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APCBEE Procedia 5 (2013) 468 – 473

ICESD 2013: January 19-20, Dubai, UAE

Simulation of Blow Molding Using Ansys Polyflow Shubham Gupta, Vikram Uday, Amit Singh Raghuwanshi, Samarth Chowkshey, Shakti Nath Das and S. Suresh Department of Chemical Engineering, Maulana Azad National Institute of Technology (MANIT) Bhopal, Madhya Pradesh - INDIA

Abstract Blow Molding is one of the most versatile and economical process available for molding hollow materials. When polyethylene is stretched, it exhibits strain-hardening properties, which are temperature, pressure, velocity and strain-rate dependent. In this paper, preform is made by extrusion and forced between two halves by pressurisation. This process includes isothermal and transient flow of newtonian fluid in complex geometries simultaneous with structuring and solidification. A time dependent problem is defined and setting material properties and boundaries condition for a 2D axisymmetric bottle blow molding. Numerical data available in POLYDATA for a time dependent problem using ANSYS POLYFLOW were applied. Results display in form contours associated with different variables at different time steps and good agreement with the bottle thickness profile is observed.

© 2013 Published by Elsevier B.V. Selection and/or peer review under responsibility of Asia-Pacific Chemical,

© 2013 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license. Biologicaland & peer Environmental Engineering Society Selection review under responsibility of Asia-Pacific Chemical, Biological & Environmental Engineering Society Keywords: Blow Molding; Ansys; Polyflow;bottle;thickness;application

1. Introduction ANSYS Polyflow software provides advanced fluid dynamics technology for solving various tasks in the polymer, glass, metals and cement processing industries [1]. It is used extensively to design and optimize processes such as extrusion, thermoforming, blow molding, glass forming, fiber drawing and concrete shaping. The design engineers have used ANSYS POLYFLOW software for more than 25 years to minimize physical prototyping when manufacturing extrusion dies or to reduce thickness variation to improve the quality of thermoformed or blown products [2]. Because of a unique inverse die design capability, dies can be cut much faster than with the traditional build-andtest method. This translates into substantial cost reduction and time savings. The quality of the blown and

Corresponding author. Tel.: +918989005393. E-mail address: [email protected]

2212-6708 © 2013 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license. Selection and peer review under responsibility of Asia-Pacific Chemical, Biological & Environmental Engineering Society doi:10.1016/j.apcbee.2013.05.079

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

469

thermoformed products is improved by running trial-and-error processes with ANSYS Polyflow rather than testing changes on the production line [3]. Glass forming and float glass engineering simulation help designers to more quickly produce higher-quality tableware, glass containers and flat glass. Cesar de Sa [4] simulated the blowing process of glass parisons assuming Arrhenius temperature dependent Newtonian behavior. Chung [5] has carried out simulations of PET stretch/blow molding using the code ABAQUS®. The model assumes elasto-visco-plastic behavior and thermal effects are neglected. Poslinski and Tsamopoulos [6] have introduced non-isothermal parison inflation in a simplified geometry. In order to take into account the phase change, the latent heat of solidification has been included in the heat capacity of the material. Recently, Debbaut et al. [7] have also performed viscoelastic blow molding simulations with a Giesekus constitutive equation. They introduce thermal effects but present numerical results only in the case of a Newtonian fluid. The problem deals with the cavity filling stage of the molding process and it is assumed that a preform has been positioned inside the mold. The contact between the fixed mold and the preform is considered. A large pressure is applied to the preform which enters the mold and eventually takes its shape. The operating conditions must account for a low pressure drop at the entrance, low material waste, and slow cooling to avoid premature solidification of the preform. 1.1. Simulation procedures Ansys Polyflow Project schematic consists of five sections, Design Modular, Meshing, Setup, Solution Result [410]. Designing cylindrical perform geometry of above mentioned dimensions Meshing up the geometry. Setup consists of the polydata which includes conditions and property settings. In solution, post processing settings, selecting of colour and variable are done with different time steps. Results display in form contours associated with different variables at different time steps. In blow molding simulations, numerical models have to take into account large deformations of the material, the evolving contact between tools (mold and stretch rod) and polymer, and temperature gradients. Table 1 shows stretch/blow molding process, the contact between the stretch rod and the bottom of the preform induces localized deformations which need volumetric approaches in order to obtain an accurate description. 1.2. ANSYS Polyflow Project Symmetric Geometry: With geometry integration solutions from ANSYS, existing native CAD geometry can be used directly, without translation to IGES or other intermediate geometry formats. Meshing: Multi-zone meshing combines the strength of various meshing tools to automatically generate a blow moulding system into small parts. Setup (Polydata): Used for assigning different parameters value and mathematical expressions into use. Solution: By the means of mathematical iteration and energy equations used to get the relations of different parameters for effectiveness. Result: Contours of different parameters are graphically represented and their relations with the dependant variables at every mesh of the structural geometry. Geometry consists of the four boundaries Boundary 1 : symmetric axis Boundary 2 : free surface Boundary 3 : zero normal velocity and zero surface velocity Boundary 4: free surface

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Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

Table 1. Numerical Parameters for iterative scheme

Numerical parameters Initial time value Upper tine unit Initial value of the time step Min admissible value of the time-step Max admissible value of the time-step Tolerance for time marching Max number of successful steps Use of the implicit Euler method for the integration No prediction of velocity field Upper Level Menu Modify the initial time value Modify the upper time value Modify the initial value of the time step Modify the minimum value of time step Modify the maximum value of time step Modify the tolerance Modify the maximum value of successful steps

values 0.0000000E+00 1.0000000E+00 1.0000000E-02 1.0000000E-04 2.5000000E-01 1.0000000E-02 200 -

1.3. SETUP (Polydata) 1.3.1. Time step control associated with tool contact monitoring The geometry of the tools (stretch rod and mold) is defined by a piecewise linear approximation. At time step t, the velocity field allows one to determine the future trajectory of each node. One can then compute the intersection of each trajectory with the tools. The smallest of these intersection times is then retained as the value to be used for the next time step . 1.3.2. Automatic remeshing With an updated Lagrangian formulation, the nodes of the mesh following the kinematic evolution of the material points. This method may result in excessively distorted elements, when large deformations occur. An automatic remeshing procedure is used [8]. For each time interval, the procedure consists in the following steps: Here we define the model governed, providing data of material, setting boundary conditions then remeshing, setting up the numerical parameters, fixing the number steps in outputs, finally setting thickness postprocessors. Model: 2D axisymmetry time dependent model. Mold is adiabatic and flow of perform is isothermal Newtonian [8]. Material data: Viscosity is constant and time dependent on shear stress. Viscosity =100000 poise. Density = 1gm/cm3; Gravity =-981 gm/cm2. Boundary condition: Setting the slip co-efficient=1e+09. Penalty co-efficient =1e+09. Normal force =-2e06 Remeshing: Defining the master moving surface. Sub domain is defined and selecting the interaction with boundary 2. Numerical parameter: Number of steps=200, tolerance=1e-01, max value of time step=1e-03, min value of time step=1e-07 Outputs: Number of steps=10 Thickness Postprocesser: boundary 2 as starting border and boundary 4 as the ending border. 2. Author Artwork Figs. 1a-c show the comparison between thickness and the stretching force vs. time (i.e. the force exerted on the moving plane which is related to the stress in the x-direction). The agreement is fair. The curve for the stretching force

471

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

starts from zero, then reaches a maximum and decreases continuously. We note that when the relaxation time increases, the thickness of the tube decreases more rapidly and the initial slope of the stretching force decreases.

(a)

(b)

(c)

Fig. 1. (a) Contour of thickness at time step 50, t=0.04925s. (b) Contour of thickness at time step 80, t= 0.59898s.(c)Contour of thickness at time step 123, t=.1s.

We pointed out that the computed stretching force using a Newtonian volumic model was very far from the experimental one. In the present work, an isothermal finite element volumic calculation of the PET stretch/blow molding is presented. The improvement in terms of force prediction will be shown. Thickness and stress profiles in the bottle will be discussed. In this paper, a splitting technique is presented. At each time step, an iterative procedure based on a fixed-point method is used. The first sub-problem, deals with an incompressible Newtonian fluid flow, perturbed by a known extra-stress tensor computed at the previous fixed-point iteration. The second sub problem consists in determining the components of the extra-stress tensor for a known velocity vector by solving the time-discretized constitutive equation. Fig. 2a-b shows the geometry of the bottle mold and the initial mesh of the preform and presents intermediate bottle shapes from the beginning of the process to the end. Figs. 1a-c presents the thickness distribution vs. longitudinal coordinate at the end of the process. A zoom of the neck and the bottom of the bottle shows the stress distribution at the end of the process. In cleary indicates that at the end of the process, the bottom of the bottle is submitted to high stresses.

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Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

Fig. 2. a, Overall Velocity distribution. b, Overall Pressure distribution at Time step 123,t=.1s.

Fig. 3. a, Velocity x gradient distribution. b, Final Velocity distribution time step 123, t=.1s

Fig. 3a-b shows velocity of the stretch rod which is applied as long as the preform contacts the bottom of the mold, Pressures is the maximum pre-blowing pressure (low pressure) imposed during step time 123s with maximum blowing pressure (high pressure). 3. Summary The present study deals with the cavity filling stage of the molding process and time-dependent problem with 2D axisymmetric geometry. An optimization of the preform shape could be performed in order to minimize the weight of the bottle while avoiding weak (too thin) bottle walls. Results showed that most suited for contact detection problems with more accurately solve a timedependent problem. The volumic mechanical computations using the finite element method have allowed us to predict the thickness

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

distribution, the contact kinetic and the stress distribution.

Acknowledgements Our thanks to MANITB for providing necessary facilities and to Ministry of Human Resource Development, Government of

India for financial support. Nomenclature A Height of the preform = 7 cm B Cylindrical Preform , internal radius =2cm, outer radius=3c C Density =1gm/cm3. D Viscosity = 100000 poise. E Inertia and gravity are taken in consideration References [1] ANSYS, Inc , Basic analysis procedures guide release 5.5, http://www.ansys.com [2] Pham X-T., F. Thibault, L-T. Lim, Modeling and simulation of stretch blow molding of polyethylene terephthalate. Polymer Engineering & Science. 2004: 44(8), 1460 1472. [3] Schmidt, F.M., J.F. Agassant, M. Bellet, L. Desoutter, Viscoelastic simulation of PET stretch/blow molding process.J. Non-Newtonian Fluid Mech.1996:64, 19-42 [4] Cesar de Sa J.M.A., Numerical modelling of glass forming processes, Eng. Comput., 3, December 1986. [5] Chung K., Finite element simulation of PET stretch/blow-molding process, J. Mater. Shap. Tech., 7 (4) (1989) 229 239. [6] Poslinski A.J. and J.A. Tsamopoulos, Nonisothermal parison inflation in blow molding, AIChE J., 36 (12) (1990). [7] Debbaut B., B. Hocq and J.M. Marchal, Numerical simulation of the blow moulding process, ANTEC '93, May 1993. [8] Paleti Srinivas, Sambana Krishna Chaitanya Datti Rajesh Kumar, Finite Element Analysis Using Ansys 11.0 [9] Saeed Moaveni, Finite Element Analysis Theory and Application with ANSYS [10] http://www.ansys.com/Products/Simulation+Technology/Fluid+Dynamics/ANSYS+Polyflow [11] http://www1.ansys.com/customer/webinars/polyflow.htmlhttp://www.leapaust.com.au/products/simulation-and-analysis/ansys-cfd/ansyspolyflow.html [12] http://www.ansys.com/Industries/Materials+&+Chemical+Processing/Polymer+Processing/Blow+Molding [13] http://www.ansys.com/en_be/Training+Center/Belgium+Training+Courses/ANSYS+POLYFLOW+Blow+Molding

Appendix: A A.1, Slip coefficient and Penalty coefficient 1e+09 = 8103.08 A.2, Normal force -2e06 = -806.8575 A.3, Max value of time step1e-03= .04978 A.4 Min value of time step 1e-07 =0.00091 A.5 Tolerance 1e-01= .9900

473

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APCBEE Procedia 5 (2013) 468 – 473

ICESD 2013: January 19-20, Dubai, UAE

Simulation of Blow Molding Using Ansys Polyflow Shubham Gupta, Vikram Uday, Amit Singh Raghuwanshi, Samarth Chowkshey, Shakti Nath Das and S. Suresh Department of Chemical Engineering, Maulana Azad National Institute of Technology (MANIT) Bhopal, Madhya Pradesh - INDIA

Abstract Blow Molding is one of the most versatile and economical process available for molding hollow materials. When polyethylene is stretched, it exhibits strain-hardening properties, which are temperature, pressure, velocity and strain-rate dependent. In this paper, preform is made by extrusion and forced between two halves by pressurisation. This process includes isothermal and transient flow of newtonian fluid in complex geometries simultaneous with structuring and solidification. A time dependent problem is defined and setting material properties and boundaries condition for a 2D axisymmetric bottle blow molding. Numerical data available in POLYDATA for a time dependent problem using ANSYS POLYFLOW were applied. Results display in form contours associated with different variables at different time steps and good agreement with the bottle thickness profile is observed.

© 2013 Published by Elsevier B.V. Selection and/or peer review under responsibility of Asia-Pacific Chemical,

© 2013 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license. Biologicaland & peer Environmental Engineering Society Selection review under responsibility of Asia-Pacific Chemical, Biological & Environmental Engineering Society Keywords: Blow Molding; Ansys; Polyflow;bottle;thickness;application

1. Introduction ANSYS Polyflow software provides advanced fluid dynamics technology for solving various tasks in the polymer, glass, metals and cement processing industries [1]. It is used extensively to design and optimize processes such as extrusion, thermoforming, blow molding, glass forming, fiber drawing and concrete shaping. The design engineers have used ANSYS POLYFLOW software for more than 25 years to minimize physical prototyping when manufacturing extrusion dies or to reduce thickness variation to improve the quality of thermoformed or blown products [2]. Because of a unique inverse die design capability, dies can be cut much faster than with the traditional build-andtest method. This translates into substantial cost reduction and time savings. The quality of the blown and

Corresponding author. Tel.: +918989005393. E-mail address: [email protected]

2212-6708 © 2013 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license. Selection and peer review under responsibility of Asia-Pacific Chemical, Biological & Environmental Engineering Society doi:10.1016/j.apcbee.2013.05.079

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

469

thermoformed products is improved by running trial-and-error processes with ANSYS Polyflow rather than testing changes on the production line [3]. Glass forming and float glass engineering simulation help designers to more quickly produce higher-quality tableware, glass containers and flat glass. Cesar de Sa [4] simulated the blowing process of glass parisons assuming Arrhenius temperature dependent Newtonian behavior. Chung [5] has carried out simulations of PET stretch/blow molding using the code ABAQUS®. The model assumes elasto-visco-plastic behavior and thermal effects are neglected. Poslinski and Tsamopoulos [6] have introduced non-isothermal parison inflation in a simplified geometry. In order to take into account the phase change, the latent heat of solidification has been included in the heat capacity of the material. Recently, Debbaut et al. [7] have also performed viscoelastic blow molding simulations with a Giesekus constitutive equation. They introduce thermal effects but present numerical results only in the case of a Newtonian fluid. The problem deals with the cavity filling stage of the molding process and it is assumed that a preform has been positioned inside the mold. The contact between the fixed mold and the preform is considered. A large pressure is applied to the preform which enters the mold and eventually takes its shape. The operating conditions must account for a low pressure drop at the entrance, low material waste, and slow cooling to avoid premature solidification of the preform. 1.1. Simulation procedures Ansys Polyflow Project schematic consists of five sections, Design Modular, Meshing, Setup, Solution Result [410]. Designing cylindrical perform geometry of above mentioned dimensions Meshing up the geometry. Setup consists of the polydata which includes conditions and property settings. In solution, post processing settings, selecting of colour and variable are done with different time steps. Results display in form contours associated with different variables at different time steps. In blow molding simulations, numerical models have to take into account large deformations of the material, the evolving contact between tools (mold and stretch rod) and polymer, and temperature gradients. Table 1 shows stretch/blow molding process, the contact between the stretch rod and the bottom of the preform induces localized deformations which need volumetric approaches in order to obtain an accurate description. 1.2. ANSYS Polyflow Project Symmetric Geometry: With geometry integration solutions from ANSYS, existing native CAD geometry can be used directly, without translation to IGES or other intermediate geometry formats. Meshing: Multi-zone meshing combines the strength of various meshing tools to automatically generate a blow moulding system into small parts. Setup (Polydata): Used for assigning different parameters value and mathematical expressions into use. Solution: By the means of mathematical iteration and energy equations used to get the relations of different parameters for effectiveness. Result: Contours of different parameters are graphically represented and their relations with the dependant variables at every mesh of the structural geometry. Geometry consists of the four boundaries Boundary 1 : symmetric axis Boundary 2 : free surface Boundary 3 : zero normal velocity and zero surface velocity Boundary 4: free surface

470

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

Table 1. Numerical Parameters for iterative scheme

Numerical parameters Initial time value Upper tine unit Initial value of the time step Min admissible value of the time-step Max admissible value of the time-step Tolerance for time marching Max number of successful steps Use of the implicit Euler method for the integration No prediction of velocity field Upper Level Menu Modify the initial time value Modify the upper time value Modify the initial value of the time step Modify the minimum value of time step Modify the maximum value of time step Modify the tolerance Modify the maximum value of successful steps

values 0.0000000E+00 1.0000000E+00 1.0000000E-02 1.0000000E-04 2.5000000E-01 1.0000000E-02 200 -

1.3. SETUP (Polydata) 1.3.1. Time step control associated with tool contact monitoring The geometry of the tools (stretch rod and mold) is defined by a piecewise linear approximation. At time step t, the velocity field allows one to determine the future trajectory of each node. One can then compute the intersection of each trajectory with the tools. The smallest of these intersection times is then retained as the value to be used for the next time step . 1.3.2. Automatic remeshing With an updated Lagrangian formulation, the nodes of the mesh following the kinematic evolution of the material points. This method may result in excessively distorted elements, when large deformations occur. An automatic remeshing procedure is used [8]. For each time interval, the procedure consists in the following steps: Here we define the model governed, providing data of material, setting boundary conditions then remeshing, setting up the numerical parameters, fixing the number steps in outputs, finally setting thickness postprocessors. Model: 2D axisymmetry time dependent model. Mold is adiabatic and flow of perform is isothermal Newtonian [8]. Material data: Viscosity is constant and time dependent on shear stress. Viscosity =100000 poise. Density = 1gm/cm3; Gravity =-981 gm/cm2. Boundary condition: Setting the slip co-efficient=1e+09. Penalty co-efficient =1e+09. Normal force =-2e06 Remeshing: Defining the master moving surface. Sub domain is defined and selecting the interaction with boundary 2. Numerical parameter: Number of steps=200, tolerance=1e-01, max value of time step=1e-03, min value of time step=1e-07 Outputs: Number of steps=10 Thickness Postprocesser: boundary 2 as starting border and boundary 4 as the ending border. 2. Author Artwork Figs. 1a-c show the comparison between thickness and the stretching force vs. time (i.e. the force exerted on the moving plane which is related to the stress in the x-direction). The agreement is fair. The curve for the stretching force

471

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

starts from zero, then reaches a maximum and decreases continuously. We note that when the relaxation time increases, the thickness of the tube decreases more rapidly and the initial slope of the stretching force decreases.

(a)

(b)

(c)

Fig. 1. (a) Contour of thickness at time step 50, t=0.04925s. (b) Contour of thickness at time step 80, t= 0.59898s.(c)Contour of thickness at time step 123, t=.1s.

We pointed out that the computed stretching force using a Newtonian volumic model was very far from the experimental one. In the present work, an isothermal finite element volumic calculation of the PET stretch/blow molding is presented. The improvement in terms of force prediction will be shown. Thickness and stress profiles in the bottle will be discussed. In this paper, a splitting technique is presented. At each time step, an iterative procedure based on a fixed-point method is used. The first sub-problem, deals with an incompressible Newtonian fluid flow, perturbed by a known extra-stress tensor computed at the previous fixed-point iteration. The second sub problem consists in determining the components of the extra-stress tensor for a known velocity vector by solving the time-discretized constitutive equation. Fig. 2a-b shows the geometry of the bottle mold and the initial mesh of the preform and presents intermediate bottle shapes from the beginning of the process to the end. Figs. 1a-c presents the thickness distribution vs. longitudinal coordinate at the end of the process. A zoom of the neck and the bottom of the bottle shows the stress distribution at the end of the process. In cleary indicates that at the end of the process, the bottom of the bottle is submitted to high stresses.

472

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

Fig. 2. a, Overall Velocity distribution. b, Overall Pressure distribution at Time step 123,t=.1s.

Fig. 3. a, Velocity x gradient distribution. b, Final Velocity distribution time step 123, t=.1s

Fig. 3a-b shows velocity of the stretch rod which is applied as long as the preform contacts the bottom of the mold, Pressures is the maximum pre-blowing pressure (low pressure) imposed during step time 123s with maximum blowing pressure (high pressure). 3. Summary The present study deals with the cavity filling stage of the molding process and time-dependent problem with 2D axisymmetric geometry. An optimization of the preform shape could be performed in order to minimize the weight of the bottle while avoiding weak (too thin) bottle walls. Results showed that most suited for contact detection problems with more accurately solve a timedependent problem. The volumic mechanical computations using the finite element method have allowed us to predict the thickness

Shubham Gupta et al. / APCBEE Procedia 5 (2013) 468 – 473

distribution, the contact kinetic and the stress distribution.

Acknowledgements Our thanks to MANITB for providing necessary facilities and to Ministry of Human Resource Development, Government of

India for financial support. Nomenclature A Height of the preform = 7 cm B Cylindrical Preform , internal radius =2cm, outer radius=3c C Density =1gm/cm3. D Viscosity = 100000 poise. E Inertia and gravity are taken in consideration References [1] ANSYS, Inc , Basic analysis procedures guide release 5.5, http://www.ansys.com [2] Pham X-T., F. Thibault, L-T. Lim, Modeling and simulation of stretch blow molding of polyethylene terephthalate. Polymer Engineering & Science. 2004: 44(8), 1460 1472. [3] Schmidt, F.M., J.F. Agassant, M. Bellet, L. Desoutter, Viscoelastic simulation of PET stretch/blow molding process.J. Non-Newtonian Fluid Mech.1996:64, 19-42 [4] Cesar de Sa J.M.A., Numerical modelling of glass forming processes, Eng. Comput., 3, December 1986. [5] Chung K., Finite element simulation of PET stretch/blow-molding process, J. Mater. Shap. Tech., 7 (4) (1989) 229 239. [6] Poslinski A.J. and J.A. Tsamopoulos, Nonisothermal parison inflation in blow molding, AIChE J., 36 (12) (1990). [7] Debbaut B., B. Hocq and J.M. Marchal, Numerical simulation of the blow moulding process, ANTEC '93, May 1993. [8] Paleti Srinivas, Sambana Krishna Chaitanya Datti Rajesh Kumar, Finite Element Analysis Using Ansys 11.0 [9] Saeed Moaveni, Finite Element Analysis Theory and Application with ANSYS [10] http://www.ansys.com/Products/Simulation+Technology/Fluid+Dynamics/ANSYS+Polyflow [11] http://www1.ansys.com/customer/webinars/polyflow.htmlhttp://www.leapaust.com.au/products/simulation-and-analysis/ansys-cfd/ansyspolyflow.html [12] http://www.ansys.com/Industries/Materials+&+Chemical+Processing/Polymer+Processing/Blow+Molding [13] http://www.ansys.com/en_be/Training+Center/Belgium+Training+Courses/ANSYS+POLYFLOW+Blow+Molding

Appendix: A A.1, Slip coefficient and Penalty coefficient 1e+09 = 8103.08 A.2, Normal force -2e06 = -806.8575 A.3, Max value of time step1e-03= .04978 A.4 Min value of time step 1e-07 =0.00091 A.5 Tolerance 1e-01= .9900

473

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