An analytical solution for transient temperature distribution in fillet arc welding including the effect of molten metal

This paper presents an analytical solution to predict the transient temperature distribution in fillet arc welding, including the effect of the molten metal generated from the electrode. The analytical solution is obtained by solving a transient three-dimensional heat conduction equation with convection boundary conditions on the surfaces of an infinite plate with finite thickness, and mapping an infinite plate on to the fillet weld geometry, including the molten metal with energy equation. The electric arc heat input on the fillet weld and on the infinite plate is assumed to have a travelling bivariate Gaussian distribution. To check the validity of the solution, flux cored arc (FCA) welding experiments were performed under various welding conditions. The actual isotherms of the weldment cross-sections at various distances from the arc start point are compared with those of the simulation result. As the result shows a good accuracy, this analytical solution can be used to predict the transient temperature distribution in the fillet weld of finite thickness under a moving bivariate Gaussian distributed heat source. The simplicity and short calculation time of the analytical solution provides the rationale for using the analytical solution to model the welding control systems or to obtain an optimization tool for welding process parameters.