occurring at the draw wall of the tapered square cup.

3.2 Effect  of the  Blank-Holder Force

It is well known that increasing  the  blank-holder  force  can help to eliminate  wrinkling  in the  stamping  process.  In order to study the effectiveness of increased blank-holder force, the stamping of a tapered square cup with die gap of  50 mm, which is associated with severe wrinkling as stated above, was simulated with different values of blank-holder force. The blank-holder force was increased from 100 kN to 600  kN, which yielded a blank-holder pressure of 0.33 MPa and 1.98 MPa, respectively. The remaining simulation conditions are maintained the same as those specified in the previous section. An intermediate blank-holder force of 300 kN was also used in  the simulation.

The simulation results show that an increase in the blank- holder force does not help to eliminate the  wrinkling  that occurs at the draw wall. The þ values along the cross-section

Fig. 5. þ-value along the cross-section  M–N for different die     gaps.

M–N, as marked in Fig. 4, are compared with one another for the stamping processes with blank-holder force of 100 kN and 600 kN. The simulation results indicate that the þ values along the cross-section M–N are almost identical in both cases. In order to examine the difference of  the wrinkle  shape for  the two  different  blank-holder  forces,  five  cross-sections  of   the

draw wall at different heights from the bottom to the line M– N, as marked in Fig. 4, are plotted in Fig. 6 for both cases. It is noted from Fig. 6 that the waviness of the cross-sections for both cases is similar. This indicates that the blank-holder force does not affect the occurrence of wrinkling in the stamp- ing of a tapered square cup, because the formation of wrinkles is mainly due to the large unsupported area at the draw wall where large compressive transverse stresses exist. The blank- holder force has no influence on the instability mode of the material  between the  punch head  and  the  die  cavity shoulder.

4. Stepped Rectangular Cup

In the stamping of a stepped rectangular cup, wrinkling occurs at the draw wall even though the die gaps are not so significant. Figure 1(b) shows a sketch of a punch shape used for  stamping a stepped rectangular cup in which the draw wall C is followed by a step D–E.  An  actual  production  part  that  has  this type of geometry was examined in the present study. The material used for this production part was 0.7 mm thick, and the stress– strain relation obtained from tensile tests is shown in Fig. 3.

The procedure in the press shop for the production of this stamping part consists of deep drawing followed  by trimming. In the deep drawing process,  no  draw  bead  is  employed on the die surface  to  facilitate  the  metal  flow.  However, owing to the small punch corner radius  and  complex  geometry,  a split occurred at the top edge of the punch and wrinkles were found to occur at the draw wall of the actual production part, as shown in Fig. 7. It is seen from Fig. 7 that wrinkles are distributed on the draw wall, but are more severe at the corner edges of the step, as marked by A–D and B–E in Fig. 1(b). The metal is torn apart along the whole top edge of the punch, as shown in Fig. 7, to form a split.

In order to provide a further understanding of the defor- mation of the sheet-blank during the stamping process, a finite- element analysis was conducted. The finite-element simulation was first performed for the original  design.  The  simulated shape of the part is shown from Fig. 8. It is noted from Fig.