Exact and Approximate Solutions for Two-Dimensional Temperature Distribution Induced by a Moving Gaussian Heat Source

摘要

In a deep penetration laser welding, a keyhole is created on the workpiece and a laser beam can be approximately considered as a line heat source. Laser energy is conducted to the surroundings of the laser beam. Therefore, the deep penetration laser welding can be simplified as a two-dimensional heat conduction process. The two-dimensional temperature distribution subject to a moving Gaussian heat source was solved by Fourier transformation method. An exact solution to the temperature distribution was obtained. The mathematical expression of the exact analytical solution was concise and relatively simple. In order to easily calculate the temperature profiles, an approximate solution was derived from the exact solution. It was found that the errors between the exact and approximate solutions were small over the entire substrate for large Peclet numbers. For small Peclet numbers, the error was insignificant at relative large distance from the laser beam such as the locations of the weld pool.