Keywords: elastohydrodynamic line, roughness, piezo-viscosity, free volume, Reynolds equation, film thickness.

In this paper a numerical solution of the elastohydrodynamic line (EHL) contact lubrication problem is presented for a cylinder which is rolling over a flat plane. As is well known, the properties of the lubricant play a significant role in the forming of a lubricating film and reducing friction between the contacting surfaces. Pressure profiles and film shapes are shown and variations of the minimum film thickness with dimensionless parameters are also presented. The model predicts that a pressure spike occurs on the outlet side of the contact, accompanied by a constriction in oil-film thickness. Increasing speed or increasing viscosity causes an increase of the pressure spike in height and its moving from the outlet side of the contact toward the inlet.

The influence of pressure on both viscosity and density has been taken into account when lubricant models have to be used in numerical calculation of film thickness and friction. The effects of different pressure-viscosity relationships, including the exponential model, the Roelands model and the free-volume model, are investigated with respect to modelling in the best possible way the real piezo-viscous behaviour at pressures as high as the typical EHL pressures. The Roelands law has been observed to fail in capturing the real film thinning behaviour. For this reason, a law based on the free-volume theory model has been used to predict the EHL characteristics over a wide range of sliding speed and applied loads with a better characterization of the shear-thinning lubricant behaviour. In fact, it was found that the film thickness becomes more thinner using the free-volume model and in particular the pressure spike magnitude increases significantly.

The role of surface roughness on EHD lubrication has become crucial, for this reason its effect on the pressure profile and film thickness in a steady state EHL line contact is, also, investigated by means of numerical simulations. One of the purposes of this work is to show how the pressure profile and film thickness are influenced by surface asperity, not only by modelling the roughness using deterministic or averaging techniques, but by introducing a real surface topography of the contact surfaces. For this reason, three types of surfaces are employed: the classical smooth profile; a second case in which the surface roughness is assumed to be transverse and its profile is generated by a sinusoidal function defined in terms of its amplitude and wavelength, subsequently, was considered a real topography of a rough surface. Numerical simulations have shown the influence of the surface roughness on the EHL properties, for this reason an optical profilometer has been used to acquire the three-dimensional surface topography in order to evaluate the values pressure and film thickness more accurately.

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