## 3 Confirmation of Structural Data According to Dynamic Characteristics  
### Structural Deflection Data of Base Metal  
The power conversion device and the contact part between the cover and the housing are shown in Figure 7. The edge and six central points of the cover were in contact with the housing, and this was set as a contact condition in the analysis. The stiffness and damping coefficients depending on the contact conditions were applied, as summarized in Table 2, and pre-welding was performed with respect to the six points of the center part of the cover to control the overall displacement. Because the deflection generated during cover edge welding was more dominant than that generated during center welding, pre-welding of the six points in the center was not significant in this study. In the process, after pre-welding at the center, welding proceeded along the welding line located on the edge of the cover. When the upper and lower directions of the cover were defined as \(+\)Z and \(-\)Z, respectively, the deflection data of the cover under the 1.2 ton load of the welding tool were recorded, as shown in Figure 8. The data in Figure 8 represent the deflection values of the cover generated only by the load of the welding tool in the state where the frictional heat condition is not applied. Moreover, because the cover plate was thin, we were able to confirm that upward displacement occurred around the welding tool, as shown in Figure 9. The maximum displacement values of the cover in the \(+\)Z and \(-\)Z directions were confirmed as 0.079 mm and 0.305 mm, respectively. Figure 8: Deflection data of cover under a 1.2 ton load: (**a**) +Z direction; (**b**) \(-\)Z direction. Figure 7: Contact area between housing and cover. According to the deflection data, the maximum displacement in the \(-\)Z direction was generated at the position pressed by the load of the welding tool, and because the center was welded, it was viewed as a cantilever-type structural system. Therefore, it was possible to numerically calculate the displacement in the \(-\)Z direction depending on the load of the welding tool. Given that the welding tool applied a vibrational load through continuous contact, it was expressed as Equation (1) based on the equation of motion. When each term was divided by mass, it was transformed, as in Equation (2), and a particular solution could be assumed, as in Equation (3), when expressed as an external force, as in Equation (1). Equation (2) can be summarized by substituting Equation (3). In the organizing process, time \(t\) was satisfied all the time; therefore, if \(\omega t-\theta=0\) and \(\omega t-\theta=\pi/2\) were to be substituted, the displacement value \(X\) can be obtained, as shown in Equation (4). At this time, \(f_{0}\) was calculated as the maximum normal force acting on the FE body by considering the load of the welding tool, as shown in Figure 10. Moreover, as shown in Figure 9, when the maximum displacement occurred in the \(-\)Z direction, the distance from the point close to the pre-welded part to the welding tool was 62.9 mm. When calculating the shoulder diameter as the width, the value of \(\omega_{n}\) was calculated as 2.15 rad/s by using Equation (5), which is the equivalent spring constant in the form of a cantilever. For the exciting frequency \(\omega\), it was calculated as 209.33 rad/s by means of conversion form 2000 RPM. \[m\ddot{x}+c\dot{x}+kx=f_{0}cos\omega t \tag{1}\]  
\[\ddot{x}+2\xi\omega_{n}\dot{x}+{\omega_{n}}^{2}x=f_{0}cos\omega t \tag{2}\]  
\[x_{p}(t)=Xcos(\omega t-\theta) \tag{3}\]  
\[X=\frac{f_{0}}{\sqrt{\left({\omega_{n}}^{2}-{\omega}^{2}\right)^{2}+\left({2 \xi\omega_{n}}{\omega}\right)^{2}}} \tag{4}\]  
Figure 8.0  
Figure 8.1 Maximum deflection of the cover along the upward and downward directions: (**a**) Deflection along \(+\)Z direction; (**b**) Deflection along \(-\)Z direction.