Solution of a stefan problem in the theory of laser welding by the method of lines

Abstract

Use of a laser beam as the source of energy for penetration welding gives rise to a long, thin cylindrical hole surrounded by molten metal. Material moves from the front to the rear of the hole as the workpiece is translated relative to the laser, by flowing around the hole. A computer program has been written which solves the equations governing a 2-dimensional steady-state mathematical model in which the only spatial variations considered are in a plane perpendicular to the axis of the hole. The program uses the method of lines applied to a reformulation of the problem suitable for solution by the isotherm migration technique. Computed results have been found to agree satisfactorily with those derived from an analytical model valid for low speeds of welding, and at higher speeds they give results similar to what is observed in practice, although lack of experimental evidence precludes a detailed quantitative comparison at present.