## 4 Model Validation via Static-Load Deflection Test  
The static-load deflection test in the gas bearing field generally represents a test that identifies a relationship between applied static loads and deflection of the bearing substructures [26]. Ref. [3] also carried out the static-load deflection tests with a test journal GFPB and GFB to identify assembled radial clearance of the bearings; however, the tests is performed for validating the simple structural model. Figure 4 shows the configuration of the static-load deflection test rig setup and a test GFPB. A test GFPB has a bearing length of 30 mm and a designed radial clearance of 200 \(\upmu\)m for a journal that has 40 mm diameter. The polymer layer, nitrile butadiene rubber (NBR), a kind of natural rubber, is used. NBR has excellent oil and abrasion resistance and is widely used for O-rings and seals. The operating temperature is \(-\)55-125 \({}^{\circ}\)C, and it has stable heat resistance. NBR has excellent damping characteristics compared to general engineering rubbers such as natural rubber (NR), stylene butadiene rubber (SBR), and ethylene propylene diene monomer (EPDM). Therefore, in this study, NBR polymer with a thickness of 2.0 mm (\(t_{p}\) = 2.0 mm), \(r_{in}\) = 20.92 mm, and \(r_{o}\) = 22.92 mm is applied to the bearing; a plate made of NBR was cut to fit the size of the bearing, then rolled up and inserted into the bearing. The design parameters for the foil structures and polymer layer are listed in Table 1. On the other hand, the bump foil is fabricated by the press process with a flat-shaped tooling (die) with a forming load of 30 MPa. [PERSON] et al. [27] reported that at least a load of 28 MPa is required to achieve the designed bump shapes. As for the test rig, a stationary shaft with a diameter of 40 mm is fixed on a lathe with a three-jaw chuck and tail chuck. A test bearing is installed on the shaft, and it can be \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parts** & **Parameters** & **Values** \\ \hline Journal & Diameter & 40.00 mm \\ \hline \multirow{2}{*}{Bearing} & Length & 30.00 mm \\  & Nominal radial clearance (designed) & 0.20 mm \\ \hline \multirow{6}{*}{Bump foil} & Thickness & 0.127 mm \\  & Height & 0.508 mm \\  & Pitch & 4.572 mm \\  & Half length & 1.810 mm \\  & Young’s modulus & 214 GPa \\  & Poisson’s ratio & 0.29 \\  & Friction coefficient & 0.1 \\  & Stiffness per unit area (free-free) & 8.7 \(\times\) 10\({}^{9}\) N/m\({}^{3}\) \\ \hline Top/bottom foil & Thickness & 0.127 mm \\ \hline \multirow{6}{*}{Polymer layer} & Thickness & 2.0 mm \\  & Young’s modulus & 1.2 MPa \\  & Poisson’s ratio & 0.33 \\ \cline{1-1}  & Polymer loss factor & 0.49 \\ \cline{1-1}  & Inner radius & 20.92 mm \\ \cline{1-1} \cline{2-4}  & Outer radius & 23.42 mm \\ \cline{1-1}  & Material & Nitrile butadiene rubber \\ \cline{1-1}  & Stiffness per unit area & 2.9 \(\times\) 10\({}^{9}\) N/m\({}^{3}\) \\ \hline \hline \end{tabular} The top, bump, and bottom foils are made of Inconel X-750.  
\end{table} 
Table 1: Specifications of the test and analysis GFPB. Figure 4: **(a)** Fabricated test GFFB and (**b**) measurement setup of the static-load deflection test with a stationary shaft and a moving bearing housing. moved to one axis by a latch tool. The lathe tool achieves forward and backward motions for the test bearing, which are measured by an eddy-current displacement sensor (BENTLY NEVADA 3300 XL NSV). When the test bearing moves over its nominal radial clearance, the bearing sub-structures come into contact with the test shaft, generating a reaction force. The force is measured by a load cell (CURIOTECH CSBA-50L) located between the test bearing and latch tool. The uncertainty of the measured displacement and force is estimated to be 2 and 3%, respectively, at room temperature 21 \({}^{\circ}\)C. For a detailed description of the test procedure, refer to Ref. [26].