Parameter optimization of cooling system in U-shape hot stamping mold for high strength steel sheet based on MOPSO

This work aims to simultaneously optimize the cooling efficiency, cooling uniformity, and mold service life of the cooling system in U-shape hot stamping mold. And three indicators of the average temperature (Tave) of the hot stamping mold surface, the standard deviation of the temperature (σT) of mold surface, and the maximum equivalent stress (σ̅max\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\sigma}}_{\max } $$\end{document}) of mold were adopted to represent the cooling efficiency, cooling uniformity, and mold service life, respectively. Such three indicators are greatly influenced and even can be adjusted by the mold structure parameters, such as the diameter of cooling channels (D), the number of cooling channels, the center distance of adjacent cooling channels (L), and the distance from the center of cooling channel to the mold surface (H). Based on the Box-Behnken design method and finite element simulation results simulated by the MSC. Marc software, the mold structure parameters D, L, and H were selected as the three independent variables, and the three response surface models of Tave, σT, and σ̅max\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\sigma}}_{\max } $$\end{document} were, respectively, established. The applicability and reliability of the response surface models were checked by analysis of variance. And then the mold structure parameters (D, L, and H) were optimized by a multi-objective particle swarm optimization to simultaneously minimize the indicators of Tave, σT, and σ̅max\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\sigma}}_{\max } $$\end{document}. After optimization, the instantaneous cooling rates of steel sheet are higher than the critical cooling rate of martensite transformation before MS, which indicate that full martensite can be obtained in the steel sheet. The temperature uniformity of mold surface was improved, and a smaller σ̅max\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\sigma}}_{\max } $$\end{document} of mold was obtained. Finally, a series of hot stamping experiments according to the optimizing scheme were conducted by a four-column hydraulic press. The experimental results verified the evolution of the mold temperature field simulated by finite element software and the reliability of the improved U-shape hot stamping mold.