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

Konstantin Gavrilov (), Yuriy Rozhdestvenskii and Ildar Umurzakov
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Konstantin Gavrilov: Department of Wheeled and Tracked Vehicles, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia
Yuriy Rozhdestvenskii: Department of Motor Transport, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia
Ildar Umurzakov: Department of Wheeled and Tracked Vehicles, Institute of Engineering and Technology, South Ural State University, 76 Prospekt Lenina, 454080 Chelyabinsk, Russia

Mathematics, 2022, vol. 10, issue 19, 1-13

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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