Porous Gas Journal Bearings: An Exact Solution Revisited and Force Coefficients for Stable Rotordynamic Performance

Having come of age, gas film bearings enable high-speed oil-free (micro) rotating machinery with gains in efficiency and reliability, longer maintenance intervals, and a reduction in contaminants released to the atmosphere. Among gas bearing types, porous surface gas bearings (PGBs) have proven successful for 50+ years and presently are off-the-shelf mechanical elements. This paper reviews the literature on PGBs since the 1970s and reproduces an exact solution for the performance of cylindrical PGBs. Both the analytical model and an accompanying finite-element (FE) model predict the performance for two PGBs, a commercially available 76 mm diameter bearing and a smaller 25 mm diameter laboratory unit whose experimental performance is available. As expected, the FE model results reproduce the analytical predictions obtained in a minuscule computing time. For a set external supply pressure, as the radial clearance increases, the flow rate through the bearing grows until reaching a peak magnitude. The PGB load capacity is a fraction of the product of the set pressure difference (p(S) - p(a)) and the bearing projected area with a significantly large centering static stiffness evolving over a narrow region of clearances. Operation with shaft speed enhances the bearing load capacity; however, at sufficiently high speeds, significant magnitude cross-coupled forces limit the stable operation of a PGB. At constant operating shaft speed, as the whirl frequency grows, the bearing effective stiffness (K-eff) increases, while the effective damping (C-eff) becomes positive for whirl frequencies greater than 50% shaft speed. Similar to a plain hydrodynamic journal bearing, the PGB is prone to a half-frequency whirl, albeit the system natural frequency can be high, mainly depending on the external supply pressure. In essence, for the cases considered, PGBs are linear mechanical elements whose load capacity is proportional to the journal eccentricity.