Predicting the Radius of a Sheet Bent Around Drawbeads

Drawbeads in production stamping dies often have insufficient penetration of the male bead into the female cavity. With insufficient penetration, the actual bending radii of the sheet metal are larger than the geometrical radii of the drawbead. The actual bending radii in the sheet directly affect the force that restrains sheet movement. To predict the restraining stress due to a drawbead, it is necessary to know the actual bending radii in the sheet as it passes though the drawbead. Data from a previous study are used to develop empirical regression equations for predicting measured radii of the sheet that is bent around the radii in a drawbead. A physical model for the evolution of the sheet radii as the drawbead closes is proposed. This model is consistent with the empirical equations and the mechanics of the sheet bending process. The key variables for predicting the sheet radii in a round drawbead are 1) elastic stiffness of the sheet, 2) unsupported length of the sheet over the female cavity, 3) a factor incorporating the strength of the sheet, and 4) the tangent-to-tangent wrap angle around the male bead. This paper describes the physical significance of each of these key variables. For a round male bead, when a 30° tangent-to-tangent wrap angle is reached, the measured radius in the bent sheet conforms to the geometrical radius of the male bead. In contrast, the constraints at the exit and entry radii of the drawbead are less, so the sheet does not conform as readily to these geometrical radii.