Blank Shape Optimization Considering 3D Space Targets for External and Internal Boundaries in Sheet Metal Forming Processes

Abstract

Optimum design of the shape of the initial blank is an important task before sheet metal forming processes. It reduces production costs, material waste and improves the quality of the product significantly. In the present work, the blank shape optimization problem is considered based on the 3D space target contours and moreover the sheet metal can have an internal boundary. In other words, the shape optimization process can be applied on the internal boundary, external boundary or both. To the best knowledge of the authors, there are no published works in this subject. Using the iterative simulation-based optimization process, a special shape error index and also updating algorithm were proposed to modify the blank geometry in each iteration until capturing the optimum shape. The sheet forming process is highly nonlinear in nature due to plastic behaviors, large deformations and frictional contact surfaces. Therefore, the updating formula should be robust enough to have less sensitivity with respect to the initial guess. To evaluate the proposed updating formula and its robustness, some numerical examples were considered and the effects of different tools geometries, 2D and 3D target contours, internal and external boundaries and different initial guesses were examined.