A SHORT BEARING THEORY FOR PARTIAL-ARC BEARING INCLUDING CAVITATION AND MISALIGNMENT EFFECTS

This work is a development of a particular mathematical technique for short journal bearing problems. In lubrication problems the Reynolds' equation has nonconstant coefficients and this complication prevents one from finding an exact solution for the pressure field. To solve this type of problem we are forced to resort to either approximate solutions or to numerical solutions. Among the approximation methods used is the method of matched asymptotic expansions. A small parameter (lamda) (e.g. the aspect ratio) is used as the perturbation parameter. The solution is usually represented by a perturbation expansion. The straightforward expansion in powers of the parameter have limited regions of validity; this solution breaks down in certain regions called boundary layer regions. To render these approximations uniformly valid one must use an asymptotic series expansion for this domain. To relate the inner and outer expansion a so-called matching procedures is used. Consequentially, a uniformly valid composite expansion for the fluid film pressure is determined.; The present work is an application of asymptotic theory to treat fluid film cavitation in bearings. The effects of non-Newtonian lubricants and misaligned bearing geometry is studied. The geometrical pattern of the cavitation bubble generally depends on the bearing aspect ratio, operating eccentricity and cavity pressure. Comparisons have been made between this asymptotic theory result and other short bearing theories. The performance of loaded, liquid-lubricated, partial-arc hydrodynamic journal bearings with shaft misalignment is shown. The misaligned problem is restricted to journal tilts about two axes. An asymptotic approximation theory is given for the fluid film pressure distribution. The load due to the lubricant pressure acting on the journal is derived for steady state, isothermal conditions. A result of bearing misalignment is the reduction of the bearing load capacity based on a fixed minimum film thickness. The pressure peak shifts from the axial centerplane toward the bearing end with higher eccentricity. To maintain the skewed pressure distribution an external torque must be applied to the journal. The asymmetric cavitation boundary is determined and compared to the aligned case. The finite difference method is adopted to check the reliability of the asymptotic scheme. Results from other published numerical methods and experiments are used to compare with this approximate solution. The asymptotic expansion solution shows good agreement with these data sources.