A one-dimensional spot welding model (Q2472039)

A one-dimensional model is proposed for the simulations of resistance spot welding, which is a common industrial method used to join metallic plates by electrical heating. The model consists of the Stefan problem, in enthalpy form, coupled with the equation of charge conservation for the electrical potential. The temperature dependence of the density, thermal conductivity, specific heat, and electrical conductivity are taken into account, since the process generally involves a large temperature range, on the order of 1000 K. The model is general enough to allow for the welding of plates of different thicknesses or dissimilar materials and to account for variations in the Joule heating through the material thickness due to the dependence of electrical resistivity on the temperature. A novel feature in the model is the inclusion of the effects of interface resistance between the plates which is also assumed to be temperature dependent. In addition to constructing the model, a finite difference scheme for its numerical approximations is described, and representative computer simulations are depicted. These describe welding processes involving different interface resistances, different thicknesses, different materials, and different voltage forms. It is worth to say that this model is meant as a tool for the design engineer to obtain quickly a reasonable estimate of the performance of the welding process under design, as well as a good indication of an efficient welding schedule. It is also to emphasize, the fact, that presented model is one-dimensional it is likely that the description of the electric curvent flow is rather inaccurate, as compared to a three-dimensional model. I think that it is worth to extend the consideration presented in this paper to three dimensional formulation together with numerical calculations.