# Effect of Thermal Boundary Condition on Tilting Pad Journal Bearing Behavior
## 2 Numerical Methods
### Simulation Model  
To investigate the effect of thermal boundary condition on TPJB behavior, the THD lubrication model is adopted. Lubricant and bearing material properties are provided in Tables 2 and 3, respectively. As described in Table 4, bearing load is applied between pads (LBP). The simulated bearing model is described in Figure 7 where geometry and load direction are described in (a) and the cross section of FE model is in (b). The FE model of shaft and bearing pads are used for the analysis of heat conduction and thermal deformation, where the FE nodal information of both temperature analysis and thermal expansion are identical. The size of the bearing used in this study was reduced being compared with the actual bearing configuration while maintaining the shape ratio of that. In order to consider the same performance as the actual bearing, the operating conditions having the same Sommerfeld number were used by changing the rotor spin speed. \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Data** \\ \hline Number of pads & 5 \\ Configuration & LBP \\ Pad arc angle (\({}^{\circ}\)) & 57.87 \\ Rotor diameter (mm) & 101.587 \\ Pad axial length (mm) & 60.325 \\ Radial pad clearance (mm) & 0.112 \\ Lubricant type & ISO VG 32 \\ Oil supply temperature (\({}^{\circ}\)C) & 43 \\ Unit load (kPa) & 1034 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test bearing parameters. [36]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Data** \\ \hline Viscosity at 40 \({}^{\circ}\)C (N-s/m\({}^{2}\)) & 0.0365 \\ Viscosity coefficient (Pa\(\cdot\)s) & 0.0297 \\ Heat capacity (J/kg\(\cdot\)\({}^{\circ}\)C) & 1,886 \\ Heat conductivity (W/(mK)) & 0.136 \\ Density (kg/m\({}^{3}\)) & 877 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Lubricant properties. Figure 6: Nondimensionalized dynamic characteristics: (**a**) \(k_{xx}\); (**b**) \(k_{yy}\); (**c**) \(c_{xx}\); (**d**) \(c_{yy}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Load Type** & **LBP** \\ \hline Number of pads & 5 \\ Pad arc length (\({}^{\circ}\)) & 60 \\ Offset & 0.5 \\ Preload & 0.4 \\ Bearing axial length (mm) & 175 \\ Pad thickness (mm) & 35 \\ Babbitt thickness (mm) & 3.5 \\ Journal diameter (mm) & 245 \\ Shaft left/right length (mm) & 175 \\ Load direction (deg.) & 270 (–y) \\ Load (N) & 60,270 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Bearing system configurations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Journal** & \\ \hline Reference temperature for thermal expansion (\({}^{\circ}\)C) & 25 \\ Therm. Exp. Coeff (1/\({}^{\circ}\)C) & 0.0000122 \\ Heat Conductivity (W/(m \({}^{\circ}\)C)) & 42.6 \\ Heat Capacity (J/(kg \({}^{\circ}\)C)) & 453.6 \\ Density (kg/m\({}^{3}\)) & 7850 \\ Young’s Modulus (Pa) & \(2.05\times 10^{11}\) \\ Poisson’s Ratio & 0.3 \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline
**Pad Material** & \\ \hline Ref. Temp. for Texp (\({}^{\circ}\)C) & 25 \\ Therm. Exp. Coeff (1/\({}^{\circ}\)C) & 0.0000121 \\ Heat Conductivity (W/(m \({}^{\circ}\)C)) & 51.9 \\ Heat Capacity (J/(kg \({}^{\circ}\)C)) & 453.6 \\ Density (kg/m\({}^{3}\)) & 7858 \\ Young’s Modulus (Pa) & \(2.00\times 10^{11}\) \\ Poisson’s Ratio & 0.3 \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline
**Babbitt Material** & \\ \hline Ref. Temp. for Texp (\({}^{\circ}\)C) & 25 \\ Therm. Exp. Coeff (1/\({}^{\circ}\)C) & 0.000021 \\ Heat Conductivity (W/(m \({}^{\circ}\)C)) & 55 \\ Heat Capacity (J/(kg \({}^{\circ}\)C)) & 230 \\ Density (kg/m\({}^{3}\)) & 7390 \\ Young’s Modulus (Pa) & \(5.3\times 10^{10}\) \\ Poisson’s Ratio & 0.3 \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline
**Housing Material** & \\ \hline Young’s Modulus (Pa) & \(1.86\times 10^{11}\) \\ Poisson’s Ratio & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties. In this study, the thermal boundary conditions around the tilting pad journal bearing system were divided into three areas. Figure 8 describes the three different areas.