A Conformal Lubricated Contact of Cylindrical Surfaces Involved in a Non-Steady Motion

Abstract

A non-steady problem for a conformal elastohydrodynamically lubricated (EHL) contact of two infinite cylindrical surfaces with parallel axes is considered. It takes into account the elasticity of cylinders, lubricant viscosity, contact surface velocities, and the applied load. The problem is solved based on the “modified” formulation proposed by Kudish et al. (2000) which is free of such defects as discontinuity of its solution and independence of the solution from some of the initial data. The problem is reduced to a system of nonlinear integro-differential equations. The additional conditions include initial and boundary conditions and Newton’s second law applied to the internal cylinder motion. The main emphasis of the paper is three fold: the analysis of the transient dynamics of the system under constant external conditions and due to abrupt changes in applied load, and the system behavior in the case of a bump/dent presence on the shaft surface. The numerical solutions exhibit damped oscillatory behavior while approaching a steady state. It is observed that in a transient motion the radial displacement of the shaft center may vary by no more than 2.5 percent while the maximum pressure may vary by as much as 350 percent. Moreover, the variations of pressure are greater for stiffer materials.