Extrusion Variables and Errors

The focus of this evaluation is on the results that were reported using four different resins [52] PC resin, LLDPE resin, EAA copolymer, and an LDPE resin. The shear viscosities for the resins at selected processing temperatures are shown in Pig. 7.17 and were modeled using the power law model provided by Eq. 7.42. The parameters for the model are given in Table 7.3. As shown in Pig. 7.17 and the n values in Table 7.3, the PC resin shear-thinned the least while the EDPE resin shear-thinned the most. The LLDPE and EAA resins have n values between those for the PC and LDPE resins. The melt density for the LDPE and LLDPE resins at 240 °C is 735 kg/mT The melt density of the EAA resin at 220 °C was 785 kg/m and the melt density of the PC resin at 280 °C was 1073 kg/mT 

Two different calculation methods were used for the simulations (1) the generalized Newtonian method as developed above, and (2) the three-dimensional numerical method presented in Section 7.5.1. The generalized Newtonian method used a shear viscosity value that was based on the average barrel rotation shear rate and temperature in the channel. The average shear rate based on barrel rotation (7ft) is provided by Eq. 7.52. Barrel rotation shear rate and the generalized Newtonian method are used by many commercial codes, and that is why it was used for this study. 

The ratio of the rotational flows indicated that the diameter of the extruder is not a factor for the deviation shown in Fig. 7.16. That is, for this channel with a small H/Wthe simplified analysis produces less than a 10% error when compared to the exact numerical solution. Thus, the rotational flow rate can be calculated quite reliably using the simple generalized Newtonian method at these conditions. 

The previous calculations were performed using a range of commercial resins with different levels of shear thinning behavior. In order to show the deviation for the generalized Newtonian method, the data presented in Figs. 7.20 and 7.21 were plotted as a function of n for several ///IF values, as shown in Figs. 7.22 and 7.23. As the n value was reduced from 1.0 towards 0, and as the/ /PFratio increases, the 

The generalized Newtonian model over-predicted the rotational flow rates and pressure gradients for the channel for most conditions. This over-prediction was caused in part by the utilization of drag flow shape factors (FJ that were too large. Then in order for the sum of the rotational and pressure flows to match the actual flow In the channel, the pressure gradient was forced to be higher than actually required by the process. It has been known for a long time [9] that the power law 

---