An exact analytical solution for dynamic loads generated by imperfect lubricated journal bearings in multibody systems

This work presents a precise analytical solution of the Reynolds equation governing the lubrication of journal bearings, this solution is valid for either an infinitely long or an infinitely short bearing, based on the side leakage condition applied. The pressure distribution solution is analytically integrated to obtain the forces generated by the lubricant in supporting external dynamic loads in imperfect journal bearings joints. The analytical solution for both the pressure distribution and the forces generated by the lubricant has been corroborated through numerical validation. This solution was implemented on two distinct multibody mechanical systems: one comprising two bodies interconnected via a lubricated imperfect journal bearing, and the other being the conventional crank-slider mechanism with a lubricated imperfect joint. The outcomes are demonstrated for both long and short journal bearings. The results indicate that an increase in side leakage diminishes the pressure at the ends of the joints and amplifies the axial pressure gradient, which, in turn, elevates the eccentricity required to generate sufficient hydrodynamic forces from the lubricant to support the external load. When exposed to identical external dynamic loading, the central axis of a short journal bearing delineates a trajectory that manifests a pronounced lubricant force overshoot. This phenomenon arises from the diminished viscous damping in short journal bearings, attributable to increased side leakage, in contrast to their long journal bearing counterparts.