Blank shape optimization considering 3D space targets for external and internal boundaries in sheet metal forming processes

The optimum design of an initial blank shape in sheet metal forming processes is an important step in many industries, especially automobile manufacturers because it reduces production costs and material waste. To the best of our knowledge, no research has been conducted on the blank shape designs based on 3D space target contours. Moreover, the present study considers parts with internal boundaries and optimum design of the internal boundary, which are among the innovations of this research. By following the iterative simulation-based optimization process, a special updating algorithm was proposed to modify the blank geometry in each iteration and reach the optimum shape. The sheet forming was severely nonlinear, due to plastic behavior, large deformations, and frictional contact surfaces. Therefore, the updating formula should be robust enough to be insensitive to the initial guess for the blank. To evaluate the proposed updating formula, some numerical examples were solved and the results were presented. Finally, the robustness of the proposed algorithm was investigated in these numerical experiences, by considering different geometries, target contours, internal boundaries, and initial guesses. The present study reveals that the proposed algorithm can be effectively used to solve blank optimization problems for the deep drawing process.