THE FINITE ELEMENT ANALYSIS OF ELECTROMECHANICAL DEVICES WITH ANISOTROPIC PERMANENT-MAGNETS (GALERKIN, ELECTROMAGNETIC FIELD, PETROV-GALERKIN, SAMARIUM-COBALT, FERRITE, NONLINEAR)

Finite element analysis is applied to solve the Poisson equation for a stationary magnetic field in an anisotropic and saturable magnetic medium typically encountered in electromechanical devices with anisotropic permanent-magnets. Finite element equations were formulated using a weighted residual standard Galerkin method. The Galerkin method is proved, through the application of certain theorems found in the literature, to be more general in nature than the Rayleigh-Ritz method.;To solve the nonlinear algebraic equations resulting from the Galerkin method, a sequential direct iteration scheme is adopted in this work. The optimum underrelaxation factor, needed for direct iteration schemes, is found both theoretically and experimentally with good correlation. The various cases that arise from adjusting the underrelaxation factor are presented. Different convergence criteria, used in solving electromagnetic field problems, are surveyed. Different methods of modeling the magnetization characteristics are compared. It is concluded that the straight-line segment method provides acceptable accuracy and appreciable reduction in computation costs.;The Galerkin method is applied to a practical problem such as a permanent-magnet linear motor used in computer disc drives. It is shown, that the total stored magnetic energy is a minimum when all the finite elements have converged. Two of the convergence criteria surveyed are found to provide acceptable agreement. It is shown that with proper choice of (1) the initial estimate of the reluctivities; (2) the method of modeling the magnetization characteristics; and (3) the underrelaxation factor, a relatively fast convergence rate and appreciable reduction in computation costs can be achieved. The flux density vector is computed at different locations inside and outside the linear motor. The computed air gap flux density distribution is compared to the measured value and resulted in an agreement with acceptable experimental error.;The Galerkin method when applied to electromagnetic field problems with anisotropic and saturable media is shown to be both theoretically accurate and requiring significantly fewer algebraic manipulations.