An analytical method for predicting the three-dimensional (3-D) magnetic flux density distribution in the air gap produced by permanent magnets of an electromagnetic planar actuator, was developed. The analytical 3-D model was validated by means of a finite-element model and by measurements. It allowed the understanding of the behavior of the flux density in the air gap and predicting the values of the involved forces.
IEEE transactions on magnetics. New York, N. Y. vol. 39, no. 5 (Sep. 2003), p. 3364-3366