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【正文】 wn in Fig. 13(b). It is seen clearly in Fig. 13(b) that the stepped rectangular cup can be manufactured without wrinkling, by a twooperation drawing process. It should also be noted that in the twooperation drawing process, if an opposite sequence is applied, that is, the lower step is formed first and is followed by the drawing of the deeper step, the edge of the deeper step,as shown by A–B in Fig. 1(b), is prone to tearing because themetal cannot easily flow over the lower step into the die cavity.The finiteelement simulations have indicated that the die design for stamping the desired stepped rectangular cup using one single draw operation is barely achieved. However, the manufacturing cost is expected to be much higher for the twooperation drawing process owing to the additional die cost and operation cost. In order to maintain a lower manufacturing cost, the part design engineer made suitable shape changes, and modified the die design according to the finiteelementsimulation result to cut off the lower step, as shown in . With the modified die design, the actual stamping die for production was manufactured and the production part was found to be free from wrinkles, as shown in part shape also agreed well with that obtained from the finiteelement simulation.Fig. 13. (a) First operation and (b) second operation in the twooperation drawing process.Fig. 14. The defectfree production part.In order to further validate the finiteelement simulation results, the thickness distribution along the crosssection G–H obtained from the simulation result as indicated in Fig. 14,was pared with those measured from the production parison is shown in Fig. 15. It can be seen in that the predicted thickness distribution by finiteelement simulation agrees well with that measured directly in the production part. This agreement confirms the effectiveness of the finiteelement analysis.Fig. 15. The simulated and measured thickness distribution along G–H.5. Summary and Concluding RemarksTwo types of wrinkling occurring in stamping processes were investigated using finiteelement analysis, and the causes for wrinkling were examined and the methods to eliminate such wrinkles were developed.The first type of wrinkling appears at the draw wall in the stamping of a tapered square cup. The occurrence of wrinkling is attributed to the large die gap, which is the difference between the side length of the die cavity opening and the side length of the punch head. The large die gap results in a large unsupported area of sheet metal when the metal is drawn into the die cavity and an unfavourable stretch between the punch head and die cavity shoulder. The large unsupported area of sheet metal is therefore prone to wrinkling. The finiteelement simulations show that this type of wrinkling cannot be suppressed by increasing the blankholder force.Another type of wrinkling investigated occurs in an actual stamping part that has a stepped rectangular geometry. It is found that wrinkling occurs at the draw wall above the step even though the die gap is not sufficiently large. The wrinkling is due to the uneven stretch between the punch head and the step edge, according to the finiteelement analysis. Several attempts were made in the die design to eliminate the wrinkling,using finiteelement simulations, and an optimum design in which the step was cut off is finally established. The modified die design for eliminating wrinkles was validated by the production of a defectfree production part. The good agreement between the simulation results and those observed in the drawn production part demonstrates the accuracy of the finiteelement analysis, and the effectiveness of using finiteelement simulations as a substitute for the expensive method of actual die tryouts is thereby confirmed.AcknowledgementsThe authors wish to thank the National Science Council of the Republic of China for the grant NSC86–2212E002–028 that made this project possible. They also wish to thank KYM for providing the production part.References1. K. Yoshida, H. Hayashi, K. Miyauchi, Y. Yamato, K. Abe, , R. Ishida and Y. Oike, “The effects of mechanical properties of sheet metals on the growth and removing of buckles dueto nonuniform stretching”, Scientific Papers, Institute of Physics and Chemistry Research, 68, pp. 85–93, 1974.2. T. X. Yu, W. Johnson and W. J. Stronge, “Stamping and springback of circular plates deformed in hemispherical dies”, International Journal of Mechanical Sciences, 26, pp. 131–148, 1984.
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