A Multi-scale Approach for Dynamical Simulations of the Surface Topography in High-pressure Frictional Contacts: Bridging Simulation Scales

In tribological dry-friction micro-contacts under high pressure the surfaces of both friction partners are subjected to constant change due to severe plastic deformation and wear. Simulations with the method of Movable Cellular Automata (MCA) have shown that a quasi-fluid layer evolves in the contact zone between the friction partners. The simulation length scales are few nanometers. With computational resources available today it is not possible to make simulations on macroscopic length and time scales. In this paper a particle model is presented that includes the basic processes—plastic deformation, mass transfer, and wear—on the micro-scale and allows for simulation and calculation of larger contact areas. With this model it is possible to combine the existing modeling and simulation tools on the micro-scale with simulations and measurements on macroscopic lengths scale. A master equation is developed that contains transition probabilities for particle-like volume-elements. Using the Fokker–Planck-Formalism the result is a stochastic partial differential equation that describes the formation and development of the stochastic surface of one frictional partner. The resulting time-dependent self-affine power spectrum of the surface profile can be used in other macroscopic methods to calculate friction, wear, traction curves, and other macroscopic quantities.