Prediction of rigid body motion in multi-pass single point incremental forming

Incremental sheet forming uses a generically shaped tool to form a clamped metal sheet into a desired shape by traversing the tool along a predetermined toolpath. This flexible manufacturing process enables low-cost and rapid manufacturing by eliminating the need for expensive part-specific tooling. Multi-Pass Single Point Incremental Forming (MSPIF) is a toolpath strategy which improves formability by designing toolpaths of intermediate geometries that start with the unformed sheet and upon completion of the last stage finishes with the desired, difficult-to-form part. The main challenge faced in MSPIF is the occurrence of stepped features in the final geometry. We attribute the formation of this step feature to the rigid body motion caused by the intermediate steps. In this work, the 3D contact patch between the tool and the sheet during an MSPIF toolpath is studied, and a method for predicting the rigid body motion (RBM) is provided. In this method, a hypothesis for RBM and a UV map, a 2D parametrization of the 3D geometry used to track both the formed geometry and the toolpath during MSPIF, are given. Then equations are derived for calculating the RBM for discrete motions of the tool along the toolpath. Using the proposed methodology, an MSPIF strategy that incorporates the prediction of the rigid body motion was tested for validation. The resulting MSPIF part demonstrated an increased formability and the absence of stepped features, thus confirming the validity of the prediction methodology.