Skip to main content
Log in

Three-Dimensional Mathematical Modeling and Numerical Simulation of Billet Shape in Spray Forming Using a Scanning Gas Atomizer

  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

A three-dimensional shape model, tracing the coordinates of the moving surface of a growing billet spray formed by a scanning gas atomizer, has been developed in this study. New mesh generation and surface smoothing algorithms for the growing billet, as well as shading algorithms, are incorporated into the model for accurate prediction of the shape and dimensions of the billet during spray forming. Mass flux distribution profiles of the spray generated by the scanning atomizer under different spraying conditions have been revealed for the shape modeling. Geometrical evolution of the billet in spray forming has been investigated based on analysis of the scanning mechanism of the atomizer. The shape modeling has been validated by different numerical algorithms and experimental investigations. Finally, the influence of processing conditions on the shape and dimensions of spray-formed deposits have been simulated and discussed. Near-net-shaped preforms with triangular or square cross section, other than the usual circular cross section, are expected to be produced under appropriate spray forming conditions.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. A.R.E. Singer: Powder Metall., 1982, 25:195–200

    Google Scholar 

  2. A.G. Leatham, A. Lawley: Int. J. Powder Metall., 1993, 29:321–29

    Google Scholar 

  3. A.G. Leatham: Mater. World, 1996, 4:317–20

    Google Scholar 

  4. E.J. Lavernia, Y. Wu: Spray Atomization and Deposition, John Wiley, New York, NY, 1996

    Google Scholar 

  5. P.S. Grant, I. Palmer, I. Stone: Mater. World, 1999, 7:331–33

    Google Scholar 

  6. P.S. Grant: Prog. Mater. Sci., 1995, 39:497–545

    Article  Google Scholar 

  7. A. Lawley: Proc. Int. Conf. on Spray Deposition and Melt Atomization. K. Bauckhage, V. Uhlenwinkel, and U. Fritsching, eds., University of Bremen, Bremen, Germany, 2000, pp. 3–16

    Google Scholar 

  8. U. Fritsching: Spray Simulation—Modelling and Numerical Simulation of Sprayforming Metals, Cambridge University Press, Cambridge, United Kingdom, 2004

    Google Scholar 

  9. P. Mathur, S. Annavarapu, D. Apelian, A. Lawley: Mater. Sci. Eng. A, 1991, A142:261–76

    Google Scholar 

  10. E. Gutierrez-Miravete, E.J. Lavernia, G.M. Trapaga, J. Szekely, N.J. Grant: Metall. Trans. A, 1989, 20A:71–85

    Google Scholar 

  11. P.S. Grant, B. Cantor, L. Katgerman: Acta Metall. Mater., 1993, 41:3097–3108

    Article  Google Scholar 

  12. P.S. Grant, B. Cantor, L. Katgerman: Acta Metall. Mater., 1993, 41:3109–18

    Article  Google Scholar 

  13. U. Fritsching, H. Zhang, K. Bauckhage: Steel Res., 1994, 65:273–78

    Google Scholar 

  14. R. Doherty, C. Cai, L.K. Warner Kohler: Int. J. Powder Metall., 1997, 33:50–60

    Google Scholar 

  15. I.A. Frigaard, O. Scherzer: SIAM J. Appl. Math., 1997, 57:649–82

    Article  MATH  MathSciNet  Google Scholar 

  16. H.K. Seok, D.H. Yeo, K.H. Oh, H.I. Lee, H.Y. Ra: Metall. Mater. Trans. B, 1998, 29B:699–708

    Article  Google Scholar 

  17. N.H. Pryds, J.H. Hattel, T.B. Pedersen, J. Thorborg: Acta Mater., 2002, 50:4075–91

    Article  Google Scholar 

  18. J.H. Hattel, N.H. Pryds: Acta Mater., 2004, 52:5275–88

    Article  Google Scholar 

  19. S. Markus, C. Cui, U. Fritsching: Mater. Sci. Eng. A, 2004, A383:166–74

    Google Scholar 

  20. R. Ristau, R. Kienzler: Proc. Int. Conf. on Spray Deposition and Melt Atomization 2003 and the 5th Int. Conf. on Spray Forming. K. Bauckhage, U. Fritsching, V. Uhlenwinkel, J. Ziesenis, and A. Leatham, eds., University of Bremen, Bremen, Germany, 2003, pp. 8-43–8-52

    Google Scholar 

  21. C. Cui, U. Fritsching, A. Schulz, Q. Li: Acta Mater., 2005, 53:2765–84

    Article  Google Scholar 

  22. S. Annavarapu, D. Apelian, A. Lawley: Metall. Trans. A, 1990, A21:3237–56

    Google Scholar 

  23. V. Uhlenwinkel, M. Buchholz, C. Kramer, K. Bauckhage: Proc. 1998 Powder Metallurgy World Congr. Exhib., EPMA, Shrewsbury, United Kingdom, 1998

    Google Scholar 

  24. F.S. Hill, Jr.: Computer Graphics Using OpenGL, 2nd ed., Prentice Hall, Upper Saddle River, NJ, 2001

    Google Scholar 

  25. J.D. Foley, A. van Dam, S.K. Feiner, J.F. Hughes: Computer Graphics: Principles and Practice, 2nd ed., Addison-Wesley, Reading, MA, 1990

    Google Scholar 

  26. W. Schroeder, K. Martin, B. Lorensen: The Visualization Toolkit, an Object-Oriented Approach to 3D Graphics, Prentice Hall, Upper Saddle River, NJ, 1997

    Google Scholar 

  27. D.A. Field, Commun. Appl. Numer. Meth., 1988, 4:709–12

    Article  MATH  Google Scholar 

  28. C. Kramer, V. Uhlenwinkel, K. Bauckhage: TMS Annual Meeting, TMS, Warrendale, PA, 1998. pp. 401–413

    Google Scholar 

  29. M. Buchholz, V. Uhlenwinkel, and N. Ellendt: Proc. 4th Int. Conf. on Spray Forming, A. Leatham, ed., Osprey Metals, Neath, United Kingdom, 1999 (CD version)

Download references

Acknowledgments

The authors gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Centre SFB 570 “Distortion Engineering” at the University of Bremen.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chengsong Cui.

Additional information

Manuscript submitted October 7, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cui, C., Fritsching, U. & Schulz, A. Three-Dimensional Mathematical Modeling and Numerical Simulation of Billet Shape in Spray Forming Using a Scanning Gas Atomizer. Metall Mater Trans B 38, 333–346 (2007). https://doi.org/10.1007/s11663-007-9036-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11663-007-9036-3

Keywords

Navigation