Parallel boundary and best neighbor searching sampling algorithm for drawbead design optimization in sheet metal forming

Koyama

Kawamoto

et al. 2016

Struct Multidisc Optim

This paper shows a case study for a simultaneous optimization of blank shape and variable blank holder force (VBHF) trajectory in deep drawing, which is one of the challenging issues in sheet metal forming in industry. Blank shape directly affects the material cost. To reduce the material cost, it is important to determine an optimal blank shape minimizing earing. In addition, VBHF approach is recognized as an attractive and crucial technology for successful sheet metal forming, but the practical application is rarely reported. To resolve these issues, the simultaneous optimization of blank shape and VBHF trajectory is performed. First, the experiment to identify the wrinkling region is carried out. Based on the experimental results, the finite element analysis (FEA) model is developed. The validity of the FEA model is examined by using the FLD. Numerical simulation in deep drawing is so intensive that a sequential approximate optimization (SAO) using a radial basis function (RBF) network is used for the numerical optimization. Based on the numerical result, the experiment using the AC servo press is carried out. It is found from the experimental results that the successful sheet metal forming is performed. In addition, it is confirmed from the numerical and experimental result that both the material cost and the forming energy are simultaneously reduced by using the design optimization technique.

Section: Evaluation Of Wrinkling and Tearing Using Forming Limit Diagrammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical and experimental case study on simultaneous optimization of blank shape and variable blank holder force trajectory in deep drawing

Koyama

Kawamoto

et al. 2016

Struct Multidisc Optim

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…Under such situations, the RSM is one of the practical approaches. A sequential approximate optimization (SAO) is recently used for improving the accuracy of the response surface (8)(9)(10)(11)(12) . In the SAO, the response surface is constructed repeatedly by adding new sampling points until terminal criteria are satisfied.…”

Section: Introductionmentioning

confidence: 99%

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

Srirat

Yamazaki

2012

JAMDSM

Optimum segmented blank holder shape and its variable blank holder gaps (VBHGs) are determined by a sequential approximate optimization (SAO) with radial basis function network. In deep drawing, wrinkling and tearing of blank sheet are major defects. The optimum segmented blank holder shape and its VBHGs are determined to avoid these defects. The Forming Limit Diagram (FLD) is employed to evaluate quantitatively the wrinkling and the tearing. In the numerical examples, a square cup deep drawing is handled. The objective is to minimize the thickness deviation after sheet forming. The wrinkling and the tearing are separately evaluated as the constraints. The dimensions of the segmented blank holder shape and the BHGs are taken as the design variables. The optimization result shows that simultaneous optimization of both the segmented blank holder shape and the VBHGs is one of the effective approaches for improving product quality.

“…，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 …”

unclassified

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

Kita²,

Yamazaki³

2011

Trans.JSME(C)

In deep drawing, a low blank holder force (BHF) will cause wrinkling, while a high BHF will lead to tearing. The Variable Blank Holder Force (VBHF) is an attractive approach in the industries, and it is important to determine the VBHF trajectory. In this paper, a sequential approximate optimization (SAO) approach is employed for determining the VBHF trajectory. The objective is taken as the minimization of the deviation of whole thickness. The constraint is quantitatively defined with the Forming Limit Diagram (FLD), in which no wrinkling and tearing can be observed. The blank holder forces are taken as the design variables. Two constraints in which wrinkling and tearing are avoided are employed in this paper. The Radial Basis Function (RBF) network is employed for constructing the response surface to capture the non-linear phenomena. In the proposed SAO approach, the optimum BHF is added to refine the VBHF trajectory, while some data points are also added to cover the entire design variable space. The result of the VBHF trajectory with the proposed SAO approach is compared with the one of the closed-loop type algorithm.