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Volume 10
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10.3390/math10193607
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Article

The Construction of Models of Rough Surfaces’ Interaction: Markov’s Approach

by
Konstantin Gavrilov
1,*,
Yuriy Rozhdestvenskii
2 and
Ildar Umurzakov
1
1
Department of Wheeled and Tracked Vehicles, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia
2
Department of Motor Transport, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(19), 3607; https://doi.org/10.3390/math10193607
Submission received: 5 September 2022 / Revised: 27 September 2022 / Accepted: 29 September 2022 / Published: 2 October 2022
(This article belongs to the Special Issue Mathematical Modeling of Engineering and Socio-Economic Processes and Systems)
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Abstract

This article shows that the change of rough surfaces in the way of their contact interaction can be analyzed using the theory of Markov’s processes. In the framework of existing models, this problem cannot be solved. In this article, the idea of reducing to Markov’s model is shown on a simple discrete scheme, which is then generalized. The approach was applied to the analysis of the friction process, to the fatigue failure mode, in which the surface element changes after multiple contacts, possibly many millions. The Kolmogorov-Feller’s equations for the model of this regime were presented and the model of the influence of lubrication is offered. A calculated example of estimating the evolution of surfaces separated by a lubricant layer is given. Additionally, the technical characteristics as functions of the friction path and the load were evaluated.
Keywords: surface asperities interaction; Markov process; tribological parameters surface asperities interaction; Markov process; tribological parameters

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MDPI and ACS Style

Gavrilov, K.; Rozhdestvenskii, Y.; Umurzakov, I. The Construction of Models of Rough Surfaces’ Interaction: Markov’s Approach. Mathematics 2022, 10, 3607. https://doi.org/10.3390/math10193607

AMA Style

Gavrilov K, Rozhdestvenskii Y, Umurzakov I. The Construction of Models of Rough Surfaces’ Interaction: Markov’s Approach. Mathematics. 2022; 10(19):3607. https://doi.org/10.3390/math10193607

Chicago/Turabian Style

Gavrilov, Konstantin, Yuriy Rozhdestvenskii, and Ildar Umurzakov. 2022. "The Construction of Models of Rough Surfaces’ Interaction: Markov’s Approach" Mathematics 10, no. 19: 3607. https://doi.org/10.3390/math10193607

APA Style

Gavrilov, K., Rozhdestvenskii, Y., & Umurzakov, I. (2022). The Construction of Models of Rough Surfaces’ Interaction: Markov’s Approach. Mathematics, 10(19), 3607. https://doi.org/10.3390/math10193607

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