Velocity synchronous bilinear distribution for planetary gearbox fault diagnosis under non-stationary conditions

Abstract This paper proposes a time-frequency method, named velocity synchronous bilinear distribution (VSBD), for planetary gearbox fault diagnosis under non-stationary conditions. This method is based on the Cohen's class bilinear distribution (CCBD). The current CCBDs are able to provide a time-frequency representation (TFR) with good time-frequency resolution for multi-component signal with constant frequencies. However, their poor time-frequency resolution in dealing with time-varying frequencies has limited their applications. As such, the VSBD is proposed to solve this problem. This method firstly uses the generalized demodulation to demodulate the signal under analysis into several signals based on the shaft rotational speed to meet the constant-frequency requirement of the bilinear distribution. The CCBD is then applied to the demodulated signals to obtain the TFRs of the demodulated signals and finally the TFR of the original signal is restored from the demodulated TFRs. This method is free from smear effect and has improved time-frequency resolution in comparison with other existing time-frequency methods. This method only considers planetary gearbox systems running under time-varying speed and fixed external load conditions. Therefore, the industrial applications of the proposed method may be restricted to such conditions.

[1]  Franz Hlawatsch,et al.  Duality and classification of bilinear time-frequency signal representations , 1991, IEEE Trans. Signal Process..

[2]  Tomasz Barszcz,et al.  A two-step procedure for estimation of instantaneous rotational speed with large fluctuations , 2013 .

[3]  Tomasz Barszcz,et al.  Measurement of instantaneous shaft speed by advanced vibration signal processing - Application to wind turbine gearbox , 2010 .

[4]  James McNames,et al.  Fourier Series Analysis of Epicyclic Gearbox Vibration , 2002 .

[5]  Ahmet Kahraman,et al.  A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors , 2010 .

[6]  Douglas L. Jones,et al.  An adaptive optimal-kernel time-frequency representation , 1995, IEEE Trans. Signal Process..

[7]  William D. Mark,et al.  Stationary transducer response to planetary-gear vibration excitation with non-uniform planet loading , 2009 .

[8]  P D McFadden,et al.  An Explanation for the Asymmetry of the Modulation Sidebands about the Tooth Meshing Frequency in Epicyclic Gear Vibration , 1985 .

[9]  Ming Liang,et al.  Time–frequency analysis based on Vold-Kalman filter and higher order energy separation for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions , 2016 .

[10]  Zhipeng Feng,et al.  Fault diagnosis of wind turbine planetary gearbox under nonstationary conditions via adaptive optimal kernel time–frequency analysis , 2014 .

[11]  Jérôme Antoni,et al.  Vibration based condition monitoring of a multistage epicyclic gearbox in lifting cranes , 2014 .

[12]  Zhipeng Feng,et al.  Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions , 2015 .

[13]  Simon Haykin,et al.  The chirplet transform: physical considerations , 1995, IEEE Trans. Signal Process..

[14]  Ahmet Kahraman,et al.  A theoretical and experimental investigation of modulation sidebands of planetary gear sets , 2009 .

[15]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[16]  William J. Williams,et al.  Improved time-frequency representation of multicomponent signals using exponential kernels , 1989, IEEE Trans. Acoust. Speech Signal Process..

[17]  Radoslaw Zimroz,et al.  A new method for the estimation of the instantaneous speed relative fluctuation in a vibration signal based on the short time scale transform , 2009 .

[18]  G. Meng,et al.  Spline-Kernelled Chirplet Transform for the Analysis of Signals With Time-Varying Frequency and Its Application , 2012, IEEE Transactions on Industrial Electronics.

[19]  Ming Liang,et al.  A velocity synchrosqueezing transform for fault diagnosis of planetary gearboxes under nonstationary conditions , 2017 .

[20]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[21]  Patrick Flandrin,et al.  Improving the readability of time-frequency and time-scale representations by the reassignment method , 1995, IEEE Trans. Signal Process..

[22]  W. M. Zhang,et al.  Polynomial Chirplet Transform With Application to Instantaneous Frequency Estimation , 2011, IEEE Transactions on Instrumentation and Measurement.

[23]  I. Daubechies,et al.  Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool , 2011 .

[24]  Peter V. E. McClintock,et al.  Linear and synchrosqueezed time-frequency representations revisited: Overview, standards of use, resolution, reconstruction, concentration, and algorithms , 2015, Digit. Signal Process..

[25]  Boualem Boashash,et al.  Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra , 1994, IEEE Trans. Signal Process..

[26]  William D. Mark.  Stationary transducer response to planetary-gear vibration excitation II: Effects of torque modulations , 2009 .

[27]  Juanjuan Shi,et al.  Gearbox fault diagnosis via generalized velocity synchronous Fourier transform and order analysis , 2019 .

[28]  Yang Yang,et al.  Multicomponent Signal Analysis Based on Polynomial Chirplet Transform , 2013, IEEE Transactions on Industrial Electronics.

[29]  Douglas L. Jones,et al.  A signal-dependent time-frequency representation: optimal kernel design , 1993, IEEE Trans. Signal Process..

[30]  Fulei Chu,et al.  Recent advances in time–frequency analysis methods for machinery fault diagnosis: A review with application examples , 2013 .

[31]  Chuan Li,et al.  A generalized synchrosqueezing transform for enhancing signal time-frequency representation , 2012, Signal Process..

[32]  Darryll J. Pines,et al.  A review of vibration-based techniques for helicopter transmission diagnostics , 2005 .

[33]  Gang Yu,et al.  General linear chirplet transform , 2016 .

[34]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[35]  Ming J. Zuo,et al.  Vibration signal models for fault diagnosis of planetary gearboxes , 2012 .

[36]  Robert J. Marks,et al.  The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

[37]  Sofia C. Olhede,et al.  A generalized demodulation approach to time-frequency projections for multicomponent signals , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[38]  Chuan Li,et al.  Time-frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform , 2012 .

[39]  Gang Yu,et al.  Synchroextracting Transform , 2017, IEEE Transactions on Industrial Electronics.