## 3 Results and Discussion
### Welding Results with Jigs  
Here, we consider the use of jigs to inhibit welding deformation, and we further examine residual stress. Figure 13 presents the configurations for four jigs and six jigs, respectively. They are used at a distance from the welding bead center of \"A\" mm to examine deformation under a depressed displacement of 0 mm, 0.05 mm, and 0.1 mm, respectively. In the simulation, jigs with a depressed displacement of 0 mm are examined for distances of 40, 50, 60, 70, 80, 90, and 100 mm from the jig center to the welding bead center. The results indicate that the X- and Z-displacement are less than 0.1 mm and are considerably smaller than the Y-displacement. Therefore, we hereafter focus only on the Y-displacement. Table 3 presents the simulation cases for the applied jig fixtures. There are a total of 14 cases, of which nine examine the application of four jigs and five examine the application of six jigs, excluding cases 2, 3, 5, and 6. Comparing the results of each case shows the extent to which deformation was inhibited and thus which setup could be used in everyday practical welding applications. Note that the jig-to-jig distances of the applied four and six jigs are 200 and 100 mm, respectively. To carry out deformation and residual stress analysis, we used discussion lines 1, 2, and 3 in Figure 14 for the cases in Table 3. Figure 15 presents the deformation differences for four and six jigs under a depressed displacement of 0 mm for CASE 1, CASE 4, and CASE 7. Every case has  
Figure 9: Deformation with and without jig constraints: (1) with; (2) without. a distance to the welding bead of 40 mm under a depressed displacement of 0 mm. This scenario is used to understand how distance influences welding deformation. From Figure 14, we can see that the deformation results for the applied four and six jigs are very similar in CASE 1, CASE 4, and CASE 7. In CASE 7, the difference is reduced to only \(10^{-2}\) mm. The simulation shows that jigs within 200 mm result in a very small change in welding deformation. Figure 11: Three-dimensional (3D) image of welding deformation without jigs. Figure 10: Gas metal arc welding (GMAW) welding deformation without jigs after cooling to 25 \({}^{\circ}\)C.  
Figure 12: Three-dimensional (3D) image of equivalent von Mises stress for test piece. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Center Distance A (mm)** & **0** & **0.05** & **0.1** \\ \hline
40 & CASE 1 & CASE 1-1 & CASE 1-2 \\
50 & CASE 2 & & \\
60 & CASE 3 & & \\
70 & CASE 4 & & \\
80 & CASE 5 & & \\
90 & CASE 6 & & \\
100 & CASE 7 & & \\ \hline \end{tabular}
\end{table} 
Table 3: Simulation situation using the applied jigs. Figure 13: Applied jigs and positions before welding: (**a**) four jigs; (**b**) six jigs. Figure 16 presents the results of four and six jigs at a distance of 40 mm from the welding bead center with a depressed displacement of 0 mm, 0.05 mm, or 0.1 mm for CASE 1, CASE 1-1, and CASE 1-2. It can be observed that the higher the depressed displacement, the smaller the benefit. The ideal setup for inhibiting deformation appears to be with a depressed displacement below 0 mm. Figure 17 depicts the application of four jigs under a depressed displacement of 0 mm. Careful consideration of the welding deformation in CASE 1 to CASE 7 shows that attaching jigs 100 mm from the depressed center to the welding bead center can effectively suppress welding deformation. Figure 18 presents a 3D image of the deformation in CASE 7 with jigs. For comparison, Figure 19 shows a 3D image of the deformation in CASE 7 without jigs. It can be clearly seen that welding with jigs considerably reduced the deformation, since the entire displacement difference from highest to lowest for a 300 \(\times\) 250 mm SUS304 steel plate is only 1.129156 mm. Using jigs to inhibit deformation hence yields remarkable results at low cost. Next, we examine residual stress when a jig fixture is applied during welding to reduce deformation.