Extensive use of circumferential gas tungsten arc (GTA) welding in industrial applications has been handicapped due to the difficulty of choosing the optimal process parameters. In Part 2 of this study, the welding current and backing gas pressure are optimized by calculating the three-dimensional transient temperature distribution and the surface profile of the resultant weld pool in circumferential GTA welding of small-diameter pipes, in order to obtain a uniform weld bead without any hang-down over the entire circumference of pipes.
A transient three-dimensional finite difference mode (FDM) of the heat flow in the circumferential GTA welding of pipes was developed and applied to calculate the temperature distribution in the workpiece. In order to minimize the computing time required for solving the FDM equations as much as possible, the alternating direction implicit (ADI) scheme which makes use of the tridiagonal matrix algorithm efficiently was adopted. Based on the characteristics of the pipe welding process, the periodic boundary condition was applied to calculate the temperature distribution in the 8 direction. For treating the moving heat source effectively, the grid meshes with variable spacings were regenerated at each time step. In order to decrease the interpolating error by grid remeshing, the temperature values at new meshes were interpolated from those at old meshes by using the periodic spline function. The temperature-dependent thermal properties, the latent heat and the convective and radiative boundary conditions were included in the model. The calculated sizes of the fusion and heat-affected zone were compared with the observed values after experiments.
It is well known that the weld bead becomes wider and the weld pool hangs down as the circumferential welding of small-diameter pipes progresses, if constant welding conditions are maintained over the entire joint length and/or no appropriate backing gas is supplied into the pipe. In order to obtain a weld bead which is uniform in width and does not hang down over the whole circumference of the pipe, the welding parameters such as welding current, welding velocity and backing gas pressure should be optimized as the welding progresses. In order to optimize the welding parameters, a mathematical model for determining the temperature distribution in the pipe workpiece and the surface profile of the resultant weld pool is indispensable. An efficient finite difference model was adopted for calculating the three-dimensional transient temperature distribution in circumferential gas tungsten arc (GTA) welding of pipes. Its solution was obtained by employing the alternating direction implicit (ADI) finite difference method, in which a periodic boundary condition and a periodic cubic spline function were used. For calculating the weld pool surface profiles in full penetration circumferential welding of pipes, a governing equation was derived in the cylindrical coordinate and solved using a simple finite difference model with the ADI scheme. In Part 2 of this paper, an efficient parameter optimization method is used to evaluate the optimal welding current for a required bead width when the welding velocity is given.
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