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.     

挤出机头内流场对玻纤取向和分布的影响

本文分析了平直和发散两种挤出机头内的流场,推得发散流道内熔体周向拉伸应变速率的表达式;研究了两种挤出流率下由这两种机头挤出的制品壁内玻纤的取向和分布,并通过流道内的剪切和周向拉伸应变速率,对玻纤取向和分布的形成机理进行解释。结果表明：经平直机头挤出的制品内,玻纤在剪切作用下基本沿流动方向排列。发散机头内熔体受剪切和周向拉伸的共同作用,使制品壁厚方向形成了“表层-次表层-芯层-次表层-表层”的五层结构,并首次发现芯层呈“W”形排列。玻纤的排列不仅受流动过程中的应变影响,更取决于应变速率的大小。     

Converging flow of polymer melts in extrusion dies

Practical extrusion processes often involve geometrically complex dies. Such dies are usually tapered, or streamlined, to achieve maximum output rate under conditions of laminar flow. These converging flows may be analysed in terms of their extensional and simple shear components to calculate the relationships between volume flow rate, pressure drop, and post extrusion swelling. The analysis can also be extended to cover the free convergence as fluid flows from a reservior into a die. Comparisons between predicted and observed data for a series of coni-cylindrical dies suggest that using this approach the pressure drop/flow rate relationship can be predicted within ±20% and the swell ratio/flow rate relationship within ±10%. Similar treatments have been in use for the last three years in solving such complex flow problems as radial flow in injection moulding and two-dimensional annular convergence in blow moulding dies.     

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.     

A new design procedure for profile extrusion dies

A new design procedure for complex profile extrusion dies is presented. This method applies to multiple channel dies, i.e. dies provided with melt flow independent channels in the land. The approach is based on the resolution of the flow inverse problem, which consists of finding the channel topology (channel land lengths, approach angles in the transition region), which gives a balanced flow at the die orifice from the knowledge of the die contour. The methodology uses a blend of the network approach and the cross-section method. The procedure is used to design an industrial die that has been tested in a manufacturing environment, showing the performance of the proposed approach.     

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.     

Design of dies for the extrusion of sheets and annular parisons: The distribution problem

A systematic design of the classical “coat hanger” die is proposed and tested experimentally. The objectives of the design are 1. distribution of the polymer over the width of the die before it reaches the final lip section for thickness adjustment, 2. invariance of distribution to flow rate, 3. invariance to changes in polymer viscosity, and 4. uniform average residence time. The die design is based on a flow model which assumes power-law viscosity, steady shear flow In each cross-section, uniform temperature, and separation of the flows into a manifold component and a component in a slit section of uniform height. The design corrects for an oversimplification of the pressure gradient that was applied in previous studies; and it differs from previous designs by suggesting a rectangular cross-section for the manifold. Applications to side-fed dies for extrusion blow molding and to a sheet extrusion die achieved uniform distribution and did not require any additional flow corrections (such as choker bars or flexible lips). With the new design, the lip region of the die can freely be used for thickness control, fine tuning, or further shaping of the extrudate.     

标准口模与小口模测试的超高MFR聚丙烯的MFR结果转换关系

分别用标准口模、半口模、小口模1和小口模2测试超高熔体流动速率(MFR)聚丙烯的MFR。结果表明,MFR为700~2600 g/10 min时,标准口模与半口模、小口模1、小口模2的MFR换算关系:标准口模测试结果为半口模测试结果的7.5倍,为小口模1测试结果的15.7倍,为小口模2测试结果的10.0倍。所得倍数关系仅限于本实验室标准口模与小口模的测试结果。各实验室在换算标准口模与小口模测试结果的倍数关系时,需先采用各口模测量超高MFR聚丙烯的MFR,然后根据测量结果换算各口模间的倍数关系。     

A network flow analysis of extrusion dies and other flow systems

A method is presented to calculate the slow viscous flow distribution in systems of passages, for which the major velocity components are substantially parallel to the axes of those passages. That condition is generally satisfied in flat extrusion dies, disc filters, in-line filters, and other now devices. A finite difference matrix method is initially used to determine the flow distribution for an assumed viscosity distribution. That flow distribution is next used to determine a new distribution of resistances, now based on a specified rheological equation. This process is iterated until there is no significant change in the flow distribution. The passages are subdivided in this method and replaced by a network of resistances. A few unknowns are introduced at one end of the network, which are solved at the other end, using a matrix marching routine. The method is described for newtonian flow through a flat die with equalizing channel, for which the analytic solution is known. Results are shown for that die for flow of power law liquids.     

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.     

Three-dimensional path line tracking and residence time distribution in fishtail dies

The flow kinematics of power-law fluids in fishtail dies is studied. A general isothermal three-dimensional finite element code developed by the authors is used for the flow analysis purpose. The basic geometry of the fishtail die is defined by simple super-elliptical curves, which allows a smooth transition from a circle to a slit. The three-dimensional path line and the residence time distribution (RTD) are calculated from the velocity field obtained from the finite element solution of the conservation equations. The effects of the rheological properties and the die geometry on the path line pattern and the residence time distribution are investigated. The results indicate that as both the length of the transition zone and the fishtail angle increases, the residence time distribution becomes more uniform. However, the power-law index does not affect the residence time distribution significantly.     

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.     

Uniformity of flow from sheeting dies

A numerical method for analyzing the uniformity of flow from sheeting dies is presented. The method assumes that the flow is isothermal and that the material is a power law fluid. A uniformity index is defined and methods are presented which enable die dimensions to be established which will result in a specified uniformity at particular flow rates and pressure drops. The analysis shows that the flow index “n” of the power law is the key parameter determining the uniformity of flow from a sheeting die.     

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.     

Flow induced fiber orientation in an expanding channel tubing dies

In the application of plastic pipes for fluid transport and for the protection of underground electrical cables, it is desirable to improve mechanical properties, particularly in the hoop direction. The use of orientable reinforcing particles such as chopped glass fibers could make possible such an improvement if the orientation of the fibers could be controlled. While conventional pipe extrusion dies tend to promote axial fiber orientation, the use of an expanding channel die has been proposed to produce a preferential hoop orientation of fibers. In this paper, a theoretical model of the flow of a fiber suspension through an expanding channel die that predicts the fiber orientation distribution at the die exit is described. The effects of Theological properties and die geometry on the final fiber orientation distribution are predicted. The results of an experimental study of fiber orientation in pipe extruded using an expanding channel die are shown to be in agreement with the theoretical predictions.     

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     

Study of the effects of feed frames on powder blend properties during the filling of tablet press dies

This paper studies systematically the effect of a feed frames, a device used in rotary tablet presses to drive the powders into compression dies, on the properties of the powders entering the tablet press dies. The work focused on the effect of blend composition, feed frame parameters (blade speed, residence time), and rotary die disc parameters (die disc speed, die diameter) on the flow pattern, uniformity of die filling, applied shear, and the flow properties of pharmaceutical blends. The flow pattern suggests a stratified filling of the dies and therefore, non-uniform properties of the tablets. The amount of powder entering the dies depended on blend flow properties, feed frame speed, and dies disc speed. In addition, blend properties changed significantly as the powder flowed through the feed frame. The flowability of lubricated blends improved significantly as the number of feed frame blade passes increased, decreasing in turn the RSD of the die filling weight.     

Determination of steady-state elongational viscosity for rubber compounds using bell-mouthed dies

A bell-mouthed die geometry was designed to cause convergent flow at a constant, uniform, elongational strain rate. An equation was derived, which showed that steady-state elongational viscosity could be calculated from a plot of pressure drop due to elongation against a simple function of die length. To obtain values of pressure drop due to elongation, it was necessary to correct the total pressure drop measured across the bell-mouthed dies for the contribution from shear occurring near the die wall. For this purpose, a simplified shape for the bell-mouthed dies was assumed, comprising several parallel sided segments. Applying a formula to pressure drop data measured across straight dies corresponding to these segments gave an estimate of the pressure drop due to shear across the bell-mouthed dies. Pressure drops due to elongation were determined by subtracting the pressure drop due to shear from the total pressure drop measured across the bell-mouthed dies. Measurements were also carried out with lubrication to validate the shear correction method. The results indicate that for the compound used in this study, a combination of bell-mouthed and straightsided dies can be used in a conventional capillary rheometer to determine steady-state elongational viscosity. An elongational viscosity of 190 kPa s at 90°C and at a strain rate of 10 s⁻¹ was determined for a simple styrene-butadiene rubber compound. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1139–1150, 1997     

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.