注塑模优化设计理论的研究与应用
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摘要
注塑成型作为一项速度快、自动化程度高的生产技术，能一次成型形状复杂，尺寸精确的制品，在整个塑料制品生产行业中占有非常重要的地位。
本文针对注塑成型过程，重点研究了注塑模充填过程的快速模拟理论，注塑模制品和模具优化设计理论。在此基础上，将快速模拟技术、数值模拟技术和优化算法相结合，用于注塑模制品和浇注系统优化设计，并数值和实验分析了成型工艺条件对注塑成型过程熔体充填模式的影响。主要工作包括：
1．基于对塑料熔体在型腔和浇注系统中流动行为的研究，通过引入等效流长概念，将熔体前峰面的追踪问题转换为带权有限元网格上任意两点间最短路径的求解，建立了注塑模充填过程快速模拟理论，并经过与两个实际产品短射实验的对比分析，表明快速模拟分析不仅可以快速地而且能够准确地得到熔体的充填模式和熔接线气穴位置。
2．论文提出了带权有限元网格上任意两点的近似最短路径算法。算法将有限元网格表示为带权图结构，利用基于动态优化思想的快速最短路径法动态计算带权图上两点的最短路径，通过不断迭代细分最短路径周围的三角形边，构造每次细分后新的带权图，从而迭代逼近网格模型上的两点间最短路径。算法的时间复杂度为0(|e|)，优于现有最好的近似最短路径算法(时间复杂度0(|e|log|e|))，利用该算法实现了熔体前锋面的自动追踪。
3．在数值模拟的基础上分析了成型工艺条件的变化对单腔注塑模的充填模式影响，并结合实验研究了成型工艺条件变化对多型腔注塑模充填模式的影响。发现对单腔等壁厚制品，熔体温度和注射时间的变化对充填模式基本无影响。对于壁厚变化非常大的单腔制品或一模多腔制品，熔体温度对制品的充填模式影响非常小，而注射时间的变化也只有积累到一定程度引发滞流效应时，才对制品的充填模式有显著影响。这说明本文提出的注塑模充填过程快速模拟理论是有很大的应用范围的。
4．论文以平衡流动为目标，实现了注塑制品壁厚优化设计。首先利用快速模拟技术和最速下降法思想对制品壁厚进行初步优化，以获得壁厚分布趋势，并以此作为制品区域划分和进一步优化的基础；然后，以制品各区域壁厚为设计变量，将数值模拟技术与修正复形法结合用于壁厚最终优化。该算法可将型腔内的流动不平衡度降到5％以下。
5．针对精度高、浇口位置可行空间很小的注塑模具，论文将数值模拟技术与改进爬山法相结合，实现了以减少翘曲和提高材料性能为目标的浇口位置优化设
中文摘要
计，取得了满意的优化效果。
6.对于浇口位置可行空间较大的注塑模具，论文分别将穷尽法和自适应模拟退火
遗传算法与快速模拟技术相结合，实现了单浇口位置和多浇口位置优化设计，
保证熔体能够同时到达型腔末端从而获得平衡的充填模式，这也是首次真正解
决可行空间大、浇口数目多的复杂模具浇口位置优化设计问题。
7.建立了一套较为系统的基于数值模拟技术的浇注系统尺寸优化设计理论和方
法，分别以获得平衡的充填模式和预期熔接线位置为目标，将最速下降法思想
和数值模拟技术结合用于优化浇注系统流道和浇口尺寸。该方法通过引入浇注
系统的自动识别技术，解决了包括薄片浇口在内的各种类型浇口的尺寸优化问
题，并且首次对熔接线的位置进行优化，取得了满意的效果。
论文得到国家杰出青年科学基金资助项目(10225211)资助。
The injection molding is a popular technique of polymer processing, by which multiple parts with tight tolerances and complex shape can be produced in a single operation. Due to its success in delivering high-value added commercial products with high quality, the global competition in the field is intense, which leads to the requirement of high quality standard, shorter producing time and lower operating cost.
This dissertation focuses on developing a fast flow simulation methodology and design optimization theory for injection molding. The optimization algorithms, fast flow simulation and numerical simulation technology are integrated to optimize part design and mold design. The relationship between processing condition and filling pattern of single and multiple cavities are studied. The main work are as follow:
1. Through studying the flow behavior of melt in cavity and runner system, a fast simulation theory is developed based on reasonable assumption and simplification. Equivalent flow length concept is introduced, by which the melt-front tracing can be transferred to the computation of the shortest path on part. Two short shot experiments demonstrated the efficiency and accuracy of the proposed theory in predicting the filling pattern and the location of weld lines and air trap. For a model with 6065 nodes and 11700 elements, it needs only 128s in Pentium IV 450 machine, while MPI (numerical simulation software) needs 1845s.
2. An O(|e|)-time algorithm is proposed for calculating the approximate shortest path
on finite element mesh model which can be represented by a weighted graph. This method combines FSPA(Fast Shortest Path Algorithm), used to dynamically calculate shortest path on weighted graph, and edge subdivision technology. By iteratively subdividing relate triangle edges adjoined the shortest path and constructing new subgraph, a shortest path with high approximation accuracy can be achieved. The method is employed successfully to tracing melt front of injection molding. It can also be applied to robotics, GIS, route finding, and so on.
3. The effect of variation of processing condition to filling pattern for single and multiple cavities is studied by numerical simulation and short shot experiment respectively. It is found that processing condition has little effect on filling pattern for single cavity mold with uniform thickness. For single cavity mold with large thickness difference or multi cavities mold, it may change the entire filling pattern when the variation of processing condition cause flow hesitation.
4. An optimization model of part thickness in injection molding is introduced, in which the aim is to get balanced filling pattern. The idea of steepest descent method
integrated with fast simulation is used to minimize the arithmetical average difference between equivalent flow length of boundary nodes and reference value, and an optimal part thickness distribution can be obtained. Based on the result, the number of part regions can be determined. Then modified complex method combined with numerical simulation is applied to further searching optimal part region thickness and achieve uniform filling pattern by minimizing the arithmetical average time difference between the time reaching to boundary nodes and reference time. The examples demonstrate that the proposed method is viable and robust, and the unbalanced percent can be drop to 5%.
5. For mold with limited gate design space and high quality requirement, a methodology, which combines modified hill-climbing algorithm and numerical simulation, is used to optimize gate location to achieve minimum warpage and improve material performance.
6. On the basis of fast simulation, a new gate optimization algorithm for mold with multi-gates or big feasible design space is proposed. Exhausted method and adaptive simulated annealing genetic algorithm are used to optimize single gate and multi-gate mold respectively. The models analyzed demonstrate that the proposed method is promising and the computation time is satisfied.
本文针对注塑成型过程，重点研究了注塑模充填过程的快速模拟理论，注塑模制品和模具优化设计理论。在此基础上，将快速模拟技术、数值模拟技术和优化算法相结合，用于注塑模制品和浇注系统优化设计，并数值和实验分析了成型工艺条件对注塑成型过程熔体充填模式的影响。主要工作包括：
1．基于对塑料熔体在型腔和浇注系统中流动行为的研究，通过引入等效流长概念，将熔体前峰面的追踪问题转换为带权有限元网格上任意两点间最短路径的求解，建立了注塑模充填过程快速模拟理论，并经过与两个实际产品短射实验的对比分析，表明快速模拟分析不仅可以快速地而且能够准确地得到熔体的充填模式和熔接线气穴位置。
2．论文提出了带权有限元网格上任意两点的近似最短路径算法。算法将有限元网格表示为带权图结构，利用基于动态优化思想的快速最短路径法动态计算带权图上两点的最短路径，通过不断迭代细分最短路径周围的三角形边，构造每次细分后新的带权图，从而迭代逼近网格模型上的两点间最短路径。算法的时间复杂度为0(|e|)，优于现有最好的近似最短路径算法(时间复杂度0(|e|log|e|))，利用该算法实现了熔体前锋面的自动追踪。
3．在数值模拟的基础上分析了成型工艺条件的变化对单腔注塑模的充填模式影响，并结合实验研究了成型工艺条件变化对多型腔注塑模充填模式的影响。发现对单腔等壁厚制品，熔体温度和注射时间的变化对充填模式基本无影响。对于壁厚变化非常大的单腔制品或一模多腔制品，熔体温度对制品的充填模式影响非常小，而注射时间的变化也只有积累到一定程度引发滞流效应时，才对制品的充填模式有显著影响。这说明本文提出的注塑模充填过程快速模拟理论是有很大的应用范围的。
4．论文以平衡流动为目标，实现了注塑制品壁厚优化设计。首先利用快速模拟技术和最速下降法思想对制品壁厚进行初步优化，以获得壁厚分布趋势，并以此作为制品区域划分和进一步优化的基础；然后，以制品各区域壁厚为设计变量，将数值模拟技术与修正复形法结合用于壁厚最终优化。该算法可将型腔内的流动不平衡度降到5％以下。
5．针对精度高、浇口位置可行空间很小的注塑模具，论文将数值模拟技术与改进爬山法相结合，实现了以减少翘曲和提高材料性能为目标的浇口位置优化设
中文摘要
计，取得了满意的优化效果。
6.对于浇口位置可行空间较大的注塑模具，论文分别将穷尽法和自适应模拟退火
遗传算法与快速模拟技术相结合，实现了单浇口位置和多浇口位置优化设计，
保证熔体能够同时到达型腔末端从而获得平衡的充填模式，这也是首次真正解
决可行空间大、浇口数目多的复杂模具浇口位置优化设计问题。
7.建立了一套较为系统的基于数值模拟技术的浇注系统尺寸优化设计理论和方
法，分别以获得平衡的充填模式和预期熔接线位置为目标，将最速下降法思想
和数值模拟技术结合用于优化浇注系统流道和浇口尺寸。该方法通过引入浇注
系统的自动识别技术，解决了包括薄片浇口在内的各种类型浇口的尺寸优化问
题，并且首次对熔接线的位置进行优化，取得了满意的效果。
论文得到国家杰出青年科学基金资助项目(10225211)资助。
The injection molding is a popular technique of polymer processing, by which multiple parts with tight tolerances and complex shape can be produced in a single operation. Due to its success in delivering high-value added commercial products with high quality, the global competition in the field is intense, which leads to the requirement of high quality standard, shorter producing time and lower operating cost.
This dissertation focuses on developing a fast flow simulation methodology and design optimization theory for injection molding. The optimization algorithms, fast flow simulation and numerical simulation technology are integrated to optimize part design and mold design. The relationship between processing condition and filling pattern of single and multiple cavities are studied. The main work are as follow:
1. Through studying the flow behavior of melt in cavity and runner system, a fast simulation theory is developed based on reasonable assumption and simplification. Equivalent flow length concept is introduced, by which the melt-front tracing can be transferred to the computation of the shortest path on part. Two short shot experiments demonstrated the efficiency and accuracy of the proposed theory in predicting the filling pattern and the location of weld lines and air trap. For a model with 6065 nodes and 11700 elements, it needs only 128s in Pentium IV 450 machine, while MPI (numerical simulation software) needs 1845s.
2. An O(|e|)-time algorithm is proposed for calculating the approximate shortest path
on finite element mesh model which can be represented by a weighted graph. This method combines FSPA(Fast Shortest Path Algorithm), used to dynamically calculate shortest path on weighted graph, and edge subdivision technology. By iteratively subdividing relate triangle edges adjoined the shortest path and constructing new subgraph, a shortest path with high approximation accuracy can be achieved. The method is employed successfully to tracing melt front of injection molding. It can also be applied to robotics, GIS, route finding, and so on.
3. The effect of variation of processing condition to filling pattern for single and multiple cavities is studied by numerical simulation and short shot experiment respectively. It is found that processing condition has little effect on filling pattern for single cavity mold with uniform thickness. For single cavity mold with large thickness difference or multi cavities mold, it may change the entire filling pattern when the variation of processing condition cause flow hesitation.
4. An optimization model of part thickness in injection molding is introduced, in which the aim is to get balanced filling pattern. The idea of steepest descent method
integrated with fast simulation is used to minimize the arithmetical average difference between equivalent flow length of boundary nodes and reference value, and an optimal part thickness distribution can be obtained. Based on the result, the number of part regions can be determined. Then modified complex method combined with numerical simulation is applied to further searching optimal part region thickness and achieve uniform filling pattern by minimizing the arithmetical average time difference between the time reaching to boundary nodes and reference time. The examples demonstrate that the proposed method is viable and robust, and the unbalanced percent can be drop to 5%.
5. For mold with limited gate design space and high quality requirement, a methodology, which combines modified hill-climbing algorithm and numerical simulation, is used to optimize gate location to achieve minimum warpage and improve material performance.
6. On the basis of fast simulation, a new gate optimization algorithm for mold with multi-gates or big feasible design space is proposed. Exhausted method and adaptive simulated annealing genetic algorithm are used to optimize single gate and multi-gate mold respectively. The models analyzed demonstrate that the proposed method is promising and the computation time is satisfied.
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65. K.K. Kabanemi, J.F. Hetu. Design sensitivity analysis of applied to injection molding process: injection pressure and multi-gate location optimization. International Polymer Processing, 2002, 17(3): 254
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68．翟明，顾元宪，申长雨．注射模浇口数目和位置的优化设计．化工学报，2003，54(8)：1141～1145
69．翟明，顾元宪，申长雨．注射模浇注系统位置优化设计．机械工程学报，2002，38(2)：40～43
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72. H. Ye and P.M. Leopold. Minimizing part sink marks using C-MOLD and genetic-optimization algorithm. ANTEC'99, p 589～593
73. D. Yao,B.H. Kim. Direct-search-based automatic minimization ofweldlines in injection-molded parts. Polym. Plast. Technol. Eng.,1998 37(4): 509～525
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77．郑占明，刘春太，申长雨．基于遗传算法的注塑模注射速率优化．工程塑料应用，2002，30(7)：25～28
78. B.H.M. Sadeghi. BP-neural network predictor model for plastic injection molding process. Journal of Materials Processing Technology,2000, 103(3): 411～416
79. P.K.D.V. Yarlagadda, C.A.T. Khong. Development of a hybrid neural network system for prediction of process parameters in injection moulding. Journal of Materials Processing Technology,2001,118(1): 110～116
80. S.H. Dillman, D. Howe, H. Robar. Optimization of the injection molding process. ANTEC'96, SPE conference, 1996,754～758
81. R.S. Chen, H.H. Lee, C.Y. Yu. Application of Taguchi's method on the optimal process design of an injection molded PC/PBT automobile bumper. Composite Structures,1997,39(3): 209～214
82. S.Chang, J. Hwang, J. Doong. Manufacturing process optimization of short glass fiber reinforced polycarbonate composites in injection molding. J. Reinforced Plastics and Composites.2000,19(4): 301～321
83. S.Chang, J. Hwang, J. Doong. Optimization of the injection molding process of short glass fiber reinforced polycarbonate using gray relational analysis. J. Material Processing Technology.2000, 186～193
84. T.C. Chang, E. Faison. Shrinkage behavior and optimization of injection molded parts studied by the Taguchi method. Polym. Eng. Sci.,2001,41(5): 703～710
85．刘春太．基于数值模拟的注塑成型工艺优化和制品性能研究．博士学位论文．郑州大学：2003
86．吴其晔，巫静安．高分子材料流变学导论．北京：化学工业出版社，1994．6
87．刘春太，申长雨，陈静波，王利霞．注塑模充模过程动态分析的有限元／控制体积法．计算物理，2002，19(4)：344-348
88. C.A. Hieber. Chapter 1 in injection and compression molding fundamental. Edited by A.I. Isayev. New York: Marcel Dekker,1987
89．吴望一．流体力学(上、下册)．北京：北京大学出版社，1983
90. Ching-Chih Lee, An improved flow analysis network(FAN) method for irregular geometries, Polym. Engrg, Sci. 30(24) (1990) 1607-1614.
91. Sharir M, Schorr A. On shortest path in polyhedral spaces[J]. SIAM Journal on Computing,
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92. Chen J, Han Y. Shortest Path on the polyhedron[A]. In: Proceedings of the 6th ACM Symposium on Computer Geometry, Berkley, California, 1990. 360～369
93. Kanai T, Suzuki H. Approximate shortest path on a polyhedral surface and its applications[J]. Computer-Aided Design, 2001, 33(11): 801～811
94. Lanthier M, Maheshwari A, Stack J-R. Approximating weighted shortest paths on polyhedral surfaces[A]. In Proceedings of the 13th ACM symposium on Computer Geometry, Nice, France, 1997.272～283
95．张丽艳，吴熹．三角网格模型上任意两点间的近似最短路径算法研究[J]．计算机辅助设计与图形学学报，2003，15(5)：592～597
96．段凡丁．关于最短路径的SPFA快速算法[J]．西南交通大学学报，1994，29(2)：207～212
97．袁中双．塑料注射成型流动和保压过程的计算机模拟及实验研究．[博士学位论文]．武汉：华中理工大学，1993．
98. Yang Weimin, Hidetoshi Yokoi, A Study on Filling Balance in Multi-cavity Molds, JSPP'02 Tech. Papers, Tokyo, June 6-8, 2002
99. G. Steinbichler, Schwertberg. Trands in process optimization. Kunststoffe. German Plastics. 1992,82(10): 902～907
100．袁亚湘，孙文瑜．最优化理论与方法．北京：科学出版社，1997
101. L. S. Turng. C-Mold design guide. AC Technology, Ithaca, N.Y., 1994
102. R. E. Nunn. In Injection Molding Handbook, Rosato, Dominick and Rosato, Donald, eds., Van Nostrand Reinhold Company Inc., New York(1986)
103．王雪梅，王义和．模拟退火算法与遗传算法的结合．计算机学报，1997，20(4)：381～384
104．张晖，吴斌，余张国．引入模拟退火机制的新型遗传算法．电子科技大学学报，2003，32(1)：39～42
105．熊范伦，邓超．退火遗传算法及其应用．生物数学学报，2000，15(2)：150～154
106．吴陈．分组选优交配与概率接受差解的两种模拟退火遗传算法．华东船舶工业学院院报，1998，12(4)：48～41
107．《现代模具技术》编委会．注射成型原理与注塑模设计．北京：国防工业出版社，1996．
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