RETRACTED: Based on PRO/E Sheet Metal Product Design Simulation

Numerical simulation is an effective method for predicting formability of metals, and the use of computer simulation enables a significant increase in the number of tool designs that can be tested before hard tools are manufactured. Based on dynamic explicit finite element software, finite element simulation of sheet metal forming was performed to investigate the applicability of applying hydrostatic pressure on blank in multi point discrete dies. Simulation results show that using the hydrostatic pressure on blank is apposite for the process of multi point discrete dies.


Introduction
Forming with Multi Point Discrete Dies (MPDD) is a new flexible manufacturing forming technology which replaces the solid die by a matrix of several punches that are adjustable in height by means of linear actuators.Recently, a multi-point forming apparatus has been developed and used, and this apparatus is provided with a matrix-type array of punches as a substitute for a matched-die on the upper and the lower sides of a blank sheet, and controls the height of each element of the punches so as to form a desired curved surface of the sheet.Using multi point forming, production time is saved because several different products can be made without changing tools.In a unitcell approach, the punches deliver concentrated loads to sheet which make the deformations of the sheet strongly localized because pins endure big forming force which can bring plastic deformation in a small region around each pin.This phenomenon is dimple.In multi point forming (MPF), one of the methods assessed to overcome this problem is to interpose an elastic pad "interpolator" between the pins and sheet metal, utilizing the deformation of elastic pad to fill the clearance between pins so as to turn the concentrated load to experience wrinkling and this is because the interpolator bends around the edges of the shape, and as it compresses, the excess material has no place to go, and as a result it will bunch up and translate wrinkles to the sheet metal.Since the idea of die forming of variable shape has always been attractive as a means of reducing die design costs, the perfect interpolator would be very cheap and would retain its qualities after many stampings.The disadvantage of using soft material is that the pins can push through the pad and dimple the sheet metal [1].If the interpolator is hard, it will not conform to the blank geometry [2].

Simulation Models
The central component of the system is a pair of matrices of punches generated by CAD, finite element model including the simulation parameters was built using FEMB and solving task was achieved using LS-DYNA.
Material Model.Two materials, steel and aluminum were involved in numerical investigations.All these materials were treated as isotropic and homogeneous.The relevant mechanical properties are listed in able 1.It is assumed that the materials obeyed the Von-Mises yield criterion and Prandtl-Ruess flow rule.The strain-hardening model applied in the investigation was isotropic hardening, and the material characteristics were represented by the power law, which is given by: σ = Kε n ( σ ≥σ y ) (1) σ = Eε (ε < σ y / E ) Where σ is the true stress (MPa), ε is the total true strain, K is the strength coefficient (MPa), n is the strain-hardening exponent, E is the Young's modulus (MPa) and y σ is the yield stress (MPa).Finite Element Model.In order to implement a FEA, the finite element model is composed of three parts: the male, the female punch matrices, and sheet blank figure 2

. Male and female die matrices
Figure 2 Forming tool developed from ball nosed punches with certain diameter are used for the system.The punch matrix was composed of 10×10 punch elements.The sheet blank was modeled using 22801 Belytschko-Tsay shell elements.The punch matrices were simulated as rigid bodies and meshed by quadrilateral shell elements.The Blank was subjected to hydrostatic pressure like in hydraulic forming.As applied force in hydrostatic pressure is always perpendicular to the applied surface, this Materials, Mechatronics and Automation force was defined as boundary condition during finite element modeling; applied load to the blank was 25tons.

Numerical results and discussion
The effect of applied hydrostatic pressure on blank was observed toward the forming quality.During the initial stage the forming force is small, and it increases very slowly since only a few punches contact with sheet.After the travel of punch reaches a value about the 75% of the total travel, more and more punches get into contact with sheet and the forming force increases sharply.At the end of MPF process the forming force reaches its maximum since all punches contact with sheet.Since the sheet blank contacted with the pins directly, it was expected that applied hydrostatic pressure on blank could distribute the load from male matrix and can eliminate the defects in multi point forming.But it was observed that deformation still occurred on the female matrix, significant dimpling arose as can be seen in figure 3.

Thickness reduction distribution formability diagram Figure 3 Forming result
The materials used in the study were steel and aluminum.Despite forming properties with different materials are different, forming results are performed good formability as the part is formed on the die as can be seen in figures 4.

Conclusion
Multi-point Forming (MPF) is a technique for the manufacture of 3D sheet metal parts that cannot be processed by conventional means.In the presented numerical study, hydrostatic pressure application to sheet is appropriate application of the method.The results demonstrate that using the hydrostatic pressure on blank is suitable for multi point forming.Formability diagrams and Forming Limit Diagrams obtained in this study have stated this applicability.

Figure 1
Figure 1 Using pad between punches and sheet blank dispersive load, can effectively increasing the forming parts quality figure 1.In addition, the interpolator

Table 1
Mechanical parameters of materials