Fringing in tubular permanent-magnet machines: Part II. Cogging force and its minimization

In Part I of the paper, analytical field solutions, which account for the fringing flux associated with the finite length of the ferromagnetic armature core in tubular permanent-magnet machines, are established. In Part II, the technique is applied to both slotless and slotted machines, and the results are verified by finite-element calculations. The analytical field solutions enable the resultant cogging force associated with the finite length of the armature to be determined as a function of the armature displacement, for both radially and Halbach magnetized stators. Thus, they not only provide an effective means for evaluating the influence of leading design parameters on the cogging force waveform, but also facilitate its minimization.