The Stefan problem for generalized heat equations describes the dynamics of melting and welding of electrical contacts at their closure

The mathematical model describing welding at contact closure is elaborated. All consecutive stages of contact closure are considered including the first touch of micro-asperities with micro-arcing, initial contact heating, softening, melting and boiling of the contact surface. Two possible phenomena are discussed, welding and bouncing. It is shown that everything depends on the relationship between dynamical characteristics of heating and contact motion such as spreading of melting and softening zones on the contact surface, action of elastic-plastic, electrodynamic and contact spring forces, metallic vapors pressure, parameters of the contact material, circuit parameters and some other factors. The mathematical model is based on the axisymmetric Stefan problem which takes into account phase transformations of the contact material. Some new methods for the solution of this problem are presented. The results of calculation are compared with experimental data.