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

  • B.C. Chen (a1), C.Y. Ho (a2), M.Y. Wen (a3), V.H. Lin (a2) and Y.C. Lee (a4)...


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.


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*Address correspondence and reprint requests to: C.Y. Ho, Department of Mechanical Engineering, Hwa Hsia University of Technology, Taipei 235, Taiwan. E-mail:


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These authors contributed equally to this work.



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