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Keywords: polymer extrusion, cooling, heat transfer, modelling, optimisation.

Summary

During the production of plastic extruded profiles, the calibrator(s) should cool down the profile both swiftly, to enable the production at high rates, and uniformly, to minimise the level of thermal residual stresses in the plastic extrudate. The main difficulty to be faced in the design of these tools arises from the fact that these two objectives are conflicting. As shown in a previous work, there are few ways to improve simultaneously both criteria [1]: i) division of the cooling length into several cooling units separated by annealing zones, which is the most effective alternative; ii) reduction of the production rate, which should be avoided whenever possible. Furthermore, one of the most effective and easy-to-control operating variable of this cooling process is the temperature of the fluid (generally water) circulating in the cooling system of the calibrator(s) [1].

This work aims at finding the most efficient calibration-cooling system, both in terms of system layout (i.e. number of calibrators, length of each calibrator and length of the annealing zones, or air gaps, existing between them) and of cooling water temperature set for each calibration unit. For this purpose, an optimisation code was developed to automatically find the set of calibrators-annealing zones lengths and cooling water temperatures that result in the most rapid and, or even cooling of the extruded plastic profile. This encompasses the integration of different routines, namely: i) a pre-processor - a code developed in-house is used to automatically generate the geometry of the calibration-cooling systems proposed by the optimisation algorithm and the corresponding computational grids; ii) a numerical heat transfer model - the thermal fields in the plastic extrudate and metallic calibrators are calculated by a 3D computational code based on the finite-volume method [1,2,3,4]; iii) criteria for performance evaluation - as in the majority of optimisation problems the definition of the optimal variables values is multi-objective, i.e., various criteria are to be satisfied simultaneously. In this particular case, the criteria used to access the performance of a specific calibration-cooling system are the cooling rate of the extrudate, represented by its average temperature, , and the cooling uniformity, represented by the corresponding temperature distribution standard deviation, , computed at the end of the domain considered (outlet of the last calibrator); iv) an optimisation algorithm - the reduced pareto set genetic algorithm with elitism (RPSGAe) is adopted [5].

The optimisation code described above was used to improve the performance of a calibration-cooling system used for a rectangular hollow plastic profile. To carry out the optimisation of the calibration-cooling zone layout, the following assumptions were considered: the number of calibration-cooling units should not exceed three; the total length of calibration should not exceed 600 mm; the minimum calibrator length was set to 50 mm (when the algorithm proposes a calibrator shorter than 25 mm that unit is removed from the system; alternatively, when the proposed length is in the range [25,50] mm it will be set to 50 mm); the minimum length for an annealing zone was set to 10 mm (when the algorithm proposes an annealing zone shorter than 5 mm that region is removed from the system; alternatively, if the proposed length is in the range [5,10] mm it will be set to 10 mm); the total length of the cooling zone should not exceed 840 mm. The optimisation algorithm parameters used were the following: a main population of 100 individuals, elitist populations of 200 individuals and 50 generations. A roulette wheel selection strategy was adopted, a crossover probability of 0.8, a mutation probability of 0.05, a number of ranks of 30 and limits of indifference of the clustering technique of 0.01 were chosen.

The results obtained showed that the optimisation methodology developed was able to improve the performance of a calibration-cooling system, finding the optimal Pareto frontier defined by two conflicting criteria, extrudate average temperature and corresponding standard deviation, taken at the end of the system.

References

1

J.M. Nóbrega, O.S. Carneiro, J.A. Covas, F.T. Pinho, P.J. Oliveira, "Design of Calibrators for Extruded Profiles. Part I: Modelling the Thermal Interchanges", Polym. Eng. Sci., 44, 2216-2228, 2004. doi:10.1002/pen.20249

2

J.M. Nóbrega, F.T. Pinho, P.J. Oliveira, O.S. Carneiro, "Accounting for Temperature-Dependent Properties in Viscoelastic Duct Flows", Int. J. of Heat and Mass Transfer, 47, 1141-1158, 2004. doi:10.1016/j.ijheatmasstransfer.2003.10.004

3

P.J. Oliveira, F.T. Pinho, G.A. Pinto, "Numerical Simulation of Non-Linear Elastic Flows with a General Collocated Finite-Volume Method", J. Non-Newt. Fluid Mec., 79, 1-43, 1998. doi:10.1016/S0377-0257(98)00082-2

4

P.J. Oliveira, F.T. Pinho, "Numerical Procedure for the Computation of Fluid Flow with Arbitrary Stress-Strain Relationships", Numerical Heat Transfer Part B-Fundamentals, 35, 295-315, 1999. doi:10.1080/104077999275884

5

A. Gaspar-Cunha, J.A. Covas, "RPSGAe - A Multiobjective Genetic Algorithm with Elitism: Application to Polymer Extrusion", in a Lecture Notes in Economics and Mathematical Systems, Volume 535, Springer, Berlin, Germany, 2004.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 84 PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro Paper 25 Optimising the Calibration System Layout in Profile Extrusion J.M. Nóbrega, O.S. Carneiro and A. Gaspar-Cunha Institute for Polymers and Composites, IPC, Department of Polymer Engineering, University of Minho, Guimarães, Portugal doi:10.4203/ccp.84.25 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Optimising the Calibration System Layout in Profile Extrusion", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 25, 2006. doi:10.4203/ccp.84.25 Keywords: polymer extrusion, cooling, heat transfer, modelling, optimisation. Summary During the production of plastic extruded profiles, the calibrator(s) should cool down the profile both swiftly, to enable the production at high rates, and uniformly, to minimise the level of thermal residual stresses in the plastic extrudate. The main difficulty to be faced in the design of these tools arises from the fact that these two objectives are conflicting. As shown in a previous work, there are few ways to improve simultaneously both criteria [1]: i) division of the cooling length into several cooling units separated by annealing zones, which is the most effective alternative; ii) reduction of the production rate, which should be avoided whenever possible. Furthermore, one of the most effective and easy-to-control operating variable of this cooling process is the temperature of the fluid (generally water) circulating in the cooling system of the calibrator(s) [1]. This work aims at finding the most efficient calibration-cooling system, both in terms of system layout (i.e. number of calibrators, length of each calibrator and length of the annealing zones, or air gaps, existing between them) and of cooling water temperature set for each calibration unit. For this purpose, an optimisation code was developed to automatically find the set of calibrators-annealing zones lengths and cooling water temperatures that result in the most rapid and, or even cooling of the extruded plastic profile. This encompasses the integration of different routines, namely: i) a pre-processor - a code developed in-house is used to automatically generate the geometry of the calibration-cooling systems proposed by the optimisation algorithm and the corresponding computational grids; ii) a numerical heat transfer model - the thermal fields in the plastic extrudate and metallic calibrators are calculated by a 3D computational code based on the finite-volume method [1,2,3,4]; iii) criteria for performance evaluation - as in the majority of optimisation problems the definition of the optimal variables values is multi-objective, i.e., various criteria are to be satisfied simultaneously. In this particular case, the criteria used to access the performance of a specific calibration-cooling system are the cooling rate of the extrudate, represented by its average temperature, , and the cooling uniformity, represented by the corresponding temperature distribution standard deviation, , computed at the end of the domain considered (outlet of the last calibrator); iv) an optimisation algorithm - the reduced pareto set genetic algorithm with elitism (RPSGAe) is adopted [5]. The optimisation code described above was used to improve the performance of a calibration-cooling system used for a rectangular hollow plastic profile. To carry out the optimisation of the calibration-cooling zone layout, the following assumptions were considered: the number of calibration-cooling units should not exceed three; the total length of calibration should not exceed 600 mm; the minimum calibrator length was set to 50 mm (when the algorithm proposes a calibrator shorter than 25 mm that unit is removed from the system; alternatively, when the proposed length is in the range [25,50] mm it will be set to 50 mm); the minimum length for an annealing zone was set to 10 mm (when the algorithm proposes an annealing zone shorter than 5 mm that region is removed from the system; alternatively, if the proposed length is in the range [5,10] mm it will be set to 10 mm); the total length of the cooling zone should not exceed 840 mm. The optimisation algorithm parameters used were the following: a main population of 100 individuals, elitist populations of 200 individuals and 50 generations. A roulette wheel selection strategy was adopted, a crossover probability of 0.8, a mutation probability of 0.05, a number of ranks of 30 and limits of indifference of the clustering technique of 0.01 were chosen. The results obtained showed that the optimisation methodology developed was able to improve the performance of a calibration-cooling system, finding the optimal Pareto frontier defined by two conflicting criteria, extrudate average temperature and corresponding standard deviation, taken at the end of the system. References 1 J.M. Nóbrega, O.S. Carneiro, J.A. Covas, F.T. Pinho, P.J. Oliveira, "Design of Calibrators for Extruded Profiles. Part I: Modelling the Thermal Interchanges", Polym. Eng. Sci., 44, 2216-2228, 2004. doi:10.1002/pen.20249 2 J.M. Nóbrega, F.T. Pinho, P.J. Oliveira, O.S. Carneiro, "Accounting for Temperature-Dependent Properties in Viscoelastic Duct Flows", Int. J. of Heat and Mass Transfer, 47, 1141-1158, 2004. doi:10.1016/j.ijheatmasstransfer.2003.10.004 3 P.J. Oliveira, F.T. Pinho, G.A. Pinto, "Numerical Simulation of Non-Linear Elastic Flows with a General Collocated Finite-Volume Method", J. Non-Newt. Fluid Mec., 79, 1-43, 1998. doi:10.1016/S0377-0257(98)00082-2 4 P.J. Oliveira, F.T. Pinho, "Numerical Procedure for the Computation of Fluid Flow with Arbitrary Stress-Strain Relationships", Numerical Heat Transfer Part B-Fundamentals, 35, 295-315, 1999. doi:10.1080/104077999275884 5 A. Gaspar-Cunha, J.A. Covas, "RPSGAe - A Multiobjective Genetic Algorithm with Elitism: Application to Polymer Extrusion", in a Lecture Notes in Economics and Mathematical Systems, Volume 535, Springer, Berlin, Germany, 2004. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £105 +P&P)
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