Optimization of a sheet metal forming process using successive multipoint approximations

An automated optimization method based on multipoint approximations and app lied to the design of a sheet metal forming process is presented. Due to th e highly complex nature of the design functions, it was decided to focus on the characterization of the final product thickness distribution as a func tion of the preforming die shape variables. This was achieved by constructi ng linear approximations to the noisy responses using response surface meth odology (RSM). These approximations are used to obtain an approximate solut ion to an optimization problem. Successive approximations are constructed, which improve the solution. An automated panning zooming scheme is used to resize and position the successive regions of approximation. The methodolog y is applied to optimally design the preforming die shape used in the manuf acture of an automotive wheel centre pressing from a sheet metal blank. The die shape is based on a cubic spline interpolation and the objective is to minimize the blank weight, subject to minimum thickness constraints. A wei ght saving of up to 9.4% could be realized for four shape variables. Restar t is introduced to escape local minima due to the presence of noise and to accelerate the progress of the optimization process.