## 4 Results Analysis
### Experimental Result Analysis  
According to the above experimental steps, when the test was terminated, the rudder bar specimens were checked for fatigue fracture location, and all of the fractures were found at the guide tie rod step, which was consistent with the results of the previous static calculation of the rudder bar mechanism. In the actual test process, the stress value at the guide rod step is larger, and after a long period of cyclic loading, due to the low temperature and multiple ice-cover effects, cracks will first occur at this location. With time, the cracks continue to expand eventually leading to fatigue fracture. The rudder bar specimen fracture at \(-\)40 \({}^{\circ}\)C is shown in Figure 11.  
Figure 10: Fatigue life cloud of the rudder bar at different temperatures: simulation and analysis of the fatigue life of the guide rods at (a) 20 \({}^{\circ}\)C (b) 0 \({}^{\circ}\)C (c) \(-\)20 \({}^{\circ}\)C, and (d) \(-\)40 \({}^{\circ}\)C.  
The rudder bar specimen cyclic load number under ice cover is shown in Table 2. The table shows that when the temperature is subzero, the number of loads is reduced by an order of magnitude. At \(-40\)\({}^{\circ}\)C the number of cycles is as low as 500 fewer, which is three percent of the number of cycles at room temperature. This also indicates that the low-temperature load of the specimen dramatically changes. The underwater vehicle rudder mechanism ice cover is mainly affected by the rudder itself, the environment, and other factors, of which the environmental factors have a greater impact on the rudder surface ice cover, so the main consideration is the impact of the Arctic low-temperature environment on the rudder surface ice cover. Rudder surface ice mainly comes from two aspects: one is that when the underwater vehicle floats, the part of the rudder emerging out of the seawater in the low-temperature environment undergoes instant water freezing and ice formation; the other is that the cold seawater droplets hitting the rudder surface instantly freeze and become ice. Therefore, the water droplet collection rate will affect the ice cover on the rudder surface to a certain extent [27]. The surface of the rudder components is cylindrical, and, according to ISO standards, the collection rate of water droplets that freeze in the air for cylindrical structures \(\eta_{1}\) can be given by Formula (1) [28]:  
\[\left\{\begin{array}{l} \begin{array}{l}\eta_{1}=A-0.028-C(B-0.0454)\\ A=1.066K^{-0.00616}e^{-1.103K^{-0.668}}\\ B=3.641K^{-0.498}e^{-1.497K^{-0.694}}\\ C=0.000637(\varphi-100)^{0.381}\\ K=\frac{\varphi uJ^{2}}{9 uD}\\ \varphi=\frac{\text{Re}^{2}}{K}\\ \end{array} \right. \tag{1}\]  
Here, \(d\) is the diameter of the water droplet, \(D\) is the diameter of the cylindrical structure, \(\rho_{w}\) is the water content in the air, \(\mu\) is the air viscosity, and Re is the Reynolds number. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature (\({}^{\circ}\)C)** & **Group I** & **Group II** & **Group III** & **Average** \\ \hline
20 & 11,037 & 12,069 & 16,689 & 13,265 \\
0 & 11,437 & 9526 & 14,071 & 11,678 \\ \(-20\) & 5936 & 7496 & 7952 & 7128 \\ \(-40\) & 193 & 656 & 469 & 439 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of cyclic loads on underwater vehicle rudder stock specimens. Figure 11: Fracture of the rudder stock specimen at \(-40\)\({}^{\circ}\)C.  
The energy conservation equation and mass conservation equation for the growth process of ice cover on the rudder bar surface are shown below:  
\[ \begin{split}&\rho_{f}\bigg{[}\frac{\partial h_{fcf}T_{f}}{ \partial t}+\overrightarrow{\
abla}\cdot\bigg{(}\overrightarrow{V}_{f}h_{f}c_ {f}T_{f}\bigg{)}\bigg{]}=\bigg{[}c_{f}\bigg{(}\widetilde{T}_{\rm co}- \widetilde{T}_{f}\bigg{)}+\frac{\|\overrightarrow{V}_{d}\|}{2}\bigg{]}V_{\rm co }(LWC)\beta-L_{evap}\dot{m}_{evap}\\ &+\Big{(}L_{fusion}-c_{S}\widetilde{T}\bigg{)}\dot{m}_{ice}+ \sigma\varepsilon\Big{(}T_{\rm co}^{2}-T_{f4}\Big{)}-c_{h}\bigg{(}\widetilde{ T}_{f}-\widetilde{T}_{ice,rec}\bigg{)}+Q_{anti-icing}\end{split}