Squeeze film flow in smooth but arbitrarily shaped infinite journal bearings is considered. The nonrotating shaft is subject to small sinusoidal oscillations. An analytic solution is presented which improves on the lubrication theory by including inertia terms in the equations of motion. The solution technique is to introduce a stream function by which the problem can be reduced to a linear partial differential equation, with time varying boundary conditions, which can be solved by conventional means. The solution to an illustrative problem is presented—the circular journal and bearing. The velocity field and pressure distribution differ qualitatively from those predicted by lubrication theory due to the existence of out-of-phase components. The results show that the lubrication solution for the amplitude of load and pressure can be significantly in error for high Reynolds number operation of a bearing at low eccentricity ratio. At high eccentricity ratios, however, the lubrication theory can be used with confidence, even at very extreme (high Reynolds number) conditions. Simple approximate closed form expressions for pressure and load are presented which are sufficiently accurate for engineering use (error <3 percent) in the range of practical applications.
The Technique of an Interconnection Problem of the Hydrodynamic Lubrication Theory and the Nonlinear Dynamics for Mechanical Systems “An Elastic Crankshaft on Journal Bearings”
