## 5 Rotordynamic Performance Analysis of GFPBs
In addition to the pressure, the minimum film thickness region becomes widened at the thick polymer layer, which indicates that a wide wedge shape is needed to support the same static load owing to the low structural stiffness of the thick polymer layer. This can be advantageous in terms of load performance of the bearings, since wider fluid-film pressure generally can support the higher static load under a same minimum fluid-film thickness, which is also a main advantage of GFBs in comparison to rigid gas bearings [35]. Figure 7: Predicted journal eccentricity and journal attitude angle versus the rotor speed and polar plot of journal equilibriums positions depending on the polymer layer thickness. Synchronous force coefficients of the fluid film of the GFPBs are estimated via the perturbation analysis of journal harmonic motions, and direct stiffness (\(k_{XX}\), \(k_{YY}\)) and damping (\(c_{XX}\), \(c_{YY}\)) results are shown in Figure 9. As the polymer layer thickness increases, direct stiffness and damping coefficients in both directions become reduced. The reductions in direct stiffness are predictable results because higher polymer thickness means lower structural stiffness. However, it is interesting that higher thickness does not generate higher direct damping coefficients of the fluid film; rather, it decreases the damping. Figure 8: Predicted fluid-film pressure and thickness distributions at a rotor speed of 50 krpm depending on the polymer layer thickness. Figure 9: Predicted synchronous force coefficients versus the rotor speed depending on the polymer layer thickness: direct stiffness coefficients and direct damping coefficients. In GFB, the direct stiffness and direct damping coefficients are generally inversely proportional to the bearing clearance [29]. In other words, a smaller bearing clearance reduces the average gas-film thickness and the journal forms its equilibrium position near the bearing center, so that the gas film provides high direct stiffness and direct damping to the journal motion. However, the increase in the polymer thickness of GFPB causes the journal to move away from the bearing center, as shown in Figure 7. Therefore, the average gas-film thickness increases as shown in Figure 8, resulting in a lower direct stiffness and direct damping coefficients of the gas film. In addition to the reduction, asymmetry of \(k_{XX}\) and \(k_{YY}\) decreases with increasing polymer layer thickness, yielding circular journal orbits. From the point of vibration amplitude, circular orbits are preferable, since their vibration amplitude is smaller when going through a critical speed compared to the major axis of an elliptical orbit [36]. Predicted cross-coupled stiffness (\(k_{XY}\), \(k_{YX}\)) is shown in \[\frac{1}{\gamma_{GFPB}}=\frac{k_{GFPB}}{k_{p}\gamma_{p}}+\frac{k_{GFPB}}{k_{b} \gamma_{b}} \tag{15}\]0 They also get reduced significantly with increasing polymer layer thickness, and \(k_{XY}\) is more sensitive to the thickness than \(k_{YX}\), which indicates that the differences in magnitude of \(|k_{YX}-k_{YX}|\) become small at high thickness. This implies a better rotodynamic stability because it means small destabilizing energy added to the rotor-bearing system [37; 38]. Cross-coupled damping coefficients are omitted in the paper for brevity.