Numerical Method for Studying Bearing Gap Pressure Wave Development and Subsequent Performance Mapping of Externally Pressurized Gas Journal Bearings

Abstract

In previous work, numerical methods were developed to determine the pressure waves (pressure distribution) in the bearing gap of round externally pressurized gas bearings (EPB’s) that were pressurized through porous liners (PL bearings) or through liners with rows of feedholes (FH bearings). When integrated and differentiated these pressure portraits yield the net hydrodynamic force (FH) between the shaft and the bushing and the mass flow rates through the bearing gap. These results successfully replicated force-deflection curves and mass flow rate data for experimentally tested prototype FH and PL bearings over a wide range of mass flow constriction and clearances. Subsequently the numerical study was expanded to a broader design space of clearance and mass flow compensation. Also, a bearing performance mapping method of mapping the normalized bearing load over the clearance-eccentric deflection plane was developed for different levels of mass compensation. These performance maps produced a very interesting result as they indicated certain areas in the design space of FH bearings where static instability (negative stiffness) would be encountered. This static instability was not observed in the experimental data but is noted in references as known to occur in practice. Because this numerical method is based on the development of pressure wave portraits, the FH pressure wave could then be “dissected” in the areas of the onset of static instability which gave much insight as to the possible causes of static instability. This initial work, then, was perhaps the first to predict where in design space static instability would occur and yield some insight via examination of the corresponding pressure waves as to the cause. The numeric techniques developed, however are in no way limited to non-rotating bearings but are extensible to rotating bearings. The method is also easily extensible to examination of any configuration of feedholes or orifices. Nor is it limited to parallel deflections but can yield results for unbalanced loads. The method is also not limited to round bearings but can be applied to any cross-section configuration of bearing gap cross section such as a 3 lobed bearing or a slotted 3 lobed bearing. Examination of the resulting pressure wave development patterns for different scenarios can be examined to garner insight as to the causes of differing performance that can be applied to alterations towards optimization. Thus sharing in detail the developed numerical method underlying these studies seems worthwhile.