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 (u_i; v_j),between points u_i on the desired and v_j 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.

• Periodical: Key Engineering Materials (Volumes 651-653)
• Pages: 1015-1020
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.651-653.1015
• Online since: July 2015
• Authors: Matthias Schweinoch*, Alexei Sacharow, Dirk Biermann, Christoph Buchheim
• Keywords: Correspondence, ICP, Non-Rigid Registration, Segmentation, Springback Analysis

References

[1] X.A. Yang and F. Ruan : A die design method for springback compensation based on displacement adjustment, International Journal of Mechanical Sciences, 53 (2011) 5, pp.399-406, doi: 10. 1016/j. ijmecsci. 2011. 03. 002.

DOI: 10.1016/j.ijmecsci.2011.03.002

[2] P.J. Besl and H.D. McKay : A method for registration of 3-D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (1992) 2, pp.239-256, doi: 10. 1109/34. 121791.

DOI: 10.1109/34.121791

[3] H. Li, R.W. Sumner and M. Pauly : Global correspondence optimization for non-rigid registration of depth scans, SGP '08 Proceedings of the Symposium on Geometry Processing, (2008) , pp.1421-1430.

DOI: 10.1111/j.1467-8659.2008.01282.x

[4] D. Hähnel, S. Thrun and W. Burgard : An Extension of the ICP Algorithm for Modeling Nonrigid Objects with Mobile Robots, Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI), (2003).

[5] O. Sorkine : Differential Representations for Mesh Processing, Computer Graphics Forum, 25 (2006) 4, pp.789-807, doi: 10. 1111/j. 1467-8659. 2006. 00999. x.

DOI: 10.1111/j.1467-8659.2006.00999.x

[6] W. -W. Xu and K. Zhou : Gradient Domain Mesh Deformation - A Survey, Journal of Computer Science and Technology, 24 (2009) 1, pp.6-18, doi: 10. 1007/s11390-009-9209-4.

[7] A. Sacharow, J. Balzer, D. Biermann and T. Surmann : Non-rigid isometric ICP: A practical registration method for the analysis and compensation of form errors in production engineering, Computer-Aided Design, 43 (2011).

DOI: 10.1016/j.cad.2011.07.007

[8] A. Sacharow : Kompensation von Formabweichungen durch adaptive Freiformdeformation der CAD/CAM-Daten, Ph.D. thesis (2013), TU Dortmund University, Germany.