Modeling of Three-Dimensional Fields of Eddy Currents during Induction Heating of Process Equipment

The problem of heat generation during induction heating of process equipment has been analyzed using the example of ferromagnetic plates used for assembling hydraulic-frame presses. We present a mathematical model of induction heating that includes the equations of the electromagnetic field and heat transfer in a three-dimensional formulation. The calculation of three-dimensional fields of eddy currents in ferromagnetic bodies is associated with the large computer time consumption for the solution of Maxwell’s equations. In addition, the engineering methods used do not provide the required accuracy since they do not take into account the features of the geometry of the object. A technique has been proposed for calculating three-dimensional fields of eddy currents in ferromagnetic bodies using linear differential equations, which makes it possible to reduce the computation time by more than an order of magnitude. This simplification of the mathematical model of induction heating is based on the assumption that the magnetic permeability of the plate material is constant during the process of heating. Solving the nonlinear equations of the electromagnetic field in the two-dimensional formulation, we have determined the magnetic permeability corresponding to the magnetization curve (in terms of active power) as a function of the characteristics of the inductor and its location. The finite-element method is implemented with the ANSYS software is used. The results obtained can be used in the design of induction heating plants that should satisfy special requirements for the temperature-field configuration.