Effect of Fluid Inertia on Journal Bearing Parameters

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Abstract
In the modeling and analysis of rotordynamic systems with journal bearings, the stiffness and damping parameters are usually obtained from the Reynolds equation of hydrodynamic lubrication. The Reynolds equation is derived from the continuity and momentum equations with several assumptions; the principal one among them being that the inertia terms are negligible since the lubricant flow is viscosity-dominated. Some previous work has shown, however, that the effect of fluid inertia on the static and dynamic properties of a bearing is not negligible in many circumstances. This paper uses a perturbation approach to present a rigorous derivation of the correction terms to be added to account for the effect of inertia in the case of a journal on a short bearing. The governing equation for pressure correction is derived and the corrected stiffness, damping, and inertia coefficients to the first order are displayed as a function of the equilibrium position.