The effect of sinusoidal roughness profile upon rolling plane layered contact

A numerical solution to the free rolling layered contact problem of a regular wavy surface is presented. Both bonded and unbonded layers are investigated. The governing dual elasticity equations are reduced to a system of linear equations where the solution provides a set of results for the unknown parameters. Sliding and complete adhesion cases are treated. The influence of roughness, coefficient of friction, layer thickness and layer compressibility on the results are examined. It is found that the stability of the present method is strongly dependent on the ratio of the amplitude of the wave to its wavelength. In the case of adhesive rolling, the shear traction becomes smooth for an incompressible layer. An asymptotic solution for the surface tractions is obtained when an unbonded layer in full sliding becomes thin. The numerical data showed good agreement with the existing analytical solutions for smooth surfaces and with the derived formula.