On-load demagnetization effect of high-coercive-force PMs in switched flux hybrid magnet memory machine

In the previous researches of hybrid magnet memory motors (HMMMs), the demagnetization characteristics of low-coercive-force (LCF) magnets have been already investigated extensively. Nevertheless, the possible irreversible demagnetization of high-coercive-force (HCF) magnets remains unexplored hitherto. In this paper, the demagnetization behaviour of HCF magnets in switched ﬂux hybrid magnet memory machines (SF-HMMMs) accounting for the high-level current pulse is revealed and investigated. A simpliﬁed magnetic circuit model is built to illustrate when and how the DC current pulse poses the risk of irreversible demagnetization to the HCF magnets. Furthermore, the inﬂuences of temperature, DC current amplitude and HCF magnet thickness on the irreversible demagnetization effect of HCF magnets in the investigated SF-HMMM are analyzed based on ﬁnite-element (FE) analyses. The theoretical and FE results are experimentally veriﬁed by the tests on an SF-HMMM prototype.


I. INTRODUCTION
Recently, memory machines (MMs) 1 are of growing research interests since the magnetization state (MS) of the low-coerciveforce (LCF) magnets can be conveniently magnetized/demagnetized with a current pulse. In order to realize a convenient magnetization control, thereafter, switched flux hybrid magnet memory machines (SF-HMMMs) 2,3 equipped with both high-coercive-force (HCF) and LCF magnets are proposed to achieve high-efficiency operation within a wide speed range. Although the parallelity between permanent magnets (PMs) and armature fields in the proposed SF-HMMMs leads to advantageous demagnetization withstand capability, the potential partial irreversible demagnetization issue is a major concern. In addition, the previous literatures [4][5][6][7][8][9] about MMs mainly focus on the demagnetization of LCF magnets. Nevertheless, no insight has been provided into the irreversible demagnetization behaviour of HCF magnets hitherto, especially accounting for the influence of the high-level transient current pulse on HCF magnets. Thus, the purpose of this paper is to comprehensively investigate the demagnetization characteristics of HCF magnets in SF-HMMMs.

II. SF-HMMM MACHINE CONFIGURATION AND MAGNETIC CIRCUIT MODELING
The topology of the investigated SF-HMMM with 6-/13-pole configuration is shown in Fig. 1 (a). 10 The tangentially magnetized NdFeB PMs are inserted into the stator teeth and the radially magnetized LCF PMs between the outer stator ring and the inner stator segments. The MS and polarities of the LCF PMs can be changed by applying DC current pulses fed by the magnetizing coils wound around the LCF PMs. The corresponding flux distributions in the states of flux enhanced and flux weakened are shown in Figs. 1 (b) and (c), respectively.
Before the analysis of the demagnetization characteristics of HCF magnets, it is essential to determine how and when the HCF magnets face the risk of irreversible demagnetization. With the assistance of finite element (FE) calculation, the flux lines corresponding to the transients when LCF magnets are subject to demagnetization and remagnetization by DC current pulse are shown in Figs. 2 (a) and (b), respectively. The major flux paths are highlighted with colored lines with arrows to indicate the circulating direction. Based on the field plot patterns, the simplified magnetic circuit is subsequently modeled to highlight the major flux paths in the machine, making it easier to visualize the relatively complex interactions between the magnetic elements. The corresponding simplified mag-netic circuits ignoring the reluctance of core are shown in Figs. 2 (c) and (d), respectively. The circulating fluxes Φ demag and Φremag at the HCF magnet branches when the LCF magnets are demagnetized and remagnetized by DC current pulse can be analytically formulated as: ϕremag (2) where FLCF and FHCF are the magnetomotive forces (MMFs) of LCF magnets and HCF magnets, respectively, RLCF and RHCF are the magnetic reluctances of LCF magnets and HCF magnets, respectively, Fmag is the MMF due to the current pulse to demagnetize/magnetize LCF magnets, and Rg is the air-gap magnetic reluctance.
In the case of LCF PM demagnetization, it can be analytically inferred from (1) that the HCF magnets fluxes rise with the increase of Fmag. This indicates that HCF magnets are unable to be demagnetized since the resultant MMF circulating the HCF PM branch shares the same direction with the magnetization direction of HCF magnets. On the other hand, in the case of LCF magnets remagnetization, as shown in (2), the HCF magnets fluxes drop with the increase of Fmag. The magnetic circuits demonstrate that only when the LCF magnets are remagnetized by DC current pulse, the HCF magnets will be prone to the demagnetization risk. Therefore, the analysis of the demagnetization characteristics of HCF magnets should be concentrated on the transient state when the LCF magnets are remagnetized.

III. DEMAGNETIZATION ASSESSMENT OF HCF MAGNETS
A. Influence of temperature Firstly, the B-H curves of the HCF magnets (NdFeB PMs) are given in Fig. 3 (a) in advance, which provides a benchmark for the following analyses. It shows that as the temperature increases, the knee point of the PM moves from the third quadrant to the  Fig. 4 (a) are more vulnerable to demagnetization. Fig. 4 (b) shows the fluctuation of the average magnetic density of the 1/4 part of HCF magnets near the air-gap as a current pulse demagnetizing the HCF magnets is applied in the middle period. To evaluate the level of the localized demagnetization of HCF magnets, the demagnetization coefficient k demag is defined as follows: where Ba1 is the average magnetic density of the 1/4 partial HCF magnets near the air-gap before applying the current pulse, while Ba2 is the average magnetic density after the current pulse. Thus, the values of k demag at 80 ○ C, 100 ○ C, 120 ○ C and 150 ○ C are 2.8%, 4.5%, 18.5% and 81.1%, respectively. When the temperature of the machine rises from 120 ○ C to 150 ○ C, k demag decreases rapidly, and the partial demagnetization of HCF magnets gets worse.

B. Influence of DC current pulse amplitude
The amplitude of DC current is another influencing factor for the demagnetization of HCF magnets. The resultant demagnetization coefficients k demag under various DC current amplitudes at different temperatures are listed in Table I. "k demag >100%" implies that HCF magnets are reversely remagnetized. From Table I, it shows that the demagnetization is more likely to occur with increasing the amplitude of DC current pulse. Nevertheless, the influence of the temperature turns out to be more pronounced. That is to say, the higher the temperature of the motor is, the stronger the impact of the DC current on the demagnetization of HCF magnets is.

C. Influence of HCF PM sizing
The influence of the HCF magnets thickness on its demagnetization is also explored. The demagnetization coefficient k demag versus HCF magnet thickness curves subject to different temperatures are shown in Fig. 5. In general, the increase of HCF magnet thickness is beneficial to the on-load demagnetization withstand capability. Thus, the thickness of HCF magnet needs to be designed as sufficiently high to resist the high-temperature demagnetization.

IV. EXPERIMENT
An SF-HMMM prototype with 6-/13-pole configuration is manufactured and tested to verify the foregoing theoretical analyses. The stator/rotor assemblies are shown in Figs. 6 (a) and (b), respectively. The FE-predicted and measured open-circuit back-EMF waveforms are compared as shown in Fig. 6 (c). Due to the good thermal dissipation, the temperature of the stator is about 80 ○ C in the rated-state, the HCF magnets can resist the impact of the high-level current pulse, making the SF-HMMM maintain high performance.

V. CONCLUSIONS
The unintentional demagnetization characteristics of HCF magnets in an SF-HMMM is investigated subject to a high-level transient current pulse. First, it can be found that the demagnetization of HCF magnets possibly occurs only in the LCF magnet remagnetization process. In addition, it shows that the on-load demagnetization withstand capability of HCF magnets can be improved when increasing HCF magnet thickness and lowering the current pulse level. Nevertheless, the temperature is a more predominant factor for the demagnetization behaviour of HCF magnets. If the temperature of the motor is designed as low enough, the effects of other factors on the demagnetization of HCF magnets turns out to be negligible. Thus, good thermal management is important for SF-HMMMs to maintain high performance especially accounting for the high-level current pulse. Finally, the experiments are carried out to confirm the theoretical analyses.