Reconstruction of the bending line for free-form bent components extracting the centroids and exploiting NURBS curves

Free-form bending belongs to the kinematics-based forming processes and allows the manufacturing of arbitrary 3D-bent components. To obtain the desired part, the tool kinematics is adjusted by comparing the target and obtained bending line. While the target geometry consists of parametric CAD data, the obtained geometry is a surface mesh, making the bending line extraction a challenging task. In this paper the reconstruction of the bending line for free-form bent components is presented. The strategy relies on the extraction of the centroids, for which a ray casting algorithm is developed and compared to an existing Voronoi-based method. Subsequently the obtained points are used to fit a NURBS parametric model of the curve. The algorithm parameters are investigated with a sensitivity analysis, and its performance is evaluated with a defined error metric. Finally, the strategy is validated comparing its results with a Voronoi-based algorithm, and investigating different cross-sections and geometries.