The electromagnetic force results from the interaction between the current flow and the induced magnetic field in the weldment. Comprehensive three-dimensional calculations of current flow and induced magnetic field are needed for accurate determination of the electromagnetic force. In the literature, several simplifying analytical expressions for the electromagnetic force have been suggested and widely used without any critical evaluation of their intrinsic merit, since accurate numerical calculations were difficult in the past because of lack of fast computers. With the advances in computational hardware and software, it is now possible to do relatively complex calculations that were much more difficult to perform just a few decades ago. The objective of the present investigation is to propose a mathematical model to numerically solve the electromagnetic force field in the wildment and determine the effect of commonly used simplifications on the accuracy of the calculated electromagnetic force field and weld pool temperature and velocity fields. A numerical model has been developed to accurately calculate the current density and magnetic flux fields and the resulting electromagnetic force field in three dimensions in the entire weldment. The computed electromagnetic force field was used in a 3-D heat transfer and fluid flow model to calculate the temperature and velocity distributions in the weld pool. The fusion zone geometry was experimentally measured for different current, voltage and arc power distribution. The agreements between the calculated and experimental FZ geometries indicate that the proposed numerical model gives accurate electromagnetic force distribution inside the workpiece.

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