## 13 Conclusions  
Porous surface gas bearings (PGBs) have come of age to enable high-speed, near friction free rotating machinery with improved reliability and availability. In the last decade (2012 and onward), numerous computational analyses for calculation of PGB forced performance, static and dynamic, have appeared. Most analyses, however, tackled the flow physical equations by computer while ignoring the vast body of archival literature on the subject. The paper reviews the archival literature on PGBs and reproduces, using modest analytical means, an exact solution to the flow field and forced performance of a cylindrical PGB. This solution has been available since 1979 [5]. Predictions from the analysis serve to validate the results of a finite element computational model. Further comparisons to recent experimental results validate the analysis results and serve to elucidate the effect of external pressure and shaft speed on PGB performance. The learning from this work is as follows:  
* For a given external pressure, the supplied flow rate increases quickly as the bearing clearance enlarges and ultimately reaches a flow limit. * There is a narrow clearance region that ensures the maximum centering stiffness for a PGB. Selecting the appropriate clearance is necessary and rather difficult to \begin{table}
\begin{tabular}{c c} \hline \hline Bearing Length, \(L\) & 57 mm \\ \hline Inner diameter, \(D\) & 25 mm (*) \\ Radial clearance, \(c\) & 16 μm, 31 μm \\ \hline Porous layer radial thickness, \(t_{p}\) & 2.5 mm \\ permeability coefficient, \(\kappa\) & 1.0 \(\times\) 10\({}^{-15}\) m\({}^{2}\) \\ Equivalent clearance porous layer, \(c_{\kappa}\) & 3.1 μm \\ \hline Supply pressure, \(p_{S}\) & 4–6 bar (*) \\ Exit pressure, \(p_{a}\) & 1 bar \\ Ambient temperature, \(T\) & 293 K \\ \hline Air density at (\(p_{a}\), \(T\)), \(\rho_{a}\) & 1.2 kg/m\({}^{3}\) \\ viscosity at (\(p_{a}\), \(T\)), \(\mu\) & 18.5 \(\times\) 10\({}^{-6}\) Pa-s \\ \hline \multicolumn{2}{c}{For \(c\) = 0.031 mm, \(p_{S}\) = 4.7 bar, and} \\ \multicolumn{2}{c}{\(\Omega\) = 2513 rad/s (24 krmm)} \\ Feed flow parameter & \(\Lambda_{\kappa}\) = 0.025 \\ Speed number & \(\Lambda_{\Omega}\) = 0.097 \\ \hline \hline \end{tabular} (*) Assumed since [23] has many clerical mistakes, as confirmed by one of the authors [28]. Ref. [23] also uses gauge pressure to report \(p_{s}\).  
\end{table} 
Table 3: Operating conditions and dimensions of a cylindrical PGB reported in Ref. [23]. achieve when also considering manufacturing costs and devising procedures for easy installation. * The load capacity of a PGB under aerostatic conditions is a fraction of the imposed pressure difference and the bearing projected area (\(L\times D\)). The bearing load is proportional to the static eccentricity. * Under aerodynamic conditions, i.e., operation with shaft speed, the PGB load capacity still remains proportional to shaft eccentricity and can be much larger than the aerostatic load. That is, shaft speed shear flow effects increase the PGB load capacity. * For operation as the shaft speed varies from low (start-up) to the mean operating speed (MOS = \(\Omega\)*) and above, the PGB bearing shows synchronous excitation (\(\omega\) = \(\Omega\)) force coefficients that increase in magnitude as \(p_{S}\) increases. Most importantly, as the shaft speed increases, \(K_{\mathit{eff}}\) increases (hardens) while C\({}_{\mathit{eff}}\) decreases rapidly. * For operation at a constant (high) speed, the bearing effective stiffness (\(K_{\mathit{eff}}\)) decreases at low whirl frequencies, reaches a dip or minimum at 1/2 whirl frequency operation (\(\omega\) = 1/2 \(\Omega\)), and then increases (hardens) as the frequency approaches synchronous speed (\(\omega\) \(\rightarrow\) \(\Omega\)) and surpasses it. The bearing effective damping coefficient \(C_{\mathit{eff}}\) < 0 at low frequencies and equals zero at \(\omega\) = 1/2 \(\Omega\).