# Effect of Thermal Boundary Condition on Tilting Pad Journal Bearing Behavior
## 3 Simulation Results and Discussion
### Bearing Thermal Behavior  
This section illustrates the bearing thermal behavior with different thermal boundary conditions. In order to understand the tendency of the change in static and dynamic characteristics of the bearing in the previous section, it is necessary to look closely at the change in the thermal characteristics of the bearing in this section. Figure 10(a),b illustrates the pad temperature at 75% circumferential position and peak temperature, respectively. The 75% temperature is measured at 75% of the bearing pad circumferential and journal spin direction. They produce almost identical results; that is why the API standard requires 75% temperature as a maximum pad temperature. Increasing pad boundary temperature (T\({}_{\text{Pad}}\)) increases pad maximum temperature, which can be easily expected. An increase in the shaft boundary temperature (T\({}_{\text{Journal}}\)) does slightly decrease the pad temperature. Figure 10: Nondimensionalized dynamic characteristics: (**a**) \(k_{xx}\); (**b**) \(k_{yy}\); (**c**) \(c_{xx}\); (**d**) \(c_{yy}\). Figure 11: Bearing thermal characteristics: (**a**) 75% bearing pad temperature; (**b**) peak bearing pad temperature; (**c**) peak lubricant temperature; (**d**) peak journal temperature; (**e**) non-dimensional journal thermal expansion; (**f**) non-dimensional minimum film thickness. Figure 11c shows an interesting phenomenon regarding the maximum oil film temperature. The maximum oil film temperature is an important factor closely related to the bearing pad Babbitt life and oil oxidation. The pad boundary temperature (T\({}_{\text{Pad}}\)) has a greater influence on the peak lubricant temperature than the oil supply temperature (T\({}_{\text{Lube}}\)). It can be seen that the maximum lubricating oil temperature change when increased from 0 \({}^{\circ}\)C to 80 \({}^{\circ}\)C is more sensitive to the pad boundary temperature change (\(\Delta\)T\({}_{\text{Pad}}\)) than the lubricating oil supply temperature (\(\Delta\)T\({}_{\text{Lube}}\)). Maximum shaft temperature is more closely related to the lubricant supply temperature (\(\Delta\)T\({}_{\text{Lube}}\)) than the shaft boundary temperature (\(\Delta\)T\({}_{\text{Journal}}\)) as shown in Figure 11d. Figure 11e shows the non-dimensional thermal expansion of the journal, which is the ratio of journal radial thermal expansion at the axial center and bearing clearance (\(C_{b}\)). The thermal expansion of the journal seems to be more sensitive to the change in the lubricant supply temperature (T\({}_{\text{Lube}}\)) than the change in the boundary temperature of the shaft (T\({}_{\text{Journal}}\)) and bearing pad (T\({}_{\text{Pad}}\)). This is believed to be due to the direct contact of the supply lubricant with the journal. Figure 11f shows the non-dimensional minimum film thickness, which is the ratio of minimum film thickness and bearing clearance (\(C_{b}\)). Increasing the pad boundary (T\({}_{\text{Pad}}\)) and supply oil temperature (T\({}_{\text{Lube}}\)) reduces the minimum oil film thickness, but increasing the journal boundary temperature creates a complex tendency to increase and decrease the minimum oil film thickness. The results shown in Figure 11f are related to this phenomenon depicted in Figure 9a. With the increasing boundary temperature of pad (T\({}_{\text{Pad}}\)) and increasing lubricant supply temperature (T\({}_{\text{Lube}}\)), eccentricity ratio was increasing, while increased shaft boundary temperature (T\({}_{\text{Journal}}\)) decreased the eccentricity ratio. Reduced eccentricity ratio is analogous to the increased minimum film thickness. Figure 12 shows the cross-section view of the temperature distribution on spinning journal, lubricant, and bearing pads at the axial center position. Lubricant thickness is exaggerated for the readers to recognize the fluid film temperature easily. Figure 12a,c,e are 1000 rpm cases and b,d,f are 3600 rpm cases. Increased rotor spin speed produces higher maximum temperature.