The mathematical models of welding dynamics in closed and switching electrical contacts

Welding in closed and opening electrical contacts is described mathematically by three models. 1) a nonlinear model of static welding based on differential equations for contact temperature and electrical potential enables one to get information about the spatial distribution of both variables. 2) a transient model of static welding, on the basis of the axisymmetric Stefan problem, describes the dynamics of phase transformation in the property dependence of contact material, current and other parameters. 3) a satisfactory description of dynamic welding during arcing can be obtained by modelling of heat transfer in a domain with two free boundaries corresponding to melting and evaporation interfaces. In conclusion, the relationship between current, parameters of contact closure and contact material, which define immediate or delayed cases of welding, are found and discussed. Results of calculations are compared with experimental data.