# Influence of Cavitation and Shaft Deformation in the Analysis of Lubrication of the Stern Bearing
## 1 Introduction  
The stern tube journal bearing is an essential component of a ship's power system, and its lubrication performance directly affects the driving efficiency and stability of the ship's power system [1]. The liquid film distribution in plain bearings is the key factor that determines the bearing's lubrication performance. In dynamic load bearings, the fracture zone of the liquid film is constantly changing due to the continuous movement of the journal, which has an impact on the subsequently established bearing oil film. Therefore, determining the starting and ending points of the oil film and accurately describing oil film pressure are always complex and important problems. The Reynolds boundary condition is widely used in the simulation of oil films [2, 3], but the mass conservation condition of the oil film reformation boundary is not taken into consideration, so the situation of oil film reformation cannot be explained correctly. [PERSON] [4] and [PERSON] [5] derived the JFO (Jacobson-Floberg-Olsson) theory of the cavitation boundary from the mass conservation of flow and obtained the mass conservation boundary condition. JFO theory is an improvement of the Reynolds boundary condition because it not only describes the cavitation condition of oil film but also considers the mass conservation condition during oil film reformation, so the JFO theory is well-suited for the actual situation of oil film [6]. [PERSON] et al. developed a numerical model for the simulation of cavitation in oscillatory porous squeeze film, analyzed different cavitation calculation methods, and found that JFO boundary conditions can best explain the gaseous cavitation on a dimpled surface [7]. The cavitation effect in oil film is an important issue in research on bearing lubrication performance [8]. [PERSON] experimentally demonstrated that the cavity pressure is almostconstant in a large dynamic bearing [9]. Subsequently, [PERSON] [10] developed this theory and proved that it is also applicable to the non-slip flow of fluid in the cavitation region. [PERSON] [11] used the multigrid method in the analysis of dynamic load bearings, and [PERSON] [12] proposed the finite element analysis method of bearing lubrication. [PERSON] [13] proposed the use of the generalized Reynolds equation in finite difference formulation according to JFO theory. Their formulation is suitable for both cavitation lubrication and lubrication with a full oil film. This formulation is called the mass-conserving cavitation algorithm, which overcomes the difficulty of numerical realization of JFO theory. [PERSON] et al. [14] studied the cavitation boundary condition of asymmetric bearings with grooves of finite length based on this method. [PERSON] et al. [15] used this method to solve the lubrication problem of non-circular bearings. Numerical methods considering cavitation in lubricated journal bearings have been widely investigated. [PERSON] et al. proposed a full three-dimensional thermohydrodynamic CFD approach to journal bearings and considered cavitation modelling based on averaged lubricant/vapor properties [16]. In their method, the pressures in the cavitation zone are not set directly, enabling subambient pressures to be predicted. [PERSON] et al. considered cavitation wear and observed significant differences in the mechanisms of wear in different materials [17]. [PERSON] et al. investigated lubricated joints in constrained rigid multibody systems and developed a general methodology for modeling [18]. [PERSON] et al. established a numerical model that can be used to accurately predict the cavitation phenomenon and performance of hydrodynamic bearings under steady state and verified the results under different working conditions [19]. [PERSON] et al. presented a mixed solution of the Navier-Stokes continuity and energy equations for multiphase flow conditionsand also considered the vapor transport equation to ensure continuity of flow in the cavitation region [20].