Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-15T01:30:30.072Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical study on deep penetration induced by focused moving high-energy beam

Published online by Cambridge University Press:  20 February 2017

B.C. Chen ,
C.Y. Ho ,
M.Y. Wen ,
V.H. Lin  and
Y.C. Lee
B.C. Chen
Affiliation:
Department of Chinese medicine, Buddhist Dalin Tzu Chi General Hospital, Chiayi 622, Taiwan
C.Y. Ho*
Affiliation:
Department of Mechanical Engineering, Hwa Hsia University of Technology, Taipei 235, Taiwan
M.Y. Wen
Affiliation:
Department of Mechanical Engineering, Cheng Shiu University, Kaohsiung 833, Taiwan
V.H. Lin
Affiliation:
Department of Mechanical Engineering, Hwa Hsia University of Technology, Taipei 235, Taiwan
Y.C. Lee
Affiliation:
Department of Architecture, National Taitung Junior College, Taitung 950, Taiwan
*
*Address correspondence and reprint requests to: C.Y. Ho, Department of Mechanical Engineering, Hwa Hsia University of Technology, Taipei 235, Taiwan. E-mail: hcy2182@yahoo.com.tw
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates the focal location effects on the penetration depth of molten region surrounding a paraboloid of revolution-shaped cavity (i.e. keyhole of this model) irradiated by a moving focused energy beam, which profile of intensity is assumed to be Gaussian distribution. Considering the momentum balance at the base of the keyhole, a quasi-steady-state thermal model relative to a constant-speed moving high-energy beam and paraboloid of revolution-shaped cavity is developed in a parabolic coordinate system. The analytical solution is obtained for this model with the adiabatic condition directly set on the workpiece surface for semi-infinite domain instead of the image method for infinite domain using the separation-of-variables method. The analytical solution of this model gives a reasonable prediction for the cavity temperatures. The predicted relation of the penetration depth to the focal location agrees with the available measured data. The effects of focal convergence angle and spot size on the penetration depth are also discussed.

Keywords

Deep penetrationFocused energy beamMoving high-energy beam
Type
Research Article
Information
Laser and Particle Beams , Volume 35 , Issue 2 , June 2017 , pp. 193 - 201
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

These authors contributed equally to this work.

References

REFERENCES

Basile, N., Gonon, M., Petit, F. & Cambier, F. (2016). Processing of a glass ceramic surface by selective focused beam laser treatment. Ceram. Int. 42, 1720–1727.Google Scholar
Béchéa, A., Winkler, R., Plank, H., Hoferc, F. & Verbeeck, J. (2016). Focused electron beam induced deposition as a tool to create electron vortices. Micron 80, 34–38.Google Scholar
Chen, G., Zhang, M., Zhao, Z., Zhang, Y. & Li, S. (2013). Measurements of laser-induced plasma temperature field in deep penetration laser welding. Opt. Laser Technol. 45, 551–557.Google Scholar
Duggan, G., Tong, M. & Browne, D.J. (2015). Modelling the creation and destruction of columnar and equiaxed zones during solidification and melting in multi-pass welding of steel. Comput. Mater. Sci. 97, 285–294.CrossRefGoogle Scholar
Elmer, J.W., Giedt, W.H. & Eagar, T.W. (1990). The transition from shallow to deep penetration during electron beam. Welding J. 69, 167-s–176-s.Google Scholar
Gau, C. & Viskanta, R. (1984). Melting and solidification of a metal system in a rectangular cavity. Int. J. Heat Mass Transfer 27, 113–123.CrossRefGoogle Scholar
Giedt, W.H. & Tallerico, L.N. (1988). Prediction of electron beam depth of penetration. Welding J. 67, 299-s–305-s.Google Scholar
Giedt, W.H., Wei, X.C. & Wei, S.R. (1984). Effect of surface convection on stationary gta weld zone temperature. Welding J. 63, 376-s–383-s.Google Scholar
Gus'kov, S.Y., Demchenko, N.N., Kasperczuk, A., Pisarczyk, T., Kalinowska, Z., Chodukowsk, T., Renner, O., Smid, M., Krousky, E., Pfeifer, M., Skala, J., Ullschmied, J. & Pisarczyk, P. (2014). Laser-driven ablation through fast electrons in PALS-experiment at the laser radiation intensity of 1–50 PW/cm2 . Laser Part. Beams 32, 177–195.Google Scholar
Hicken, G.K., Giedt, W.H. & Bentley, A.E. (1991). Correlation of joint penetration with electron beam current distribution. Welding J. 70, 69-s–75-s.Google Scholar
Ho, C.Y. (2005 a). Apparent absorption in a paraboloid of revolution-shaped cavity irradiated by a focused beam. Heat Mass Transfer 42, 91–103.Google Scholar
Ho, C.Y. (2005 b). Fusion zone during focused electron-beam welding. J. Mater. Process. Technol. 167, 265–272.CrossRefGoogle Scholar
Ho, C.Y. & Wei, P.S. (1997). Energy absorption on a conical cavity truncated by spherical cap subject to a focused high-intensity beam. Int. J. Heat Mass Transfer 40, 1895–1905.Google Scholar
Kalashnikov, M., Andreev, A., Ivanov, K., Galkin, A., Korobkin, V., Romanovsky, M., Shiryaev, O., Schnuerer, M., Braenzel, J. & Trofimov, V. (2015). Diagnostics of peak laser intensity based on the measurement of energy of electrons emitted from laser focal region. Laser Part. Beams 33, 361–366.CrossRefGoogle Scholar
Konkol, P.J., Smith, P.M., Willebrand, C.F. & Connor, L.P. (1971). Parameter study of electron-beam welding. Welding J. 50, 765–776.Google Scholar
Luo, M. & Shin, Y.C. (2015). Vision-based weld pool boundary extraction and width measurement during keyhole fiber laser welding. Opt. Lasers Eng. 64, 59–70.Google Scholar
Mara, G.L., Funk, E.R., Mcmaster, R.C. & Pence, P.E. (1974). Penetration mechanisms of electron beam welding and the spiking phenomenon. Welding J. 53, 246-s–251-s.Google Scholar
Mrña, L. & Šarborta, M. (2014). Plasma bursts in deep penetration laser welding. Phys. Proc. 56, 1261–1267.Google Scholar
Schauer, A. & Giedt, W.H. (1978). Prediction of electron beam welding spiking tendency. Welding J. 57, 189-s–195-s.Google Scholar
Seidgazov, R.D. (2011). Thermocapillary mechanism of deep penetration in laser beam welding. Math. Models Comput. Simul. 3, 234–244.Google Scholar
Seiji, K., Masami, M. & Yousuke, K. (2011). Deep penetration welding with high-power laser under vacuum. Trans. JWRI 40, 15–19.Google Scholar
Shawrav, M.M., Gökdeniz, Z.G., Wanzenboeck, H.D., Taus, P., Mika, J.K., Waid, S. & Bertagnolli, E. (2016). Chlorine based focused electron beam induced etching: a novel way to pattern germanium. Mater. Sci. Semicond. 42, 170–173.Google Scholar
Sibillano, T., Ancona, A., Berardi, V., Schingaro, E., Basile, G. & Lugarà, P.M. (2006). A study of the shielding gas influence on the laser beam welding of AA5083 aluminium alloys by in-process spectroscopic investigation. Opt. Lasers Eng. 44, 1039–1051.Google Scholar
Sibillano, T., Rizzi, D., Ancona, A., Saludes-Rodil, S., Rodríguez Nieto, J., Chmelíčková, H. & Šebestová, H. (2012). Spectroscopic monitoring of penetration depth in CO2 Nd:YAG and fiber laser welding processes. J. Mater. Process. Technol. 212, 910–916.Google Scholar
Tan, W. & Shin, Y.C. (2015). Multi-scale modeling of solidification and microstructure development in laser keyhole welding process for austenitic stainless steel. Comput. Mater. Sci. 98, 446–458.Google Scholar
Tenner, F., Brock, C., Gürtler, F.J., Klämpfl, F. & Schmidt, M. (2014). Experimental and numerical analysis of gas dynamics in the keyhole during laser metal welding. Phys. Proc. 56, 1268–1276.CrossRefGoogle Scholar
Webster, P.J.L., Wright, L.G., Ji, Y., Galbraith, C.M., Kinross, A.W., Van Vlack, C. & Fraser, J.M. (2014). Automatic laser welding and milling with in situ inline coherent imaging. Opt. Lett. 39, 6217–6220.Google Scholar
Wei, P.S. & Ho, C.Y. (1998). Beam focusing characteristics effect on energy reflection and absorption in a drilling or welding cavity of paraboloid of revolution. Int. J. Heat Mass Transfer 41, 3299–3308.Google Scholar
Wei, P.S. & Shian, M.D. (1993). Three-dimensional analytical temperature field around the welding cavity produced by a moving distributed high-intensity beam. Trans. ASME J. Heat Transfer 115, 848–856.Google Scholar
Wicki, F., Longchamp, J.N., Escher, C. & Fink, H.W. (2016). Design and implementation of a micron-sized electron column fabricated by focused ion beam milling. Ultramicroscopy 160, 74–79.Google Scholar