## 3 Confirmation of Structural Data According to Dynamic Characteristics
### Structural Deflection Data of Base Metal
According to Figure 10, the maximum normal force is 10.76 N. Because the confirmed \(f_{0}\) of 10.76 N is dominant in Equation (4), the damping ratio \(\zeta\) has little effect on the displacement \(X\) when its value is 0-2. Consequently, the theoretical value calculated using Equation (4) is 0.303 mm, and it has a relatively small error rate of 0.7%, as summarized in Figure 8.2 This result confirmed that the modeling conditions implemented in the analysis program were correct. Figure 11 shows the stress data and stress distribution image of the cover subjected to the 1.2-ton load of the welding tool. The yield strength of the cover material is 193 MPa, as summarized in Figure 8.3 Because the maximum stress identifiable from the graph is 83.53 MPa, according to Equation (6), the \(S_{F}\) (safety factor) exceeds 2. Figure 8.4  
Therefore, for a welding tool load of 1.2 tons, there is no structural problem because the cover is in the elastic region. In addition, according to Table 5, it can be seen in the stress data that under the welding tool loads of 0.8-1.2 tons reduces the stress by an average of 6.5 % per 0.1 ton. Based on this, designers can infer the maximum stress acting on the cover for the load value of the welding tool. In the case of frictional heat, there is a method of setting the temperature condition using the welding tool as the FE body and performing an FE analysis. However, this requires excessive analysis time, and it is difficult to ensure that the resulting data are correct because of the instability due to contact between elements. Therefore, the welding tool was set as a rigid body to calculate the deflection along the upper and lower directions of the cover according to the load. Then, the total deflection in the section with the largest displacement was calculated by considering the frictional heat. In this manner, it was possible to proceed with a comparison of the results obtained in the cases with and without the application of frictional heat. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data** & **Numerical** & **Analysis** & **Error Rate** \\ \hline \(-Z\) direction max. displacement (mm) & 0.303 & 0.305 & 0.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the theoretically calculated and analytically determined data. Figure 10: Normal force of FE body due to welding tool load. The deflection data of the cover depending on the load when the welding tool was considered a rigid body are shown in Figure 12 and summarized in Table 6. As the welding tool load decreased by 0.1 ton, the average displacement values decreased by 5.5% and 4.8% in the +Z and \(-Z\) directions, respectively. The displacement value generated in the +Z direction may decrease if a fixing clamp is used, and along the \(-Z\) direction, the welding tool load should be selected considering the depth of the welding pin relative to the deflection. The welding pin depth applied in this study was 1.5 mm, as shown in Figure 3, and the shoulder penetrated 0.2 mm into the upper surface of the base material to proceed with FSW; when the welding tool load was 1.2 tons, the shrinkage was 0.305 mm. Therefore, when a load of 1.2 tons was applied, unnecessary defects could have occurred  
Figure 11: Stress data of the cover according to welding tool load: (**a**) maximum stress under the 1.2 ton load; (**b**) maximum stress data under the 1.2 ton load; (**c**) stress data by load; (**d**) maximum stress value by load. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Welding Tool Load (N)** & **Max. Stress (MPa)** & **Decrease Rate (\%)** \\ \hline
11,772 (1.2 ton) & 83.53 & default \\
10,791 (1.1 ton) & 79.66 & 5 \\
9810 (1.0 ton) & 72.19 & 14 \\
8829 (0.9 ton) & 67.67 & 19 \\
7848 (0.8 ton) & 61.62 & 26 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of stress data for different welding tool loads. during the welding process because the welding pin was inserted with a thickness of 2 mm or more of the cover.