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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.

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Plastic injection molding (PIM) is one of the most important manufacturing processes for producing plastic products. The process parameters in the PIM, such as mold temperature, melt temperature, and injection pressure affect the product quality and the manufacturing cost. In general, these are determined by a trial-and-error method, but computer-aided engineering coupled with optimization technique is recognized as one of the useful tools available. Numerical simulation in the PIM is so numerically intensive that response surface approach is valid for determining the optimal process parameters. In particular, a sequential approximate optimization (SAO) that response surface is constructed and optimized repeatedly is valid to find the optimal process parameters with a small number of simulation runs. In this paper, a cup-type plastic product is considered. The volume shrinkage is one of the major defects for dimension accuracy. In addition, it is important to produce the product with a minimum clamping force for the productivity. Short shot that the melt plastic is not filled into the die cavity is a serious defect, and this is handled as the design constraint. Thus, a multi-objective optimization problem is formulated. The pareto-frontier is identified by using the SAO with the radial basis function network. The difference of pareto-frontier with and without the injection and packing time is discussed. It is clear from the numerical result that the injection and packing time have influence on the product quality.