Thermophysics and Aeromechanics

, Volume 25, Issue 5, pp 741–750 | Cite as

Analytical approach for determining the surface shape of a liquid metal under laser cladding conditions

  • D. V. BedenkoEmail author
  • O. B. Kovalev


We propose an improvement of an analytical approach presented previously for determining the surface shape formed during laser cladding process at the goods manufacturing in additive technologies. The approach is based on the balance of pressures on the liquid metal surface, which occurs under the gravity and surface tension. A method generalization is proposed for the case of a curvilinear shape of a substrate, which allows determining the surface ge-ometry at arbitrary contact angles for single beads, vertical walls, and coatings formed by overlapping beads. The verification of the considered approach was carried out for laser cladding problems with the use of experimental data obtained by other authors.

Key words

laser cladding analytical model surface equation surface tension contact angle 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.J. Pinkerton and L. Li, An investigation of the effect of pulse frequency in laser multiple-layer cladding of stainless steel, Applied Surface Sci., 2003, Vol. 208, 209, P. 405–410.ADSCrossRefGoogle Scholar
  2. 2.
    P. Peyre, P. Aubry, R. Fabbro, R. Neveu, and A. Longuet, Analytical and numerical modeling of the direct metal deposition laser process, J. Phys. D: Appl. Phys., 2008, Vol. 41, No. 2, P. 025403–1-025403-10.CrossRefGoogle Scholar
  3. 3.
    D. Novichenko, A. Marants, L. Thivillon, Ph. Bertrand, and I. Smurov, Metal matrix composite material by direct deposition, Physics Procedia, 2011, Vol. 12, P. 296–302.ADSCrossRefGoogle Scholar
  4. 4.
    H. El Cheikh, B. Courant, S. Branchua, J.-Y. Hascoët, and R. Guillén, Analysis and prediction of single laser tracks geometrical characteristics in coaxial laser cladding process, Optics and Lasers in Engng, 2012, Vol. 50, P. 413–422.ADSCrossRefGoogle Scholar
  5. 5.
    D.V. Bedenko and O.B. Kovalev, Modelling of heat and mass transfer in the laser cladding during direct metal deposition, Thermophysics and Aeromechanics, 2013, Vol. 20, No. 2, P. 251–261.ADSCrossRefGoogle Scholar
  6. 6.
    B. Cárcel, A. Serrano, J. Zambrano, V. Amigó, and A.C. Cárcel, Laser cladding of TiAl intermetallic alloy on Ti6Al4V. Process optimization and properties, Physics Procedia, 2014, Vol. 56, P. 284–293.ADSCrossRefGoogle Scholar
  7. 7.
    D.V. Bedenko, O.B. Kovalev, I. Smurov, and A.V. Zaitsev, Numerical simulation of transport phenomena, for-mation the bead and thermal behavior in application to industrial DMD technology, Int. J. Heat and Mass Transfer, 2016, Vol. 95, P. 902–912.CrossRefGoogle Scholar
  8. 8.
    Z. Gan, H. Liu, S. Li, X. He, and G. Yu, Modeling of thermal behavior and mass transport in multi-layer laser additive manufacturing of Ni-based alloy on cast iron, Int. J. Heat and Mass Transfer, 2017, Vol. 111, P. 709–722.CrossRefGoogle Scholar
  9. 9.
    C. Lalas, K. Tsirbas, K. Salonitis, and G. Chryssolouris, An analytical model of the laser clad geometry, Int. J. Adv. Manuf. Technol., 2007, Vol. 32, P. 34–41.CrossRefGoogle Scholar
  10. 10.
    I.L. Emelyanov, Influence of the forces of surface tension and external pressure on the shape of deposited bead, Trudy Leningradskogo instituta inzhenerov vodnogo transporta, 1972, Vol. 135, P. 135–145.Google Scholar
  11. 11.
    K. Nishiguchi, T. Ohji, and H. Matsui, Fundamental research on bead formation in overlaying and fillet welding processes (Report 1). Surface tensional analysis of bead surface profile, J. Japan Welding Soc., 1976, Vol. 45, P. 82–87.CrossRefGoogle Scholar
  12. 12.
    B.M. Berezovsky and V.A. Stikhin, Influence of forces of surface tension on formation reinforcement of weld, Svarochnoe proizvodstvo, 1977, No. 1, P. 51–53.Google Scholar
  13. 13.
    B.M. Berezovsky and A.V. Stikhin, Optimization of the formation of a metal layer in arc deposition, Welding International, 1991, Vol. 5, No. 11, P. 888–891.CrossRefGoogle Scholar
  14. 14.
    I.M. Fedotkin, Mathematical Modeling of Technological Processes, Vyshcha Shkola, Kiev, 1988.Google Scholar

Copyright information

© Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Khristianovich Institute of Theoretical and Applied Mechanics SB RASNovosibirskRussia

Personalised recommendations