On the Effect of Lubricant Inertia in the Theory of Hydrodynamic Lubrication

Abstract

A theoretical study is made of the corrections required to the basic lubrication equations to allow for small effects of lubricant inertia in the laminar regime. The problem is approached by first determining the stream function for a wedge-shaped oil film with purely viscous flow and then obtaining the first-order correction for inertia. For the particular case when the convergence of the film is small, the resulting expressions for pressure gradient and tangential drag are compared with those obtained by other methods. Close agreement is found with Kahlert’s equations, but the present expressions are more general in form. It would appear that, in general, the effect of lubricant inertia is to cause a slight increase in the load capacity of a bearing.