# Digital Twin-Based Clamping Sequence Analysis and Optimization for Improved Geometric Quality
## 5 Discussion  
A method for the modeling, simulation, and optimization of the clamping sequences is proposed for the geometry assurance digital twin, taking into account non-nominal part geometries. The proposed method is applied to two reference assemblies, and the geometric outcomes are analyzed and compared to unideal clamping sequences. The results show that the proposed objective of the weld relative displacement for the clamping sequence optimization establishes a better assembly condition for the follow-up welding step. This aspect can be explicitly seen in Figure 7, where the ranges of the displacements after welding in a sequence with an optimal clamping sequence are considerably lower for both assemblies compared to the unideal clamping sequences. Therefore, an optimal clamping sequence enhances the robustness of the assembly with respect to the geometric quality after welding in a sequence. In other words, the assembly with an optimal clamping sequence is less sensitive to the changes in the follow-up welding sequences in the assembly fixture.  
Furthermore, the results show that clamping sequence optimization leads to reducing the geometric deviation of the assembly after welding and releasing the part from the fixture. Figures 5 and 6 specifically visualize this improvement. For Assembly I, the clamping sequence optimization has resulted in a 31% reduction in the overall assembly deviation after springback, while similar welding conditions and sequences have been considered (from 0.13 to 0.09 mm). Similarly, for Assembly II, the assembly deviation after springback has reduced by 40% (from 0.52 to 0.31 mm). The results also show that the two-stage optimization of the clamping and welding sequences results in a reduction in the assembly deviation of 47% for Assembly I, Table 1. For Assembly II, this two-stage optimization results in a 77% reduction in the overall assembly deviation. Assembly II has a geometry that is more sensitive to the clamping sequences compared to Assembly I. For this reason, optimizing the clamping and welding sequences results in a more significant reduction in the overall assembly deviation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Assembly I** & **Clamping Step** & **Weld Relative Disp.** & **Welding Step** & **Nodal Disp.** \\  & **Sequence** & **RSS (mm)** & **Sequence** & **RMS (mm)** \\ \hline Optimal & C8-C5-C1-C3-C4-C7-C2-C6 & 0.228 & W1-W3-W2 & 0.091 \\ Unideal & C3-C8-C7-C4-C6-C2-C5-C1 & 0.579 & W3-W1-W2 & 0.171 \\ \hline Assembly II & & & & \\ \hline Optimal & C2-C3-C4-C6-C5-C1 & 9.364 & W8-W1-W7-W6-W5-W4-W3-W2 & 0.290 \\ Unideal & C6-C2-C4-C5-C3-C1 & 13.903 & W3-W8-W7-W6-W5-W4-W2-W1 & 1.255 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sequence optimization results.  
Figure 7: Comparison of the welding sequence optimization performed with optimal clamping and unideal clamping sequences.  
Another discussion point is the physical interpretation for achieving the optimized geometric outcome. From this perspective, the clamping sequence can be achieved in an automatic assembly cell introducing delays in the locking mechanism at each clamping point. For adjusting the welding sequences, however, an automated assembly cell requires readjusting the robot arm program for welding in the defined sequences. Often, for changing the welding sequences, other constraints such as assembly lead time and robot path planning are also considered in the assembly cell, making the optimization more costly. Therefore, defining and optimizing the clamping sequences in the assembly cell is more cost-efficient, improving the geometric quality and increasing the assembly robustness to the follow-up welding operation.