## 2 Methodology
### Simplification of Experimental Interference Factors
In addition, the presence of such non-ideal substances will significantly affect oil viscosity, density, and lubrication performance, and even induce local blockage, which requires complex calculations, such as the multiphase flow model, particle transport model, and imperfect-wall interaction model, and is beyond the modeling goal of \"system-level flow modeling and reliability analysis\" as the core of this study. The main effect is thelong-term reliability evolution, rather than the transient flow effect: impurities and moisture affect the chemical stability, corrosion, and equipment wear degree of the lubricity more, and their effect gradually appears on a longer time scale. The AMESim software framework adopted in this paper is mainly a single-phase fluid module, and the current simulation scope has difficulty covering the water-oil particle multiphase synergistic effect. Although the model system can be extended to support multiphase flow simulation in theory, this operation will greatly increase the cost of parameter calibration and model verification, and reduce the stability of modeling. In this study, the AMESim software was used to construct a simulation model of the lubricating oil system, which includes the flow process of the lubricating oil. Figure 2 below illustrates the flow path of the lubricating oil, detailing its movement through the system and the interactions between key components. The mathematical models of some key components are as follows:  
Lubricating oil pump (Three-Screw Pump):  
Flow rate is \(Q_{1}=(ATn_{p})/60\)  
where: \(Q_{1}\)--theoretical flow rate of the screw pump, m\({}^{3}\)/s; \(A\)--flow cross-sectional area of the screw pump, m\({}^{2}\); \(T\)--lead of the driving screw thread, m; \(n_{p}\)--rotational speed of the driving screw, r/min. Lubricating oil cooler:  
The logarithmic mean temperature difference (LMTD) is:  
\[\Delta t_{\rm In}=\frac{(t^{\prime}_{fh}-t^{\prime\prime}_{fc})-(t^{\prime \prime}_{fh}-t^{\prime}_{fc})}{{\rm In}\left(\frac{t^{\prime}_{fh}-t^{\prime}_ {fc}}{t^{\prime\prime}_{fh}-t^{\prime\prime}_{fc}}\right)} \tag{1}\]  
where: \(t^{\prime}_{fc}\)--cooling water inlet temperature, \({}^{\circ}\)C; \(t^{\prime\prime}_{fc}\)--cooling water outlet temperature, \({}^{\circ}\)C; \(t^{\prime}_{fh}\)--lubricating oil inlet temperature, \({}^{\circ}\)C; \(t^{\prime\prime}_{fh}\)--lubricating oil outlet temperature, \({}^{\circ}\)C.  
Valve:  
The flow characteristic of the linear valve is \(Q=(\frac{R-1}{R}I+\frac{1}{R})\cdot Q_{\rm max}\). where: \(I\)--valve opening degree; \(Q\)--flow rate at valve opening \(l\), kg/s; \(Q_{\rm max}\)--maximum flow rate when the valve is fully open, kg/s; \(R\)--valve turndown ratio, a constant. The flow characteristics of the percentage valve are: \(Q=R^{(l-1)}Q_{\rm max}\). The flow characteristics of the quick-opening valve are: \(Q=\frac{\sqrt{1+(R^{2}-1)I}}{R}Q_{\rm max}\). The flow characteristics of the parabolic valve are: \(Q=\frac{[1+(\sqrt{R}-1)I]^{2}}{R}Q_{\rm max}\). Comparison of simulation results: Under the same boundary conditions and operating conditions, the calculation results of the Simulink model are compared with the simulation results of the AMESim model to verify the accuracy of the model. A comparison of some simulation results is shown in Table 1. The data source is obtained from the literature [28]. Figure 2: AMESim simulation of ship lubricating oil system. To enhance the modeling accuracy and the targeted reliability analysis of the diesel engine lubrication system, this study explicitly defines a set of fixed lubrication oil parameters, for use in the quantitative modeling of system operating characteristics and performance evaluation. These parameters remain constant throughout the analysis and serve as boundary input conditions that reflect the physical behavior of the lubricating oil under real operating environments, directly influencing equipment wear, thermal balance, and failure risk.