Modelling mold filling

The construction of a mold-filling model has been considered in the theory of thermoplastics processing. A rapid increase in viscosity also occurs in the flow of these materials, but the effect is different than in flow during reactive processing. The increase in viscosity of thermoplastic polymer materials is due to physical phenomena (crystallization or vitrification), while the increase in viscosity of reactive liquids occurs due to chemical polymerization reactions and/or curing. This comparison shows that the mathematical formulation of the problem is different in the two cases, although some of the velocity distributions may have similar features. 

A. C. Garcia, Reactive Mold Filling Modeling, Ph.D. Thesis, Chemical Engineering Department, University of Minnesota, Minneapolis, 1991. 

Fig. 10-16. A mold fill model of a keyboard cover constructed with CAD finite element modeling techniques. Courtesy GE CAE International.)...

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. 

The third region of flow near the front is of special interest. The important feature of this region is the fountain effect, which must be considered in modelling all types of mold filling. It is important not only for estimating the hydrodynamic flow pattern, but also because the deformation of the macromolecules near the front influences their orientation and the properties of the end product. 

A complete description of model of filling a rectangular mold and the subsequent solidification of an article was developed,47 and in this case a fountain effect near the stream front was included. The authors used the model to predict pressure increase during mold filling, and the distribution of the degree of conversion and temperature at both stages (filling and solidification). The results... 

As an example, let us analyze mold filling with a model polyurethane formulation. Let the kinetics of curing be described by an equation with the self-deceleration term (as was discussed above). The following values of the parameters were used U = 49.1 kJ/mol ko = 3.8xl06 = 1.1 ATmax = 25.8°C where ATmax is the maximum expected increase in temperature for adiabatic curing. 

There are only a few exact or analytical solutions of the momentum balance equations, and most of those are for situations in which the flow is unidirectional that is, the flow has only one nonzero velocity component. Some of these are illustrated below. We end the section with a presentation of the, which today is widely accepted to model the flows that occur during mold filling processes. 

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... 

There are various special forms and simplifications of the above equation and they are given below. In subsequent chapters of this book we will illustrate how the various forms of the Hele-Shaw model are implemented to solve realistic mold filling problems. 

When solving for the energy equation an implicit FDM was used with a backward (up-winded) difference representation of the convective term. The viscous dissipation term was evaluated with velocity components from the previous time step. The equation of motion was integrated using a trapezoidal quadrature. Stevenson tested his model by comparing it to actual mold filling experiments of a disc with an ABS polymer. Table 8.8 presents data used for the calculations. 

To illustrate the effect of fiber orientation on material properties of the final part, Fig. 8.60 [5] shows how the fiber orientation distributions that correspond to 67 50 and 33% initial mold coverage affect the stiffness of the finished plates. The Folgar-Tucker model has been implemented into various, commercially available compression mold filling simulation programs and successfully tested with several realistic compression molding applications. 

The second integral on the right hand side of eqn. (9.67) can be evaluated for problems with a prescribed Neumann boundary condition, such as heat flow when solving conduction problems. For the Hele-Shaw approximation used to model some die flow and mold filling problems, where 8p/8n = 0, this term is dropped from the equation. 

Two-Dimensional Mold Filling Simulation of Non-Planar Parts (2.5D Model)... 

Monodiefperse Spheres The rheology of concentrated ceramic suspensions is very important for good mold filling. For concentrated suspensions that are colloidally stable (by steric means, giving a hard sphere model), there is a particle volume fraction (i.e., = 0.63 for... 

Problem 4-8. Pressure-Driven Radial Flow Between Parallel Disks. The flow of a viscous fluid radially outward between two circular disks is a useful model problem for certain types of polymer mold-filling operations, as well as lubrication systems. We consider such a system, as sketched here ... 

Such an analysis, however, necessarily Involves the acquisition and correlation of data related to the viscosity and kinetics of the curing polymer. Computer modeling of mold filling and curing events is then possible (2.,. Coupling these... 

For prediction of mold filling and flow-through dies, computer modelling is increasingly used. In addition to viscosity, measurements may be needed for specific heat, shrinkage, thermal conductivity, and pressure- volume -temperature (PVT) relationship. A differential scanning calorimeter (DSC) can be used for specific heal measurements. 

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