signal segments that are strongly affected by the crack is more sensitive; the proposed DWT approach can improve the sensitivity of the RMS indicator, and the RMS indicator becomes more sensitive with the increase of the DWT level up to a best DWT level, beyond which either the monotonicity is lost or the sensitivity decreases; the proposed approach is effective with the presence of noise; with the increase of the noise level, the DWT level at which the best performance is achieved, and thus the sensitivity, decreases. Gearbox systems with different sizes and different input shaft frequencies are also investigated, and it is found that the observations presented above hold for different gearbox system settings.

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References

  • Bartelmus W. (2001) Mathematical modelling and computer simulations as an aid to gearbox diagnostics. Mechanical Systems and Signal Processing 15(5): 855–871

    Article  Google Scholar 

  • Baydar N., Ball A. (2001) A comparative study of acoustic and vibration signals in detection of gear failures using Wigner-Ville distribution. Mechanical Systems and Signal Processing 15: 1091–1107

    Article  Google Scholar 

  • Baydar N., Ball A. (2003) Detection of gear failures via vibration and acoustic signals using wavelet transform. Mechanical Systems and Signal Processing 17(4): 787–804

    Article  Google Scholar 

  • Dron J. P., Bolaers F., Rasolofondraibe I. (2004) Improvement of the sensitivity of the scalar indicators (crest factor, kurtosis) using a de-noising method by spectral substraction: Application to the detection of defects in ball bearings. Journal of Sound and Vibration 270(1–2): 61–73

    Article  Google Scholar 

  • Fan X.F., Zuo M.J. (2006) Gearbox fault detection using Hilbert and wavelet packet transform. Mechanical Systems and Signal Processing 20(4): 966–982

    Article  Google Scholar 

  • Forrester, B. D. (1996). Advanced vibration analysis techniques for fault detection and diagnosis in geared transmission systems. PhD thesis, Swinburne University of Technology.

  • Guo, M., Xie, L., Wang, S.-Q., & Zhang, J.-M. (2003). Research on an integrated ICA-SVM based framework for fault diagnosis. In Proceedings of the 2003 IEEE international conference on systems, man and cybernetics (Vol. 3, pp. 2710–2715), Washington, DC.

  • He S., Gunda R., Singh R. (2007) Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness. Journal of Sound and Vibration 301(3–5): 927–949

    Article  Google Scholar 

  • Howard I., Jia S. X., Wang J. D. (2001) The dynamic modelling of a spur gear in mesh including friction and a crack. Mechanical Systems and Signal Processing 15(5): 831–853

    Article  Google Scholar 

  • Jardine A. K. S., Lin D. M., Banjevic D. (2006) A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing 20(7): 1483–1510

    Article  Google Scholar 

  • Jia S. X., Howard I. (2006) Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations. Mechanical Systems and Signal Processing 20(2): 332–349

    Article  Google Scholar 

  • Kar C., Mohanty A. R. (2006) Monitoring gear vibrations through motor current signature analysis and wavelet transform. Mechanical Systems and Signal Processing 20(1): 158–187

    Article  Google Scholar 

  • Kartik V., & Houser D. R. (2003) Analytical predictions for the transmission error excitation in various multiple-mesh gear-trains. In Proceedings of the 2003 ASME design engineering technical conferences and computers and information in engineering conference: Ninth international power transmission and gearing conference (Vol. 4, pp. 515–524), September 2–6, Chicago.

  • Kramberger J., Sraml M., Glodez S., Flasker J., Potrc I. (2004) Computational model for the analysis of bending fatigue in gears. Computers and Structures 82(23–26): 2261–2269

    Article  Google Scholar 

  • Lai W. X., Tse P. W., Zhang G. C., Shi T. L. (2004) Classification of gear faults using cumulants and the radial basis function network. Mechanical Systems and Signal Processing 18(2): 381–389

    Article  Google Scholar 

  • Lewicki D. G. (2002) Gear crack propagation path studies guidelines for ultrasafe design. Journal of the American Helicopter Society 47(1): 64–72

    Article  Google Scholar 

  • Li B., Chow M.-Y., Tipsuwan Y., Hung J. C. (2000) Neural- network-based motor rolling bearing fault diagnosis. IEEE Transactions on Industrial Electronics 47: 1060–1069

    Article  Google Scholar 

  • Li C. J., Lee H., Choi S. H. (2002) Estimating size of gear tooth root crack using embedded modelling. Mechanical Systems and Signal Processing 16(5): 841–852

    Article  Google Scholar 

  • Lin D., Wiseman M., Banjevic D., Jardine A. K. S. (2004) An approach to signal processing and condition-based maintenance for gearboxes subject to tooth failure. Mechanical Systems and Signal Processing 18(5): 993–1007

    Article  Google Scholar 

  • Liu Z., Yin X., Zhang Z., Chen D., Chen W. (2004) Online rotor mixed fault diagnosis way based on spectrum analysis power in squirrel cage induction motors. IEEE Transactions on Energy Conversion 19: 485–490

    Article  Google Scholar 

  • Luo G.Y., Osypiw D., Irle M. (2003) On-line vibration analysis with fast continuous wavelet algorithm for condition monitoring of bearing. Journal of Vibration and Control 9: 931–947

    Article  Google Scholar 

  • McFadden P. D. (1987) Examination of a technique for the early detection of failure in gears by signal processing of the time domain average of the meshing vibration. Mechanical Systems and Signal Processing 1(2): 173–183

    Article  Google Scholar 

  • Mohanty A. R., Kar C. (2006) Fault detection in a multistage gearbox by demodulation of motor current waveform. IEEE Transactions on Industrial Electronics 53(4): 1285–1297

    Article  Google Scholar 

  • Ozguven H. N., Houser D. R. (1988) Mathematical-models used in gear dynamics—a review. Journal of Sound and Vibration 121(3): 383–411

    Article  Google Scholar 

  • Rao V. B. (1999) Kurtosis as a metric in the assessment of gear damage. Mechanical Systems and Signal Processing 31(6): 443–448

    Google Scholar 

  • Samuel P.D., Pines D.J. (2005) A review of vibration-based techniques for helicopter transmission diagnostics. Journal of Sound and Vibration 282(1–2): 475–508

    Article  Google Scholar 

  • Smith C., Akujuobi C. M., Hamory P., Kloesel K. (2007) An approach to vibration analysis using wavelets in an application of aircraft health monitoring. Mechanical Systems and Signal Processing 21(3): 1255–1272

    Article  Google Scholar 

  • Staszewski W., Boller C., Tomlinson G. R. (2004) Health monitoring of aerospace structures: Smart sensor technologies and signal processing. Wiley, West Sussex

    Google Scholar 

  • Tamminana V. K., Kahraman A., Vijayakar S. (2007) A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs. Journal of Mechanical Design 129: 75–84

    Article  Google Scholar 

  • Thompson D. F., Gupta S., Shukla A. (2000) Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units. Mechanism and Machine Theory 35(5): 609–627

    Article  Google Scholar 

  • Tian, X. H., Zuo, M. J., & Fyfe, K. R. (2004) Analysis of the vibration response of a gearbox with gear tooth faults. In Proceedings of IMECE04, 2004 ASME international mechanical engineering congress and exposition, November 13–20, Anaheim, CA, USA.

  • Vedmar L., Andersson A. (2003) A method to determine dynamic loads on spur gear teeth and on bearings. Journal of Sound and Vibration 267: 1065–1084

    Article  Google Scholar 

  • Velex P., Ajmi M. (2007) Dynamic tooth loads and quasi-static transmission errors in helical gears approximate dynamic factor formulae. Mechanism and Machine Theory 42: 1512–1526

    Article  Google Scholar 

  • Wang W. Y. (2001) Early detection of gear tooth cracking using the resonance demodulation technique. Mechanical Systems and Signal Processing 15(5): 887–903

    Article  Google Scholar 

  • Wang W. J., McFadden P. D. (1993) Early detection of gear failure by vibration analysis I. Calculation of the time-frequency distribution. Mechanical Systems and Signal Processing 7: 193–203

    Article  Google Scholar 

  • Wang W. J., McFadden P. D. (1996) Application of wavelets to gearbox vibration signals for fault detection. Journal of Sound and Vibration 192: 927–939

    Article  Google Scholar 

  • Wu, S. (2007) Gearbox dynamic simulation and estimation of fault growth, Master’s Thesis, Department of Mechanical Engineering, University of Alberta, Edmonton.

  • Wu S., Zuo M. J., Parey A. (2008) Simulation of spur gear dynamics and estimation of fault growth. Journal of Sound and Vibration 317(3-5): 608–624

    Article  Google Scholar 

  • Yang D. C. H., Lin J. Y. (1987) Hertzian damping, tooth friction and bending elasticity in gear impact dynamics. Journal of Mechanisms, Transmissions, and Automation in Design 109(2): 189–196

    Article  Google Scholar 

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Authors and Affiliations

  1. Concordia Institute for Information Systems Engineering, Concordia University, 1515 Ste-Catherine Street West EV-7.637, Montreal, H3G 2W1, Canada

    Zhigang Tian

  2. Department of Mechanical Engineering, University of Alberta, Edmonton, T6G2G8, Canada

    Ming J. Zuo & Siyan Wu

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  1. Zhigang Tian
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  2. Ming J. Zuo
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  3. Siyan Wu
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Correspondence to Zhigang Tian.

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Tian, Z., Zuo, M.J. & Wu, S. Crack propagation assessment for spur gears using model-based analysis and simulation. J Intell Manuf 23, 239–253 (2012). https://doi.org/10.1007/s10845-009-0357-8

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  • DOI: https://doi.org/10.1007/s10845-009-0357-8

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