# Digital Twin-Based Clamping Sequence Analysis and Optimization for Improved Geometric Quality
## 6 Conclusions  
The assembly process for non-rigid parts comprises four main steps: positioning the parts in the fixture, clamping, joining, and releasing the parts in the fixture. In this process, two of the operations, i.e., clamping and welding, involve a sequence of actions, where the parts are locked in different directions by applying forces on the positions of predefined points. Previous research has shown the impact of the welding and clamping steps on the overall assembly geometric outcome. Optimizing the sequence of operations is a combinatorial optimization problem, and physical experimentation is infeasible. In this paper, a method for the modeling, simulation, and optimization of the clamping sequences is introduced for the geometry assurance digital twin, Sections 1.3 and 2. The interaction of the clamping step with the follow-up welding step is analyzed. The method is applied to two sheet metal assemblies, and the simulation and optimization results are compared with unideal clamping and welding sequence conditions. The results show that the clamping sequence optimization results in quality improvements by up to 31% in the assemblies. Furthermore, it has been shown that an optimal clamping sequence condition results in a more robust assembly for the follow-up welding step. The results also reveal that combining the welding and joining sequence optimization results in an up to 77% quality improvement in the welded assemblies compared to the unideal clamping and welding sequence.  
Future research includes further applying the proposed method to problems with a large number of clamping and welding points. Furthermore, the proposed clamping sequence optimization method can be combined with the clamping position optimization method to enhance the accuracy of the simulation representation in fixture design. This aspect can be integrated into fixture layout optimization considering the position and the sequence of the clamping conditions. The proposed method enables the implementation of the clamping sequence analysis and optimization of the software platforms used for geometry assurance of the sheet metal assemblies during the concept and prototyping phases. The sequence of the clamping operation is a necessary aspect for the simulation of the geometric outcome of the welded assemblies, as exact simultaneity in performing the operation is not physically achievable.  
Conceptualization, R.S.T.; methodology, R.S.T., H.Z. and F.L.; software, R.S.T. and L.L.; validation, R.S.T., H.Z., F.L. and L.L.; formal analysis, R.S.T., H.Z. and F.L.; investigation, R.S.T. and H.Z.; resources, R.S.T. and H.Z.; data curation, R.S.T.; writing--original draft preparation, R.S.T. and H.Z.; writing--review and editing, R.S.T., H.Z., F.L., K.P.-B., K.W. and R.S.; visualization, R.S.T. and H.Z.; project administration, R.S.T., H.Z., F.L., K.P.-B., K.W. and R.S.; funding acquisition, K.W. and R.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Swedish Innovation Agency, Vinnova, Project Digital Quality Assurance for Sustainable Industry, Digi-Q.  
Not applicable.  
Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
This work was carried out at the Wingquist Laboratory within the Area of Advance Production at Chalmers and supported by the priority area Sustainable Industry at the Swedish Innovation Agency (VINNOVA). The support is gratefully acknowledged.  
Authors [PERSON] and [PERSON] were employed by the company Mercedes-Benz AG. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.