A closed-loop type algorithm for determination of variable blank holder force trajectory and its application to square cup deep drawing

In deep drawing, a low blank holder force (BHF) can cause wrinkling, while a high BHF can lead to tearing. Thus, it is important to determine the appropriate BHF to be utilized in the forming process. In this study, a variable blank holder force (VBHF) approach to deep drawing is employed, and a simple closed-loop type algorithm is developed to obtain 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, which is the cause of wrinkling, is used as the initial BHF; it is then increased to prevent wrinkling. The algorithm is terminated when tearing occurs. In a numerical simulation, the distance between the die and the blank holder is used to measure wrinkling. On the other hand, the thickness of the blank is used to determine the tearing. Next, in the second phase, the deviations in thickness are examined. Wrinkles are also checked in the second phase. By iterating the above two phases, the VBHF trajectory can be obtained. One of the advantages of the VBHF is that it reduces the forming energy. The validity of the proposed algorithm is examined through both a numerical simulation and experiment.