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    The deformed mesh is shown in Fig. 9. As seen in this figure, the cup is formed without causmg any wrinkling.As for the thickness contour shown in Fig.10, the darker area represented the thinner portion of the steel sheet. It can be seen from this figure that the thinnest portion is at the cup wall near to the bottom: this location agrees with that found in the production panel.In addition. the distribution of the major and minor principal strains around the thinnest portion obtained from the finite-element simulation, as shown in Fig. 11, is very consistent with that found in the real production panel, as shown in Fig.7, Hence, the finite-element simulation confirms the previous circle-grid analysis and is validated by the production process. With the validated process parameters, the finite-element analysis can be used for the analysis of any modified die design to substitute for the real die try-out. Compared with the real die try-out, the finite-element simulation is not only cost-effective but also time-saving, the example given in the following section demonstrating this advantage.

      

           blank-holder               die

      

      Sheet-blank                       Punch

          Fig .8. Mesh system for the original die design .

    Fig. 9. Deformed shape for the original die design

    4. A modified die design

    Since the split-defect is due to the lack of metal around the cup, one possible modification is to open the blank-holder at one side of the cup. as shown in Fig.12, which may cause more metal to flow into the cup. The geometries of the die and the sheet-blank remain the same as in the original design and. hence,are iiot shown iii Fig. 12. In order to validate this modification, a 3-D finite-element simulation was performed instead of revamping the real die. The simulation conditions were the same as those for the original design. except that the geometries of the punch and the blank-holder were changed. as shown in Fig. 12. 

    The distribution of the major and minor strains of the whole panel obtained from the finite-element simulation for the modified die design is shown in Fig. 13. As seen in this figure, due to a lot of material being drawn into the cup from the unconstrained area, the strain distribution moves down a little bit but is still in the marginal area. Fig.14 shows the deformed shape, ir] which serious wrinkles are observed in the unconstrained area. Although the split problem might be avoided in this modified design, the serious wrinkles are unacceptable. As a result, the modified design was not feasible according to the 3-D finite-element simulation, and the re-vamping of the real die was avoided.

    Fig.11. The strain distribution obtained from finite-element simulation for the original die design

    Punch                                    Blank-holder

                       Fig.12. The modified die design

      Fig.13. The strain distribution for the modified die design

    Fig 14 . The deformed shape for the modified die design

      Fig 15 the separate die face and the wedge mechanism

          Fig16. Measured strains for the first draw of the optimum die design

    Fig 17. Measured strains for the first and second-draw of the optimum die design

    5. The optimum die design

    As discussed in the previous sections, the most effective method to eliminate the split-defect from the production panel is to provide more metal for the cup area. Several attempts have been made to achieve this end but only the die design depicted below has been found to be feasible and efficient.

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