A gradient-based decomposition approach to optimize pressure path and counterpunch action in Y-shaped tube hydroforming operations

In tube hydroforming, the concurrent actions of pressurized fluid and mechanical feeding allows obtaining tube shapes characterized by complex geometries such as different diameters sections and/or bulged zones. Main process parameters are material feeding history (i.e., the punches velocity history), internal pressure path during the process, and (in T- or Y-shaped tube hydroforming) counterpunch action. What is crucial, in such processes, is the proper design of operative parameters aimed to avoid defects (for instance underfilling or ductile fractures). Actually, 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 process parameters is performed. In this paper, a design procedure for Y-shaped tube hydroforming operations was developed. The aim of the presented approach is to calibrate both internal pressure history during the process and counterpunch action in order to reach a sound final component. The approach utilized to optimize the aforementioned parameters is founded on gradient-based techniques and the optimization problem here addressed depends on a considerable number of design variables. In order to reduce the total number of numerical simulations/experiments necessary to reach the optimal values of the design variables, the basic idea of this paper is to develop a sort of decomposition approach aimed to take into account subsets of design variables in the most effective way. The proposed decomposition approach allows avoiding about 50% of the numerical simulations necessary to solve the same problem by traditional gradient technique.