Mathematical models of the vapor, liquid and solid states of the arc erosion in electrical contacts

The mathematical models described the mechanism of the arc erosion in electrical contacts due to vaporization, liquid metal and solid particles ejection are presented. The model of the erosion in the vapor state is based on the two-phase axisymmetric Stefan problem for the multi-component arc heat flux. The special method of the upper and lower majorant functions is elaborated for the solution of this problem. The problem of the identification of the arc heat flux using an additional information about the dynamics of the phase transition surface is also discussed in the frame of the inverse Stefan problem. The erosion of refractory contact materials, such as tungsten, molybdenum, zirconium etc. can be explained by the thermocapillary (Marangoni) effect stipulated by the significant temperature dependence of the coefficient of the surface tension. The corresponding mathematical model takes into account phenomena in the surface layer of the melted pool. The model for the erosion in the solid state may be considered for a high-power pulse arc discharge, when the rate of current growth reaches very high values, thermal stresses, exceeding the yield strength of contact materials, can be generated and lead the erosion of the contact in solid state. Thermal stability of the contact material can be maintained by a careful selection of the contact materials and parameters controlling the current pulse. The numerical calculations for each form of erosion are represented and compared with the experimental data.