Dry elasto-plastic contact of nominally flat surfaces

In mixed lubrication the lubricant film is not sufficiently thick to prevent contact between the working surfaces. As a result, the influence of the surface roughness on the pressure distribution becomes significant with large pressures being generated in the interaction regions of the most prominent surface asperities. In addition the flow of lubricant is obstructed by the asperities and therefore the flow cannot be described by the classical Reynolds equation for smooth surfaces. The flow of lubricant between rough surfaces was studied by e.g. Patir and Cheng, who introduced flow factors to modify the Reynolds equation so as to take roughness effects into account in an averaged way and this approach has been subsequently generalised to incorporate an homogenised Reynolds equation. These methods take account of roughness based on the distribution of gap between the loaded surfaces obtained from a dry contact analysis. This paper presents a method to solve dry contact problems for this purpose in the case of plane surfaces using a simple elastic–plastic model at the asperity contacts and a differential formulation for the elastic deflection, and provides validation for the method in terms of comparison with the results of an elastic–plastic rough surface contact analysis obtained using a finite element analysis.

► The rough surface contact problem for surfaces with periodic 2D roughness is solved.
► The elastic deflection is formulated as a second order differential equation.
► A simple elastic–plastic model at the asperity contacts is used.
► Results are compared with a detailed Finite Element elastic–plastic contact analysis.
► Method can be used in a homogenised Reynolds equation approach to mixed lubrication.