Enhancing slit die performance by optimization of restrictor profiles

A gradient‐based method is applied to determine optimum profiles of the restrictor (choker bar) required to obtain the best possible flow distribution uniformity in a 1.2 m wide slit die of given design, in a range of applications involving three materials of varying degrees of shear thinning, each at a high and a low flow rate. The kernel of the optimization is a simulation of die performance that takes into account the effects of die body deflection (‘clam shelling’) in a fully coupled flow/deflection analysis. For the most sharply varying restrictor profile, a linear elastic analysis is carried out, which shows that the optimum profile cannot be obtained by bending the bar without exceeding the tool steel yield point. The use of inter‐changeable bars, machined to the optimum profiles computed for various applications, is proposed to extend the operating range of dies. Alternatively, the highly adjustable membrane restrictor technology may be used. The developed software makes it possible to predict whether restrictor adjustment can produce acceptably uniform flow distribution in a given application, using a given die, and shows what restrictor profile should be set up, thereby eliminating or reducing the need for online trial and error adjustment.     

Improved interfacial surface generator for the co‐extrusion of micro‐ and nanolayered polymers

Two dies for polymer co‐extrusion layer multiplication are evaluated experimentally and computationally in terms of pressure drop and layer uniformity. The first design is that of the original die, is compact, and has successfully been used to co‐extrude low elasticity polymers with closely matched rheological properties. The second die design, the one that is being modified, achieves a more balanced flow path with constant cross‐sectional area. Flow visualization experiments and computational simulations show matched performance between the dies when layering similar viscosity materials and better layering performance of rheologically dissimilar materials with the improved dies compared to the original die design. Furthermore, the improved die has a much lower pressure drop. This facilitates decreased energy consumption or the allowance of additional multiplier dies to be added resulting in an increased total number of layers. POLYM. ENG. SCI., 54:636–645, 2014. © 2013 Society of Plastics Engineers     

Design and optimization of an extrusion die for the production of wood–plastic composite profiles

In this work, the optimization of an extrusion die designed for the production of a wood–plastic composite (WPC) decking profile is investigated. The optimization was performed with the help of numerical tools, more precisely, by solving the continuity and momentum conservation equations that govern such flow, and aiming to balance properly the flow distribution at the extrusion die flow channel outlet. To capture the rheological behavior of the material, we used a Bird‐Carreau model with parameters obtained from a fit to the (shear viscosity versus shear‐rate) experimental data, collected from rheological tests. To yield a balanced output flow, several numerical runs were performed by adjusting the flow restriction at different regions of the flow‐channel parallel zone cross‐section. The simulations were compared with the experimental results and an excellent qualitative agreement was obtained, allowing, in this way, to attain a good balancing of the output flow and emphasizing the advantages of using numerical tools to aid the design of profile extrusion dies. POLYM. ENG. SCI., 55:1849?1855, 2015. © 2014 Society of Plastics Engineers     

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.     

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.     

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。     

Inertia and gravitational effects in extrusion dies for non-Newtonian fluids

An analysis is presented which allows the sheet or film die designer to estimate when inertial and gravitational effects are important. General theoretical equations are developed for end fed dies with arbitrary variation of the cavity cross sectional shape, cavity taper, slot length, and gap over the width. The method assumes viscous flow and a two dimensional approximation for the cavity flow. For fluid flow properties, it is assumed only that the apparent viscosity is a single valued function of the shear rate. In the important special case of constant die geometry and power law fluids, three dimensionless numbers plus the power law index are the parameters controlling the uniformity of flow from the die. Results are presented that illustrate when die orientations with respect to gravity and when fluid inertia are important. When they are not, simple expressions for die inlet pressure and uniformity index are given.     

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.     

Compensating for die swell in the design of profile dies

Because of the effects of die swell, the final shape of an extrudate is often substantially different from that of the exit opening of the die. As a result, the design of profile dies producing complex shapes often involves more than just “balancing” the die but also compensating for the effects of die swell. Typically, a successful design of such dies is achieved only through much “cut and try,” However, with the use of a fully three‐dimensional finite element flow algorithm along with quick mesh generating capabilities, the usual cut and try involved in the design of many profile dies can be greatly reduced, if not eliminated. This paper demonstrates how the effects of die swell can be compensated for in the design of profile dies. For profiles with one plane of symmetry, this includes compensating for the sideways translation of the extrudate as well as the change in shape that the extrudate experiences. Completely asymmetric profiles undergo a “twisting” downstream of the die. This twisting, which appears not to have been reported in the literature (at least for isothermal extrusion), is also accounted for here, along with the change in shape that the extrudate undergoes. The translation or twisting of profiles downstream of a die is often attributed to non‐Newtonian or non‐isothermal effects. Only isothermal Newtonian examples are considered here. These results clearly show that asymmetry of the profile will result in a translation and twisting of the extrudate even in the isothermal Newtonian case.     

基于流动平衡的塑料挤出模优化设计

在构建流道三维参数化模型的基础上,将有限元数值分析和优化技术相结合,以口模出口处型材截面上各子区域平均流速相等为优化目标,以压缩段入口壁厚和平直段长度为设计变量,对挤出模优化设计进行了研究。并以实例说明了优化设计的具体过程,验证了所用方法的正确性和有效性。     

隔热条异型材挤出模具设计

通过对隔热条异型材截面形状及原材料挤出成型性能的分析,设计了异型材挤出口模形状、流线形流道及挤出模具结构。经实践证明,该模具口模形状及尺寸设计正确,流线形流道设计合理,能生产出满足尺寸精度要求的隔热条异型材。     

Model for a two‐cavity coating die with pressure and temperature deformation

Coating dies uniformly distribute liquid for application as a film to moving substrates using one or two cavities spanning the coating width and adjoining precision narrow slots of much higher resistance to flow. If the slots are deformed by the pressure of the liquid or by temperature gradients in the die bars, degradation in flow distribution can result. Consequently, dies are designed to be sufficiently stiff and are thermally jacketed to keep slot deformations within fabrication tolerances. To aid in design and operation, a model of low computational load is developed in which the flow and deformation analyses are directly coupled. Die deformation is modeled using classical beam theory taking account of the varying thickness of the bars due to cavity geometry. Two‐dimensional finite element analysis of die deformation gives marginally higher slot deformation. Three‐dimensional finite element analysis agrees with the two‐dimensional analysis except near the center of the die where the symmetry boundary condition reduces deformation. The effects of die geometry on deformation and flow distribution are illustrated. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

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。     

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.     

Numerical Simulation of the Conditioning of Volatile Particles in Laminar Flow Tube Reactors

The conditioning of aerosol particles to a predefined composition and size can be considered as a standard problem in aerosol technology. Quite often aerosols generated by dispersing diluted solutions are conditioned in a subsequent flow reactor.To make the design of such reactors easier, a computer model was developed to simulate the behavior of particles with a volatile component during their passage through the reactor. The model is based on the assumption that part of the surface of the reactor is covered with a layer of the requested activity of the volatile component whose fraction has to be adjusted. The diffusion to or from this surface and the corresponding change of the particle size and composition is calculated for each streamline of the flow on the basis of a laminar flow profile. At the moment data for the system H 2 O/H 2 SO 4 are implemented in the model, but an extension to other systems can easily be done. Circular as well as annular flow cross sections can be taken into account.     

Studies on melt spinning. VII. Temperature profile within the filament

An attempt was made to numerically compute the temperature profile within the melt spinning filament without assuming axisymmetry and using the data on the variation of the coefficient of heat transfer from a cylinder cooled by cross flow of air as given by Eckert.⁴ The computed constant-temperature contours were approximately concentric circles with their center shifted from the filament center in the downstream direction of the cooling air flow. A filament yarn melt spun under spinning conditions corresponding to the computation was dyed, and its cross sections were observed under the microscope. The border between the dyed and undyed portion of the cross sections approximately coincided with one of the computed temperature contours, suggesting indirectly the general validity of the computed temperature profile.     

Wirecoating die design using finite element methods

The design of wire-coating dies is described using finite element numerical analysis as a guide. Finite elements are able to accommodate awkward geometries and non-Newtonian fluid properties in a realistic manner, and produce streamline and stress patterns within the die. Two basic die geometries are examined and a new design which eliminates recirculation within the die is proposed.     

Design,optimization, and manufacturing of a multiple‐thickness profile extrusion die with a cross flow

This article presents a procedure to achieve a uniform outlet flow of molten polymer for a complex die profile with various thicknesses in die outlet cross section. According to a specific optimization methodology, the die was optimized based on varying die land length. The scope of this article includes: 3D flow simulation, optimization of the die velocity outputs based on the results of simulation process, and comparison of numerical predictions with the experimental data. Finally a significant result obtained by this work indicates higher ratio of the land length to the height of the zone with cross flow rather than the zones that are directly fed by the extruder. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers.     

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。     

塑料异型材挤出口模设计的数值模拟概述

从挤出口模设计原则出发,综述了数值模拟技术在塑料异型材口模流道的曲面构型,入口角和压缩比、降低或消除挤出胀大和挤出口模成型段的设计、熔体流动平衡和压力降的研究进展,以及口模设计的发展趋势.