Volume 61 Issue 2 (2011) - Годишник на ТУ - София - Технически ...

2 A J(1)where μ is magnetic permeability;J is the current density in the coil;A is the magnetic vector potential.For open boundary electromagnetic problem the homogeneous Dirichlet’s boundaryconditions are imposed on its boundary. On the planes of symmetry either homogeneousDirichlet’s or natural boundary conditions are imposed.The electromagnetic force is calculated by the Maxwell stress tensor method. As themotion is only in y-direction, only y-component of the velocity is non-zero.Magnetic inductance L is calculated by stored magnetic field energy – W expresed by(2)1 W Li2(2)2where i is the coil current.Results for magnetic field distribution is shown in Fig.5.3.2. Thermal problemThe thermal field at steady-state is governed by the Poisson’s equation with respect tothe temperature T 2T Q (3)where Q is the heat source defined by the electric losses in the coil;λ is the thermal conductivity.Heat source density Q defined by the electric losses in the coil are calculated by(4)2JQ (4)where σ is specific electric conductivity of coil material.For the thermal problem buffer zone is not introduced and convection boundary conditionsare imposed on the outer surface of the electromagnet. On the planes of symmetrynatural boundary conditions are used.Convection boundary conditions expressed by (5) are imposed on the outer surface ofelectromagnet.Tk q(5)nwhere q is the heat flux and k is the convection coefficient and n is unit outward surfacenormal vector.On the planes of symmetry natural boundary conditions are used (6)T 0 (6)n3.3. FEM CouplingDC electromagnet is described with its two FEMM thermal and magnetic field models(Fig.3). Simple first order coupling between two field models is made. The couplingof the two fields is in both directions. The electromagnetic field analysis de-116