Approximated analytical approach for temperature calculation in pulsed arc welding

  • Volker KempfEmail author
Short Original Paper


In the modern welding industry, numerical modeling and simulation has become an invaluable tool in order to set up or tune new welding processes. For this purpose, the temperature distribution in a work piece can be modeled by a variety of different heat source models and numerical methods, including finite elements, volumes or differences. Arc welding applications usually employ pulsed power sources to increase efficiency and precision, which, by having to choose finer time stepping, increases the numerical expenses required in the simulations. Instead of the classical methods, in this contribution a Green’s function approach and the classical Goldak double-ellipsoidal heat source is used, getting an approximate analytical solution for the temperature field for a pulsed arc welding process, which is computationally efficient to evaluate and thus highly applicable. We derive an explicit equation for the temperature distribution, where only the time integration has to be solved approximately, run numerical tests and compare the results with FEM calculations.


Heat equation Welding Pulsed power source Heat kernel Arc welding 

Mathematics Subject Classification

35K05 35K08 



  1. 1.
    Goldak, J., Chakravarti, A., Bibby, M.: A new finite element model for welding heat sources. Metall. Trans. B 15B, 299–304 (1984)CrossRefGoogle Scholar
  2. 2.
    Roshyara, N.R., Wilhelm, G., Semmler, U., Meyer, A.: Approximate analytical solution for the temperature field in welding. Metall. Mater. Trans. B 42B, 1253–1273 (2011)CrossRefGoogle Scholar
  3. 3.
    Strauss, W.A.: Partial Differential Equations: An Introduction, 2nd edn. Wiley, Hoboken (2008)zbMATHGoogle Scholar
  4. 4.
    Rosenthal, D.: Mathematical theory of heat distribution during welding and cutting. Weld. J. 20, 220–234 (1941)Google Scholar
  5. 5.
    Eager, T.W., Tsai, N.S.: Temperature fields produced by travelling distributed heat sources. Weld. J. 62, 346–355 (1983)Google Scholar
  6. 6.
    Komanduri, R., Hou, Z.B.: Thermal analysis of the arc welding process: Part II: effect of variation of thermophysical properties with temperature. Metall. Mater. Trans. B 32, 483–499 (2001)CrossRefGoogle Scholar
  7. 7.
    Nguyen, N.T.: Thermal Analysis of Welds. WIT Press, Southampton (2004)CrossRefGoogle Scholar
  8. 8.
    Hirata, Y.: Pulsed arc welding. Weld. Int. 17, 98–115 (2003)CrossRefGoogle Scholar
  9. 9.
    Antimirov, M.Y., Kolyshkin, A.A., Vaillancourt, R.: Applied Integral Transforms. American Mathematical Society, Providence (1993)zbMATHGoogle Scholar
  10. 10.
    Scott, L.R.: Introduction to Automated Modeling with FEniCS, Computational Modeling Initiative, (2018)Google Scholar
  11. 11.
    Logg, A., Mardal, K.-A., Wells, G.N.: Automated Solution of Differential Equations by the Finite Element Method. Springer, Berlin (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Mathematics and Computer-based SimulationBundeswehr University MunichNeubibergGermany

Personalised recommendations