Rectangular Cup Research Articles

Numerical modeling of the multi-stage sheet pair hydroforming process

The need for reduction of the weight is an important issue in the sheet metal forming industry. The hydroforming process has become an effective manufacturing process, because it can be adapted to the manufacturing of complex structural components into a single body with high structural stiffness. Tube hydroforming has been successfully developed in industry such as in the manufacturing of the components of automotive vehicles. There still, however, remains the constraint of the geometrical shape that can be fabricated by tube hydroforming. In order to improve such a constraint in product shape of the tube hydroforming process and in the formability of conventional sheet metal forming, the hydroforming process of sheet metal has been studied. The sheet pair hydroforming process has been reported to have several important advantages compared with the conventional deep drawing process. Uniform deformation over the whole region is a main advantage in the sheet hydroforming process. However, the deformation of the sheet metal can be concentrated on a small region in the case of rectangular cup with a steep slope in the wall.In this paper, the multi-stage hydroforming process of a sheet pair is proposed in order to increase the formability of a structural parts having a shape like that of an oil pan. For the strict comparison of the proposed process, the blank holding force is controlled by a hydraulic valve to a constant value during deformation. The deformed shape and strain distribution of the manufactured parts with the proposed process are compared with the results of simulation.

Key technologies of the simulation of the hydrodynamic deep drawing of irregular parts

Because of the complex boundary conditions to be dealt with, it is a difficult task to simulate the hydrodynamic deep drawing of irregular cups. If the boundary conditions on the loading of liquid pressure onto the blank are not considered correctly, the results obtained from the FEM will differ greatly from the experimental results. In this paper a mathematical model is proposed for the liquid flow between the flange and the die when drawing a tapered rectangular cup using hydrodynamic deep drawing. The proposed model was incorporated into a commercial FEM software (LS-DYNA3D), successfully. Process parameters including die entrance radius, lubrication, blank geometry, and the control of material flow for the hydrodynamic deep drawing of a tapered rectangular cup were investigated. Based an experimental unit mounted onto a single-action hydraulic press, the hydrodynamic deep drawing process was also investigated experimentally. It was shown that the FE results matched well with the experimental results, which may suggest that the proposed method can be used to determine the main process parameters during the hydrodynamic deep drawing of irregular cups.

Construction of sliding constraint surfaces and initial guess shapes for intermediate steps in multi-step finite element inverse analysis

Multi-step inverse analysis has been developed for more accurate results while one-step analysis can affirm qualitative deformation behavior. An inverse finite element approach has more capability to design the optimum blank shape from the desired final shape with small amount of computation time and effort. In forming simulation with the inverse method, multi-step inverse analysis is difficult to apply because sliding constraint surfaces and initial guesses of intermediate steps described by complex die and punch set are hard to generate with present mapping schemes. In this paper, intermediate sliding constraint surfaces for multi-step finite element inverse analysis are automatically constructed from the die–punch set at each step with the given stroke. The initial guess of intermediate steps is constructed by a direct mesh mapping scheme that is suggested to generate an initial guess on the constructed sliding constraint surface. Construction of sliding constraint surfaces and initial guesses for intermediate steps is applied to a multi-step rectangular cup drawing process and an S-rail forming process. The numerical example of the multi-step rectangular cup drawing process demonstrates that the proposed mapping scheme is applicable to construct sliding constraint surfaces and initial guesses for analysis of a multi-step drawing process with large aspect ratio. The analysis result of the S-rail forming process is compared with that of a direct finite element analysis to evaluate the effectiveness of the mapping scheme proposed.

유한요소해석을 이용한 세장비가 큰 직사각컵 다단계 디프 드로잉-아이어닝 공정의 최적 금형설계

Optimum tool design is carried out for a multi-stage rectangular cup deep-drawing and ironing process with the large aspect ratio. Finite element simulation is carried out to investigate deformation mechanisms with the initial design made by an expert. The analysis considers the deep drawing process with ironing for the thickness control in the cup wall. The analysis reveals that the difference of the drawing ratio within the cross section and the irregular contact condition produce non-unifonrm metal flow to cause wrinkling and severe extension. For remedy, the modification guideline is proposed in the design of the tool and the process. Analysis results confirm that the modified tool design not only improves the quality of a deep-drawn product but also reduces the possibility of failure. The numerical result shows fair coincidence with the experimental one. After tryouts of the tool shape. the rectangular cup has been produced in the transfer press.

An Analysis of Draw-Wall Wrinkling in a Stamping Die Design

Wrinkling that occurs in the stamping of tapered square cups and stepped rectangular cups is investigated. A common characteristic of these two types of wrinkling is that the wrinkles are found at the draw wall that is relatively unsupported. In the stamping of a tapered square cup, the effect of process parameters, such as the die gap and blank-holder force, on the occurrence of wrinkling is examined using finite-element simulations. The simulation results show that the larger the die gap, the more severe is the wrinkling, and such wrinkling cannot be suppressed by increasing the blank-holder force. In the analysis of wrinkling that occurred in the stamping of a stepped rectangular cup, an actual production part that has a similar type of geometry was examined. The wrinkles found at the draw wall are attributed to the unbalanced stretching of the sheet metal between the punch head and the step edge. An optimum die design for the purpose of eliminating the wrinkles is determined using finite-element analysis. The good agreement between the simulation results and those observed in the wrinkle-free production part validates the accuracy of the finite-element analysis, and demonstrates the advantage of using finite-element analysis for stamping die design.

Tool design in a multi-stage drawing and ironing process of a rectangular cup with a large aspect ratio using finite element analysis

Tool design is carried out for a multi-stage deep drawing and ironing process of a rectangular cup with the large aspect ratio using the result of the finite element analysis. The analysis incorporates three-dimensional continuum elements for an elasto-plastic finite element method with the explicit time integration scheme using LS-DYNA3D. The analysis simulates the five-stage deep drawing and ironing process with the thickness control of the cup wall. Simulation is performed in order to investigate the failure by tearing during the forming process at the initial state of tool design. The analysis reveals that the difference of the drawing ratio within the cross section induces non-uniform metal flow which causes severe local extension. The irregular contact condition between the blank and the die also induces non-uniform metal flow which causes local wrinkling. This paper identifies such unfavorable mechanism in the rectangular cup drawing with ironing and proposes a new tool design with the guideline for modification in the design of the process and the sequential tool shape. The finite element analysis result with the improved tool design confirms that the proposed design not only reduces the possibility of failure but also improves the quality of a deep-drawn product. The numerical result shows fair coincidence with the experimental result.

Design modification in a multi-stage rectangular cup drawing process with a large aspect ratio by an elasto-plastic finite element analysis

Finite element analysis of multi-stage deep drawing processes is carried out for the process design of rectangular cup drawing with a large aspect ratio. The analysis incorporates shell elements for an elasto-plastic finite element method with an explicit time integration scheme using LS-DYNA3D. Simulation is performed for thorough investigation of failures such as tearing and wrinkling during the forming process. The analysis reveals that the difference of the drawing ratio within the cross-section produces non-uniform metal flow to cause wrinkling and severe extension. The irregular contact condition between the blank and the die also induces non-uniform metal flow. This paper identifies such an unfavorable mechanism in rectangular cup drawing and proposes a modification guideline in the design of the process and the tool shape. The analysis result confirms that the modified design not only improves the quality of a deep-drawn product but also reduces the possibility of failure.

Finite element inverse analysis for the design of intermediate dies in multi-stage deep-drawing processes with large aspect ratio

An inverse finite element approach for multi-stage deep-drawing processes is introduced for robust capability to determine the optimum blank shape from the desired final shape and to obtain the thickness strain distribution in the final shape with a small amount of computing time and effort. A direct numerical analysis of multi-stage deep-drawing processes is extremely difficult to carry out because of its complexities and convergence problems as well as tremendous computing time. The analysis of elliptical or rectangular cup drawing with large aspect ratio is likewise very difficult with respect to the design process parameters including the intermediate die profiles. In order to overcome the difficulties, an inverse scheme is proposed in the present analysis and design. The multi-stage inverse analysis deals with the convergence among intermediate shapes and the corresponding sliding constraint surfaces. In this paper, finite element inverse analysis is applied to multi-stage deep-drawing processes in order to calculate the thickness strain distribution in each intermediate shape and to design the intermediate die shapes. The original design has been modified to enhance the discrepancy in the thickness strain distribution for each intermediate shape.

Milli-component forming of rectangular cup drawing

Milli-structure components are classified as a component group for which the size is between macro- and micro-scales, i.e., less than about 20 mm and larger than 1 mm. The forming of these components has the typical phenomenon of bulk deformation with thin sheets because of the forming size. In this study, milli-structure rectangular cup drawing is analyzed and designed using the finite element method and experiment. Usually milli-structure containers or cases such as those of cellular phone vibrators and battery cases consist of rectangular-shaped drawings to save installation space. A systematic approach is established for the design of the forming processes for rectangular milli-structure cases. For the consideration of bulk forming effects, 8-node brick elements are used in the analysis and design of the milli-structure forming process. Also spring-back and cracking during forming will be discussed. The result of the finite element analysis is confirmed by that from a series of experiments.

Rapid design of corner restraining force in deep drawn rectangular parts

With the development of finite element method and computer technology, the complete modeling of the forming of a 3D sheet metal part is becoming realistic. However, an accurate 3D simulation is usually too time-consuming to be used in the early stage of design. One solution is to model the straight side of a 3D part as a plane strain problem and the corner section as an axisymmetric problem. Unfortunately, the axisymmetric solution often over-predicts the severity of the deformation at the corner and leads to a very conservative design. In this study, a modified axisymmetric model with a center offset is proposed to predict tearing failure in the corner sections of 3D parts. The proposed offset is found to be a function of the center strains, failure height, and tooling/process parameters, including tooling geometry, material properties, friction coefficient, and restraining force provided by the binder. Finite element analyses of both 3D and 2D axisymmetric models for square and rectangular cup forming are utilized to verify the proposed concept and to define the function. Excellent predictions of the failure heights are obtained. The proposed model enables engineers to rapidly specify the right amount of the restraining force in the corner section based on the desired center strains and forming depth. A detailed design algorithm is provided.

Sheet metal forming analysis of planar anisotropic materials by a modified membrane finite element method with bending effect

Abstract A modified membrane finite element with proper formulation is introduced to correctly enhance the flexural rigidity not only within an element but amongst elements. A finite element formulation is derived for the incremental analysis for non-steady large deformation in sheet metal forming. The formulation employs the convective coordinates to keep the objectivity in large deformation and rotation, and considers the planar anisotropy with Hill's quadratic yield criterion. The formulation is then combined with an effective contact algorithm to deal with the contact between the material and the dies. The simulation examples demonstrate the validity and versatility of the computer code, showing the earing phenomenon in cylindrical cup deep drawing processes and the variation in deformation with different orientations of the initial blank in rectangular cup drawing. The present simulation allows the thickness variation in the flange region to redistribute the blank-holding force during deformation, which can predict a more precise contour line in the flange region and a more precise deformed shape with strain distribution than the prediction made by conventional simulation.

Sheet metal forming analysis of planar anisotropic materials with a proper numerical scheme for the blank holding force

A modified membrane finite element with a proper formulation for planar anisotropic materials is introduced to correctly enhance the flexural rigidity not only within an element but among elements. The strain energy term in the formulation is decomposed into the membrane energy term for mean stretching and the bending energy term for pure bending. This procedure needs careful evaluation for the orientation of the anisotropic axes. The formulation is then combined with an effective algorithm to deal with the contact between the material and the dies. Distribution of the blank holding force is calculated in each step according to the thickness in the flange region. The calculation employs a special relation between the thickness and the blank holding force. The simulation examples demonstrate the validity and versatility of the computer code by showing the earing phenomenon in circular cup drawing and the variation of the blank holding force in rectangular cup drawing. The results shows that the thickness variation in the flange region redistributes the blank holding force during the deformation. The present algorithm can predict more precise contour lines in the flange region and a more precise shape and strain distribution.

Application of the finite element method to the simulation of sheet forming processes: Comparison of calculations and experiments

AbstractElastic‐plastic finite element calculations have been carried out to analyse sheet forming processes such as hydrostatic bulging of circular and rectangular blanks and the axisymmetric stretching of sheets (with different punch radii). The results, partly obtained by different finite element models, are compared with experimental data. It could be shown that, regarding the examples considered, experiments and calculations fit well and that a more sophisticated modelling of the contact boundary conditions improves the accuracy of the results. As a first attempt to handle more complex sheet forming operations, the deep drawing of a rectangular cup has been analysed. A summary of the theoretical background as well as some comments on the solution method and the implementation are given.

An analysis method for deep drawing process design

An analysis method has been developed that predicts the strain distribution in deep drawn sheet parts. The method is based on plane stress characteristic theory, which neglects both normal and shear stresses acting across the thickness of the material, as well as variations through the thickness of in-plane stresses. Isotropic hardening and normal anisotropy have been introduced, and the von Mises yield condition and associated flow rule are employed. The theory is valid for regions in the sheet which are characterized by drawing as opposed to stretching deformation. The process model has been implemented as a computer program capable of modeling circular, square, and rectangular cups. The model considers only the deformation taking place in the flange region of the part, where most of the work of deformation occurs, but the resulting strain distribution is displayed on a geometric model of the entire part by making geometric assumptions about the movement of the material on the face of the punch. Computed strains are compared with experimental results and causes for discrepancies are discussed.

Determination of blank shapes for drawing irregular cups using an electrical analogue method

An electrical analogue method is introduced to determine optimum blank shapes for deep-drawing cups of irregular cross-section. Square and rectangular cups were drawn from aluminium and steel blanks having these shapes and required very little trimming. Comparison is made with other methods of developing blanks and although one empirical method gave reasonable results for rectangular cups it is concluded that the electrical analogue method is preferred; it is also applicable to irregularly shaped cups.

Blank design in rectangular cup drawing by an approximate method

An approximate geometrical method is developed to determine an optimum blank profile in rectangular cup drawing which gives a drawn cup with the residual flange of uniform size around its periphery or with the levelled height. By assuming a velocity field in a curvilinear, orthogonal coordinate system, flow lines of material points in the blank are formulated and the contours of the flange for given blank shapes were determined at several punch steps for the rectangular and square cup-drawing. The two parameters involved in describing the velocity field were determined by comparing the results of calculation with those of experiment. Then, optimum blank profiles were designed for the required drawn cup configurations. Validation of the design by experiment was performed and the results show that the method is a good approximation, although some improvement of the method is possible.