用于精密挤出成型的气辅挤出口模设计数值模拟和实验研究
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摘要
气辅挤出作为一种新型的聚合物材料成型工艺,通过在熔体和口模内壁之间形成一层气体辅助层,使熔体以完全滑移非粘着的方式挤出成型,可有效减小挤出胀大,因此在精密挤出成型方面有着潜在的应用价值。国内外的研究者在气辅挤出成型方面开展了多年的研究工作,利用数值模拟技术探讨了气辅挤出成型机理,并搭建了实验系统,取得了颇有成效的研究成果。但是要实现气辅挤出的工业化应用,还必须在以下几方面展开进一步的研究:(1)稳定气辅挤出的工艺条件;(2)实验中挤出缩小问题;(3)口模入口部位的设计如何判定:(4)对精密挤出条件下口模滑移段长度或工艺条件设定不能进行预测/判断。因此,围绕上述四个方面继续深入研究,进一步改进和提高挤出制品的径向尺寸精度,对于气辅挤出工艺、口模优化设计和挤出过程智能控制,都具有非常重要的理论意义和工程价值。
首先采用有限体积法和Generalized Navier's slip law方程,建立了气辅挤出口模内熔体流动的数学模型,并给出了控制方程组的Galerkin有限元离散化形式,针对气辅挤出过程高We数难收敛的问题,提出采用EVSS/SUPG混合有限元方法,同时结合渐变法和汤普森变换实现数值模拟的稳定收敛。
实验研究了工艺参数对气辅层稳定性的影响。结果表明,气体压力与熔体压力大致相等是实现稳定气辅挤出的前提条件。当气体压力过大时,气体会穿透熔体,在熔体内部形成气泡,从而对制品质量造成较大影响;反之,则不能形成气辅层。气体流量对实现稳定气辅挤出非常重要,大流量容易引起气体紊流,使挤出物表面产生波纹形状,合理设置气体流量,可获得稳定的气辅挤出。
数值模拟研究了气体和熔体在非等温热交换作用下的熔体的温度场、黏度场。研究结果表明:当气体温度低于熔体温度时,聚合物熔体粘流活化能大的,口模滑移段尺寸长的,在气辅挤出中相对容易出现半固态熔膜现象,从而堵塞口模通道,引起挤出缩小现象。提高气体温度使之等于熔体温度,可在根本上消除半固态熔膜引起的挤出缩小现象。并通过实验验证了模拟结果。
针对直角形、圆锥形和圆弧形口模入口结构中存在不光滑的连接点,构建了反向相切和三次高精度插值两种流线形入口几何构型。对聚合物在五种不同入口气辅口模内的熔体流动进行了数值模拟研究,考察了各口模中压力场、速度场、应力场和挤出胀大的特点。结果发现流线形口模挤出压力小、流动速度大、N_1应力集中程度小、挤出胀大比小,成为非流线型口模强有力的竞争者。同时发现成型段L/D≥1且滑移段为成型段1/2的气辅口模,离模后挤出胀大比与口模入口几何结构无关。
将气辅挤出口模简化为圆棒模型,对熔体在不同滑移段长度的气辅口模内的流动进行模拟研究。考察了剪切速率、松弛时间对挤出胀大的影响,讨论了滑移段长度与压力降、挤出胀大、应力集中之间的关系。通过大量的数值模拟研究发现,熔体在滑移段的停留时间与材料松弛时间之比与挤出胀大比之间存在指数衰减关系,其关系可用方程B=1+Ae~(-t/λ)表示。并通过其它文献给出的实验数据论证本文所提方程的有效性和可靠性,为滑移段长度设计或工艺参数控制提供理论依据。
对HDPE、PP、ABS三种通用性热塑性塑料进行了气辅挤出试验,测量并观察了挤出制品的径向尺寸、表面质量和压力降。对上章数值模拟结果进行了实验验证。基于数值模拟和实验结果,证明了本文所提出的方程可以用来预测气辅挤出制品的径向尺寸,用来指导气辅挤出口模滑移段长度的设计。
Gas-assisted extrusion (GAE) is a new polymer molding technique. In the extrusion processing, a stable gas layer is established at the interface of metal die and molten polymer by injecting gas into the extrusion die, which makes the molten polymer is extruded out with a full slip mode. GAE technology can significantly reduce die swell ratio, so it has potential applications in the manufacturing of precise extrusion. Researchers have been studying gas-assisted extrusion for many years, and get many research achievements in numerical simulation and experiments. While for achieving industrial applications, it is also necessary to further study in the following three areas:(1) the stable process of gas-assisted extrusion is not perfect; (2) the extrudate's radius is smaller than the die's radius; (3) the die entrance is difficult to design; (4) no predicting or judging methods can be applied to the slip length of GAE die and the process conditions under the precise extrusion. Thus, more attention is required to be paid to the deep study of the four problems mentioned above, and further improvement on the radial dimensional accuracy of extrusion products is of great theoretical and practical significance for gas-assisted extrusion process optimum design and intelligent control.
Based on the finite volume method and Generalized Navier's slip law, a numerical simulation system describing the flow of visco-elastic polymer when it passes through the gas-assisted extrusion die is established; at the same time, the finite element discrete forms of the governing equations are built, and the mixed finite element methods of EVSS/SUPG (Elastic-Viscous Stress Split elastic/Streamline Upwind Petrov-Galerkin), the Evolution method, and Thompson transformation are utilized to resolve the problem that high weissenberg often made computations difficult.
Drawing on an experimental assemble system of gas-assisting extrusion, we can find the effect which the technical parameters have on the stability of gas-assisting extrusion. These experiments show that the gas can be injected into the GAE die when the gas pressure is higher than the melt pressure at the gas injection point. The GAE process could not be operated when the pressure of melt is beyond the pressure of gas. When the gas pressure is equal to the flowing polymer' s pressure, then a stable, uniform gas layer is formed at the interface between the molten polymer and the metal die. In addition these experiments also indicate that the control of gas mass flow appears to be an important part of obtaining a stable extrusion. When the gas flow is small, the melt extrudate in the form of laminar flow. When the gas mass flow is large, a periodic product deformation termed 'blistering' is observed and the gas generated turbulence forced the melt vibration extrusion.
By using the model and method developed in this study, the temperature profile and viscocity profile were numerically simulated for non-isothermal heat exchange from cool-gas to hot- melt. The results reveal that when the temperature of the gas is below the temperature of the melt, when the polymer melt flow activation energy is larger and when the slip length is longer, it is easier to form a stationary polymer layer attached to the die wall and to leave a "semisolid" layer of polymer at the wall, which blocked the die and caused the diminishing of the extrudate. To raise the temperature of gas near the melt might eliminate semi-solid membrane. The simulation results are verified though this experiment and the diminished problem of extrusion products in previous research is successfully solved.
In view of the uneven junctions in the right-angle shape, the conical shape, or the arc shape entrance structure, two stream-lined entrance geometric configurations is constructed, which are reverse-tangent and coped with three supra-precision interpolations respectively. Numerical simulations are conducted with the melt flow in five different entrance gas-assisted dies. The features of the pressure field, the velocity field, the stress field, and the extrusion swell in each die are also investigated. The analysis showed that the stream-lined dies had smaller extrusion pressure, bigger flow velocity, smaller concentration degree, and smaller die swell ratio although it is difficult to design and process them. As for those gas-assisted dies whose formed segments' L/D was equal to or beyond 1 and whose slip segments is half of formed segments, the extrusion swell ratio released from the die had nothing to do with the die's entrance because the elastic strain stored in the entrance could be released completely in the gas-assisted section.
By simplifying the gas-assisted extrusion dies into rod models, a numerical simulation is conducted to investigate the flow of melts of different lengths of slip parts in the gas-assisted dies. The effects of shear rate and relaxation time on die swell ratio are investigated with the aid of this simulation. The interrelation among the slip length on the drop pressure, die swell and the stress concentration is also examined. It is found that drop pressure could be largely reduced while surface quality could be greatly raised with the increase of slip length. From the simulation, an equation about the die swell ratio is proposed which can be applied to the design of GAE die, relating the residence time of melt in slip part and relaxation time. The mathematical relationship can be written in B = 1 + Ae~(-t/λ), which essence is that molten polymer at slip part in deformation attenuation process. With reference to the available documents, the validity and reliability of the formula mentioned above was proved experimentally, thus providing a solid theoretical basis for the design of slip part and the control of technical parameters.
In this simulation, GAE experiments on HDPE, PP and ABS were carried out; The major parameters of extrusion products, such as the pressure drop, radial dimension, and the surface quality, are measured or examined. The numerical simulation results are validated. Constructed on the basis of simulation and experiments, it has been verified that the formula can be used to predict the radial dimension of extrusion products and be used to guide the optimum design of the slip length as well as the design of the length of slip parts in the gas-assisted extrusion dies.
首先采用有限体积法和Generalized Navier's slip law方程,建立了气辅挤出口模内熔体流动的数学模型,并给出了控制方程组的Galerkin有限元离散化形式,针对气辅挤出过程高We数难收敛的问题,提出采用EVSS/SUPG混合有限元方法,同时结合渐变法和汤普森变换实现数值模拟的稳定收敛。
实验研究了工艺参数对气辅层稳定性的影响。结果表明,气体压力与熔体压力大致相等是实现稳定气辅挤出的前提条件。当气体压力过大时,气体会穿透熔体,在熔体内部形成气泡,从而对制品质量造成较大影响;反之,则不能形成气辅层。气体流量对实现稳定气辅挤出非常重要,大流量容易引起气体紊流,使挤出物表面产生波纹形状,合理设置气体流量,可获得稳定的气辅挤出。
数值模拟研究了气体和熔体在非等温热交换作用下的熔体的温度场、黏度场。研究结果表明:当气体温度低于熔体温度时,聚合物熔体粘流活化能大的,口模滑移段尺寸长的,在气辅挤出中相对容易出现半固态熔膜现象,从而堵塞口模通道,引起挤出缩小现象。提高气体温度使之等于熔体温度,可在根本上消除半固态熔膜引起的挤出缩小现象。并通过实验验证了模拟结果。
针对直角形、圆锥形和圆弧形口模入口结构中存在不光滑的连接点,构建了反向相切和三次高精度插值两种流线形入口几何构型。对聚合物在五种不同入口气辅口模内的熔体流动进行了数值模拟研究,考察了各口模中压力场、速度场、应力场和挤出胀大的特点。结果发现流线形口模挤出压力小、流动速度大、N_1应力集中程度小、挤出胀大比小,成为非流线型口模强有力的竞争者。同时发现成型段L/D≥1且滑移段为成型段1/2的气辅口模,离模后挤出胀大比与口模入口几何结构无关。
将气辅挤出口模简化为圆棒模型,对熔体在不同滑移段长度的气辅口模内的流动进行模拟研究。考察了剪切速率、松弛时间对挤出胀大的影响,讨论了滑移段长度与压力降、挤出胀大、应力集中之间的关系。通过大量的数值模拟研究发现,熔体在滑移段的停留时间与材料松弛时间之比与挤出胀大比之间存在指数衰减关系,其关系可用方程B=1+Ae~(-t/λ)表示。并通过其它文献给出的实验数据论证本文所提方程的有效性和可靠性,为滑移段长度设计或工艺参数控制提供理论依据。
对HDPE、PP、ABS三种通用性热塑性塑料进行了气辅挤出试验,测量并观察了挤出制品的径向尺寸、表面质量和压力降。对上章数值模拟结果进行了实验验证。基于数值模拟和实验结果,证明了本文所提出的方程可以用来预测气辅挤出制品的径向尺寸,用来指导气辅挤出口模滑移段长度的设计。
Gas-assisted extrusion (GAE) is a new polymer molding technique. In the extrusion processing, a stable gas layer is established at the interface of metal die and molten polymer by injecting gas into the extrusion die, which makes the molten polymer is extruded out with a full slip mode. GAE technology can significantly reduce die swell ratio, so it has potential applications in the manufacturing of precise extrusion. Researchers have been studying gas-assisted extrusion for many years, and get many research achievements in numerical simulation and experiments. While for achieving industrial applications, it is also necessary to further study in the following three areas:(1) the stable process of gas-assisted extrusion is not perfect; (2) the extrudate's radius is smaller than the die's radius; (3) the die entrance is difficult to design; (4) no predicting or judging methods can be applied to the slip length of GAE die and the process conditions under the precise extrusion. Thus, more attention is required to be paid to the deep study of the four problems mentioned above, and further improvement on the radial dimensional accuracy of extrusion products is of great theoretical and practical significance for gas-assisted extrusion process optimum design and intelligent control.
Based on the finite volume method and Generalized Navier's slip law, a numerical simulation system describing the flow of visco-elastic polymer when it passes through the gas-assisted extrusion die is established; at the same time, the finite element discrete forms of the governing equations are built, and the mixed finite element methods of EVSS/SUPG (Elastic-Viscous Stress Split elastic/Streamline Upwind Petrov-Galerkin), the Evolution method, and Thompson transformation are utilized to resolve the problem that high weissenberg often made computations difficult.
Drawing on an experimental assemble system of gas-assisting extrusion, we can find the effect which the technical parameters have on the stability of gas-assisting extrusion. These experiments show that the gas can be injected into the GAE die when the gas pressure is higher than the melt pressure at the gas injection point. The GAE process could not be operated when the pressure of melt is beyond the pressure of gas. When the gas pressure is equal to the flowing polymer' s pressure, then a stable, uniform gas layer is formed at the interface between the molten polymer and the metal die. In addition these experiments also indicate that the control of gas mass flow appears to be an important part of obtaining a stable extrusion. When the gas flow is small, the melt extrudate in the form of laminar flow. When the gas mass flow is large, a periodic product deformation termed 'blistering' is observed and the gas generated turbulence forced the melt vibration extrusion.
By using the model and method developed in this study, the temperature profile and viscocity profile were numerically simulated for non-isothermal heat exchange from cool-gas to hot- melt. The results reveal that when the temperature of the gas is below the temperature of the melt, when the polymer melt flow activation energy is larger and when the slip length is longer, it is easier to form a stationary polymer layer attached to the die wall and to leave a "semisolid" layer of polymer at the wall, which blocked the die and caused the diminishing of the extrudate. To raise the temperature of gas near the melt might eliminate semi-solid membrane. The simulation results are verified though this experiment and the diminished problem of extrusion products in previous research is successfully solved.
In view of the uneven junctions in the right-angle shape, the conical shape, or the arc shape entrance structure, two stream-lined entrance geometric configurations is constructed, which are reverse-tangent and coped with three supra-precision interpolations respectively. Numerical simulations are conducted with the melt flow in five different entrance gas-assisted dies. The features of the pressure field, the velocity field, the stress field, and the extrusion swell in each die are also investigated. The analysis showed that the stream-lined dies had smaller extrusion pressure, bigger flow velocity, smaller concentration degree, and smaller die swell ratio although it is difficult to design and process them. As for those gas-assisted dies whose formed segments' L/D was equal to or beyond 1 and whose slip segments is half of formed segments, the extrusion swell ratio released from the die had nothing to do with the die's entrance because the elastic strain stored in the entrance could be released completely in the gas-assisted section.
By simplifying the gas-assisted extrusion dies into rod models, a numerical simulation is conducted to investigate the flow of melts of different lengths of slip parts in the gas-assisted dies. The effects of shear rate and relaxation time on die swell ratio are investigated with the aid of this simulation. The interrelation among the slip length on the drop pressure, die swell and the stress concentration is also examined. It is found that drop pressure could be largely reduced while surface quality could be greatly raised with the increase of slip length. From the simulation, an equation about the die swell ratio is proposed which can be applied to the design of GAE die, relating the residence time of melt in slip part and relaxation time. The mathematical relationship can be written in B = 1 + Ae~(-t/λ), which essence is that molten polymer at slip part in deformation attenuation process. With reference to the available documents, the validity and reliability of the formula mentioned above was proved experimentally, thus providing a solid theoretical basis for the design of slip part and the control of technical parameters.
In this simulation, GAE experiments on HDPE, PP and ABS were carried out; The major parameters of extrusion products, such as the pressure drop, radial dimension, and the surface quality, are measured or examined. The numerical simulation results are validated. Constructed on the basis of simulation and experiments, it has been verified that the formula can be used to predict the radial dimension of extrusion products and be used to guide the optimum design of the slip length as well as the design of the length of slip parts in the gas-assisted extrusion dies.
引文
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