SpringerLink
Log in

An optimization strategy for die design in the low-density polyethylene annular extrusion process based on FES/BPNN/NSGA-II

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

An optimization strategy for die design in the polymer extrusion process is proposed in the study based on the finite element simulation, the back-propagation neural network, and the non-dominated sorting genetic algorithm II (NSGA-II). The three-dimensional simulation of polymer melts flow in the extrusion process is conducted using the penalty finite element method. The model for predicting the flow patterns in the extrusion process is established with the artificial neural network based on the simulated results. The non-dominated sorting genetic algorithm II is performed for the search of globally optimal design variables with its objective functions evaluated by the established neural network model. The proposed optimization strategy is successfully applied to the die design in low-density polyethylene (LDPE) annular extrusion process. A constrained multi-objective optimization model is established according to the characteristics of annular extrusion process. The minimum of velocity relative difference, δu, and the minimum of swell ratio, S w, that, respectively, ensure the extrinsic feature, mechanical property, and dimensional precision of the final products are taken as optimization objectives with a constrained condition on the maximum shear stress. Three important die structure parameters, including the die contraction angle α, the ratio of parallel length to inner radius L/R i, and the ratio of outer to inner radius R o /R i, are taken as design variables. The Phan-Thien–Tanner constitutive model is adopted to describe the viscoelastic rheological characteristics of LDPE whose parameters are fitted by the distributions of material functions detected on the strain-controlled rheometer. The penalty finite element model of polymer melts flowing through out of the extrusion die is derived. A decoupled method is employed to solve the viscoelastic flow problem with the discrete elastic-viscous split-stress algorithm. The simulated results are selected and extracted to constitute the learning samples according to the orthogonal experimental design method. The back propagation algorithm is adopted for the training and the establishment of the predicting model for the optimization objective. A Pareto-optimal set for the constrained multi-objective optimization is obtained using the constrained NSGA-II, and the optimal solution is extracted based on the fuzzy set theory. The optimization for die parameters in the annular extrusion process of low-density polyethylene is performed and the optimization objective is successfully achieved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Smith DE (2003) Design sensitivity analysis and optimization for polymer sheet extrusion and mold filling process. Int J Numer Methods Eng 57(10):1381–1411

    Article  MATH  Google Scholar 

  2. Caneiro OS, Nbbrega JM, Pinho FT (2001) Computer aided rheological design of extrusion dies for profiles. J Mater Process Technol 114(1):75–86

    Article  Google Scholar 

  3. Michaeli W, Kaul S, Wolff T (2001) Computer-aided optimization of extrusion dies. J Polym Eng 21(2):225–237

    Google Scholar 

  4. Chung JS, Hwang SM (1997) Application of a genetic algorithm to the optimal design of the die shape in extrusion. J Mater Process Technol 72(1):69–77

    Article  Google Scholar 

  5. Svabik J, Placek L, Saha P (1999) Profile die design based on flow balancing. Internal Polymer Processing 3:247–253

    Google Scholar 

  6. Koziey BL, Vlachopoulos J, Vlcek J (1996) Profile die design by pressure balancing and cross flow minimization. Proceedings of SPE Annual Technical Conference, pp 247–252

  7. Huang CC, Tang TT (2006) Parameter optimization in melt spinning by neural networks and genetic algorithms. Int J Adv Manuf Technol 27:1113–1118

    Article  Google Scholar 

  8. Kuo CF, Wu YS (2006) Application of a Taguchi-based network prediction design of the film coating process for polymer blends. Int J Adv Manuf Technol 27:455–461

    Article  Google Scholar 

  9. Cunha AG, Covas JA, Oliveira P (1998) Optimization of polymer extrusion with genetic algorithms. Journal of Mathematics Applied in Business and Industry 9(3):207–277

    Google Scholar 

  10. Phan-Thien N, Tanner RI (1977) A new constitutive equation derived from network theory. J Non-Newton Fluid Mech 2:353–365

    Article  Google Scholar 

  11. Mitsoulis E (1999) Three-dimentional non-Newtonian computations of extrudate swell with the finite element method. Computation Methods in Applied Mechanics and Engineering 180:333–344

    Article  MATH  Google Scholar 

  12. Mu Y, Zhao GQ (2007) An optimization approach for polymer sheeting die design. Proceedings of SPE Annual Technical Conference, pp 2581–2585

  13. Tanner RI (1970) A theory of die-swell. J Polym Sci Part A 8:2067–2078

    Article  Google Scholar 

  14. Chung TJ (1978) Finite element analysis in fluid dynamics. McGraw-Hill, NewYork

    MATH  Google Scholar 

  15. Mu Y, Zhao GQ (2007) Modeling and simulation of the complex flows in the extrusion process of plastic profile with metal insert. Proceedings of SPE Annual Technical Conference, pp 352–358

  16. Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworths, Boston

    Google Scholar 

  17. Mu Y, Zhao GQ, Qin SX, Chen AB (2007) Numerical simulation of three-dimensional polymer extrusion flow with differential viscoelastic model. Polym Adv Technol 18(12):1004–1014

    Article  Google Scholar 

  18. Mu Y, Zhao GQ (2008) Numerical study of nonisothermal polymer extrusion flow with a differential viscoelastic model. Polym Eng Sci 48(2):316–328

    Article  Google Scholar 

  19. Guénette R, Fortin M (1995) A new mixed finite element methods for computing viscoelastic flows. J Non-Newton Fluid Mech 60:27–52

    Article  Google Scholar 

  20. Gallant S (1994) Neural network learning and expert system. The MIT Press, Cambridge

    Google Scholar 

  21. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann arbor

    Google Scholar 

  22. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  23. Kanagarajan D, Karthikeyan R, Palanikumar K, Paulo Davim J (2008) Optimization of electrical discharge machining characteristics of WC/Co composites using non-dominated sorting genetic algorithm (NSGA-II). Int J AdvManuf Technol 36:1124–1132

    Article  Google Scholar 

  24. Saravanan R, Ramabalan S, Balamurugan C (2008) Evolutionary optimal trajectory planning for industrial robot with payload constraints. Int J AdvManuf Technol 38:1213–1226

    Article  Google Scholar 

  25. Wei Z, Feng YX, Tan JR, Wang JL, Li ZK (2009) Multi-objective performance optimal design of large-scale injection molding machine. Int J AdvManuf Technol 41:242–249

    Article  Google Scholar 

  26. Sarkar D, Modak JM (2005) Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using non-dominated sorting genetic algorithm. Chem Eng Sci 60(2):481–492

    Article  Google Scholar 

  27. Michalewicz Z, Janikow CZ, Krawczyk JB (1992) A modified genetic algorithm for optimal control problems. Comput Math Appl 23:83–94

    Article  MATH  Google Scholar 

  28. Mu Y, Zhao GQ, Li HP, Liu J, Xu XM (2009) Measurement and simulation of low-density polyethylene extrudate swell through a circular die. Polym Int 58:475–483

    Article  Google Scholar 

  29. Abido MA (2006) Multiobjective evolutionary algorithms for electric power dispatch problem. IEEE Trans Evol Comput 10(3):315–329

    Article  Google Scholar 

  30. Deb K, Agrawal RB (1995) Simulated binary crossover for continuous search space. Complex Syst 9:115–148

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory for Liquid–Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, **an, Shandong, 250061, People’s Republic of China

    Yue Mu, Guoqun Zhao & **anghong Wu

  2. Engineering Research Center for Mould & Die Technologies, Shandong University, **an, Shandong, 250061, People’s Republic of China

    Yue Mu, Guoqun Zhao & **anghong Wu

  3. School of Mechanical Engineering, Shandong University, **an, Shandong, 250061, People’s Republic of China

    Yue Mu & Chengrui Zhang

Authors
  1. Yue Mu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoqun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. **anghong Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chengrui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guoqun Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mu, Y., Zhao, G., Wu, X. et al. An optimization strategy for die design in the low-density polyethylene annular extrusion process based on FES/BPNN/NSGA-II. Int J Adv Manuf Technol 50, 517–532 (2010). https://doi.org/10.1007/s00170-010-2556-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-010-2556-z

Keywords

Search

Navigation