Modelling and Optimisation of Single Screw Extrusion,
PhD Thesis of
A. Gaspar-Cunha
University of Minho, Guimarães, Portugal
February 2000
ABSTRACT
Upon manufacturing plastics parts by extrusion or injection, polymers are plasticised in single screw units The mechanisms involved in this process are complex and material, geometry and operation dependent. Usually, the setting of the extruder operating conditions or the establishment of the adequate screw geometry is based on trial-and-error. A more efficient method consists in determining the operating conditions or screw geometry that produce the desired performance, i.e. to solve the inverse problem. This is not an easy task, since the inverse formulation of plasticating extrusion cannot be explicitly obtained. Also, the solution is probably not unique, since different combinations of screw geometry and/or operating conditions might produce the same performance. An alternative strategy is to develop an optimisation algorithm, where the equations available to solve the direct problem are used iteratively, until the solution converges to an optimum.
In this work such an automatic optimisation scheme is implemented. Genetic Algorithms (GAs) are chosen as the optimisation algorithm, given their capacity for dealing with combinatorial-type problems and the fact that they do not require neither derivative information nor other additional knowledge. The performance of such an optimisation scheme depends, mainly, on the validity of the predictions and also, on the sensitivity of the modelling package to changes in the input variables. Therefore, a numerical modelling package able to take these aspects into consideration and, simultaneously, produce results with lower computation time, is also implemented and validated.
The linkage between the optimisation algorithm and the modelling package is made through an objective function that quantifies the relevant criteria and their relative importance to the process. Given the complexity of the search space and the existence of some conflicting criteria a new multiobjective optimisation method using GAs – Reduced Pareto Set Genetic Algorithm (RPSGA) – was developed. This method incorporates a technique for reducing the Pareto set. Well known benchmark problems were used to validate the algorithm. Also, a “real world” extrusion problem is solved. Comparisons are made with Nondominated Sorting Genetic Algorithm (NSGA). The results obtained seem to indicate that this approach can be very useful, especially where there is the need to use large populations. This optimisation methodology is able to produce results with physical meaning.
The methodology developed in this work is applied to the optimisation of the operating conditions and screw design for specific case studies. A full factorial analysis, using extrusion experiments, was carried out in order to assess the computational results, obtained by both analytical (implemented previously) and numerical modelling packages. The results allow one to conclude that the approaches where the numerical model is used yield better results. The results obtained for screw design show that the optimisation algorithm is sensitive to the importance of the different criteria, to changes in the operating conditions and to changes in the polymer properties.