With the availability of VBHF press, researchers continued to conduct in-depth study to develop optimization strategy for regulating the BHF trajectories in terms of punch stroke. CAO et al presented PI (proportional–integral)[9] and ARMA (Auto-Regressive and Moving Average)[10] method, which increased the part quality of conical cup and hemispherical cup, respectively. SUN et al[11] proposed an RSM model combined with the FEM simulation to increase the formability of aluminum sheet when being applied to a rectangular box. In work of SHENG et al[12], the adaptive simulation was used to predict the variable blank holder force in conical cup drawing. AYED et al[13] investigated the BHF optimization of Numisheet’99 front door panel with three inequality constraints.
In  our  previous  research[14],  a  proportional integral derivative (PID) optimization strategy has been presented based on the analysis of BHF formability window and integrated into commercial FEM code to obtain time-variable and spatial-variable optimal BHF in a single round of forming simulation. Then, a stepped rectangular box of 60 mm in drawing height with 10 segmental binders was adopted. The constant BHF experiment and the derived trajectory of optimal BHF were verified on a multipoint variable BHF hydraulic press and the experiment results corresponded well with FEM optimization, which increased the drawing depth by 33%.
In this study, the above closed loop optimization strategy is applied to a complex automobile  deck  lid inner panel, which is the benchmark of Numisheet’05[15]. The primary goal is to design proper segmented binders for the drawing tool set and achieve time-variable BHF trajectories for each segmented binder. To verify the improvement of part quality, the thickness distribution and variation of stamped part under the optimal VBHF trajectories derived in this study are compared with those under constant BHF drawing published by Numisheet’05 Committee.
2    Quick review of Numisheet’05 deck lid benchmark and PID closed loop VBHF optimization strategy
The forming tools used in this benchmark are shown in Fig.1. The participators can use either physical drawbeads or line drawbeads in the forming simulation. The distributing information for the physical drawbead geometry is shown in Fig.2. The line drawbeads could save the calculation time by equivalent virtual resistance. However, the precision is inadequate as the line drawbeads model couldn’t truly simulate the material draw-in and draw-out at the drawbeads location. Therefore, in this study, physical drawbeads were chosen to simulate the drawbead behavior for high precision.
The strategy developed in this work is based on the extended BHF formability window. Fig.3 shows three types of BHF formability windows representing three materials with different levels of deep drawing formability. The part will have cracking defect if the
Fig.1 Forming tools used in Numisheet’05 rear deck lid benchmark
 Fig.2 Drawbead centerlines, transition points, and coordinate system orientation, and thickness measurement locations of Numisheet’05 rear lid
Fig.3 Extended BHF formability windows: (a)  Feasible constant BNF window; (b) Feasible VBHF window; (c) Infeasible VBHF window
BHF is larger than cracking BHF value. While if the BHF is smaller than the wrinkling BHF, wrinkling will occur in the part. The area between the cracking BHF and the wrinkling BHF is the safety region. The required punching depth is denoted as the design target and intersection I tells the punching limit for the material. In Fig.3(a), the design target is smaller than the limit depth and the safety region is wide enough to contain constant BHF trajectory. Therefore, the part could be formed successfully by constant BHF or VBHF as long as they are in the scope of the safety region. In Fig.3(b), the safety region is limited so that constant BHF couldn’t form this part to the required depth. Under this circumstance, VBHF is a perfect choice to form this part. In Fig.3(c), the design target is larger than the limit depth of the material, which indicates that neither  constant BHF nor VBHF could form this part to the required depth. Through these BHF formability windows, one can see that wrinkling BHF is the minimum BHF that could suppress the defect of wrinkling. In the meantime, the wrinkling BHF enables the maximum draw-in of sheet material during deep drawing, postponing the onset of necking and decreasing the possibility of cracking. Therefore, the wrinkling BHF is served as the optimal BHF trajectory in this study. 深变压边力的优化英文文献和中文翻译(5):http://www.751com.cn/fanyi/lunwen_48238.html