Development of a simple closed-loop type algorithm for determination of variable blank holder force trajectory and its applications to square cup deep drawing

Abstract

In deep drawing, a low blank holder force (BHF) can cause wrinkling, while a high BHF can lead to tearing. In this study, a variable blank holder force (VBHF) approach to deep drawing is employed, and a simple closed-loop type algorithm is developed for the VBHF trajectory. The proposed algorithm is divided into two phases. The objective of the first phase is to check wrinkling and tearing. In this phase, a low BHF is used as the initial BHF, which is then increased to prevent wrinkling while controlling tearing. This phase of the algorithm is terminated when tearing occurs. In numerical simulation, the distance between the die and the blank holder is used to measure wrinkling, and the minimum thickness of the blank is used to determine the tearing. In the second phase of the algorithm, the deviations in thickness of the part are iteratively examined, without neglecting the occurrence of wrinkling. One of the advantages of using VBHF instead of constant BHF is that it reduces the forming energy. The validity of the proposed algorithm is examined comparing numerical simulation and experimental results. Finally, the proposed algorithm is also applied to obtain the segmented VBHF trajectory. © 2010 Satoshi Kitayama et al.