A New Geometry Modification Algorithm for Blank Shape Optimization in the Deep Drawing Process

Deep drawing is a popular process in sheet metal forming. The goal of shape optimization of the initial blank which is considered in the present work is to find the shape of the blank in a manner in which after a deep drawing process the contour of the edges of the produced part meets a target contour.  Such problems are highly nonlinear because the simulation consists of large deformation, plastic deformation, and contact.  Therefore, the general approach to solving such problems is using iterative methods which are based on numerical simulation.  Such an approach is also followed in the present work and a new algorithm for geometry modification of initial blank in each iteration is proposed.  In the proposed algorithm, the normal distance between the final contour and target contour is used as a criterion to modify the initial blank.  To evaluate the proposed algorithm a computer program is developed and to automatically execute the iterative process.  One numerical example solved and the results are compared with those reported in the literature.  One of the benefits of the proposed algorithm is its insensitivity to the initial guess.  Therefore, to evaluate the effect of the initial guess on its performance the example was solved using different initial guesses. The results show that the proposed algorithm is robust regarding the initial guess and convergence to the optimum shape will be achieved by starting from an initial guess.