A digital twin for geometry assurance contains a set of analyses that are performed to steer the real production for securing the geometry of the final assembly. In sheet metal assemblies, spot welding is performed to join the parts together. The sequence of the welding has a considerable influence on the geometrical outcome of the final assembly. In industry, the sequence of welding to secure the geometry is mainly derived by tacit manufacturing knowledge. Including such knowledge to mimic the production process requires extensive knowledge management, and the result might be just a good enough solution. Theoretically, spot welding sequence optimization for the optimal geometrical quality is among NP-hard combinatorial problems. In a geometry assurance digital twin, where assembly parameters are selected for the individual assemblies, time constraints define the quality of the optimal sequence. In this paper, an efficient method for spot welding sequence optimization with regards to the geometrical quality is introduced. The results indicate that the proposed method reduces 60–80% of the time for the sequencing of the spot welding process to achieve the optimal geometrical quality.

Geometrical variation is the main cause of the aesthetic and functional problems in the product geometry. Variation and disturbances are caused by several sources during the manufacturing process. In the automotive industry, one of the main sources of variation is the spot welding sequence. Optimising this sequence is of combinatorial Nondeterministic Polynomial (NP)-hard problems. In a typical automotive sheet metal assembly, there are a large number of spot welds. Today, if the number of spot welds in a sub-assembly is more than 10, the sequence optimisation will be a challenging and time-consuming task. Therefore, industry is mainly dependent on the experiential approach or simultaneous welding simulations for predicting the geometrical outcome. In this paper, a method is introduced to identify the geometry weld points to reduce the optimisation problem size in a geometry assurance digital twin context. This method is then applied to three automotive body-in-white assemblies and optimisation is performed. The results show that reducing the size of the problem by the proposed approach can help to save a considerable amount of time while getting geometrical outcomes within the satisfactory error levels.

In an individualized shee metal assembly line, form and dimensional variation of the in-going parts and different disturbances from the assembly process result in the final geometrical deviations. Securing the final geometrical requirements in the sheet metal assemblies is of importance for achieving aesthetic and functional quality. Spot welding sequence is one of the influential contributors to the final geometrical deviation. Evaluating spot welding sequences to retrieve lower geometrical deviations is computationally expensive. In a geometry assurance digital twin, where assembly parameters are set to reach an optimal geometrical outcome, a limited time is available for performing this computation. Building a surrogate model based on the physical experiment data for each assembly is time-consuming. Performing heuristic search algorithms, together with the FEM simulation, requires extensive evaluations times. In this paper, a neural network approach is introduced for building surrogate models of the individual assemblies. The surrogate model builds the relationship between the spot welding sequence and geometrical deviation. The approach results in a drastic reduction in evaluation time, up to 90%, compared to the genetic algorithm, while reaching a geometrical deviation with marginal error from the global optimum after welding in a sequence.

Spot welding is the predominant joining process for the sheet metal assemblies. The assemblies, during this process, are mainly bent and deformed. These deformations, along with the single part variations, are the primary sources of the aesthetic and functional geometrical problems in an assembly. The sequence of welding has a considerable effect on the geometrical variation of the final assembly. Finding the optimal weld sequence for the geometrical quality can be categorized as a combinatorial Hamiltonian graph search problem. Exhaustive search to find the optimum, using the finite element method simulations in the computer-aided tolerancing tools, is a time-consuming and thereby infeasible task. Applying the genetic algorithm to this problem can considerably reduce the search time, but finding the global optimum is not guaranteed, and still, a large number of sequences need to be evaluated. The effectiveness of these types of algorithms is dependent on the quality of the initial solutions. Previous studies have attempted to solve this problem by random initiation of the population in the genetic algorithm. In this paper, a rule-based approach for initiating the genetic algorithm for spot weld sequencing is introduced. The optimization approach is applied to three automotive sheet metal assemblies for evaluation. The results show that the proposed method improves the computation time and effectiveness of the genetic algorithm.

Joining sequence optimization is a combinatorial problem, requiring extensive computational time. The significance of determination of an optimal sequence for improved geometrical quality is substantial. Previously, genetic algorithms have been studied for defining the optimal sequence. However, these algorithms are highly dependent on the internal parameters, requiring additional computational analysis and thereby extended evaluation time. In this article, a novel robust stepwise algorithm is introduced to determine the optimal weld sequence. Application of the proposed algorithm leads to drastic time improvements for defining the optimal weld sequence of each assembly. Three industrial assemblies are evaluated. Comparison with the previously applied population-based optimization algorithms indicates that the optimization time can be reduced drastically with the proposed stepwise algorithm. The stepwise algorithm is intended to be applied in a geometry assurance digital twin, where the assembly parameters are being optimized for each individual assembly.