Modeling fluid inertia forces of short journal bearings for rotordynamic applications

It has been recently suggested that fluid inertia may play an important role in the dynamic behavior of rotors supported on journal bearings. This paper presents a model for fluid inertia forces in short cylindrical journal bearings based on an energy approximation. The inertialess velocity profiles predicted by the solution of Reynolds' equation are inserted in the axial momentum equation multiplied by the axial velocity profile and integrated across the film thickness, to obtain the pressure in short journal bearings including the fluid inertia effect. The pressure is then integrated to obtain the fluid inertia forces. It is shown that the inertia forces thus obtained are proportional to the usual radial, centripetal, tangential and coriolis accelerations of the journal, in addition to a nonlinear radial acceleration. Moreover, it is shown that the inertia forces contribute to the stiffness and damping characteristics of the journal bearings. The inertia coefficients of the bearings are obtained in cartesian and cylindrical coordinates, for both uncavitated and cavitated bearings, and are plotted versus the eccentricity ratio. The model thus obtained is an approximate analytical closed form model for fluid inertia forces in short journal bearings. Such a model is the most suitable for rotordynamic applications, particularly for time transient rotordynamic simulations.