A hierarchical and localized node-to-analytical surface contact search algorithm for flow forming simulation

Existing contact search algorithms most rely on a generic two-stage framework, which tends to yield suboptimal efficiency by neglecting problem-specific features. Therefore, a novel five-stages node-to-analytical surface contact search algorithm is proposed to reduce the elapsed time by confining the search to localized regions conforming to the point-contact feature of incremental processes like flow forming. In this algorithm, the rigid tools are analytically represented by parametric surfaces, which enhances the geometric accuracy and reduces search volume. Considering the local loading characterization of the process and building upon the master-slave search framework, the algorithm divides the contact search into five sequential stages. The hierarchy gradually excludes non-contact cases and confines the search region to the vicinity of the rollers. At the top level of the hierarchy, kinematic information of moving objects is used to rapidly determine whether contact is about to occur. Next, a two-level bucket sorting method further narrows the search regions. Then, the slave nodes are projected onto the meridional plane of rigid master surface to generate candidate pairs using the bounding volume hierarchy of the segments in its generatrix. Finally, the contact pairs are identified by the close point projection method. This hierarchical algorithm is implemented in the in-house software PySFEM, and is evaluated against the two-stage algorithm using flow forming examples with varying heights of workpiece and different numbers of rollers. The results show the proposed algorithm maintains consistent state variable distributions in the workpiece and reduces the elapsed time by up to 85.14%. Since the proposed algorithm localizes the search region, its elapsed time increases by no >25.7% even if the size of contact surface doubles.