【正文】 tamping of tapered square cups and stepped rectangular cups is investigated. A mon characteristic of these two types of wrinkling is that the wrinkles are found at the draw wall that is relatively the stamping of a tapered square cup, the effect of process parameters, such as the die gap and blankholder force, on the occurrence of wrinkling is examined using finiteelement simulations. The simulation results show that the larger the die gap, the more severe is the wrinkling, and such wrinkling cannot be suppressed by increasing the blankholder force. In the analysis of wrinkling that occurred in the stamping of a stepped rectangular cup, an actual production part that has a similar type of geometry was examined. The wrinkles found at the draw wall are attributed to the unbalanced stretching of the sheet metal between the punch head and the step edge. An optimum die design for the purpose of eliminating the wrinkles is determined using finiteelement analysis. The good agreement between the simulation results and those observed in the wrinklefree production part validates the accuracy of the finiteelement analysis, and demonstrates the advantage of using finiteelement analysis for stamping die design.Keywords: Drawwall wrinkle。 Stamping die。 Tapered square cups1. IntroductionWrinkling is one of the major defects that occur in the sheet metal forming process. For both functional and visual reasons,wrinkles are usually not acceptable in a finished part. There are three types of wrinkle which frequently occur in the sheet metal forming process: flange wrinkling, wall wrinkling, and elastic buckling of the undeformed area owing to residual elastic pressive stresses. In the forming operation of stamping a plex shape, drawwall wrinkling means the occurrence of wrinkles in the die cavity. Since the sheet metal in the wall area is relatively unsupported by the tool, the elimination of wall wrinkles is more difficult than the suppression of flange wrinkles. It is well known that additional stretching of the material in the unsupported wall area may prevent wrinkling,and this can be achieved in practice by increasing the blankholder force。) and at angles of 45176。to the rolling average flow stress σ,calculated from the equation σ=（σ0+2σ45+σ90）/4, for each measured true strain,as shown in , is used for the simulations for the stampings of the tapered square cup and also for the stepped rectangular cup. All the simulations performed in the present study were run on an SGI Indigo 2 workstation using the finiteelement program PAMFSTAMP. To plete the set of input data required for the simulations, the punch speed is set to 10 m s_1 and a coefficient of Coulomb friction equal to is assumed.Fig. 2. Finiteelement mesh.Fig. 3. The stress–strain relationship for the sheet metal.3. Wrinkling in a Tapered Square CupA sketch indicating some relevant dimensions of the tapered square cup is shown in Fig. 1(a). As seen in Fig. 1(a), the length of each side of the square punch head (2Wp), the die cavity opening (2Wd), and the drawing height (H) are considered as the crucial dimensions that affect the of the difference between the dimensions of the die cavity opening and the punch head is termed the die gap (G) in the present study, . G = WdWp. The extent of the relatively unsupported sheet metal at the draw wall is presumably due to the die gap, and the wrinkles are supposed to be suppressed by increasing the blankholder force. The effects of both the die gap and the blankholder force in relation to the occurrence of wrinkling in the stamping of a tapered square cup are investigated in the following sections. Effect of Die GapIn order to examine the effect of die gap on the wrinkling, the stamping of a tapered square cup with three different die gaps of 20 mm, 30 mm, and 50 mm was simulated. In each simulation, the die cavity opening is fixed at 200 mm, and the cup is drawn to the same height of 100 mm. The sheet metal used in all three simulations is a 380 mm 380 mm square sheet with thickness of mm, the stress–strain curve for the material is shown in Fig. 3.Fig. 4. Wrinkling in a tapered square cup (G =50 mm).The simulation results show that wrinkling occurred in all three tapered square cups, and the simulated shape of the drawn cup for a die gap of 50 mm is shown in Fig. 4. It is seen in Fig. 4 that the wrinkling is distributed on the draw wall and is particularly obvious at the corner between adjacent walls. It is suggested that the wrinkling is due to the large unsupported area a