Technical Diagnostics and Non-Destructive Testing, 2022, №04



2022 №04 (06)

DOI of Article 10.37434/tdnk2022.04.01

2022 №04 (02)

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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

¹G.V. Karpenko Physico-Mechanical Institute of NASU. 5 Naukova str., 79060, Lviv, Ukraine. Е-mail: roman.yuzefovych@gmail.com
²Bydgoszcz University of Sciences and Technology. 7 Prof. S. Kaliskiego al., 85796, Bydgoszcz, Poland.
³Lviv Polytechnic National University. 12 S. Bandery str., Lviv, 79013, Ukraine.
⁴Odessa 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.
Keywords: diagnostics, bi-periodic correlated random processes, periodical nonstationarity, deterministic oscillations, amplitude spectrum, stochastic high-frequency modulation

Received: 21.10.2022

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