INJECTION MOLDING COOLING TIME REDUCTION AND THERMAL STRESS ANALYSIS Tom Kimerling University of Massachusetts, Amherst MIE 605 Finite Element Analysis Spring 2002 ABSTRACT A FEA transient thermal structural analysis was performed to determine the effects of rapidly cooling the mold surface. The results from the thermal analysis correlate closely to theoretical values. One drawback of rapidly cooling the mold surface is that large thermal stresses are induced in the surrounding material. For this reason a standard cooling channel and microchannel cooling were both analyzed to determine robustness. The values from the analysis predict a fatigue life of 1000 cycles for the standard cooling channel and 1615 cycles for the microchannel cooling. Also an analysis was performed on a system that uses a plate that contains micro-channels. This plate is welded around the edge to the mold. The analysis showed that a large deflection would occur in the center of the plate and very large stresses would be produced in the weld. This leads to the conclusion that the micro-channels should be attached all the way across the mold surface rather than just the edges. BACKGROUND Injection molding represents a large portion of the entire plastics processing industry. Due to this fact a large number of injection molding machine hours are spent each year making products for the consumer market. Any reduction in the number of machine hours required to make a certain number of parts would result in a substantial cost savings. A new technology developed by the injection molding laboratory at the University of Massachusetts has demonstrated the ability to substantially reduce injection molding cycle time and therefore machine time. An injection molding cycle is composed of many components. The critical components of this cycle are shown in Figure 1. Figure 1. Typical injection molding cycle clock As seen in figure 1, part cooling time accounts for approximately two thirds of the cycle. Cooling time is a function of polymer material properties, part thickness and molding temperatures. The relationship between these variables is given in the following equation. 1 Copyright #### by ASME
In a standard molding process each of these variables is fixed when the part and material have been selected. However, the injection molding laboratory at the University of Massachusetts has developed a new technology that allows independent control of mold wall temperature (RTR). Figure 2 shows an experimental temperature profile of the mold wall over time. The temperature is raised above the melt temperature of the polymer and lowered to ambient temperature in approximately 5 seconds. Figure 2. Temperature profile of mold wall over time This technology allows the ambient temperature of the mold to be much lower than what is currently used. In effect, once the cavity has been filled a much larger temperature differential exists between the polymer and the mold, which results in an enhanced heat transfer rate and therefore decreased cooling time. Cooling time reduction results have been calculated for different materials and are shown in Table 1. Minimum cooling time (s) Tw(C) Minimum cooling time (s) Percent Improvement Material Tw(C) PC 104 46 10 24 48 PC/ABS 79 63 10 32 48 ABS 57 26 10 17 37 PMMA 60 89 10 55 38 HDPE 33 26 10 22 18 PBT 41 24 10 20 16 PS 55 36 10 25 30 Nylon 85 37 10 27 29 PP 45 32 10 27 14 Table 1. Cooling time improvement Average material and molding temperature values have been used for different types of thermoplastics in table 1. A constant thickness of 3/16 inches has been used for comparison purposes. The first minimum cooling time column represents a standard molding process while the second cooling time column represents a mold at ambient temperature. The final column represents the percent improvement, which results from using the new technology. While most injection molders try optimizing process settings to achieve a one or two percent cycle time reduction, this new technology shows the ability to reduce cycle time anywhere from 10 to 50 percent. RAPID COOLING EFFECTS Although there are many benefits to rapid cooling as mentioned previously, there are also drawbacks in terms of thermally induced stresses in the mold. For this reason a transient thermal structural analysis has been performed to determine if the new mold will be able to withstand the rapid cooling of the part. This analysis was performed using ANSYS? FEA software. A 2-D model was created of a slab with a large length to width ratio. This model was used to simulate a section of a thin walled part. For the thermal analysis only the temperature at the center of the part was analyzed since this point experiences the least amount of end effects. In addition, due to the symmetry of the part and the mold, only a quarter section of the model needed to be analyzed. This reduced the processor time needed to analyze the model. Material properties were next assigned to the part and mold geometries. PMMA was chosen for the thermoplastic due to its large range for cycle time improvement and its use in common products such as an LCD light guide panel. The mold material was assigned as 420 stainless steel. This is the metal currently used by the injection molding laboratory for the construction of mold inserts for the RTR process. The material properties for each of these materials were found using the matweb website (1). Initial and boundary conditions were assigned to the model based on an actual molding process. This included both free edge convection from the mold exterior to the air as well as forced edge convection from the mold to the cooling channels. Initial conditions included setting the part temperature to the melt temperature of PMMA as well as the mold temperature to the cooling channel temperature. In order to perform a coupled structural analysis, displacement constraints were needed. These included fully constraining the exterior surface of the mold as well as constraining the symmetric surfaces from moving across the associated plane of symmetry. An appropriate element needed to be used for the transient thermal structural analysis. For this purpose, Plane13 was selected. This element is a 2-D four noded quadrilateral element that has temperature and displacement degrees of freedom as well as limited coupling between fields. The only drawback of this element is that it also has magnetic properties. In this analysis, however, the magnetic properties were set to zero, which negated their effect. 2 Copyright #### by ASME
Since a coupled element was chosen for the analysis it was possible to perform a direct coupled analysis. For a transient analysis this is an advantage, because the sequential method requires inputting the last time step temperature solution from the transient thermal analysis. With a large number of time steps this becomes an arduous process. Using the center temperature nodal values for both regular cooling and micro-channel cooling the following plot was created. Figure 4. Maximum stress in standard cooling channel Figure 3. Part centerline temperature The theoretical cooling curves represent the solution obtained using the minimum cooling time equation (theoretical 1) as well as an adjusted equation which more accurately represents a standard molding process (theoretical 2). To find the cooling time, an ejection temperature is set and the corresponding time values are read off the chart. In the case of a PMMA LCD light guide panel this value is approximately 85?C. The following table gives the cooling time results for the FEA models as well as the theoretical formulas. Minimum Cooling Time (sec) Ejection Temperature (C) Standard Micro- Channel Theoretical 1 Theoretical 2 85 7.4 6.3 5.9 9.1 Table 2. Cooling time comparison Table 2 and Figure 3 show that the micro-channel results more closely conform to the theoretical minimum cooling time while the standard cooling channel results are closer to the adjusted theoretical value. The thermal results from the preceding analysis were coupled with a structural analysis. This coupling produced equivalent stress results for each of the geometries. Figure 4 shows the maximum stress in the standard cooling channel configuration. The maximum stress occurs during the initial time step. This is due to the temperature gradient having the greatest value at the start of the transient analysis. The location of maximum stress occurs in the region of minimum cross-section between the two channels. This is the expected location because the mold surface displacing upwards due to the temperature gradient thus causing the material between the cooling channels to elongate. The maximum equivalent stress on the legend (306 ksi) occurs at the corner where the part and mold intersect (not shown in figure). This point is considered to be an artificially induced stress concentration and is therefore disregarded in the analysis. Using the maximum value between the cooling channels of 238 ksi a high cycle fatigue analysis was performed (figure 5). Figure 5. Fatigue analysis of standard cooling 3 Copyright #### by ASME
The high cycle fatigue formula is only applicable in the range of 10 3 to 10 6 cycles. Since the calculated fatigue life is at the lower limit of the formula the results may have a certain amount of error. Also, the formula assumes the loading is fully reversed. The calculation is therefore conservative since the mold heating and cooling only produces tensile stress in the critical region between the cooling channels. An equivalent transient structural analysis was also performed on the micro-channel cooling. Figure 6 shows the equivalent stress for the microchannel cooling. As can be seen in this figure the maximum stress occurs between the micro-channels. This result is expected for the same reasons as the standard cooling channel. Figure 7. Fatigue analysis of micro-channel cooling An unexpected result of the micro-channel stress analysis is that the maximum stress is lower than that of the standard cooling channel. A possible reason for this is the load is distributed over a greater area thus causing a lower stress. However, the channels are in close proximity to the mold surface and therefore experience a larger thermal gradient, which balance this affect. A final structural analysis was performed on a that simulates a separate thin layer of microchannels on the mold surface that are welded to the mold around the edge. This is similar to what can be easily constructed for a physical test of the micro-channel cooling. Of interest in this analysis is the maximum deflection of the welded micro-channel plate as well as the maximum stresses that occur in the weld. The maximum stress for this is shown in figure 8. Figure 6. Maximum stress in micro-channel cooling As in the standard cooling channel, a stress concentration exists in the corner where the part intersects the mold (not shown in figure). For the fatigue analysis the average equivalent stress value between the microchannels was used (224 ksi). The fatigue calculation is shown in figure 7. Figure 8. Maximum equivalent stress in welded micro-channel plate According to the analysis, the maximum equivalent stresses are large enough to cause failure during the first cooling cycle. While the location of the stress is correct, the value may be influenced by an artificial stress concentration due to the exact right angle formed at the intersection of the surfaces. To analyze the deflection of the micro-channel plate a theoretical calculation was first performed to determine an approximate value for the displacement. This calculation is shown in figure 9. 4 Copyright #### by ASME
Figure 9. Theoretical deflection of beam with temperature gradient The formula in figure 9 assumes a beam with free ends. Smaller deflection results are expected for the model since the ends are fixed. A graph of the deflection of the center node on the surface of the welded piece is shown in figure 10. Figure 10. Mold surface displacement The displacement results match well with the prediction. The curve indicates the maximum deflection value from the FEA analysis will be slightly less than the theoretical value. The values also become negative after 13 seconds, which is due to the welded micro-channel piece displacing through the mold surface. This could not physically occur, but the model did not contain any contact parameters between the two surfaces. CONCLUSION A FEA transient thermal structural analysis was performed to determine the effects of rapidly cooling the mold surface. The results from the thermal analysis correlate closely to theoretical values. An important observation from the thermal analysis is that the cooling time of the micro-channel will approach the theoretical minimum cooling time, as the channels are placed closer to the mold surface. This is due to the ability of the micro-channels to maintain a near perfect surface temperature, which is assumed by the cooling time formula. One drawback of rapidly cooling the mold surface is that large thermal stresses are induced in the surrounding material. For this reason a standard cooling channel and micro-channel cooling were both analyzed to determine robustness. This was accomplished by coupling the results from the transient thermal analysis to obtain a transient structural analysis. The maximum equivalent stress values were then used in a high cycle fatigue formula to determine the number of cycles to failure of the mold. As expected a large stress occurs on the initial time step between the cooling channels. This was due to the thermal gradient being the largest during the initial time step and the minimum cross-section being located between the cooling channels. The values from the analysis predict a fatigue life of 1000 cycles for the standard cooling channel and 1615 cycles for the micro-channel cooling. An analysis was also performed on a micro-channel cooling that represents a system that can currently be easily produced. This system uses a plate that contains the micro-channels which has been welded around the edge. The major concern for this is the deflection of the center of the plate due to thermal loading and the associated stresses in the weld. The analysis showed that a large deflection would occur in the center of the plate and very large stresses would be produced in the weld. This leads to the conclusion that the micro-channels should be attached all the way across the mold surface rather than just the edges. REFERENCES 1. www.matweb.com 5 Copyright #### by ASME