Mathematical modeling of the evolution of a tribosystem in the process of formation of equilibrium roughness of a frictional contact

As the science of friction developed, tribologists showed that reliable operation of friction units is determined by the wear resistance of the surface layer, its ability to adapt to changing operating conditions. In this regard, there is a need not only to create structures on the surfaces of friction units that have the properties of self-regulation and self-organization, but also to monitor changes in the characteristics of the surface layer. This article presents an innovative methodology for monitoring the life cycle of surface layers coated by vacuum ion-plasma treatment. In this paper, we propose a dynamic model based on the hypothesis that roughness is both a factor that excites mechanical vibrations and a consequence of these vibrations, whereas roughness changes as a result of wear under the influence of local dynamic forces. It is shown that a friction pair is a nonlinear system with complex feedbacks. Its stationary motion can be considered as a strange attractor. The randomness of motion in the vicinity of the limit cycle is due to the presence of a link of constant delay with rigid positive feedback in the model. As a result, there is constant reconfiguration of the amplitude and phase of the oscillations.