## 5 Rotordynamic Performance Analysis of GFPBs
The result shows that \(k_{GFPB}\) becomes identical to \(k_{p}\), whereas \(\gamma_{GFPB}\) approaches \(\gamma_{b}\) at a thick thickness. Notably, inserting a polymer layer into the GFB significantly reduces the structural stiffness of the bearing, which is accompanied by increased structural loss factor. This result implies that the engineer can properly tune bearing stiffness and damping with polymer thickness; this is a flexible and easy way for engineers. Similar consequence also can be observed in the dynamic test for structural parameter identification of GFBs and GFPBs in the early study conducted by [PERSON] et al. [3]. As a next step, the following performance analysis is conducted with the assumption that analysis bearings having a designed radial clearance of 200 \(\upmu\)m are adjusted to have the clearance of 50 \(\upmu\)m by inserting metal shims beneath the bottom foil, while not changing the inner radius of the polymer layer. That is because the bearing radial clearance is usually less than 50 \(\upmu\)m in most practices [30]. Note that the bearing clearance was intentionally designed as large to adjust the value as we want. The journal is subjected to a static load of 49.1 N in \(X\)-direction, which corresponds to a journal mass of 5 kg. The important design parameter for GFPBs, that is, polymer layer thickness \(t_{p}\), changes from 1 to 10 mm during the analysis. Figure 7 shows a change in journal equilibrium positions determined by the eccentricity and attitude angle depending on the polymer layer thickness as the rotor speed changes. The nondimensional form of the eccentricity is calculated from \(e/Cr\) where \(e=\left(e\chi^{2}+e\gamma^{2}\right)^{1/2}\). As the polymer thickness increases, the eccentricity becomes increased significantly, i.e., the equilibrium position shifts away from the bearing center. On the other hand, the attitude angle shows a decrease trend with an increasing the thickness. These  
Figure 6: Predicted structural stiffness per unit area and structural loss factor versus the polymer layer thickness. Outer radius of the polymer layer is varied, while the inner radius remains as 20.92 mm. changes are mainly attributed to the small structural stiffness of GFPBs with the thick polymer layer. Another thing to discover is that as \(t_{p}\) increases, the slope of eccentricity and attitude angle with rotating speed decreases slightly. That is, as \(t_{p}\) increases, the change in the journal position to the speed becomes less sensitive, which is important information in the layout design of the rotating machinery. The journal position information including the journal eccentricity and the attitude angle enables us to speculate the stability of GFPBs in terms of subsynchronous motions, i.e., self-excited whirls in gas bearings. It is popularly assumed that the high eccentricity and the low attitude angle indicate a potentially stable bearing [31; 32; 33], because these conditions contribute to reduce the cross-coupled effect of the fluid film of bearings, which is one of main causes for instability in gas bearings. These desired conditions can be achieved by utilizing a thick polymer layer in GFPBs according to the results in Figure 7. However, note that too-thick polymer layers might cause other practical problems because they produce journal's high eccentricity of several hundred micrometers; for example, excessive radial shift of a rotor core on the rotor shaft in induction motors can bring about an electromagnetic excitation on the rotor shaft [34]. Therefore, the selection of the polymer layer thickness in bearing design requires a comprehensive judgment including the layout of the other components and the interference with other parts. Fluid-film pressure and thickness distributions for polymer layer thickness of 1, 5, and 10 mm at a rotor speed of 50 krpm are shown in the Figure 8. It can be seen that the thick polymer layer reduces the peak value in the pressure and widens the pressure distribution.