Modeling injection molding

Agarwala, M. K., Patterson, B. R., and Clark, P. E. 1992. Rheological behavior ofpowder injection molding model slurries, y. Rheol. 36 319-334. 

In comparing the Carreau and Cross models on a variety of commercial-grade polymer melts, Hieber and Chiang (1992) found that the Cross model provides a better overall fit for the shear-rate dependence. The Cross model has been widely used in injection molding modeling. 

Soil, S.K. and Chang, C. J., 1986. Boundary conditions in the modeling of injection mold-filling of thin cavities. Polym. Eng. Sci. 26, 393-399. 

To constitute the We number, characteristic values such as the drop diameter, d, and particularly the interfacial tension, w, must be experimentally determined. However, the We number can also be obtained by deduction from mathematical analysis of droplet deforma-tional properties assuming a realistic model of the system. For a shear flow that is still dominant in the case of injection molding, Cox [25] derived an expression that for Newtonian fluids at not too high deformation has been proven to be valid ... 

As shown by Fig. 3.11 for an applied force, the creep strain is increasing at a decreasing rate with time because the elongation of the spring is approaching the force produced by the stress. The shape of the curve up to the maximum strain is due to the interaction of the viscosity and modulus. When the stress is removed at the maximum strain, the strain decreases exponentially until at an infinite time it will again be zero. The second half of this process is often modeled as creep recovery in extruded or injection-molded parts after they cool. The creep recovery usually results in undesirable dimensional changes observed in the cooled solid with time. 

Koppi, K. A., Ceraso, J.M., eleven, J. A., and Salamon, B. A., Gloss Modeling of Injection Molded Rubber-Modified Styrenic Polymers, SPE ANTEC Tech. Papers, 48, 390 (2002)... 

The chapter is divided into a section on development of process cycles or plans and a section on in-process control. The tools to be discussed include design of experiments, expert systems, models, neural networks, and a variety of combinations of these techniques. The processes to be discussed include injection molding, resin transfer molding, autoclave curing, and prepreg manufacturing. The relative cost and difficulty of developing tools for these applications will be discussed where data is available. 

Figure 5 presents the results of tensile tests for the HPC/OSL blends prepared by solvent-casting and extrusion. All of the fabrication methods result in a tremendous increase in modulus up to a lignin content of ca. 15 wt.%. This can be attributed to the Tg elevation of the amorphous HPC/OSL phase leading to increasingly glassy response. Of particular interest is the tensile strength of these materials. As is shown, there is essentially no improvement in this parameter for the solvent cast blends, but a tremendous increase is observed for the injection molded blend. Qualitatively, this behavior is best modeled by the presence of oriented chains, or mesophase superstructure, dispersed in an amorphous matrix comprised of the compatible HPC/OSL component. The presence of this fibrous structure in the injection molded samples is confirmed by SEM analysis of the freeze-fracture surface (Figure 6). This structure is not present in the solvent cast blends, although evidence of globular domains remain in both of these blends appearing somewhat more coalesced in the pyridine cast material.

In addition to high-speed photography, which was used to obtain the results discussed above, other methods have been used to visualize flow, for example, the tracer method.279"281 A typical experimental device consists of a capillary viscometer connected to a mold, which is a simple model of plunger-type injection molding unit.279 A special device was used to introduce tracers of different colors in regular succession. After sample solidification, it is possible to examine the position of the various colors on the surface (Fig. 4.47 a) or through the volume by cutting sections (Fig. 4.47 b). It can be seen that the tracers are positioned symmetrically near the surfaces and that they have a V-type shape, with the tip oriented toward the stream. 

There are no generalized models that include all these variables for thermosetting polymers. However, extensive work has been done on the viscosity of polyurethanes [9, 10] used in the reaction injection molding process. An empirical relation which models the viscosity of these mixing-activated polymers, given as a function of temperature and degree of cure, is written as... 

Today, the most widely used model simplification in polymer processing simulation is the Hele-Shaw model [5], It applies to flows in "narrow" gaps such as injection mold filling, compression molding, some extrusion dies, extruders, bearings, etc. The major assumptions for the lubrication approximation are that the gap is small, such that h < . L, and that the gaps vary slowly such that... 

E. Broyer, C. Gutfinger, and Z. Tadmor. A theoretical model for the cavity filling process in injection molding. J. of Rheology, 9(3) 423, 1975. 

Fig. 13.27 Deformation of PS at different displacements 0, 22, 33, 44, and 55 mm. (a) Experimental, (b) Calculated using the Carreau model (T — 230°C). [Reprinted by permission from E. Vos, H. E. H. Meijer, and G. W. M. Peters, Multilayer Injection Molding, Int. Polym. Process., 6, 42 (1991).]...

S. D. Lipshitz, R. Lavie, and Z. Tadmor, A Melting Model for Reciprocating Screw Injection Molding Machines, Polym. Eng. Set, 14, 553 (1974). 

B. Friedrichs and S. I. Gujeri, A Novel Hybrid Numerical Technique to Model 3-D Fountain Flow in Injection Molding Processes, J. Non-Newt. Fluid Meek, 49, 141-173 (1993). 

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