№73-3
Identification and study of the characteristics of friction oscillations in the brake
О. Коptovets1, L. Shyrin1, V. Yavorska1, А. Herasymenko1
1Dnipro University of Technology,Dnipro, Ukraine
Coll.res.pap.nat.min.univ. 2023, 73:33-44
https://doi.org/10.33271/crpnmu/73.033
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ABSTRACT
Purpose.The task of researching modes of established frictional oscillations of the braking mechanism is to find a solution to the initial dynamic problem with friction that satisfies the periodicity conditions. At the same time, the period of motion of the dynamic system is not known in advance. This dynamic system is described by a non-linear dissipative non-autonomous system of differential equations.
The methods. The developed technique of spectral analysis of the braking mechanism's oscillations is based on the assumption that its movements are periodic. If deterministic chaos occurs in the analyzed dynamic system, then the autocorrelation function of the time series of movements must have a finite carrier, that is, vanish outside a finite time interval.
Findings. In the paper, the method of computational experiment is used to identify and study the characteristics of oscillatory processes in brake mechanisms. At the first stage of the computational experiment, a numerical solution of the considered dynamic problem with friction is carried out using a computational algorithm. As a result, the time series of block movements are calculated. At the second stage of the computational experiment, the obtained time series are studied.
The originality. The paper uses phase diagrams in the "displacement-velocity" variables to analyze the process of establishing the oscillations of the brake mechanism and visual detection of attractors. When studying the dependence of amplitudes of displacements, velocities and accelerations of the dynamic system under consideration on changes in its parameters, the method of continuation by parameter was used with a stepwise change in the parameters of the system.
Practical implementation. The developed mathematical model of vibrations of the braking mechanism and the computational algorithm for its numerical study are implemented in the form of a computer program for personal computers in the FORTRAN algorithmic language. Almost all available commercial compilers can be used to compile the program, including Compaq Visual Fortran 6.6 and Intel Visual Fortran 10, as well as non-commercial compilers distributed under the GNU license.
Keywords: brake, tribological system, nonlinear dynamic problem with friction, computational experiment, autocorrelation functions, oscillation period, spectral analysis, phase diagrams, parameter continuation method.
References
1. Koptovets, А.N., Koroviaka, Е.А., Samusia, S.V., Diachkov, P.А., & Yavorska, V.V. (2013). Modeling of the controlled motion of mine trains. Mining electric engineering and automation: collection of scientific papers of the National Mining University, 91, 105–110.
2. Shyrin, A., Rastsvetaev, V., & Morozova, Т. (2012). Estimation of reliability and capacity of auxiliary vehicles while preparing coal reserves for stoping. Geomechanical Processes During Underground Mining. 105–108.
3. Shyrin, L.N., Rastsvetaiev, V.А., Lebed, А.L., & Halushko, N.N. (2012). Prospects to improve schemes of auxiliary transport in the context of “Shakhta “1/3 Novogrodovskaia” UE. Collection of scientific papers of the National Mining University, 38, 79–83.
4. Koptovets, А.N., Bobyliov, А.А., & Diachkov, P.А. (2009). Generalizing the practices concerning the use of various frictional materials for brake shoes. Hoisting and transportation facilities, 3, 52–62.
5. Sviridenok, А.I., Chizhik, S.А., & Petropovets, М.I. (1990). Mechanics of discrete frictional contact. Nauka i Tekhnika.
6. Goriacheva, I.G. (2001). Mechanics of frictional interaction. Nauka.
7. Goriacheva, I.G., & Dobychin, М.P. (1988). Contact problems in tribology. Mashinostroenie.
8. Barmin, Yu.I. (1964). A technique to compile empiric formula for friction coefficient of brake shoes on a slugger. Proceedings of Khabarovsk Institute of Railway Transport, 16, 186–195.
9. Grebeniuk P.Т. (2004). Regulations to calculate brakes. Intext.
