三维塑料注射成形及结晶过程数值模拟关键技术研究
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摘要
注射成形是塑料制品最重要的成形方式之一,提高塑料制品质量和工艺成形性的一个有效方法是采用数值模拟技术,对成形过程进行准确预测,为优化产品设计和优选工艺参数提供指导。由于基于Hele-Shaw假设的表面模型数值模拟,不能满足日益复杂和大型制品的精确模拟要求,因此迫切需要采用三维实体模拟技术。本文对塑料注射成形及结晶过程的三维有限元模拟进行了比较系统的研究,并编制了数值模拟软件,研究内容主要包括以下几个方面:
(1)在充模过程的模拟中,针对流动数值模拟中的速度与压力的插值空间不协调导致的数值振荡问题,分别建立了基于GLS(Galerkin least-squares)法的速度、压力任意插值的集成格式稳定有限元计算模型和基于PSPG(Pressure-Stabilizing /Petrov-Galerkin)法的速度、压力同次插值的分离格式稳定有限元计算模型。而对于能量场方程中对流占优和小扩散系数造成的数值不稳定问题,则建立了基于GLS/GGLS(Galerkin gradient least-squares)法的稳定有限元计算模型。此外,扩展的三维FAN法用于充模过程中的流动前沿跟踪。
(2)在充模后的保压过程模拟中,熔体与凝固层相互作用,作为一个整体受保压压力的作用,建立了三维可压缩熔体流动和粘弹性凝固层变形的固熔两相耦合计算模型;在冷却过程模拟中,制品在型腔内受约束变形,建立了三维粘弹性有限元计算模型;在翘曲模拟中,建立了三维弹性变形的有限元计算模型,由此完成了三维注射成形充模后模拟的有限元计算模型的建立。
(3)根据所建立的充模过程计算模型,对注射成形的充模过程进行了模拟,研究了流动前沿、喷泉效应、跑道效应和充模过程中的温度场;采用不同的网格密度考察了本文算法的精度对网格粗细程度的依赖性;分析了充模工艺参数对充模过程的影响;比较了不可压缩与可压缩假设的熔体充模过程的差异;通过对具有一定形状复杂程度的制品的模拟,表明所建立的充模计算模型具有很好的精度、稳定性和实用性。
(4)在所建立的保压、冷却和翘曲计算模型基础上,研究了工艺参数对制品残余应力、收缩和翘曲的影响;在保压、冷却模拟中,分别采用弹性模型和粘弹性模型计算了凝固层的热残余应力及模内变形。
(5)基于剪切应力能提高等效熔点的理论,建立了剪切诱导时间指数和剪切诱导结晶的计算模型,给出了结晶对注射成形过程中熔体粘度的影响模型及考虑结晶放热的注射成形能量场控制方程,模拟研究了成形工艺参数对结晶及结晶对注射成形过程的影响。
此外,在数值算例中,本文的模拟结果与实验结果及国外著名的注射成形模拟软件Moldflow的模拟结果进行了对比,吻合得比较好,验证了本文提出的计算模型的精确性与合理性,表明所开发三维实体模拟软件可为提高制品质量和注射成形工艺提供指导。
Injection molding is one of the most important manufacturing processes for plastic products. The quality and performance of injection molded parts depend not only on the material, but also on how the material is processed. With computer-aided engineering(CAE) tools, better understanding of parts during process can be achieved to help engineers to improve part design and optimize processing conditions. However the traditional CAE techniques for the simulation of injection molding, called by the middle-plane technique and dual domain technique based on Hele-Shaw approximation, pose inherent limitations when the part has complex geometrical configuration or thick walls. Three dimensional (3D) simulation based on the solid element can give deeper insight into molding process by providing more detailed information than traditional techniques.
Injection molding process and crystallization of semicrystalline polymers were modeled systematically using the finite element method, and programs were developed to simulate the injection molding and crystallization. The following work was included:
(1) The GLS(Galerkin/Least-squares) method is employed to prevent the potential numerical instabilities by adding to the weighting functions with their derivatives, resulting in the integrated symmetric and stabilized finite element formulations using arbitrary interpolation functions for velocity and pressure. The similar segregated stabilized finite element formulation using equal-order interpolation functions for velocity and pressure can be obtained based on the PSPG(Pressure-Stabilizing/ Petrov-Galerkin) method. Because of the convection term and small heat conduction coefficient in the governing equation of energy, spurious oscillation associated with the classic Galerkin finite element method is induced. And GLS/GGLS(Galerkin gradient least-squares) methods are applied to avoid these oscillations. The expanded 3D FAN scheme is applied to capture the advanced melt front.
(2) During the packing stage, the polymer melt solidifies partly with the decrease of temperature. Molten and solid polymers interact, and act as a whole entity by the packing pressure. A 3D two-phase coupling model combining the flow of compressible melt with the deflection of viscoelastic solid is established. During the cooling stage, a 3D viscoelastic constitutive model is presented to show the evolvement of residual thermal stresses while part deflects confined to the mold cavity. To simulate the warpage of plastic parts ejected from cavity, a 3D elastic constitutive model is given. And so far, the complete 3D approximation of postfilling is made.
(3) In the numerical simulation of filling stage, advanced melt front, fountain flow, effect of runway and temperature field of the part were studied. Fine and coarse finite element mesh were used to show the stability and accuracy of the proposed algorithms. Different processing conditions were adopted to investigate the effect of processing parameters on the filling stage. Results were compared to show that the hypothesis of compressible flow leads to more reasonable injection pressure than incompressible flow. Examples showed that the proposed algorithms could be accurate and practical for parts with complex geometry.
(4) Numerical simulations were carried out to study the effect of processing parameters on the residual thermal stresses and shrinkage of parts. The elastic and viscoelastic constitutive models were adopted seperately to computer residual thermal stresses and deflection for the solid during the packing and cooling stages.
(5) The stress-induced induction time index and crystallization models for semicrystalline plastics were proposed based on the theory that stress-induced orientation of polymer chains increases the equilibrium melting temperature. The effect of crystallinity on viscosity of the polymer melt and temperature due to latent heat of fusion is described. To investigate the effect of processing parameters on the crystallinity, the injection molding process of semicrystalline plastics was simulated under different processing conditions.
In addition, lots of numerical examples showed the results of presented 3D approaches developed herein were in good agreement with the experimental results or results of the well-known commercial software Moldflow. It was suggested that the presented 3D approaches could present accurate, stable and practical results.
(1)在充模过程的模拟中,针对流动数值模拟中的速度与压力的插值空间不协调导致的数值振荡问题,分别建立了基于GLS(Galerkin least-squares)法的速度、压力任意插值的集成格式稳定有限元计算模型和基于PSPG(Pressure-Stabilizing /Petrov-Galerkin)法的速度、压力同次插值的分离格式稳定有限元计算模型。而对于能量场方程中对流占优和小扩散系数造成的数值不稳定问题,则建立了基于GLS/GGLS(Galerkin gradient least-squares)法的稳定有限元计算模型。此外,扩展的三维FAN法用于充模过程中的流动前沿跟踪。
(2)在充模后的保压过程模拟中,熔体与凝固层相互作用,作为一个整体受保压压力的作用,建立了三维可压缩熔体流动和粘弹性凝固层变形的固熔两相耦合计算模型;在冷却过程模拟中,制品在型腔内受约束变形,建立了三维粘弹性有限元计算模型;在翘曲模拟中,建立了三维弹性变形的有限元计算模型,由此完成了三维注射成形充模后模拟的有限元计算模型的建立。
(3)根据所建立的充模过程计算模型,对注射成形的充模过程进行了模拟,研究了流动前沿、喷泉效应、跑道效应和充模过程中的温度场;采用不同的网格密度考察了本文算法的精度对网格粗细程度的依赖性;分析了充模工艺参数对充模过程的影响;比较了不可压缩与可压缩假设的熔体充模过程的差异;通过对具有一定形状复杂程度的制品的模拟,表明所建立的充模计算模型具有很好的精度、稳定性和实用性。
(4)在所建立的保压、冷却和翘曲计算模型基础上,研究了工艺参数对制品残余应力、收缩和翘曲的影响;在保压、冷却模拟中,分别采用弹性模型和粘弹性模型计算了凝固层的热残余应力及模内变形。
(5)基于剪切应力能提高等效熔点的理论,建立了剪切诱导时间指数和剪切诱导结晶的计算模型,给出了结晶对注射成形过程中熔体粘度的影响模型及考虑结晶放热的注射成形能量场控制方程,模拟研究了成形工艺参数对结晶及结晶对注射成形过程的影响。
此外,在数值算例中,本文的模拟结果与实验结果及国外著名的注射成形模拟软件Moldflow的模拟结果进行了对比,吻合得比较好,验证了本文提出的计算模型的精确性与合理性,表明所开发三维实体模拟软件可为提高制品质量和注射成形工艺提供指导。
Injection molding is one of the most important manufacturing processes for plastic products. The quality and performance of injection molded parts depend not only on the material, but also on how the material is processed. With computer-aided engineering(CAE) tools, better understanding of parts during process can be achieved to help engineers to improve part design and optimize processing conditions. However the traditional CAE techniques for the simulation of injection molding, called by the middle-plane technique and dual domain technique based on Hele-Shaw approximation, pose inherent limitations when the part has complex geometrical configuration or thick walls. Three dimensional (3D) simulation based on the solid element can give deeper insight into molding process by providing more detailed information than traditional techniques.
Injection molding process and crystallization of semicrystalline polymers were modeled systematically using the finite element method, and programs were developed to simulate the injection molding and crystallization. The following work was included:
(1) The GLS(Galerkin/Least-squares) method is employed to prevent the potential numerical instabilities by adding to the weighting functions with their derivatives, resulting in the integrated symmetric and stabilized finite element formulations using arbitrary interpolation functions for velocity and pressure. The similar segregated stabilized finite element formulation using equal-order interpolation functions for velocity and pressure can be obtained based on the PSPG(Pressure-Stabilizing/ Petrov-Galerkin) method. Because of the convection term and small heat conduction coefficient in the governing equation of energy, spurious oscillation associated with the classic Galerkin finite element method is induced. And GLS/GGLS(Galerkin gradient least-squares) methods are applied to avoid these oscillations. The expanded 3D FAN scheme is applied to capture the advanced melt front.
(2) During the packing stage, the polymer melt solidifies partly with the decrease of temperature. Molten and solid polymers interact, and act as a whole entity by the packing pressure. A 3D two-phase coupling model combining the flow of compressible melt with the deflection of viscoelastic solid is established. During the cooling stage, a 3D viscoelastic constitutive model is presented to show the evolvement of residual thermal stresses while part deflects confined to the mold cavity. To simulate the warpage of plastic parts ejected from cavity, a 3D elastic constitutive model is given. And so far, the complete 3D approximation of postfilling is made.
(3) In the numerical simulation of filling stage, advanced melt front, fountain flow, effect of runway and temperature field of the part were studied. Fine and coarse finite element mesh were used to show the stability and accuracy of the proposed algorithms. Different processing conditions were adopted to investigate the effect of processing parameters on the filling stage. Results were compared to show that the hypothesis of compressible flow leads to more reasonable injection pressure than incompressible flow. Examples showed that the proposed algorithms could be accurate and practical for parts with complex geometry.
(4) Numerical simulations were carried out to study the effect of processing parameters on the residual thermal stresses and shrinkage of parts. The elastic and viscoelastic constitutive models were adopted seperately to computer residual thermal stresses and deflection for the solid during the packing and cooling stages.
(5) The stress-induced induction time index and crystallization models for semicrystalline plastics were proposed based on the theory that stress-induced orientation of polymer chains increases the equilibrium melting temperature. The effect of crystallinity on viscosity of the polymer melt and temperature due to latent heat of fusion is described. To investigate the effect of processing parameters on the crystallinity, the injection molding process of semicrystalline plastics was simulated under different processing conditions.
In addition, lots of numerical examples showed the results of presented 3D approaches developed herein were in good agreement with the experimental results or results of the well-known commercial software Moldflow. It was suggested that the presented 3D approaches could present accurate, stable and practical results.
引文
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