Abstract

We present a finite element (FE) approach to compute the stress-free shapes of non-rigid sheet metal parts, scanned in an over-constrained fixture set-up. These set-ups are commonly used for measuring non-rigid parts where one must compensate gravitational effects to comply with quality requirements. The over-constrained fixture set-up induces part tensions, and one must understand how these affect the geometry. Wrong interpretations can be made during quality inspection. This can lead to wrong decisions regarding countermeasures, and inappropriate tool modifications or undesirable adjustments to manufacturing processes might be made. Post-processing of measured part geometry helps with the understanding of deflections caused by gravity or external fixture forces. We optically scan and digitize a part’s geometry and use this data to generate a mesh for a simulation. The simulation model also considers the material behavior and boundary conditions of the fixture. This “digital twin” is used to calculate the stress-free part shape with an FE software package, involving iterative shape optimization. As the mesh is derived from the acquired point cloud, a CAD geometry representation is not needed in our workflow, assuming that the entire part can be scanned. Our approach is motivated by applications in the automotive and aerospace industries, where one must understand the deformable behavior of thin sheet metal parts for quality assurance purposes. We demonstrate the performance of our approach for experimentally generated and simulated data for a simple experimental set-up, and we discuss use cases from the automotive industry. Our experimental results have maximal absolute error values less than 0.05mm, measured in surface normal direction. These error values are on the same scale as measurement uncertainty for commonly used 3D scanning systems. In particular, the main contributions of this paper are: -Iterative shape optimization algorithm based on FE simulation models. -Calculating the stress-free shape of measured parts by resolving deflections caused by gravity and over-constrained fixture set-up. -Validations with experimental and simulation data showing the usability for real-world use-cases.