A systematic approach for the design of a spiral mandrel die

An effective design strategy is presented for the determination of optimal flow channel geometry of a spiral mandrel die, which can produce annular, thin, and uniform products of polymer melt. This strategy includes two steps: First, a two-dimensional flow simulation associated with the Taguchi approach is applied to search several sets of die geometric parameters, from which process the flow uniformity is assessed. Second, the optimum one parameter set selected by further considering total pressure drop, mixing degree and residence time distribution (RTD). The strategy is illustrated through the design of a spiral mandrel die with four spirals traveling a full 360°, and the viscosity of polymer melt is assumed to be power law model. The results indicated that the design criteria such as high flow uniformity, low pressure drop, good mixing degree and narrow RTD are difficult to attain simultaneously. For a particular polymer melt, there exists a design window for the geometric parameters; within the window the geometric parameter set may satisfy most of the design criteria.     

衣架型模头内流道参数的确定和优化

根据聚合物加工流变学理论 ,采用衣架型单流道模头计算公式确定了模头的流道参数并加以优化 ,然后设计出适用于HDPE平膜的衣架型宽幅模模头尺寸。     

Study of the stability of the film casting process

A theoretical study of the film casting process has been carried out. In this industrial process, a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This involves mainly an extensional flow. Between the die and the chill roll, thick edges are formed and a neck-in phenomenon is observed. Above a critical take-up speed, a drawing instability, known as draw resonance, may occur. In this paper, a one-dimensional model adapted from the classical model of the fiber spinning is developed (for a Newtonian or a Maxwell fluid). The influence of the processing parameters (draw ratio, Deborah number, and aspect ratio) on geometry of the lateral free surface (the so-called neck-in phenomenon) is studied. An unattainable zone very similar to the one encountered in fiber spinning is predicted, which only slightly depends on the stretching geometry (initial film width and stretching distance). The onset of draw resonance is studied through the linear stability method. A stability zone, depending on the geometry of the process, the elasticity of the polymer, and the draw ratio, has been obtained. This instability is observed with simultaneous width and thickness film variations. It is proved that the aspect ratio (stretching distance divided by die width) has a strong influence on the onset of the draw resonance instability.     

Numerical simulation of fluid flow and heat transfer in a single-screw extruder with different dies

In a plasticating screw extruder, a polymer melt forms in the melting zone of the extruder. Pressurization of the molten polymer takes place in the melting and the metering sections so that the melt can flow through the restricted passage of the die and assume a desired shape. In a melt fed extruder, the throughput is governed by the pressure rise over the entire length of the extruder. The pressure developed in the screw channel may also be employed in rapid filling of molds, such as those in injection molding. When the geometry of the screw, the barrel temperature, and the die are selected, a unique set of operating parameters arise for a particular flow rate or screw speed. In the present study, numerical and analytical methods are used to calculate the transport in the extruder and the pressure drop in the die. An iterative numerical method based on solving the equations of motion and energy in the screw channel and a correction scheme to couple the die with the screw channel is discussed. The numerical algorithm is capable of handling an arbitrary variation of the viscosity of the polymeric fluid with the shear rate and temperature. The results obtained by simulating the fluid flow in the screw channel are compared with available numerical and experimental results in the literature, indicating good agreement. The performance characteristics of the extruder, for chosen thermal boundary conditions and screw geometry, are presented for different die geometries and different fluids. The important considerations that arise in the numerical simulation of the extrusion process are also discussed.     

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.     

在挤出机口模中聚合物不稳定流动的模拟

对挤出机口模流道中高聚物的流动情况进行了分析。引用高聚物黏弹性流体本构方程,建立了高聚物在挤出机机头口模中流动的数学模型。用MathCAD软件对该模型进行了数值模拟,结果表明:机头压力、材料的松弛时间以及口模流道的几何尺寸对高聚物在机头中应力张量的变化影响较大,适当调整口模流道尺寸会有利于高聚物的稳定挤出。     

Analysis of the fluid–structure interaction in the optimization‐based design of polymer sheeting dies

A polymer‐sheeting‐die‐design methodology is presented that integrates a simulation of the polymer melt flow and die‐cavity deformation with numerical optimization to compute a die‐cavity geometry capable of giving a nearly uniform exit flow rate. Both the polymer melt flow and sheeting‐die deformation are analyzed with a general‐purpose finite‐element program. The approach includes a user‐defined element that is used to evaluate the purely viscous non‐Newtonian flow in a flat die. The flow analysis, which is simplified with the Hele–Shaw approximation, is coupled to a three‐dimensional finite‐element simulation for die deformation. In addition, shape optimization of a polymer sheeting die is performed by the incorporation of the coupled analyses in our constrained optimization algorithm. A sample problem is discussed to illustrate the die‐design methodology. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3994–4004, 2007     

Residence time distribution of polymer melt in the T-die

Theoretical or rheological calculations for crosshead die geometry were thought not worthwhile until recently, and restrictor, or choker, bars were often excessively relied upon for film uniformity. Thus, the residence time distribution of a polymer melt was infrequently calculated especially in the T-die, because it was assumed to be very wide in T-dies. This report provides a general equation expressing the residence time distribution of polymer melts in T-dies, and indicates how to take an optimum combination of the flow-path dimensions in order to obtain both a high flow uniformity and a comparatively narrow residence time distribution across the die width. Such a T-die designed by the above considerations will produce a shorter heat history and improved physical properties of the sheet or film produced.     

Numerical investigation of spinneret geometric effect on spinning dynamics of dry‐jet wet‐spinning of cellulose/[BMIM]Cl solution

In this study, the effect of spinneret geometry, including the entrance angle α of the entrance channel, the length L_s, and the diameter D₀ of the exit channel, on the spinning dynamics of dry‐jet wet‐spinning of cellulose/1‐butyl‐3‐methylimidazolium chloride ([BMIM]Cl) solution was simulated by using finite element method. Based on the mathematical model of dry‐jet wet‐spinning established in our previous work (Xia et al., Cellulose 2015, 22, 1963) the radial and axial profiles of velocity, pressure, and shear rate in the spinneret and the profiles of diameter, temperature, and tensile stress in the air‐gap region were obtained. From the simulated profiles, the effect of spinneret geometric parameters on the flow behavior and the pressure drop of polymer solution in the spinneret and the die‐swell ratio near the spinneret was discussed. The entrance angle α of the entrance channel mainly influences the flow behavior of polymer solution in the spinneret and the die‐swell effect near the spinneret. As the decrease of the entrance angle α of the entrance channel, the vortices in the spinneret could be removed and the die‐swell ratio decreases. The increase of the length L_s of the exit channel results in the increase of pressure drop in the spinneret and the decrease of the die‐swell ratio. It is also found that the increase of the diameter D₀ of the exit channel reduces the flow velocity of polymer solution and decreases the pressure drop in the spinneret at a constant mass flow rate. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43962.     

Analysis of a cross head die with the flow analysis network (FAN) method

The Flow Analysis Network (FAN) method was adapted for solving the isothermal flow problem in a cross head die. Given the polymer rheology and the die geometry, the flow streamlines in the die and the flow rate uniformity at the exit can be calculated for any given head pressure. The optimum geometrical configuration of the die can be computed by repeated simulations. Results of the computations with the present method are shown to be in good agreement with previously published computations.     

Temperature measurements of polymer melts in the heating barrel during injection molding. Part 2: Three-dimensional temperature distribution in the reservoir

A new method has been developed to measure the three-dimensional temperature distribution of polymer melts in the reservoir of the heating barrel in the dynamic state. The procedure involves the use of a small-sheathed thermocouple in the nozzle of the machine. The tip of the thermocouple can be varied in depth from the surface to the center of the nozzle. The polymer melt of a shot is found to have a three-dimensional temperature distribution dependent on the geometry of the screw and the order of shot. These results reflect clearly the thermal histories of the polymer melt in the channel of the screw during plastication and conveyance, and indicate part of the dynamics of injection molding. Further, these measurements contribute to optimization of the design for the screw and the process conditions.     

Optimization of the coathanger manifold via computer simulation and an orthogonal array method

A well-designed coathanger die may deliver a polymer melt through the die more uniformly. However, it is difficult to optimize the manifold profile because of the complexity of flow distribution with regard to problems of die geometry, temperature, shear, and viscoelastic effects. The empirical methods have been widely used to design the manifold of a flat slit die. But this approach is time consuming and causes die material waste due to the iterative design process. With computer simulation, die designers can repeat modifications to obtain the optimal manifold shape easily. In this research, the Taguchi method was used to investigate the influences of the materials, die geometry, and processing conditions on optimizing the manifold profile. The comparison of the thickness distributions with and without modified manifold showed that the modified manifold improves the thickness uniformity significantly.     

Three-Dimensional Simulation of the Non-Isothermal Cast Film Process of Polymer Melts

A modeling system is proposed to simulate the non-isothermal three-dimensional cast film process of viscous polymer melts. The finite element method (FEM) is used to solve the system and the numerical results are compared with the experimental measurements, including temperature, velocity fields, and final film shape. It is found from these results that the model is able to predict the film shape accurately under the steady-state processing conditions. The model considers the flow in the thickness direction, shear-thinning, non-isothermal effect, self-weight, and viscous dissipation, but it excludes die swell at the die exit, elasticity of materials, crystallization, and film sag. Using the model, the influence of temperature variation, draw ratio, and air gap length on the final film shape is also investigated.     

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.     

Experimental study and modeling of wall slip of polymethylmethacrylate considering different die surfaces

Wall slip of polymethylmethacrylate (PMMA) was studied on different flow channel surfaces using a rheological slit die and a high pressure capillary rheometer. As die surfaces polished steel, ground steel, and Si doped Diamond like carbon (DLC) were used. A new wall slip model is presented in this paper which assumes a lubricating film between the polymer melt and the die surface. The slip velocity has a power law dependency on wall shear stress. In the double logarithmic plot the wall slip curves are linear and can be parallel shifted to higher values with increasing temperature. The predicted dependencies of the wall slip velocity could be confirmed with experiments conducted with PMMA on polished steel. Furthermore, the die surface influences the flow behavior of PMMA. No wall slip was found on ground steel and on DLC. No complete film could be established by the lubricant on the ground steel die wall. The DLC‐coating exhibits a similar surface roughness and surface energy to polished steel, but the chemical composition is different. It is a metastable form of amorphous carbon containing sp² and sp³ bonds. As a consequence slip additives have a low ability to bond to this material. POLYM. ENG. SCI., 58:1391–1398, 2018. © 2017 Society of Plastics Engineers     

The processing of polypropylene cast films. I. Impact of material properties and processing conditions on film formation

Material properties have a significant impact on the response of polymers to industrial flow processes such as film casting. During film casting, molten polymer is extruded through an (approximately) rectangular die and then cooled rapidly. Subsequent biaxial stretching can be employed to manipulate the film properties. In this work, we investigate the effect of polymer viscosity (molecular weight), draw ratio, and die temperature on polypropylene film formation. We measure the width, two components of the velocity vector, and the temperature profiles throughout the film web. The polymer rheology and the die temperature affect the film geometry and temperature profiles in the air‐gap. The magnitude of the machine direction velocity component depends on both the machine and transverse position in the film. The velocity shows a maximum at the centerline and decreases toward the film edge. The measured transverse velocity component, a consequence of the film neck‐in, is seen to decrease from the film edges to the centerline. POLYM. ENG. SCI., 2010. © 2009 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.     

Effect of wall slip on blown film thickness distribution

One of the most important materials for blown film is high‐density polyethylene (HDPE) with wide molecular weight distribution. First, we computed a wall stress at the entrance of a spiral groove in a particular die during blown film processing on a particular condition, to which a similar condition is widely utilized in a film works. The computed value is about 170 kPa, while the HDPE melt slips at die wall at stresses above approximately 50 kPa. The stress of 170 kPa is sufficiently large for the slip occurrence of the melt. Then, we investigated the effects of wall slip and melt visosity on film thickness distribution in the circumferential direction; the distribution tends to decrease with decreasing wall slip and melt viscosity. This tendency is explained by considering flow distribution in a spiral mandrel die and polymer melt flow characteristics.     

Sharkskin and oscillating melt fracture: Why in slit and capillary dies and not in annular dies?

The sharkskin and stick‐slip polymer extrusion instabilities are studied primarily as functions of the type of die geometry. Experimental observations concerning the flow curves, the critical wall shear stress for the onset of the instabilities, the pressure and flow rate oscillations, and the effects of geometry and operating conditions are presented for linear low‐density polyethylenes. It is found that sharkskin and stick‐slip instabilities are present in the capillary and slit extrusion. However, annular extrusion stick‐slip and sharkskin are absent at high ratios of the inside‐to‐outside diameter of the annular die. This observation also explains the absence of these phenomena in other polymer processing operations such as film blowing. These phenomena are explained in terms of the surface‐to‐volume ratio of the extrudates, that is, if this ratio is high, sharkskin and stick‐slip are absent. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers