Fringing in tubular permanent-magnet machines: Part I. Magnetic field distribution, flux linkage, and thrust force

This paper extends an analysis developed for tubular permanentmagnet machines to account for the effect of fringing associated with the finite length of the ferromagnetic armature core. The magnetic field distribution, established by using an analytical technique formulated in the cylindrical coordinate system, provides an accurate means of evaluating the effect of the fringing flux on the thrust force and the back-electromotive force. Finite-element calculations confirm the analytically derived results. In Part II of the paper, the analysis is used to predict the cogging force that results from end effects and to facilitate minimization of the force.