Influence of Mesh Density on Injection Molding

Transcription

Influence of Mesh Density on Injection Molding
Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern.
www.kunststofftech.com
© 2007 Carl Hanser Verlag, München
Wissenschaftlicher
Arbeitskreis der
UniversitätsProfessoren der
Kunststofftechnik
Zeitschrift Kunststofftechnik
Journal of Plastics Technology
archivierte, rezensierte Internetzeitschrift des Wissenschaftlichen Arbeitskreises Kunststofftechnik (WAK)
archival, reviewed online Journal of the Scientific Alliance of Polymer Technology
www.kunststofftech.com; www.plasticseng.com
eingereicht/handed in: 07.12.2006
angenommen/accepted: 26.02.2007
Prof. Maria Vicoria Candal, Rosa Amalia Morales, Kathleen Gorrin,
Universidad Simón Bolívar, Departamento de Mecánica, Grupo de Polímeros,
Venezuela
Influence of Mesh Density on Injection Molding
Simulation Results
The principal objective of this work was to study the influence of the number of elements has on a finite element mesh’s (FEM) simulation results. The simula-tion results analyzed were weight, and
linear shrinkage along the length and width of a injected plastic specimen. Also, simulation results
were compared with results obtained from solids modeling software (CAD) and from a simulator
software (CAE). The convergence simulation results showed similar trends with the experimental
ones. The modeling mesh gives a faster convergence than the simulator one.
Einfluss der Netzdichte auf die Ergebnisse von
Spritzgießsimulationen
Das Hauptziel dieser Arbeit besteht in dem Studium des Einflusses der Num-mer von Elementen eines Finite-Elementen-Netzes (FEM) auf die Ergebnisse der Simulation. Die Ergebnisse der Simulation, die analysiert wurden, waren das Gewicht und die lineare Kontraktion in der Länge und Breite
Richtungen eines Kunststoffteiles, das durch Spritzgiessen hergestellt wurde. Die Ergebnisse, die mit
einem CAD-Netz erhalten wurden, wurden mit einem CAE-Netz verglichen. Die Simulationserbegnisse, die konvergiert wurden, haben ähnliche Tendenzen gezeigt wie die experimetellen Ergebnisse.
Die mit dem Modellierungsprogramm erhaltene Netze konvergieren schneller als die mit dem Simulationsprogramm erhaltene Netze.
Autor/author
Prof. Maria Vicoria Candal, Rosa Amalia Morales,
Kathleen Gorrin,
Universidad Simón Bolívar,
Departamento de Mecánica, Grupo de Polímeros,
Apartado 89000,
Caracas 1080-A, Venezuela
© Carl Hanser Verlag
E-Mail-Adresse: [email protected]
Zeitschrift Kunststofftechnik/Journal of Plastics Technology 3 (2007) 1
Influence of Mesh Density on Injection
Molding Simulation Results
Influence of Mesh Density on Injection Molding
Simulation Results
Maria Vicoria Candal, Rosa Amalia Morales, Kathleen Gorrin,
Universidad Simón Bolívar, Departamento de Mecánica, Grupo de Polímeros,
Venezuela
The principal objetive of this work was to study the influence of the number of
elements has on a finite element mesh’s (FEM) simulation results. The simulation results analyzed were weight, and linear shrinkage along the length and
width of a injected plastic specimen. Also, simulation results were compared
with results obtained from solids modeling software (CAD) and from a simulator
software (CAE). The convergence simulation results showed similar trends with
the experimental ones. The modeling mesh gives a faster convergence than the
simulator one.
Das primäre Ziel dieser Arbeit war es, den Einfluss der Anzahl von Elementen
in einem Finite-Elemente-Netz (FEM) auf die Ergebnisse einer Simulation zu
untersuchen. Die analysierten Ergebnisse waren das Gewicht und die Längenund Breitenkontraktion eines Spritzgießbauteils. Die Ergebnisse bei Verwendung eines CAD-Netzes wurden mit denen eines CAE-Netzes verglichen.
Die Konvergenz der Simulationsergebnisse zeigte vergleichbare Trends wie die
experimentellen. Die Netze aus dem Modellierungsprogramm konvergierten
schneller als die aus dem Simulationsprogramm erzeugten Netze.
© 2007 Carl Hanser Verlag, München
www.kunststofftech.com
Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern.
M.V. Candal et. al.
Zeitschrift Kunststofftechnik 3 (2007) 3
1
© 2007 Carl Hanser Verlag, München
www.kunststofftech.com
Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern.
M.V. Candal et. al.
1
Influence of Mesh Density on Injection
Molding Simulation Results
INTRODUCTION
Nowadays, the search of greater productivity and improvement in the product
quality, by the manufacturers, of plastic components has lead to the rapid development of computer aided engineering (CAE) and computer aided design
(CAD) systems. There exist plenty of software available in the market that give
numerous advantages to the design and manufacturing areas, as well as to the
engineering area by means of the computerized simulation of different processes.
Development of CAD tools for polymers has been carried out since the early
80´s, and since those days it has been considered the main source of predictive
engineering. The tools, part of this category, are known as flow analysis. They
allow specialist Engineers to create a prototype of one piece or mold for specific
processes.
During the last ten years, the use of polymers in manufacturing and the demand
of the quality improvement of the molded pieces has increased rapidly, giving
as a result, a greater interest in the mathematical modeling of the mold injection
process. The first software packages allowed the users to determine the basic
processing conditions (temperature injection, mold temperature and injection
time), and to balance the flow in the cavities and mold cooling system. For that,
the package required a flat model of the selected piece to reduce the fluid problem from 3-D to 2-D. However, during the years the use of CAD software has
considerably developed. Among recent advances is the introduction of the Finite Element Method, FEM, which is considered as an important improvement of
the molding injection simulation. The benefits in the development of the simulation software of the injection process are not only found in the filling mold phase, but also in the cooling phase and in the shrinkage and warpage analysis.
Moreover, alternative methods such as injection assisted by gas, coinjection
and thermostabile materials injection, among others are introduced.
Now it is more common to use CAD and CAE for modeling a variety of processes. In the plastic industry these resources are mostly used in the simulation of
the injection process. Generally, those tools carried out a numerical analysis
through FEM, allowing for engineers to obtain reliable results. Chan et al [1]
analyzed the cooling system of a complex panel car using the Fast Finite Elements Method (FFEM) to determine the mold temperatures distribution, in this
way the warpage analysis can be performed. Chan et al concluded that the cooling system was well optimized, and they also proved that the suggested method gives an excellent performance calculation without convergence problems
even in the most complicated cases.
Specifically, CAE tools use a numerical analysis of the designed model in order
to predict the real behavior of the piece. One of the numerical techniques more
widely used in the science and engineering field is the Finite Element Method
(FEM). Basically, this technique requires the idealization of a real physical problem into a mathematical model, transforming the structure into various eleZeitschrift Kunststofftechnik 3 (2007) 3
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M.V. Candal et. al.
Influence of Mesh Density on Injection
Molding Simulation Results
ments, all of which are connected by a nodes [2]. Then, the model is resolved
with a great algebraic equation system.
FEM is a numerical procedure to resolve complex engineering problems. Important considerations should be taken into account to provide accurate analysis of
the results and the numerical solution convergence [3], and to understand the
convergence process that leads the numerical method closer to the exact solution. The convergence in FEM can be obtained by two different ways: refinement of the mesh (greater number of elements) known as convergence-h, where the “h” term stands for the size of the element side that is reduced giving rise
to a finer discretization, and increase in the polynomial degree of equations
known as convergence-p [4].
Wang [5] focused his attention on studying the limitations of the CAE software
for the simulation of an injection molding process. This investigator modeled a
part with different meshes, to show that the results of air-trap depend on the
elements employed. Also, Villarroel et al [6] studied the effect of the number of
elements in the simulation of injection molded pieces. They found that when the
number of elements increased, the time for obtaining simulation results also
increased, but with a better convergence in the values obtained. Morales et al
[7] studied some results of the CAE software for the simulation of an injection
molding process where a convergence was obtained by means of increasing
the number of elements. Such areas of interest are: wall shear stress, cycle
and filling times.
Furthermore, Jawoski and Yuan [8] discussed the advantages and disadvantages of four different mesh types (1D, 2.5D, modified 2.5D, and 3D) in simulation
of the injection process through theoretical and experimental data. They compared the reality of the simulation, the injection of a rack, with each type of mesh
to demonstrate how the acceptance of the different types of mesh can affect the
accuracy of the filling analysis results. Jawoski and Yan found that the simulation results with 2.5-D meshes and 2.5-D modified meshes, particularly for this
piece, are not precise in the tooth section, while simulations for filling pattern
with elements 1-D and 3-D are precise.
This work has the purpose of studying the influence of the modification of the
characteristics of a finite element mesh (elements number, distribution, and size) and of the CAD/CAE tools for its generation, on the results of weight and
linear shrinkage along the length and width of the piece, obtained by the simulation of the injection molding process. This analysis was done for two different
materials, one amorphous and one semi-crystalline.
2
METHODOLOGY
A homopolymer PP J600 from Propilven (MFI = 7.0 g/10 min at 230 ºC) and a
HIPS 4320 from Estirenos del Zulia (MFI = 8.5 g/10 min at 200 ºC) were used.
Both materials are injection molding grades.
Zeitschrift Kunststofftechnik 3 (2007) 3
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M.V. Candal et. al.
Influence of Mesh Density on Injection
Molding Simulation Results
Such materials are Venezuelan national production, and they cannot be found
in the data base of the simulator software. In order to overcome this limitation, a
rheological characterization was executed, since the analysis requires accuracy
on the data of materials properties, so the best predictions can be generated
[9].
Melt capillary flow properties for both materials were measured using a capillary
rheometer, Rheograph Model 2000, at several crosshead speeds. Tests were
done at 190ºC, 210ºC, and 230ºC for the PP and 170ºC, 190ºC, and 210ºC for
the HIPS with a length/diameter ratio (L/D) of 30/1, 20/1, 10/1, and 5/1. Afterwards, a plastometer was used in order to measure the Melt Flow Indexes of
both materials, ASTM D3835 and D1238 procedures were followed.
Bagley and Rabinowitsch corrections were done. The Cross, exponential of
hydraulic loss and William-Landel-Ferry, WLF, models were also employed to
calculate the specific constants for both materials in order to include them in the
simulator software. Then, simulation of the injection molding process of a normalized tensile test specimen type I was done. This was performed with 3-D
solids modeler software. Figure 1 shows the mold employed. For simulation,
processing conditions found to be optimal for the experimental injection process
of the specimens were used. Moreover, results convergence of wall shear
stress, cycle and filling times, were verified. Simulation time was recorded for all
simulations, with the meshes of the modeling software as well as with the simulation software.
Figure 1: Representation of a mold for injection of normalized tensile test
specimen type I
Specimen mesh was done with nine different models, varying the elements
number, using both programs with a midplane meshing (2 ½ mesh), and triangular elements. The filling, cooling, and solidification of the mold were simulated, and the convergence of the results of weight and lineal shrinkage along the
length and width of the piece as a function of the element number of the mesh
was studied.
The number of elements studied is presented in Table 1.
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M.V. Candal et. al.
Table 1:
Influence of Mesh Density on Injection
Molding Simulation Results
Elements Number using fort he study
Specimens were injection molded experimentally in search of the optimum processing conditions. An injection molding machine with a clamping force of 100
ton was used. Such specimens were weighed in a digital balance with an accuracy of 0.01 g. Also, length and width of each specimen were measured by
means of a digital Vernier with an accuracy of 0.01 mm, 1 h and 24 h after
being injection molded, as suggested by ASTM D955 procedure.
3
RESULTS AND DISCUSSION
Simulation software of an injection molding process include analysis of the filling
stage, where accuracy on the data of materials properties is very important, since the reproduction of best predictions by the simulation depends on this fact
[9]. Thus, a rheological characterization of the materials employed was executed since they are not reported in the software data base.
Semi-crystalline polymers as well as amorphous polymers have complex thermo-rheological behaviors, which influence significantly the injection molding
process. Thermoplastic materials exhibit non-Newtonian properties in the flow
behavior, their melt viscosity decreases when shear rate or temperature increases. Besides, injection molded pieces are generally thin-walled, so high injection rates are needed in order to fill the mold, with the subsequent generation of
high shear stresses, and dynamical changes in polymer properties while it flows
[10].
There exist various models employed by these software in order to describe the
resin behavior under different processing variables. The Cross and WLF models
permit the simulation of the filling and post-filling stages of the injection molded
piece, since they incorporate the dependency of the viscosity with shear rate
and with temperature. Another model employed is the exponential of hydraulic
loss for the filling stage, which calculates the loss occurred when the melt passes along a very small but long diameter, from the end of the channel to the
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M.V. Candal et. al.
Influence of Mesh Density on Injection
Molding Simulation Results
entrance of the cavity [9]. From these models, different rheological constants
required by the software so simulation could take place, were calculated.
Afterwards, injection molding of normalized tensile specimens type I was done,
thus obtaining the optimum processing conditions for each material under study.
Injection molding temperature for PP was 210 ºC while for HIPS it was 190 ºC.
Injection and packing/holding pressures were similar (800 psi). Cooling time
used for PP specimens was 18 s and 33 s for HIPS specimens. Weight and lineal shrinkage along the length and width of each specimen were measured 1 h
and 24 h after being injection molded.
Simulation of the injection molding process followed, for both materials under
the processing conditions mentioned above. Firstly, values of the specimen
weight were compared. Figures 2 (left) and (right) show the convergence of the
last four runs for this result.
Figure 2: Weight convergence for (a) PP and (b) HIPS
left:
right:
Polypropylene
High Impact Polystyrene
When comparing theoretical results reported by the software with the experimental data, it can be noticed that they do not vary significantly for the specimen weight, as seen in Table 2. The difference between both values is slightly
higher for HIPS (3.44% between simulation and experimental values, and
3.476% between modeler and experimental values). While for the semicrystalline polymer the difference is unnoticeable (0.0641% and 0.0595% in the meshes created by the simulator and modeler respectively).
Weight (g)
Material
Experimental
Polypropylene
21.840 ± 0.026
21.854
21.853
High Impact
Polystyrene
27.150 ± 0.010
26.216
26.206
Table 2:
Simulator Software
Modeler Software
Weight of the normalized tensile test specimen
Also, it can be observed that theoretical values obtained from the meshes of the
modeller resemble more to the machine results, since this mesh better copies
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M.V. Candal et. al.
Influence of Mesh Density on Injection
Molding Simulation Results
the details of the specimen due to its capability for modifying size and position
of the triangles employed. The user can locate more element density where a
more exhaustive study is required. However, with the CAE meshes only the
number of elements can be chosen and the software distributes them equally
along the specimen.
Other result evaluated, related to the quality of the molded piece and its dimensional stability, was the shrinkage percentage. The linear shrinkage along the
length of the specimen after demolding and 24 h afterwards was measured. An
increasing tendency on contraction was observed when element number increased, Figure 3 left and right. Convergence was found on the last four meshes,
resulting values of 0.01482 mm for PP and 0.0038 for HIPS.
Figure 3: Linear shrinkage along lenght convergence
left:
right:
Polypropylene
High Impact Polystyrene
When comparing the shrinkage values of PP and HIPS (Table 3), it was found
that the smaller percentage corresponds to the amorphous material HIPS. This
finding agrees with the values reported in the literature for this material (0.004 0.007 mm/mm) [10]. In this type of material, the chain mobility is not enough for
forming crystals, thus contraction is not favored.
Linear shrinkage along the length
(mm/mm)
Material
1h
24 h
Polypropylene
0,014191
0,015822
High Impact Polystyrene
0,002433
0,004500
Table 3:
Linear shrinkage along lenght fort he normalized tensile test
specimen
In addition, the tendency on shrinkage along the width of the specimen is presented, obtaining the same behavior explained previously, Figure 4 left and
right.
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M.V. Candal et. al.
Influence of Mesh Density on Injection
Molding Simulation Results
Figure 4: Linear shrinkage along width convergence fort he (a) PP and (b)
HIPS
left:
right:
Polypropylene
High Impact Polystyrene
Concerning the simulation time, possible differences between the simulation
with a mesh obtained from modeler software and a mesh obtained from simulator software, were studied. There were no clear differences in the run time (Figure 5), probably due to the fact that the element size in both meshes was very
similar. Figure 6 illustrates the more dense meshing of specimens created with
each software. It can be seen that elements of similar size exist in the majority
of the part. Moreover, the number of elements compared for both types of meshes was also similar (Table 1).
Figure 5: Run Time vs Elements Number
left:
right:
Polypropylene
High Impact Polystyrene
Figure 6: Density Mesh maked with
up:
down:
Simulator Software
Modeler Software
The results obtained for the correlation of simulation time with increasing element number agree with Villarroel's et al conclusion that run time increases with
increasing number of mesh elements [6].
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M.V. Candal et. al.
Influence of Mesh Density on Injection
Molding Simulation Results
Other results from the simulation of the injection molding process were also verified. Similar results compared to those presented by Morales et al were found
[7]. By means of increasing the number of elements, the values of cycle time,
filling time and wall shear stress increased until a convergence was obtained.
This is evident for the amorphous and the semi-crystalline materials, and for
meshes made with the modeler and the simulator software. The type of specimen does not influence these results.
4
CONCLUSIONS
The semi-crystalline material presented convergence in the results faster than
its amorphous peer.
When increasing the number of elements for the simulation, the results of
weight and linear shrinkage along the length and width of the specimen are modified, increasing until convergence is reached, so an optimum mesh could be
chosen, combining results similar to reality and reducing simulation time.
The mesh of the modeler software exhibits a faster convergence than the simulator software, and its results are closer to experimental data.
The results from the simulation software using a mesh from the modeler program as well as a mesh from the simulation program about weight and shrinkage along the length and width of the specimen achieve a high accuracy compared to experimental data.
5
[1]
REFERENCES
[2]
Chang, R.,
Yang, W.,
Liu, L.,
Yanh, V.,
Hsu, D.
Cook, R.
[3]
Bathe, K.
[4]
Reddy, J.
Three-Dimensional Computer-Aided Mold
Cooling Design For Injection Molding
SPE´s ANTEC Proceedings, 2003, 656
Finite Elements Modeling for Stress Analysis
John Wiley & Sons Inc., USA, 1995
Finite Element Procedures
Prentice Hall, USA, 1996
An Introduction to the Finite Element Method
McGraw Hill, USA, 1993
Zeitschrift Kunststofftechnik 3 (2007) 3
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www.kunststofftech.com
Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern.
M.V. Candal et. al.
[5]
Wang, T.
[6]
Villarroel, S.,
Morales, R.,
Sanchez, A.
[7]
Morales, R.,
Candal, M.,
González, O.
[8]
Jaworski, M.,
Yuan, Z.
[9]
C-MOLD
[10] Mark, H.,
Bikales, N.,
Overberger, C.,
Menges G. (eds)
Influence of Mesh Density on Injection
Molding Simulation Results
Numerical Simulation and Process Window
design of Injection/Compression Molding
SPE´s ANTEC Proceedings, 1999, 658
Effect of the Mesh Number Elements in the
Simulation Results of Normalized Test
Specimens Injection Molded
SPE´s ANTEC Proceedings, 2002, w/p
Effect of the finite element meshing for
designing plastic pieces
Polymer Plastics Technology and
Engineering 44 (8-9), 1573 (2005)
Theoretical And Experimental Comparison
Of The Four Major Types Of Mesh Currently
Used In CAE Injection Molding Simulation
Software SPE´s ANTEC Proceedings, 2003,
w/p
C-MOLD Reference Manual
Advanced CAE Technology Inc., USA, 1998
Encyclopedia of Polymer Science and Engineering”
John Wiley & Sons, Vol. 16, USA, 1990
Keywords:
injection molding, mesh, computer aided design, engineer aided design,
software
Kontakt:
Autoren:
Prof. Maria Victoria Candal,
Rosa Amalia Morales,
Kathleen Gorrin
Herausgeber:
Prof. em. Dr.-Ing. Dr. h.c. Gottfried W. Ehrenstein,
Prof. Dr. Tim Osswald
Erscheinungsdatum:
Mai/Juni 2007
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www.kunststofftech.com
Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern.
M.V. Candal et. al.
Influence of Mesh Density on Injection
Molding Simulation Results
Herausgeber/Editor:
Europa/Europe
Prof. Dr.-Ing. Dr. h.c. G. W. Ehrenstein, verantwortlich
Lehrstuhl für Kunststofftechnik
Universität Erlangen-Nürnberg
Am Weichselgarten 9
91058 Erlangen
Deutschland
Phone:
+49/(0)9131/85 - 29703
Fax.:
+49/(0)9131/85 - 29709
E-Mail-Adresse: [email protected]
Amerika/The Americas
Prof. Dr. Tim A. Osswald, responsible
Polymer Engineering Center, Director
University of Wisconsin-Madison
1513 University Avenue
Madison, WI 53706
USA
Phone:
+1/608 263 9538
Fax.:
+1/608 265 2316
E-Mail-Adresse: [email protected]
Verlag/Publisher:
Carl-Hanser-Verlag
Jürgen Harth
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Fachbuchanzeigen und Elektronische Lizenzen
Kolbergerstrasse 22
81679 Muenchen
Tel.: 089/99 830 - 300
Fax: 089/99 830 - 156
E-mail: [email protected]
Beirat/Editorial Board:
Professoren des Wissenschaftlichen Arbeitskreises Kunststofftechnik/
Professors of the Scientific Alliance of Polymer Technology
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