# Effect of Thermal Boundary Condition on Tilting Pad Journal Bearing Behavior
## 3 Simulation Results and Discussion  
### Bearing Static and Dynamic Behavior  
Figure 9 depicts the bearing static characteristics. 1000 rpm conditions are illustrated with a square notation and 3600 rpm are illustrated with a diamond notation. Each thermal condition is drawn with different line style as described in Table 5. Firstly, the journal eccentricity ratio is drawn in Figure 9a. With the increasing boundary temperature of pad (T\({}_{\text{Pad}}\)) and increasing lubricant supply temperature (T\({}_{\text{Lube}}\)), the eccentricity ratio is increasing. On the other hands, increased shaft boundary temperature (T\({}_{\text{Journal}}\)) decreases the eccentricity ratio. Increased boundary temperature around the pad (T\({}_{\text{Pad}}\)) and supply temperature (T\({}_{\text{Lube}}\)) might tighten the bearing clearance, leading to the increased eccentricity ratio; the increased shaft boundary temperature (T\({}_{\text{Journal}}\)) might heat the lubricant and the clearance might be increased, leading to the reduced eccentricity ratio. Journal attitude angle is illustrated in Figure 9b. The ideal tilting pad journal bearing has a zero attitude angle, and this property is closely related to the zero cross-coupled dynamic characteristics. However, due to thermal deformation, elastic deformation, and other unknown reasons of the bearing structure, there may be a case where the attitude angle is not zero, and it is not well seen in general analysis models. The numerical model presented in this research adopts the 3D THD lubrication model where the 3D thermal deformation resulting from the 3D temperature change is considered. With the increasing boundary temperature around the bearing pad (T\({}_{\text{Pad}}\)), attitude angle decreased, whereas the increasing lubricant supply temperature (T\({}_{\text{Lube}}\)) increased the attitude angle. The tilting angle of bearing pad no. 5 and non-dimensional pivot deformation are illustrated in Figure 9c,d. The non-dimensional is calculated by dividing the pivot deformation by the initial bearing clearance. The effects of boundary temperature around the bearing pad and the shaft have different effects on tilt angle and pivot deformation. The boundary temperature around the bearing system and the lubricant supply temperature leads to complex physical phenomena. For example, increased lubricant supply temperature (T\({}_{\text{Lube}}\)) may lead to two different phenomena. The first scenario is that the increased T\({}_{\text{Lube}}\) may decrease lubricant viscosity and lower the heat generation. The decreased heat generation may lead to increase the film clearance arising from the lowered thermal expansion of the journal and bearing pads. The second opposite scenario is that the increased T\({}_{\text{Lube}}\) heats the bearing pad and journal, and the thermally expanded structure may decrease the film clearance. These two different cases are possible but depends on complex physical boundary condition and bearing system configurations. Bearing dynamic properties are illustrated in Figure 10, where the synchronously reduced dynamic coefficients are used with the assumption of the synchronous vibration of bearing pads [19; 20]. In the case of the stiffness coefficients depicted in Figure 10a,b, increased boundary temperature around bearing/journal and lubricant supply temperature stiffen the bearing system except for the T\({}_{\text{Lube}}=80\)\({}^{\circ}\)C case at 3600 rpm. It seems that the increased boundary temperature (T\({}_{\text{Pad}}\), T\({}_{\text{Journal}}\)) causes thermal expansion of the bearing-journal structure leading to the decreased film thickness. It also possible that the increased lubricant supply temperature (T\({}_{\text{Lube}}\)) heats the structure and the structure is thermally expanded. This thermal expansion stiffens the bearing. However, for the case of