Uncertainty analysis and multi-objective billet robust optimization for transitional region of multi-rib component under isothermal local loading forming

Isothermal local loading forming is promising to manufacture the large-scale Ti-alloy multi-rib component, but the folding, die underfilling, and strain concentration (SC) are undesired characteristics existing in transitional region due to the reciprocating material transfer between loading region and unloading region. The current research showed that the optimized billet could eliminate or improve these defects. However, it may also lead to unacceptable results due to the variation of the uncertainty factors, such as the manufacturing tolerance of the billet, the fluctuation of the stroke length, friction factor, and forming temperature. Aiming at this issue, an uncertainty analysis and the multi-objective robust optimization of the billet are performed based on 3D finite element simulation and dual-response surface model. Firstly, a valid FE model of the eigenstructure is established to represent the transitional region. Then, the significance analysis of the uncertainty factors is carried out and the significant uncertainty factors are obtained. Subsequently, a multi-objective robust optimization model concerning the mean and standard deviation of the die underfilling rate and average strain of SC zone under the condition of avoiding folding is established. Finally, the Pareto-optimal solutions are obtained by NSGA-II and the minimum distance selection method is employed to acquire the satisfied solution. The comparison results between the robust optimization and deterministic optimization showed that not only the folding is effectively avoided under the uncertainty factors, but also more robust die filling and deformation homogeneity can be achieved.