Blank Shape Design Research Articles

Optimum blank shape design in deep drawing process using a new boundary updating formula

Optimum blank shape design in deep drawing process using a new boundary updating formula

Formability Investigation of a Thin-wall Part of Double Curvature Using an Integrated Reverse Engineering Environment

ABSTRACTAn integrated reverse engineering (RE) environment composed of modeling, forming simulation, tooling design and manufacturing, and forming operation was employed to solve an existing problem, in which a thin-wall part of double curvature was not able to be physically formed without tearing and wrinkle after numerous attempts at a logistics center. This paper focuses on the formability study of this challenging part using the newly established RE environment. Forming simulation was heavily employed to explore a narrow window that ensures a successful part forming by investigating blank shape design and understanding the material flow in forming. A key factor that ensures a successful part without tearing or wrinkle was clearly suggested by forming simulations. A physical forming process that incorporates such a factor was implemented at shop floor, which produced an accurate part without tearing and wrinkle for the first time after numerous attempts. Lessons learned are presented and the feasibilit...

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

Optimal blank shape minimizing earing in deep drawing has a direct influence on material saving as well as product quality. A number of methods for blank shape optimization have been previously proposed, most of which adopt a closed-loop type algorithm that requires a large number of simulation runs. Numerical simulation in sheet metal forming is so numerically intensive that it is preferable to find an optimal blank shape with a small number of simulation runs. This paper proposes a method for determining the optimal blank shape design in square cup deep drawing using sequential approximate optimization (SAO) with a radial basis function (RBF) network. Sheet metal forming is multi-objective in nature, and thus the blank shape design problem is formulated as a multi-objective design optimization. The aim is therefore to identify the pareto-frontier with a small number of simulation runs. The earing is minimized under tearing and wrinkling constraints with a variable blank holder force (VBHF), which varies through the punch stroke. Numerical results show that the disconnected pareto-frontier is well identified with a small number of simulation runs. The earing of the optimal blank shape with the VBHF is also drastically reduced, when compared to a reference blank shape. Based on the numerical results, the experiments using a servo press are carried out. Consequently, the validity of the proposed approach is confirmed through the numerical and experimental results.

Topology Optimization of an Asymmetric Elliptical Cone Subjected to Blast Loading

This paper describes a numerical procedure for the blank shape design of thin aluminum components achieved by explosive forming. The objective is to specify the initial blank shape considering the geometry of the final product. The numerical procedure consists of three steps: At first, the forming process of an asymmetric blank in an elliptical cone die cavity and without blank holder is simulated. To rectify the wrinkles without optimization the square of the primary blank will be increased. In the next step, topology optimization is employed to obtain the optimum geometry of the blank whose diameter has been increased finally, the modified blank achieved previous step is used in the new simulation to check whether or not the wrinkles mentioned in first step has been rectified. Results show the proposed numerical procedure can provide the optimal blank shape in a few iterations.

Blank Shape Design for Sheet Metal Forming based on Geometrical Resemblance

In sheet metal forming, the optimal blank shape has many advantages, i.e. reduction of the material cost, minimizing the forming defects, improvement of the quality of formed part, etc. However, finding the optimal blank shapes could be difficult and time consuming. In this paper, an efficient blank design methodology is proposed based on geometrical resemblance, which requires several iterations of finite element analysis simulation to obtain an optimal blank shape. In order to verify this methodology, two case studies on deep drawing processes and one experimental validation have been carried out. The methodology has been shown to be computationally efficient, requiring as few as four finite element iterations to obtain an optimal blank shape.

Optimum blank shape design using shape error and deformation path length of boundary nodes

The initial blank geometry plays an important role on the quality of deep drawn parts. The present paper develops a new approach for optimizing the blank shape. In this approach the three-dimensional model of the final part is used to design an initial blank geometry for the given part. The deep drawing process is simulated using the initial blank shape. The blank is optimized in an iterative process based on the shape error and the deformation path length of the boundary nodes of the blank in the previous iteration. Optimum blank shapes for four case studies are determined. The results of the presented method are compared with some other methods in the literature and the presented method is found to be more efficient.

Research on the Blank Design Method of Closed Rolling the High-Neck Flange

Blank shape design is the prerequisite and foundation of optimization for the closed forming the high-neck flange. This paper obtained the design formulas of blank size with analyzing the mathematical model of flank blank based on the principle of volume invariably during the rolling process.The blank of a special flange was designed by this method which was validated by the numerical simulation under the DEFORM software. The results indicate that the product is qualified with the blank shape based on this method. These research conclusions can provide scientific basis for forming the high-neck flange with rolling method.

Blank Optimization in Elliptical-Shape Sheet Metal Forming Using Response Surface Model Coupled with Reduced Basis Technique and Finite Element Analysis

The present study aims to determine the optimum blank shape design for the deep drawing of Elliptical-shape cups with a uniform trimming allowance at the flange i.e. cups without ears. This earing defect is caused by planar anisotropy in the sheet and the friction between the blank and punch/die. In this research, a new method for optimum blank shape design using finite element analysis has been proposed. Present study describes the approach of applying Response Surface Methodology (RSM) with Reduced Basis Technique (RBT) to assist engineers in the blank optimization in sheet metal forming. The primary objective of the method is to reduce the enormous number of design variables required to define the blank shape. RBT is a weighted combination of several basis shapes. The aim of the method is to find the best combination using the weights for each blank shape as the design variables. A multi-level design process is developed to find suitable basis shapes or trial shapes at each level that can be used in the reduced basis technique. Each level is treated as a separated optimization problem until the required objective – minimum earing function – is achieved. The experimental design of RSM method is used to build the approximation model and to perform optimization. MATLAB software has been used for building RSM model. Explicit non-linear finite element (FE) Code Abaqus/CAE is used to simulate the deep drawing process. FE models are constructed incorporating the exact physical conditions of the process such as tooling design like die profile radius, punch corner radius, etc., material used, coefficient of friction, punch speed and blank holder force. The material used for the analysis is Stainless steel St12. A quantitative earing function is defined to measure the amount of earing and to compare the deformed shape and target shape set for each stage of the analysis. The cycle is repeated until the converged results are achieved. This iterative design process leads to optimal blank shape. So through the investigation the proposed method of optimal blank design is found to be very effective in the deep drawing process and can be further applied to other stamping applications.

A numerical method for the optimal blank shape design

This paper describes a numerical procedure for the blank shape design of thin metallic parts obtained by stamping. The objective is to determine the initial blank shape knowing the geometry of the desired 3D CAD part. The numerical procedure consists of two stages: At first, an estimation of the initial blank shape is given using the one step inverse approach (IA). Then, update of the blank shape is continued by iterations combining optimization algorithms and finite element analysis (FEA). The numerical procedure for the blank shape design is tested in the case of an industrial stamping process where the part is formed using a manual press without blank-holder. The proposed numerical procedure can provide very quickly the optimal blank shape in a few iterations.

An Heuristic Optimization Algorithm for the blank shape design of high precision metallic parts obtained by a particular stamping process

The present paper deals with the blank shape design of high precision thin metallic parts obtained by a particular stamping process. The main objective is to optimize the blank shape in order to produce a desired 3D final part within severe fixed tolerances ( ± 0.05 mm ). Presently, to overcome this issue, a very expensive and time consuming trial and error method is used. Here an attempt is made to develop an automatic numerical procedure based on commercial finite element modeling (FEM) code and Heuristic Optimization Algorithms (HOA). This procedure is composed of two stages: first, an initial guess of the blank shape is performed using the inverse approach (IA), then an update of the blank shape is obtained iteratively combining HOA and incremental FEM code ( ABAQUS ® or STAMPACK ® ). The proposed approach is validated on industrial case where the part is stamped in two stages by the mean of manual press, without blank-holder and using tools characterized by complex 3D geometry. This approach has demonstrated its effectiveness and simplicity to provide with a reasonable number of iterations an optimal solution which is in a very good agreement with the experimental results.

Optimum blank shape design in sheet metal forming by boundary projection method

The optimum blank shape is the minimization of the difference between the target contour of the part and the outer contour of the deformed blank. The main objective of this paper is to introduce a new blank design method based on iterative finite element (FE) sheet metal forming simulations. The algorithm is based on the projection of the target contour on the deformed blank and modifying the blank shape accordingly. The developed algorithm is applied a square cup drawing in order to confirm its validity.

Blank optimization for sheet metal forming using multi-step finite element simulations

The present study aims to determine the optimum blank shape design for deep drawing of arbitrary shaped cups with a uniform trim allowance at the flange, i.e., cups without ears. The earing, or non-uniform flange, is caused by non-uniform material flow and planar anisotropy in the sheet. In this research, a new method for optimum blank shape design using finite element analysis is proposed. The deformation process is first divided into multiple steps. A shape error metric is defined to measure the amount of earing and to compare the deformed shape and target shape set for each stage of the analysis. This error metric is then used to decide whether the blank needs to be modified. The blank geometry change is based on material flow. The cycle is repeated until the converged results are achieved. This iterative design process leads to optimal blank shape. To test the proposed method, three examples of cup drawing are presented. In every case converged results are achieved after a few iterations. The proposed systematic method for optimal blank design is found to be very effective in the deep drawing process and can be further applied to other sheet metal forming applications such as stamping processes.

Determination of optimal blank shape by the radius vector of boundary nodes

A new method of optimal blank shape design for the drawings of arbitrary shapes has been proposed. Similar to the sensitivity method, as detailed in past work of the present author, the basic nature of this method is iterative modification of an undeformed blank shape by moving the nodal positions at the boundary of the blank, until the final shape satisfies a target shape. The main difference from the sensitivity method is that the radius vector, determined by three adjacent boundary nodes during the deformation, is utilized in this method. The direction of the radius vector is utilized as a main parameter for the blank shape modification. Even though the sensitivity method has been proven to be excellent through both comparison and experiment, there still remain problems such as two runs of finite element analyses for each design stage, and hence huge computational effort. For the rigid-body rotation dominant problems, the method often fails to find the optimal shape. The present method requires only a single deformation analysis for each design step and there is no problem due to the rigid-body rotation during forming. Drawings of L-shaped cup, oil pan and wheel housing have been chosen as the examples to verify the present method through comparison with the result predicted by the sensitivity method. In every case the optimal blank shapes have been obtained after a few iterations without a predetermined deformation path and it has been verified that the deformed shape with the predicted optimal blank almost coincides with the target shape. Through this investigation, the present method is found to be as good as or better than the sensitivity method in the optimal blank design.

Optimal blank shape design using the initial velocity of boundary nodes

A new method of optimal blank shape design using the initial nodal velocity (INOV) has been proposed for the drawings of arbitrary shaped cups. With the given information of tool shape and the final product shape, corresponding initial blank shape has been found from the motion of boundary nodes. Although the sensitivity method, the past work of the present authors, has been proved to be an excellent method to find optimal blank shapes, the method has a problem that a couple of deformation analysis is required at each design step and it also exhibits an abnormal behaviors in the rigid body rotation prevailing region. In the present method INOV, only a single deformation analysis per each design stage is required. Drawings of L-shaped cup and oil pan have been chosen as the examples. At every case the optimal blank shapes have been obtained only after a few times of modification without predetermined deformation path. The deformed shape with predicted optimal blank almost coincides with the target shape at every case. Through the investigation the INOV is found to be very effective in the arbitrary shaped drawing process design.

초기 속도법을 이용한 최적 블랭크 설계 프로그램의 개발

A new method of optimal blank shape design using the initial nodal velocity (INOV) has been proposed for the drawings of arbitrary shaped cups. With the given information of tool shape and the final product shape, corresponding initial blank shape has been found from the motion of boundary nodes. Although the sensitivity method, the past work of the present authors, has been proved to be excellent method to find optimal blank shapes, the method has a problem that a couple of deformation analysis is required at each design step and it also exhibits an abnormal behaviors in the rigid body rotation prevailing region. In the present method INOV, only a single deformation analysis per each design stage is required. Drawings of practical products as well as oil-pan, have been chosen as the examples. At every case the optimal blank shapes have been obtained only after a few times of modification without predetermined deformation path. The deformed shape with predicted optimal blank almost coincides with the target shape at every case. Through the investigation the INOV is found to be very effective in the arbitrary shaped drawing process design.

Optimal blank shape design by the iterative sensitivity method

In order to realize net shape manufacturing of drawn parts, determination of the optimal blank shape plays a key role in the process development stage. The sensitivity method has many successful applications of the optimal blank design. In the method, the undeformed blank shape is modified iteratively by moving boundary nodes in the initial moving direction until the deformed shape satisfies a target shape. To determine the magnitude of the movement of the nodes, both the shape error measured at the deformed shape and the shape sensitivity defined by the effect of initial shape change on the final shape are utilized. To obtain shape sensitivity for each boundary node numerically, a couple of deformation processes has been analysed at each design stage with an original blank and offset blank. Drawings of the trapezoidal cup, cross-shaped cup and oil pan have been chosen as examples to verify the sensitivity method. Both the cross-shaped cup and oil pan are examples of complicated material flow during forming while the trapezoidal cup is of a simple flow. For every case the optimal blank shape has been obtained after only a few modifications without any predetermined deformation path. With the predicted optimal blank, a corresponding experiment has been carried out. The deformed shapes of the experiment almost exactly coincide with the desired target shape in every case. Through the investigation, the sensitivity method is found to be excellent in the blank design of arbitrary shaped drawing products.

Optimum blank shape design by sensitivity analysis

A method of blank shape design based on sensitivity analysis for the non-circular deep drawing process has been proposed. By assuming the final deformation shape to be a drawn cup with a uniform trimming allowance at the flange, the corresponding initial blank which gives the final shape after deformation has been found. With the aid of a well-known dynamic explicit analysis code PAM-STAMP, shape sensitivity has been obtained. To obtain the shape sensitivity numerically, a couple of deformation processes have been analyzed. In order to validate this method, deep drawings of a square cup, a clover shaped cup and an L-shaped cup have been chosen as the examples. In every case converged results have been obtained only after a few times of modification. With the predicted optimal blank, both computer simulation and experiment are performed. Excellent agreement is noted between simulation and experiment in every case. Through the investigation, the proposed systematic method of optimal blank design is found to be very effective in the design of a deep drawing process.

Optimum blank design of an automobile sub-frame

A roll-back method is proposed to predict the optimum initial blank shape in the sheet metal forming process. The method takes the difference between the final deformed shape and the target contour shape into account. Based on the method, a computer program composed of a blank design module, an FE-analysis program and a mesh generation module is developed. The roll-back method is applied to the drawing of a square cup with the flange of uniform size around its periphery, to confirm its validity. Good agreement is recognized between the numerical results and the published results for initial blank shape and thickness strain distribution. The optimum blank shapes for two parts of an automobile sub-frame are designed. Both the thickness distribution and the level of punch load are improved with the designed blank. Also, the method is applied to design the weld line in a tailor-welded blank. It is concluded that the roll-back method is an effective and convenient method for an optimum blank shape design.

Blank shape design for a planar anisotropic sheet based on ideal forming design theory and FEM analysis

A sequential design procedure to optimize sheet forming processes was developed utilizing ideal forming design theory, FEM analysis and experimental trials. For demonstration purposes, this procedure was used to design a blank shape for a highly anisotropic aluminum alloy sheet (2090-T3) that results in a deep-drawn, circular cup with minimal earing. All blank shape design methods require a certain number of iterations. However, the sequential procedure can be more effective than the other iterative methods based on FEM analysis in conjunction with experimental trials or on experimental trials alone. For this design demonstration, the anisotropic constitutive behavior of the 2090-T3 sheet was expressed using plastic potentials previously proposed by Barlat et al. The implementation of the anisotropic strain-rate potential in the ideal forming design code is also briefly summarized.