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The Behaviour of Transverse Roughness in EHL Contacts

By assuming the contact geometry in elastohydrodynamic lubrication (EHL) to be that of an infinitely long contact with given nominal film thickness and mean pressure and considering the elastic displacements of the separate components of the initial roughness, it is possible to extend the Greenwood and Johnson analysis for sinusoidal pressure to any two-dimensional roughness. For typical EHL pressures the viscosity effects are negligible, so the Reynolds equation can be linearized and solved analytically; the solution provides a criterion to relate the amplitudes of the undeformed and deformed roughness to the wavelength, and shows that roughness with a short wavelength is likely to persist after deformation. The linearization of the Reynolds equation is extended to the transient case and it is found that the complete solution is made of two separate parts: the particular integral (steady state solution) and the complementary function (which depends on the entry of the partly deformed roughness into the Hertzian zone).