Sheet metal assembly is a common assembly process for several products such as automobiles and airplanes. Since all manufacturing processes are affected by variation, and products need to have a high geometric quality, geometry-related production problems must be analyzed during early design phases. This paper discusses two methods of performing this analysis. One way of performing the simulations relatively fast is to establish linear relationships between part deviation and assembly springback deviation by using the method of influence coefficient (MIC). However, this method does not consider contact between the parts. This means that the parts are allowed to penetrate each other which can affect the accuracy of the simulation result. This paper presents a simple contact modeling technique that can be implemented in to MIC to avoid penetrations. The contact modeling consists of a contact detection and a contact equilibrium search algorithm. When implemented, MIC still only requires two finite element analysis (FEA) calculations. This paper describes the steps in the contact algorithm and how it can be used in MIC, and finally the proposed contact modeling is verified by comparing the simulation result with commercial FEA software ABAQUS contact algorithm.

This paper presents a methodology and a software that allows assemblies to be evaluated with respect to robustness and geometrical stability. The assembly robustness evaluation aims at detecting design and assembly solutions that are sensitive to variation and may cause problems later during production. It is based on Suh's independence axiom, stating that in a good, uncoupled design, each functional requirement is satisfied by one and only one design parameter. The methodology enables the designer to evaluate the geometrical sensitivity of the assembly, what the sources of variation are, their importance for the overall robustness and in what order to improve the design. A possible result from the analysis may be that the concept must be changed in some way, either by changing the way parts are located with respect to each other or by using assembly fixtures for positioning. The software is implemented in a Microsoft Windows environment and has an IGES interface that enables the designer to import computer aided design (CAD) geometry from an arbitrary CAD system, and perform assembly robustness analysis.

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.

This paper presents an analysis tool that allows non-rigid parts and assemblies to be evaluated with respect to geometrical robustness. The robustness evaluation aims at detecting design and assembly solutions that are sensitive to variation and may cause problems later on during production. The analysis tool enables the designer to evaluate the geometrical sensitivity of a part or assembly, what the sources of variation are, their importance for the overall robustness and in what order to improve the design. It allows designers and production engineers to evaluate and improve different types of locating, clamping and joining schemes with respect to non-rigid deformation of parts due to part variation and fixture variation. The analysis tool is implemented in a Windows environment and has interfaces to IGES, VRML, STL and ABAQUS, which enables the user to import computer-aided design geometry, finite element meshes and stiffness matrices, and to perform robustness and tolerance analysis for different locating, clamping and joining layouts. The results are presented in stability matrices, as sensitivity factors and with colour-coding of the sensitivity of the geometry.

Applying the concept of Digital Twin in production processes supports the manufacturing of products of optimal geometry quality. This concept can be further supported by a strategy of finding the optimal combination of individual parts to maximise the geometrical quality of the final product, known as selective assembly technique. However, application of this technique has been limited to assemblies where the final dimensions are just function of the mating parts' dimensions and this is not applicable in sheet metal assemblies. This paper develops a selective assembly technique for sheet metal assemblies and investigates the effect of batch size on the improvements. The presented method utilises a variation simulation tool (Computer-Aided Tolerancing tool) and an optimisation algorithm to find the optimal combination of the mating parts. The approach presented is applied to three industrial cases of sheet metal assemblies. The results show that using this technique leads to a considerable reduction of the final geometrical variation and mean deviation for these kinds of assemblies. Moreover, increasing the batch size reduces the amount of achievable improvement in variation but increases the amount of achievable improvement in the mean deviation.