带嵌件型腔内熔接过程的数值模拟研究

李强; 李五明

doi:10.7498/aps.65.064601

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摘要

基于充模过程的两相黏弹性流体模型, 采用同位网格有限体积法, 结合浸入边界法和界面追踪的复合水平集流体体积方法实现了带嵌件型腔内充模过程的动态模拟. 基于上述模型和算法模拟了熔体前沿界面及熔接线的动态演化过程, 而且通过线性应力-光学定律得到了熔接线附近的流动诱导应力分布情况; 讨论了熔体温度及模具温度对熔接线区域凝固层厚度的影响. 数值结果表明: 本文提出的方法可用于模拟复杂型腔内的充模过程以及熔接线的自动追踪; 由于聚合物黏弹性熔体流动的复杂性, 当两股熔体相遇后, 熔接线不同位置的应力分布变化较大; 熔体或模具温度越高, 熔接线区域凝固层厚度越薄, 提高熔体或模具温度能够改善甚至消除充模过程中的熔接线.

关键词:

作者及机构信息

李强¹,
李五明^1,2

1.
河南理工大学数学与信息科学学院, 河南焦作 454000;

2.
西北工业大学应用数学系, 陕西西安 710129

通信作者: 李强, qianglinan@126.com

基金项目: 国家自然科学基金(批准号: 11301157)、天元基金(批准号: 11326232, 11326245)、河南省高等学校重点科研项目(批准号: 15A110001)和河南理工大学博士基金(批准号: B2013-057)资助的课题.

参考文献

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[2]	Hetu J F, Gao D M, Rejon A G, Salloum G 1998 Polym. Eng. Sci. 38 223
[3]	Jiang T, Ouyang J, Ren J L 2012 Comp. Phys. Comm. 183 50
[4]	Chiu P H, Lin Y T A 2011 J. Comput. Phys. 230 185
[5]	Liu R X, Shu Q W 2003 Some New Methods of Computational Fluid Dynamics (Beijing: Science Press) (in Chinese) [刘儒勋, 舒其望 2003 计算流体力学的若干新方法(北京:科学出版社)]
[6]	Bonito A, Picasso M, Laso M 2006 J. Comput. Phys. 215 691
[7]	Han Y, Cai G B, Xu X, Renou B, Boukhalfa A 2014 Chin. Phys. B 23 058901
[8]	Wang F, Li J L, Yang B X 2014 Acta Phys. Sin. 63 084601 (in Chinese) [王芳, 李俊林, 杨斌鑫 2014 物理学报 63 084601]
[9]	Park I R, Kim K S, Kim J, Van S H 2009 Int. J. Numer. Meth. Fl. 61 1331
[10]	Sussman M 2003 J. Comput. Phys. 187 110
[11]	Dai J F, Fan X P, Meng B, Liu J F 2015 Acta Phys. Sin. 64 094704 (in Chinese) [戴剑锋, 樊学萍, 蒙波, 刘骥飞 2015 物理学报 64 094704]
[12]	Li Q, Ouyang J, Yang B X, Li X J 2012 Appl. Math. Model. 36 2262
[13]	Zheng S P, Ouyang J, Zhao Z F, Zhang L 2012 Comput. Math. Appl. 64 2860
[14]	Ren J L, Lu W G, Jiang T 2015 Acta Phys. Sin. 64 080202 (in Chinese) [任金莲, 陆伟刚, 蒋涛 2015 物理学报 64 080202]
[15]	Shen C Y 2009 Simulation of Injection Molding and Theories and Methods for Optimization of Moulds Designing (Beijing: Science Press) (in Chinese) [申长雨 2009 注塑成型模拟及模具优化设计理论与方法(北京:科学出版社)]
[16]	Yang B X, Ouyang J, Wang F 2013 J. Appl. Math. 2013 856171
[17]	Araujo B J, Teixeira J C F, Cunha A M, Groth C P T 2009 Int. J. Numer. Meth. Fl. 59 801
[18]	Peskin C S 1972 J. Comput. Phys. 10 252
[19]	Yuan R F, Zhong C W, Zhang H 2015 J. Comput. Phys. 296 184
[20]	Cai Li, Gao H, Luo X Y, Nie Y F 2015 Sci. China: Phys. Mech. Astron. 45 024702 (in Chinese) [蔡力, 高昊, 罗小玉, 聂玉峰 2015 中国科学: 物理, 力学, 天文学 45 024702]
[21]	Boronat T, Segui V J, Peydro M A, Reig M J 2009 J. Mater. Process. Tech. 209 2735
[22]	Isayev A I, Shyu G D, Li C T 2006 J. Polym. Sci. Pol. Phys. 44 622
[23]	Osher S, Fedkiw R 2003 Level Set Methods and Dynamic Implicit Surfaces (New York: Springer) p9
[24]	Pijl S P 2005 Ph. D. Dissertation (Delft: Delft University of Technology)
[25]	Li Q, Ouyang J, Yang B X, Jiang T 2011 Appl. Math. Model. 35 257

施引文献

[1]	Kim S W, Turng L S 2006 Polym. Eng. Sci. 46 1263
[2]	Hetu J F, Gao D M, Rejon A G, Salloum G 1998 Polym. Eng. Sci. 38 223
[3]	Jiang T, Ouyang J, Ren J L 2012 Comp. Phys. Comm. 183 50
[4]	Chiu P H, Lin Y T A 2011 J. Comput. Phys. 230 185
[5]	Liu R X, Shu Q W 2003 Some New Methods of Computational Fluid Dynamics (Beijing: Science Press) (in Chinese) [刘儒勋, 舒其望 2003 计算流体力学的若干新方法(北京:科学出版社)]
[6]	Bonito A, Picasso M, Laso M 2006 J. Comput. Phys. 215 691
[7]	Han Y, Cai G B, Xu X, Renou B, Boukhalfa A 2014 Chin. Phys. B 23 058901
[8]	Wang F, Li J L, Yang B X 2014 Acta Phys. Sin. 63 084601 (in Chinese) [王芳, 李俊林, 杨斌鑫 2014 物理学报 63 084601]
[9]	Park I R, Kim K S, Kim J, Van S H 2009 Int. J. Numer. Meth. Fl. 61 1331
[10]	Sussman M 2003 J. Comput. Phys. 187 110
[11]	Dai J F, Fan X P, Meng B, Liu J F 2015 Acta Phys. Sin. 64 094704 (in Chinese) [戴剑锋, 樊学萍, 蒙波, 刘骥飞 2015 物理学报 64 094704]
[12]	Li Q, Ouyang J, Yang B X, Li X J 2012 Appl. Math. Model. 36 2262
[13]	Zheng S P, Ouyang J, Zhao Z F, Zhang L 2012 Comput. Math. Appl. 64 2860
[14]	Ren J L, Lu W G, Jiang T 2015 Acta Phys. Sin. 64 080202 (in Chinese) [任金莲, 陆伟刚, 蒋涛 2015 物理学报 64 080202]
[15]	Shen C Y 2009 Simulation of Injection Molding and Theories and Methods for Optimization of Moulds Designing (Beijing: Science Press) (in Chinese) [申长雨 2009 注塑成型模拟及模具优化设计理论与方法(北京:科学出版社)]
[16]	Yang B X, Ouyang J, Wang F 2013 J. Appl. Math. 2013 856171
[17]	Araujo B J, Teixeira J C F, Cunha A M, Groth C P T 2009 Int. J. Numer. Meth. Fl. 59 801
[18]	Peskin C S 1972 J. Comput. Phys. 10 252
[19]	Yuan R F, Zhong C W, Zhang H 2015 J. Comput. Phys. 296 184
[20]	Cai Li, Gao H, Luo X Y, Nie Y F 2015 Sci. China: Phys. Mech. Astron. 45 024702 (in Chinese) [蔡力, 高昊, 罗小玉, 聂玉峰 2015 中国科学: 物理, 力学, 天文学 45 024702]
[21]	Boronat T, Segui V J, Peydro M A, Reig M J 2009 J. Mater. Process. Tech. 209 2735
[22]	Isayev A I, Shyu G D, Li C T 2006 J. Polym. Sci. Pol. Phys. 44 622
[23]	Osher S, Fedkiw R 2003 Level Set Methods and Dynamic Implicit Surfaces (New York: Springer) p9
[24]	Pijl S P 2005 Ph. D. Dissertation (Delft: Delft University of Technology)
[25]	Li Q, Ouyang J, Yang B X, Jiang T 2011 Appl. Math. Model. 35 257

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带嵌件型腔内熔接过程的数值模拟研究

1. 河南理工大学数学与信息科学学院, 河南焦作 454000;

2. 西北工业大学应用数学系, 陕西西安 710129

通信作者: 李强, qianglinan@126.com

基金项目:

国家自然科学基金(批准号: 11301157)、天元基金(批准号: 11326232, 11326245)、河南省高等学校重点科研项目(批准号: 15A110001)和河南理工大学博士基金(批准号: B2013-057)资助的课题.

收稿日期: 2015-10-10

修回日期: 2015-12-01

刊出日期: 2016-03-05

摘要: 基于充模过程的两相黏弹性流体模型, 采用同位网格有限体积法, 结合浸入边界法和界面追踪的复合水平集流体体积方法实现了带嵌件型腔内充模过程的动态模拟. 基于上述模型和算法模拟了熔体前沿界面及熔接线的动态演化过程, 而且通过线性应力-光学定律得到了熔接线附近的流动诱导应力分布情况; 讨论了熔体温度及模具温度对熔接线区域凝固层厚度的影响. 数值结果表明: 本文提出的方法可用于模拟复杂型腔内的充模过程以及熔接线的自动追踪; 由于聚合物黏弹性熔体流动的复杂性, 当两股熔体相遇后, 熔接线不同位置的应力分布变化较大; 熔体或模具温度越高, 熔接线区域凝固层厚度越薄, 提高熔体或模具温度能够改善甚至消除充模过程中的熔接线.

关键词:

Numerical simulation on weld line development of injection molding in mold cavity with inserts

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;

2.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

Fund Project:

Project supported by the National Natural Science Foundation of China (Grant No.11301157), the NSFC Tianyuan Fund for Mathematics (Grant Nos.11326232, 11326245), the Natural Science Foundation of Education Department of Henan Province, China (Grant No. 15A110001), and the Research Fund for the Doctoral Program of Henan Polytechnic University, China (Grant No. B2013-057).

Received Date: 10 October 2015

Accepted Date: 01 December 2015

Published Online: 05 March 2016

Abstract: A gas-liquid two-phase model for a viscoelastic fluid is proposed and used to simulate and predict the behavior of melt welding in injection molding process, in which the extended pom-pom (XPP) model and cross-WLF viscosity model combined with Tait state equation are used to describe the constitutive relationship and viscosity change of the viscoelastic melt in this paper, respectively. Meanwhile, the coupled level-set and volume-of-fluid (CLSVOF) method is employed to capture the melt front, and the immersed boundary method is applied to the simulation of the polymer melt flows with the aid of a shaped level-set function to describe and treat the irregular mold cavities. A finite volume method on non-staggered grid is used to solve the mass, momentum, and energy conservation equations. Firstly, the benchmark problem of the single shear flow is simulated to verify the validity of the CLSVOF method. Then, the non-isothermal filling process of the viscoelastic fluid based on the XPP model in a mold with square inset is simulated, and the behavior of the weld line devolopment in the filling process is shown and compared with the experimental result. Finally, it is to simulate the evolution processes of the melt front interface and weld line in a mold with the circular notched inset; and the linear stress-optical rule is adopted to calculate the flow-induced birefringence. Numerical results show that the numerical model proposed in this paper can be employed to simulate the non-isothermal filling process in complex mold cavity and to capture the weld line automatically. Because of the complexity of polymer melt flows, the flow-induced stress increases quickly near the weld line region and then decreases gradually until reaching the mold cavity wall. The maximum value of the flow-induced stress appears at some point after the insert. The distributions of physical quantities, such as pressure and temperature in the mold, are given during the mold filling process. Moreover, it is also discussed the influence of melt and mold temperatures on the solidified layer thickness. The higher the melt or mold temperature, the thinner the solidified layer is. Thus, raising the melt or the mold temperature will improve or remove the weld line in melt filling process.

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