A finite element based die design algorithm for sheet-metal forming on reconfigurable tools

Tooling cost is a major contributor to the total cost of small-lot producti on of Sheet metal components. Within the framework of an academic/industria l/government partnership devoted to the development of a reconfigurable too l for stretch forming, we have implemented a Finite Element-based procedure to determine optimal die shape. In the reconfigurable forming tool (Hardt, D. E. et al., 1993, "A CAD Driven Flexible Forming System for Three-Dimens ional Sheet Metal Parts," Sheet Metal and Stamping Symp., Int. Congress and Exp., Detroit, MI, SAE Technical Paper Series 930282, pp. 69-76.), the die surface is created by the ends of an array of square pins, which can be in dividually repositioned by computer driven servo-mechanisms. An interpolati ng polymer layer is interposed between the part and the die surface to atta in a smooth pressure distribution. The objective of the die design algorith m is to determine optimal positions for the pin array, which will result in the desired part shape. The proposed "spring-forward" method was originall y developed for matched-die forming (Karafillis, A. P., and Boyce, M. C., 1 992, "Tooling Design in Sheet Metal Forming using Springback Calculations, " Int. J. Mech. Sci., Vol. 34, pp. 113-131.; Karafillis, A. P., and Boyce, M. C., 1996, "Tooling And Binder Design for Sheet Metal Forming Processes C ompensating Springback Error, " Int. J. Tools Manufac., Vol. 36, pp. 503-52 6.) and it is here extended and adapted to the reconfigurable tool geometry and stretch forming loading conditions. An essential prerequisite to the i mplementation of the die design procedure is the availability of an accurat e FE model of the entire forming operation. The particular nature of the di screte die and issues related to the behavior of the interpolating layer in troduce additional challenges. We have first simulated the process using a model that reproduces, as closely as possible, the actual geometry of the d iscrete tool. In order to optimize the delicate balance between model accur acy and computational requirements, we have then used the information gathe red from the detailed analyses to develop an equivalent die model. An autom ated algorithm to construct the equivalent die model based on the discrete tool geometry (pin-positions) is integrated with the spring-forward method, to generate an iterative die design procedure that can be easily interface d with the reconfiguring tool. The success of the proposed procedure in sel ecting an optimal die configuration is confirmed by comparison with experim ental results.