## 7 Conclusions  
The scope of this paper includes development of the simple structural model for journal GFPBs and performance analysis with respect to the polymer layer thickness.  
The polymer layer in a GFPB is modeled as a thick elastic cylinder having an elastic modulus and a Poisson's ratio. Assuming a plane strain condition for the differential element of the polymer layer enables us to calculate the stress and strain relation as well as the equivalent structural stiffness; the model is called to the structural elasticity model of  
Figure 12: Predicted effective stiffness and damping versus the rotor speed depending on the polymer layer thickness.  
polymer layers. The model is combined with a structural deflection model for GFPBs with equivalent springs of bump foils and the polymer layer.  
The presented models for the GFPB are validated by comparing prediction results with those estimated from the static-load deflection tests. The comparison yields reasonable displacement and stiffness relations compared to the tests, validating the proposed structural model for GFPBs in the limited condition where lightly loaded and low-speed regions that the viscoelastic effect is not dominate. The simple model allows us to easily understand the structural mechanism of GFPB. For example, it is possible to intuitively analyze how the structural characteristics of bump foil and polymer are each and what characteristics they have when they are connected in series.  
Next, performance analysis is performed for the GFPB depending on the polymer layer thickness ranging from 1 to 10 mm with a journal mass of 5 kg and nominal clearance of 50 \(\upmu\)m. The thick polymer layer significantly changes equilibrium positions of GFPBs, in particular, increasing the polymer layer thickness makes journal positions more eccentric with low attitude angle; this finding gives us the understanding that using a thick polymer layer is beneficial for weakening cross-coupled effects of the gas film. Note that it makes sure that utilizing a high thickness also accompanies large eccentricity of the journal, which may cause practical problems in applications.  
Finally, stability performance of GFPBs is examined with assumption that the journal is supported by linearized springs and dampers and moves around its centered position. Analysis results reveal that there is optimized thickness of the polymer layer in terms of damping characteristics of GFPBs; in this study, the \(t_{p}=3\) mm case has the highest effective damping over all rotating speeds.  
Consequently, the presented structural model for GFPBs provides a reasonable performance prediction in the limited condition. The selection of the appropriate thickness considering effective stiffness and damping characteristics will determine the performance of GFPBs. We plan to design and manufacture test GFPBs with various polymer thicknesses through the simple structural model presented in this study and verify static and dynamic performance through a rotor dynamics test. Through this, we aim to provide guidelines for integrated bearing analysis, design, and application of GFPB.  
Conceptualization, K.S.; methodology, K.S.; model development, J.P.; experimental validation, J.P.; formal analysis, J.P.; writing--original draft preparation, J.P.; writing--review, K.S.; visualization, J.P.; supervision, K.S.; project administration, K.S.; funding acquisition, K.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 2018201010633B).  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.