Analysis of the Fractal Structure of Rough Friction Surfaces to Establish Transient Regimes of Frictional Contact

Abstract

It is shown that friction fracture surfaces can be self-affine with a local fractal dimension. However, the intersection of such a self-affine surface with a plane gives similar contour lines, which are undoubtedly self-similar. The above considerations regarding the fractal properties of fracture surfaces give reason to believe that a rough surface in contact with metallic bodies in the process of friction is also self-similar. This article presents the fractal dimensions of the transient contact regimes (from elastic to elastoplastic and from elastoplastic to plastic contact) for self-affinity curves, which are the curves of the reference surface at various combinations of material parameters: Poisson’s ratio, hardness, and modulus of elasticity. In the calculations, the Minkowski dimension, calculated by the cellular method, was taken as the fractal dimension of curved reference surfaces. This method, based on the consideration of contact interaction, formed the basis of the method for calculating the contact characteristics of bodies, taking into account their macroshape and the roughness of friction surfaces. The results of the study are of great importance for the development of engineering methods for calculating homogeneous and inhomogeneous rough bodies.