A Combined Dynamic Programming / Finite Element Approach for the Analysis and Optimization of Multi-Stage Deep Drawing of Box-Shaped Parts

In this paper, traditional process design rules for deep drawing of box shapes are used to develop constraints within a dynamic programming (DP) approach to generate a set of alternative optimized process plans that minimize the number of drawing stages and heat treatments. The DP approach is capable of scanning a wide range of different alternative values for process parameters which allows for generating more rational process plans compared to a traditional rule-based (RB) approach. The validation of the process parameters for the multi-stage deep drawing of box-shaped parts are investigated using the finite element method with full account of formability limits. This careful finite element analysis guides the selection of the appropriate optimized process plan leading to the least severity of deformation. Two case studies are presented which suggest that the combination of DP and finite element validation could be a valuable, reliable and a more rational computer aided process planning (CAPP) approach to this complicated problem.