Finite-Element Analysis of Magnetically Saturated D-C Machines

The magnetic field distribution in saturated iron parts of electric machines is defined by a nonlinear quasi-Poisson equation. Solution of this equation is equivalent to minimization of a nonlinear energy functional. A recent paper has proposed approximate minimization by means of a finite element method, using triangular finite elements and a quadratically convergent iteration scheme. This new method is now applied to a 5 KW d-c machine, whose no-load and on-load characteristics are predicted and compared with experimental measurements. Good agreement is obtained. Since the pole axis is not an axis of magnetic symmetry under load, a periodicity condition is introduced to relate all magnetic vector potentials to those one pole pitch away. This condition is enforced by means of a special connection matrix, whose derivation is shown in the paper. An automatic plotting program has been developed for graphical plotting of the flux distributions, and several field plots for the machine are shown.