# Helical Flow of Polymer Melts in Extruders : Model Development and Validation with Experiments

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- Helical Flow of Polymer Melts in Extruders : Model Development and Validation with Experiments

## Abstract

Operating and processing conditions as well as the selection of the screw design in injection molding industry are largely based on trial-and-error exercise, which is expensive and time consuming. A better approach is to develop mathematical models for prediction of the final process performance where the conditions and parameters of a process can be used as inputs in those models. However, most of the models developed and used so far contain unrealistic geometrical and mathematical simplifications. The objective of this work is to develop a steady-state three dimensional mathematical model to describe the flow of an incompressible polymer melt inside a helical geometry, which represents the polymer's true motion in extrusion and injection molding processes. In order to develop the model in helical geometry, where at least two axes are not perpendicular, the mathematical model is first developed in a natural system (i.e. cylindrical) and using transformation tools are then changed to the physical helical one. In this initiative, we develop an iterative computational alogrithm based on shooting Newton-Raphson method in order to simulate the process. The transformation matrices to adapt the equations of change form a natural system (i.e. orthogonal cylindrical systems) to a physical system (i.e. Helical coordinates) are also developed for velocity and derivative profiles. Subsequently the solution approach to solve the indirectly coupled equations of change is explained and the simulation results are compared with experimental data. The simulation results are vallidated against data obtained from ten different experiments with an industrial injection molding machine, processing two different polymers - high density polyethylene (HDPE) and poly ethylene terephthalate (PET). It is observed that the simulation results are in good agreement with experimental data. This outcome demonstrates the utility of the developed mathematical model and simulation approach. Important features of this work are the consideration of the linear backward motion of the screw leading to calculation of proper process shot size and the incorporation of the tapering screw designs with upward and downward sections in the direction of the flow into the model. Another important feature in the development of the mathematical model is that the rheological and physical properties of plastic resins are not constant and change as the melt temperature changes during the process. From the standpoint of industrial practice, the direct benefit of this work is the ability to effectively calculate adequate shot size, recovery rate, and various state variables throughout the extent of the machine.