Int J Adv Manuf Technol (2002) 19:2532592002 Springer-Verlag London LimitedAn Analysis of Draw-Wall Wrinkling in a Stamping Die DesignF.-K. Chen and Y.-C. LiaoDepartment of Mechanical Engineering, National Taiwan University, Taipei, TaiwanWrinkling that occurs in the stamping of tapered square cupsand stepped rectangular cups is investigated. A commoncharacteristic of these two types of wrinkling is that thewrinkles are found at the draw wall that is relatively unsupported.In the stamping of a tapered square cup, the effect ofprocess parameters, such as the die gap and blank-holderforce, on the occurrence of wrinkling is examined using finiteelementsimulations. The simulation results show that the largerthe die gap, the more severe is the wrinkling, and suchwrinkling cannot be suppressed by increasing the blank-holderforce. In the analysis of wrinkling that occurred in the stampingof a stepped rectangular cup, an actual production part thathas a similar type of geometry was examined. The wrinklesfound at the draw wall are attributed to the unbalancedstretching of the sheet metal between the punch head and thestep edge. An optimum die design for the purpose of eliminatingthe wrinkles is determined using finite-element analysis. Thegood agreement between the simulation results and thoseobserved in the wrinkle-free production part validates theaccuracy of the finite-element analysis, and demonstrates theadvantage of using finite-element analysis for stamping diedesign.Keywords: Draw-wall wrinkle; Stamping die; Stepped rectangularcup; Tapered square cups1. IntroductionWrinkling is one of the major defects that occur in the sheetmetal forming process. For both functional and visual reasons,wrinkles are usually not acceptable in a finished part. Thereare three types of wrinkle which frequently occur in the sheetmetal forming process: flange wrinkling, wall wrinkling, andelastic buckling of the undeformed area owing to residualelastic compressive stresses. In the forming operation of stampinga complex shape, draw-wall wrinkling means the occurrenceof wrinkles in the die cavity. Since the sheet metal in the wallarea is relatively unsupported by the tool, the elimination ofwall wrinkles is more difficult than the suppression of flangewrinkles. It is well known that additional stretching of thematerial in the unsupported wall area may prevent wrinkling,and this can be achieved in practice by increasing the blankholderforce; but the application of excessive tensile stressesleads to failure by tearing. Hence, the blank-holder force mustlie within a narrow range, above that necessary to suppresswrinkles on the one hand, and below that which producesfracture on the other. This narrow range of blank-holder forceis difficult to determine. For wrinkles occurring in the centralarea of a stamped part with a complex shape, a workablerange of blank-holder force does not even exist.In order to examine the mechanics of the formation ofwrinkles, Yoshida et al. 1 developed a test in which a thinplate was non-uniformly stretched along one of its diagonals.They also proposed an approximate theoretical model in whichthe onset of wrinkling is due to elastic buckling resulting fromthe compressive lateral stresses developed in the non-uniformstress field. Yu et al. 2,3 investigated the wrinkling problemboth experimentally and analytically. They found that wrinklingcould occur having two circumferential waves according totheir theoretical analysis, whereas the experimental results indicatedfour to six wrinkles. Narayanasamy and Sowerby 4examined the wrinkling of sheet metal when drawing it througha conical die using flat-bottomed and hemispherical-endedpunches. They also attempted to rank the properties thatappeared to suppress wrinkling.These efforts are focused on the wrinkling problems associatedwith the forming operations of simple shapes only, suchas a circular cup. In the early 1990s, the successful applicationof the 3D dynamic/explicit finite-element method to the sheetmetalforming process made it possible to analyse the wrinklingproblem involved in stamping complex shapes. In the presentstudy, the 3D finite-element method was employed to analysethe effects of the process parameters on the metal flow causingwrinkles at the draw wall in the stamping of a tapered squarecup, and of a stepped rectangular part.A tapered square cup, as shown in Fig. 1(a), has an inclineddraw wall on each side of the cup, similar to that existing ina conical cup. During the stamping process, the sheet metalon the draw wall is relatively unsupported, and is thereforeprone to wrinkling. In the present study, the effectof various process parameters on the wrinkling was investigated. In thecase of a stepped rectangular part, as shown in Fig. 1(b),another type of wrinkling is observed. In order to estimate theeffectiveness of the analysis, an actual production part withstepped geometry was examined in the present study. Thecause