Analytical solution for transient temperature distribution in gas tungsten arc welding with consideration of filler wire

Abstract

This paper is focused on deriving an analytical solution to predict the transient temperature distribution of the plate during the process of gas tungsten arc (GTA) welding in which a filler wire is fed. An analytical solution is derived from the transient three-dimensional heat conduction equation by applying a convection boundary condition to the top and bottom surface of an infinite plate of finite thickness. The heat input that is applied on the plate is exactly the same as the amount of heat lost from the electric arc while fusing the filler wire. The electric arc is assumed to be a moving heat source with a Gaussian distribution. The point heat sink is located in the spot where the filler wire is fed to the weld pool. However, the feed position of the filler wire is ever-evolving with time because the size of the weld pool changes in accordance with the welding conditions. Nevertheless, the algorithm is capable of determining the feed position. Also, the influence of the filler wire on the temperature distribution of the plate is established by removing the filler wire from the analytical solution and comparing these two different situations. In order to verify the validity of this solution, a GTA welding experiment is conducted for various welding conditions. After this stage, the resulting isotherms of the cross-sections of the plate and the analytical results are compared. The analytical solution, which is in good agreement with experimental results, is the very first to take the filler wire feed into consideration. It can be used as a model to control the GTA welding process with account taken of the filler wire, and it can also be used as an optimization tool for welding process parameters.