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 production of sheet metal components. Within the framework of an academic/industrial/government partnership devoted to the development of a reconfigurable tool 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-Dimensional 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 individually repositioned by computer driven servo-mechanisms. An interpolating polymer layer is interposed between the part and the die surface to attain a smooth pressure distribution. The objective of the die design algorithm is to determine optimal positions for the pin array, which will result in the desired part shape. The proposed “spring-forward” method was originally developed for matched-die forming (Karafillis, A. P., and Boyce, M. C., 1992, “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 Compensating Springback Error,” Int. J. Tools Manufac., Vol. 36, pp. 503–526.) and it is here extended and adapted to the reconfigurable tool geometry and stretch forming loading conditions. An essential prerequisite to the implementation of the die design procedure is the availability of an accurate FE model of the entire forming operation. The particular nature of the discrete die and issues related to the behavior of the interpolating layer introduce additional challenges. We have first simulated the process using a model that reproduces, as closely as possible, the actual geometry of the discrete tool. In order to optimize the delicate balance between model accuracy and computational requirements, we have then used the information gathered from the detailed analyses to develop an equivalent die model. An automated 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 interfaced with the reconfiguring tool. The success of the proposed procedure in selecting an optimal die configuration is confirmed by comparison with experimental results.