Technical Diagnostics and Non-Destructive Testing #4, 2022, pp. 4-11
Diagnostics of gear pair damage using the methods of biperiodically correlated random processes. Part 1. Theoretical aspects of the problem
I.M. Javorskyj2, R.M. Yuzefovych3, O.V. Lychak1, R.T. Slyepko1, M.Z. Varyvoda1, P.O. Semenov4
G.V. Karpenko Physico-Mechanical Institute of NASU. 5 Naukova str., 79060, Lviv, Ukraine.
Bydgoszcz University of Sciences and Technology. 7 Prof. S. Kaliskiego al., 85796, Bydgoszcz, Poland.
Lviv Polytechnic National University. 12 S. Bandery str., Lviv, 79013, Ukraine.
Odessa National Maritime University. 34 I. Mechnikova str., 65029, Odesa, Ukraine.
A model of the vibration of a gear pair in the form of bi-periodically correlated random processes (BPCRP) describing its
stochastic repeatability with two diff erent periods is proposed and analyzed. It is shown that the models, proposed before in the
literature can be considered as partial cases of BPCRP. It is noted, that in the case of damage of one of the gears, the diagnostics
of the mechanism can be carried out within the framework of the BPCRP, approximated to periodically correlated random
processes (PCRP). The fi rst stage in the proposed approach is the estimation of the period of non-stationarity (fundamental
frequency) of the fi rst and second order moment functions. Least squares (LS) estimates of the periods of the deterministic part
of the vibration signal and the power of its stochastic part were obtained. The amplitude spectra of deterministic oscillations
and variation of stochastic oscillations for diff erent degrees of damage to the gear pair were analyzed. Eff ective indicators of
the degree of development of gear pair damage, which are formed on the basis of sums of the amplitudes of the components of
the spectrum of the deterministic vibration component are proposed. Ref. 20.
diagnostics, bi-periodic correlated random processes, periodical nonstationarity, deterministic oscillations, amplitude
spectrum, stochastic high-frequency modulation
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18. Javorskyj, I., Dzeryn, O., Yuzefovych, R. (2019) Analysis of mean function discrete LSM-estimator for biperiodically nonstationary random signals. Math. Model. Comput., 6(1), 44-57.
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20. Raad, A., Antoni, J., Sidahmed, M. (2008) Indicators of cyclostationarity: Theory and application to gear fault monitoring. Ibid, 22, 574-587.
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