Estimation of the friction coefficient by identifying the evolution of rough surface topography

The complexity and randomness of surface roughness make the origin of friction always puzzling. Is there a potential correlation mechanism between the evolution of friction force and surface topography, and is it possible to estimate the friction coefficient from the topography evolution? Here, we explore the evolution of surface topography in metallic materials during friction by defining the characteristic orientation of the surface and analyzing its changes over time, which closely mirrors the behavior of friction forces. Then, we propose a simple relationship that relates the characteristic orientation and friction force via the friction coefficient. Therefore, the friction coefficient can be evaluated based on topography evolution without relying on any theoretical modeling assumptions. These results reveal the mechanism between complex surface topography and friction force through a simple formula and provide a method to estimate the friction coefficient. This method has promising applications when the friction coefficient is difficult to measure, such as in large-scale landslides and geologic faults.