## 2 Dynamic System Model
### Parameter Setting for Loads  
The magnitude of the load for which the welding tool presses against the base material was analyzed, and the vertical downward displacement of the welding tool was calculated as a reaction force of 1.2 tons generated, as shown in Figure 5. Except for an interval of 1 mm set for the stabilization of the analysis, the vertical downward displacement for which a reaction force of 1.2 ton occurred was calculated to be 0.342 mm. The load range of the welding tool to be applied for FSW of the power converter was 0.8-1.2 tons, and the vertical downward displacement of the welding tool for this load range was calculated, as summarized in Table 3. In addition, to check for the deflection due to frictional heat, a temperature condition of 600 \({}^{\circ}\)C was applied to the welding line of the cover and the part in contact with the shoulder. Frictional heat varies depending on the rotation speed (RPM) of the welding tool and the characteristics of the base material. In this study, a temperature of 600 \({}^{\circ}\)C was applied as a reference value. Thereafter, we compared the structural deflection  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **AL5052** & **Titanium Alloy** \\  & **(Housing, Cover)** & **(Welding Tool)** \\ \hline Density (kg/m\({}^{3}\)) & 2680 & 4500 \\ Young’s Modulus (GPa) & 69.3 & 110 \\ Poisson’s Ratio & 0.33 & 0.33 \\ Yield Strength (MPa) & 193 & 800 \\ Tensile Strength (MPa) & 228 & 860 \\ Thermal Coefficient (1/\({}^{\circ}\)C) & 2.38 \(\times\) 10\({}^{-5}\) & - \\ Thermal Reference Temp. (\({}^{\circ}\)C) & 20 & - \\ Specific Heat (J/(kg \({}^{\circ}\)C)) & 880 & - \\ Thermal Conductivity (W/(m \({}^{\circ}\)C)) & 138 & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties.  
Figure 4: Physical time required to achieve the velocity of 600 mm/min.  
data of the base metal depending on the load range of the welding tool in the state where frictional heat of 600 \({}^{\circ}\)C was applied.  
Because the cover considered in this study is a thin plate, deflection may occur due to the load of the welding tool or frictional heat. In the manufacture of high-quality power converter products, there should be little error in the flatness of the housing and the cover. Therefore, it is necessary to install a fixing clamp that can control the deflection of the cover generated during FSW. As shown in Figure 1, because the overall size of the power converter was not large, there was a limit in terms of the space where the fixing clamps could be applied. The fixing clamps were applied as shown in Figure 6, such that they could be fixed as close to the welding line as possible, and we confirmed the data according to whether or not the fixing clamp was applied.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Reaction Force (N)** & **Vertical Downward Displacement (mm)** \\ \hline
11,772 (1.2 ton) & 0.342 \\
10,791 (1.1 ton) & 0.328 \\
9810 (1.0 ton) & 0.313 \\
8829 (0.9 ton) & 0.297 \\
7848 (0.8 ton) & 0.280 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Displacement data of the welding tool for the reaction force generated after contact.  
Figure 5: Reaction force depending on the vertical downward displacement of the welding tool: (**a**) Reaction force of the cover; (**b**) vertical downward displacement of the welding tool.  
Figure 6: 8 Fixing clamps applied.