ANALYSIS OF FLOW IN INJECTION MOLDS, THE DERIVATION OF THE GOVERNING EQUATIONS FOR THE MATHEMATICAL MODELLING OF THE FLOW OF POLYMER MELT

Abstract

ABSTRACT

In the injection molds, the governing equations that describe the flow front of a polymer melt and form of the pressure, velocity and temperature distribution have been derived for the mathematical modeling. The continuity, the momentum and the energy equations derived from different methods in the literature wereobtained in detail and they were prepared as a set on which the solving methods of differential equations can be applied. In discretization process using Finite Control Volume, Full Implicit and Upwind methods were used. For two dimensional cavity, variations of density were calculated using Boussinesq Approach by Phoneics program. Filling simulation in the cavity were achieved. In addition, solid layer was determined by Darc’y method.

Keywords

• Key Words: Injection molding, Flow analysis and simulation, Melt flow, Finite control volume method

Abstract

Plastik enjeksiyon kalıplarında, kalıp boşluğu içerisinde ergimiş plastiklerin akışının matematiksel modellenmesi, akış burnu hareketlerinin tayini ve basınç, hız ve sıcaklık dağılımlarının belirlenmesi için kullanılan temel denklemler türetilmiştir. Literatürde farklı metotlarla türetilen fakat, çok anlaşılır olarak verilmeyen süreklilik, momentum ve enerji denklemleri daha detaylı bir şekilde elde edilmiş ve diferansiyel denklem çözüm metotlarının uygulandığı biçime getirilmiştir. Sonlu Kontrol Hacmi formülasyonu’na göre yapılan ayrıklaştırma işleminde Tam Implicit metodu ve Upwind metodu kullanılmıştır. Kalıp boşluğunun iki boyutlu olarak ele alındığı çalışmada, Phoenics programı ile yapılan çözümlemede, yoğunluğun değişimleri Boussinesq Yaklaşımı’na göre hesaplanmıştır. Plastiğin kalıp boşluğunu doldurması simüle edilmiştir. Ayrıca, Darc’y yöntemi kullanılarak katı katman tabakası tespit edilmiştir

Keywords

• Enjeksiyonla kalıplama, Akış analizi ve simülasyon, Ergimiş plastiğin akışı, Sonlu kontrol hacmi metodu

References

1. Rosato, D. V., Rosato, D. V., Injection Molding Handbook 2nd ed., Kluwer Academic Publishers, Boston/London (1999).
2. Buckleitner, E. V., Plastics Mold Engineering Handbook 5th ed., Chapman & Hall, An International Thomson Publishing Company, USA (1995).
3. Miles, D.C., Briston, J.H., Polymer Technology 3rd Ed., Chemical Publishing Co. Inc., New York, USA (1996).
4. Rees H., Mold Engineering, Hanser/Gardner Inc., Cincinnati, USA (1995).
5. Subbiah, S., Trafford, D. L., Güçeri, S. I., “Non- Isothermal Flow of Polymers Into Two -Dimensional, Thin Cavity Molds: A Numerical Grid Generation Approach”, International Journal Heat Mass Transfer, 32 (3), 415-434 (1989).
6. Seow, L. W., Lam, Y. C., “Optimising Flow in Plastic Injection Molding”, Journal of Materials Processing Technology, 72: 333-341 (1997).
7. Smith, D. E., Tortorelli, D. A., Tucker III, C. L., “Analysis and Sensivity Analysis For Polymer Injection and Compression Molding”, Computer Methods Applied Mechanics Engineering, 167: 325-344 (1998).
8. Hill, D., “Further Studies of The Injection Moulding Process”, Applied Mathematics Modelling, 20: 719-720 (1996).

9. Shen, Y. K., “Study on Moving Boundary Problems of Injection Molding”, International Communicate Heat Mass Transfer, 25: 701-710 (1998).
10. Chiang, H. H., Hieber, C. A., Wang, K. K., “A Unified Simulation of The Filling and Postfilling Stages in Injection Molding. Part I: Formulation”, Polymer Engineering and Science, 31 (2): 116-124 (1991).
11. Carreau, P.J., Kee, D., Chhabra, R.P., Rheology of Polymeric Systems Principle and Applications, Hanser/Gardner Inc., Cincinnati, USA (1997).
12. White, F.M., Fluid Mechanics 4th ed., McGraw-Hill, Inc., New York, USA (1994).
13. Umur, H., Akışkanlar Mekaniği, Alfa Basım Yayım Dağıtım, İstanbul (1998).
14. Wendt, J.F., Computational Fluid Dynamics an Introduction 2nd ed., Springer, Berlin, Germany (1996).
15. Versteeg, H.K., Malalasekera, W., “An Introduction to Computional Fluid Dynamics, The Finite Volume Method”, Addison Wesley Longman, England (1995).
16. Schlichting, H., Boundary-Layer Theory, McGraw-Hill, 17th ed., USA (1979).
17. Welty, J.R., Wicks, C. E., Wilson, R.E., Fundamentals of Momentum, Heat, and Mass Transfer 3rd ed., John Wiley & Sons Inc., USA (1984).
18. Yaman, G., İren, M., “İnce Kesitli Bir Kanal İçerisindeki Akımın İncelenmesi İçin -Boyutlu Formülasyon”, Makina Tasarım ve İmalat Dergisi, 4 (2): 78-88 (2001)
19. Pozrikidis, C., Introduction to Theoretical and Computational Fluid Dynamics, Oxford University Press (1997)
20. Street, R.L., Watters, G.Z., Vennard, J.K., Elementary Fluid Mechanics 7th ed., John Wiley & Sons Inc., USA (1996)
21. Leal, L.G., “Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis”, Butterworth-Heinemann In Chemical Engineering, Stoneham, Ma, USA (1992)
22. Crochet, M.J., Davides, A.R., Walters, K., Numerical Simulation of Non-Newtonian Flow 3. Ed., Elsevier Rheology Series 1, Amsterdam, Netherlands (1991)
23. Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Published Corparation, New York, USA (1980)
24. Versteeg, H.K., Malalasekera, W., An Introduction to Computational Fluid Dynamics, The Finite Volume Method”, Longman, England (1995)