Stick–slip oscillations: Dynamics of friction and surface roughness

Abstract

While its classical model is relatively simple, friction actually depends on both the interface properties of interacting surfaces and on the dynamics of the system containing them. At a microscopic level, the true contact area changes as the surfaces move relative to each other. Thus at a macroscopic level, total friction and normal forces are time-dependent phenomena. This paper introduces a more detailed friction model, one that explicitly considers deformation of and adhesion between surface asperities. Using probabilistic surface models for two nominally flat surfaces, the stick–slip model sums adhesive and deformative forces over all asperities. Two features distinguish this approach from more traditional analyses: (i) Roughness distributions of the two interacting surfaces are considered to be independent, (ii) Intersurface contacts occur at both asperity peaks, as in previous models, and on their slopes. Slope contacts, in particular, are important because these oblique interactions produce motion normal to the plane of sliding. Building the model begins by analyzing local friction forces as composites of resistance to elastic deformation and shear resistance arising from adhesion between asperity surfaces. By extending the expressions obtained for normal and tangential friction forces over the macroscopic surfaces, the model then describes the stick–slip behavior frequently observed in dynamic systems and permits simulating a rigid body on a moving platform. Numerical results for several surface and system parameters illustrate both time-dependent and time-averaged frictional forces. These analyses also show that, although total averaged friction remains constant with respect to sliding velocity for the cases considered, the relatively small deformation component exhibits resonancelike behavior at certain speeds. Stick–slip occurs only within a narrow range around these critical speeds of a system. External damping can prevent stick–slip motion, and both deformative and adhesive frictional forces must be present for it to occur at all.