塑料异型材挤出成型的流动平衡分析

介绍了一种基于横截面法和流动路径法混合的异型材挤出成型中熔体流动平衡的分析方法，可用于确定具有多个分支流道、截面复杂的异型材挤出模头出口处物料的平均流速，帮助设计者判断模头流道设计是否合理，且计算量较小，适于工程应用。     

基于灵敏度分析的挤出平缝口模优化设计

给出了以直接微分法计算稳态非线性系统设计灵敏度的方法。在基于挤出平缝口模熔体流动机理分析的基础上，建立了口模内熔体流动数学模型。并把设计灵敏度分析法和数值成型模拟技术相结合，运用于口模流道优化设计中，降低挤出平缝口模的出口速率变化率，从而改善了产品质量。通过实例验证，提出的口模优化设计方法非常有效。     

用三维有限元法设计橡胶挤出机板机头

从板机头的特点出发,分析了运用三维有限元法对其进行设计的必要性;在等温假设的基础上,介绍了运用三维有限元法计算机头内流场的基本步骤;给出了以三维有限元法为工具,有用波阵技术对板机头流道进行理论设计的程序框图 。     

Pressure drop through tapered dies

A simple method is presented for calculating the pressure drop for the flow of power law liquids in dies with a wide slit profile and with vertical and/or lateral tapers, as well as in dies with the shape of a circular truncated right cone. Tapered dies are known to give improved extrudate quality and/or higher output rates without encountering extrudate defects which occur in dies with parallel channels at similar extrusion pressures. A possible ultimate optimization of the extrusion process—as far as die design is concerned—is discussed. It is suggested that this be based upon an extension of the method from dies with a rectilinear convergent taper to dies with a curvilinearly converging channel aspect the generation of which latter is indicated.     

Effect of wall slip on the uniformity of flow from sheeting extrusion dies

A theoretical study for analyzing the uniformity of flow from sheeting extrusion dies is presented. In this study it is assume that a slip condition exists at the wall of the die, the magnitude of slip velocity is proportional to the shear stress at the wall, the flow is isothermal and steady state, and a power law model is valid for viscosity. Two extrusion dies, T-dies and coat-hanger dies, are examined. The flow uniformity at the exit of the die is calculated and compared with that for a nonslip analysis. The discrepancies between the slip and nonslip models imply that the wall slip condition induces a significant nonuniform flow distribution. Traditional design criticism based on the nonslip model are invalid for flow with the wall slip condition, and it is necessary to increase the length of the die land to even the flow distribution at the exit of the die.     

圆环型材挤出模塑料熔体流量分析与结构设计

塑料熔体在挤出模中的流动状态分析是挤出模设计的基础。尽管塑料异型材的成型模具种类繁多、形状各异，但都可视为圆环和孔隙的组合。分析了模头流道结构和熔体在圆环型材挤出模中的流量，为环类型材挤出模设计提供了依据。     

A personal computer software program for coathanger die simulation

A good extrusion die must distribute the polymer melt in the flow channel such that the material exits from the die with a uniform velocity and temperature. Coathanger dies are commonly used for the extrusion of plastic sheets and films. The die is usually provided with a straining bar allowing a regulation of the flowrate in the case of a poor design. But this, in turn, can affect temperature uniformity. Therefore, the design of coathanger die is a complex task which is mainly accomplished by trial and error in industry. Analyses of the flow in coathanger dies have been reported in the literature. Analytical and numerical approaches are used to solve this problem. The first one involves many simplifying assumptions: the most important ones being the unidirectional and isothermal flow of the polymer. Most numerical methods deal with a 2-D geometry, but only a few of them have considered the non-isothermal flow. A new model has been developed using a modified FAN method (Flow Analysis Network introduced by Tadmor) for the calculation of the 2-D flow, coupled with a finite-difference scheme for the calculation of temperature. The overall model can run on a PC with only a few minutes of calculation. Good agreement was obtained between experimental data and simulations.     

Practical interpretation of laboratory die swell behavior of PVC extrudates—through correlating circular with non-circular die performance

Laboratory die swell measurements are routinely measured on many viscoelastic polymer extrudates to characterize thier ability to maintain a specified shape during extrusion operations. The diameters of downstream extrudates obtainable through selected round dies can then be routinely scanned by optical or laser type devices to compare the degree of swell relative to the die diameter itself. Such measurements, while yielding good relative die swell performance between compounds, frequently do not predict the actual die swell levels observed later when the same compound is extruded through production dies of different cross-sectional shapes and land lengths. This study discusses an alternate method of correlating die swell between dies of different shapes by using a technique derived from fluid mechanics. This concept, used to characterize fluid velocity through non-circular channels with that observed through circular pipes and ducts, involves the inclusion of a shape factors known as the “Hydraulic Radius” in fluid flow comparisons. When this technique was applied to die swell measurements for extrudates of both a flexible PVC wire jacket compound and a rigid PVC pipe compound, good agreement in actual die swell measurements through both round dies and dies with non-circular cross sections was obtained. This approach can lend credibility to laboratory die swell measurements and greatly expand their use in predicting production extrusion performance.     

Computer-aided geometric design of the preform dies for flat film extrusion through 3-D finite element flow analysis

A rational computer-aided design procedure is presented for determining the optimum flow channel geometry of a flat film die, which yields a minimum pressure drop and produces a uniform transverse flow rate distribution. The three-dimensional die surface is generated by analytic expressions that represent a dumbbell-like contour. The die surface may be specified by several geometric parameters. The length of the transition zone turns out to be the controlling parameter. Because of the complicated geometric boundary, it is not possible to optimize the flow channel geometry explicitly; instead, a computer trial procedure is employed. The numerical computation is based on an isothermal three-dimensional flow model, which assumes power law behavior for the polymer melts. The calculated results indicate that for a particular polymer and a particular aspect ratio of slit, there may exist an optimum transition length from which the flow channel geometry of a flat film die may be uniquely defined.     

Experimental studies on extrudate swell behavior of PS and LLDPE melts in single and dual capillary dies

Extrudate swell behavior of polystyrene (PS) and linear low‐density polyethylene (LLDPE) melts was investigated using a constant shear rate capillary rheometer. Two capillary dies with different design configurations were used, one being a single flow channel and the other being a dual flow channel. A number of extrudate swell related parameters were examined, and used to explain the discrepancies in the extrudate swell results obtained from the single and dual flow channel dies, the parameters including output rate and output rate ratio, power law index, wall shear rate, wall shear stress, melt residence time, pressure drop induced temperature rise, flow channel position relative to the barrel centerline, and the flow patterns. It was found in this work that the power law index (n value) was the main parameter to determine the output rate ratio and the extrudate swell between the large and small holes for the dual flow channel die: the greater the n value the lower the output rate ratio and thus decreased extrudate swell ratio. The differences in the extrudate swell ratio and flow properties for PS and LLDPE melts resulted from the output rate ratio and the molecular chain structure, respectively. The extrudate swell was observed to increase with wall shear rate. The discrepancies in the extrudate swell results from single and dual dies for a given shear rate were caused by differences in the flow patterns in the barrel and die, and the change in the melt velocities flowing from the barrel and in the die to the die exit. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1713–1722, 2003     

Design of extruder dies using thermoplastics melt properties data

The procedures developed in this paper enable the die designer to estimate the dimensions of the die at the exit and to define a flow channel within the body of the die appropriate to the required dimensions and output rate of the extruded product. Design procedures are given for predicting die swell (and hence die exit dimensions) from a knowledge of product dimensions, output rate and the basic shear, elasticity, and viscosity data. Within the body of the die the length and included angle of a convergent tapered section should be such that the critical tensile deformation rate is not exceeded. At the die entry the taper angle is related to the tensile and shear viscosities. Analytical expressions based on flow data are given for predicting pressure drops resulting from flow through circular and slot dies of constant cross-section and through conical and wedge-shaped dies. A numerical example shows how the theory may be applied to the design of a die for a thin-walled tube. For the resultant die design, the likely effects are predicted to changes in output rate and melt temperature for the chosen material, of changes in grade of the same type of polymer, and of changes in polymer type.     

The flow distribution of molten polymers in slit dies and coathanger dies through three-dimensional finite element analysis

The isothermal flow of power-law fluids in slit dies and coathanger dies is studied. A general three-dimensional finite element code is developed for the purpose of flow analysis. The pressure distribution, the velocity distribution, and the transverse flow rate distribution are obtained. The effect of the die geometry on the flow distribution is critically discussed. It is found that a die channel with cross section of dog bone profile produces a flatter transverse flow rate distribution.     

塑料异型材挤出模头稳定性设计的数值方法

根据挤出模头设计的最小横向流动理论，运用ANSYS有限元分析软件，模拟分析了两副模头分流段流道的三维非牛顿流场，讨论了分流段流道设计对模头稳定挤出的影响；指出分流段流道设计满足流动平衡条件时，流道横向流动最小，模头的稳定性能较好；并通过两副实际使用的挤出模具，验证了理论分析与实际的一致性，从而给出了塑料异型材挤出模头稳定性设计的数值方法。     

Modeling of three‐dimensional flow and heat transfer in polystyrene foam extrusion dies

A three‐dimensional mathematical model was developed to investigate the nonisothermal, non‐Newtonian polymer flow through the dies used in the polystyrene foam extrusion process. The model, based on the computational fluid dynamics (CFD) code, Polyflow, allowed for the shear rate and temperature dependence of the shear viscosity of the blowing agent laden polystyrene melt. The model also accounted for viscous heating. The shear viscosity of the polystyrene‐blowing agent mixture was measured experimentally at several temperatures. The model was used to calculate pressure, flow, and temperature distributions in two different dies used for industrial‐scale extrusion of polystyrene foams. The article presents a selection of computed results to illustrate the effect of die design on uniformity of flow at the die exit, the overall pressure drop in the die, relative magnitudes of pressure drop in the land section versus the rest of the die, and temperature distribution in the die. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Theoretical Analysis on Flow of Polymer Melts in Screw Die

Abstract

Flow of polymer melt in screw dies is theoretically analyzed by the broken section method with the uniformity of the extrudates. An isothermal, laminar and steady state power law fluid is assumed. The analysis is discussed in two parts, i.e., screw flow and die slit flow. A way of computer calculation by means of a method of iteration is presented by considering volume balance between screw flow and slit flow.

An ideal screw die is one in which pressure distribution is constant along the screw axis, i.e., the shape of the die slit is constant along the axis and the screw is such that the depth of screw channel decreases almost linearly.     

衣架式口模设计计算的一种改进

采用表征值方法，根据等压线平行于模唇的流动模式，并考虑歧管斜率的影响，对衣架式口模圆形截面歧管系统的设计公式进行了改进，不但使口模结构设计与材料的性能与流率无关，而且修正了以前文献中对歧管斜率影响的忽略而造成的流率分配的误差，从而使流动均匀性指数提高到１，并对两种流动模式的等效性给予了证明     

基于正交试验与数值模拟的木塑异型材挤出机头流道设计方法

建立了一种基于正交试验与数值模拟的木塑异型材挤出机头流道的设计方法,其主要原理是在结合木塑复合材料流变数据的基础上,将异型材挤出机头流道的主要几何参数定义为正交试验的试验因素,利用正交试验设计方法对这些几何参数进行试验安排;使用Inventor软件三维参数化尺寸驱动系统实现流道模型的迅速建立;通过专业计算流体力学有限元分析软件Polyflow完成机头流道内熔体的模拟计算和仿真分析;选择适当的评价标准对模拟结果进行正交优化,最终获得机头流道的合理参数。依据这种方法,对立柱木塑异型材进行了机头流道的设计,最终得到其理想的设计结果。     

A three-dimensional analysis of the effect of die body deflection in the design of extrusion dies

Flat extrusion dies operating under high pressure often experience a significant amount of distortion. Satisfactory designs of such dies require an accurate prediction of the deflection of the die body as well as the flow in the internal channels of the die. Here a three-dimensional deflection analysis is coupled to a three-dimensional flow analysis. Such analyses are now being used by design engineers on personal computers for routine design of deflecting dies.     

The effect of wall slip on the performance of fiat extrusion dies

Flat extrusion dies are commonly used in a wide variety of film. Sheet and coating applications. Although flal dies can be designed to produce an exit flow distribution that is very uniform across most of the width, there will usually be a region along each side where it drops gradually to zero. This often requires trimming the edges of the film or sheet downstream in order to meet product specifications. It is commonly believed that treating the land area of the die with coatings that promote a small amount of wall slip will reduce the size of this edge effect and therefore improve die performance. This analysis shows that slip over the entire land region of the die will adversely affect die performance. Better performance is possible but only if the sides of the land are treated.     

Processing history in extrusion dies and its influence on the state of the polymer extrudate at the die exit

A method is proposed to describe the processing history in extrusion dies and its influence on the state of the polymer after processing. The approach differs from conventional processing analysis, which uses the shear viscosity function to calculate pressure drop vs flow rate relations. The approach also differs from heuristic analysis which tries to find empirical correlations between rheological observations and processing behavior. The method is applied to the flow in annular extrusion dies. An integral constitutive equation is chosen to calculate the flow and to describe the flow history at the die exit as memorized. In the analysis, the kinematics are locally approximated by isothermal steady shear flow. The velocity and the velocity gradient are used to determine the Finger strain tensor, the path lines, and the residence times of the deforming material elements. Measures of the state of the polymer at the die exit are chosen to be the stress ratio N₁/2τ₁₂ and the free recovery. The free recovery calculations presume that the extrudate is chopped into small volumes of homogeneous flow history. The results of the calculations show the polymer very sensitively reacts to small changes of the die geometry. Important applications of this analysis are film blowing and blow molding, where the extensional behavior during the blowing process outside the die depends greatly on the preceding shaping process inside the die.