Nonstationary analytic model of hydrodynamic rolling lubrication

Abstract

A model of normal oscillations of a roller moving along the surface at a constant speed in the presence of a liquid lubricant layer is considered. The pressure distribution along the lubricant layer is obtained by integrating the Reynolds equation, taking into account both the tangential and normal speed of the roller relative to the support surface. An analytical solution of this equation is constructed by the method of asymptotic expansion in a singular small parameter. The solution contains both regular terms of the expansion in powers of a small parameter and boundary-layer functions that rapidly decay over time.