PSI - Issue 36

Ihor Javorskyj et al. / Procedia Structural Integrity 36 (2022) 122–129

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Ihor Javorskyj et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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where . For the indicator I we obtained the following values 1.29, 13.82 and 30.72 for increasing damage stage of gear. The significant increasing of the indicator I demonstrates its high sensitivity to the changes of gear conditions in spite of the small values of the variance of the Fourier coefficients in comparison with the amplitudes of the harmonics of the deterministic oscillations. 3. Conclusions The PCRP approach was used in this paper to analyze the vibration of a wind turbine gearbox. It showed that the first and the second order PCRP parameters of the vibration at the frequency band 0,1.8     m f , where m f is the mesh frequency, are sufficiently sensitive to damage development and they provide the successful detection of the fault and monitoring of its development. It was established that the mean function of the least square statistics for the period estimation have a sharp peaks for the different damage development stages. The spectrum shape for all three damage stages of gear teeth differs insignificantly and its width covers about the whole of the investigated frequency band. The low-frequency harmonics can be interpreted as order harmonics of the rotation frequency and the frequencies of the higher harmonics are linear combinations of the mesh and the rotation frequencies. The total power of the harmonics rapidly increases as the damage grows. On the basis of the obtained period estimators, the variance Fourier coefficients for its amplitude spectrum were calculated. This spectrum characterizes the time periodic variations of the stochastic oscillation power. The total amplitude of the variance harmonics was chosen for the comparison of the different states. The average power essentially increases as the damage grows. The obtained results offer base for usage of the stochastic power indicator for the monitoring of the wind turbine gearbox condition. References Antoni, J., Bonnardot, F., Raad, A., El Badaoui, M., 2004. Cyclostationary modeling of rotating machine vibration signals. Mech. Syst. Signal Process., 18, 1285 – 1314. Borghesani, P., Pennacchi, P., Randall, R.B., Sawalhi, N., Ricci,R., 2013. Application of cepstrum pre-whitening for the diagnosis of bearing faults under variable speed conditions. Mech. Syst. Signal Process., 36(2), 370 – 384. Javorskyj, I., Yuzefovych, R., Kravets, I., Matsko, I., 2012. Properties of Characteristics Estimators of Periodically Correlated Random Processes in Preliminary Determination of the Period of Correlation. Radioelectron. Commun. Syst., 55(8), 335 – 348. Javorskyj, I., Yuzefovych, R., Kurapov, R., Lychak, O. The Quadrature Components of Narrowband Periodically Non-Stationary Random Signals. In: Advances in Intelligent Systems and Computing V. 2021, 1293, 696 – 713. Mykhailyshyn, V., Javorskyj, I., Vasylyna, Ya., Drabych, O. and Isaev, I., 1997. Probabilistic models and statistical methods for the analysis of vibrational signals in the problems of diagnostics of machines and structures. Mater. Sci., 33, 655 – 672. Obuchowski, J., Wyłomańska, A. , Zimroz, R., 2014. Selection of informative frequency band in local damage detection in rotating machinery. Mech. Syst. Signal Process., 48, 138 – 152. Randall, R.B., Antoni, J., Chobsaard, S., 2001. The relationship between spectral correlation and envelope analysis. Mech. Syst. Signal Process., 15(5), 945 – 962. Sawalhi, N., Randall, R.B., Endo, H., 2017. The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis. Mech. Syst. Signal Process., 31(6), 2616 – 2633. Smith, W.A., Randall, R.B., 2015. Rolling element bearing diagnostics using the Case Western Reserve University data: A benchmark study. Mech. Syst. Signal Process., 64 – 65, 100 – 131. Wang, D., Zhao, X., Kou, L.-L., Qin, Y., Zhao, Y., Tsui, K.L., 2019. A simple and fast guideline for generating enhanced/squared envelope spectra from spectral coherence for bearing fault diagnosis. Mech. Syst. Signal Process., 122, 754 – 768. ( ) 0 i c R R R ( ) 0 ( ) ( ) 0 0 0 0  = −