Manufacturing and Modeling of an Extrusion Die Spider Head for the Production of HDPE Tubes

Journal of Manufacturing Technology Research ISSN: 1943-8095

Volume 6, Number 1-2, pp. 1-15 © 2015 Nova Science Publishers, Inc.

MANUFACTURING AND MODELING

OF AN EXTRUSION DIE SPIDER HEAD

FOR THE PRODUCTION OF HDPE TUBES

Georgios N. Kouzilos, Angelos P. Markopoulos

and Dimitrios E. Manolakos Manufacturing Technology Division, School of Mechanical Engineering,

National Technical University of Athens,

Zografou, Athens Greece

ABSTRACT

A spider extrusion die was designed and manufactured with the aid of a three-

dimensional polymer flow analysis. The methods used were the computer fluid dynamics

analysis and the arbitrary Lagrangian Eulerian method, both realized with a commercial

Finite Element software. The aim of the computer fluid dynamics analysis was to

investigate the non-isothermal, non-Newtonian flow in the extrusion die. In addition, the

arbitrary Lagrangian Eulerian method was used to examine the mechanical stresses

exerted on the spider leg, which is the weakest part of the extrusion die. The experimental

results of pressure drop and temperature distribution in the die were compared with

analytical and numerical results, indicating good agreement. The validated finite element

model was then used to examine whether the manufactured die can successfully

withstand the applied stresses during operation.

Keywords: Finite Elements Analysis, Pressure flow, HDPE, Spider extrusion die

1. INTRODUCTION

Polymer extrusion has been a major industrial process for the production of films, rods,

tubes and pipes employed mainly in fluid transport in several industrial sectors. The extrusion

die design process can become very difficult to execute and its cost can increase up to

prohibitive levels, when complex geometries are concerned. The process itself and the

extrusion dies used have been the subject of investigations over many years (Zhu, Xie and

Yuan, 2007; Kaiyuan et al, 2009; Matin et al, 2012). The design of extrusion dies for the

production of complex geometries requires vast experience, which is usually based on

Corresponding author, E-mail [email protected]

Georgios N. Kouzilos, Angelos P. Markopoulos and Dimitrios E. Manolakos 2

experimental trial-and-error approaches, involving, therefore, the use of huge amounts of time

and material resources. According to manufacturers, 10 to 15 iterations are required to

optimize complex profile geometries while the cost of the preliminary tests and corrections of

a profile die may be as much as 10–50% of the total cost (Michaeli, 2003).

The process of extrusion die design can be considerably simplified when modeling

techniques are considered. Huang and Huang (2007) optimized parison thickness for

extrusion blow molding using a hybrid modeling method consisting of finite elements,

artificial neural networks and genetic algorithms. Choudhary and Kulkarni (2008) developed

a three-dimensional mathematical model based on a Computational Fluid Dynamics (CFD)

code to investigate the non-isothermal, non-Newtonian polymer flow through the dies used in

the polystyrene foam extrusion process. Lebaal, Schmidt and Puissant (2009) designed and

optimized a 3D extrusion flat die using the constraint optimization algorithm. Despite all the

available tools, the main decisions are still left to the designer’s intervention and knowledge

(Shahreza et al, 2010). However, in order to automate the extrusion die design process,

numerical codes have been developed, aiming to transfer critical decisions to the code;

Gonçalves, Carneiro and Nóbrega (2013) developed a numerical modeling code and utilized

it in a case study that involves the design of a medical catheter extrusion die, focused on the

search of a balanced flow distribution.

In an effort to test the characteristics of the extrusion die in industrial use, an actual die is

manufactured. The geometrical characteristics of the extrusion die are based on a design

optimization procedure; a CFD based model using the generalized Newtonian approach was

employed, to investigate pressure drop, flow and temperature uniformity in the die.

Numerical and analytical results are compared to experimental data indicating very good

agreement. Furthermore, numerical analysis of the stresses exerted on the spider legs of

extrusion dies, using the Arbitrary Lagrangian-Eulerian (ALE) technique was performed. The

ALE technique revealed that the maximum stresses developed on the die during the extrusion

process, even at the spider legs, which are the weakest members of the die, can withstand the

applied stresses during die operation.

2. DESIGN OF EXTRUSION DIE AND MANUFACTURING

OF THE SPIDER HEAD

The extrusion die is initially modeled with SolidWorks®; Figure 1 illustrates the

assembled die in 135o cut section view in order to show all the parts that constitute it.

A 3D heat transfer model is developed for non-Newtonian materials being processed in

the extrusion die based on the configuration of Figure 1. The numerical solution assumes that

a homogeneous and isotropic High Density Polyethylene (HDPE) melt with a uniform

temperature is flowing into the spider die. The temperature of the die wall is kept constant

and the volumetric flow rate of the polymer melt is fixed. Polymer properties critically affect

the analysis of the entire processing operation and thus reliable quantitative models are

essential. However, in many polymer processes, the elastic memory effects are often

neglected because the melts are subjected to large steady rates of deformation for a relatively

long time. Since this work is concentrated on a qualitative analysis of the flow regime, the

inelastic model is selected as the most appropriate for describing melt flow.

Manufacturing and Modeling of an Extrusion Die Spider Head … 3

Figure 1. Assembled extrusion die in 135o cut view, (1) die housing, (2) middle ring, (3)

spider head, (4) torpedo, (5) middle mandrel, (6) center pin, (7) outer ring, (8) die ring,

(9) outer mandrel, (10) four screws M6x25-12.9 DIN 912, (11) four screws M12x75-

12.9 DIN 912, (12) four screws M12x120-12.9 DIN 912, (13) four screws M12x50-

12.9 DIN 912.

Polymer melts are non-Newtonian fluids and various models have been developed to

describe the dependence of viscosity on shear rate and temperature. Flexibility is provided by

the Carreau–Yasuda model:

(1)

where n0, λ, α and n are the fitting parameters of the model and αT is the shift factor given as:

(2)

The temperature dependence is introduced in equation (2) through the shift factor, αΤ,

while Eο is the activation energy and R is the universal gas constant.

According to the theory of computational fluid dynamics, the governing equations to

solve the melt flow problems can be obtained from the continuity, motion and energy

equations, based on the conservation of mass, momentum and energy, respectively.

Considering the characteristics of the polymer melts flow in the die channel when the steady-

state of the extrusion is achieved, the following assumptions are made:

Incompressible steady laminar flow prevails, i.e. the variation of the system

physical variables versus time can be neglected.


No slip conditions on the wall surface pertain, i.e. the melt flow velocity on the

fluid-die/mold interface is equal to the moving velocity of the die wall.

Inertial and gravitational forces are neglected, since Reynolds number of

polymer melts is relatively low.

Fully developed inlet velocity corresponding to actual volumetric flow rate and

uniform inlet temperature are considered.

Die-wall temperature is uniform.

Based on the above assumptions, the boundary conditions are set. Governing equations

can be written as:

Continuity equation: (3)

Motion equation: (4)

Energy equation: (5)

where is the Hamilton differential operator, u the velocity vector and σ the Cauchy stress

tensor, which is expressed as:

(6)

p is the hydrostatic pressure, S the extra stress tensor, I the Kronecker delta, Cp the heat

capacity, T the temperature and Q the total source term, incorporating the streamline-upwind

Petrov-Galerkin scheme employed to improve the computation stability.

Flow Simulation add-in of SolidWorks® is used to create the fluid domain by deleting

from the extrusion die all the unneeded subparts. Then, governing equations are solved

numerically using the finite element CFD code COMSOL 4.3b that incorporates the Carreau-

Yasuda viscosity model.

This numerical model investigates the effect of viscous dissipation, which causes an

increase in the fluid temperature. Shear heating plays a significant role in the extrusion of

polymeric materials and, therefore, it is taken under consideration in order to optimize the

polymeric material processing.

Due to the complex 3D geometry of the die and the nonlinear relationship between

polymer viscosity and shear rate, an elaborate, functional finite element mesh is developed to

facilitate numerical stability of the solution. The model consists of 95215 tetrahedral elements

with unstructured mesh, with maximum element size 13∙10-3

mm and minimum element size

5.56∙10-4

mm. Fluid domain geometry and the generated mesh is illustrated in Figure 2.

The Taguchi method is used with the numerical model; analysis of variance (ANOVA) is

employed for sensitivity analysis and the quadratic RSM is applied to determine the final

spider die geometry, by optimization performed on the effects of six design parameters of the

spider legs on the flow homogeneity. Optimization procedure is thoroughly described by

Mamalis, Kouzilos and Vortselas (2011). After the optimum geometry is determined,

manufacturing of the required parts and especially the spider die are produced.


Figure 2. Fluid domain geometry and mesh for the finite element analysis.

All parts of the extrusion die were manufactured and assembled in the Manufacturing

Technology Division of the National Technical University of Athens. Most of the required

machining processes were performed in an OKUMA MX-45VE CNC mill cutting center and

an OKUMA LB10II CNC lathe; some parts were produced with electrodischarge machining.

The related G-code for each part was created with SolidCAM® and was transmitted to CNC

machine tools with DNC technology. Figure 3 depicts the final design of the spider head.

Figure 3. Final spider head geometry.

The material of the spider head is selected to be IMPAX, a P20 hot work tool steel. This

material is commonly used for dies and its high strength and wear resistance guarantees the

unproblematic, repeated use of the die. Hard materials such as the one used in this extrusion

die require special machining practices in order for the required precision to be attained

(Davim, 2011; Kundrák, Ráczkövi and Gyáni, 2014; Sztankovics and Kundrák, 2014). The

manufactured extrusion die is shown in Figure 4(a) without the housing and outer rings and in

Figure 4(b) fully assembled. Figure 4(c) illustrates a detail of the spider leg.

Mechanical and physical properties of the extruder die material are tabulated in Table 1.

The spider die is mounted on a single screw Johnson Plastics Extruder for the production of

HDPE tubes; extruder characteristics: length/diameter ratio 24:1, screw diameter 38 mm and

compression ratio 2.75. High density polyethylene tubes with external diameter of 32 mm and

wall thickness of 2.4 mm are produced using the above mentioned equipment. The polymeric

material is the SABIC B 5823 with material characteristics presented in Tables 2 and 3.


Furthermore, the pressure drop in the die can be measured by manometer and the temperature

by infrared thermometer; these parameters are found to be 95.15 bar and 1.72 K, respectively.

Figure 4. (a) Semi assembled extrusion die, (b) fully assembled extrusion die and (c)

detail of the spider leg.

Table 1. IMPAX tool steel properties

Parameter Value

Elastic modulus 2.0∙105 MPa

Poisson's ratio 0.33

Shear modulus 7.3∙104 MPa

Mass density 7.8∙103 kg/m³

Tensile strength 9.2∙102 MPa

Yield strength 8.0∙102 MPa

Thermal expansion coefficient 1.3 10-5

per 0C

Thermal conductivity 43 W/m.K

Specific heat 440 J/kg.K


Table 2. Density and melt flow rate of HDPE

Parameter Value

Melt Flow Rate (MFR) (ISO 1133)

0.16 dg/min (at 190 0C, 2.16 Kg)

0.89 dg/min (at 190 0C, 5.00 Kg)

23.00 dg/min (at 190 0C, 21.6 Kg)

Density (ISO 1183) 958 kg/m3

Table 3. Shear rate and viscosity of HDPE

Shear Rate (1/s) at 190 °C Viscosity (Pa∙s)

12 4770

23 3426

58 1991

115 1301

230 836

565 443

3. EXTRUSION DIE MODELING AND EXPERIMENTAL RESULTS

In the next paragraphs an analytical and a numerical model, based on the optimized

geometry presented in the previous section, are discussed. The proposed models calculate

pressure drop and temperature rise in the die. Additionally, a stress FEM analysis is provided

for the spider head.

3.1. Analytical Modeling

The power-law exponential model is utilized to determine the pressure drop in the

extrusion die. According to Michaeli (2003), the volumetric flow rate of a non-Newtonian

fluid is described as:

(7)

where, is the die conductance, applicable to the power law model, ΔP is the pressure drop,

φ the fluidity and m the flow exponent. The volumetric flow rate of the Johnson Plastics

extruder is obtained as:

(8)

where and

.


is the volumetric rate, N the screw speed, D the inner barrel diameter, μ the melt

viscosity, H the channel depth, φ the helix angle of flight and L the axial length of the screw.

Therefore, the volumetric flow rate for screw speed 100 rpm is m3/s.

Pressure drop for various cross-sections of the die is calculated using equations by Michaeli

(2003). Total pressure drop through the die zones is ΔPtotal = 92.17 bar.

The analytical approach for determining the mean temperature rise at the outlet of the die

is based on the assumption that adiabatic conditions occur throughout the whole procedure.

This means that there is no heat exchange between the die wall and the material and,

therefore, the whole mechanical energy is converted to heat. The maximum bulk temperature

rise is calculated analytically as (Mamalis et al, 2010):

(9)

where ΔΡ is the total pressure drop in the die, ρ the density and Cp the specific heat and hence

3.2. Numerical Modeling

According to the analysis presented in section 2, the numerical solution assumes a

homogeneous and isotropic HDPE melt with uniform temperature of T=469K flowing into

the spider die. The temperature of the die wall is kept constant at Tw=469K and the

volumetric flow rate of the polymer melt is fixed at m3/s. The various

parameters used in the Carreau–Yasuda model are listed in Table 4 (Mamalis, Kouzilos and

Vortselas, 2011).

Table 4. Carreau–Yasuda model material constants

Parameter Value

n 0.2723

n0 5.43∙103 Pa∙s

λ 0.063 s

Eo 6.5 kcal/mol

TR 190 0C

α 2

An important aspect of the presented models is the ability to accurately predict the

pressure drop in the die. Figure 5(a) shows the pressure distributions in the entire domain of

the die. It can be observed that the pressure decreases continuously from die inlet to outlet.

The pressure distribution throughout the die as calculated by the FE simulation indicates a

total pressure drop of 97.24 bar.

The temperature distribution is obtained by solving the equations describing energy

balance in the die domain. Figure 5(b) illustrates the temperature distribution of the polymer

during extrusion. The polymer enters the die at a temperature of 469 K and the die walls are

considered to have the same constant temperature. The temperature of the polymer fluid


gradually increases in a direction perpendicular to the flow from the die wall towards its

central axis, as the fluid advances towards the exit of the die. The bulk temperature of the

molten polymer, as described by the numerical model, is obtained as:

(10)

where u and T are the velocity and temperature in the flow direction respectively. The

temperature rise is ΔT=Tout-Tin=1.53K, with Tout and Tin being the bulk inlet and outlet

temperatures of the molten polymer.

Figure 5. Numerically obtained data on (a) Pressure and (b) temperature distribution.

3.3. Numerical Stress Analysis

When designing an extrusion die, it is essential to investigate the mandrel support with

regard to its ability to absorb the generated loads, and minimize the possibility of failure

during die operation. A numerical stress analysis was conducted for one of the spider legs;

this part of the spider head is the weakest member of the mandrel support. The fluid structure

interaction solutions were used, which couple the continuum equations of solid mechanics

with the Navier-Stokes equations of fluid mechanics. The COMSOL Multiphysics® code was

employed to solve these equations simultaneously over the same computational domain using

an Arbitrary Lagrangian-Eulerian formulation.

In the ALE method, material and mesh displacements are separated; mesh distortion and

entanglement of elements is eliminated and the mesh can move arbitrarily. The concept of

ALE finite element analysis was originally developed for application in fluid structure

interaction problems, and was later adopted for solid mechanics applications (Hughes, Liu

and Zimmermann, 1981; Ganvir et al, 2007; Zhuang, Xiang and Zhao, 2010).

ALE method handles the dynamics of the deforming geometry and the moving

boundaries with a moving grid. COMSOL Multiphysics®

computes new mesh coordinates on

the channel area based on the movement of the structure’s boundaries and mesh smoothing.


The Navier-Stokes equations that solve the flow are formulated for these moving coordinates.

The structural mechanics portion of the model does not require the ALE method, and

COMSOL Multiphysics® solves it in a fixed coordinate system as usual.

The fluid flow in the channel is described by the Navier-Stokes equations, solving for the

velocity field u (u, v) and the pressure, p:

(11)

(12)

where I is the unit diagonal matrix, and F is the volume force affecting the fluid. The model

neglects gravitation and other volume forces affecting the fluid, so F = 0. Navier-Stokes

equations are solved in the spatial, deformed coordinate system. At the inlet, the model uses a

fully developed laminar flow. Zero pressure is applied at the outlet. At all other boundaries,

no-slip conditions are considered, i.e. u = 0. The problem is solved in transient state so the

spider leg commences from an undeformed state. It is worth noticing that the fluid flow

velocity coincides with the velocity of the deforming spider leg.

Structural deformations are solved by using elastic formulation and nonlinear geometry

formulation to allow large deformations. As boundary conditions, the spider leg is fixed to the

lower and upper ring of the spider so that it cannot move in any direction. All other

boundaries experience a load from the fluid, given by:

(13)

where n is the normal vector to the boundary. This load represents a sum of pressure and

viscous forces. In addition, the predefined fluid load takes the area effect between the

reference frame for the solid and the moving ALE frame in the fluid into account. The

Navier-Stokes equations are solved on a freely moving deformed mesh, which constitutes the

fluid domain. The deformation of this mesh relative to the initial shape of the domain is

computed using Winslow smoothing. This is the default smoothing when using the Fluid-

Structure Interaction interface.

The mesh of the spider leg is illustrated in Figure 6(a) and consists of 8732 tetrahedral

elements with unstructured mesh with maximum element size 2.36∙10-3

mm and minimum

element size 1.01∙10-4

mm; flow mesh is illustrated in Figure 6(b) and consists of 62412

tetrahedral elements with the same element size. The combination of the above two meshes is

illustrated in Figure 6(c).

The results of the analysis are presented in Figures 7(a) and (b). The extrusion die was

manufactured using IMPAX tool steel, with a yield stress of 8∙102

MPa. Based on the

analysis, the maximum stress developed on the spider legs during the extrusion, which

corresponds to maximum flow rate of the molten polymer, is 14.79∙10-2

MPa. The equivalent

stresses obtained using the von Mises yield criterion, are significantly lower than the material

yield stress and, therefore, it may be concluded that the above mentioned tool steel is suitable

for manufacturing spider dies for polymer extrusion applications. The total displacement as

determined by the ALE model is 2.12∙10-6

mm. Finally the pressure drop of the flow channel

is computed and illustrated in Figure 8.


Figure 6. (a) Spider leg mesh, (b) fluid flow mesh and (c) combination of two meshes.

Figure 7. (a) Total displacement and (b) equivalent stress distributions on the spider leg.


Figure 8. Pressure drop in spider leg.

4. RESULTS AND DISCUSSION

Generally speaking, the pressure drop results from the experimental, analytical and

numerical results exhibit very little discrepancies. The pressure data derived by the numerical

Carreau–Yasuda model indicate a good agreement with the experimental results; 97.24 bar

for the former and 95.15 bar for the latter, just over 2% difference between the two values.

Pressure drop, as calculated by the analytical model, is 92.17 bar, approximately 3% lower

than the actual experimental results. This can be explained by the fact that the analytical

model simplifies the pressure drop calculation in cases of complex geometries.

Bulk temperature rise of the molten polymer taken from the model is 1.53 K, which is

approximately 11% higher than the experimental temperature value, which is 1.72K.

Maximum bulk temperature rise of the analytical model presents a value of 4.72 K which is

quite higher than the corresponding temperature obtained experimentally. In order to test the

adiabatic boundary conditions assumption of the analytical model, a second FEM model is

created. This corresponds to adiabatic boundary conditions, i.e. no heat flux, and the bulk

temperature rise of the molten polymer is considerably higher than the experimental value,

namely 6.7K. It is worth noticing that both FEM models, i.e. with constant wall temperature

and without heat flux, exhibit exactly the same pressure drop. The results of the analytical and

the numerical models suggest that the constant wall temperature assumption gives better

results.

The comparison between the experimental and non-isothermal or non-Newtonian die

flow simulation appears to reveal the expected—good agreement with the overall pressure

drop and good agreement with the constant wall temperature boundary conditions, because

the effect of the viscous energy dissipation is small, resulting in a slight cup-average

temperature rise, hardly affecting the wall temperature. A summary of the analytical,


experimental, and numerical results reported in the current work including the pressure drop

and temperature rise in the die, is presented in Table 5.

Table 5. Analytical, Numerical and Experimental Data

Analytical

Carreau – Yasuda

(Numerical)

Constant Wall

Temperature

Carreau – Yasuda

(Numerical)

No Heat

Flux

Experimental

dP (bar) 92.17 97.24 97.24 95.15

dT (K) 4.72 1.53 6.67 1.72

Figure 9 illustrates the pressure drop percentage through the die zones of both the

numerical and the analytical model. It is obvious that the majority of the pressure drop is

observed along the zone V, at the exit of extrusion die.

Figure 9. Analytical and numerical results pertaining to pressure drop percentage through

the die zones.

The equivalent stresses, obtained through the von Mises yield criterion, are significantly

lower than the material yield stress and, therefore, it may be concluded that the above

mentioned tool steel is suitable for manufacturing spider dies for polymer extrusion

applications.

CONCLUSION

Summarizing the main features of the results reported, it may be concluded that the

proposed models can predict the pressure drop in the extruder die with success. Although

there is significant difference comparing the numerical and analytical models with regard to


the temperature rise in the fluid during the extrusion process, this can be explained by the fact

that the analytical model is based on the assumption that adiabatic conditions occur, which

means that there is no heat transfer between the wall and the polymer material as described

above. On the other hand, the numerical analysis assumes constant temperature of the die

wall, which is a boundary condition very close to what actually occurs during the real

extrusion process, thus providing reliable predictions of the conditions within the extrusion

die during polymer processing.

Finally, it was demonstrated by the stress analysis, that the die construction is strong

enough to withstand the pressure developed during the die operation and that the stresses do

not exceed the material yield strength in any case.

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Manufacturing and Modeling of an Extrusion Die Spider Head for the Production of HDPE Tubes

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