## 3 An Appraisal of the Past Literature
In a companion paper, [PERSON] [16] described the outcome of experiments that for the most part validated the theoretical predictions, in particular the PGB load capacity and the direct force coefficients. The test bearing has \(L=D=50.4\) mm and a porous liner with thickness \(t_{p}=6.4\) mm and permeability \(\kappa=2.3\times 10^{-9}\) mm\({}^{2}\) (\(c_{\kappa}=5.6\)\(\mu\)m). The experiments also revealed the onset of unstable behavior characterized by vibrations of the test system at its natural frequency. The tests conducted with various radial clearances, \(c=3\) to 17 \(\mu\)m, demonstrated that the test aerostatic PGB produced a journal displacement directly proportional to the applied load, even up to the point of journal contact with the porous liner surface. Hybrid operation, i.e., with shaft rotation (\(\Lambda_{\Omega}>0\)), increases the PGB load capacity and its stiffnesses, direct and cross-coupled. Incidentally, the higher the supply pressure, the larger the bearing centering stiffness (and natural frequency), and hence the more likelihood of a PGB to be tailored for dynamically stable operation. After a long hiatus, in 2006, [PERSON] et al. [17] assessed the stability of a rotor supported on PGBs coated with a surface layer that was \(\sim\)300 times more restrictive than that of the porous media itself. The manufacturing of surface loaded porous materials is a major breakthrough in PGBs, as they practically eliminate the potential for pneumatic hammer; see [PERSON] et al. [18]. In practice, PGBs are mounted in series with elastomeric supports (o-rings) to add more effective damping, albeit the soft mounts also reduce the system natural frequency. See for example the synopsis by [PERSON] [14]. Most recently, various publications detail the application of tilting pad PGBs to enable oil-free turbomachinery operating at high speeds; see [PERSON] et al. [2; 4; 19; 20] and [PERSON] et al. [21; 22; 23]. Tilting pad journal bearings effectively eliminate the cross-coupled stiffness coefficient that could easily excite a hydrodynamic instability and thus extend the maximum operating shaft speed of rotor-bearing systems. At Texas A&M University, since 2015, [PERSON] et al. have been conducting measurements of the rotodynamic response of solid rotors supported on carbon-graphite PGBs: one rotor of small diameter (29 mm) and operating at a high shaft angular speed (55 krpm) [19], and another with large diameter (100 mm) and turning at 18 krpm maximum [4; 20]. The rotors' surface speeds (\(U_{s}=\Omega R\)) equal 82 m/s and 94 m/s, respectively. Rotodynamic tests show stable responses, free of sub synchronous whirl frequencies. Imbalance mass induced synchronous whirl speed rotor motion amplitudes show peak magnitudes while crossing critical speeds largely determined by the pressure (\(p_{S}\)) supplied to the bearings. Derived from recorded amplification factors, the system damping ratio is larger than 10%, uncharacteristically high for gas bearing supported rotors. The computational analysis in [4] solves the Reynolds equation and Darcy's diffusion equation that couple the flow in the PGB film land to that through the porous layer. The model produces force coefficients that agree well with experimentally-derived effective damping and stiffness coefficients and shows that the magnitude of supply pressure (\(p_{S}\)), the permeability coefficient (\(\kappa\)), the pad-pivot stiffness, and the assembly clearance affect significantly the performance, static and dynamic, of the test bearings. In addition, just published in 2021, [2] describes an experimental campaign and the results that quantify the force coefficients of a large size, four tilting pad PGB. From dynamic load experiments conducted with shaft speeds at 6 and 9 krpm (32 and 64 m/s surface speed), the identified PGB's direct stiffness and damping coefficients are practically invariant with excitation frequency (to max 200 Hz). The pads' pivot compliance largely determines the bearing direct stiffness coefficients.