# Performance of Tilting Pad Journal Bearings with the Same Sommerfeld Number
## 3 Simulation Results and Discussions
### Bearing Thermal Behavior  
The Sommerfeld number is a convenient method to quantify the static and dynamic performance of bearing with various geometry, size, and operating condition. However, a great deal of discretion is needed to utilize the Sommerfeld number for TPJB because TPJB has a flexible pad and undergoes pivot deformation and thermal deformation at large load conditions. These factors make it hard to pinpoint the bearing performance covering various geometry using the Sommerfeld number.  
When designing turbomachinery, an engineer needs to fully account for thermal effect in their machine. This practice helps to improve long-term reliability and prevent unexpected failures. Hence, this section presents the thermal characteristic of TPJB for three sets of different Sommerfeld numbers--S = 0.065 (500 rpm), 0.129 (1000 rpm), and 0.466 (3600 rpm).  
Figure 7 presents the thermal effect for different Sommerfeld number by showing (a) pad trailing edge (outlet) temperature, (b) peak lubricant temperature, (c) peak bearing temperature, and (d) peak journal temperature. As expected, for low Sommerfeld number S = 0.065 (500 rpm), the variation of the temperature for small (Scale No. 1, \(\phi\) = 35 mm) to large (Scale No. 2, \(\phi\) = 245 mm) bearing sizes is minute. But, for high Sommerfeld number S = 0.466 (3600 rpm), the peak temperature increases with the increasing size of the bearing. There is \(\sim\)40 \({}^{\circ}\)C increase in temperature from Scale No. 1 to Scale No. 7. This is most likely due to the large bearing load for No. 7 bearing, but not necessarily large enough pad thickness and Babbitt thickness. In other words, the thermal energy generated by the large bearing load is larger than the thermal reservoir of the journal, the pad, and Babbitt. Hence, the thermal expansion can be more significant than the smaller bearing No. 1  
Figure 8: Thermal gradient of tilting pad journal bearing system.  
Figure 9: Nondimensionalized thermal deformation properties.  
increase in temperature. In practice, to reduce the peak temperature at the bearing, in particular for larger size, an engineer could (1) introduce bleed holes in the bearing sidewall to relief the hot lubricant to the sump and/or (2) increase the lubricant flow rate.  
Figure 8 shows the thermal gradient of TPJB for small (Scale No. 1, \(\phi\) = 35 mm) to large (Scale No. 2, \(\phi\) = 245 mm) bearing sizes. It shows the temperature distribution at the bearing pad, film thickness, and the shaft. For all cases, the loaded bearing pads (#4, #5) have the highest temperature. TPJBs with higher speed 3600 rpm, tends to have larger film thickness than the lower speed 500 rpm cases. This is due to larger bearing stiffness generation at higher operating speed.  
Figure 9 presents the minimum film thickness and journal thermal expansion versus three sets of Sommerfeld number S = 0.065, 0.129 and 0.466. It is again clearly showing that for large Sommerfeld number S = 0.466, the variations of film thickness and thermal expansion of journal are significant. Figure 10 shows the film thickness distribution of five-pads (LBP) TPJB (Scale No. 2, \(\phi\) = 245 mm) for S = 0.065 (500 rpm), and 0.466 (3600 rpm), respectively. The visual graphic shows the rotor spinning speed largely affects the film thickness distribution.  
As shown in Figures 7-10, these thermal distortions affect the static/dynamic performance of TPJB which lead to the dissimilarity of bearing performance from bearing-to-bearing for constant Sommerfeld number.