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 2 © 2007 Carl Hanser Verlag, München 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 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 3 © 2007 Carl Hanser Verlag, München 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 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. Zeitschrift Kunststofftechnik 3 (2007) 3 4 © 2007 Carl Hanser Verlag, München www.kunststofftech.com Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern. 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 Zeitschrift Kunststofftechnik 3 (2007) 3 5 © 2007 Carl Hanser Verlag, München 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 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 Zeitschrift Kunststofftechnik 3 (2007) 3 6 © 2007 Carl Hanser Verlag, München 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 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. Zeitschrift Kunststofftechnik 3 (2007) 3 7 © 2007 Carl Hanser Verlag, München 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 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]. Zeitschrift Kunststofftechnik 3 (2007) 3 8 © 2007 Carl Hanser Verlag, München 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 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 9 © 2007 Carl Hanser Verlag, München 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 Zeitschrift Kunststofftechnik 3 (2007) 3 10 © 2007 Carl Hanser Verlag, München 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 Ltg. 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