Theoretical analysis of an infinitely wide rigid cylinder rotating over a grooved surface in hydrodynamic conditions

A theoretical model that evaluates the frictional properties of an infinitely wide rigid cylinder rotating over a grooved surface in a hydrodynamic lubrication regime is presented in this article. The parabolic approximation of the film thickness is used in order to analytically compute the pressure distribution in the fluid film. At the discontinuities of the grooved surface, the conservation of the flowrate is applied. The pressure distribution was also computed using a commercial CFD software. Different groove depths are tested using the two methods in order to establish whether the Reynolds equation is valid for low dimple aspect ratios. It is found that the Reynolds equation is not valid when the depth of the groove is comparable with its width. In the case where the width of the grooves is much larger than their depth, the obtained results (CFD and analytical) are perfectly similar. The load-carrying capacity and the friction force of the couple are also computed.