挤出加工流场中聚合物成型机理及其工艺模拟与优化研究
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摘要
高分子材料、木材、金属和硅酸盐并称世界四大材料体系,是国民经济和国防建设中重要的生产材料。围绕高分子材料,目前已形成了门类齐全的高分子材料加工工业体系并在国民经济中占有重要地位。挤出是高分子材料成型加工中一类重要工艺,通过挤出模具能够模塑所有的热塑性材料和某些热固性材料,可以生产管材、板材、棒材、网材、单丝、薄膜、异型材、发泡型材、多种材料复合制品以及线缆等带包覆层的工业制品。挤出成型过程中,受温度、压强、应力以及作用时间等变化的影响,体系中聚合物熔体的聚集态结构和化学结构会发生变化。挤出工艺条件在很大程度上决定着材料的结构和性能,并最终影响成型制品的外观和质量。
由于挤出成型过程影响因素较多,借助常规实验方法,成本高且耗时费力。目前,围绕聚合物挤出流动过程所开展的实验研究大多在实验室中完成,其实验目的主要是从研究材料自身流变性出发,以简单剪切和拉伸流动为测试模型。由于先进测试方法难以直接引入挤出工艺现场,普通测试方法又不可避免会对挤出加工流场中聚合物熔体流动行为造成影响并导致大量系统误差,因此,实验方法只能定性但难以定量描述聚合物加工中的实际流变行为。数值模拟技术经过近几十年的发展,其对于大规模复杂物理和工程问题的优秀解算能力吸引了科研人员的目光,并逐步在力学、传热学、材料学等诸多领域得到广泛应用,加快了现代科技发展步伐。
本文探讨了数值模拟技术在聚合物流变学中的应用,研究了聚合物挤出成型过程的模型化理论和数值计算方法,构造了能够描述挤出过程中聚合物流变行为特点的物理和数学模型。通过数值模拟技术,成功预测挤出加工流场中聚合物熔体的流动速度、应力和温度等重要场变量分布特点及其变化规律,讨论并分析聚合物的复杂流变行为及其成型机理。将成型过程数值模拟技术与现代优化设计理论相结合,建立并运用相应的优化模型和算法,实现成型工艺与制品质量的优化控制。
在聚合物流变学基础上,结合流体动力学理论,建立了基于Euler描述的非牛顿流体三维非等温流动数学模型。采用基于低阶插值的罚函数有限元方法,成功避免了混合有限元方法中为稳定压力项求解所采用的高阶插值,从而有效利用运算资源,将求解空间扩展至三维。充分考虑了剪切速率和温度变化对材料流动性的影响,采用非线性粘度模型,实现了流动与传热的耦合求解。通过线性化交替迭代算法,在迭代过程中实现非线性项的线性化,减小了初始变量分布对计算收敛性影响。采用流线迎风Petrov-Galerkin(SUPG)方法,通过构造非对称权函数来增大流场中来流上游效应,克服了标准伽辽金(Galerkin)方法在处理对流扩散方程时因对流占优所引起的数值振荡问题。通过理论分析,推导了幂率流体圆管泊肃叶(Poiseuille)流动中的各场变量分布函数,将模拟与理论结果进行比较,以验证该非牛顿流动数学模型与数值计算方法的可靠性。
本文所建立的非牛顿流体三维非等温流动数值模拟技术不仅可用于分析一般非牛顿流动问题,在处理目前流动模拟技术难以预测的复杂工艺问题时也表现出较强的适应性。基于该方法,本文首次针对一类新型复合共挤出工艺——异型材钢塑共挤工艺过程开展了数值建模及其工艺分析工作。根据其不同于常规挤出工艺的特点,建立了该工艺过程中聚合物成型的数学模型,通过模拟计算,得到聚合物熔体由测向导入至复合成型整个流动过程的速度、温度、应力和压力等各场变量的分布,掌握了聚合物熔体的流动特点与成型规律,讨论了体积流量和钢衬移动速度变化对各场变量分布的影响。定义流速分布相对均差作为判断挤出流动平衡性的依据,模拟并得到不同导入角角度和分流段长度对挤出流动平衡的影响,分析结论可为实际异型材钢塑共挤工艺设计提供理论指导与支持。
挤出加工流场中的聚合物熔体除了具有非牛顿流动特性外,还表现出较强的弹性流动特点。针对该问题,本文建立了能够真实反映成型过程中聚合物熔体粘弹流变特性的三维粘弹非等温流动数学模型,构造了稳定的有限元数值求解方法并将其成功应用于聚合物挤出工艺模拟与分析中。采用PTT(Phan-Thien—Tanner)本构模型描述聚合物熔体的粘弹流变行为,在反映聚合物熔体剪切流动特点的同时,能较真实地反映其拉伸流动特点。考虑粘弹介质特有的能量耗散模式,在热力学第一定律基础上,根据非平衡不可逆热力学理论首次推导了该粘弹介质的能量守恒方程。将粘弹性附加应力张量作为有限元基本解,采用解耦方法实现了三维空间中速度场、温度场和流动应力场的多物理场稳定求解。将应力张量作为拟体力项处理后,动量方程会失去椭圆性并导致计算结果发散。通过分离粘弹分裂(DEVSS)方法,引入稳定化因子对动量方程进行椭圆化处理,提高了速度场求解的稳定性。采用非协调流线迎风(SU)方法克服了本构方程在对流占优时的数值振荡问题,实现了应力场的稳定求解。通过对粘弹流体4:4:1收缩流动模拟结果与polyflow软件模拟结果的比较,证明本文所建立的粘弹流动模型和数值计算方法的合理与可靠性。将该模型与方法成功应用于异型材挤出工艺过程模拟,讨论了网格密度、罚数和能量分割系数等计算控制参数对模拟结果的影响。分析了中空异型材挤出过程中聚合物熔体的流动速度、温度和应力分布,讨论了加工流场中聚合物熔体的粘弹流动特点,获得了工艺条件和口模结构参数变化对聚合物流变行为的影响规律。
挤出胀大是聚合物挤出成型工艺中无法回避的一个问题。由于加工中聚合物熔体的粘弹流变特性,熔体离开口模时,形变回复等会导致聚合物熔体的挤出胀大,表现为挤出物截面形状和尺寸发生变化,对挤出制品的尺寸和精度造成影响。本文在粘弹流动数值模拟技术基础上,建立了聚合物熔体三维挤出胀大的数学模型和数值求解方法并编制了相应的有限元模拟程序。针对一种工业用低密度聚乙烯(LDPE)的挤出胀大问题开展了实验及其数值模拟研究。通过控制应变流变仪分别得到小幅振荡剪切流动中储能和耗能模量的分布以及稳态剪切流动中剪切粘度和第一法向应力差的分布。采用非线性回归方法拟合流变测量实验结果,得到以PTT本构模型表征的材料线性和非线性粘弹流变参数。通过间接测量,得到不同螺杆转速时LDPE通过圆形口模时的出口挤出胀大比。采用本文所建立的聚合物挤出胀大数学模型及其数值求解方法,对实验条件下LDPE的挤出胀大过程进行模拟,比较了挤出胀大比的实验和模拟结果。通过挤出胀大数值模拟,进一步讨论了LDPE通过圆环口模时的出口挤出胀大问题,得到实验中难以测得的流动速度和应力等场变量分布,可对挤出胀大特点及其形成机理进行定性与定量分析和预测。
聚合物挤出成型过程数值模拟是被动式的,实际应用中需依靠专业工程技术人员的智力、知识和经验,对计算结果进行分析、评价,然后修改设计。本文将挤出成型过程数值模拟技术与优化设计理论相结合以实现成型过程与制品质量的优化控制。在成型过程模拟技术基础上,提出了一种基于数值模拟、前馈神经网络和遗传算法的聚合物挤出工艺与模具优化设计方法。根据挤出流动平衡原则,建立了以出口流动均匀性为目标,以工艺和模具结构参数为设计变量的优化模型。通过成型过程数值模拟获得目标函数值以建立训练神经网络模型的样本库,采用反向误差传播算法进行网络学习,建立用于预测隐目标函数的神经网络模型,从而有效减小有限元模拟计算量。通过遗传算法与神经网络的交互运算,得到优化结果,使设计建立在科学分析的基础上从而提高挤出加工工艺设计水平。探讨了该优化设计方法各模块计算实施中的关键技术问题,编制了聚合物挤出工艺与模具优化设计程序。分别针对异型材钢塑共挤工艺过程和片材挤出工艺过程进行优化设计并达到相应的优化目标。
数值模拟技术在聚合物加工工程领域的应用已成为计算流变学的重要分支之一。近年来,尽管流体力学数值方法取得了较大进展,但在处理复杂流动问题时,其解算能力仍受到流动区域和计算稳定性的限制。尤其对于复杂工程与工艺问题,其数学建模和数值模拟关键技术研究鲜有报道。本文针对挤出加工流场中聚合物熔体非牛顿粘性和弹性流动特点所建立的数学模型以及所构造的稳定数值计算方法,对于丰富计算流变学具有一定的理论意义。针对挤出工艺过程中聚合物熔体的复杂流变行为及其成型机理所作的分析与研究,以及基于此所开展的成型工艺模拟与优化工作具有较大的工程应用价值。
Polymer is a kind of important manufacturing material in national industry and defence construction which is called the four most important material system incooperating with wood, metal and silicate. With the development of polymer processing technology, the industrial system of polymer processing is established with many kinds of departments and it is playing an important role in national economy. Extrusion is one of the most important polymer processing technologies by which all the thermoplastic polymers and some thermosetting polymers can be molded, such as pipes, sheets, rods, nets, monofils, films, profiles, foaming profiles, composite products and coated products. In the extrusion process, the accumulative structure and chemical structure of polymer melts can be varied with the change of temperatue, pressure and stress. The processing conditions determine the material structure and ultimately affect the performance and quality of final products.
It is hard to afford to traditional experimental method for the reason that the influencing factors are multiplex and it is also expensive, time-consuming and laborious. Currently, the related experiments on polymer melts flow are mainly conducted in the laboratory and the aim of which is to investigate rheological properties based on the simple model of shear or extensional flows. As for the experiments conducted in practical extrusion process, advanced testing method is diffucult to be directly introduced and general testing method is inevitably affect real flow patterns. It is hard to quantitatively but can only qualitatively reflect practical rheological behaviours of polymer melts by using experimental method. After several years' development, numerical simulation method gradually attracts the attention of scientific and technical researchers for its excellent solving ablility to complex physical and engineering problems. It is now widely adopted in mechanics, thermotics, material science and other fields which greatly accelerate the development of modern science and technology.
The application of numerical simulation technology in fluid dynamics is discussed in the present research. The modeling theory and numerical method is studied and the mathematical model is established to investigate polymer rheological behaviours in the extrusion process. The distribution and changing law of some important field functions, such as velocity, stress and temperature, are discussed and analysed to explain the forming mechanism of polymer melts. The numerical simulation method is combined with optimal design theory and the optimization model and algorithm is established to realize the optimal control of extrusion process and products' quality.
The mathematical model of three-dimensional non-isothermal flow of non-newtonian fluid is established under Euler frame on the basis of polymer rheology and fluid dynamics. The penalty finite elment method is adopted to avoid high-order interpolation which is usually used in the mixed finite element method so as to effectively make use of computational resources. The effects of shear rate and temperature on melts flow are considered and the coupled calculation of flow and heat transfer is realized based on the nonlinear viscosity model. The non-linear term is linearized by using linearation iterative algorithm and hence to reduce the effects of valiables' initial distribution. The stream upwind Petrove-Galerkin method is performed to enlarge the upwind effects by using asymmetry weight function to overcome the oscillation of convection terms dominated problems. The field variables' function in the pipe poiseuille flow of power-law fluid is deduced and the corresponding simulated results are compared with the analysed results to prove the reliability of current mathematical model and numerical algorithm for non-newtonian flow.
The numerical method established above can not only be used in the analysis of general non-newtonian fluid flow problem but also can be adopted to solve complex engineering problem. Based on the proposed method, the mathematical modeling and processing analysis of a novel co-extrusion process of plastic profile with metal insert is performed in the study for the first time. The whole flow characteristic of polymer melts in flow channel is obtained by the calculation of velocity, stress, temperature and pressure. The influences of volume flow rate and metal insert moving velocity on the distribution of field variables is discussed and the corresponding advice on the processing design is put forward. The velocity relative difference is defined to jugde the outlet flow balance. The influences of both the inlet angle and the length of allocation region are investigated by the calculation of velocity relative difference.
Polymer melts in the extrusion process not only have non-newtonian flow characteristics but also have strong viscoelastic flow characteristics. The mathematical model of three-dimensional viscoelastic non-isothermal flow is established and a stable numerical algorithm is proposed which has been successfully adopted in the analysis of polymer extrusion process. The PTT (Phan Thien-Tanner) model is adopted to depict such viscoelastic properties of polymer melts which can reflect the extensional flow characteristic better. The special energy consumption pattern of viscoelastic medium is considered and its energy conservation equation is deduced according to the nonequilibrium irreversible thermodynamical theory. A decoupled algorithm is adopted to realize stable calculation for the three-dimensional multi-variables field consisting of velocity, temperature and flow stress. The momentum equation will lose its ellipticalness when the stress term is taken as the quasi-body force term and the discrete elastic-viscous stress split algorithm is adopted to improve the stability of velcocity calculation by introducing the stabilization factor. The non-consistant stream upwind method is adopted to overcome the oscillation in the calculation of stress. The mathematical model and numerical method for viscoelastic flow simulation of polymer melts established in the study is introduced to the analysis of general profile extrusion process. The effects of calculation control parameters, such as mesh division, penalty factor and energy partitioning factor, are investigated. The viscoelastic flow characteristics of polymer melts in the profile extrusion process are analysed based on the simulated results of velocity, temperature and stress. The influences of processing conditions and die structure on flow characteristics are further discussed.
Extudate swell is a common phenomenon for the reason of polymer melts' elastic deformation in the extrusion process which can severely influence the shape and dimensional precision of final products. Based on the viscoelastic flow simulation technology proposed in the study, the mathematical model and numerical algorithm for the simulation of three-dimensional extrudate swell is established and its finite element simulation program is worked out. The extrudate swell of an industrial LDPE is then investigated by both experimental method and numerical method. The distributions of stored-energy modulus and consumed-energy modulus in small amplitude oscillating shear flow and the distributions of shear viscosity and the first normal stress difference in steady shear flow are obtained by using the strain-controlled rheometer. Both linear and nonlinear viscoelastic rheological parameters of PTT model are obtained by using nonlinear regression method. The swelling ratios of LDPE through circular die under different volume flow rates are detected by using indirect measurement and they are compared with the simulated results. The distributions of flow velocity and stress in LDPE annular extrudate swell flow field obtained by simulation are analysed and the corresponding mechanism is further discussed.
The numerical simulation of polymer extrusion process is a passive system whose results have to be judged and analysed by professional worker with corresponding experiences and knowledge. In the study, the numerical simulation technology is combined with optimal design theory to realize the automatic optimal design and control for products. An optimal design method for polymer extrusion process is put forward based on numerical simulation, artificial neural net and generic algorithm. The optimization model is established by using the outlet flow balance as the optimization object. The processing parameters and die structure parameters are taken as design variables. The neural net model is trained by using the sample database obtained by simulated results so as to reduce the calculated amount of numerical simulation. The optimal design is achieved based on the scientific analysis through the iteration of genetic algorithm and neural net model. The corresponding optimization program for processing parameters and die structure parameters is worked out and the optimal design both for the co-extrusion process of plastic profile with metal insert and for the sheet extrusion process are further achieved.
The application of numerical simulation technology in the polymer processing engineering becomes one of the important branches in the computational rheology field. Although great progresses have been made in numerical methods on fluid dynamics in the recent years, its solving ability is still restricted to flow regions and computational stability. Researches on the complex mathematical modeling and the key technologies for numerical simulation are rarely reported especially for the solving of complex engineering and technology problem. The mathematical model and numerical method for the simulation of both viscous and viscoelastic characteristics of polymer melts in the study are of great interest to enrich the theory of computational rheology. It is also of much industrial interest to take research on rheological behaviour and the related forming mechanism in the polymer extrusion process based on the simulation and optimization technology.
由于挤出成型过程影响因素较多,借助常规实验方法,成本高且耗时费力。目前,围绕聚合物挤出流动过程所开展的实验研究大多在实验室中完成,其实验目的主要是从研究材料自身流变性出发,以简单剪切和拉伸流动为测试模型。由于先进测试方法难以直接引入挤出工艺现场,普通测试方法又不可避免会对挤出加工流场中聚合物熔体流动行为造成影响并导致大量系统误差,因此,实验方法只能定性但难以定量描述聚合物加工中的实际流变行为。数值模拟技术经过近几十年的发展,其对于大规模复杂物理和工程问题的优秀解算能力吸引了科研人员的目光,并逐步在力学、传热学、材料学等诸多领域得到广泛应用,加快了现代科技发展步伐。
本文探讨了数值模拟技术在聚合物流变学中的应用,研究了聚合物挤出成型过程的模型化理论和数值计算方法,构造了能够描述挤出过程中聚合物流变行为特点的物理和数学模型。通过数值模拟技术,成功预测挤出加工流场中聚合物熔体的流动速度、应力和温度等重要场变量分布特点及其变化规律,讨论并分析聚合物的复杂流变行为及其成型机理。将成型过程数值模拟技术与现代优化设计理论相结合,建立并运用相应的优化模型和算法,实现成型工艺与制品质量的优化控制。
在聚合物流变学基础上,结合流体动力学理论,建立了基于Euler描述的非牛顿流体三维非等温流动数学模型。采用基于低阶插值的罚函数有限元方法,成功避免了混合有限元方法中为稳定压力项求解所采用的高阶插值,从而有效利用运算资源,将求解空间扩展至三维。充分考虑了剪切速率和温度变化对材料流动性的影响,采用非线性粘度模型,实现了流动与传热的耦合求解。通过线性化交替迭代算法,在迭代过程中实现非线性项的线性化,减小了初始变量分布对计算收敛性影响。采用流线迎风Petrov-Galerkin(SUPG)方法,通过构造非对称权函数来增大流场中来流上游效应,克服了标准伽辽金(Galerkin)方法在处理对流扩散方程时因对流占优所引起的数值振荡问题。通过理论分析,推导了幂率流体圆管泊肃叶(Poiseuille)流动中的各场变量分布函数,将模拟与理论结果进行比较,以验证该非牛顿流动数学模型与数值计算方法的可靠性。
本文所建立的非牛顿流体三维非等温流动数值模拟技术不仅可用于分析一般非牛顿流动问题,在处理目前流动模拟技术难以预测的复杂工艺问题时也表现出较强的适应性。基于该方法,本文首次针对一类新型复合共挤出工艺——异型材钢塑共挤工艺过程开展了数值建模及其工艺分析工作。根据其不同于常规挤出工艺的特点,建立了该工艺过程中聚合物成型的数学模型,通过模拟计算,得到聚合物熔体由测向导入至复合成型整个流动过程的速度、温度、应力和压力等各场变量的分布,掌握了聚合物熔体的流动特点与成型规律,讨论了体积流量和钢衬移动速度变化对各场变量分布的影响。定义流速分布相对均差作为判断挤出流动平衡性的依据,模拟并得到不同导入角角度和分流段长度对挤出流动平衡的影响,分析结论可为实际异型材钢塑共挤工艺设计提供理论指导与支持。
挤出加工流场中的聚合物熔体除了具有非牛顿流动特性外,还表现出较强的弹性流动特点。针对该问题,本文建立了能够真实反映成型过程中聚合物熔体粘弹流变特性的三维粘弹非等温流动数学模型,构造了稳定的有限元数值求解方法并将其成功应用于聚合物挤出工艺模拟与分析中。采用PTT(Phan-Thien—Tanner)本构模型描述聚合物熔体的粘弹流变行为,在反映聚合物熔体剪切流动特点的同时,能较真实地反映其拉伸流动特点。考虑粘弹介质特有的能量耗散模式,在热力学第一定律基础上,根据非平衡不可逆热力学理论首次推导了该粘弹介质的能量守恒方程。将粘弹性附加应力张量作为有限元基本解,采用解耦方法实现了三维空间中速度场、温度场和流动应力场的多物理场稳定求解。将应力张量作为拟体力项处理后,动量方程会失去椭圆性并导致计算结果发散。通过分离粘弹分裂(DEVSS)方法,引入稳定化因子对动量方程进行椭圆化处理,提高了速度场求解的稳定性。采用非协调流线迎风(SU)方法克服了本构方程在对流占优时的数值振荡问题,实现了应力场的稳定求解。通过对粘弹流体4:4:1收缩流动模拟结果与polyflow软件模拟结果的比较,证明本文所建立的粘弹流动模型和数值计算方法的合理与可靠性。将该模型与方法成功应用于异型材挤出工艺过程模拟,讨论了网格密度、罚数和能量分割系数等计算控制参数对模拟结果的影响。分析了中空异型材挤出过程中聚合物熔体的流动速度、温度和应力分布,讨论了加工流场中聚合物熔体的粘弹流动特点,获得了工艺条件和口模结构参数变化对聚合物流变行为的影响规律。
挤出胀大是聚合物挤出成型工艺中无法回避的一个问题。由于加工中聚合物熔体的粘弹流变特性,熔体离开口模时,形变回复等会导致聚合物熔体的挤出胀大,表现为挤出物截面形状和尺寸发生变化,对挤出制品的尺寸和精度造成影响。本文在粘弹流动数值模拟技术基础上,建立了聚合物熔体三维挤出胀大的数学模型和数值求解方法并编制了相应的有限元模拟程序。针对一种工业用低密度聚乙烯(LDPE)的挤出胀大问题开展了实验及其数值模拟研究。通过控制应变流变仪分别得到小幅振荡剪切流动中储能和耗能模量的分布以及稳态剪切流动中剪切粘度和第一法向应力差的分布。采用非线性回归方法拟合流变测量实验结果,得到以PTT本构模型表征的材料线性和非线性粘弹流变参数。通过间接测量,得到不同螺杆转速时LDPE通过圆形口模时的出口挤出胀大比。采用本文所建立的聚合物挤出胀大数学模型及其数值求解方法,对实验条件下LDPE的挤出胀大过程进行模拟,比较了挤出胀大比的实验和模拟结果。通过挤出胀大数值模拟,进一步讨论了LDPE通过圆环口模时的出口挤出胀大问题,得到实验中难以测得的流动速度和应力等场变量分布,可对挤出胀大特点及其形成机理进行定性与定量分析和预测。
聚合物挤出成型过程数值模拟是被动式的,实际应用中需依靠专业工程技术人员的智力、知识和经验,对计算结果进行分析、评价,然后修改设计。本文将挤出成型过程数值模拟技术与优化设计理论相结合以实现成型过程与制品质量的优化控制。在成型过程模拟技术基础上,提出了一种基于数值模拟、前馈神经网络和遗传算法的聚合物挤出工艺与模具优化设计方法。根据挤出流动平衡原则,建立了以出口流动均匀性为目标,以工艺和模具结构参数为设计变量的优化模型。通过成型过程数值模拟获得目标函数值以建立训练神经网络模型的样本库,采用反向误差传播算法进行网络学习,建立用于预测隐目标函数的神经网络模型,从而有效减小有限元模拟计算量。通过遗传算法与神经网络的交互运算,得到优化结果,使设计建立在科学分析的基础上从而提高挤出加工工艺设计水平。探讨了该优化设计方法各模块计算实施中的关键技术问题,编制了聚合物挤出工艺与模具优化设计程序。分别针对异型材钢塑共挤工艺过程和片材挤出工艺过程进行优化设计并达到相应的优化目标。
数值模拟技术在聚合物加工工程领域的应用已成为计算流变学的重要分支之一。近年来,尽管流体力学数值方法取得了较大进展,但在处理复杂流动问题时,其解算能力仍受到流动区域和计算稳定性的限制。尤其对于复杂工程与工艺问题,其数学建模和数值模拟关键技术研究鲜有报道。本文针对挤出加工流场中聚合物熔体非牛顿粘性和弹性流动特点所建立的数学模型以及所构造的稳定数值计算方法,对于丰富计算流变学具有一定的理论意义。针对挤出工艺过程中聚合物熔体的复杂流变行为及其成型机理所作的分析与研究,以及基于此所开展的成型工艺模拟与优化工作具有较大的工程应用价值。
Polymer is a kind of important manufacturing material in national industry and defence construction which is called the four most important material system incooperating with wood, metal and silicate. With the development of polymer processing technology, the industrial system of polymer processing is established with many kinds of departments and it is playing an important role in national economy. Extrusion is one of the most important polymer processing technologies by which all the thermoplastic polymers and some thermosetting polymers can be molded, such as pipes, sheets, rods, nets, monofils, films, profiles, foaming profiles, composite products and coated products. In the extrusion process, the accumulative structure and chemical structure of polymer melts can be varied with the change of temperatue, pressure and stress. The processing conditions determine the material structure and ultimately affect the performance and quality of final products.
It is hard to afford to traditional experimental method for the reason that the influencing factors are multiplex and it is also expensive, time-consuming and laborious. Currently, the related experiments on polymer melts flow are mainly conducted in the laboratory and the aim of which is to investigate rheological properties based on the simple model of shear or extensional flows. As for the experiments conducted in practical extrusion process, advanced testing method is diffucult to be directly introduced and general testing method is inevitably affect real flow patterns. It is hard to quantitatively but can only qualitatively reflect practical rheological behaviours of polymer melts by using experimental method. After several years' development, numerical simulation method gradually attracts the attention of scientific and technical researchers for its excellent solving ablility to complex physical and engineering problems. It is now widely adopted in mechanics, thermotics, material science and other fields which greatly accelerate the development of modern science and technology.
The application of numerical simulation technology in fluid dynamics is discussed in the present research. The modeling theory and numerical method is studied and the mathematical model is established to investigate polymer rheological behaviours in the extrusion process. The distribution and changing law of some important field functions, such as velocity, stress and temperature, are discussed and analysed to explain the forming mechanism of polymer melts. The numerical simulation method is combined with optimal design theory and the optimization model and algorithm is established to realize the optimal control of extrusion process and products' quality.
The mathematical model of three-dimensional non-isothermal flow of non-newtonian fluid is established under Euler frame on the basis of polymer rheology and fluid dynamics. The penalty finite elment method is adopted to avoid high-order interpolation which is usually used in the mixed finite element method so as to effectively make use of computational resources. The effects of shear rate and temperature on melts flow are considered and the coupled calculation of flow and heat transfer is realized based on the nonlinear viscosity model. The non-linear term is linearized by using linearation iterative algorithm and hence to reduce the effects of valiables' initial distribution. The stream upwind Petrove-Galerkin method is performed to enlarge the upwind effects by using asymmetry weight function to overcome the oscillation of convection terms dominated problems. The field variables' function in the pipe poiseuille flow of power-law fluid is deduced and the corresponding simulated results are compared with the analysed results to prove the reliability of current mathematical model and numerical algorithm for non-newtonian flow.
The numerical method established above can not only be used in the analysis of general non-newtonian fluid flow problem but also can be adopted to solve complex engineering problem. Based on the proposed method, the mathematical modeling and processing analysis of a novel co-extrusion process of plastic profile with metal insert is performed in the study for the first time. The whole flow characteristic of polymer melts in flow channel is obtained by the calculation of velocity, stress, temperature and pressure. The influences of volume flow rate and metal insert moving velocity on the distribution of field variables is discussed and the corresponding advice on the processing design is put forward. The velocity relative difference is defined to jugde the outlet flow balance. The influences of both the inlet angle and the length of allocation region are investigated by the calculation of velocity relative difference.
Polymer melts in the extrusion process not only have non-newtonian flow characteristics but also have strong viscoelastic flow characteristics. The mathematical model of three-dimensional viscoelastic non-isothermal flow is established and a stable numerical algorithm is proposed which has been successfully adopted in the analysis of polymer extrusion process. The PTT (Phan Thien-Tanner) model is adopted to depict such viscoelastic properties of polymer melts which can reflect the extensional flow characteristic better. The special energy consumption pattern of viscoelastic medium is considered and its energy conservation equation is deduced according to the nonequilibrium irreversible thermodynamical theory. A decoupled algorithm is adopted to realize stable calculation for the three-dimensional multi-variables field consisting of velocity, temperature and flow stress. The momentum equation will lose its ellipticalness when the stress term is taken as the quasi-body force term and the discrete elastic-viscous stress split algorithm is adopted to improve the stability of velcocity calculation by introducing the stabilization factor. The non-consistant stream upwind method is adopted to overcome the oscillation in the calculation of stress. The mathematical model and numerical method for viscoelastic flow simulation of polymer melts established in the study is introduced to the analysis of general profile extrusion process. The effects of calculation control parameters, such as mesh division, penalty factor and energy partitioning factor, are investigated. The viscoelastic flow characteristics of polymer melts in the profile extrusion process are analysed based on the simulated results of velocity, temperature and stress. The influences of processing conditions and die structure on flow characteristics are further discussed.
Extudate swell is a common phenomenon for the reason of polymer melts' elastic deformation in the extrusion process which can severely influence the shape and dimensional precision of final products. Based on the viscoelastic flow simulation technology proposed in the study, the mathematical model and numerical algorithm for the simulation of three-dimensional extrudate swell is established and its finite element simulation program is worked out. The extrudate swell of an industrial LDPE is then investigated by both experimental method and numerical method. The distributions of stored-energy modulus and consumed-energy modulus in small amplitude oscillating shear flow and the distributions of shear viscosity and the first normal stress difference in steady shear flow are obtained by using the strain-controlled rheometer. Both linear and nonlinear viscoelastic rheological parameters of PTT model are obtained by using nonlinear regression method. The swelling ratios of LDPE through circular die under different volume flow rates are detected by using indirect measurement and they are compared with the simulated results. The distributions of flow velocity and stress in LDPE annular extrudate swell flow field obtained by simulation are analysed and the corresponding mechanism is further discussed.
The numerical simulation of polymer extrusion process is a passive system whose results have to be judged and analysed by professional worker with corresponding experiences and knowledge. In the study, the numerical simulation technology is combined with optimal design theory to realize the automatic optimal design and control for products. An optimal design method for polymer extrusion process is put forward based on numerical simulation, artificial neural net and generic algorithm. The optimization model is established by using the outlet flow balance as the optimization object. The processing parameters and die structure parameters are taken as design variables. The neural net model is trained by using the sample database obtained by simulated results so as to reduce the calculated amount of numerical simulation. The optimal design is achieved based on the scientific analysis through the iteration of genetic algorithm and neural net model. The corresponding optimization program for processing parameters and die structure parameters is worked out and the optimal design both for the co-extrusion process of plastic profile with metal insert and for the sheet extrusion process are further achieved.
The application of numerical simulation technology in the polymer processing engineering becomes one of the important branches in the computational rheology field. Although great progresses have been made in numerical methods on fluid dynamics in the recent years, its solving ability is still restricted to flow regions and computational stability. Researches on the complex mathematical modeling and the key technologies for numerical simulation are rarely reported especially for the solving of complex engineering and technology problem. The mathematical model and numerical method for the simulation of both viscous and viscoelastic characteristics of polymer melts in the study are of great interest to enrich the theory of computational rheology. It is also of much industrial interest to take research on rheological behaviour and the related forming mechanism in the polymer extrusion process based on the simulation and optimization technology.
引文
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