## Abstract

Geometric variation is one of the sources of quality issues in a product. Spot welding is an operation that impacts the final geometric variation of a sheet metal assembly considerably. Evaluating the outcome of the assembly, considering The existing geometrical variation between the components can be achieved using the Method of Influence Coefficients (MIC), based on the Finite Element Method (FEM). The sequence, with which the spot welding operation is performed, influences the final geometric deformations of the assembly. Finding the optimal sequence that results in the minimum geometric deformation is a combinatorial problem that is experimentally and computationally expensive. For an assembly with N number of welds, there are N! possible sequences to perform the spot welding operation. Traditionally, spot welding optimization strategies have been to simulate the geometric variation of the spot-welded assembly after the assembly has been positioned in an inspection fixture, using an appropriate measure of variation. When performing the variation simulation of the spot welding process today the standard approach is to assume small displacement, elastic material response and neglecting effects stemming from temperature. In this paper, using these standard assumptions, the source of deviation and hence variation is the relative displacement of the weld, i.e. the relative displacement of the two nodes that together define a weld pair in a simulation. In this paper, we will investigate this observation. First, by showing that it is possible to calculate the deformation given the relative displacement in weld pairs. Then, by investigating the sensitivity of the relative displacement, and finally, following this approach, we will investigate the consequences of optimizing the relative displacement instead of optimizing the variation in the inspection fixture. In the standard approach, the calculation of deformation is one of the most time-consuming steps, therefore this approach may lead to large time savings during sequence optimization. Also, this approach is independent of the inspection fixture. Consequences of this have been investigated.

The relative weld displacement has been evaluated on three sheet metal assemblies. The optimization problem has been solved for the three assemblies using this approach. The optimal sequence, the corresponding final assembly deformations, and the time-consumption have been compared to the traditional approach. The results show that considering the relative weld displacement makes each assembly evaluation less time-consuming, and thereby less optimization time is required. Considering the relative weld displacements results in a similar optimal weld sequence compared to the traditional and time-consuming approach, final assembly deformations in an inspection fixture.