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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Konstantin Gavrilov & Yuriy Rozhdestvenskii & Ildar Umurzakov, 2022. "The Construction of Models of Rough Surfaces’ Interaction: Markov’s Approach," Mathematics, MDPI, vol. 10(19), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3607-:d:932047
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    Cited by:

    1. Konstantin Gavrilov & Yuriy Rozhdestvenskii & Ildar Umurzakov, 2023. "A Method for Mathematical Modeling of Hydrodynamic Friction of Plunger Pairs with Consideration of Microgeometry," Mathematics, MDPI, vol. 11(12), pages 1-11, June.

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