An Error-Adaptive, Non-Rigid Registration Method for the Analysis of Springback in Sheet Metal Forming

Abstract

Springback effects, as occuring in sheet metal forming processes, pose a challenge to manufacturingplanning: the as-built part may deviate from the desired shape rendering it unusable forits intended purpose. A compensation can be achieved by modifying the forming tools to counteractthe shape deviations. A prerequisite to compensation is the knowledge of correspondences (ui; vj),between points ui on the desired and vj on the actual shape. FEM-based simulation software providesmeans to both virtually predict springback and directly obtain correspondences. In case of experimentalprototyping and validation, however, finding correspondences requires solving a registrationproblem: given a test shape Q (scan points of the as-built geometry) and a reference shape R (CADdata of the desired geometry), a transformation S has to be found to fit both objects. Correspondencesbetween S(Q) and R may then be computed based on a metric.If S is restricted to Euclidean transformations, then S(Q) results in a rigid transformation, whereevery point of Q is subject to the same translation and rotation. Local geometric deviations due tospringback are not considered, often resulting in invalid correspondences. In this contribution, a nonrigidregistration method for the efficient analysis of springback is therefore presented. The test shape Q is iteratively partitioned into segments with respect to an error metric. The segments are locally registeredusing rigid registration subject to regulatory conditions. Resulting discontinuities are addressedby minimization of the deformation energy. The error metric uses information about the deviationscomputed based on the correspondences of the previous iteration, e.g. maximum errors or changes ofthe sign. This adaptive per-segment registration allows appropriate correspondences to be determinedeven under local geometric deviations.