|
|
|
|
   
|
||||||
|
|
Three-dimensional simulation of multi-material injection molding: Application to gas-assisted and co-injection molding
INSIGHT INTRODUCTION
Gas-assisted injection and co-injection molding are increasingly used since they present many advantages over traditional injection molding. Gas-assisted injection molding requires lower injection- packing pressure, smaller cooling times and less material resulting in smaller part weight. Gas-assisted molded parts present more uniform properties, reduced shrinkage, warpage and residual stresses. Therefore, better final products are produced at lower costs. Co-injection has the potential of providing optimal properties of the molded part by using a proper combination of the skin and core materials. It may also reduce part weight, part cost, injection pressure, residual stresses and warpage comparing with the traditional single material injection molding. The popularity of gas- assisted and co-injection molding has been increasing as recent developments in machines, materials and design concepts have made the processes more flexible and useful. Multi-material molding involves injection of a polymer that forms the skin of the part, followed by the injection of a second material, which forms the core of the part. In co-injection, a second polymer is injected to complete the filling of the cavity, (usually in the core of the part). For gas-assisted injection molding (GAIM), gas is injected instead of a core material, thus generating a void inside the part. Getting the proper combination of materials into the same cavity makes multi-material molding more difficult. For these processes, very often the successful design involves a long trial and error route. Accurate simulations of the process behavior can help the part manufacturer to reach near optimal designs and generate substantial savings in both time and money. Until now, little has been done in terms of computer modeling and simulation for such processes. As for traditional injection molding, the first attempts were based on simplifying hypotheses that could not represent the full 3D nature of the phenomena observed, thus limiting their predictive capabilities. The numerical simulation of those processes is mostly based on the Hele-Shaw model, an approximation well suited to model creeping flows confined between thin walls (1-5). For parts presenting thick sections, expansions, contractions, sudden changes in direction, etc. such an approach is inappropriate. Even for thin parts, a 2.5D approach may be a rough approximation in processes such as co-injection or GAIM; the penetration of a gas or a second polymer into a partially filled cavity is clearly a three-dimensional phenomenon. In many applications, it is important to provide not only the depth of the gas or core polymer penetration, but also details on the core shape and polymer skin thickness. Therefore, a true three-dimensional solution of the injection process is needed (6, 7). This paper presents numerical simulations of gas-assisted and co- injection molding problems. The work reported here is based on earlier papers by the authors (8-12). The finite element solution of the complete 3D equations describing the flow and heat transfer is obtained. The procedure provides the evolution of the polymer/air and core/skin interfaces and the final shape and depth of the core. The influence of different parameters is analyzed and their effect on the predictions quantified. The proposed procedure is effective for thin parts as well as for thick 3D cavities. The resolution of the true 3D mold-filling problem allows the computation of accurate and detailed information regarding the shape and the size of the core material, as well as the thickness of the skin. Those results are especially useful in critical regions such as near corners, obstacles, or in regions presenting changes in part thickness. A robust and accurate solution algorithm will also provide the framework for detailed analysis of the role played by different parameters determining the final characteristics of the part. In such a way the prediction of an optimal design of the process using simulation is a realizable task. PHYSICAL MODEL The equations governing the incompressible melt flow are the Stokes and continuity equations 0 = - [nabla]p + [nabla] [middot] (2[eta][gamma] ), (1) - [nabla] [middot] u = 0 (2) where [gamma] = ([nabla]u + ([nabla]u)^sup T^)/2 is the shear stress tensor. Heat transfer is modeled by the energy equation: In the above equations, t, u, p, T, [rho], [eta], c^sub p^, and k denote time, velocity, pressure, temperature, density, viscosity, specific heat and thermal conductivity respectively. The polymer/air and skin/core interfaces are modeled using a pseudo-concentration method (13). The approach defines smooth functions F^sub i^ (x, t) such that the critical value, F^sub c^, represents the position of the interface. We consider i = 1 and i = 2 for the polymer/air and skin/core interfaces, respectively. A front tracking value greater than F^sub c^ denotes a region filled by the tracked material (i.e. skin polymer, core polymer or gas), while a value smaller than F^sub c^ corresponds to an unfilled region. As two interfaces are present, the various combinations are summarized in Table 1. The pseudo-concentration functions are transported using the velocity field provided by the solution of the momentum-continuity equations: Table 1. Definition of Filled (Skin/Core) and Empty Regions. Boundary conditions must complete the statement of the problem. No-slip boundary conditions are imposed on the cavity walls filled by the polymer, while on the unfilled part, a free boundary condition allows for the formation of the typical fountain flow. The heat transfer between the cavity and the mold is given by q^sub m^ = h^sub c^(T - T^sub m^) on [Gamma]^sub mold^ (5) where h^sub c^ is a surface heat transfer coefficient and T^sub m^ is the mold temperature. FINITE ELEMENT SOLUTION PROCEDURE At each time step, the global system of equations is solved in a partly segregated manner. The solution algorithm is illustrated in Fig. 1. The momentum-continuity equations are solved by a mixed velocity-pressure finite element method. Continuous piecewise linear elements are used for all variables (14). Details on the solution algorithm and the finite element formulation can be found in reference (15). APPLICATIONS Gas-Assisted Injection Molding This application consists of the gas-assisted injection of a rectangular plate with a flow channel on the longitudinal axis as shown in Fig. 2. This problem was the object of an experimental and numerical study by Gao et al. (3). Dimensions of the molded plate in Fig. 2 are shown in mm. Material properties correspond to a high- density polyethylene (HDPE). Results were reported by the authors in reference (15) for the viscosity modeled by the Cross-WLF. In the present case a modified Carreau-WLF model describes the viscosity dependence upon the shear rate and temperature: Computations were performed in order to quantify the solution dependence on various parameters as melt temperature, mold temperature, gas pressure, polymer/gas volume ratio, and gas injection delay. The computational parameters, namely melt temperature T^sub melt^, mold temperature T^sub mold^, gas pressure p^sub gas^, and gas volume, are summarized in Table 3. For each case, three series of computations were performed: (a) gas injected with no delay, (b) with a one-second delay, and (c) with a four- second delay, respectively. For the given polymer injection speed, complete filling of the part would take 1 second. The cavity/mold heat transfer coefficient was taken h^sub c^ = 4kW/(m^sup 2^ [middot] [degrees]C). The results for the gate pressure at the end of the polymer injection, gas injection time and the length of the gas core are listed in Table 3. Fig. 1. Solution algorithm. Case 1 is considered a reference against which the other cases are compared. This way, the effect of different parameters on the solution behavior is quantified. Figure 3 shows the solution at the end of the gas injection for case 1. The plot was made in transparency in order to make visible the gas region inside. Gas corresponds to the darkest region and mainly follows the central channel. When gas injection is delayed, the cooling of the plate is such that the gas does not penetrate laterally in the thin plate region. Therefore, gas penetration in the flow leader is more profound. The length of the gas core is 42% longer when gas injection is delayed by four seconds than on the case with no delay. The gas injection time is also affected. When part temperature decreases, the viscosity increa\ses, causing a slower polymer flow. For a gas delay time of four seconds, the gas injection time increases by a factor of almost three compared to the case without delay time. Figure 4 illustrates the shape of the gas bubble at different positions along the flow leader. The solution on the top is for case 1(a), followed by the solutions for cases 1(b) and 1(c). When gas is injected with no delay, gas penetrates in the thin plate. Increasing the gas injection delay results in lower temperatures and, hence, higher viscosities. Therefore, the gas enters mostly through the flow leader and penetration into the thin section is eliminated. For case 2, the melt temperature is increased to 270[degrees]C. The polymer, being at higher temperature, becomes less viscous. This effect can be observed on the gate pressure at the end of polymer injection, which decreases from 62.7 MPa in case 1 to 52.1 MPa in case 2. Therefore, the gas penetrates more in the thin regions of the plate. Results listed in Table 3 indicate that melt temperature influences less the length of the gas core but has larger impact on the gas penetration time. Meanwhile, with an increase in the mold temperature (case 3), the time injection delay exhibits little change, while the length of the gas core varies more significantly. The explanation of this behavior is that gas injection time is determined by the core polymer viscosity, which in turns depends on the melt temperature. The length of the gas core depends on the skin polymer thickness, which is influenced mostly by the mold temperature. Comparing cases 1, 2 and 3, we observe that for the same gas injection delay, the gas injection time varies in the same way as the gate pressure at the end of polymer injection. This is as expected because for the same gas pressure, the gas injection time depends on the polymer viscosity, which in turns is proportional to the polymer pressure. Fig. 2. Geometry for the gas-assisted injection molding of a rectangular plate. Case 4 is completed in order to evaluate the influence of the gas pressure. The gas pressure is increased to 34.5 MPa, twice the pressure in the reference case. For the case with one-second delay, the gas pressure determines little change in the length of the gas channel. Remark that the gas pressure directly affects the gas injection duration. Gas injection takes more time at lower gas pressure. We expect that for a gas pressure below a critical value, the gas injection duration will be so long that the cooling of the polymer will cause an incomplete filling. In case 5, the volume of gas injected is increased from 8% to 10%. As expected, the length of the gas core increases by almost 25% (see case 1(a) compared with 5(a), and 1(b) compared with 5(b)). The gas injection time exhibits little change. In case 5(c), the gas occupies the entire length of the channel when only 98.22% of the part is filled. At this point, the gas penetrates into the thin plate near the end of the central channel, producing gas fingering. Figure 5 shows the final gas penetration for case 5(c) and the mid- plane temperature distribution at the end of the plate filling. On the temperature plot, the dark color region corresponds to lower temperature, while the light color region has a higher temperature. As expected, the temperature is larger on the flow channel that has greater thickness and where the polymer flows at higher velocity. High temperatures are also observed at the end of the plate because this part fills late and presents less cooling time. Table 2. Material Properties for HDPE. Table 3. Simulation Cases for the Thin Plate. A summary of the effect of different processing parameters on the gas injection time and gas bubble length is shown in Table 4. Faster gas injection is obtained for increased melt or mold temperature and increased gas pressure. A larger temperature results also in thinner polymer skin and a shorter length of the gas bubble. The results are similar to those obtained by using a 3D model and the Cross-WLF model for the polymer viscosity (15). The solution of Gao et al. (3), obtained from a 2.5D approach, indicates a larger gas penetration into the thin plate than observed experimentally, and does not provide any information on the gas core shape. The present 3D solution overcomes this deficiency and is a clear improvement over the 2.5D model. Fig. 3. Gas penetration for case 1 with various gas injection delays. The solution algorithm is applied also to a thick part corresponding to a car door handle. Material properties are as for the previous application. The polymer is injected at 260[degrees]C and the mold is at 50[degrees]C. The gas injection starts when the polymer fills 75% of the cavity. Figure 6 shows the solution for different positions during the gas injection. Here again, the polymer is shown in transparency and the darker region indicates the gas core. The algorithm performs well and provides the final form of the gas penetration inside the polymer. Fig. 4. Gas core shape at different locations for cases 1(a), 1(b) and 1(c) (x denotes the distance in mm along the flow leader from the gate). Fig. 5. Solution for case 5(c). (a) Gas fingering at the end of the channel, (b) Mid-plane temperature distribution at the end of gas injection. Table 4. Effect of Processing Parameters on Gas Injection. Co-Injection Molding The three-dimensional solution procedure is applied also to solve co-injection
molding problems. The first case consists of a center- gated rectangular
plate. The plate is illustrated in Fig. 7 with all dimensions shown in
mm. The material used here was ABS. Viscosity is modeled with the Cross-WLF
model: Model constants are summarized in Table 5. Fig. 6. Gas-assisted injection molding of a car door handle. The melt temperature was considered either at 250[degrees]C or 220[degrees]C, while the mold temperature was 70[degrees]C or 20[degrees]C. Injection speed was considered constant and filling of the part was completed in 9.14 sec. An initial set of computations was made considering the same material for both the skin and the core. Solutions were obtained for 15%, 25%, and 35% core/skin volumetric ratio, respectively. Table 6 summarizes the processing parameters and results obtained for the core penetration inside the cavity. Fig. 7. Co-injection: Geometry of the rectangular plate. Figure 7 illustrates the solution obtained for case 1. The skin polymer is plotted in transparency in order to allow the core to be visible. As can be seen, the core material advances more rapidly in the direction corresponding to the plate length. Because the plate fills first in the width, the core penetrates less in this direction. The front view in Fig. 7 shows that core shape is three- dimensional. Material enters the cavity from the top and generates different skin polymer thicknesses at the top and bottom of the cavity. Final solutions for cases 1, 2 and 3 are compared in Fig. 8. The melt/mold temperatures are 250[degrees]C/70[degrees]C and core/ skin ratio is varied from 15% to 35%. As more core material is injected in the cavity, the core penetrates deeper inside the skin. Core penetration changes mostly in the length of the plate as the filling during core injection occurs mostly in this direction. Solutions for case 3 at different instants during the filling are shown in Fig. 9. Front view figures are shown on the left side, and top view figures are plotted on the right. The 3D solution of the co- injection process is able to predict core shape in all directions. Most important, the residual skin thickness is computed and critical regions can be identified. In this case, a thin polymer skin is predicted in the region of the gate. The hot polymer is directed into the opposite wall and the skin thickness is very small at this location. Far from the center, the core polymer penetrates by the mid-plane and the skin thickness is almost the same on top and bottom of the part. Co-injection conditions of case 1 were reconsidered this time with different viscosities for skin and core. Two runs were performed for which the skin viscosity was the same as on the previous computations, while the core viscosity was varied. The solution corresponding to a core viscosity 100 times lower than that of the skin is shown in Fig. 10b, while the solution for a core viscosity 10 times higher is shown in Fig. 10c. Because the core material is injected when the skin fills part of the cavity, the core advances through the path of less resistance. In the case of a skin much more viscous than the core, the skin opposes most of the resistance to the flow. Therefore, core penetration is faster in the longitudinal direction toward the free surface, while the core advances at a lower speed in the transversal direction. As can be observed in Fig. 10, the result is opposite when the core material has a higher viscosity. The core causes most of the resistance to the flow, and therefore, the core material has closer to a circular shape around the injection point. Table 5. Cross-WLF Model Constants for ABS. Table 6. Simulation Results for the Co-Injection of a Rectangular Plate. Fig. 8. Co-injection of a plate - Effect of the skin/core ratio. Fig. 9. Co-injection of a plate - Filling pattern for case 3. The second co-injection application is the filling of a C-shaped plate. This problem was the object of an experimental and numerical analysis by Turng and Wang (4). Polypropylene resin with different colors was used for skin and core. The polymer viscosity was computed from the Cross model equation (9) with an Arrhenius temperature dependence of the form: Material properties and model constants are summarized in Table 7. Filling of the part was completed in 0.65 second, while the switchover
time from skin to core was 0.47 second. Melt/mold temperatures were 235[degrees]C/27[degrees]C.
Fig. 10. Effect of the core/skin polymer viscosities o\n the core penetration. Figure 11 illustrates the skin and core filling pattern for the three-dimensional solution. Remark that the core material fills through the path of less resistance. Therefore the flow is accelerated near corners, and the low-velocity regions remain filled with the skin material. Note also that the core flows through the middle of the plate and therefore this front advances faster than the skin flow front. Figure 12 shows that the 3D solution compares extremely well with the experiment of Turng and Wang (4) and is a clear improvement over the 2.5D solution. The numerical approach of Turng and Wang (4) was based on the Hele-Shaw approximation. Therefore the non-slip condition and the mold-wall temperature were not imposed along the lateral boundaries. Consequently, their work cannot predict the thin layer of skin material formed along the inner lateral boundary. The present 3D approach is able to predict the residual skin thickness at any point and provides the full shape of the core material inside the part. CONCLUSION This work presents a three-dimensional finite element method for solving the gas-assisted injection molding and co-injection molding processes. The procedure provides the evolution of the polymer/air and skin/core interfaces and the final shape and depth of the core material. For gas-assisted injection, the influence of different parameters was analyzed and their effect on the numerical solution was quantified. The solution depends on such various molding conditions as melt temperature, gas pressure, polymer/gas ratio, and gas injection delay. Part defects, as incomplete filling and gas fingering, are predicted. The solution is very sensitive and an optimal setting of processing parameters is difficult to obtain. Table 7. Material Properties for Polypropylene. Fig. 11. Co-injection of a C-shaped plate. For co-injection molding, solutions were presented for a center- gated plate at different melt/mold temperatures and ratios of the skin/core materials. The influence of different viscosities for skin and core was also investigated. The solution for a C-shaped plate illustrates the net advantage of 3D simulation over the 2.5D approach. The proposed procedure works in the same manner for thin parts and for thick three-dimensional parts. The solution method is effective in both cases and is of special interest when dealing with parts presenting thick sections for which mid-plane approximations are not valid. It is able to deal with changes in part thickness or flow direction, and provides all the needed information concerning skin thickness and core shape. Fig. 12. Comparison of 3D solution with experimental data and 2.5D solution of Turng and Wang (4) (2.5D solution shows contours of the skin thickness as ratio of the plate thickness; maximum value is 1.0 with increments of 0.05). This paper was presented at "Emerging Technologies for the New Millennium," held in Montreal, Dec. 10-11, 2001. REFERENCES 1. S. C. Chen, N. T. Cheng, and K. S. Hsu, Int. J. Mech. Sci., 38, 335 (1995). 2. T. Wang, H. Chiang, X. Lu, and L. Fong, SPE ANTEC, 44, 447 (1998). 3. D. M. Gao, K. T. Nguyen, A. Garcia-Rejon, and G. Salloum, Int. Polymer Proc., 12, 267 (1997). 4. L. S. Turng and V. W. Wang, SPE ANTEC, 37, 297 (1991). 5. S. C. Chen and K. F. Hsu, Num. Heat Transfer, Part A, 28, 503 (1995). 6. R. E. Khayat, A. Derdouri, and L. P. Herbert, J. Non- Newtonian Fluid Mech., 57, 253 (1995). 7. G. Haagh, H. Zuidema, F. V. de Vosse, G. Peters, and H. Meijer, Int. Polymer Proc., 12, 207 (1997). 8. F. Ilinca and J.-F. Hetu, SPE ANTEC, 46, 444 (2000). 9. F. Ilinca and J.-F. Hetu, Proc. MOLDING 2001. Exec. Conf. Managem., 10 p. (2001). 10. F. Ilinca, J.-F. Hetu, and A. Derdouri, Proc. MOLDING 2001, Exec. Conf. Managem., 10 p. (2001). 11. F. Ilinca and J.-F. Hetu, 17th An. Meet. Polymer Proc. Soc., Montreal (21-24 May 2001). 12. F. Ilinca and J.-F. Hetu, Proc. SPE Topical Conf., Emerging Technologies for the New Millennium, 201 (2001). 13. F. Ilinca and J.-F. Hetu, Inter. J. Num. Methods in Fluids, 34, 729 (2000). 14. F. Ilinca and J.-F. Hetu, Proc. 1998 ASME Fluids Eng. Div. Sum. Meeting, FEDSM-4931 (1998). 15. F. Ilinca and J.-F. Hetu, Inter. J. Num. Methods in Engng., 53, 2003 (2002). FLORIN ILINCA* and JEAN-FRANCOIS HETU Industrial Materials Institute, National Research Council 75 de Mortagne, Boucherville, Quebec, Canada, J4B 6Y4 *E-mail: florin.ilinca@nrc.ca
Did you find this material interesting? Comment via FEEDBACK
Source: Source:
Polymer Engineering and Science
Have
you seen the great deals from top brand
name manufacturers? You haven't?
|
|
|
|
