## 3 Simulation Modeling and the Validation of the Rudder Mechanism  
### Simulation Modeling  
For single mechanisms such as crank linkage mechanisms and cam mechanisms, based on [PERSON]'s laws and the Lagrange equations, the dynamic output characteristics of the mechanism can be obtained by establishing a system of dynamic differential equations to solve [17; 18]. However, the rudder system structure of underwater vehicles is complex, and directly establishing a dynamic equation system and numerically solving the life _a-N_ curve of its weak components is difficult. Simultaneously considering the contact between multiple pairs of motion pairs is also difficult, resulting in significant errors in simulation results [19]. The UMT model unifies [PERSON]'s laws of motion and the second law of thermodynamics, using the analytically derived fundamental equations of thermodynamics to compute the thermodynamic state index (TSI), which can be used to predict the lifetime of a material. [PERSON] [20] used the Unified Mechanics Theory to predict the fatigue life of Ti-6 Al-4V alloy. Traditionally, fatigue life was predicted using empirical models, but this study suggests using a three-dimensional computational model based on material and thermodynamic basic equations. [PERSON] has conducted a large amount of research using the UMT model. [PERSON] [21] used the Unified Mechanics Theory (UMT) to predict the fatigue life of pre-corroded steel samples, studied the fatigue behavior of materials in corrosive environments, and explored the impact of corrosion on material properties. The focus was on developing a UMT-based model and conducting experimental verification, which was in good agreement with the experimental data, proving its accuracy. In addition, he also used the Unified Mechanics Theory (UMT) to predict the high cycle fatigue life of metals [22] and modeled the fatigue life and hydrogen embrittlement of low-carbon steel using UMT [23]. His findings emphasize that the fatigue model of the UMT is entirely based on physical fields and does not require curve fitting. [PERSON] [24] discussed an experimental and numerical modeling approach for the thermomechanical low cycle fatigue analysis of cyclically non-stabilized steels. The document emphasized the importance of selecting and identifying proper fatigue parameters to accurately evaluate the reliability of structures. ANSYS Workbench is based on the principle of finite element analysis (FEA) for simulation analysis. It divides the object into a finite number of elements, calculates physical quantities such as mechanics, thermodynamics, and electricity for each element, and obtains the numerical solution for each element. Then, by combining the numerical solutions of each element, the numerical solution for the entire object is obtained. This article takes the elevator mechanism of underwater vehicles as the research object, establishes its dynamic simulation model in ANSYS Workbench, and studies the influence of a low-temperature environment on its fatigue life. The modeling process is shown in Figure 4.  
Figure 3: Guiding rod structure: (**a**) composition; (**b**) dimensions. The main modeling process is as follows:  
1. Set up the working environment and material properties. After importing the 3D model of the rudder mechanism into ANSYS Workbench, adjust the grid settings, gravitational acceleration direction, coordinate axes, and other system operating environments. At the same time, couple and fix the components that do not have relative motion with each other, to reduce the number of model components, rename the components of the simplified model, and define their material properties. 2. Add constraints. After defining the material properties of the components, define the relative position and relative motion between the components, i.e., add constraints to the model and couple the components to form a mechanical system to simulate the actual operating conditions of the machinery.