Variable Blank Holder Force Trajectory Research Articles

Numerical optimization of blank shape and sloped variable blank holder force trajectory for an automotive part

Numerical optimization of blank shape and sloped variable blank holder force trajectory for an automotive part

Optimization of variable blank holder force in deep drawing based on support vector regression model and trust region

Blank holder force (BHF) is one of the important process parameters for successful sheet metal forming. Variable blank holder force (VBHF) that the BHF varies through the forming process is recognized as one of the advanced manufacturing technologies. Therefore, optimization of VBHF trajectory is a crucial issue in industries. One of the effective approaches to determine the VBHF trajectory is to use the surrogate modeling techniques. However, it is very inaccurate and time-consuming to determine the VBHF trajectory for successful sheet forming through surrogate-based optimization methods. Therefore, this paper proposes an improved surrogate-based optimization method by integration of support vector regression (SVR) and trust region strategy to optimize VBHF in deep drawing. First, a random sampling test of VBHF in deep drawing is designed and a SVR approximate model of VBHF under random sampling is developed. Then, a trust region algorithm is adopted to predict and control the accuracy of the SVR approximate model of VBHF. Response surface is repeatedly constructed and optimized that is adopted to identify the Pareto-frontier of VBHF. The validity of the proposed approach is examined through the comparison of numerical and experimental results. The results of this research provide a reliable reference for future efforts to optimize VBHF in deep drawing.

Numerical optimization of variable blank holder force trajectory and blank shape for twist springback reduction using sequential approximate optimization

This paper proposes an approach for twist springback reduction using variable blank holder force (VBHF) trajectory that the blank holder force (BHF) varies through the stroke. In addition, the blank shape is optimized. Therefore, design optimization of VBHF trajectory and blank shape for twist springback reduction is performed. Springback of U-shaped product is a simple deformation, whereas the one of S-rail-shaped product shows more complicated behavior due to twisting. As the result, compared with the springback of U-shaped product, it is difficult to evaluate the twist springback. A novel evaluation method for the twist springback is proposed, and the optimal VBHF trajectory and blank shape for the twist springback reduction are determined under several design constraints. Numerical simulation of the S-rail-shaped product is so intensive that response surface approach is valid. In particular, a sequential approximate optimization that the response surface is repeatedly constructed and optimized is used to determine the optimal VBHF and blank shape. Through numerical result, the validation of the proposed approach is examined.

Design optimization of variable blank holder force trajectory and slide velocity for minimizing thickness variation in sheet metal forming

Design optimization of variable blank holder force trajectory and slide velocity for minimizing thickness variation in sheet metal forming

Design optimization of variable blank holder force trajectory and blank shape for S-rail shaped product using a novel springback evaluation

Design optimization of variable blank holder force trajectory and blank shape for S-rail shaped product using a novel springback evaluation

段付き円筒カップを対象としたシートハイドロフォーミングにおける内圧経路と可変ブランクホルダー力の同時最適軌道設計

段付き円筒カップを対象としたシートハイドロフォーミングにおける内圧経路と可変ブランクホルダー力の同時最適軌道設計

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

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.

318 プレス成形加工における可変ブランクホルダー力の最適軌道設計(OS1-3 最適設計と解析)

318 プレス成形加工における可変ブランクホルダー力の最適軌道設計(OS1-3 最適設計と解析)

Numerical optimization of blank shape considering flatness and variable blank holder force for cylindrical cup deep drawing

Both blank shape minimizing earing and blank holder force (BHF) have an influence on the product quality as well as product cost. Recently, variable blank holder force (VBHF) that the BHF varies through the punch stroke is an attractive approach for improving the product quality as well. This paper proposes a method to simultaneously determine both optimal blank shape minimizing earing and the optimal VBHF trajectory for a cylindrical cup deep drawing. In this paper, the earing is separately evaluated as (1) the area above the trimmed line, and (2) the area below the trimmed line, and both are then minimized. The distance between the trimmed line and the cup height is also considered in the objective functions for the flatness of earing. Therefore, a multi-objective optimization problem is formulated. 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 blank shape and VBHF trajectory. In the numerical simulation, a cylindrical cup deep drawing based on NUMISHEET 2011(BM1) is considered, and the validity of the proposed approach is examined.

Sequential approximate robust design optimization using radial basis function network

This paper proposes a sequential approximate robust design optimization (SARDO) with the radial basis function (RBF) network. In RDO, the mean and the standard deviation of objective should be minimized simultaneously. Therefore, the RDO is generally formulated as bi-objective design optimization. Our goal is to find a robust optimal solution with a small number of function evaluations, not identifying a set of Pareto-optimal solution using Multi-Objective Evolutionary Algorithms. The weighted sum is often used to find a robust optimal solution. In contrast, the weighted lp norm method is used in this paper. Through illustrative examples, some validations of the weighted lp norm method to the RDO are clarified. Next, SARDO with the RBF network is discussed. In general, the standard deviation of functions is obtained by using the finite difference method. Thus, in order to obtain the standard deviation of functions, the finite difference method is directly applied to the response surface. High accuracy of the finite difference method will leads to highly accurate robust optimal solution. In order to avoid the inaccurate numerical calculation, the standard deviation is expressed by only the Gaussian kernel. As the result, it is expected that a highly accurate robust optimal solution can be found with a small number of function evaluations. Through numerical examples, the validity of the proposed approach is examined. Finally, the variable blank holder force trajectory for reducing springback is examined.

2102 角筒深絞り加工を対象とした初期ブランク形状と可変ブランクホルダー力の最適設計(OS5-3 設計と最適化3)

In deep drawing, area above the trimmed line is called earing. Reduction of the earing is one of the major issues for cost reduction. In addition, it is well known that blank holder force (BHF) has a direct influence on the product quality. A high BHF causes tearing, while a low BHF leads to wrinkling. Therefore it is important to determine an appropriate BHF through drawing. Recently, variable BHF (VBHF) approach which varies through the punch stroke has received a lot of attention, and its validity is discussed. In this study, both initial blank shape minimizing the earing and VBHF trajectory are simultaneously determined under tearing/wrinkling constants. In particular, two objective functions are defined for evaluation the earing. In other words, our design problem is formulated as a multi-objective design optimization. First objective function is the area above the trimmed line, and second one is the area below the trimmed line. In general, numerical simulation in sheet forming is so expensive that a sequential approximate optimization (SAO) using the radial basis function (RBF) network is adopted to identify the Pareto-frontier. The validity of the proposed approach is examined through numerical simulation. It can be found from the numerical result that earing is drastically reduced by the proposed approach.

1309 逐次近似最適化を用いた可変ブランクホルダーカの軌道と工具モーションの同時最適化

In this paper, variable blank holder force (VBHF) trajectory and tools motion are optimized simultaneous by a sequential approximate optimization (SAO) with radial basis function (RBF) network. In deep drawing, wrinkling and tearing are major defects that are strongly avoided in sheet forming. These defects are then taken as the objectives directly. The Forming Limit Diagram (FLD) is employed to evaluate the risk of wrinkling and tearing quantitatively. The design variables are taken so as to optimize the VBHF trajectory and the tools motion simultaneously. In numerical examples, a square cup deep drawing is handled. The optimum result shows that simultaneous optimization of the VBHF trajectory and the tools motion result in the successful deep drawing. In particular, the forming energy can be drastically reduced, in comparison with only the optimization of VBHF trajectory. This result implies that the simultaneous optimization of both VBHF trajectory and tools motion will be effective approach to reduce the forming energy.

1914 多目的逐次近似最適化を用いた可変ブランクホルダーカの最適軌道設計

1914 多目的逐次近似最適化を用いた可変ブランクホルダーカの最適軌道設計

Optimization of variable blank holder force trajectory for springback reduction via sequential approximate optimization with radial basis function network

Springback is one of the major defects in sheet metal forming. Variable blank holder force (VBHF) approach is one of the effective ways for the springback reduction. In this paper, the VBHF trajectory is optimized to reduce the springback by a sequential approximate optimization (SAO) with radial basis function (RBF) network. The U-shaped forming in NUMISHEET'93 is employed to determine an optimum VBHF trajectory, for example. In this paper, the bending moment is taken as the objective function. The tearing of sheet during the forming is considered as the design constraint, and the forming limit diagram (FLD) is employed to evaluate the design constraint quantitatively. It has been found from numerical results that the optimal VBHF trajectory can drastically reduce the springback in comparison with various VBHF trajectories. Through the theoretical examination and numerical simulation, the springback reduction of metal forming by the VBHF trajectory is discussed.

1209 スプリングバック抑制を目的とした可変ブランクホルダー力の最適軌道設計(OS7-2 近似最適化II)

Springback is one of the major defects in sheet metal forming. Numerical simulation based on finite element analysis is a powerful tool for springback prediction. Variable blank holder force (VBHF) approach is one of the effective ways for the springback reduction. In this paper, the VBHF trajectory is optimized by a sequential approximate optimization (SAO) with radial basis function network. U-shaped forming is handled for determining an optimum VBHF trajectory. In general, three objective functions are formulated in the springback reduction. These objective functions are not considered the state of the blank. In this paper, the residual bending moment is taken as the objective function. In order to evaluate the constraint quantitatively, the forming limit diagram (FLD) is employed. The forming by VBHF trajectory can drastically reduce the springback in comparison with the forming with the constant blank holder force.

Optimization of Variable Blank Holder Force Trajectory for Springback Reduction

Springback is one of the major defects in sheet metal forming. Numerical simulation based on finite element analysis is a powerful tool for springback prediction. Variable blank holder force (VBHF) approach is one of the effective ways for the springback reduction. In this paper, the VBHF trajectory is optimized by a sequential approximate optimization (SAO) with radial basis function network. U-shaped forming is handled for determining an optimum VBHF trajectory. In general, three objective functions are formulated in the springback reduction. These objective functions are not considered the state of the blank. In this paper, the residual bending moment is taken as the objective function. In order to evaluate the constraint quantitatively, the forming limit diagram (FLD) is employed. In particular, the tearing is considered as the constraint. It can be found from numerical results that the residual bending moment is more effective than the maximum nodal displacement for the springback reduction. In addition, the forming by VBHF trajectory can drastically reduce the springback in comparison with the forming with the constant blank holder force.

Simultaneous Optimization of Variable Blank Holder Force Trajectory and Tools Motion in Deep Drawing via Sequential Approximate Optimization

Simultaneous Optimization of Variable Blank Holder Force Trajectory and Tools Motion in Deep Drawing via Sequential Approximate Optimization

CO-JP-4 Simultaneous Optimization of Variable Blank Holder Force Trajectory and Tools Motion in Deep Drawing via Sequential Approximate Optimization

CO-JP-4 Simultaneous Optimization of Variable Blank Holder Force Trajectory and Tools Motion in Deep Drawing via Sequential Approximate Optimization

1112 スプリングバック抑制を目的とした可変ブランクホルダー力の最適軌道設計(OS07-1 最適設計と解析,オーガナイズドセッション 7:「最適設計と解析」)

1112 スプリングバック抑制を目的とした可変ブランクホルダー力の最適軌道設計(OS07-1 最適設計と解析,オーガナイズドセッション 7:「最適設計と解析」)

Optimization of variable blank holder force trajectory by sequential approximate optimization with RBF network

Sequential approximate optimization (SAO) is an attractive approach for design optimization. In this paper, the radial basis function (RBF) network is employed for the SAO. First, we examine the width of the Gaussian kernel, which affects the response surface. By examining the simple estimate proposed by Nakayama, four sufficient conditions are introduced. Then, a new simple estimate of the width in the Gaussian kernel is proposed. Second, a new sampling strategy with the RBF network is also proposed. In order to find the sparse region, the density function with the RBF network is developed. The proposed width and sampling strategy are examined through benchmark problems. Finally, the proposed SAO is applied to the optimal variable blank holder force (VBHF) trajectory for square cup deep drawing. The objective is taken as the minimization of the deviation of whole thickness. The constraints are quantitatively defined with the forming limit diagram in which no wrinkling and tearing can be observed. The design variables are the blank holder force. In particular, the risk of both tearing and wrinkling can be handled as the constraints separately. Numerical simulation is carried out by the optimal VBHF trajectory with SAO. It is clear from the numerical simulation that no tearing and wrinkling can be observed.