Fractal dimension of a discrete contact

Abstract

. Contact interaction ability rating for engineering surfaces and their fractal models is carried out. Fractal models describe roughness component geometry properly, they are adequate to the initial engineering surfaces and possess a random component when modeled, which makes it possible to generate a new surface with the desired geometric parameters at all times, allowing the study of the contact interaction of surfaces to be carried as many times as necessary. When solving contact problems of rough surfaces for simplification of calculations, the replacement of the initial contact with the interaction of a smooth surface with a surface having an equivalent roughness, necessary to be determined, is usually used. The paper outlines the principles of finding the fractal dimension of engineering surfaces, as well as an equivalent surface in contact with a smooth one, when the conjugation of both is equivalent to the contact of the initial surfaces. At the same time, it is shown in this work that for anisotropic initial surfaces there are completely different parameters of contact interaction in different directions of their combination, which must be taken into account in the analysis and modelling. The fractal dimension of the equivalent surface was done using the well-known "perimeter-area" method, which, when determining the contact parameters, including the fractal dimension, allows taking into account the direction of the processing traces. Thus, this paper presents a method for determining the fractal dimension of both the surface and the fractal object, and also a contact spots map, an area ratio turndown for the actual contact area to the area of the maximum spot is shown as well, a procedure for estimating the fractal dimension necessary to determine the parameters of the contact interactions of rough surfaces, is proposed.