Determination of the Optimum Blank Shape of a Nonaxisymmetric Drawn Cup by the Finite-Element Method. 3rd Report. The Limiting Drawing Ratios of Optimum Blank Shapes.

Abstract

The limiting drawing ratio of the optimum blank is considered theoretically and experimentally, with particular reference to the improvement of the deep drawability of sheet metal for nonaxisymmetric cups with a flat-headed punch. The authors' calculation methods for the optimum blank and the limiting drawing ratio have been applied to the square, the false elliptical, the rectangular and the rhombic cups, and the prediction was obtained in terms of the relationship between the optimum blank shape and the drawing ratio. The forming limit diagrams of those drawing cups were conceived theoretically, taking account of the die radius, Coulomb friction and the blank holder force. The calculated results agreed well with experimental results from deep drawing tests on a brass sheet, and it was found that the limiting drawing ratio and the maximum drawing depth of the cups drawn from theoretical optimum blank shapes were much larger than commendable values based on practical experience.