A mathematical model of gas tungsten arc welding considering the cathode and the free surface of the weld pool
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I.
INTRODUCTION
THE gas tungsten arc (GTA) welding process has been widely used and has produced spectacular results. The studies of heat transfer and fluid flow in the weld pool, especially in the GTA weld pool, has been an area of active research in recent years. For the effective usage of these models with the weld pool, accurate information about the welding arc influencing the molten pool is a prerequisite, and so the study of heat transfer and fluid flow in the welding arc is equally important. Modeling heat transfer and fluid flow in the arc plasma has been well documented[1–4] These studies all dealt with an arc plasma between a tungsten electrode (cathode) and a water-cooled copper plate (anode). The anode was represented as a flat surface having a constant temperature. Figure 1 shows a schematic sketch of a GTA welding operation with a deformed weld pool. It has been observed that the surface of the weld pool becomes markedly depressed at high current levels, and the assumption of a flat surface is no longer valid.[5] Although Choo et al.[6] presented a model of high-current arcs with a deformed anode surface, the specified weld-pool shapes have been approximated as stepwise, and the cathode tip shape was limited to being flat-ended. Experimentally, Lin and Eager[7] measured the arc pressure with different electrode shapes, and showed that the sharp cathode produces a higher arc pressure than the blunt one. Therefore, the cathode shape is an important factor influencing the welding arc characteristics and the transferring phenomena on the base plate. It should also be emphasized that in most previous studies on heat transfer and fluid flow in the arc plasma, a current density profile has to be assumed over the surface plane of the cathode,[6,8] although it has been found that the theoretical predictions are sensitive to the current density W.-H. KIM, Senior Researcher, is with the Agency for Defense Development, Taejon, 305-600, Korea. H.G. FAN, Postdoctoral Fellow, and S.-J. NA, Professor, are with the Department of Mechanical Engineering, KAIST, Taejon, 305-701, Korea. Manuscript submitted August 27, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS B
at the cathode.[3] A model without any assumption of the current density at the cathode surface was presented until recently,[9,10,11] and Fan et al.[12] used a similar model to describe the heat and mass transfer in pulsed GTA welding. In the present article, the model addresses a pointed-tip cathode that fits with the actual situation. The distribution of current density, which is determined primarily by the welding current and the cathode shape, is calculated with the combined arc plasma–cathode system,[3] independent of the assumption of current density distribution in the cathode. The welding arc is modeled with a predeformed weldpool surface, which is deduced from previous experimental observations,[13] and the current and the heat flux to the anode calculated for various cathode shapes are compared. Because the cathode shape and the free surface at th
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