Keywords: extrusion die design, optimisation, finite volumes, flow balance.

As a result of the large number of phenomena and restrictions involved and the complexity of the polymer melt rheological behaviour, extrusion die design was, and still is, more an art than a science [1]. In fact, traditionally the design of a new die was based on experimental trial-and-error procedures, which are very time, human, machine and raw materials consuming and do not guarantee the achievement of the optimal solution. Currently, and due to the availability of numerical modelling codes, this trial-and-error design approach is being progressively transformed from experimental into a numerical based operation, however, it is still dependent on the designer's experience [2]. The advantages of this approach are an overall reduction in the cost of the project and a higher probability of finding the optimal solution. Recently, there is a trend towards the automatic die design concept [3,4,5] with the objective to turn its design as automatic as possible, ideally without any user intervention, and to guarantee the achievement of the optimal solution. In this case, the process is almost all carried out by the computer, with obvious savings in the time consumed and in the remaining resources.

The authors of the present work have successfully implemented and validated a numerical code able to automatically balance the flow in profile extrusion dies [3,6,7]. To accomplish this, several problems had to be solved, namely: geometry parameterisation, minimisation of the computation time, evaluation of the quality of each trial geometry and the optimisation technique. The parameterisation problem was solved by the division of the profile cross section into elemental sections and by the introduction of an additional region in the die flow channel, which allowed the definition of the die geometry through some parameters. The minimisation of the computation time was achieved by the employment of a numerical code based in the finite volume method coupled with a progressive mesh refinement technique. An objective function was proposed to evaluate the performance of each trial geometry. For optimisation purposes two algorithms were implemented, one based on the simplex method and other in the traditional trial-and-error approach usually employed in the design of these tools, and two alternative design strategies were developed.

A case study is used to compare the adequacy of several die design strategies implemented, not only in terms of the performance attained for the resulting dies when used in the conditions adopted in their optimisation, but also in terms of their robustness when those conditions are varied. The results obtained allowed the following conclusions:

• The traditional methods employed in the design of extrusion dies can be significantly improved by the automatic design concept.
• The developed flow balancing code is able to clearly improve the performance of extrusion dies within acceptable computational times;
• The thickness based optimisation strategy is more efficient from the flow balance point of view and generates dies more stable. However, these dies are expected to originate profiles more prone to distort;
• Optimisation strategies based on the length control may be difficult to apply in profiles presenting significant differences in flow restriction. This can be minimised through the use of flow separators. However, the flow separators may reduce the mechanical resistance of the profile and promote higher sensitivity of the die. This has negative consequences in the final profile usage and during its production.

1

J.H. Schut, "Computer Flow Analysis Helps Develop New Profile Dies Faster", Plastics Technology(August), 2003.

2

J.P. Forest, "Design: The End of Empiricism", Revue Generale des Caoutchoucs et Plastiques, 748(March 1996), 58, 1996.

3

J.M. Nobrega, O.S. Carneiro, F.T. Pinho, and P.J. Oliveira, "Flow Balancing in Extrusion Dies for Thermoplastic Profiles - Part III: Experimental Assessment", International Polymer Processing, 19(3), 225-235, 2004.

4

J.-M. Marchal and A. Goublomme, "Parametric Optimization of Extrusion Dies through Numerical Simulation", in "The Polymer Processing Society - Europe/Africa Regional Meeting", Zlín, Czech Republic, 2000.

5

J. Sienz, J.-M. Marchal, and J.F.T. Pittman, "Profile Extrusion Die Design Using Optisation Techniques and an Expert System", in "Third Esaform Conference on Material Forming", Stuttgart, Germany, 2000.

6

J.M. Nóbrega, O.S. Carneiro, P.J. Oliveira, and F.T. Pinho, "Flow Balancing in Extrusion Dies for Thermoplastic Profiles Part I: Automatic Design", International Polymer Processing, 18(3), 298-306, 2003.

7

O.S. Carneiro, J.M. Nóbrega, P.J. Oliveira, and F.T. Pinho, "Flow Balancing in Extrusion Dies for Thermoplastic Profiles Part II: Influence of the Design Strategy", International Polymer Processing, 18(3), 307-312, 2003.

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