# Effect of Thermal Boundary Condition on Tilting Pad Journal Bearing Behavior
###### Abstract
The following is a summary of the reasons why the numerical approach developed by various researchers to date has had difficulty in considering precise temperature boundary conditions. 1. Difficulty in modeling heat transfer between a spinning journal and an oil film (boundary A, Figure 1a)
2. Difficulty in modeling heat transfer between oil film-bearing pads (boundary B, Figure 1a)
3. Difficult to consider the axial thermal boundary condition of the shaft. In conventional 2D bearing model, it is impossible. (boundary C, Figure 1b)
4. Difficult to calculate the film thickness due to thermal deformation of the journal and bearing pads (Figure 1b)
5. Difficulties in multi-physics modeling of bearing systems to simultaneously consider bearing dynamics, lubrication, and heat transfer/heat distortion problems  
The temperature of the oil film and bearing pad is closely related to the life of the bearing. The temperature of the lubricant affects the oxidation rate of the lubricating oil, and the temperature of the pad influences the life of the Babbitt metal. This is the reason why predicting the temperature of bearings in the design stage of turbomachinery is important. The temperature change of the bearing-journal leads to the thermal deformation of the structure; this thermal deformation changes the oil film thickness at the running condition, and the changed thickness changes the temperature distribution of the bearing system by changing the viscous shearing in the oil film. This complicated interaction makes accurate temperature prediction of the bearing system difficult. Figure 1: Heat flux boundary conditions and deformation in bearing–journal system. In this study, to overcome these difficulties, a 3D bearing numerical modeling approach and algorithm is presented, and the static, dynamic, and thermal characteristics of the bearing are analyzed according to the change of thermal boundary conditions. The numerical model provided in this research is based on the earlier studies performed by [PERSON] and [PERSON] [19; 20], and is an extension of their research. This research is performed based on an in-house code that has been developed in MATLAB, a commercial numerical analysis software, based on the 2019b version. It also has been updated through various research projects since 2015 when the first study was published. This bearing model was firstly verified through comparison with the published textbook about journal bearing [35] at the development stage, and it was secondarily verified through comparison with [PERSON]'s experimental results [36]. The following are the modified and improved features adopted in this research since the bearing numerical model was first published in 2015 [19; 20]. 1. Consideration of the thermal boundary condition around shaft
2. Addition of Babbitt material at the inner surface of the bearing pad with the consideration of heat transfer and thermal deformation
3. Addition of the prescribed temperature boundary condition around the bearing-journal structure
4. Improvement of stability of prediction of pivot stiffness
5. Improvement of the boundary condition of the FE thermal deformation model  
The purpose of this study is to investigate the change in bearing performance according to (a) journal boundary temperature, (b) bearing boundary temperature, and (c) lubricant supply temperature. It was found that the thermal boundary conditions make noticeable changes in bearing behavior.