The Markov Model for Alteration of Rough Surfaces during Their Mechanical Interaction
Abstract
A general approach to constructing a model describing interaction of rough surfaces that involves a Markov process analysis is described, and a new substantiation of the Markov-like behavior of the interaction is given. The surface is represented as a random one, consisting of the totality of elements (irregularities and protrusions) with random states. The surface elements change each other as they come in contact with one another. A description for different interactions (mechanical, thermal, and electrical) on the entire surface can be obtained by specifying in different ways the state of an element and the functions of interaction between two elements. This approach involves a Markov process with recalculating the distribution of the probabilities of its states in a time-recurrent manner. The obtained distribution of probabilities can be used for estimating different characteristics of interaction as a function of time. The developed approach is applied to a friction phenomenon. Any protrusion on one surface is subjected to the influence of moving protrusions on the other surface, which are characterized by random states (heights). Interaction only occurs between the highest protrusions as they come in mechanical contact with each other, and their change resulting from the coming in contact takes place with a low probability. This gives grounds to assume that the changes occurring in any surface element can be described in terms of a Poisson flow. The element’s next state is the result of interaction between the previous state and the next effect caused by some protrusion on the other surface. The result is described by a known interaction function. If the sequential interactions are independent random quantities, the state variation process is a Markov process. Therefore, the probability distribution can be recalculated in a recurrent way, and it should be noted that the transition probabilities depend on the distribution of heights on the other surface. Since the surfaces mutually affect each other, a similar recalculation is valid for any protrusion on the other surface. Thus, recalculation of two distributions is obtained, in which the recalculation operator for one surface depends on the distribution for the other surface. The friction characteristics at any moment of time can be calculated from the obtained distributions. The approach is applied to a particular case of fatigue failure conditions under which a surface element is destroyed after having come in a large number (several million) of contacts. The choice of the distribution recalculation quantization interval the use of which makes it possible to significantly speed up the numerical analysis for a model at the expense of changing the transition distribution matrix is substantiated. The Kolmogorov–Feller equations for the fatigue failure model are written. The application of the contact interaction model is illustrated on the example of analyzing the piston guide wearing process in a ChN 13/15 diesel engine with evaluating the tribotechnical parameters determining the «piston–cylinder» mating life.
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Для цитирования: Горицкий Ю.А., Гаврилов К.В., Исмаилова Ю.С., Шевченко О.В. Марковская модель изменения шероховатых поверхностей при механическом взаимодействии // Вестник МЭИ. 2017. № 5. С. 101—110. DOI: 10.24160/1993-6982-2017-5-101-110.
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For citation: Goritsky Yu.A., Gavrilov K.V., Ismailova Yu.S., Shevchenko O.V. The Markov Model for Alteration of Rough Surfaces during Their Mechanical Interaction. MPEI Vestnik. 2017;5:101—110. (in Russian). DOI: 10.24160/1993-6982-2017-5-101-110.
