# Mathematical Models and Software Package for Extrusion Control at Flexible Multi-Assortment Productions of Polymeric Materials

T.B. Chistyakova, A.N. PolosinWe develop mathematical models of extrusion and the software package helping production staff to solve problems of resource and energy saving control of the extruders applied in flexible multi-assortment productions of packing polymeric materials. Also, we propose the combined modelling method for complex assessment of throughput, energy consumption of extrusion and quality indices of material in the extruders differing in hardware flexibility and complexity of flow structure. The method is based on use of static and dynamic models. The software package is adjusted according to production method, type of products, as well as requirements to throughput and energy consumption. The software package includes databank of extrusion characteristics, module for extrusion equipment choice, module for design of virtual models of extruder screws, subsystem for structural and parametrical synthesis of mathematical model and calculation of output parameters for extrusion, subsystem for visualization of results, in particular, in the form of trends of output parameters and 3D graphs of their dependences on controlling actions. The operability was confirmed by testing of the software package according to data from productions of polyvinylchloride and polyethylene films at the factories in Russia and Germany. The software package can be used as the effective instrument for support of decision-making when determining configurations and operation modes of the extruders that ensure the set consumer characteristics of the products.Full text

- Keywords
- mathematical models; numerical methods; software package; extrusion; polymeric materials.
- References
- 1. Kohlert M., Hissmann O. Applied Industry 4.0 in the Polymer Film Industry. Proceedings of the 16th TAPPI European PLACE Conference. Basel, 2017, pp. 183-190.

2. Chistyakova T., Teterin M., Razygraev A., Kohlert C. Intellectual Analysis System of Big Industrial Data for Quality Management of Polymer Films. Advances in Neural Networks - ISNN 2016: 13th International Symposium on Neural Networks Proceedings. Cham, Springer, 2016, pp. 565-572.

3. Rauwendaal C. Polymer Extrusion. Munich, Carl Hanser Verlag, 2014.

4. Gartner H., Schnabel A., Kohlert C. Control Systems for Calenders - from Mixer to Take-off. Kunststoffe Plast Europe, 1997, vol. 87, no. 6, pp. 24-27.

5. Chistyakova T.B., Razygraev A.S., Polosin A.N., Kohlert C. [Software Package for Color Control of the Thin Rigid Polymeric Materials]. Avtomatizatsiya v promyshlennosti [Industrial Automation], 2012, no. 7, pp. 12-18. (in Russian)

6. Shapiro J., Halmos A.L., Pearson J.R.A. Melting in Single Screw Extruders. Part 1: The Mathematical Model. Polymer, 1976, vol. 17, no. 10, pp. 905-918.

7. Basov N.I., Volodin I.N., Kazankov Yu.V., Pervushin V.E. Hydrodynamics and Heat Exchange in Melting in the Screw Channel of an Extruder. Theoretical Foundations of Chemical Engineering, 1983, vol. 17, no. 1, pp. 61-67.

8. Elbirli B., Lindt J.T., Gottgetreu S.R., Baba S.M. Mathematical Modeling of Melting of Polymers in a Single-Screw Extruder. Polymer Engineering and Science, 1984, vol. 24, no. 12, pp. 988-999.

9. Pervadchuk V.P., Trufanova N.M., Yankov V.I. Mathematical Model and Numerical Analysis of Heat-Transfer Processes Associated with the Melting of Polymers in Plasticating Extruders. Journal of Engineering Physics, 1985, vol. 48, no. 1, pp. 60-64.

10. Lee K.Y., Han C.D. Analysis of the Performance of Plasticating Single-Screw Extruders with a New Concept of Solid-Bed Deformation. Polymer Engineering and Science, 1990, vol. 30, no. 11, pp. 665-676.

11. Voskresenskiy A.M., Kuchinskaya E.A. Pererabotka polimernykh materialov v chervyachnykh mashinakh. Metody tekhnologicheskikh raschetov [Processing of Polymeric Materials in Screw Machines. Technological Calculation Methods]. St. Petersburg, Saint Petersburg State Institute of Technology (Technical University), 2000. (in Russian)

12. Zhu L., Narh K.A., Geng X. Modeling of Particle-Dispersed Melting Mechanism and Its Application in Co-Rotating Twin-Screw Extrusion. Journal of Polymer Science. Part B: Polymer Physics, 2001, vol. 39, no. 20, pp. 2461-2468.

13. Vergnes B., Souveton G., Delacour M.L., Ainser A. Experimental and Theoretical Study of Polymer Melting in a Co-Rotating Twin-Screw Extruder. International Polymer Processing, 2001, vol. 16, no. 4, pp. 351-362.

14. Thibault F., Tanguy P.A., Blouin D. А Numerical Model for Single Screw Extrusion with Poly(Vinyl Chloride) (PVC) Resins. Polymer Engineering and Science, 1994, vol. 34, no. 18, pp. 1377-1386.

15. Tadmor Z., Broyer E. Solids Conveying in Screw Extruders. Part II: Non Isothermal model. Polymer Engineering and Science, 1972, vol. 12, no. 5, pp. 378-386.

16. Wilczy'nski K., White J.L. Melting Model for Intermeshing Counter-Rotating Twin-Screw Extruders. Polymer Engineering and Science, 2003, vol. 43, no. 10, pp. 1715-1726.

17. White J.L., Chen Z. Simulation of Non-Isothermal Flow in Modular Co-Rotating Twin Screw Extrusion. Polymer Engineering and Science, 1994, vol. 34, no. 3, pp. 229-237.

18. Lyu M.-Y., White J.L. Simulation of Non-Isothermal Flow in a Modular Buss Kneader and Comparison with Experiment. International Polymer Processing, 1997, vol. 12, no. 2, pp. 104-109.

19. Skul'skiy O.I. [Numerical Modeling of Single-Screw Extruders]. Plasticheskie massy [Plastics], 1997, no. 8, pp. 39-44. (in Russian)

20. Monchatre B., Raveyre C., Carrot C. Influence of the Melt Viscosity and Operating Conditions on the Degree of Filling, Pressure, Temperature, and Residence Time in a Co Kneader. Polymer Engineering and Science, 2018, vol. 58, no. 2, pp. 133-141.

21. Mehranpour M., Nazokdast H., Dabir B. Computational Study of Velocity Field in the KE Element of a Modular Ko-Kneader with CFD Method. International Polymer Processing, 2003, vol. 18, no. 4, pp. 330-337.

22. Lewandowski A., Wilczy'nski K.J., Nastaj A., Wilczy'nski K. A Composite Model for an Intermeshing Counter-Rotating Twin-Screw Extruder and Its Experimental Verification. Polymer Engineering and Science, 2015, vol. 55, no. 12, pp. 2838-2848.

23. Vergnes B., Della Valle G., Delamare L. A Global Computer Software for Polymer Flows in Corotating Twin Screw Extruders. Polymer Engineering and Science, 1998, vol. 38, no. 11, pp. 1781-1792.

24. Todd D.B. Residence Time Distribution in Twin-Screw Extruders. Polymer Engineering and Science, 1975, vol. 15, no. 6, pp. 437-443.

25. Puaux J.P., Bozga G., Ainser A. Residence Time Distribution in a Co-Rotating Twin-Screw Extruder. Chemical Engineering Science, 2000, vol. 55, no. 9, pp. 1641-1651.

26. Hoppe S., Detrez C., Pla F. Modeling of a Cokneader for the Manufacturing of Composite Materials Having Absorbent Properties at Ultra-High-Frequency Waves Polymer Engineering and Science, 2002, vol. 42, no. 4, pp. 771-780.

27. Monchatre B., Raveyre C., Carrot C. Residence Time Distributions in a Co-Kneader: A Chemical Engineering Approach. Polymer Engineering and Science, 2015, vol. 55, no. 6, pp. 1237-1245.

28. Lyu M.-Y., White J.L. Residence Time Distributions and Basic Studies of Flow and Melting in a Modular Kneader. Polymer Engineering and Science, 1998, vol. 38, no. 9, pp. 1366-1377.

29. Chistyakova T.B., Razygrayev A.S., Polosin A.N., Araztaganova A.M. Joint Innovative IT Projects in the Field of Production of Polymeric Sheet Materials. Proceedings of the 2016 IEEE V Forum ''Strategic Partnership of Universities and Enterprises of Hi-Tech Branches (Science. Education. Innovations)''. St. Petersburg, Saint Petersburg Electrotechnical University ''LETI'', 2016, pp. 61-64.

30. Skachkov V.V., Torner R.V., Stungur Yu.V., Reutov S.V. Modelirovanie i optimizatsiya ekstruzii polimerov [Modeling and Optimization of Polymer Extrusion]. Leningrad, Chemistry, 1984. (in Russian)

31. Polosin A.N., Chistyakova T.B. [Mathematical Model of Single-Screw Extrusion for Control of Plastic Material Quality in Multi-Assortment Productions of Polymeric Films]. Sistemy upravleniya i informatsionnye tekhnologii [Control Systems and Information Technologies], 2009, no. 2, pp. 87-92. (in Russian)

32. Polosin A.N., Chistyakova T.B. [The Mathematical Models of Reciprocating Flow and Melting of Polymers for Design and Control of Extruders]. Sistemy upravleniya i informatsionnye tekhnologii [Control Systems and Information Technologies], 2006, no. 4, pp. 30-36. (in Russian)

33. Chistyakova T.B., Polosin A.N. [Methods and Technologies for Synthesis of Mathematical Models for Extrusion in Flexible Productions of Polymeric Materials]. Vestnik Saratovskogo gosudarstvennogo tekhnicheskogo universiteta [Vestnik Saratov State Technical University], 2011, no. 4, pp. 170-180. (in Russian)

34. Polosin A.N. [Modeling Technology of Non-Isothermal Flow of Polymer Melts in Single-Screw Extruders Based on the Theory of Plane Flows]. Informatsionnye tekhnologii modelirovaniya i upravleniya [Information Technologies of Modeling and Control], 2007, no. 3, pp. 376-386. (in Russian)

35. Chiruvella R.V., Jaluria Y., Sernas V. Extrusion of Non-Newtonian Fluids in a Single-Screw Extruder with Pressure Back Flow. Polymer Engineering and Science, 1996, vol. 36, no. 3, pp. 358-367.

36. Chistyakova T.B., Polosin A.N., Gol'tseva L.V. Matematicheskoe modelirovanie khimiko-tekhnologicheskikh ob'ektov s raspredelennymi parametrami [Mathematical Modeling of Chemical Technological Objects with Distributed Parameters]. St. Petersburg, Center for Educational Progr. ''Profession'', 2010. (in Russian)

37. Chistyakova T.B., Polosin A.N. [Simulation System for Extruder Control in Flexible Productions of the Polymeric Materials]. Avtomatizatsiya v promyshlennosti [Industrial Automation], 2010, no. 7, pp. 35-40. (in Russian)

38. Polosin A.N., Chistyakova T.B. The Mathematical Models and Program Complex for Synthesis of Reciprocating Extruders with Adjustable Configurations. Journal of Physics: Conference Series, 2019, vol. 1202, no. 1, article number 012007, 12 p.

39. Chistyakova T.B., Polosin A.N. Computer Modeling System of Industrial Extruders with Adjustable Configuration for Polymeric Film Quality Control. Proceedings of 2017 IEEE II International Conference on Control in Technical Systems. St. Petersburg, Saint Petersburg Electrotechnical University ''LETI'', 2017, pp. 47-50.

40. Chistyakova T.B., Novozhilova I.V. Intelligence Computer Simulators for Elearning of Specialists of Innovative Industrial Enterprises. Proceedings of the XIX International Conference on Soft Computing and Measurements (SCM'2016). St. Petersburg, Saint Petersburg Electrotechnical University ''LETI'', 2016, pp. 329-332.