Numerical investigation and optimization of pulsating and variable blank holder force for identification of formability window for deep drawing of cylindrical cup

When a difficult-to-draw material is used, it is important to clarify a formability window representing the relationship between the blank holder force (BHF) and the punch stroke. In many cases, variable blank holder force (VBHF) that the BHF varies through the punch stroke is useful for the successful sheet metal forming to the difficult-to-draw materials. Another approach is to use pulsating blank holder force (PBHF). Therefore, the use of both the PBHF and the VBHF is useful for identifying the formability window of difficult-to-draw materials. In this paper, the formability window of a difficult-to-draw material is clarified with the PBHF and the VBHF. A design optimization problem is constructed to identify the formability window, in which the punch stroke is maximized subject to wrinkling and tearing. Several parameters in the VBHF and PBHF are included, and these are taken as the design variables. Numerical simulation in sheet metal forming is so numerically intensive that response surface approach is used. In particular, a sequential approximate optimization (SAO) using a radial basis function (RBF) network is used to determine the optimal parameter of PBHF and VBHF. In the numerical simulation, deep drawing of a cylindrical cup based on NUMISHEET 2011(BM1) is used. The approach using the PBHF and VBHF for identifying the formability window is examined through the numerical simulation coupled with the SAO using the RBF network. It is found from the numerical result that the proposed approach is useful for clarifying the formability window of a difficult-to-draw material. In addition, the optimal PBHF can reduce the maximum punch load that affects the tool life.