Марковский подход к построению моделей взаимодействия шероховатых поверхностей

Abstract

Interaction of rough surfaces determines many processes in electrical engineering, thermal engineering, machinery construction, motor vehicle industry, engine technology, and other industries. Rough surface relief is a space random function. It is shown that the change in rough surfaces that occurs during their contact interaction can be analyzed using the theory of Markov processes. Noteworthy is that this problem is not solved within the framework of existing models. An approach in which each of two surfaces is represented by a set of protrusions is proposed. Each protrusion is described by its random state (a set of selected parameters), and each surface is described by a probability distribution in the set of states. When the surfaces move with respect to each other, the protrusions interact with one another, and the result of this interaction for two protrusions looks as a known two-dimensional function of interaction. The state of a fixed protrusion in the next moment is determined by its previous state and a random effect of the protrusion on the other surface. If these effects are independent, the state alteration process can be considered to be a Markovian. Recurrent recalculation in time is valid for probability distributions. Recalculating the distributions, we obtain time-varying distributions, from which the desired characteristics of interaction are obtained, such as the average contact area, average height of protrusions, friction force, wear, etc. Choosing different options of what is understood to mean the protrusion state and the interaction function, the models of different complexity and precision are obtained. The idea of bringing the interaction to a Markov model is illustrated on a simple discrete scheme with subsequently generalizing it. The approach is applied to analyzing a friction process and a fatigue failure (taking lubrication into account) that results from the protrusions repeatedly coming in contact with one another. An example of numerically analyzing the evolution of surfaces separated by a lubricant layer is given. The technical characteristics as functions of friction path and load are estimated.