Integro-differential model of eddy currents in axi-symmetric non-magnetic bodies heated by moving inductor

摘要

Continual induction heating represents a technological process used in numerous applications (surface drying, tempering and a lot of others). The work-piece (mostly of rectangular Or circular cross-section) is heated by a cylindrical inductor carrying harmonic current slowly moving along it. The basic mathematical model of the process consists of two partial differential equations describing the distribution of electromagnetic and temperature fields. Both fields are characterized by time variable boundary conditions. The model is usually solved by numerical algorithms starting from differential techniques. This way requires, however, remeshing of the definition area at each time level (position of the inductor is permanently changing), which may prove to be somewhat awkward. The paper offers an alternative to this method based on the integral approach, suitable for solving linear problems of this kind. Instead of magnetic field within the whole definition area this approach directly provides the time evolution of eddy current densities in the heated body. Derived is the complete system of the integro-differential equations, representing the continuous mathematical model for a general 3D arrangement. Its discretization including creation of corresponding numerical schemes is performed, however, only for 2D axisymmetric arrangements.' The methodology is illustrated on a typical example.