Integration of gradient based and response surface methods to develop a cascade optimisation strategy for Y-shaped tube hydroforming process design

In the last years a strong research effort was produced in order to develop and design new forming technologies able to overcome the typical drawbacks of traditional forming operations. Among such new technologies, hydroforming proved to be one of the most promising. The design of tube hydroforming operations is mainly aimed to prevent bursting or buckling occurrence and such issues can be pursued only if a proper control of both material feeding history and internal pressure path during the process is performed. In this paper, a proper optimisation strategy was developed on Y-shaped tube hydroforming process which is characterized by a quite complex process mechanics with respect to axi-symmetric tube hydroforming operations. The design procedure was aimed to properly calibrate the internal pressure histories. The basic idea, in this paper, is to integrate a steepest descent method with a moving least squares approach in order to reach the optimal internal pressure curve in the hydroforming of an Y-shaped steel tube. Thus, a cascade optimisation procedure was implemented which consisted of two optimisation steps: the former is focused on the application of a steepest descent method, the latter is based on a response surface approach utilising a moving least squares approximation. The cascade procedure was driven by the will to reduce the total number of numerical simulations necessary to reach the optimum with respect to other optimisation methods.