Guaranteed fillet weld geometry from heat transfer model and multivariable optimization

Numerical heat transfer models of gas metal arc (GMA) fillet welding do not always predict correct temperature fields and fusion zone geometry. The inaccuracy results, to a large extent, due to the difficulty in correctly specifying several input parameters such as arc efficiency from scientific principles. In order to address this problem, a heat transfer model is combined with an optimization algorithm to determine several uncertain welding parameters from a limited volume of experimental data. The resulting smart model guarantees optimized prediction of weld pool penetration, throat and leg-length within the framework of phenomenological laws. A boundary fitted coordinate system was used to account for the complex fusion zone shape. The weld pool surface profile was calculated by minimizing the total surface energy. Apart from the direct transport of heat from the welding arc, heat transfer from the metal droplets was modeled considering a volumetric heat source. The Levenberg–Marquardt and two versions of conjugate gradient method were used to calculate the optimized values of unknown parameters. An appropriate objective function that represented the difference between the calculated and experimental values of the penetration, throat and leg-length was minimized. The calculated shape and size of the fusion zone, finger penetration characteristic of the GMA welds and the solidified free surface profile were in fair agreement with the experimental results for various welding conditions.