A typical 12/10 flux-switching permanent magnet (FSPM) machine is analyzed using finite element (FE) method with special considerations of the silicon steel oversaturation, permanent magnet (PM) irreversible demagnetization and the dc-biased magnetic induction on the hysteresis loss. The high flux density range of B-H curve which is difficult to measure is deduced with the combination of polynomial extrapolation and silicon steel saturation magnetization. A temperature-dependent sloped linear PM demagnetization model is incorporated into the FE model to analyze PM irreversible demagnetization and estimate the maximum allowable working temperature for PM. The influence of dc-biased magnetic induction on hysteresis loss is taken into account in core loss calculation. The FE analysis package is developed with the help of finite element program generator (FEPG).Index Terms-Flux-switching permanent magnet (FSPM) machine, high flux density, irreversible demagnetization, dc-biased magnetic induction, finite element program generator (FEPG) 0018-9464 (c)

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I . INTRODUCTIONIn finite element (FE) analysis of flux switching permanent magnet (FSPM) machine, there are several challenges due to the unique structure and principle . Firstly, the local flux density in stator and rotor teeth may reaches 2 .5T or even higher [1] . However, high flux density range of B-H curve is difficult to measure and reasonable extrapolation is indispensible . Secondly, the region of permanent magnet (PM) near the air gap is likely to be locally demagnetized when the rotor teeth is aligned to the PM, but this phenomena is rarely considered during transient FE calculation because commercial FE software just models the PM with remanence and permeability and irreversible demagnetization is assumed to not appear . Thirdly, the dc-biased magnetic induction in stator may influence the hysteresis loss [2] . In this this paper, more reasonable material models and loss calculation model are proposed so that they can be incorporated into the FE analysis package developed with the help of finite element program generator (FEPG) [3] for more accurate analysis of FSPM machine . II . MODELING OF SILICON STEEL AT OVERSATURATED RANGE With traditional Epstein test frame or single sheet tester, only B-H curve of the silicon steel below 1 .8T can be measured accurately . Hence an extrapolation polynomial for B-H curve at high flux density is shown as:where a i is the coefficient for extrapolation which can be determined with n+1 known data points, n is the order of the extrapolation . When silicon steel becomes oversaturated, B-H curve is simply expressed with the silicon steel saturation magnetization M s as:where u 0 is the permeability of air and for silicon steel, M s is 2 . 03T[4] . In calculation, n is first assumed and parameters in (1) are got with polynomial fitting . Then, Solving (1) and (2) gets the intersection point . When the flux density is below intersection point, (1) is used to represent the extrapolation part of B-H curve and when the flux density is over the intersection point, (2) is used . As shown in Fig .1(a-b), n=3 with (2) gives the best fitting results, for it gives the smoothest handover with (2) and real B-H curve should be naturally smooth . It is shown in Fig . 1(c-d) that the M s plays key role on open circuit back-EMF and the back-EMF calculated under n=3 with (2) is also the closest to the measured one . Here, the calculated back EMF has been modified with stack factor and 3D factor . III . TEMPERATURE-DEPENDENT PM LINEAR DEMAGNETIZATION MODEL The flux density variation waveforms in each element of one PM at open circuit condition are shown in Fig . 2(a-b) . It can be seen from Fig .2 (a) that the work points in some elements become rather low when the PM is aligned to rotor teeth, which makes irreversible demagnetization very likely to happen . In addition, the intrinsic coercivity of NdFeB will decrease rapidly with the increase of temperature . Here, a temperature-dependent PM linear demagnetization model [5] is incorporated in the transient FE analysis package for an...