Accessible Requires Authentication Published by De Gruyter March 1, 2013

Extrusion Scale-up: An Optimization-based Methodology

J. A. Covas and A. Gaspar-Cunha

Abstract

Given a reference extruder with a certain geometry and operating point, the aim of scale-up is to define the geometry and operating conditions of a target extruder (generally of significantly different size) in order to subject the material being processed to the same flow and heat transfer conditions, thus yielding products with the same characteristics. Since existing scale-up rules are crude, as they usually consider a single performance measure and produce unsatisfactory results, this work approaches scale-up as a multi-criteria optimization problem, where the aim is to define the geometry/operating conditions of the target extruder that minimize the differences between the values of various performance criteria for the reference and target extruders. Some case studies are discussed involving individual and multi-criteria scaling-up in terms of operating conditions, geometry, and both together, the usefulness of the approach being demonstrated. A few experiments are also performed in order to validate the concept.


2 Mail address: Antonio Gaspar-Cunha, Institute for Polymers and Composites/I3N, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal E-mail:

References

Broyer, E., Tadmor, Z., Solids Conveying in Screw Extruders – Part I: A Modified Isothermal Model, Polym. Eng. Sci., 12, 1224(1972).10.1002/pen.760120103 Search in Google Scholar

Carley, J. F., McKelvey, J. M., Extruder Scale-up Theory and Experiments, Ind. Eng. Chem., 45, 985989(1953). Search in Google Scholar

Carneiro, O. S., et al., Experimental and Theoretical Study of Twin Screw Extrusion of Polypropylene, J. Appl. Polym. Sci., 78, 14191430(2000).10.1002/1097-4628(20001114)78:7<1419::AID-APP130>3.0.CO;2-B Search in Google Scholar

Chung, C. I., On the Scale-up of Plasticating Extruder Screws, Polym. Eng. Sci., 24, 626632(1984).10.1002/pen.760240904 Search in Google Scholar

Coello Coello, C. A., et al.: Evolutionary Algorithms for Solving Multi-Objective Problems, Kluwer, Amsterdam(2002). Search in Google Scholar

Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms, Wiley, New York(2001). Search in Google Scholar

Elbirli, B., et al., Mathematical Modelling of Melting of Polymers in a Single-Screw Extruder, Polym. Eng. Sci., 24, 988999(1984).10.1002/pen.760241208 Search in Google Scholar

Elemans, P. H. M., Meijer, H. E. H., Scale-up of the Mixing Process in Continuous Mixers, in Mixing and Compounding of Polymers, Manas-Zloczower, I., Tadmor, Z. (Ed.), Carl Hanser Verlag, Munich, p. 457470(1994). Search in Google Scholar

Fenner, R. T., Williams, J. G., Some Melt Flow and Mechanical Design Aspects of Large Extruders, Polym. Eng. Sci., 11, 474483(1971).10.1002/pen.760110606 Search in Google Scholar

Ferreira, J. C., et al., A New Methodology to Select the Preferred Solutions from the Pareto-optimal Set: Application to Polymer Extrusion, 10th Esaform Conference on Material Forming, Zaragoza(2007). Search in Google Scholar

Gaspar-Cunha, A., Modelling and Optimization of Single Screw Extrusion, PhD Thesis, University of Minho, Guimarães, Portugal(2000). Search in Google Scholar

Gaspar-Cunha, A., Covas, J. A., The Design of Extrusion Screws: An Optimisation Approach, Int. Polym. Proc., 16, 229240(2001). Search in Google Scholar

Gaspar-Cunha, A., Covas, J. A., RPSGAe – A Multiobjective Genetic Algorithm with Elitism: Application to Polymer Extrusion, in Metaheuristics for Multiobjective Optimisation, Lecture Notes in Economics and Mathematical Systems, Gandibleux, X., Sevaux, M., Sörensen, K., T'kindt, V. (Eds.), Springer, Berlin, Heidelberg, 221249(2004).10.1007/978-3-642-17144-4_9 Search in Google Scholar

Gaspar-Cunha, A., et al., Defining the Configuration of Co-rotating Twin Screw Extruders with Multiobjective Evolutionary Algorithms, Polym. Eng. Sci., 45, 11591173(2005).10.1002/pen.20391 Search in Google Scholar

Goldberg, D. E.: Genetic Algorithms in Search, Optimisation and Machine Learning, Addison-Wesley(1989). Search in Google Scholar

Hyun, K. S., Spalding, M. A., Bulk Density of Solid Polymer Resins as a Function of Temperature and Pressure, Polym. Eng. Sci., 30, 571576(1990).10.1002/pen.760301003 Search in Google Scholar

Kacir, L., Tadmor, Z., Solids Conveying in Screw Extruders – Part III: The Delay Zone, Polym. Eng. Sci., 12, 387395(1972).10.1002/pen.760120511 Search in Google Scholar

Lindt, J. T., Pressure Development in the Melting Zone of a Single Screw Extruder, Polym. Eng. Sci., 21, 11621166(1981).10.1002/pen.760211708 Search in Google Scholar

Machado, A.V., Covas, J. A., van Duin, M., Chemical and Morphological Evolution of PA6/EPM/EPM-g-MA Blends in a Twin Screw Extruder, J. Polym. Sci.: Part A: Polym. Chem., 37, 13111318(1999).10.1002/(SICI)1099-0518(19990501)37:9<1311::AID-POLA11>3.0.CO;2-Y Search in Google Scholar

Maddock, B. H., A Visual Analysis of Flow and Mixing in an Extruder, Society of Plastics Engineers Journal, 15, 383394(1959). Search in Google Scholar

Maddock, B. H., Extruder Scale-up by Computer, Polym. Eng. Sci., 14, 853858(1974).10.1002/pen.760141208 Search in Google Scholar

Pearson, J. R. A., Scale-up of Single Screw Extruders for Polymer Processing, Plastics and Rubber: Processing, 1, 113118(1976). Search in Google Scholar

Pinto, G., Tadmor, Z., Mixing and Residence Time Distribution in Melt Screw Extruders, Polym. Eng. Sci., 10, 279288(1970).10.1002/pen.760100505 Search in Google Scholar

Potente, H., Fischer, P., Model Laws for the Design of Single Screw Plasticating Extruders, Kunststoffe, 67, 242247(1977). Search in Google Scholar

Potente, H., Existing Scale-up Rules for Single-screw Plasticating Extruders, Int. Polym. Proc., 6, 267278(1991). Search in Google Scholar

Rauwendaal, C.: Polymer Extrusion, Hanser Publishers, Munich(1986). Search in Google Scholar

Rauwendaal, C., Scale-up of Single Screw Extruders, Polym. Eng. Sci., 27, 10591068(1987).10.1002/pen.760271406 Search in Google Scholar

Schenkel, G., Extruder Series with Variable L/D Ratios, Kunststoffe, 68, 155162(1978). Search in Google Scholar

Spalding, M. A., Hyun, K. S., Coefficients of Dynamic Friction as a Function of Temperature, Pressure, and Velocity for Several Polyethylene Resins, Polym. Eng. Sci., 35, 557563(1995).10.1002/pen.760350702 Search in Google Scholar

Stevens, M. J., Covas, J. A.: Extruder Principles and Operations, Springer, Berlin, Heidelberg(1995).10.1007/978-94-011-0557-6 Search in Google Scholar

Tadmor, Z., Broyer, E., Solids Conveying in Screw Extruders-Part II: Non Isothermal Model, Polym. Eng. Sci., 12, 378391(1972).10.1002/pen.760120510 Search in Google Scholar

Walker, D. M., An Approximate Theory for Pressures and Arching in Hoppers, Chem. Eng. Sci., 21, 975997(1966).10.1016/0009-2509(66)85095-9 Search in Google Scholar

Wang, W., Manas-Zloczower, I., Temporal Distributions: The Basis for the Development of Mixing Indexes for Scale-up of Polymer Processing Equipment, Polym. Eng. Sci., 41, 10681077(2001).10.1002/pen.10807 Search in Google Scholar

Wang, C., et al., Frame Indifference, Fluid Flow in Single Screw Pumps and Extruders, Int. Polym. Proc., 11, 199207(1996). Search in Google Scholar

Yi, B., Fenner, R. T., Scaling-up Plasticating Screw Extruders on the Basis of Simular Melting Performances, Plastics and Rubber Processing, 1, 119123(1976). Search in Google Scholar

Received: 2008-08-03
Accepted: 2008-11-11
Published Online: 2013-03-01
Published in Print: 2009-03-01

© 2009, Carl Hanser Verlag, Munich