# Thermal Characteristics Study of the Bump Foil Thrust Gas Bearing
## 3 Thermal Analysis
### Analysis of Influence Factors of Bearing Temperature  
Figures 8 and 9 present the top foil deformations and the dimensionless gas film pressure distributions when the rotor speed is 50 krpm and the initial minimum gas film thickness is 7 \(\mu\)m. Figure 8a,b show the calculation results of the isothermal model and THD model, respectively. It can be seen that the basic variation trends of the top foil deformations calculated by different models are the same, but the top foil deflection calculated by the THD model is larger. This is because the gas film pressure is larger when the temperature effect is considered. The top foil deformation in the inclined section is larger than that of the plane section due to the absence of the corrugated bump foil underneath. The larger foil stiffness in the plane section helps increase the bearing load capacity. It can be seen from Figure 9 that the pressure distribution under the two calculation models is basically the same. Along the circumferential direction, the gas film pressure increases sharply from the inlet area, and reaches the maximum value when the gas film transits from the inclined area to the horizontal area. Then it slowly decreases, and finally the air pressure drops to atmospheric pressure in the gas outlet area. In the radial direction, both the inner and outer outlet area are atmospheric pressure, so the pressure presents a trend of increasing first and then decreasing from the inner radius to the outer radius boundaries. There is continuous leakage of gas from the radial boundaries when the bearing is under working condition because of the pressure distribution characteristics. Compared with the isothermal model, the gas film pressure calculated by the THD model is larger than that by the isothermal model. This is due to the fact that the gas viscosity \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Values** \\ \hline Bearing inner radius \(r_{1}\) (mm) & 16 \\ Bearing outer radius \(r_{2}\) (mm) & 32 \\ Pitch ratio \(b\) & 0.4 \\ Sector tiles number \(N\) & 6 \\ Slope height \(\delta_{h}\) (um) & 40 \\ Top foil thickness \(t_{d}\) (mm) & 0.2 \\ Bump foil thickness \(t_{b}\), height \(h_{b}\) (mm) & 0.15, 0.5 \\ Bump half length \(l\), Bump pitch \(s\) (mm) & 0.98, 3 \\ Elastic modulus \(E_{b}\) (GPa) & 214 \\ Poisson’s ratio \(\gamma_{b}\) & 0.31 \\ Housing thickness \(t_{k}\) (mm) & 16 \\ Foil thermal conductivity \(k_{t}\) (W/K\(\cdot\)m) & 16.9 \\ Thrust plate thickness \(t_{z}\) (mm) & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: This is a table. Tables should be placed in the main text near to the first time they are cited. Figure 8: Deformation distribution of top foil under different thermal model. (**a**) Isothermal model; (**b**) THD model. continues to increase as the temperature rises, and the gas film thickness is reduced to a certain extent due to the thermal expansions of the thrust plate and the foil structures. Figure 10 shows the change of bearing load capacity and friction loss power with the initial minimum gas film thickness calculated by the isothermal and THD models. It can be seen from the Figure 10a that bearing load capacity decreases with the increase in the initial minimum gas film thickness. When the initial minimum gas film thickness is increased to 30 \(\upmu\)m, the gap between the thrust plate and the top foil is too large. Thus, the lubricating gas film is difficult to form, and the bearing almost has no load capacity. It can be seen from Figure 10b that the frictional loss power decreases as the initial minimum gas film thickness increases, which is because the gas film pressure is very small when the initial minimum gas film thickness is large. However, there is no obvious difference between the values of friction loss power calculated by the isothermal model and the THD model.