Analytical Calculation of Back EMF Waveform for Linear PM Motors in Slotted and Slotless Structures

This paper presents the analytical calculation of back electromotive force (EMF) waveform for linear permanent magnet motors in either slotted or slotless structures. The predictions are based on the analysis of the 2-D magnetic field distributions and the 3-D end effects. In the slotted structure, the relative permeance function obtained by the Schwarz-Christoffel conformal mapping is used to take into account the effects of slotting and to calculate the air-gap flux density. Subsequently, to evaluate the leakage components resulting from the slot opening, slot opening factor is introduced to reflect the elements which do not follow the intended path to produce the back EMF. In the slotless structure, the effective values of the magnetic field quantities, together with the extended theory of winding factors, are employed to evaluate the back EMF waveform. For the analysis of the axial end effects, the 3-D leakage factor is incorporated into the analytical solutions by adding the end leakage permeance to the entire magnetic circuit models. The validity of the analytical results for each topology is confirmed by 2-D finite element and experimental results.