Book 7x10 - Template - version_15

Journal of Manufacturing Technology Research Volume 6, Number 1-2, pp. 1-15

ISSN: 1943-8095 © 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 threedimensional 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]

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

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 …

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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 M12x7512.9 DIN 912, (12) four screws M12x120-12.9 DIN 912, (13) four screws M12x5012.9 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 steadystate 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.

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

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 CarreauYasuda 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.


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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.

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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 Elastic modulus Poisson's ratio Shear modulus Mass density Tensile strength Yield strength Thermal expansion coefficient Thermal conductivity Specific heat

Value 2.0∙105 MPa 0.33 7.3∙104 MPa 7.8∙103 kg/m³ 9.2∙102 MPa 8.0∙102 MPa 1.3 10-5 per 0C 43 W/m.K 440 J/kg.K


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Table 2. Density and melt flow rate of HDPE Parameter

Value 0.16 dg/min (at 190 0C, 2.16 Kg) 0.89 dg/min (at 190 0C, 5.00 Kg)

Melt Flow Rate (MFR) (ISO 1133)

23.00 dg/min (at 190 0C, 21.6 Kg) 958 kg/m3

Density (ISO 1183)

Table 3. Shear rate and viscosity of HDPE Shear Rate (1/s) at 190 °C

Viscosity (Pa∙s)

12 23 58 115 230 565

4770 3426 1991 1301 836 443

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

.

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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 n n0 λ Eo TR α

Value 0.2723 5.43∙103 Pa∙s 0.063 s 6.5 kcal/mol 190 0C 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


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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.

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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 FluidStructure 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.

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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,


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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 dP (bar) dT (K)

92.17 4.72

Carreau – Yasuda (Numerical) Constant Wall Temperature 97.24 1.53

Carreau – Yasuda (Numerical) No Heat Flux 97.24 6.67

Experimental 95.15 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

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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.

REFERENCES Choudhary M.K and Kulkarni J.A. (2008), “Modeling of three-dimensional flow and heat transfer in polystyrene foam extrusion dies”, Polymer Engineering and Science, 48(6), 1177-1182. Davim J.P. (Ed.) (2011), “Machining of Hard Materials”, Springer-Verlag London. Ganvir V., Lele A., Thaokar R. and Gautham B.P. (2007), “Simulation of visco-elastic flows of polymer solutions in abrupt contractions using an arbitrary Lagrangian Eulerian (ALE) based finite element method”, Journal of Non-Newtonian Fluid Mechanics, 143,157–169. Gonçalves N.D., Carneiro O.S. and Nóbrega J.M. (2013), “Design of complex profile extrusion dies through numerical modeling”, Journal of Non-Newtonian Fluid Mechanics, 200, 103-110. Huang G.-Q and Huang H.-X. (2007), “Optimizing parison thickness for extrusion blow molding by hybrid method”, Journal of Materials Processing Technology, 182(1-3), 512518. Hughes J.R., Liu W.K. and Zimmermann T.K. (1981), “Lagrangian-Eulerian finite element formulation for incompressible viscous flows”, Computer Methods in Applied Mechanics and Engineering, 29, 329-349. Kaiyuan C., Nanqiao Z., Bin L. and Shengping W. (2009), “Effect of vibration extrusion on the structure and properties of high-density polyethylene pipes”, Polymer International, 58(2), 117-123. Kundrák J., Ráczkövi L. and Gyáni, K. (2014), “Machining performance of CBN cutting tools for hard turning of 100Cr6 bearing steel”, Applied Mechanics and Materials, 474, 333-338. Lebaal N., Schmidt F and Puissant S. (2009), “Design and optimization of three-dimensional extrusion dies, using constraint optimization algorithm”, Finite Elements in Analysis and Design, 45(5), 333-340. Mamalis A.G., Kouzilos G. and Vortselas A.K. (2011), “Design Feature Sensitivity Analysis in a Numerical Model of an Extrusion Spider Die”, Journal of Applied Polymer Science, 122, 3537–3543. Mamalis A.G., Spentzas K.N., Kouzilos G., Theodorakopoulos I. and Pantelelis N.G. (2010), “On the high-density polyethylene extrusion: Numerical, analytical and experimental modeling”, Advances in Polymer Technology, 29(3), 173-184.


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Matin I., Hadzistevic M., Hodolic J., Vukelic D. and Lukic D. (2012), “A CAD/CAEintegrated injection mold design system for plastic products”, The International Journal of Advanced Manufacturing Technology, 63(5-8), 595-607. Michaeli, W. (2003), “Design and Engineering Computation”, 3rd ed. Hanser Publishers, Munich. Shahreza A.R., Behravesh A.H., Jooybari M.B. and Soury E. (2010), “Design, optimization, and manufacturing of a multiple-thickness profile extrusion die with a cross flow”, Polymer Engineering and Science, 50(12), 2417-2424. Sztankovics I. and Kundrák, J. (2014), “Determination of the chip width and the undeformed chip thickness in rotational turning”, Key Engineering Materials, 581, 131-136. Zhu X.Z, Xie Y.J and Yuan H.Q (2007), “Numerical Simulation of Extrusion Characteristics for Co-rotating Tri-Screw Extruder”, Polymer-Plastics Technology and Engineering, 46(4), 401-407. Zhuang C., Xiang H. and Zhao Z. (2010), “Analysis of Sheet Metal Extrusion Process Using Finite Element Method”, International Journal of Automation and Computing, 7(3), 295302.