ANALYSIS OF SINK MARKS FOR PLASTIC PARTS MOLDED IN STEEL AND ALUMINUM ALLOY MOLDS
Natraj Iyer Research Assistant Purdue University 1288 Mechanical Engineering West Lafayette, Indiana 47906 USA Phone: (765)-494-0309 Fax: (765)-494-0539 Email:
[email protected]
Karthik Ramani Associate Professor Purdue University 1288 Mechanical Engineering West Lafayette, Indiana 47906 USA Phone: (765)-494-5725 Fax: (765)-494-0539 Email:
[email protected]
ABSTRACT Recently developed aluminum alloys show significant potential as injection mold materials for their ability to cool plastic parts faster than steel. These alloys maintain more uniform mold temperatures that can have significant effects in reducing post-molding shrinkage. Commercially available software can be used to predict the global shrinkage in a part. However, none of the currently available software predicts localized sink mark formation. In the present work, temperature and pressure histories from a three-dimensional molding analysis using C-Mold™ are used to determine the initial conditions for a sequentially coupled thermal and structural finite element analysis using ANSYS™. The thermal conductivity, density and specific heat of the polymer are input as temperature dependent properties. The polymer is modeled as a temperature dependent elastic material. Correlations made between numerical and experimental data for sink mark depths in parts molded in P-20 steel and QE-7™ aluminum alloy molds validate the use of the sink mark simulation method. Numerical comparison of sink mark depths for parts molded in aluminum alloy and steel molds show that aluminum alloys reduce sink mark depths in molded parts.
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INTRODUCTION Injection molding is the most widely used manufacturing process for plastic parts. In a typical injection molding process, part cooling time contributes to around 60-70% of the total cycle time. Recently, Alcoa has developed a new aluminum alloy, QE-7 which has improved hardness and yield strength than pure aluminum and has better thermal properties than P-20 tool steel. The properties of the two mold materials are listed in Table 1. The effect of using non-ferrous materials as mold materials on molded part quality has not been studied in great detail, because studies have mainly pertained to cycle time reduction. Mellinger (1997) compared heat transfer characteristics of an aluminum alloy with steel as a case study for a specific part geometry using C-Mold computer simulation and experiments. The simulation results correlated well with experimental results and indicated significant cycle time reduction by using the aluminum alloy over steel. Stokes (1960) concluded that a copper alloy coating on steel cores reduces cycle time by as much as 50%. Houska (1990) reported that beryllium copper molds with more uniform heat removal rate minimizes residual stresses and reduces post-molding shrinkage in injection molded plastic parts. Typically, injection molded parts have thin walls reinforced with ribs and bosses for additional stiffness. Often, a small depression called a sink mark is formed on the surface opposite a rib or boss. This aesthetic defect is caused by non-uniform shrinkage near the base of the reinforcement during mold cooling. Owing to its larger thermal mass, material in this area cools slower and solidifies last. As the material in this area shrinks, it causes the already solidified outer skin to deform inwards creating a sink mark. Sink marks are usually visible if they are greater than 13 µm in depth (Ramachandra, 1989). Some methods used to minimize sink marks include changing part geometry by reducing rib thickness (Ramachandra, 1989), texturing the mold surface to disguise sink marks (Malloy, 1994), and increasing packing pressure (Ramachandra, 1989). The process of bringing down or eliminating the sink mark to an acceptable level is a time consuming and iterative process. Isaias (1991) reported around 25% reduction in cycle time with copper alloy molds over steel. A reduction in mold temperature and more uniform part cooling was observed. However, sink mark depth decreased with lower thermal conductivity molds, which was exactly opposite to the expected trend. The reason cited for this difference was a large gate size, gate freeze-off due to lower cavity temperature and manufacturing defects. The use of aluminum alloys can aid in reducing post-molding shrinkage and thereby sink mark depth. However there has been no data available to support this premise until our study. The objectives of this study are to gather data to support the premise and to develop a sink mark simulation procedure for further work. We developed an analysis approach that uses C-Mold simulation until the packing stage for estimates of gate freezing time and continues further thermo-mechanical analysis in ANSYS. Our simulation method takes into consideration the mold geometry (which is explicitly modeled in the ANSYS thermal analysis), which is not possible in commercially available molding analysis software as well as in earlier developed simulation methods. The thermo-mechanical analysis makes use of initial conditions from C-Mold and it consists of two steps – a transient thermal analysis and a structural analysis. The thermal analysis calculates the nodal temperature distribution in the rib cross-section while cooling and after ejection while the structural analysis makes use of the nodal temperature values calculated from the thermal analysis and uses it to calculate the nodal thermal strains at every time step.
Background Sink marks have been studied both numerically and experimentally. In one of the earliest studies, Marchewka (1974) experimentally investigated the effects of rib thickness, rib distance from the gate
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the rib thickness is lesser than 60% of the part wall thickness. Since then, a rib to wall thickness ratio close to 0.6 has been used extensively as an effective guideline for designing ribs. Naka et al. (1987) concluded that for a given part geometry increasing packing pressure reduces sink mark depth. They also concluded that increasing the rib thickness led to increase in sink mark depth while rib height and wall thickness did not have significant effects on sink mark formation. They also developed a numerical method to study sink mark formation using a transient finite difference thermal analysis and the corresponding shrinkage of the part. Their numerical predictions agreed well with experimental data. Ramachandra (1989) conducted an extensive experimental study of sink mark formation in a plastic part with a single rib. Their conclusions reaffirmed the importance of rib thickness and packing pressure as the most important parameters in sink mark formation. Reifschneider (1990) used a finite element approach for sink mark prediction using a thermoviscoplastic formulation and a sequentially coupled thermal-structural analysis. The effect of packing pressure on sink mark formation was modeled by selecting an appropriate initial temperature and pressure state for the structural analysis. Their results predicted the trend of increasing sink mark depth with increasing rib thickness. Their method relied on an assumption of gate freezing time and they suggested the use of molding analysis software for better estimates of gate freezing time. Battey (1997) conducted an extensive study of sink mark formation in injection molding. He used C-Mold molding analysis software to predict the initial conditions for a sequentially coupled thermalstructural analysis. His approach was similar to the one used by Xu et al. (1993) and Ho (1993) for analyzing sink marks in compression molding of sheet molding compounds and his results agreed well with experimental data from literature. Mold material is a very important parameter in sink mark analysis because it decides the heat transfer rate. The simulation approach developed by Battey (1997) used temperature boundary conditions for the thermal analysis that were predicted by C-Mold. However, he found that the use of a high thermal conductivity mold material causes C-Mold™ to over predict the effect of ambient air cooling. Any errors due to assumptions made in C-Mold™ are magnified due to the high thermal conductivity of the mold material. The difference between our approach and the one by Battey is in using the C-Mold™ program only until the packing stage and in explicitly modeling the mold geometry for the thermal analysis. Our simulation approach is independent of the C-Mold™ Cooling module (in which most of the heat transfer calculations are performed). Hence the results are closer to actual values. The simulation results obtained were verified against experimental data for two rib geometries molded at three different cycle times.
EXPERIMENTAL WORK The part used in this study is shown in figure 1. The part was designed with two ribs each of 3.05 mm and 1.52 mm thickness. Two separate P-20 steel and QE-7 aluminum alloy molds were manufactured. A number of thermocouple positions were identified (shown by arrows in figure 1) and Omega Type K thermocouples were mounted at 0.1” away from the mold surface to gather information about the temperature pulses in both molds. The experiments were performed under controlled conditions on a 55-ton Cincinnati Milacron VST55 molding machine and all other operating parameters except cycle time were varied. Thermocouple data using National Instruments Labview™ was gathered at three different cycle times – 23.32 seconds, 35.32 seconds and 52.32 seconds. After the system had attained thermal equilibrium, twenty parts were molded at each cycle time and six of them were chosen at random for measurement of sink mark depth. The other important processing parameters are shown in Table 2.
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SINK MARK ANALYSIS Analysis Methodology Our approach uses a three-step procedure for sink mark analysis that integrates a molding analysis with a sequentially coupled thermal and structural analysis. A commercially available molding simulation package C-Mold (1998) is used to determine temperature and pressure histories in the mold cavity. For an accurate pr ediction of the temperature distribution in the geometry, a finite element heat transfer analysis is performed. The analysis results generate a more detailed temperature distribution across the thickness of the part, which is used for calculating the thermal stresses and resultant non-uniform material shrinkage by performing a sequentially coupled structural analysis. A commercially available finite element package ANSYS (1996) is used for thermal and structural analyses. The steps of the analysis as shown in figure 2 begin at different times during the injection molding process. The C-Mold analysis begins at the time the polymer is injected into the cavity and continues until the packing stage. The ANSYS thermal analysis begins about 2 seconds after the end of filling, usually in the pack and hold stage when the pressure in the cavity has reached its maximum value. By this time the cavity is full and there is very little flow in the cavity or the gates. Hence, shear heating within the cavity is negligible. The thermal analysis uses the through-thickness temperature distribution as predicted by CMold as initial conditions for the part. The mold is assumed to be at room temperature. The thermal analysis continues into the cooling and ejection phases and extends until one hour after ejection which is usually adequate for the entire part to cool to room temperature. The structural analysis begins only at the time when the flow in the cavity has ceased completely and it is assumed to start at the point when the cavity pressure drops to zero. This is a reasonable assumption since the polymer is free to shrink independent of any pressure in the cavity. The time taken for the pressure to drop to zero might be before or after the machine packing pressure has been released depending on the value of packing pressure, distance from gate and runner system design. The structural analysis also continues until one hour after part ejection.
C-Mold Injection Molding Simulation The C-Mold simulation is an integrated fluid flow and heat transfer analysis of the filling and packing stages of the injection molding process. The flow simulation is based on a hybrid finite elementfinite difference analysis for a non-isothermal, generalized Hele-Shaw flow including compressibility of the polymer during the packing phase (Hieber and Shen, 1980). The mesh used for the C-Mold simulation is shown in figure 3. A semi-crystalline polypropylene resin, Marlex HGL 120-01 from Phillips was used in this analysis. The viscosity of the polymer is represented by a Cross-WLF model proposed by Chiang et al. (1991). The values for the seven parameters in the Cross-WLF model for the polymer used in the study are given in Table 3. The PVT (Pressure-volume-Temperature) properties are modeled by a two-domain Tait equation proposed by Chiang et al. (1991), which uses thirteen parameters to represent specific volume as a function of temperature and pressure. The values of the thirteen parameters for the PVT model are summarized in Table 4. The two most important results from the molding simulation are the pressure history and the through-thickness temperature distribution. The results are shown in figures 4 and 5. The throughthickness temperature distribution shown in figure 5 is used as the initial condition for the polymer in the thermal analysis.
Transient Thermal Finite Element Analysis We use thermal analysis for a localized study of heat transfer effects in the cross section to be analyzed. The mesh used in the analysis is shown in figure 6. The assumption made is that heat
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the two edges where edge effects are quite important. Also, shear heating effects can be neglected since the analysis begins only after flow rates in the cavity have become very small (Battey, 1997). ANSYS Thermal was used for performing the finite element analysis. The thermal conductivity, specific heat and density were input as temperature dependent material properties. However, the material properties of the mold were input as constant values. Convective heat transfer boundary conditions are applied at the cooling channels until part ejection at air. The coolant flow was calculated to be turbulent flow with a Reynolds number of 12000. After ejection, the entire part is subjected to convective heat transfer at the boundaries since it is in contact 2 with air. A convection coefficient of 10 W/m is used which is quite standard for natural convection in air (Incropera and Dewitt, 1990). The through-thickness temperature distribution at the centroid of the finite element nearest to the base of the geometry is used as the initial thermal state for the entire part. The one-dimensional temperature profile shown in figure 5 is mapped on to the two-dimensional mesh. The rib area is divided into two regions classified ‘R’ and ‘F’ depending on their position with respect to the rib side or the flat side of the mold as shown in figure 7. Since the rib side is hotter than the flat side, the temperature profile is mapped appropriately (the temperature profile also has a slightly unsymmetrical distribution because the heat transfer rate across the flat side is more than that across the rib side). The mapping procedure is a time consuming part of the analysis. The initial temperature distribution in the polymer and the mold is shown in figure 8. We tried using a constant melt temperature as the initial condition for the entire part, but the results were only found to be correct for thin rib thickness values. This can be attributed to the lower heat content at thin rib thickness values. Hence, the heat transfer rates were insignificant as compared to those at high rib thickness values. The mold was assumed to be at a constant temperature of 25°C for all cases. The result of the thermal analysis is a detailed temperature history in the part with time. Figure 9 shows the temperature distribution in the 3.05 mm rib cross-section just before ejection. It is seen that though the C-Mold analysis predicts that the entire part would be below the ejection temperature of 93°C by this time, the ANSYS analysis predicts that the thermal mass at the rib base remains significantly warmer at this time. It can be said that the ANSYS thermal analysis provides a more detailed description of the temperature distribution at every time step in the part. Since, very few assumptions are made in the ANSYS analysis as compared to C-Mold, we can say that the re sults from ANSYS such as the one in figure 9 are closer to reality. This is one of the reasons that C-Mold and other molding simulation software cannot be used to perform sink mark analysis. Figure 10 shows the temperature distribution in the part one hour after ejection. It is seen that the entire part has attained equilibrium at room temperature. This slow, non-uniform cooling is one of the most important reasons for sink mark formation.
Structural Finite Element Analysis The detailed temperature history from the thermal analysis is used to determine the shrinkage and thermal stresses using the ANSYS structural package. The structural analysis starts at the instant the cavity pressure drops to zero. Before the part is ejected, the mold surfaces have additional contact elements to prevent penetration of the part into the mold as the part warps. The mold is assumed to be a rigid body where the target contact elements are placed. However, after ejection, the contact boundary conditions are relaxed and the part is allowed to deform freely. The only boundary conditions that persist until the end of the analysis are those required to prevent rigid body motion. The polymer is modeled as an elastic material with temperature dependent material properties. The temperature dependence of elastic modulus was found experimentally using a TA Instruments DMA 2980 Dynamic Mechanical Analyzer. A sample of polypropylene was subjected to a tension test at temperatures varying from 30°C to 140°C and the modulus is calculated. The frequency used was 10 Hz and the temperature was ramped at a rate of 2 °C/min. Figure 11 shows the temperature dependence of elastic modulus. The Poisson’s ratio ( ) and coefficient of thermal expansion ( ) are
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The result from the structural analysis is a detailed history of shrinkage in the part. The displacement plot in figure 12 shows a clear sink mark formed at the base of the rib across the thermal mass. The displacements have been magnified tenfold to make them visible. The sink mark depth is measured as described by Battey (1997) as the vertical distance from the bottom of a sink mark to a tangent line drawn between the high points on either side.
RESULTS The sink mark analysis approach described earlier was used to study sink mark formation in P-20 steel and QE-7 aluminum molds. Parts were molded at three different cycle times in both molds and the sink mark depths were measured. Figures 13 and 14 show comparisons between mold wall temperature data gathered by the thermocouples and C-Mold data for P-20 steel and QE-7 aluminum molds respectively. The injection molding cycle was simulated in C-Mold until the end of the cooling phase. It is seen that C-Mold predictions are closer to experimental values for P-20 than for QE-7. This is because of the overestimation of the effect of ambient air cooling (Himasekhar et al., 1992). The mold boundary is also approximated as a sphere of equivalent radius, without any use of the mold dimensions. C-Mold uses heat transfer coefficients based on correlations found in literature. Part geometry is an important factor in the analysis. For simple part geometries, C-Mold predictions are closer to experimental values regardless of mold material (Nerone, 2000). Figures 15 and 16 show the correlation between sink mark depths measured experimentally and from the simulation. The numerical results are higher than the experimental values because of the material model chosen. Viscoelastic effects, which contribute to stress relaxation, have been neglected in the present model. If we had considered a viscoelastic material model, we would have obtained sink mark depths closer to the actual numerical values. However, since trends match reasonably well, the present analysis method can be used for constructing design guidelines with aluminum molds. It is seen that sink mark depths reduce with increasing cycle time. As the cycle time increases, the mold temperature reduces and thereby a thicker frozen layer is formed which prevents excessive deformation of the part after ejection. For similar reasons, parts molded in aluminum molds exhibit lesser sink mark depths than those molded in steel molds.
CONCLUSIONS Clearly, the premise that aluminum alloy molds reduce sink mark depths as compared to steel molds has been verified. Since aluminum alloys are easier to machine than steel, they offers additional benefits of faster time to production with better part quality, which is the very basis of concurrent engineering. It is seen that sink mark depth increases as the thermal conductivity of mold material decreases. A sink mark simulation procedure that combines injection molding simulation and finite element analysis has been developed. The results of the simulation compare well with experimental results. However not many plastic part designers would be keen on using this time consuming approach. Hence, design guidelines for commonly used geometries such as ribs and bosses, developed entirely by numerical analysis would help part designers optimize part geometry and processing conditions during the design cycle. With the benefits they provide, aluminum alloys are mold materials to be looked forward to in the future.
REFERENCES A.C. Technology, Inc., 1998, C-Mold™ Software, Software, Ithaca NY. Battey. D.J., 1997, Sink Mark Prediction in Injection Molded Plastic Parts by Finite Element Analysis, M.S. Thesis, Thesis, Michigan Technological University, Houghton MI. MI.
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Chiang. H.H., Himasekhar. K., Santhanam. N., Wang. K.K., 1991, “A Unified Simulation of the Filling and Postfilling Stages in Injection Molding, Part I: Formulation and Part II: Experimental Verification”, Polymer Engineering and Science, Vol. 31, p.116-139. Hieber. C.A., Shen. S.F., 1980, “A Finite Element/Finite Difference Simulation Simulation of the Injection Molding Process”, Journal of Non-Newtonian Fluid Mechanics, Vol. 7, p.1-32. Himasekhar. K., Lottey. J., Wang. K.K., 1992, “CAE of Mold Cooling in Injection Molding Using a Three-Dimensional Numerical Simulation”, Journal of Engineering for Industry, Vol.114, pp.213-221. Ho. C.T., 1993, An Investigation of Sink Mark Formation in Compression Molding of Polymeric Composites, Ph.D. Thesis, Ohio State University, C olumbus OH. Houska. C., 1990, “Solving Molding Problems with Beryllium Copper”, Plastics Engineering, Vol. 6, pp.31-35. Incropera. F.P., Dewitt. D.P., 1990,
Introduction to Heat Transfer ,
Wiley and Sons, NY.
Isaias. S., 1991, A Study of Heat Transfer Characteristics of Copper Alloy Materials for use in Injection Molding, M.S. Thesis, Ohio State University, Columbus OH. Malloy. R.A., 1994, Plastic Part Design for Injection Molding, Hanser Gardner Publications. Marchewka.T., 1974, “Sink Marks can be eliminated”, Plastics Technology, Vol. 3, pp.37-38. Mellinger. D.C., 1997, Heat Transfer Analysis of an Injection Molding System, M.S. Thesis, University of Kentucky, Lexington KY. Naka. H., Ichiyanagi. T., Kenmochi. K., 1987, “A Study of Injection Molding (Analysis of the Partial Thermal Shrinkage in Rib Structures)”, JSME International Journal, Vol. 30, No. 265, pp.1060-1068. Nerone. J., 2000, An Exploration of the use of Advanced Aluminum Alloys for Injection Molding Dies, M.S. Thesis, Purdue University, W est Lafayette IN. Ramachandra. D.M., 1989, Study of Sink marks in Injection Molded Plastic Parts, M.S. Thesis, Ohio State University, Columbus OH. Reifschneider. L.G., 1990, Sink Mark Modeling of Injection Molded Parts, Ph.D. Thesis, Ohio State University, Columbus OH.
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Figure 1. Test Part for experimental study. Arrows show thermocouple positions in the mold wall.
Figure 2. Analysis Methodology
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150 140 130 End of Packing 120 110 ) 100 a P M 90 ( e r 80 u s s 70 e r P y 60 t i v a 50 C
20.68 MPa 51.71 MPa 72.39 MPa 155.13 MPa
40 30 20 10 0 0
5
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45
Postfilling Postfilling Time (secs)
Figure 4. Cavity Pressure v/s Postfilling time at different packing pressures. At higher values of packing pressure, even after the packing phase is complete, the cavity pressure takes longer to fall to zero . 0 5 2
) s u i s l e C ( e r u t a r e p m e T s s e n k c i h T h g u o r h T
0 0 2
0 5 1
0 0 1
0 5
-1
-0.75
-0.5
-0.25
0 0
0.25
0.5
0.75
1
Normalized Thickness
Figure 5. Through-thickness temperature v/s Normalized Thickness
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Figure 6. ANSYS mesh – 4 noded Plane 55 and Plane 42 elements are used in the thermal and structural analyses respectively. Arrows show the convective boundary conditions at the cooling channels.
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Figure 8. Temperature distribution at the beginning of the thermal analysis. The through thickness temperature distribution from C-Mold is mapped on to the mesh in ANSYS™.
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Figure 10. Temperature distribution in the polymer for a 3.05 rib one hour after ejection. The temperature of the entire part has equilibrated to a temperature of 32°C. 1800 1600 1400 ) a P1200 M ( s u 1000 l u d o 800 M
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35
1.57 Rib (E)
) 30 C ( e r u t a r e p 25 m e T
3.05 Rib (E) Channel (E) 0.1Corepin (E) 0.2 Corepin (E) 1.57 rib (N) 3.05 rib (N) Channel (N) 0.1Corepin (N) 0.2 Corepin (N)
20
15 0
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Time (s)
Figure 13. Correlations for experimental (E) and C-Mold™ (N) mold wall temperature for 35.32 cycle time with P-20 steel mold. Reasonably good correlation with P-20 steel mold.
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100
90 ) m ( h 80 t p e D k r a 70 M k n i S
Steel (Experiment) Steel (FEM)
60
Al umin um (Ex perim ent) Al umin um (FEM )
50 20
25
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Cycle Time (secs)
Figure 15. Comparison of experimental and numerical values of sink mark de pth for 3.05 rib.
100
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Table 1. Comparison of Material properties of QE-7, QC-7 and P-20
Table 2. Processing parameters used in e xperiments
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Table 4. Two-domain PVT model parameters
