Fig. 10. Wrinkle formed when the sheet blank touches  the  stepped edge.

Fig. 11. Cut-off  of  the  stepped corner.

the step corner. In order to verify this  idea, two  modifications of the die design were suggested: one is to cut the whole step off, and the other is to add one more drawing operation, that is, to draw the desired shape  using  two  drawing operations. The simulated shape for the former method is shown in Fig.

12. Since the lower step is cut  off,  the  drawing  process  is quite similar to that of a rectangular cup drawing, as shown in Fig. 12. It is seen in Fig. 12 that the wrinkles were eliminated. In the two-operation drawing process, the sheet blank was first drawn to the deeper step, as shown in Fig. 13(a). Sub- sequently, the lower step was formed in the second drawing operation, and the desired shape was  then  obtained, as shown in Fig. 13(b). It is seen clearly in Fig. 13(b) that the stepped rectangular cup can be manufactured without wrinkling, by a two-operation drawing process. It should also be noted that in the two-operation 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 the metal cannot easily flow over the lower step into the die cavity. The finite-element 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 two- operation 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  finite-element

Fig. 12. Simulated shape for the modified die    design.

Fig. 13. (a) First operation  and (b) second operation in the  two-operation drawing    process.

simulation result to cut off the lower step, as shown in Fig.

12. 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 Fig. 14. The part shape also agreed well with that obtained from the finite- element simulation.

In order to further validate the finite-element simulation results, the thickness distribution along the cross-section G–H obtained  from  the  simulation  result  as  indicated  in  Fig.  14,

Fig. 14. The  defect-free  production part.

was compared with those measured from the production part. The  comparison  is  shown  in  Fig.  15.  It  can  be  seen  in Fig.

15 that the predicted thickness distribution by finite-element simulation agrees well with that measured directly in the production part. This agreement confirms the effectiveness of the finite-element analysis.

在带有斜度的方形盒和带有阶梯的方形盒的拉深中发生的起皱现象一直在被研究。这两中类型的起皱现象有一个共同的特征：全都发生在相对无支撑、无压边的拉深壁处。在带有斜度的方形盒的拉深中，常受到工序参数的影响，例如：模具的间隙值和压边力等，所以常用有限元模拟的方法来研究分析起皱的发生。模拟的结果表明模具的间隙值越大，起皱现象就越严重，而且增加压边力也不能抑制和消除起皱现象的发生。在带有阶梯的方形盒拉深的起皱现象分析中，常通过实际生产中一种近似的几何结构来研究、试验。当凸模与阶梯边缘之间的金属板料在拉深时分布并不均衡，就会在侧壁发生起皱现象。为了消除起皱现象的发生，一个最优的模具设计常采用有限元的方法进行分析。模拟的结果和起皱试验论证了有限元分析的准确性，并且表明了在拉深模具设计中使用有限元方法分析的优越性。