Determination of Pressure Path and Punch Velocity in Hydroforming of Cup-Shaped Products Using Adaptive Simulation-Based Optimization

In this paper, a practical method of combined finite element simulation and adaptive simulated annealing (ASA) optimization was developed to design and analyze sheet hydroforming process. Process simulation using finite element code with parametric definition of process parameters creates flexibility on the proposed method in which geometrical dimensions and properties of the workpiece and the die comprise a part of input data of optimization program. Redefinition of simulated annealing parameters with respect to hydroforming process caused to achieve data convergence in a shorter time and higher precision. An intermediate MATLAB code was developed to manage data transfer automatically between optimization and simulation codes, in which there would be no need to any interference of user/designer during the optimization process. The aim of this research for presenting the combinatorial procedure of flexible simulation is to achieve optimal forming pressure loading path, determine the desired punch velocity, produce the desired workpiece with minimum thinning, and avoid wrinkling and rupturing. Two different loading paths proportionate to the ram’s stroke of press unit are proposed to synchronize optimal pressure path and desired punch velocity in forming of cup-shaped products. Using the optimization approaches of constant and variable velocity, thinning values of 12.9778 and 12.3295 for a steel part with conical shape were obtained by implementing simulation iteration of 202 and 148, respectively. This result demonstrates improvement of product quality and decrease of simulation iterations in variable velocity. Appropriate conformity between numerical and experimental results verified the reliability and accuracy of the proposed optimization method.