A Friction Model of Fractal Rough Surfaces Accounting for Size Dependence at Nanoscale

Traditional laws of friction believe that the friction coefficient of two specific solids takes constant value. However, molecular simulations revealed that the friction coefficient of nanosized asperity depends strongly on contact size and asperity radius. Since contacting surfaces are always rough consisting of asperities varying dramatically in geometric size, a theoretical model is developed to predict the friction behavior of fractal rough surfaces in this work. The result of atomic-scale simulations of sphere-on-flat friction is summarized into a uniform expression. Then, the size dependent feature of friction at nanoscale is incorporated into the analysis of fractal rough surfaces. The obtained results display the dependence of friction coefficient on roughness, material properties and load. It is revealed that the friction coefficient decreases with increasing contact area or external load. This model gives a theoretical guideline for the prediction of friction coefficient and the design of friction pairs.