Modeling of normal and tangential contact stiffness of rough surfaces

It is well recognized that the contact stiffness is one of the key features in the study of friction system behavior. The stiffness of a rough surface influences the contact state as well as the behavior of the surrounding system. It is the goal of this work to investigate the elastic deformation of surface asperities and propose mathematical model in treating its influence. The mathematical model of contact is utilized to develop formulae for normal and tangential contact stiffness. Stiffness 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 developed and used to analyze the profile data to yield the asperity density, average asperity radius, and the standard deviation for each test area. Examining the results show that both normal and tangential contact stiffness decrease exponentially with normalized separation. As the normalized separation increases both normal and tangential stiffness become very small and insensitive for the high normalized separation.