Journal of Applied Mathematics
Volume 2006 (2006), Article ID 17936, 24 pages
A one-dimensional spot welding model
1Department of Mathematics and Statistics, Oakland University, Rochester 48309-4478, MI, USA
2Department of Mechanical Engineering, Oakland University, Rochester 48309-4478, MI, USA
Received 3 July 2006; Revised 3 November 2006; Accepted 22 November 2006
Copyright © 2006 K. T. Andrews et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
The differences in the process due to AC or DC currents are depicted as well.