Wrinkling that occurs in the stamping of tapered square cups and stepped rectangular cups is investigated. A common characteristic of these two types of wrinkling is that  the wrinkles are found at the draw wall that is relatively unsup- ported. In the stamping of a tapered square cup, the effect of process parameters, such as the die gap  and  blank-holder force, on the occurrence of wrinkling is examined using finite- element 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 blank-holder 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 finite-element analysis. The good agreement between the simulation results and those observed in the wrinkle-free production part validates the accuracy of the finite-element analysis, and demonstrates the advantage of using finite-element analysis for stamping die design.71225

Keywords: Draw-wall wrinkle; Stamping die; Stepped rec- tangular  cup; Tapered square  cups

1. Introduction

Wrinkling 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 compressive stresses. In the forming operation of stamp- ing a complex shape, draw-wall wrinkling means the occurrence

Correspondence and offprint requests to: Professor F.-K. Chen, Depart- ment of Mechanical Engineering, National Taiwan University, No. 1 Roosevelt Road, Sec. 4, Taipei, Taiwan 10617. E-mail: fkchen@ w3.me.ntu.edu.tw

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 blank- holder force; but the application of excessive tensile stresses leads to failure by tearing. Hence, the blank-holder force  must lie within a narrow range, above that necessary to suppress wrinkles on the one hand, and below that which produces fracture on the other.  This narrow  range  of blank-holder force is difficult to determine. For wrinkles occurring in the central area of a stamped part with a  complex  shape,  a  workable range of blank-holder force does not even     exist.

In order to examine the mechanics of the formation of wrinkles, Yoshida et al. [1] developed a test in which a thin plate was non-uniformly stretched along one of its diagonals. They also proposed an approximate theoretical model in which the onset of wrinkling is due to elastic buckling resulting from the compressive lateral stresses developed in the non-uniform stress field. Yu et al. [2,3] investigated the wrinkling problem both experimentally and analytically. They found that wrinkling could occur having two circumferential waves according  to their theoretical analysis, whereas the experimental results indi- cated four to six wrinkles. Narayanasamy and Sowerby [4] examined the wrinkling of sheet metal when drawing it through a conical die using flat-bottomed and hemispherical-ended punches. They also attempted to rank the properties that appeared  to  suppress wrinkling.