Determining the optimum variable blank-holder forces using adaptive response surface methodology (ARSM)

Abstract

Wrinkling and fracture are main defects in sheetmetal forming. They can be reduced or eliminated by manipulating a suitable blank-holder force (BHF). But it is difficult to attain the optimum BHF during sheet-metal forming. In this article, a new optimization algorithm integrating the finite element method (FEM) and adaptive response surface methodology £(r)ARSM£(c) is presented to determinate the optimum BHF. To assure convergence, the trust region modes management strategies are used to adjust the move limit of design spaces. Finally, the optimum results of rectangular box deep drawing are given. Experiments are performed to verify the optimal result.

Multi-objective optimization of blank shape for deep drawing with variable blank holder force via sequential approximate optimization

“…(STEP3) All functions are approximated by the RBF network; wherein the approximated objective functions are denoted asf i x ð Þ i ¼ 1; 2; ⋯; K ð Þ , and the approximated constraint functions are denoted asg j x ð Þ j ¼ 1; 2; ⋯; ncon ð Þ . (STEP4) A pareto-optimal solution for the response surface is found using the weighted lp norm method formulated as follows (Chengzhi et al 2005):…”

“…The weighted lp norm method is used to find a paretooptimal solution, and the weight for each objective function should be assigned. Unlike the weighted sum, the weighted lp norm method can find a set of paretooptimal solutions of the non-convex pareto-frontier with various weights (Chengzhi et al 2005). 3.…”

“…In most cases, a constant BHF through the punch stroke is simply used. By adopting variable BHF (VBHF) approach, in which BHF varies throughout the punch stroke, improvements in the final product quality should be achievable (Chengzhi et al 2005;Lin et al 2007;Kitayama et al 2010). Furthermore, the VBHF is not only useful for reducing the earing in deep drawing, but also for controlling the material flow into the die.…”

Optimization of Segmented Blank Holder Shape and Its Variable Blank Holder Gap in Deep-Drawing Process

“…Thus, the objective of the VBHF approach is to find the VBHF trajectory through the punch stroke. The VBHF approaches can be roughly classified into two categories: One is based on the closed-loop type algorithm and the other is the response surface method (RSM) (7)(8)(9)(10)(11)(12) . The authors have already proposed both approaches for avoiding these defects, and the detailed procedures can be found in Refs.…”

Optimum Trajectory of the Variable Blank Holder Force in the Square Cup Deep Drawing

“…，これらは本来，制約条件として扱う ほうが自然である． (P2) 複数の目的関数を設定し，線形加重和法を用いて，単一目的関数の最小化問題に変換している (10,14,(16)(17)(18)(19) ． 線形加重和法における重みの決定について，何ら指針が得られておらず，一組の重みを設定して最適化 を終了している．重みに関する有効な知見，すなわち，目的関数間のトレードオフ関係について，何ら 言及されていない． (P3) 多くの研究では，複数存在する目的関数の応答曲面作成において，二次多項式近似が基本となっており， 交互作用等に関する注意が払われていない (10)(11)(12)(13)(14)(15)(16)20) ．近年，Kriging や Support Vector Machine を用いた研究 が報告されているが (17)(18)(19) ，BHF の大きさを求める研究であり，VBHF の最適軌道を求める研究ではない． (P4) 逐次近似最適化のアプローチが取られている研究も行われているが (10,12,15,16) ，これらの研究では，応答曲 面の最適解のみを追加してゆく Zooming 法である …”