## 2 Electric Propulsion Shaft System Model and Static Characteristic Analysis
### High Elasticity Coupling Model and Characteristic Analysis
#### 2.1.2 High-Elasticity Coupling Model  
The current propulsion shaft system uses a double-row multi-disk rubber diaphragm coupling, which primarily transmits the power output from the motor to the rear transmission shaft system through elastic rubber blocks and metal diaphragms, thereby driving the rear shaft system and simultaneously transmits high torque and compensating for the axial misalignment between the motor and the rear shaft system. During the process where the propulsion shaft system is subjected to impact loads, the high-elasticity coupling compensates for the impact response displacement to reduce the harm caused by poor vibration of the propulsion shaft system. A three-dimensional model of the high-elasticity coupling entity is shown in Figure 1a, with its cross-sectional view depicted within the red circle, with a total mass of 3550 kg. In the actual simulation calculation process, due to the complexity of its three-dimensional model and issues such as mesh division, computational resources, and local model analysis, it is necessary to simplify the physical model and use a three-dimensional equivalent model of the high-elasticity coupling for simulation analysis. The simplified model should maintain basic parameters such as mass, axial length, center of gravity, and  
Figure 1: High-elasticity coupling model: (**a**) three-dimensional solid model diagram; (**b**) Equivalent model diagram. inertia consistent with the original model to meet the requirements for impact resistance calculation of the propulsion shaft system after the ship is subjected to explosive impact. It should also be able to successfully calculate the displacement compensation capability of the high-elasticity coupling. Based on its main structural features, it is simplified into parts such as the driving and driven flanges, diaphragms, and rubber blocks that compensate for the impact response displacement. The structure size is similar to that of the physical model. The equivalent model is established using three-dimensional modeling software and assembled in the software, as shown in Figure 1b. The density of the active and passive flanged diaphragm components is adjusted to 7850 kg/m\({}^{3}\), and the density of the rubber material component is adjusted to 1748.6 kg/m\({}^{3}\). The total mass of the equivalent model is 3550 kg. When calculating the stress-strain relationship to determine [PERSON]'s modulus, the high-elasticity coupling is analogized to the deformation problem of a beam model under simple load action in material mechanics theory, as shown in Figure 2 for the simplified diagram of the high-elasticity coupling beam model, where each part of the coupling deforms under the action of external forces. During the deformation process, the work performed by the impact load is converted into energy, which is temporarily stored within the solid, that is, strain energy. As the external force gradually decreases, the deformation gradually recovers, and the coupling releases the stored energy to do work. \[\theta_{B}=-\frac{Fl^{2}}{2 EI} \tag{6}\]  
\[y_{B}=-\frac{Fl^{3}}{3 EI} \tag{7}\]  
where \(\theta_{B}\) and \(y_{B}\) are the end section rotation angle and the maximum deflection, respectively; \(F\) denotes the applied external force; and \(E\) signifies the modulus of elasticity. In the calculation of its moment of inertia, the elastic coupling end face can be simplified into an annular section with an outer diameter of \(D\) and an inner diameter of d, and its moment of inertia is:  
\[I_{z}=I_{y}=\frac{\pi}{64}(D^{4}-d^{4}) \tag{8}\]  
By combining Equations (6)-(8), and knowing that the rated torque of the high-elasticity coupling is 315 kN-m, the material properties of the equivalent model parts can be obtained. This material property is also applicable to the entire propulsion shaft system impact resistance simulation and calculation analysis. In addition, the established equivalent model of the high-elasticity coupling is directly imported into the static analysis module of the finite element analysis software.