Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble
On the Use of Comsol Multiphysics® to Understand and Optimize the Filling Phase in Injection and Micro-Injection Molding Process. M. Moguedet*1, P. Namy2 and Y. Béreaux3 1 2
Pôle Européen de Plasturgie, 2 rue Curie, 01100 - Bellignat- France *Corresponding author :
[email protected]
SIMTEC, 26 rue du pont Carpin, 38100 – Grenoble – France 3 LAMCOS UMR 5564, Site de Plasturgie INSA Lyon, 85 rue Becquerel, 00100 – Bellignat - France Abstract: The work presented here deals with the simulation of the cavity filling stage of the injection and micro-injection molding process, for thermoplastic materials. Within a research project lead by the Pôle Européen de Plasturgie on optimizing replication of micro-features on plastic parts, a challenge is to better understand physical phenomena during the process to optimize designs and process conditions. Comsol Multiphysics® gives us the means to take into consideration some other aspects usually neglected in commercial 3D softwares dedicated to polymer processing. In particular, tracking of the flow front is based on a Level Set approach. Results are presented for a Newtonian and non-Newtonian polymer, and in an isothermal or thermal dependant configuration. Calculations are compared to experimental results on a polypropylene. In a second part, surface tension effects are analyzed when filling micro-geometries. Computations show no effect, unless the flow front proceeds down to less than 1 mm/s. Finally, our work shows the extended possibilities of Comsol Multiphysics® to deal with multi-phase flow topics for the polymer processing community. Keywords: Injection molding, level-set, surface tension, microstructures.
1. Introduction The evolution of technologies since several decades is dominated by the race to miniaturization and complexity of objects. The increasing competition in the polymer processing industry makes us looking for new technologies to enlarge the possible applications and enter new markets. An important way for it is to understand and optimize micro-features replications on thermoplastics with the injection
molding process. The high rates and low costs, compared to other processes, allow for integrating new markets in micro-electronic, biomedical, optic or cosmetic for example, where micro-structured objects can play an important part. In this context, the Pôle Européen de Plasturgie (PEP, technical center dedicated to polymer processing) began three years ago a new research and development project called “Microstructure” which focuses on controlling conception and realization of micro-structured thermoplastic parts. However, the transposition of technology to the micro-scale level is not as direct, because models must account for effects neglected during macro injection, but which can have more influence in micro-features, such as thermal exchanges through lateral walls, important pressure gradients, specific rheological behavior, and also surface effects. Several 3D softwares do exist for injection molding simulations such as Moldflow®, Sigma3D®, Cadmould®, Rem3D®, SIMPOE®, Moldex®… They are well suited to help conception and design of molds and parts, but show limits when considering micro-geometries [1-5]. Indeed, some laboratories developed their home made FEM 3D softwares to better consider specific conditions of the micro-injection process, with flow front tracking methods such as pseudo-concentration, Volume Of Fluid (VOF), or Level-Set method. [6-13] Finally, when considering micrometric geometries, other modeling methods based on molecular dynamics have been studied, and in reference [14] reducing the flow channel size resulted in density fluctuations, an effect which is neglected by the continuum approach. When looking on the objectives of this “Microstructure” project, the first one considering simulation aspects was to establish surface tension impact on cavity filling, especially when reaching micro-features. The
Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble
use of Comsol Multiphysics® was the best way for us, for two reasons : - usual CAD softwares dedicated to polymer processing do not consider these effects, and do not allow for integrating other models, - our goal is definitely not to develop new software. In this work, the PEP, SIMTEC, a COMSOL Certified Consultant company, and INSA Lyon tackle a more theoretical aspect of microinjection molding, to better understand physics during the process, through numerical simulations of cavity filling. After having made simulations with commercial codes dedicated to injection-molding, we noticed, like in many literature articles, that the obtained results show differences with experiments, mainly because of the simpler models and hypothesis used to facilitate computations. Indeed, assumptions such as surface tension effects might have an importance on micro-cavity filling. As a consequence, we have decided to develop a two phase flow approach by the use of Comsol Multiphysics®. In a first step, a Level Set model is applied to several configurations: Newtonian and non-Newtonian fluid, with isothermal or non-isothermal considerations. Our simulations are compared to experimental results obtained on an industrial injection molding machine. In a second part, we show results of the filling of micro-features. We analyze the effects of surface tension. All these results show the extended possibilities of Comsol Multiphysics® to deal with multi-phase flow topics for the polymer processing network.
2. Governing equations To simulate numerically this model, a level set approach is coupled to the classical NavierStokes equations. This method is very well suited to describe the motion of an interface. ⎧ ∂u T ⎪ρ + ρu.∇u = ∇. − pId + η ∇u + (∇u ) + ρg + σκδn ⎪⎪ ∂t ∇.u = 0 ⎨ ⎡ ⎪ ∂Φ ∇Φ ⎤ + u.∇Φ = γ∇.⎢ε∇Φ − Φ(1 − Φ ) ⎥ ⎪ t ∂ ∇Φ ⎦ ⎣ ⎩⎪
[
(
)]
where ρ is the density, η the dynamic viscosity, Id the identity tensor, g the gravitational field, σ the surface tension coefficient, n the unit normal to the interface, κ = −∇.n the curvature of the fluid interface, δ a delta function concentrated at the interface between the fluids, u the velocity field (m/s), p the pressure (Pa) and ϕ is the characteristic function of the polymer ( ϕ (x, y ) = 1 if M (x, y ) is located inside the polymer, 0 otherwise). In this equation, the term σ.κ.nδ defines the surface tension forces. Non-slip conditions are applied on each boundary, except of those describing the exit of fluids (above and on the right) where the pressure is set to 0. For a newtonian fluid, the dynamic viscosity is assumed to be constant. For a non-newtonian fluid, the dynamic viscosity is assumed to follow the Cross’s law : η=
η0
. ⎛ η 0 γ ⎞⎟ ⎜ + 1 ( ) ⎜ τ * ⎟⎟ ⎜ ⎝ ⎠
( n −1)
where η 0 is the zero shear rate viscosity at a
given temperature, τ * and n are model parameters and γ& is the shear rate. When the influence of the temperature is taken into account, the temperature is described by the following convection and diffusion equation: ∂T ρC p + ρC pu.∇T − ∇.[k∇T ] = 0 ∂t where Cp is the heat capacity, k the thermal conductivity, and T is the temperature (K) in the medium. The temperature of the boundaries of the mold is set to Tmold, except for exit boundaries, where a convective flux condition is applied. Initially, the temperature of the mold is Tmold. The temperature of the injected polymer is Tinj. The influence of temperature is taken into consideration by a change in the polymer viscosity following an Arrhénius model : ⎡
⎛E⎛1
⎣⎢
⎝ R ⎝T
η = η0 ⎢exp⎜⎜ ⎜⎜
−
⎤ ⎛E⎛ 1 1 ⎞ ⎞⎟ 1 ⎞ ⎞⎟ ⎟ * (T > Tcrys ) + exp⎜ ⎜⎜ ⎟ ⎜ R Tcrys − T ⎟ ⎟ * (T ≤ Tcrys )⎥ T0 ⎟⎠ ⎟⎠ 0 ⎠⎠ ⎝ ⎝ ⎦⎥
where E is the activation energy, R the universal gas constant, and Tcrys the onset crystallization temperature of the polymer.
Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble
3. Methods
4. Injection-molding experiments
The following table describes the numerical values of functional parameters used in this paper, considering injection molding of a polypropylene PP 86MF97 from the Sabic company.
Injection molding is a common manufacturing technique for making thermoplastic parts at high rate of production. Polymer pellets are molten in a screw-barrel unit, and then injected at high speed and pressure with a translation movement of the screw to fill a mold cavity, which is the inverse of the product's shape. Then the part is cooled down, to finally eject the manufactured plastic part, and so on.
Parameter Density: ρ Dynamic viscosity (for Newtonian calculations) : η Gravitational field: g Surface tension coefficient: σ Reinitialization parameter: γ Parameter controlling interface thickness: ε Zero shear rate:
η0
Cross model parameter: τ* Cross model parameter: n Heat capacity: Cp Heat conductivity: k Temp. of the mold: Tmold Temp. of polymer: Tinj Injection flow rate
Unit Kg/m3 Pa.s
Num. Value for air 1.199
Num. Value for polymer 833
1e-5
50
m/s2
-9.82
N/m
0.073 N/m
m/s
0.1 ; 1
m
hmax
Pa.s
-
823.72 at 260°C
Pa
-
42419.7
-
-
0.2614
J/(Kg.K)
1100
2800
W/(m.K)
0.03
0.18
K
293
K
533
m3/s
The object presented on Figure 1 is made with a demonstration mold, which has been designed to test replication of micro-features on one side of the part, as shown on Figure 2. As our first simulations were carried out in classical injection-molding, the present part does not have any micro-features.
Figure 1. Picture of the part which filling is simulated.
8,04.10-6
Table 1 : Numerical values of functional parameters used in our simulations. The domain is meshed by 3014 nodes and 5635 triangle elements, corresponding to more than 50.000 DOF. Computations have been performed with the direct solver UMFPACK, COMSOL MULTIPHYSICS® version 3.3a.
Figure 2. Example of microfluidic design realized on the mold insert.
To compare our simulations to experimental results, we carried out incomplete injections : it consists in injecting different volumes of polymers, from the smallest, up to the volume necessary to fill completely the cavity. It usually brings important information on the way taken by the polymer to fill the mold cavity.
Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble
e r Figure 3. Axisymetric section of the polymer part, r going from 0 to 17,96 mm and e from 0 to 5,69 mm.
5. Simulation results and discussion 5.1 Newtonian isothermal model Results concerning a Newtonian viscosity are shown in Figure 5. The flow front profile is materialized by the isolevel ϕ = 0.5 , and the polymer is red colored. In this case Reinitialization parameter γ is set to 1. Computations with lower values (γ=0.1) show no significant differences with this case, except at the end of the cavity. Because of the non-slip boundary conditions, the polymer flows faster in the middle of the cavity. As the downside geometry does not present vent hole experimentally (contrary to the upside and the right one, cf Figure 3), it is not fully filled. If we compare this simulation to experimental injections, we notice first of all that
the model leads to faster velocities. Two reasons can explain these discrepancies. The first one is the hypothesis and models chosen here, too far from reality. As an example, if the downside geometry does not fill, it’s due to the incompressible hypothesis made in the equations, which is definitely not the case of the air. The experimental curve on Figure 4 show that the final thickness e reaches around 5 mm, contrary to 2,37 mm with the model, mainly because of the downside geometry (Cf Figure 5 (c)). The second reason for these differences might be the initial and limit conditions imposed in the model, which are not exactly the same as the experience. For example, we set the velocity entrance at 40 mm/s, whereas in reality there is an acceleration ramp for the screw to reach 40 mm/s, and the same at the end of the injection. 40 35 30 Dimensions (mm)
The dimensions measured here are the diameter and the thickness of the part (Figure 3). They will be compared in the next section to simulations (cf Figure 4).
25 20
Diameter (mm) Thickness (mm)
15
Simulated diameter (mm) Simulated thickness (mm)
10 5 0 0
0,05
0,1
0,15
0,2
0,25
0,3
Time (s)
Figure 4. Experimental and simulated evolution of plastic part thickness and diameter.
Figure 5. Newtonian front profile at (a) t=0.01 s, (b) t=0.07 s and (c) t=0.18 s
Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble
Figure 6. Non-Newtonian front profile at t=0.01, t=0.07 s and t=0.18 s
5.2 Non Newtonian fluid : Cross law Polymer viscosity is shear-rate dependent (nonNewtonian). Compared to a Newtonian flow, the sharpness of flow front profile is not as important (Figure 6), mainly because the significant shear rate near the walls is inducing a viscosity reduction, so the profile corresponds better to those observed in the literature. Nevertheless, the influence is not as important as expected, as the filling time and final part does not change significantly. 5.3 Thermal influence When the influence of the temperature is taken into account, the flow front profile is even sharper than the Newtonian case. Actually, the thermo-dependence of the polymer involves higher viscosities near the cold walls, in addition to the non-slip boundary condition. As a consequence, full-filling of the cavity is very difficult, and the polymer has troubles to reach the walls.
Figure 7. Anisothermal Newtonian front profile at (a) t=0.01 and (b) t=0.18s
In this case, both considerations overestimate the fountain flow observed in reality, but in the next future non-Newtonian flow will be considered, and should generate better results. 5.4 Influence of surface tension on the filling of micro-cavities Figure 9 shows the filling of an axisymetric micro geometry (1 µm wide). These simulations have been made with a newtonian PP, with an homogeneous velocity at the entrance of 1 m/s. The influence of the surface tension is studied here. For polymers, surface tension is usually between 20 and 60 mN/m. It appears in Figure 9 that an evolution from 5 to 50 mN/m does not have any effect on the micro-feature filling. To have so, the surface tension has to be increased up to 50 N/m, which is never reached in the reality. If we look at the capillary number, which represents viscous effects on capillary ones, in the present case we get to 104, which comforts our observations on simulated results. However, for capillary effects to be as important to viscous
Figure 8. Temperature profile in the mold cavity at t=0.04s
Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoble
Figure 9. Influence of surface tension coefficient on a microgeometry filling : 0.005, 0.05 and 50 N/m
ones, the characteristic velocity would need to be around 10-4 m/s. 2 0 . Ca = η .u ~ 10 × 10 = 10 4 −2 σ 10 We know by experience that the polymer velocity can decrease considerably when reaching the end of the cavity, or when the pressure drop is very important such as in microfeatures. A future work will be to consider multiscale simulations and analyze the velocity in these microstructures.
6. Conclusions and future work Finally, our work shows the extended possibilities of Comsol Multiphysics® to deal with multi-phase flow topics for the polymer processing network, with first very interesting results. The main conclusions we established on this preliminary work are : i. numerical simulations show disparities from experimental results mainly because of the non-compressible hypothesis. The next step of our work on simulating the filling phase in injection molding will be to consider compressible fluids. ii. non-Newtonian and thermal considerations have influence on the flow front profile, but not too much on filling capacity or filling times. With compressible fluids, we will then combine the level-set equation with a Cross viscosity law and a WLF model for the polymer thermal dependence, coupled with an energy equation. iii. surface tension effects can clearly be neglected when injecting with high velocities in micro-structures, but if the polymer slows
down sufficiently, their influence can become important. Indeed, we will work on combining previous studies for a multi-scale geometry to analyze micro-features filling and velocities inside, and compare our results to experiments of micro-structured plastic parts.
7. References 1. Shen et al., Journal of Reinforced Plastics and Composites, 2004. 17: p.1799-814. 2. Ilinca et al., ANTEC 2004, Chicago. 3. Yu et al., Polymer Engineering and Science, 2002, 5(42). 4. Yu et al., ANTEC 2001, Dallas. 5. Chen et al., ANTEC 2005, Brookfield. 6. Kemmannet al., ANTEC 2000, Orlando. 7. Illinca, et al., ANTEC 2004, Chicago. 8. Young et al., Microsystem Technologies, 2005. 11: p. 410-415. 9. Yu et al., ANTEC 2003, Nashville. 10. Han et al., ANTEC, 1999. New York City. 11. McFarland et al., Polymer Engineering and Science, 2004. 3: p. pp. 564-79. 12. Guo, Thesis, in Department of Mechanical Engineering. 2000, Faculty of New Jersey Institute Technology: New Jersey. p. 178. 13. Maître, Thesis, in Department of Applied Mathematics 1997, Joseph Fourier University – Grenoble 1:p. 168.. 14. Kauzlaric et al., Polytronic 2003, Montreux.
8. Acknowledgements The authors would like to acknowledge the Région Rhône-Alpes and DRIRE Rhône-Alpes for their financial support in the Microstructure project.
