Extrusion die design for slowly reacting materials

The flow distribution of slowly reacting polymeric materials inside an extrusion die was analyzed by lubrication theory. The viscosity of the polymeric liquid was assumed to be time-dependent owing to chemical reaction. Three types of extrusion dies were considered: a T-die, a linearly tapered coat-hanger die with a choker bar, and a curvilinearly tapered coat-hanger die. It was found that the T-die is not suitable to deliver the polymeric liquid films, whereas the two coat-hanger dies can deliver the polymeric liquid films with acceptable flow uniformity and residence time distribution.     

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.     

Extrusion die design for multiple stripes

Two numerical approaches have been applied to examine the possibility of adding shims to conventional extrusion dies such as T-dies and coat-hanger dies to produce multiple stripes. The first numerical approach is based on a one or two-dimensional lubrication approximation and the second one is the three-dimensional finite element simulation. Both approaches are applicable, but the lubrication approximation is accurate and much simpler to use. The extruded stripes are assumed to obey a non-Newtonian power-law model. It has been found that the T-die with a shim can produce multiple stripes of acceptable uniformity, irrespective of the strip numbers and widths and the power-law index. The coat-hanger die with a shim did not deliver multiple stripes with good uniformity. Adding an outer manifold to the coat-hanger die can serve as an effective means to reduce flow nonuniformities.     

衣架式口模设计灵敏度分析

在对衣架式口模体溶液机理分析的基础上,对衣架式口模中熔体的流动行为进行了合理的假设和间化,采用Hele-Shaw流动模型和幂率粘率模型,建立了衣架式口模内的非弹性,非牛顿熔体在等温条件下流动数学模型,将灵敏度分析理论与成型模拟结合运用于衣架式口模流道优化设计中,降低了衣回式口模的出口横向速率变化率。     

Two-dimensional multilayer coextrusion flow in a flat coat-hanger die. Part 2: Experiments and theoretical validation

In a previous paper (1), a two-dimensional computation model for multilayer flows in coat-hanger dies was proposed. It was based on lubrication approximation theory and enabled us to obtain the pressure field, the streamlines, and the interface positions in the whole die. The present paper is aimed to present experimental results obtained on an industrial line for a three-layer configuration and to compare the results to the theoretical computation. The order of magnitude of pressure drops, flow rates, and interface positions were correctly predicted by the model. Some remaining discrepancies may be explained by the isothermal assumption and the lack of encapsulation mechanism in the computation.     

Design of coat-hanger sheeting dies based on ratio of residence times in manifold and slot

A new coat-hanger die geometry with a uniform flow rate and optional ratio of residence times in manifold and slot is proposed. Such a die will be effective when thermal degradation in the die occurs, especially at die far end. This geometry is easily determined if the flow behavior index n of polymer is assumed. A suitable ratio greater than unity may be taken considering die-height and cost, because lower height is attained as the ratio increases above unity. An example of a design calculation is shown.     

A unified lubrication approach for the design of a coat-hanger die

A simple unified lubrication approach has been proposed to design a coat-hanger die that can deliver wide and uniform liquid sheets. This approach requires that the wall stress in the manifold be constant. With this constraint, any inelastic non-Newtonian fluid model can be used to describe the liquid motion inside the die. Fluid models that can represent the pseudoplastic or viscoplastic behavior of polymeric liquids have been selected for illustration. A general equation that can be solved to determine the effect of production variations on flow uniformity inside the die has also been derived.     

A simple numerical approach for the optimal design of an extrusion die

A simple numerical approach that is based on the lubrication approximation is developed for the optimal design of a linearly tapered coat-hanger die. This approach does not require the analytic pressure drop / flow rate equations for flow in the manifold and in the slot section, therefore any generalized Newtonian fluid model can be easily incorporated. Example calculations have demonstrated that the predictions based on this approach are reasonably accurate as compared with those from the complete 3-D finite element simulations.     

Three-dimensional modelling of Non-Newtonian fluid flow in a coat-hanger die

The three-dimensional model of isothermal flow of power-law fluid in a coat-hanger die has been developed using finite element method. The shape of coat-hanger die used in the present model was determined according to the previous analytical design equation which is based on one-dimensional flow model in the manifold and the slot. Because uniform flow rate across the die outlet is most important to achieve uniform thickness of extruded polymer sheet or film, flow rate distribution is mainly examined to determine the valid process condition for the design equation as the design parameters are changed. The effects of fluid property in terms of power-law index and process parameters not considered in one-dimensional design equation such as die inlet size and the presence of land were analyzed. Results show that the manifold angle is the most influencing design parameter on flow rate distribution. When the material of different power-law index from design value is processed, the change of power-law index affects the uniformity of flow rate appreciably.     

线性锥形衣架机头流率分布数值模拟

给出了预测线性锥形歧管衣架机头出口流率分布的计算程序,研究了影响出口流率分布的相关因素。模拟结果表明:衣架机头的出口流率分布与机头的几何参数和材料的物性参数都有关系,其中调节块区的缝隙高对出口流率分布的影响最大;基于流动指数n为常数而设计的衣架机头,如果没有调节块的调节作用是很难满足实际生产需要的。     

Design of Sheet Dies for Minimum Residence Time Distribution: A Review

The various die designs that have been proposed for the manufacture of sheets and flat films from polymeric materials are reviewed, along with the corresponding flow analysis and derived design equations. Successively, the T-die, the linearly tapered coat-hanger die, the curvilinearly tapered coat-hanger die (with manifold of circular or rectangular cross-section), and the fishtail die are examined. In each case, care is taken to outline the assumptions used to derive the equations, and to state the advantages and disadvantages of each design. The limits of these mentioned assumptions are explained and illustrated. Particular attention is paid to the aspects of the design which affect the processing of sensitive or reactive materials (i.e., residence time distribution and wall shear stress).     

衣架式流延模头内熔体流动与模具变形的三维耦合数值模拟

利用Polyflow软件对一种衣架式流延模头内熔体的流动和模具变形进行了三维耦合数值模拟。结果表明:衣架式模头中熔体的流动可视为歧管内(沿歧管方向)和狭缝中(沿挤出方向)的压力流的组合;模头狭缝表面在模具厚度方向的变形沿挤出方向近似为线性增加,而沿模具宽度方向为非线性减小;模具变形后的熔体出口流率由狭缝的实际间隙和扇形区出口处的压力共同决定,单位宽度的出口流率沿模具宽度方向先增加后减小。     

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。     

Residence time distribution of polymer melts in the linearly tapered coat-hanger die

This article analyzes the average residence time distribution of polymer melt across the die width in a common linearly tapered coat-hanger die, which excells the T die but is a little inferior to the curvilinearly tapered coat-hanger die in residence time uniformity according to the approximated calculation of ten used. From another point of view, a linearly tapered coat-hanger die may be designed so that a desired ratio of the residence time through the die far end to that along the die center line may be imposed as one of the design constraints.     

Numerical analysis of new modified melt‐blowing dies for dual rectangular jets

According to the aerothermodynamic analysis and turbulence characteristic analysis, there might be two main kinds of kinetic energy loss of the jets from rectangular nozzles for the blunt melt‐blowing die. To reduce the energy loss, the new modified dies with stabilizing pieces are designed and compared with the blunt die. The air flow fields for the new dies are simulated using computational fluid dynamic technology, whereby the shear stress transport model is used for turbulence simulation. Three parameters (i.e., the velocity along the y‐direction, the static temperature, and the turbulence intensity) are vitally important for producing fibers and thus are used to evaluate the performances of the slot dies. The simulation results reveal that the inner stabilizing pieces is helpful to decrease the negative velocity in the recirculation zone, enhance the downward centerline mean velocity, slow the centerline temperature decay, and make the air flow near the nose piece smoother. However, the external stabilizing pieces conduce only to increase the centerline velocity in the local area. POLYM. ENG. SCI., 54:110–116, 2014. © 2013 Society of Plastics Engineers     

Numerical simulation of multi-layer flow for polymer melts—A study of the effect of viscoelasticity on interface shape of polymers within dies

A two-dimensional simulation was developed for multi-layer confluent viscoelastic flow in dies, using a finite element method. The simulated interface shape was compared with the experimental results of previous researchers, and the simulated results were confirmed. Two-layer and three-layer flows of two or three kinds of viscoelastic fluids were simulated. Fluids with different non-Newtonian viscosities and the first normal stress differences were used. The layer thicknesses in dies are mainly determined by the shear viscosity and less by the elasticity of the fluid. The normal stress difference between the fluids forming an interface may be related to interfacial instability, and normal stresses near the interface were examined. The normal stress difference between both fluids was affected by the first normal stress difference and elongational viscosity.     

Extrudate swell of high density polyethylene. Part III: Extrusion blow molding die geometry effects

Two high density polyethylene resins—801 and 802— are examined with regard to their isothermal, time-dependent, and nonisothermal swelling properties when emerging from two annular and three diverging dies. The short time swelling characteristics of samples 801 and 802 are very important for these dies, resulting in a lower diameter swell for the latter, independent of the die geometry or flow rate. Output variations have much less impact on the swelling behavior than small changes in the geometry of the die mandrel. Accordingly, shear stress and shear rate parameters alone cannot be used to explain the swelling properties of a HDPE resin in the different die geometries. Straight annular dies induce higher diameter swelling than diverging dies.     

Analysis and simulation of non-Newtonian flow in the coat-hanger die of a meltblown process

Meltblown is one of the fastest growing processes for nonwoven production. The design of the coat-hanger geometry of a die is very important for meltblown technology. In this article, melt rheological properties were studied based on capillary rheometry, followed by analysis and simulation of the melt flow in the die and its experimental verification. It is essential for the optimal design of the die and helps to better understand the meltblown process as well. The result of this research showed that the rheological properties of melt flow in the die obey the power-law equation very well in the meltblown process. The coat-hanger die has a good operation feasibility for different resins and various operation conditions from the view of web uniformity. The pressure drop through the orifices is the major contribution to the pressure drop in the die. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67: 193–200, 1998     

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     

Shear and extensional flow of reinforced plastics in injection molding. II. Effects of die angle and bore diameter on entry pressure with bulk molding compound

Orifice flow measurements have been performed at high strain rates on bulk molding compound (BMC) using convergent dies. A range of die angles and bore diameters was examined. Two models for flow behavior have been compared. It appears that, with BMC, there is a transition from constrained convergence to convergence with recirculation at a die semiangle of approximately 56 degrees.