Annular Die Research Articles

Numerical Study of Residual Stresses Due to External Cooling in Extruded Polymer Profiles

AbstractProfile extrusion is a production technique to make polymer profiles and hollow tubes. At a certain distance after the die exit the polymer extrudate is guided into a cooling chamber, where the polymer is cooled extensively to set the part dimensions. Uniform cooling in the cooling chamber is required to avoid warpage and twisting of the extrudate due to differential shrinkage. The effect of extrudate cooling on the shape of the extrudate and the residual stresses in the final extrudate product are numerically studied. Two different cases are studied: a 2D axisymmetric problem of a viscoelastic fluid exiting an annular die and a 3D problem of a hollow square shaped die. The extrudate is extensively cooled from a distance from the die exit. Extrudate cooling is modeled by subjecting the extrudate to heat loss via convection. For the Nusselt number Nu is fixed to 1 to represent the part of the extrudate in between the die exit and the entrance of the cooling chamber. For the Nusselt number is varied to mimic different cooling speeds. The Weissenberg number Wi, the Nusselt number and are varied in this work. Results show that for high values of Wi a significant skin‐effect of high residual stresses appear near the extrudate edges for high Nusselt numbers and small values of . It is also shown that for high Weissenberg numbers the shape of the extrudate is significantly altered due to extrudate swell, when the extrudate is cooled slower. For fast cooling and small values of , the polymer does not have time to relax and the elastic stresses are “frozen in.” This leads to less extrudate swell but large residual stresses near the extrudate edges.

Producing Microlayer Pipes and Tubes through Multiplication Coextrusion and Unique Annular Die: Simulation and Experiment

Traditional tubular structures with multilayer annular structures (MAS) are limited in the number of layers; as a result of fewer layers, the layers are typically thick, rigid, and unsuitable for many tubular applications. An advanced technique to produce MAS with layer numbers up to 2048 and individual layer thickness remaining low to a few micrometers is successfully designed here. Planar multilayers with high layer numbers were first produced via a flat-die layer multiplication coextrusion, followed by being shaped into an annular structure by using a custom-made annular die that is designed with the aid of numerical simulation. Experimental verifications show that the microlayer pipes with layer numbers up to 2048 and uniform thickness on the circumference can be readily produced by using this advanced technique. Therefore, this work may provide a valuable solution to develop the processes and equipment for tubes with microlayer structures.

Double-layer optical fiber coating analysis using viscoelastic Sisko fluid as a coating material in a pressure-type coating die

Double-layer optical fiber coating is performed using a melt polymer satisfying a Sisko fluid model in a pressure-type die. For this purpose, wet-on-wet coating process is applied. The assumption of fully developed flow of a Sisko fluid model, two-layer liquid flows of an immiscible fluid is modeled in an annular die of length L, where the bare glass fiber is dragged at a higher speed. The nonlinear governing equations are modeled and then solved by utilizing optimal homotopy asymptotic method (OHAM). The convergence of series solution is established. The convergence of OHAM is also verified by the Adomian decomposition method. In addition, the shear-thinning and shear-thickening characteristics of the non-Newtonian Sisko fluid are examined, and a comparison is made with the Newtonian fluid. At the end, the present work is also compared with the experimental results already available in the literature by taking the non-Newtonian parameter that tends to zero.

Steady flow and heat transfer analysis of MHD flow of Phan-Thien-Tanner fluid in double-layer optical fiber coating analysis with slip conditions

Abstract Modern optical fibers require a double-layer coating on the glass fiber in order to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride, low- and high-density polyethylene, nylon, and polysulfone. One of the most important things that affect the final product after processing is the design of the coating die. In the present study, double-layer optical fiber coating is performed using melt polymer satisfying the Phan-Thien-Tanner (PTT) fluid model in a pressure-type die. The fluid is electrically conducted in the presence of applied magnetic field. Wet-on-wet coating process is applied for double-layer optical fiber coating. The assumption of fully developed flow of PTT fluid model, two-layer liquid flows of an immiscible fluid, is modeled in an annular die of length L, where the fiber is dragged at a higher speed. The equations characterizing the flow ad heat transfer phenomena are solved exactly and the effects of emerging parameters are shown with the help of graphs. It is interesting to remark that an increase in the non-Newtonian parameters increases the velocity in the absence or presence of slip parameters, which coincides with the results reported earlier. Also, the effect of important parameters such as Deborah numbers, slip parameters, magnetic parameter, characteristic velocity, radii ratio, and Brinkman numbers on the axial velocity, flow rate, thickness of coated fiber optics, and temperature distribution are investigated. Furthermore, the results were compared with the experimental results already published. To the best of our knowledge, no such analysis of the double-layer coating flows of PTT fluid using slip conditions is available in the literature. At the end, the result of the present work is also compared with the experimental results already published by taking λ → 0 (non-Newtonian parameter).

Steady flow and heat transfer analysis of Phan-Thein-Tanner fluid in double-layer optical fiber coating analysis with Slip Conditions.

Modern optical fibers require double-layer coating on the glass fiber to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride (PVC) and low-high density polyethylene (LDPE/HDPE), nylon and Polysulfone. In this paper, double-layer optical fiber coating is performed using melt polymer satisfying PTT fluid model in a pressure type die using wet-on-wet coating process. The assumption of fully developed flow of Phan-Thien-Tanner (PTT) fluid model, two-layer liquid flows of an immiscible fluid is modeled in an annular die, where the fiber is dragged at a higher speed. The equations characterizing the flow and heat transfer phenomena are solved exactly and the effects of emerging parameters (Deborah and slip parameters, characteristic velocity, radii ratio and Brinkman numbers on the axial velocity, flow rate, thickness of coated fiber optics, and temperature distribution) are reported in graphs. It is shown that an increase in the non-Newtonian parameters increase the velocity in the absence or presence of slip parameters which coincides with related work. The comparison is done with experimental work by taking λ → 0 (non-Newtonian parameter).

Modeling the nanofiber fabrication with the melt blowing annular die

Melt blowing is commonly used to convert polymer resin directly into nonwoven fabrics of superfine fibers. Further decrease of the fiber diameter will improve the filtration and adsorption properties remarkably and thus has been appealing to the researchers. Besides the dual slot die, the annular die is utilized to manufacture superfine fibers in the melt blowing process as well. In the dual slot die, the high velocity air flow from both sides of the polymer melt. However, the air encircles the polymer melt entirely in the annular die, which is in favor of the polymer drawing and thus manufacture of nanofibers. In this paper, the air flow field model of the annular die is established and solved numerically. The polymer drawing with the melt blowing annular die is modeled and simulated by introducing the simulation results of the air flow field. The predicted fiber diameters coincide with the experimental data. Effects of the polymer flow rate and initial air velocity on the fiber diameter are also explored. The results show good perspective of using melt blowing technology to manufacture nanofibers materials because melt blowing has a higher output than electrospinning.

Investigation on a New Annular Melt-Blowing Die Using Numerical Simulation

In this study, a new annular melt-blowing die with an inner stabilizing piece was designed to obtain finer fibers and consume less energy than for the common annular die. The effects of the new annular die design on the velocity field, temperature field, and turbulence fluctuation field at the die centerline were investigated using numerical simulation. The simulation results reveal that, compared with the corresponding annular die, the new annular die decreases the negative velocity in the recirculation zone, enhances the mean velocity along the centerline, slows the temperature decay of the flow field, and reduces the velocity fluctuations of the air flow near the outlet of the polymer capillary. In the local region, the centerline turbulence intensity for the new annular die is stronger than that for the corresponding annular die, but the difference is not large.

Extrusion of humidity-resistant starch foam sheets

An annular die is used to extrude cylindrical starch foams which are then sliced to yield foam sheets suitable for cushioning protection and insulation of shipping containers. Although starch foams, as a possible replacement of petroleum-based foams, have been prepared in the past, their sensitivity to humidity remained a problem. Extensive research in the last few years has been focused on resolving the collapse of the foam at high humidity, improve the cushioning protection, and develop an economical foaming process. However, these issues are still problematic and need to be resolved before such biobased foams can gain entry into the marketplace. In this study, a Box–Behnken statistical design of experiment was used to optimize the properties of foams extruded with various additives. It was found that the density, cell structure, and the rate of water penetration of these foams were affected by the feed rates (e.g., foam composition) of the water, talc, and poly(hydroxy ether) (PHE). The use of PHE was found to be extremely effective to minimize the water sensitivity and it significantly increased the water penetration time of the foam sheets. These starch foams efficiently absorb impacts and recover its physical shape quickly to provide multiple cushion protection for moderately delicate products. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers

Experimental investigations of the liquid-film instabilities forming on a wire under the action of a die

The liquid film remaining on a wire withdrawn from a liquid bath and forced through an annular die is experimentally investigated on a dedicated facility. An optical laser-based technique recently introduced to study liquid-film instabilities on small-radius cylinders allows the measurement of the mean final thickness and wave characteristics. Experimental results are compared to analytical predictions obtained with simple models specifically derived for this configuration and based on liquid-film properties (density, viscosity and surface tension) and operating parameters (wire speed and die dimensions). The experimental measurement of surface-perturbation features (wave amplitude, wavelength and amplification factor) as a function of the operating parameters reveals the presence of a single wavelength for low values of the withdrawing velocity and a progressive wave disappearance for high speeds, in accordance with theoretical predictions.

Pressure Profile in Annular Die using PP/CO2 Solution Viscosity

In this paper, a rheological die with a rectangular channel was designed to determine the solution viscosity of supercritical CO2 in non-crosslinked high-melt-strength (HMS) polypropylene (PP). The shear viscosity of this solution was modeled as a function of temperature, pressure, gas content, and shear rate. With interest in producing highly-expanded foamed wire coatings using an annular die, an analysis of the annular die pressure profile using the measured viscosity data and an analytical method was also conducted.

Power-law numerical solution for post-die extrusion of plastic pipe

In a continuous plastic-pipe extrusion, melt emerges from an annular die and is then drawn freely into a sizing sleeve. Here, we investigate this extensional flow when a pressure difference is applied across the melt cone. A numerical solution to a power-law fluid is presented. Differential equations for the melt-cone shape are derived from a force balance on the melt cone. Design curves are then constructed from the solutions to these equations. These curves are helpful in predicting the pipe-extrusion operating conditions. The model is also used to predict an operating envelope for sizing-sleeve placement. Examples demonstrate how to use these results. We also compare it to an earlier analytical solution that excludes a pressure difference across the melt cone.

Design and Analysis of Crosshead Annular Die for Braided Medical Tubing Extrusion

A theoretical method is proposed for optimum design of a crosshead annular die used for medical tubing. According to this method, the geometric variables are determined to minimize the change in gapwisely-averaged flow velocities due to the variation in flow patterns inside the transitional region of the flow channel of the die, namely the gum space. To achieve this, a numerical approach to flow analysis is put forward based upon the simplified motion and energy equations as well as the approximation of the flow channel using a series of varying annular slits, each having constant geometric parameters. Accordingly, the numerical schemes for flow analysis and design optimization are established, and the computer program is developed using Microsoft Visual C++ 6.0. For an optimum die design, the heat adhesion between the cold-fed inner tube and the hot melt during the over-extrusion is evaluated based upon the temperature rise and pressure profile of the melt in the die land. Based upon the optimum die design obtained from the method, the flow is well balanced with enhancement of extrusion quality. Also, it is found that the optimum die designs are less sensitive to extrusion conditions within a certain range.

Design and Analysis of Crosshead Annular Die for Braided Medical Tubing Extrusion

A theoretical method is proposed for optimum design of a crosshead annular die used for medical tubing. According to this method, the geometric variables are determined to minimize the change in gapwisely-averaged flow velocities due to the variation in flow patterns inside the transitional region of the flow channel of the die, namely the gum space. To achieve this, a numerical approach to flow analysis is put forward based upon the simplified motion and energy equations as well as the approximation of the flow channel using a series of varying annular slits, each having constant geometric parameters. Accordingly, the numerical schemes for flow analysis and design optimization are established, and the computer program is developed using Microsoft Visual C ++ 6.0. For an optimum die design, the heat adhesion between the cold-fed inner tube and the hot melt during the over-extrusion is evaluated based upon the temperature rise and pressure profile of the melt in the die land. Based upon the optimum die design obtained from the method, the flow is well balanced with enhancement of extrusion quality. Also, it is found that the optimum die designs are less sensitive to extrusion conditions within a certain range.

Design and Analysis of Crosshead Annular Die for Braided Medical Tubing Extrusion

Design and Analysis of Crosshead Annular Die for Braided Medical Tubing Extrusion

The steady annular extrusion of a Newtonian liquid under gravity and surface tension

The steady extrusion of a Newtonian liquid through an annular die and its development outside and away from the die are studied under the influence of gravitational and surface tension forces. The finite element method (FEM) is used for the simulations. The positions of the inner and outer free surface profiles are calculated simultaneously with the other unknown fields, i.e. using the Newton–Raphson iterative scheme. The effects of three relevant parameters, i.e. the Reynolds, the Stokes and the capillary numbers, on the shape of the annular film are studied for two values of the inner to the outer diameter ratio, corresponding to a thick and a thin annular film respectively. A one-dimensional model for the extrudate region, valid for thin annular films, is also presented, and its predictions are compared with the two-dimensional finite element calculations. Despite the fact that it is valid away from the die exit, the one-dimensional model predicts satisfactorily the effects of the Stokes and capillary numbers. Copyright © 2000 John Wiley & Sons, Ltd.

Overall numerical simulation of extrusion blow molding process

AbstractThis paper focuses on the overall numerical simulation of the parison formation and inflation process of extrusion blow molding. The competing effects due to swell and drawdown in the parison formation process were analyzed by a Lagrangian Eulerian (LE) finite element method (FEM) using an automatic remeshing technique. The parison extruded through an annular die was modeled as an axisymmetric unsteady nonisothermal flow with free surfaces and its viscoelastic properties were described by a K‐BKZ integral constitutive equation. An unsteady die‐swell simulation was performed to predict the time course of the extrudate parison shape under the influence of gravity and the parison controller. In addition, an unsteady large deformation analysis of the parison inflation process was also carried out using a three‐dimensional membrane FEM for viscoelastic material. The inflation sequence for the parison molded into a complex‐shaped mold cavity was analyzed. The numerical results were verified using experimental data from each of the sub‐processes. The greatest advantage of the overall simulation is that the variation in the parison dimension caused by the swell and drawdown effect can be incorporated into the inflation analysis, and consequently, the accuracy of the numerical prediction can be enhanced. The overall simulation technique provides a rational means to assist the mold design and the determination of the optimal process conditions.

POSTDIE EXTRUSION OF PLASTIC PIPE

In continuous plastic pipe extrusion, melt emerges from an annular die and is then freely drawn down into a sizing sleeve. Here, we investigate this extensional flow with and without internally applied air pressure. For the case without internal air pressure, an analytic solution is derived. For the case with internal air pressure, a numerical solution is presented, where differential equations for the melt cone shape are derived from a force balance. Design curves are then constructed from the solutions to these models. These curves are helpful in predicting pipe-extrusion operating conditions for the postdie region.

The steady annular extrusion of a Newtonian liquid under gravity and surface tension

The steady extrusion of a Newtonian liquid through an annular die and its development outside and away from the die are studied under the influence of gravitational and surface tension forces. The finite element method (FEM) is used for the simulations. The positions of the inner and outer free surface profiles are calculated simultaneously with the other unknown fields, i.e. using the Newton–Raphson iterative scheme. The effects of three relevant parameters, i.e. the Reynolds, the Stokes and the capillary numbers, on the shape of the annular film are studied for two values of the inner to the outer diameter ratio, corresponding to a thick and a thin annular film respectively. A one-dimensional model for the extrudate region, valid for thin annular films, is also presented, and its predictions are compared with the two-dimensional finite element calculations. Despite the fact that it is valid away from the die exit, the one-dimensional model predicts satisfactorily the effects of the Stokes and capillary numbers. Copyright © 2000 John Wiley & Sons, Ltd.

共押出成形プロセスの数値シミュレーション

Numerical simulations of the coextrusion process used in producing multi-layer plastics products have been carried out. The isothermal multi-layer axisymmetric coextrusion flow was analyzed with a streamline finite element method. Extrudate swell from an annular die was predicted and the position of the multi-layer fluid interface was also determined. The K-BKZ integral type viscoelastic constitutive equation was employed to provide good descriptions of rheological properties for polymer melts. A double nodes technique at the interfaces was used to capture pressure discontinuity and to ensure continuity of total stress and velocity. Numerical case studies were performed to examine the behaviors of two or three layers extruded from a straight type annular die. Numerical results show that even at the same flow rate, variations of the layer configurations produce changes in the extrudate swell. For Newtonian fluids, the less viscous outer layer material reduces the extrudate swell relative to the mono-layer configuration. On the other hand, for viscoelastic fluids, the more elastic outer layer material enhances the extrudate swell even if the outer layer is less viscous than the inner layer. These are in general agreement with the numerical results found in the literatures. The numerical predictions for the extrudate swell of a practical problem were quantitatively examined with experimental data.

押出加工 二重管ダイスウェルとブロー成形

押出加工 二重管ダイスウェルとブロー成形