Shape optimization and demagnetization analysis of interior permanent magnet synchronous machine with hybrid cores

Compared with non-grain oriented silicon sheet (NGO), the magnetic characteristic of grain-oriented silicon sheet (GO) is much better along its rolling direction, while that along the other directions is lower. By analyzing the magnetic field of electrical machine, it can be found that the magnetic fluxes on its stator teeth is nearly alternating. Taking the advantage of high permeability of GO along its rolling direction, it was employed for filling part of magnetic barrier of a synchronous reluctance machine.¹ It showed that the torque ability of this machine has been improved especially when the applied current density is high as its d-axis magnetizing ability has been enhanced. By using GO for fabricating stator teeth while stator yoke still made by using NGO, the performance of axial flux switched reluctance machine and permanent magnet synchronous machine for automotive application can be improved greatly.^2,3

By installing PM in different rotor position, the PMSM includes the surface mounted PMSM and interior PMSM (IPMSM). Currently, the IPMSM has shown its higher torque ability than the surface mounted PMSM, as the reluctance torque is existed. The reluctance torque is produced by the difference between d-axis and q-axis inductance and further determined by the rotor structure. However, the rotor structure of IPMSM is very complex, as it can be designed with various shapes for achieving good electromagnetic performance.

Meanwhile with the exists of cogging torque, the torque ripple of IPMSM is high as well. Both improving the machine structure and control algorithm can reduce the torque ripple.^4,5 In Ref. 6, the torque ripple of an IPMSM has been reduced by notching the rotor bridge with different shapes, while the average torque kept no decreased. For achieving best rotor barrier shape, a moving asymptotes-based topology optimization method (MMA)is proposed for a SynRM.⁷ 

At present, the biggest disadvantage of PMSM is the fluctuation of permanent magnetic field and inherent irreversible demagnetization risk of PM is high. In Ref. 8, The rotor barrier of IPMSM was designed by automatic design system that combines coarse-mesh finite element method (FEM) and genetic algorithm (GA), a machine with high anti-demagnetization ability was obtained. In Ref. 9, the demagnetization of PM with different shapes of flux barrier are compared, and the region of high demagnetization rate can be reduced by adding a flux barrier to block the flow of the demagnetizing field flux.

In this paper, a IPMSM with hybrid GO-NGO cores (for simplicity it is named as GO-IPMSM) is designed, where GO is used for fabricating the stator teeth and the other stator part still made by using NGO. Meanwhile, as the GO adopted for the stator teeth, the average torque of IPMSM can be increased greatly while the torque ripple increased greatly as well, the shape of the rotor barrier will be optimized to reduce its torque ripple (for simplicity GO-IPMSM after rotor barrier shape optimization is named as GO-IPMSMb). Lastly, the anti irreversible demagnetization ability of PM is analyzed by FEM to make sure the optimized GO-IPMSM can operate safely.

By employing GO silicon sheets replacing NGO silicon sheets on the stator teeth of IPMSM (GO-IPMSM) as shown in Fig. 1(a), the electromagnetic performance of IPMSM can be improved greatly. With the traditional IPMSM with 8 poles and 48 slots (NGO-IPMSM(48))as shown in Fig. 1(b) and IPMSM with 8 pole 12 slots (NGO-IPMSM(12)) made all by NGO silicon sheets determined as the benchmark machines, it can be seen that GO-IPMSM is with higher torque ability and efficiency. While as the GO silicon sheet is employed, its anti irreversible demagnetization ability may be reduced. Table I tabulates its main dimensions and parameters.

Figure 2(a) shows the torque versus the current density comparison of these machines. Figure 2(b) compares the core loss of these machines when their average torque is about 150 Nm. Figure 2(c) shows the efficiency versus torque comparison. As shown, compared with the other machines, the torque ability of GO-IPMSM is the highest one. For achieving same average torque of about 150 Nm, the core loss consumed in GO-IPMSM is about 261 W while that in NGO-IPMSM(12) is about 285 W. As shown, the core loss has been reduced about 8.42% with the GO adopted. However, the core loss in NGO-IPMSM (48) is about 203 W for obtaining the average torque of 150 Nm, as it is designed with integrated slot distributed winding configuration. With the current density increases the ratio of torque to current density decreases for the IPMSM with 12 stator slots. Moreover, the required current in GO-IPMSM is much lower than other two machines, therefore the efficiency of GO-IPMSM is higher as shown in Fig. 2(c).

With adoption of GO designing the stator teeth of IPMSM, its torque ability has been improved and its core loss has been reduced. On the other hand, its torque ripple has been increased greatly. For IPMSM, its rotor barrier shape determines the air gap flux density distribution and further the torque ripple. To reduce its torque ripple, optimizing its rotor barrier shape is an effective way. In this paper, the irregular magnetic barriers are established symmetrical with q-axis as central line. The first magnetic barrier near the air gap is determined by five curves, and the second magnetic barrier is determined by six curves as shown in Fig. 3(a). All these curves are determined by,

where a_i, b_i, c_i, and d_i are the coefficients for determining the curve, x and y are the horizontal and vertical coordinates. Figures 3(b)–3(d) shows the rotor structure that determined by using the proposed polynomial method while with different parameters. As shown, various kind of rotor structures can be achieved by using the proposed polynomial method. Compared with the piecewise linear interpolation method, the obtained rotor barrier will be more smooth while with less parameters by using the polynomial method.

The multi-level design optimization algorithm is employed for optimizing the rotor barrier structure as 46 parameters needs to be optimized. Specifically, the parameters for determining the first rotor barrier are taken as the first group while that determining the second rotor barrier are taken as the second group. Taking the average torque and torque ripple before optimization as the reference value, the optimization objective is defined by,

where T_{original_ave_Torque} is average torque before optimization and T_{original_Ripple} is torque ripple before optimization.

Specifically the GA is adopted for the optimization with the O₁ determined as the objective. During the optimization process, the magnetization direction of the PM is fixed while its shape changes with the rotor barrier changes. After design optimization, the shape of PM is not a rectangular. However with the improvement of PM magnetization technology, the cost of manufacturing process will be not high especially when many pieces of PMs are adopted for reducing the PM eddy current loss.

Figure 4(a) shows the optimized rotor structure of the GO-IPMSMb. Figure 4(b) shows the electromagnetic torque waveform comparison between GO-IPMSM and GO-IPMSMb. It can be seen that the average torque is about 162 Nm and torque ripple is about 11.1% with the new rotor barrier shape employed. Therefore, optimizing the rotor barrier is an effective way to improve the machine performance.

The PM irreversible demagnetization is resulted by many factors, for example the working temperature over its Curie point, applied external magnetic field strength over its kneel point magnetic field strength or chemistry corrosion. Figure 5 shows the intrinsic demagnetization curve and demagnetization curve of the NdFeB (NTP-256H) under different working temperature that employed in the GO-IPMSM developed in this paper. When the applied external magnetic field intensity is higher than the kneel point magnetic field strength, then the new recovery line will no longer coincide with the original demagnetizing curve. Furthermore when the demagnetizing field is removed, the residual magnetic flux density will decrease and the PM will be irreversible demagnetized.¹⁰ 

As shown, the NdFeB PM is more easy to be demagnetized when its working temperature is high. When the IPMSM is under normal operation state, the temperature rise of PM is about 80 °C. Assuming room temperature is about 20 °C, the PM working temperature in IPMSM is about 100 °C. Therefore, PM working temperature of 100 °C is employed for the demagnetization analysis in this paper.

The residual magnetic flux density corresponding to the original demagnetization curve is B_r0, and the residual magnetic flux density corresponding to the recovery line after irreversible demagnetization is B_r1, as shown in Fig. 5. The demagnetization coefficient can be calculated by,

As shown, the Demag_coef is within 0 to 1, when it equals 1, no irreversible demagnetization occurs on the analyzed PM. On the other hand when it equals 0, the PM for analyzed is fully irreversible demagnetized.

To achieve the output torque of 150 Nm, the applied current density and the corresponding current phase angle for NGO-IPMSM(48), NGO-IPMSM(12), and GO-IPMSM are 18 A/mm² with 53°, 18 A/mm² with 37°, and 12 A/mm² with 37°, respectively, and the corresponding efficiency are 94.06%, 90.47%, 95.02% respectively. Moreover, the torque ability of GO-IPMSM is improved, after its rotor shape is optimized. For obtaining the torque of 150 Nm, the required current density for GO-IPMSMb is about 10 A/mm². Meanwhile its operation efficiency has been improved to about 96.22%.

Through the PM demagnetization analysis, it can be seen that both the NGO-IPMSM(48), NGO-IPMSM(12), GO-IPMSM and GO-IPMSMb can work safely without irreversible demagnetization risk. Furthermore, NGO-IPMSM(48) and NGO-IPMSM(12) are without the irreversible demagnetization risk though the applied armature current is with any current phase angles. For the GO-IPMSM, it is without irreversible demagnetization risk before its rotor barrier shape is optimized as well. However after its rotor barrier shape is optimized, it will face a little irreversible demagnetization risk especially when its current phase angle equals 70^o. Figure 6(a) shows B_y map of NGO-IPMSM(48) when its applied current density equals 18 A/mm², and the current phase angle equals 53°. Figure 6(b) shows B_y map of NGO-IPMSM(12) when its applied current density equals 18 A/mm², and the current phase angle equals 37°. Figure 6(c) shows B_y map of GO-IPMSM when its applied current density equals 12 A/mm², and the current phase angle equals 37°. Figure 6(d) shows B_y map of GO-IPMSMb when its applied current density equals 10 A/mm², and the current phase angle equals 37°. Figure 6(e) and 6(f) shows B_y map and demagnetization map of GO-IPMSMb when its applied current density equals 10 A/mm², and the current phase angle equals 70°. Figures 6(g) and 6(h) shows B_y map and demagnetization map of GO-IPMSMb with its PM moves more far away from the rotor surface when its applied current density equals 10A/mm², and the current phase angle equals 70°. Figures 6(i) and 6(j) shows B_y map and demagnetization map of GO-IPMSMb with its magnetic bridge becomes more wide when its applied current density equals 10 A/mm², and the current phase angle equals 70°.

It can be seen that optimizing the rotor barrier shape can improve the machine torque ability and efficiency, however its anti irreversible demagnetization ability is reduced. The main reason is that the PM is close to the rotor surface and the magnetic bridge becomes more thick. However, though the proposed machine is with little irreversible demagnetization risk, it can still work safely. The prototype and experiment of the proposed machine will be presented in our future work.

The shape optimization and demagnetization analysis of IPMSM with hybrid GO-NGO cores are presented in this paper. With employing GO replacing NGO stator teeth, the torque ability and efficiency of IPMSM has been improved, however its torque ripple is increased as well. By establishing the rotor barrier shape using the proposed polynomial method, various kinds of rotor barrier shape can be obtained. The torque ripple can be reduced and the torque ability can be improved through optimizing the rotor barrier shape. After the demagnetization analysis, it can be seen that the anti irreversible demagnetization ability of GO-IPMSM after its rotor barrier shape is optimized is reduced, however it still can work safely under the rated working state.

This work was supported by the National Natural Science Foundation of China under project 52007047, and in part by the Outstanding Youth Innovation Project funded by State Key Laboratory of Reliability and Intelligence of Electrical Equipment EERI_OY2021005, and EERI_KF2021014.

The authors have no conflicts to disclose.

Chengcheng Liu: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal). Xiaorui Huang: Methodology (equal); Writing – original draft (equal). Wenfeng Zhang: Investigation (equal). Youhua Wang: Investigation (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.