Analytical study of the velocity of the lubricating fluid in the hydrodynamic journal bearing with the effect of centrifugal force for short bearing type

The paper aims to obtain the expression of the velocity of lubricating fluid in the hydrodynamic journal bearings by analytical method. In the classical short-bearing theory, the fluid flow was studied by ignoring the effect of centrifugal force of the lubricating fluid film. However, the self-oscillation of the shaft of high-power motors does not follow the rules in classical hydrodynamic lubrication theory. To explain this phenomenon, a modified form of Reynolds equation, in which the influence of centrifugal force of the lubricant is not ignored, is established. The study aims to establish the modified Reynolds equation by including the effect of centrifugal forces for the case of the short bearing type. Integration of the Navier-Stokes equations, yield the expressions for the components of velocity of the lubricating fluid in the gap. The oil's pressure in the hydrodynamic journal bearing is obtained by solving the modified Reynolds equation. The numerical results are considered in the case of the stable equilibrium position of the motion of the shaft, i.e. the symmetry axis of the shaft does not move. The plots of the velocity components in the tangential axial direction are displayed too. The theoretical results of a parabolic velocity distribution similar to that of a Newtonian fluid, derived from a Bingham plastic flow model. The flow in the gap, which are obtained by analytical method, are completely consistent with its boundary conditions and its physical properties. Further, with these results, the paper as a lemma to solve the dynamics problem in floating ring bearing with the influence of the centrifugal force of the lubricant