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合金凝固过程中的收缩行为是决定铸锭质量的关键因素之一, 利用数值模拟方法可以预测铸锭缩孔. 本文建立了一种基于机器学习的动网格模型, 能够模拟铸件凝固过程的动态收缩行为. 采用元胞自动机进行铸件凝固模拟, 采用径向基函数算法(radial basis function, RBF)和支持向量机算法(support vector machines, SVM)计算凝固收缩过程的网格运动位移, 从而对凝固过程收缩的动态模拟. 采用该模型计算了Al-4.7%Cu合金铸锭的缩孔形貌, 并进行了对应的浇铸实验验证, 模拟结果与实验结果的误差不超过2%, 符合较好. 说明该模型能够有效捕捉凝固收缩引起的铸件变形的动态过程, 且能够捕捉固液界面复杂形貌的演变, 为凝固过程数值模拟提供了一种新思路.Shrinkage cavities and porosity are the main defects generated in the solidification process of castings. These defects are caused by the alloy’s contraction during solidification, with the final solidified area not being effectively compensated for by the liquid metal, resulting in cavitation defects. Shrinkage cavities and porosity significantly reduce the mechanical properties of castings and shorten their service lives, thus necessitating appropriate process to eliminate them. Utilizing numerical simulation technology can effectively predict the shrinkage of castings during solidification and optimize the process based on simulation results, thereby reducing the occurrence of shrinkage defects, which is a low-cost and high-efficiency method. In this work, a machine learning-driven dynamic mesh model is established to simulate the dynamic shrinkage behavior of castings during solidification. Cellular automata are used to simulate the solidification process of castings, dynamically marking the displacement of boundary points and calculating the displacement of other grids using RBF neural network algorithms and support vector machine algorithms, thereby achieving the dynamic simulation of the solidification process. The model is used to simulate the shrinkage cavity morphology of the Al-4.7%Cu alloy solidification process, and corresponding casting experiments are designed for verification. Comparisons between simulation results and experimental results indicate that this coupled method can effectively capture the casting deformation caused by solidification shrinkage, the evolution of complex solid-liquid interface morphologies, and the deformation of internal grids within the castings. Compared with the experimental results, the simulation results have an error of no more than 2%, providing a new approach for numerically simulating the solidification process.
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Keywords:
- machine learning /
- dynamic mesh /
- cellular automata /
- lattice Boltzmann
[1] 赵健, 张毅 1985 铸造 5 1
Zhao J, Zhang Y 1985 Foundry 5 1
[2] 俞占扬, 张慧, 王明林, 王学兵, 张开发, 王飞 2023 特种铸造及有色合金 41 1073
Yu Z Y, Zhang H, Wang M L, Wang X B, Zhang K F, Wang F 2023 Special Casting & Nonferrous Alloys 41 1073
[3] Piwonka H, Flemings M C 1966 Metallurgical Trans. 1 1431
[4] Niyama H 1960 Tran. Jpn. I. Met. 2 57
[5] 贾宝仟, 柳百成 1996 热加工工艺 2 34
Jia B Q, Liu B C 1996 Hot Working Technol. 2 34
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Google Scholar
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Google Scholar
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Yang C R, Sun D K, Pan S Y, Dai T, Zhu M F 2009 Acta Metall. Sin. 45 43
[16] 杨莹莹, 李日, 周靖超, 赵朝阳 2016 工程热物理学报 37 2613
Yang Y Y, Li R, Zhou J C, Zhao C Y 2016 J. Eng. Thermophys 37 2613
[17] 周靖超 2017 硕士学位论文(天津: 河北工业大学)
Zhou J C 2017 M. S. Thesis (Tianjin: Hebei University of Technology
[18] 连庆庆 2017 硕士学位论文(天津: 河北工业大学)
Lian Q Q 2017 M. S. Thesis (Tianjin: Hebei University of Technology
[19] 刘林 2018 硕士学位论文(天津: 河北工业大学)
Liu L 2018 M. S. Thesis (Tianjin: Hebei University of Technology
[20] 马旺 2020 硕士学位论文(天津: 河北工业大学)
Ma W 2020 M. S. Thesis (Tianjin: Hebei University of Technology
[21] Guo Z L, Shi B C, Wang N C 2000 J. Comput. Phys. 165 288
Google Scholar
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Google Scholar
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图 1 动网格方案示意图 (a) t = 5; (b) t = 10
Fig. 1. Schematic diagram of dynamic grid scheme: (a) t = 5; (b) t = 10.
图 4 凝固收缩示意图, 其中I为未凝固区域, II为新近凝固的区域, III为已凝固区域
Fig. 4. Schematic diagram of solidification shrinkage, where I is unsolidified area, II is newly solidified area, III is sofidified area.
图 5 凝固收缩过程中质点位移示意图
Fig. 5. Schematic diagram of mass displacement during solidification and shrinkage.
图 8 (a) t = 25时固相率分布; (b) t = 25时温度分布; (c) t = 50时固相率分布; (d) t = 50时温度分布; (e) t = 75时固相率分布; (f) t = 75时温度分布; (g) t = 100时固相率分布; (h) t = 100时温度分布; (i) t = 125时固相率分布; (j) t = 125时温度分布
Fig. 8. (a) Distribution of solid phase rate when t = 25; (b)distribution of temperature when t = 25; (c) distribution of solid phase rate when t = 50; (d) distribution of temperature when t = 50; (e) distribution of solid phase rate when t = 75; (f) distribution of temperature when t = 75; (g) distribution of solid phase rate when t = 100; (h) distribution of temperature when t = 100; (i) distribution of solid phase rate when t = 125; (j) distribution of temperature when t = 125.
图 9 (a) 图8(a)左上角局部放大图; (b) 图8(a)左下角局部放大图
Fig. 9. (a) Localized enlargement of the upper left corner in Fig. 8 (a); (b) localized enlargement of the lower left corner in Fig. 8 (a).
图 10 图8(e)左下角局部放大图
Fig. 10. Localized enlargement of the lower left corner in Fig. 8 (e).
图 11 浇注试样形状尺寸及浇注结果 (a)试样; (b)浇注结果
Fig. 11. Shape and size of casting specimen and casting result: (a) Casting specimen; (b) casting result.
图 12 计算结果与实验结果对比 (a) RBF算法; (b) SVM算法
Fig. 12. Comparison of calculated and experimental results: (a) RBF; (b) SVM
表 1 Al-0.5%Cu合金热物性参数
Table 1. Physical properties of Al-0.5%Cu alloy.
热物性参数 符号 取值 熔点 Tm/K 733.3 液相线温度 TL/K 717 固相线温度 TS/K 621 液相线斜率 mL/(m·K/%) –3.44 热扩散率 α/(m2·s–1) 2.7×10–7 流体黏度 ν/(m2·s–1) 1.2×10–6 溶质扩散系数 D/(m2·s–1) 3.0×10–9 平衡分配系数 k 0.145 液相密度 ρ/(kg·m–3) 2606 各项异性系数 ε 0.0467 Gibbs-Thomson系数 Γ/(m·K) 2.4×10–7 
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[1] 赵健, 张毅 1985 铸造 5 1
Zhao J, Zhang Y 1985 Foundry 5 1
[2] 俞占扬, 张慧, 王明林, 王学兵, 张开发, 王飞 2023 特种铸造及有色合金 41 1073
Yu Z Y, Zhang H, Wang M L, Wang X B, Zhang K F, Wang F 2023 Special Casting & Nonferrous Alloys 41 1073
[3] Piwonka H, Flemings M C 1966 Metallurgical Trans. 1 1431
[4] Niyama H 1960 Tran. Jpn. I. Met. 2 57
[5] 贾宝仟, 柳百成 1996 热加工工艺 2 34
Jia B Q, Liu B C 1996 Hot Working Technol. 2 34
[6] Stefanescu D M, Wang T 1992 Int. J. Heat Mass Tran. 35 1125
Google Scholar
[7] Carlson K D, Beckermann C 2009 Metall. Mater. Trans. A 40 163
Google Scholar
[8] Lee C Y 1998 Metallurgical and Materials Transactions A 29 3255
[9] Khalajzadeh V, Carlson K D, Backman D G, Beckermann C 2017 Metall. Mater. Trans. A 48 1797
Google Scholar
[10] Li K, Yin J, Lu Z, Kong X, Zhang R, Liu W Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012) Tsukuba, Japan, November 11–15, 2012 p170
[11] Guo Z L, Shi B C, Wang N C 2000 J. Comp. Phys. 165 288
[12] Rendall T C, Allen C B 2009 J. Comput. Phys. 228 6231
Google Scholar
[13] Beckert A, Wendland H 2001 Aerosp. Sci. Technol. 5 125
Google Scholar
[14] 董士虎, 张红伟, 吕文朋, 雷洪, 王强 2024 金属学报 60 388
Dong S H, Zhang H W, Lv W P, Lei H, Wang Q 2024 Acta Metall. Sin. 60 388
[15] 杨朝蓉, 孙东科, 潘诗琰, 戴挺, 朱鸣芳 2009 金属学报 45 43
Yang C R, Sun D K, Pan S Y, Dai T, Zhu M F 2009 Acta Metall. Sin. 45 43
[16] 杨莹莹, 李日, 周靖超, 赵朝阳 2016 工程热物理学报 37 2613
Yang Y Y, Li R, Zhou J C, Zhao C Y 2016 J. Eng. Thermophys 37 2613
[17] 周靖超 2017 硕士学位论文(天津: 河北工业大学)
Zhou J C 2017 M. S. Thesis (Tianjin: Hebei University of Technology
[18] 连庆庆 2017 硕士学位论文(天津: 河北工业大学)
Lian Q Q 2017 M. S. Thesis (Tianjin: Hebei University of Technology
[19] 刘林 2018 硕士学位论文(天津: 河北工业大学)
Liu L 2018 M. S. Thesis (Tianjin: Hebei University of Technology
[20] 马旺 2020 硕士学位论文(天津: 河北工业大学)
Ma W 2020 M. S. Thesis (Tianjin: Hebei University of Technology
[21] Guo Z L, Shi B C, Wang N C 2000 J. Comput. Phys. 165 288
Google Scholar
[22] Estruch O, Lehmkuhl O, Borrell R, Segarra C P, Oliva A 2013 Comput. Fluids 80 44
Google Scholar
[23] Buhmann M D 2000 Acta Numer. 9 1
Google Scholar
[24] Vapnik V, Golowich S, Smola A 1996 Advances in Neural Information Processing Systems Denver, USA, December 3–5, 1996 p281
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