Simple numerical method for contact analysis of rough surfaces

This paper presents a simple method that may be used to calculate the pressures and surface displacements in contacts of rough surfaces. A main feature of the method is that the pressure is calculated (updated) individually at each surface location rather than simultaneously at all locations by solving a system of equations. The pressure update at a given location is computed solely based on the surface interpenetration at that location; consequently, both 2-D and 3-D contact problems are solved in exactly the same way. Furthermore, this scheme of calculation does not produce negative pressures in the solution process, which is a main source of numerical instability in other types of methods of solution. The method is conceptually simple and easy for computer implementation. It is numerically stable and can solve various types of problems of high contact severity. Measured roughness data can be used directly without any mathematical treatment such as filtering or frequency decomposition. The method is also computationally efficient and requires minimum computer storage, making it suitable for integration into computer programs for design-analysis calculations of practical contact/lubrication problems.