Bridge erosion in electrical contacts

The physical process of bridge erosion in low-current electrical contacts is described by a model of mass transfer during switching, without assuming steadiness of the process and one-dimensionality of the corresponding Stefan problem. Changing of the current density, redistribution of Joule-effect sources with attendant shifting of the hot spot, and the skin effect following an increase of electrical resistance are taken into account, all these effects resulting from changes in bridge cross sections, as well as second-order thermoelectric effects. Two problems are formulated and successively solved on the basis of this model. The first problem is determining the evolution of the bridge shape from the originally cylindrical one. The equation of motion for the melting front is used for this purpose with the melting coefficients most closely approximating the solution to the exact Stefan problem. The second problem is determining the temperature field of a variable-section bridge, taking into account the temperature dependence of electrical resistivity but disregarding the less significant temperature dependence of thermal conductivity and specific heat.