Modeling of Contact Area, Contact Force, and Contact Stiffness of Mechanical Systems With Friction

Abstract

It is well recognized that the contact stiffness, true contact area, and the contact force are among the key features in the study of friction system behavior. This paper presents the development of formulae for the mechanical component of dry-friction at the interface of two microscopic rough surfaces. Elastic deformation under the influence of the contact forces is considered. The elastic contact model formulation between interacting asperities is not assumed to occur only at asperity peaks, thus allowing the possibility of oblique contacts wherein the local contact surfaces are no longer parallel to the mean planes of the mating surfaces. It is shown that the approach enables the separation of the contact area into its normal and tangential projections and the contact force into its normal and tangential components. The mathematical model of contact is utilized to develop formulae for normal and tangential contact stiffness. The analytical method is used to estimate contact stiffness components. Contact parameter values for the sample are derived from the surface profile data taken from a 1.0-mm by 10-mm test area. The profile is measured using a Mahr profilometer. A computer program is written and used to analyze the profile data. The analysis yields the asperity density, average asperity radius, and the standard deviation for each test area.