3D electromagnetic analysis and experimental verification of multi-pole magnetization BLDC motor

ABSTRACT
This paper presents a quasi-3D electromagnetic analysis of the multi-pole magnetization BLDC motor. The permanent magnet (PM) of a multi-pole magnetization BLDC motor has several poles in a magnet. The polar separation section of the multi-pole PM is implemented through the magnetization pattern function. The analysis model of this study, as the outer rotor type, has two 3D structures: the PM overhang and housing-integrated rotor core. Because the 3D analysis is time consuming, 3D structures are corrected to 2D analysis model. The PM overhang is corrected by considering the magnitude of magnetic energy, and the housing-integrated rotor core is corrected by considering the radial direction flux of the rotor core. Finally, the corrected 2D analysis model of a multi-pole magnetization BLDC motor is verified experimentally.

I. INTRODUCTION
Multi-pole magnetization PM has two or more poles in one magnet. Therefore, even if the number of PMs is reduced, the same number of poles can be obtained. Reducing the number of PMs has the advantage of reducing the assembly time and manufacturing tolerances. Meanwhile, a polar separation section by the structure of the magnetizer is generated in the multi-pole magnetization process. In this study, to consider the section, the magnetization pattern function is applied to multi-pole PM.1
The analysis model have two 3D structures. One is the PM overhang and the other is the housing-integrated rotor core. The PM overhang can increase the power density in a magnetically weak PM like ferrite. Also, the housing-integrated rotor core is a structure commonly used in the outer rotor type. These 3D structures require 3D analysis for accurate prediction of the electromagnetic characteristics. However, a 3D analysis is considerably time-consuming and inefficient in the initial design process. Therefore, in this study, a quasi-3D electromagnetic analysis that corrects the 3D to 2D structures is performed. The PM overhang is corrected by changing the operating point of PM, and the housing-integrated rotor core is corrected by increasing the rotor core thickness. The quasi-3D electromagnetic analysis of the multi-pole magnetization of the BLDC motor is validated by comparing experimental results to the corrected 2D and 2D analysis model.

3D electromagnetic analysis and experimental verification of multi-pole magnetization BLDC motor

3D electromagnetic analysis and experimental verification of multi-pole magnetization BLDC motor

II. MULTI-POLE MAGNETIZATION BLDC MOTOR
A. Analysis model
Fig. 1(a) shows a multi-pole PM and housing-integrated rotor core of the analysis model. Fig. 1(b) depicts a corrected 2D analysis model by quasi-3D electromagnetic analysis. The analysis model have five multi-pole PMs, 12 slots, and a concentrated winding type as shown in Fig. 1(a) and (b). In multi-pole PMs, there are two poles in one magnet.
FIG. 1. (a) Analysis model (b) Corrected 2D analysis model (c) Polar separation section of multi-pole PM (d) Magnetization patter function.
B. Function of the magnetization pattern
Fig. 1(c) is the magnetic flux density vector in the multi-pole magnetization PM. We can observe that the polar separation section has a small magnetic flux density at the center of the PM, as shown in Fig. 1(c). In this study, the magnetization pattern function shown in Fig. 1(d) is used to implement the polar separation section. Nonlinear modeling in the polar separation section are very complex and difficult and this section is relatively short for the entire polar section. Therefore, it is assumed that the magnetic force decreases linearly in this study.
III. QUASI-3D ELECTROMAGNETIC ANALYSIS
Fig. 2(a) represents the 3D structures of the analysis model that are the PM overhang and housing-integrated rotor core.

A. Correction of PM overhang
π‘Šπ‘š=12∫(𝐁⋅𝐇)π‘‘π‘‰β‰ˆ12π΅π‘šπ»π‘šπ‘‰
(1)
The magnetic energy is proportional to the operating point of the magnetic flux density and the magnetic field intensity as shown in equation.1 Therefore, the PM increasing by overhang can be compensated by changing Bm and Hm. Fig. 2(b) is the demagnetization curve of the PM, and it represents changing the operating point of the PM from P1 to P2. The symbols in Fig. 2(b) are shown in Table I.
π΅β€²π‘š=βˆ’πœ‡π‘ƒπΆπ‘‰π‘‰β€²π΅π‘šπ»π‘šβŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βˆš
(2)
𝑃𝐢=π΅π‘šπœ‡0||π»π‘š||=1π‘“πΏπΎπΊπ‘™π‘ƒπ‘€π‘”β€²π΄π‘”π΄π‘š
(3)
𝑓𝐿𝐾𝐺=Ξ¦π‘”Ξ¦π‘š=Ξ¦π‘”Ξ¦π‘š+Φ𝐿

Parameters Description Parameters Description
Br Residual magnetic flux density of analysis model Hc Coercive force of analysis model
Br’ Corrected residual flux density Hc’ Corrected Coercive force
Bm Magnetic flux density operating point of analysis model Hm Magnetic field intensity operating point of analysis model
Bm’ Corrected magnetic flux density operating point Hm’ Corrected magnetic field intensity operating point
The corrected operating point of the magnetic flux density can be calculated by equation.2 V and Vβ€² are the PM volume of the analysis model and the corrected 2D analysis model, respectively. PC is the permeance coefficient and defined slope of the load line. It can be calculated by equation.3 g is the length of the air-gap. Ag and Am are the axial cross-sectional area per pole of the air-gap and PM, respectively. fLKG is a leakage coefficient and defined as the ratio of air-gap flux to magnet flux as shown in equation.4 Ξ¦g, Ξ¦m, and Ξ¦L are respectively flux of air-gap, magnet, and leakage. Since it is known to have a value of 0.85-0.95, the average value 0.9 is chosen in this study.2,3
B. Correction of housing-integrated rotor core
Fig. 3(a) is the magnetic flux density in the housing-integrated rotor core. It can be confirmed that there is not only the flux of axial direction, but also the flux of radial direction, 078 T. Fig. 3(b) and (c) show that the magnetic saturation occurs in the rotor core of the uncorrected 2D analysis model. When the rotor core is saturated, the leakage flux occurs and electromagnetic characteristics are changed. Therefore, the thickness of the rotor core in the corrected 2D analysis model is further corrected to equal the volume of the housing-integrated rotor core, considering the radial flux path and the magnetic saturation.

ABSTRACT
This paper presents a quasi-3D electromagnetic analysis of the multi-pole magnetization BLDC motor. The permanent magnet (PM) of a multi-pole magnetization BLDC motor has several poles in a magnet. The polar separation section of the multi-pole PM is implemented through the magnetization pattern function. The analysis model of this study, as the outer rotor type, has two 3D structures: the PM overhang and housing-integrated rotor core. Because the 3D analysis is time consuming, 3D structures are corrected to 2D analysis model. The PM overhang is corrected by considering the magnitude of magnetic energy, and the housing-integrated rotor core is corrected by considering the radial direction flux of the rotor core. Finally, the corrected 2D analysis model of a multi-pole magnetization BLDC motor is verified experimentally.
I. INTRODUCTION
Multi-pole magnetization PM has two or more poles in one magnet. Therefore, even if the number of PMs is reduced, the same number of poles can be obtained. Reducing the number of PMs has the advantage of reducing the assembly time and manufacturing tolerances. Meanwhile, a polar separation section by the structure of the magnetizer is generated in the multi-pole magnetization process. In this study, to consider the section, the magnetization pattern function is applied to multi-pole PM.1
The analysis model have two 3D structures. One is the PM overhang and the other is the housing-integrated rotor core. The PM overhang can increase the power density in a magnetically weak PM like ferrite. Also, the housing-integrated rotor core is a structure commonly used in the outer rotor type. These 3D structures require 3D analysis for accurate prediction of the electromagnetic characteristics. However, a 3D analysis is considerably time-consuming and inefficient in the initial design process. Therefore, in this study, a quasi-3D electromagnetic analysis that corrects the 3D to 2D structures is performed. The PM overhang is corrected by changing the operating point of PM, and the housing-integrated rotor core is corrected by increasing the rotor core thickness. The quasi-3D electromagnetic analysis of the multi-pole magnetization of the BLDC motor is validated by comparing experimental results to the corrected 2D and 2D analysis model.
II. MULTI-POLE MAGNETIZATION BLDC MOTOR
A. Analysis model
Fig. 1(a) shows a multi-pole PM and housing-integrated rotor core of the analysis model. Fig. 1(b) depicts a corrected 2D analysis model by quasi-3D electromagnetic analysis. The analysis model have five multi-pole PMs, 12 slots, and a concentrated winding type as shown in Fig. 1(a) and (b). In multi-pole PMs, there are two poles in one magnet.
figure
FIG. 1. (a) Analysis model (b) Corrected 2D analysis model (c) Polar separation section of multi-pole PM (d) Magnetization patter function.
PPT|High-resolution
B. Function of the magnetization pattern
Fig. 1(c) is the magnetic flux density vector in the multi-pole magnetization PM. We can observe that the polar separation section has a small magnetic flux density at the center of the PM, as shown in Fig. 1(c). In this study, the magnetization pattern function shown in Fig. 1(d) is used to implement the polar separation section. Nonlinear modeling in the polar separation section are very complex and difficult and this section is relatively short for the entire polar section. Therefore, it is assumed that the magnetic force decreases linearly in this study.
III. QUASI-3D ELECTROMAGNETIC ANALYSIS
Fig. 2(a) represents the 3D structures of the analysis model that are the PM overhang and housing-integrated rotor core.
figure
FIG. 2. (a) 3D structures of analysis model (b) Demagnetization curve of PM.
PPT|High-resolution
A. Correction of PM overhang
π‘Šπ‘š=12∫(𝐁⋅𝐇)π‘‘π‘‰β‰ˆ12π΅π‘šπ»π‘šπ‘‰
(1)
The magnetic energy is proportional to the operating point of the magnetic flux density and the magnetic field intensity as shown in equation.1 Therefore, the PM increasing by overhang can be compensated by changing Bm and Hm. Fig. 2(b) is the demagnetization curve of the PM, and it represents changing the operating point of the PM from P1 to P2. The symbols in Fig. 2(b) are shown in Table I.
π΅β€²π‘š=βˆ’πœ‡π‘ƒπΆπ‘‰π‘‰β€²π΅π‘šπ»π‘šβŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βŽ―βˆš
(2)
𝑃𝐢=π΅π‘šπœ‡0||π»π‘š||=1π‘“πΏπΎπΊπ‘™π‘ƒπ‘€π‘”β€²π΄π‘”π΄π‘š
(3)
𝑓𝐿𝐾𝐺=Ξ¦π‘”Ξ¦π‘š=Ξ¦π‘”Ξ¦π‘š+Φ𝐿
(4)
Table icon
TABLE I.
Parameters.
Parameters Description Parameters Description
Br Residual magnetic flux density of analysis model Hc Coercive force of analysis model
Br’ Corrected residual flux density Hc’ Corrected Coercive force
Bm Magnetic flux density operating point of analysis model Hm Magnetic field intensity operating point of analysis model
Bm’ Corrected magnetic flux density operating point Hm’ Corrected magnetic field intensity operating point
The corrected operating point of the magnetic flux density can be calculated by equation.2 V and Vβ€² are the PM volume of the analysis model and the corrected 2D analysis model, respectively. PC is the permeance coefficient and defined slope of the load line. It can be calculated by equation.3 g is the length of the air-gap. Ag and Am are the axial cross-sectional area per pole of the air-gap and PM, respectively. fLKG is a leakage coefficient and defined as the ratio of air-gap flux to magnet flux as shown in equation.4 Ξ¦g, Ξ¦m, and Ξ¦L are respectively flux of air-gap, magnet, and leakage. Since it is known to have a value of 0.85-0.95, the average value 0.9 is chosen in this study.2,3
B. Correction of housing-integrated rotor core
Fig. 3(a) is the magnetic flux density in the housing-integrated rotor core. It can be confirmed that there is not only the flux of axial direction, but also the flux of radial direction, 078 T. Fig. 3(b) and (c) show that the magnetic saturation occurs in the rotor core of the uncorrected 2D analysis model. When the rotor core is saturated, the leakage flux occurs and electromagnetic characteristics are changed. Therefore, the thickness of the rotor core in the corrected 2D analysis model is further corrected to equal the volume of the housing-integrated rotor core, considering the radial flux path and the magnetic saturation.4
figure
FIG. 3. Distribution of magnetic flux density in (a) Analysis model (b) Corrected 2D analysis model (c) 2D analysis model.
PPT|High-resolution
IV. EXPERIMENTAL VERIFICATION AND DISCUSSION
A. Experimental verification
Fig. 4(a) shows the experimental setup for the induced voltage measured by a drive motor at 1,000 rpm. Fig. 4(b) shows the experimental setup for the cogging torque by torque sensor. The experimental results of the induced voltage and cogging torque are shown along with the analysis results of the corrected 2D and 2D analysis model in Fig. 4(c) and (d). In Fig. 4(c), we can see that the phase induced voltage of the corrected 2D analysis model is nearly identical to the experimental results, but not in the 2D analysis model. The magnitude of cogging torque is defined as peak to peak value. In Fig. 4(d), we can see that the maximum and minimum value of the cogging torque in the corrected 2D analysis model is nearly identical to the experimental results, but not in 2D analysis model. And the error rate of corrected 2D analysis model and 2D analysis model are respectively 9.45% and 39.65%.
figure
FIG. 4. The experimental set up for (a) Induced voltage (b) Cogging torque. Comparing experimental results to the corrected 2D and 2Danalysis model in (c) Phase induced voltage at 1,000 rpm (d) Cogging torque.

Fig. 5 shows the experimental set up for the electromagnetic performance of the analysis model. In Fig. 5, the dynamometer generates load torque for the analysis model. The PCB is the controller of the BLDC motor. The power analyzer measures the parameters of electromagnetic performance. Table II summarizes the results of the electromagnetic performance in the experiment, and the corrected 2D and 2D analysis model under the same terminal DC voltage and torque generating conditions.

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