Geometrical variation is a problem in all complex, assembled products. Recently, the Digital Twin concept was launched as a tool for improving geometrical quality and reduce costs by using real time control and optimization of products and production systems. The Digital Twin for geometry assurance is created together with the product and the production systems in early design phases. When full production starts, the purpose of the Digital Twin turns towards optimization of the geometrical quality by small changes in the assembly process. To reach its full potential, the Digital Twin concept is depending on high quality input data. In line with Internet of Things and Big Data, the problem is rather to extract appropriate data than to find data. In this paper, an inspection strategy serving the Digital Twin is given. Necessary input data describing form and shape of individual parts, and how this data should be collected, stored and utilized is described.

Virtual tools and methods are becoming increasingly important in order to predict the geometric outcome in early phases of the product realization process. Method of influence coefficients (MIC) in combination with Monte Carlo simulation (MCS) is a well-known technique that can be used in nonrigid variation simulation. In these simulations, contact modeling is important to ensure a correct result. Contact modeling simulates how mating surfaces are hindered from penetrating each other, giving rise to contact forces that contribute to the deformation of the parts when assembled and the final shape of the subassembly after springback. These contact forces have to be taken into consideration in each MCS-iteration. To secure reasonable response times, the calculation of the contact forces needs to be fast. In this paper, we formulate a quadratic programming (QP) problem to solve the contact problem. The case studies presented show that node-based contact modeling can be efficiently solved through QP.

Geometrical variation is closely related to fulfillment of both functional and esthetical requirements on the final product. To investigate the fulfillment of those requirements, Monte Carlo (MC)-based variation simulations can be executed in order to predict the levels of geometrical variation on subassembly and/or product level. If the variation simulations are accurate enough, physical tests and try-outs can be replaced, which reduce cost and lead-time. To ensure high accuracy, the joining process is important to include in the variation simulation. In this chapter, an overview of nonrigid variation simulation is given and aspects such as the type and number of joining points, the joining sequence and joining forces are discussed.

During product development one important aspect is the geometric robustness of the design. This is due to the fact that all manufacturing processes lead to products with variation. Failing to properly account for the variability of the process in the design phase may lead to expensive redesign. One important tool during the design phase in many industries is variation simulation, which makes it possible to predict and optimize the geometric quality of the design. However, despite the increase in computer power, calculation time is still an obstacle for the wider use of variation simulation. In this article, we propose a new method for efficient compliant variation simulation of spot-welded sheet metal assemblies. The method is exact, and we show that the method leads to time savings in simulation of approximately 40–50% compared to current state-of-the-art variation simulation.

Variation simulation for assembled products is one important activity during product development. Variation simulation enables the designer to understand not only the features of the nominal product but also how uncertainty will affect production, functions and the aesthetic properties of the final product. For parts that are able to deform during assembly, compliant variation simulation is needed for accurate prediction. For this the Finite Element Method (FEM) is used. Despite many effective efforts to decrease simulation times for compliant variation simulation, simulation time is still considered an obstacle for full scale industrial use. In this paper, a new formulation for compliant variation simulation of assemblies that are joined in sequential spot-welding will be presented. In this formulation the deformation in the intermediate springback steps during the simulation of a spot-weld sequence do not have to be calculated. This is one of the most time consuming steps in sequential spot-welding simulation. Furthermore, avoiding the intermediate springback calculation will reduce the size of memory of the computer models since the number of sensitivity matrices is reduced. The formulation is implemented using the latest developments in compliant variation simulation, that is the Method of Influence Coefficients (MIC) where the Sherman-Morrison-Woodbury-formula is used to update the resulting sensitivity matrices and the contact- and weld forces are solved using a Quadratic Programme (QP). Industrial cases are used to demonstrate the reduced simulation time. It is believed that the reduction in simulation times will have future implications on sequence optimization for spot-welded assemblies.