狭缝型腔微注塑成型充填过程的数值模拟
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摘要
伴随着微机电系统技术而发展的微注塑成型技术,目前已在微机械、微电子、微光学及生物医学等领域获得了较广泛的应用。然而,由于微型塑件的结构尺寸与体积极其微小,在微注塑成型充填过程中,高聚物熔体流过微小通道时的流变特性与传统注塑成型时有许多不同,因而影响微型塑件成型质量与传统大尺寸塑件成型质量的关键因素有所不同。
微注塑成型中,聚合物熔体充填过程直接影响着微塑件的成型质量和生产效率,是成型中最重要的阶段。因此,对微尺度型腔内熔体充填流动行为,尤其对微尺度效应进行深入研究,建立描述微注塑成型的数学模型及高效的数值方法,实现对微注射成型过程的数值模拟,对优化设计微注塑模具、合理设置成型工艺参数和提高微型塑件质量都具有重要的理论意义和实用价值。
本文结合微注塑成型的特点,对微注塑成型充填过程进行了数值模拟,主要工作和结论如下:
1.借鉴宏观熔体充填流动理论,比较了微型注塑成型技术与传统注塑成型技术的差异。对微注塑成型熔体充填过程中的影响因素进行了系统的分析,并引入了Eringen-Okada微观粘度模型和Rosenbaum-Hatzikiriakos壁面滑移速度模型。
2.针对狭缝微流道中高聚物熔体的稳态流动进行了分析,分别考虑了微观粘度、壁面滑移对稳态流动的影响及二者的共同作用对稳态流动的影响,通过算例分析了微观粘度和壁面滑移对微流道中熔体流动的影响规律及重要性。
3.从粘性流体力学的基本方程出发,结合微注塑成型过程的流动特点,进行合理简化和假设,并引入微观粘度模型和壁面滑移模型,建立熔体在狭缝微型腔内充填的数学模型;采用混合有限元/有限差分/控制体积法实现微注塑充填过程的数值模拟;通过算例分析讨论了微观粘度和壁面滑移对高聚物熔体在微型腔内充填过程的粘度、速度、压力等参数变化的影响。模拟结果表明,微观粘度有阻碍熔体流动的趋势,而壁面滑移有促进熔体流动的趋势。两者的综合作用决定了微注塑成型充填过程中熔体的流动。
With the development of the Micro Electro Mechanical System (MEMS), micro-injection molding technology is developed and widely used in the micro-mechanical, micro-electronics, micro-optics , biomedical and many other fields now. However, because of the very small size and volume of micro-plastic parts, the flow behavior of polymer in the filling stage of micro-injection molding has many differences compared with that of the traditional injection molding, Therefore, the key factors affecting the qualities of micro-parts are different with that the factors in the traditional injection molding.
The filling stage is the most important stage in the micro-injection molding process and influences the part quality and production efficiency of micro-injection molding directly. Therefore, it has great theoretical and practical significance for designing micro-injection mould, setting processing parameters reasonably and improving micro-plastic parts quality to investigate the melt flow behavior in the filling stage in the micro-scale cavity, especially the micro-scale effect on the flow behavior, build mathematical model and efficient numerical method, and implement the numerical simulation of filling stage in micro-injection molding.
The objective of the paper is to analysis the main factors and to simulate the filling stage of the micro-injection molding process. The works and achievements are as following:
1. The differences of the process characteristic between micro-injection molding and traditional injection molding were compared. The influence factors in the micro-injection process were analyzed systematically and the micro viscosity model and wall slip velocity model were introduced.
2. The steady-state flow of polymer in slit cavity was analyzed. The effects of the micro-viscosity and wall slip and the comprehensively effect of two factors on steady-state flow were investigated, and the influence laws of the micro-viscosity and wall slip on the steady-state flow were analyzed.
3. Based on the viscous fluid mechanics and the flow characteristics of micro-injection molding process, the reasonable simplification and hypothesis were introduced, the micro-scale viscosity model based on Eringen and Okada theory and the power-law wall slip model were adapted, and the mathematical model of the filling stage in slit micro-cavity was built. Numerical simulation of the filling stage of micro-injection molding was implemented using hybrid Finite Element/ Finite Difference/Control Volume method. The effects of the micro-viscosity and wall slip on the viscosity, velocity and pressure field of the melt in the cavity in filling stage were investigated. The simulation results indicate that the micro-viscosity has the effect of hindering the melt flow and wall slip has the effect of promoting the melt flow. The melt flow condition in the filling stage of micro-injection molding is determined by the combined effects of micro-viscosity and wall slip.
微注塑成型中,聚合物熔体充填过程直接影响着微塑件的成型质量和生产效率,是成型中最重要的阶段。因此,对微尺度型腔内熔体充填流动行为,尤其对微尺度效应进行深入研究,建立描述微注塑成型的数学模型及高效的数值方法,实现对微注射成型过程的数值模拟,对优化设计微注塑模具、合理设置成型工艺参数和提高微型塑件质量都具有重要的理论意义和实用价值。
本文结合微注塑成型的特点,对微注塑成型充填过程进行了数值模拟,主要工作和结论如下:
1.借鉴宏观熔体充填流动理论,比较了微型注塑成型技术与传统注塑成型技术的差异。对微注塑成型熔体充填过程中的影响因素进行了系统的分析,并引入了Eringen-Okada微观粘度模型和Rosenbaum-Hatzikiriakos壁面滑移速度模型。
2.针对狭缝微流道中高聚物熔体的稳态流动进行了分析,分别考虑了微观粘度、壁面滑移对稳态流动的影响及二者的共同作用对稳态流动的影响,通过算例分析了微观粘度和壁面滑移对微流道中熔体流动的影响规律及重要性。
3.从粘性流体力学的基本方程出发,结合微注塑成型过程的流动特点,进行合理简化和假设,并引入微观粘度模型和壁面滑移模型,建立熔体在狭缝微型腔内充填的数学模型;采用混合有限元/有限差分/控制体积法实现微注塑充填过程的数值模拟;通过算例分析讨论了微观粘度和壁面滑移对高聚物熔体在微型腔内充填过程的粘度、速度、压力等参数变化的影响。模拟结果表明,微观粘度有阻碍熔体流动的趋势,而壁面滑移有促进熔体流动的趋势。两者的综合作用决定了微注塑成型充填过程中熔体的流动。
With the development of the Micro Electro Mechanical System (MEMS), micro-injection molding technology is developed and widely used in the micro-mechanical, micro-electronics, micro-optics , biomedical and many other fields now. However, because of the very small size and volume of micro-plastic parts, the flow behavior of polymer in the filling stage of micro-injection molding has many differences compared with that of the traditional injection molding, Therefore, the key factors affecting the qualities of micro-parts are different with that the factors in the traditional injection molding.
The filling stage is the most important stage in the micro-injection molding process and influences the part quality and production efficiency of micro-injection molding directly. Therefore, it has great theoretical and practical significance for designing micro-injection mould, setting processing parameters reasonably and improving micro-plastic parts quality to investigate the melt flow behavior in the filling stage in the micro-scale cavity, especially the micro-scale effect on the flow behavior, build mathematical model and efficient numerical method, and implement the numerical simulation of filling stage in micro-injection molding.
The objective of the paper is to analysis the main factors and to simulate the filling stage of the micro-injection molding process. The works and achievements are as following:
1. The differences of the process characteristic between micro-injection molding and traditional injection molding were compared. The influence factors in the micro-injection process were analyzed systematically and the micro viscosity model and wall slip velocity model were introduced.
2. The steady-state flow of polymer in slit cavity was analyzed. The effects of the micro-viscosity and wall slip and the comprehensively effect of two factors on steady-state flow were investigated, and the influence laws of the micro-viscosity and wall slip on the steady-state flow were analyzed.
3. Based on the viscous fluid mechanics and the flow characteristics of micro-injection molding process, the reasonable simplification and hypothesis were introduced, the micro-scale viscosity model based on Eringen and Okada theory and the power-law wall slip model were adapted, and the mathematical model of the filling stage in slit micro-cavity was built. Numerical simulation of the filling stage of micro-injection molding was implemented using hybrid Finite Element/ Finite Difference/Control Volume method. The effects of the micro-viscosity and wall slip on the viscosity, velocity and pressure field of the melt in the cavity in filling stage were investigated. The simulation results indicate that the micro-viscosity has the effect of hindering the melt flow and wall slip has the effect of promoting the melt flow. The melt flow condition in the filling stage of micro-injection molding is determined by the combined effects of micro-viscosity and wall slip.
引文
[1]Kukla C,lroibl H,Detter H,et al.Micro-injection moulding-the aims of a project partnership.Kunststoffe Plast Europe,1998,88(9):1331-1336.
[2]W.Michaeli,A.Spermemann.A new Injection Molding Technology for Micro Parts[J].Journal of Polymer Engineering,2001,20(2,3):87-98.
[3]蒋炳炎,谢磊.微注射成型机发展现状与展望,中国塑料-2004,13(9):6-11.
[4]蒋炳炎,汤美林.微注射成型的核心技术.中国科技论文在线.
[5]Tom Kimerling.Design of a rapid thermal cycling mold for injection molding and hot embossing of micro and nano features.MIE 616-Design Optimization,2003.
[6]于同敏,宫德海.微型模具制造技术研究与发展.中国机械工程,2005,16(2):179-183.
[7]宋满仓,张巧丽,王敏杰.微成型领域的关键技术,中国塑料,2003,17(9):6-10.
[8]Mikell Knights.Mold Micro Parts Just One Pellet at A Time[J]Plastics Technology,2001,11:39.
[9]Mikell Knights.Micro Molds Make Micro Parts[J]Plastics Technology,2002,12:38-47.
[10]王立鼎,刘冲.微机电系统科学与技术发展趋势[J].大连理工大学学报,2000,40(5):505-508.
[11]Piotter V,Hanemann T,Ruprecht R,et al.Injection molding and related techniques for fabrication of microstructures.Microsys.Tech,1997,3(3):129-133.
[12]Zhao J,Mayes R H,Chen G,et al.Effects of process parameters on the micro molding process.Poly.Eng.Sci,2003,43(9):1542-1554.
[13]Kukla C.Micro injection molding.Proceeding of The 20d ESAFORM Conference on Material Forming,Liege,2001:81-84.
[14]Despa M S.Molding large area plastic parts covered with HARMs:missertationJ.Louisiana State University,2001.
[15]Shen Y K,Wu W Y.An analysis of the three-dimensional micro-injection molding Int.Comm.Heat Mass Transfer,2002,29(3):423-431.
[16]Shen Y K,Yeh S L and Chen S H.Three-dimension non-newtonian computations of micro-injection molding with the Finite Element Method.Int Comm.Heat Mass Transfer,2002,29(5):643-652.
[17]Don sung Kim,Kwang-Cheol Lee,Tar Hun Kwon,Seung S Lee,Micro-channel filling flow considering surface tension effect,Micromesh,Microeng.12(3003):236-246.
[18]W.B.Yong,Simulation of the filling process in molding components with micro channels,Microsystem Technologies 11(2005)410-415.
[19]Xu B,Ooi KT,Wong TN,Liu CY,Study on the viscosity of the liquid flowing in microgeometry.J Micromech Microeng,1999,9:337-384.
[20]Rosebaun EE,Hatzikiriakos SG,Wall slip in the capillary flow of molten polymers subject to viscous heating AICHE J,1997,43:598-608.
[21]Pioter V,Mueller K,Plewa K,Ruprecht R,Hausselt J(2002),Performance and simulation of thermoplastic micro injection molding,Microsystem Technologies 8:387-390.
[22]Mala G M,Li D Q,Dale J D.Heat transfer and fluid flow in microchannels,International Journal of Heat and Mass Transfer,1997,40(13):3079-3088.
[23]Yao D G,Kim B.Simulation of the filling process in micro channels,for polymeric materials,Journal of Micromechanics and Micro engineering,2002,12(5):604-610.
[24]徐佩弦.高聚物流变学及其应用,北京,化学工业出版社,2003.
[25]C.A.Hiber,S.F.Shen,A finite-element/finite-difference simulation of the injection-molding filling process,Journal of Non-Newtonian Fluid Mechanics,7(1980):1-32.
[26]H.H.Chiang,C,A.Hiber,K.K.Wang,A unified simulation of the filling and postfilling stages in injection molding,Part Ⅰ:Formulation,Polymer Engineering and Science,1991,31(2):116-124.
[27]郑伟.微注塑成型工艺的模拟分析与试验研究[学],大连理工大学,2005,12-81.
[28]McNeely M R 1999 Hydrophobic microfluidcs Proc.SPIE 3877 210-20.
[29]Ahn C H 2000 Structurally programmable microfluidic systems Proc.Micro-TAS Enschede,The Netherlands,pp 206-8.
[30]李又民.微注塑成型充模理论模型与数值模拟,大连理工大学硕士学位论文,2005.
[31]Georg Menges等[德].注射模具制造工程.北京:化学工业出版社,2002:626-629.
[32]Eringen A C and Okada 1995 A lubrication theory for fluids with microstructure int.J.Eng.sci 33 2297-308.
[33]Israelachvili J N 1986 Measurements of the viscosity of liquids in very thin films J.Colloid Imterface Sci.110 263-71.
[34]Forcada M L and Mate C M 1993 The flow of thin viscous-liquid films on roating-disks.J.Colloid Imterface Sci.169 218-25.
[35]吴其晔,巫静安.高分子材料流变学.北京:高等教育出版社,2002:296-316.
[36]Mhetar,L.A.Archer.Slip in entangled polymer solutions,Macromolecules.1998,31(19):6639-6649.
[37]William Brian Black.Wall slip and boundary effects in polymer shear flows.Doctor of Philosophy.MADISION:University of Wisconsin.2000.
[38]黄兴元,柳和生,郡超等.聚合物挤出过程中壁面滑移现象研究.中国塑料,2004 18(8):12-16.
[39]和克智.C++程序设计,西安:西安交通大学出版社,1999.8
[40]谭浩强.C程序设计.清华大学出版社,1999.
[41]何曼君,陈维孝,董西侠.高分子物理,复旦大学出版社,上海,1988.
[42]Subbiah S,Stratford D L and Guceri S I.Non-isothermal flow of polymers into two-dimensional thin cavity molds:a numerical grid generation approach[J].Int.J.Heat Transfer,1989.32,415-434.
[43]Wang V W,Hiber C A and Wang K K.Dynamic simulation and graphics for the injection molding of three-dimensional thin parts[J].Journal of Polymer Engineering,1986,7:22-45.
[44]Dupret and Vanderschuren L.Calculation of the temperature field in injection molding[J].AICHEJ.,1988,34:1959-1972.
[45]王勖成.有限单元法,北京:清华大学出版社,2002:18-25.
[46]王利霞,注塑成型充模过程的温度场计算[J],计算力学学报,2002,5(19),173-178.
[47]申长雨.塑料模具计算机辅助工程[M],河南科学技术出版社,1998.
[48]Peter Kennedy.Flow Analysis of Injection Molds[D],Hanser Publishers,Munich Vienna New York.
[49]李开泰,黄艾香,黄庆怀.有限元方法及其应用.西安:西安交通大学出版社,1984.
[50]李立康,於崇华,朱政华.微分方程数值方法.北京:复旦大学出版社,1999.
[51]胡建伟,汤怀民.微分方程数值解法.北京:科学出版社,1999.
[2]W.Michaeli,A.Spermemann.A new Injection Molding Technology for Micro Parts[J].Journal of Polymer Engineering,2001,20(2,3):87-98.
[3]蒋炳炎,谢磊.微注射成型机发展现状与展望,中国塑料-2004,13(9):6-11.
[4]蒋炳炎,汤美林.微注射成型的核心技术.中国科技论文在线.
[5]Tom Kimerling.Design of a rapid thermal cycling mold for injection molding and hot embossing of micro and nano features.MIE 616-Design Optimization,2003.
[6]于同敏,宫德海.微型模具制造技术研究与发展.中国机械工程,2005,16(2):179-183.
[7]宋满仓,张巧丽,王敏杰.微成型领域的关键技术,中国塑料,2003,17(9):6-10.
[8]Mikell Knights.Mold Micro Parts Just One Pellet at A Time[J]Plastics Technology,2001,11:39.
[9]Mikell Knights.Micro Molds Make Micro Parts[J]Plastics Technology,2002,12:38-47.
[10]王立鼎,刘冲.微机电系统科学与技术发展趋势[J].大连理工大学学报,2000,40(5):505-508.
[11]Piotter V,Hanemann T,Ruprecht R,et al.Injection molding and related techniques for fabrication of microstructures.Microsys.Tech,1997,3(3):129-133.
[12]Zhao J,Mayes R H,Chen G,et al.Effects of process parameters on the micro molding process.Poly.Eng.Sci,2003,43(9):1542-1554.
[13]Kukla C.Micro injection molding.Proceeding of The 20d ESAFORM Conference on Material Forming,Liege,2001:81-84.
[14]Despa M S.Molding large area plastic parts covered with HARMs:missertationJ.Louisiana State University,2001.
[15]Shen Y K,Wu W Y.An analysis of the three-dimensional micro-injection molding Int.Comm.Heat Mass Transfer,2002,29(3):423-431.
[16]Shen Y K,Yeh S L and Chen S H.Three-dimension non-newtonian computations of micro-injection molding with the Finite Element Method.Int Comm.Heat Mass Transfer,2002,29(5):643-652.
[17]Don sung Kim,Kwang-Cheol Lee,Tar Hun Kwon,Seung S Lee,Micro-channel filling flow considering surface tension effect,Micromesh,Microeng.12(3003):236-246.
[18]W.B.Yong,Simulation of the filling process in molding components with micro channels,Microsystem Technologies 11(2005)410-415.
[19]Xu B,Ooi KT,Wong TN,Liu CY,Study on the viscosity of the liquid flowing in microgeometry.J Micromech Microeng,1999,9:337-384.
[20]Rosebaun EE,Hatzikiriakos SG,Wall slip in the capillary flow of molten polymers subject to viscous heating AICHE J,1997,43:598-608.
[21]Pioter V,Mueller K,Plewa K,Ruprecht R,Hausselt J(2002),Performance and simulation of thermoplastic micro injection molding,Microsystem Technologies 8:387-390.
[22]Mala G M,Li D Q,Dale J D.Heat transfer and fluid flow in microchannels,International Journal of Heat and Mass Transfer,1997,40(13):3079-3088.
[23]Yao D G,Kim B.Simulation of the filling process in micro channels,for polymeric materials,Journal of Micromechanics and Micro engineering,2002,12(5):604-610.
[24]徐佩弦.高聚物流变学及其应用,北京,化学工业出版社,2003.
[25]C.A.Hiber,S.F.Shen,A finite-element/finite-difference simulation of the injection-molding filling process,Journal of Non-Newtonian Fluid Mechanics,7(1980):1-32.
[26]H.H.Chiang,C,A.Hiber,K.K.Wang,A unified simulation of the filling and postfilling stages in injection molding,Part Ⅰ:Formulation,Polymer Engineering and Science,1991,31(2):116-124.
[27]郑伟.微注塑成型工艺的模拟分析与试验研究[学],大连理工大学,2005,12-81.
[28]McNeely M R 1999 Hydrophobic microfluidcs Proc.SPIE 3877 210-20.
[29]Ahn C H 2000 Structurally programmable microfluidic systems Proc.Micro-TAS Enschede,The Netherlands,pp 206-8.
[30]李又民.微注塑成型充模理论模型与数值模拟,大连理工大学硕士学位论文,2005.
[31]Georg Menges等[德].注射模具制造工程.北京:化学工业出版社,2002:626-629.
[32]Eringen A C and Okada 1995 A lubrication theory for fluids with microstructure int.J.Eng.sci 33 2297-308.
[33]Israelachvili J N 1986 Measurements of the viscosity of liquids in very thin films J.Colloid Imterface Sci.110 263-71.
[34]Forcada M L and Mate C M 1993 The flow of thin viscous-liquid films on roating-disks.J.Colloid Imterface Sci.169 218-25.
[35]吴其晔,巫静安.高分子材料流变学.北京:高等教育出版社,2002:296-316.
[36]Mhetar,L.A.Archer.Slip in entangled polymer solutions,Macromolecules.1998,31(19):6639-6649.
[37]William Brian Black.Wall slip and boundary effects in polymer shear flows.Doctor of Philosophy.MADISION:University of Wisconsin.2000.
[38]黄兴元,柳和生,郡超等.聚合物挤出过程中壁面滑移现象研究.中国塑料,2004 18(8):12-16.
[39]和克智.C++程序设计,西安:西安交通大学出版社,1999.8
[40]谭浩强.C程序设计.清华大学出版社,1999.
[41]何曼君,陈维孝,董西侠.高分子物理,复旦大学出版社,上海,1988.
[42]Subbiah S,Stratford D L and Guceri S I.Non-isothermal flow of polymers into two-dimensional thin cavity molds:a numerical grid generation approach[J].Int.J.Heat Transfer,1989.32,415-434.
[43]Wang V W,Hiber C A and Wang K K.Dynamic simulation and graphics for the injection molding of three-dimensional thin parts[J].Journal of Polymer Engineering,1986,7:22-45.
[44]Dupret and Vanderschuren L.Calculation of the temperature field in injection molding[J].AICHEJ.,1988,34:1959-1972.
[45]王勖成.有限单元法,北京:清华大学出版社,2002:18-25.
[46]王利霞,注塑成型充模过程的温度场计算[J],计算力学学报,2002,5(19),173-178.
[47]申长雨.塑料模具计算机辅助工程[M],河南科学技术出版社,1998.
[48]Peter Kennedy.Flow Analysis of Injection Molds[D],Hanser Publishers,Munich Vienna New York.
[49]李开泰,黄艾香,黄庆怀.有限元方法及其应用.西安:西安交通大学出版社,1984.
[50]李立康,於崇华,朱政华.微分方程数值方法.北京:复旦大学出版社,1999.
[51]胡建伟,汤怀民.微分方程数值解法.北京:科学出版社,1999.