Formation of Heterogeneous Spatial Structures in the Boundary Lubricant Layer During Friction
Ya. A. Lyashenko1,2
1Sumy State University, Sumy 40007, Ukraine
2Technical University of Berlin, Berlin 10623, Germany
Keywords: система Лоренца, сдвиговые напряжения и деформации, граничное трение, кинетические режимы трения, моделирование, дифференциальные уравнения в частных производных, самоорганизация, Lorenz system, shear stresses and strains, boundary friction, kinetic friction regimes, modeling, partial differential equations, self-organization
Abstract
This paper presents a synergetic model that can be used to describe the boundary friction of two atomically smooth solid surfaces separated by an ultrathin lubricant layer. The model is constructed using the Lorenz equations, which are parameterized by shear stresses, shear strains, and the lubricant temperature. Given the spatial heterogeneity of these parameters, it is shown that a structure with two types of domains is formed during friction on the contact plane. Time dependences of the fractal dimensions of the domain distributions over the contact plane are calculated, and it is shown that there exists a time when the fractal dimensions take minimum values. During the evolution, the system tends to a homogeneous state in which the entire contact area is subjected to constant shear stresses which determine the relative velocity of motion of the friction blocks.
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