Magnetic Characteristics of FeSiB Cores in Motors Revealed by Experiment and Finite-Element Simulation

Abstract

Iron core loss (P_cm) is the main source of energy dissipation in motors, primarily affected by the stator material, which necessitates the optimization of soft-magnetic materials. In this work, the magnetic characteristics of FeSiB amorphous alloys and their influence on motors were systematically investigated via both experiment and finite-element simulation. It was found that the P_cm of the FeSiB core initially decreased significantly during heating but subsequently increased with a further temperature rise. In particular, after annealing at 460 °C for 10 min, the FeSiB core exhibited the lowest P_cm of 0.11 W/kg (50 Hz, 1 T) and 5.45 W/kg (1 kHz, 1 T), which correlated well with the changes in the magnetization. With the help of the finite-element analysis, the low P_cm of the motor using the FeSiB core was further demonstrated, and was closely associated with the dominance of the stator loss. Additionally, the magnetic flux density cloud and the related electromagnetic torque of the motor were comparatively analyzed to unveil the potential advantages of the current FeSiB core. This work provides an important theoretical basis for the design and development of amorphous/nanocrystalline motors.

1. Introduction

Under the background of the carbon emissions peak and carbon neutrality, the energy crisis and the continued growth of electrical power generation need to minimize their wasteful energy dissipation and maximize the conversion efficiency of the electronic power devices that are used [1,2,3]. As the largest consumer of electricity, the motor has become one of the key aspects of national energy conservation and emission reduction work, with its energy dissipation mainly originating from iron core loss (P_cm) [3]. The soft-magnetic iron core is one of the key factors that determine the loss and efficiency of the motor [4,5]. Currently, electrical steels, mainly composed of iron (Fe) with less than 6.5 wt.% silicon (Si), remain the predominant materials used in applications such as transformers and motors owing to their relatively low cost and high saturation magnetization (1.8–2.0 T). However, electrical steels are hindered by high-frequency core loss caused by their inherently low electrical resistivity (48–82 µΩ·cm) [6,7]. Inversely, Fe-based amorphous soft-magnetic alloys, rendering tremendous interest, have become the focus of academia and industry due to their wide range of applications in motors and transformers by virtue of their low loss characteristics at high frequencies [8,9,10]. Sun et al. reported the influence of stators made of different magnetic materials on the efficiency of a high-speed asynchronous motor and found that the P_cm can be significantly reduced by 91.1% using a stator made of an FeSiB amorphous alloy in 0–800 Hz [11]. Liu et al. studied the magnetic field distribution, stator core loss, and efficiency of two motors and demonstrated that amorphous material improved the electromagnetic performance of low-speed motors, and also exhibited higher efficiency than that of a silicon steel motor with an increasing frequency [5]. Gao et al. verified that by replacing the silicon steel stator with the amorphous metal stator and improving the motor design, the efficiency of the motor can be increased by 4.76%, and the weight can be reduced by 11.36% [12]. Although extensive studies about motors using soft-magnetic amorphous alloys have been reported [13,14,15,16], the performance and process optimization of amorphous magnetic cores, as well as their compatibility with motor design, are still a long-term issue that needs to be explored urgently.

In this work, a typical FeSiB amorphous alloy and silicon steel as the stator materials were selected for comparison, and the influences of the stator material on the magnetic characteristics including core loss, magnetic flux density, and electromagnetic torque were systematically investigated via experiment and finite-element simulation.

2. Materials and Methods

Commercially available amorphous ribbons with a nominal composition of Fe₈₀Si₉B₁₁ (at.%) were purchased from Jiangsu Guoneng Alloy Technology Co., Ltd. Jiangsu, China. The purity of the raw materials, including iron (Fe), silicon (Si), and boron (B), was 99.9 wt%. As-spun ribbons with widths of approximately 15 mm and thicknesses of approximately 28 μm were produced using the single roller melt-spinning method, which were then wound into round cores with an outer diameter of 28 mm, an inner diameter of 20 mm, and a height of 15 mm. Heat treatment was performed by keeping the ribbons or iron cores in a quartz tube under a vacuum atmosphere (10⁻³ Pa), and then pushing the quartz tube into a tubular furnace preheated to annealing temperature (420–480 °C) for various lengths of time, followed by water quenching cooling.

The microstructures of the air-sides of specimens were verified by X-ray diffraction (XRD, Bruker D8 Discover, Bruker AXS, Karlsruhe, Germany) with Cu Kα radiation and transmission electron microscopy (TEM; Talos F200X, FEI, Hillsboro, OR, USA). Here, for the XRD test, the scanning angle range is 20–90°, and the step size is 0.02°. Thermal behaviors were confirmed by differential scanning calorimeter (DSC, NETZSCH 404 C, Netzsch, Selb, Germany) with a heating rate of 0.33 °C/s under high-purity Ar protection. Similar to the previous works [17,18], the as-quenched ribbons were cut into 6 mm and then isothermally annealed in the vacuum chamber (10⁻³ Pa) to prepare the annealed ribbons. The magnetic properties of ribbons including B-H curves, maximum magnetic flux density (Bs), and coercivity (Hc) can be obtained by a vibrating sample magnetometer (VSM, EZ7, MicroSense, Lowell, MA, USA) under an applied field of 800 kA/m and a B-H loop tracer (BHS-40, RIKEN Machinery, Tokyo, Japan) under a field of 1 kA/m in DC mode, respectively. Moreover, the core loss and magnetization curves of the wound cores were measured via a silicon steel measuring instrument (MATS-3000M, Ningbo Economic and Technological Development Zone Kainuo Instrument Co., Ltd., Jinan, China) and soft-magnetic AC measuring device (MATS-2010SD, Lianzhong Technology Co., Ltd., Beijing, China), respectively. The electrical resistance was measured using a conventional DC four-probe method (SZJG ST2742B, Suzhou Jingge Electronics Co., Ltd., Suzhou, China). The finite-element simulation on the electromagnetic properties of motors using different soft-magnetic materials as stator components was carried out using ANSYS Maxwell software (ANSYS Electronics 2019 R3).

3. Results and Discussion

3.1. Microstructure and Thermal Behavior

Figure 1a shows the XRD patterns of the FeSiB amorphous alloys which are subjected to annealing for 10 min at different temperatures, corresponding to the temperatures just below the first exothermic peak in the DSC curve (shown in the inset in Figure 1a). With the temperature rising, a slightly sharp peak on a broad diffuse diffraction peak in the vicinity of 45° can be detected. Some works have elucidated that this change is assigned to the (110)-reflection of α-Fe crystalline phase and/or the formation of the clusters of crystal nuclei [19,20,21], which favors the optimized magnetic softness of the post-annealed alloys. It should be noted that this is different from the annealing temperature and time, which are 653 K and 60 min in Fe₈₀Si₉B₁₁ [22]; the annealing temperature in the current work is relatively high for probing into the microstructure evolution. Furthermore, the microstructure of the present FeSiB alloy subjected to annealing at 460 °C for 10 min was illustrated using the TEM test, as shown in Figure 1b. A small number of nanocrystals can be identified on the amorphous matrix, revealing a slight crystallization, which coincides well with the XRD results. From the selected area electron diffraction pattern in the inset (top), there exist some bright dots in the diffraction ring. This is the typical characteristic of the (110)-reflection of α-Fe nanocrystals [23]. The local enlarged HRTEM image is given, as also shown in the inset (bottom). Some heterogeneous regions (crystal-like ordered clusters) are observed. These heterogeneities may act as the heterogeneous sites of α-Fe nanocrystals for the alloy during the post-annealing. Such amorphous nanocrystals and their transitional microstructures endow the alloy with potentially excellent magnetic properties.

3.2. Magnetization

Figure 2 exhibits the magnetic softness of an example alloy after annealing at 420 °C for different annealing times. One can see that the lower B_s (172 Am²/kg) and larger H_c (0.91 A/m) in the as-quenched state are obtained, which is very close to the B_s of 1.56 T reported by the amorphous ribbon manufacturer [24]. With the annealing time increasing, the H_c drops to 0.67 A/m (10 min) and then increases, while B_s increases continuously, implying structural changes in the alloy after a shorter annealing time at a higher temperature. Based on this, the magnetic responses of the wound amorphous cores after annealing at different temperatures were analyzed, as shown in Figure 3. A regular magnetization curve for each amorphous core can be found, and the magnetization quickly saturates at a low applied field, implying good permeability and magnetic softness. The difference is that the amorphous core after annealing at 460 °C exhibits a quicker magnetization process and possesses a larger B_s of 1.54 T than that of 1.49 and 1.47 T at 420 °C and 480 °C, respectively, meaning a fast magnetic response of the present soft-magnetic material, which matches well with the fast start of the motor and other magnetic electronic devices [1,16]. Moreover, the inset in Figure 3 displays the changes in the electrical resistivity (ρ_e) of annealed amorphous cores. One can see that the ρ_e of cores initially increased and then decreased, and the maximum value of ρ_e is measured to be 130 μΩ·cm at 420 °C.

3.3. Amorphous Core Loss

Furthermore, according to the lower ρ_e of the annealed amorphous core at 420 °C, the comparative P_cm of the amorphous cores annealed at 420 °C for various times is shown in Figure 4. It can be clearly seen that the P_cm displays a similar trend at the different frequencies, which declines compared to the as-quenched state but seems to be equal for 10 and 20 min. Moreover, similar to the phenomenon in other amorphous cores, the P_cm manifests a strong dependence on frequency (f) and B_m. According to the classical loss separation model, the total iron loss can be described as follows [11,12,25]:

$$P_{\mathrm{c}\mathrm{m}}=P_{hyst}+P_{ec}+P_r=k_{h}f{B}_s^2+k_e{f}^2{B}_s^2+k_{ex}{f}^{1.5}{B}_s^{1.5}$$

where, P_hyst, P_ec, and P_r are hysteresis loss, eddy current loss, and residual loss, and k_h, k_e, and k_ex correspond to the coefficients of hysteresis, eddy current, and residual loss, respectively. It is apparent that each loss component exhibits a different sub-exponential relationship with frequency (f) and B_s, but both support an increase in P_cm. Apart from f and B_s, the H_c and resistivity (ρ_e) should be highlighted. For instance, the P_hyst is $\propto$ B_sH_c [26]; P_ec $\propto B_s^2/{\rho }_e$ [27]; and P_r$\propto B_s f/{\rho }_e$ [8]. It can be clearly seen that compared to the as-quenched amorphous core, the annealed ones at 10 and 20 min show a lower P_cm, especially at 20 min, implying the influence of microstructural changes in amorphous cores after annealing relaxation on P_cm. As a result, taking into account the magnetization and ρ_e features, the 420 °C and 10 min were determined as the optimal parameters for the further exploration of the annealing process.

To gain a deeper understanding of the correlation between P_cm and structural changes, the P_cm of amorphous cores after annealing at various temperatures is investigated, with the results shown in Figure 5. One can see that at both 50 Hz and 1 kHz, P_cm significantly drops as the annealing temperature increases from 350 °C to 460 °C, and then increases at 480 °C; similar trends are evident in Figure 5a,b. The comparative P_cm at 1 and 1.2 T as a function of the temperature is further extracted, as shown in Figure 5c,d. The P_cm declines first and then increases as the temperature rises. In particular, at 460 °C, the lower P_cm values of 0.11 W/kg at 50 Hz and 5.45 W/kg at 1 kHz are recorded at a magnetic field of 1 T. When the magnetic field is increased to 1.2 T, the P_cm increases to 0.16 W/kg at 50 Hz and 7.54 W/kg at 1 kHz under the same conditions. These values are still at the minimum across all temperature ranges, indicating the optimal microstructure at the current annealing temperature for amorphous cores.

Next, the dependence of P_cm on magnetic flux density B for the current work (highlighted by the larger symbols in green, red, and blue) is compared with that of other FeB-based amorphous and Fe-Si crystalline alloys, as reported in references [15,25,28,29,30,31,32,33,34], and is shown in Figure 6. The figure on the right is a locally enlarged image for the rectangle dotted line area in the left figure. As can be seen, the P_cm of the displayed Fe-based amorphous alloys is much lower than that of the Fe-Si alloy, unveiling the unique magnetic properties and great application advantages of the former. Particularly, compared with the previous reports, the P_cm in the current work appears to be the lowest value at the same f and B, manifesting a better heat treatment process.

3.4. Finite-Element Simulation

To accurately represent the real-time performance of the present amorphous cores as a stator component, the finite-element simulation model was utilized to analyze the loss, magnetic flux density distribution, torque, and efficiency of the motor during operation. In this work, a permanent magnet synchronous motor with a rated power of 750 W is employed, and the motor model is designed in Figure 7, which mainly involves four parts: rotor core, permanent magnet (PM), coil, and stator core. The detailed parameters are outlined in

Table 1. Main parameters of motor model.

Parameters	Values	Parameters	Values
Rated power/W	750	Pole numbers	10
Rated speed/rpm	3000	Slot numbers	9
Rated voltage/V	110	Rotor inside diameter/mm	10
Length of core/mm	56.7	Rotor outer diameter/mm	39.8
Stator inside diameter/mm	41.1	Connection type	Wye
Stator outer diameter/mm	76	Permanent magnet (PM)	NdFeB

.

Figure 8 exhibits the core loss distribution of a simulated motor operating at a rated speed of 3000 rpm. Also, the data of a typical silicon steel (SS, 50WW270) are shown for comparison. As shown in Figure 8a, the current amorphous core exhibits significantly lower core loss, approximately 1/10 to 1/14 of SS, which is crucial for power electronic devices and represents a distinctive advantage that is not observed in other soft-magnetic materials. This result is also consistent with the previous works reported in FeSiBC, FeSiBPCu, and FeSiBNbCu amorphous/nanocrystalline alloys, where the core loss is 1/2 to 1/5 smaller than that of Fe-Si alloy [3,35]. Moreover, the tiny difference in loss spectra for the present annealed alloys can be discerned, where the lowest loss for the amorphous core annealed at 460 °C is confirmed. This is in accordance with the above result in Figure 5. In addition, the loss of the separate stator and rotor are extracted from the total loss spectra, as shown in Figure 8b,c. It can be observed that the stator loss shows the same tendency and values as the total loss, while the rotor loss is significantly lower, being only approximately 1/200 of the total loss, and thus can be considered negligible in the current motor design. This unveils the dominance of stator losses in the overall loss profile and further implies the importance of designing soft-magnetic materials tailored to the stator in motor design. It is noted that the larger fluctuations in the loss of SS after stable operation can likely be attributed to the rapid increase in loss with the magnetization increase. However, when subjected to the minor influence of the present loss on magnetization, it manifests a small fluctuation. All of the above further confirm the superiority of the current soft-magnetic material for the stator design.

To comprehend the magnetic response of the amorphous/nanocrystalline cores required for the stator in a motor, the magnetic flux density cloud of the motor using different soft-magnetic alloys under rated operating conditions is analyzed. Here, the amorphous core annealed at 460 °C and SS are comparatively given in Figure 9, with the motor running times being 5 and 30 ms. As shown in Figure 9a,b, when the motor initially starts and runs for 5 ms, the magnetic flux density is mainly concentrated at the tip of the teeth (red regions), while other areas such as the yoke are less dense, a fact widely accepted in the literature [11,14]. The current of the motor during startup is approximately 4–7 times that of the rated current. The magnetic motive force generated by the stator winding is directly proportional to the current passing through it. Thus, the enhancement of the magnetic motive force leads to a highly saturated state of the amorphous core part of the leakage magnetic circuit. This may be one of the reasons for the high loss of the motor when it first starts. After running for 30 ms, as shown in Figure 9c,d, the magnetic flux density in the vicinity of the tip of the teeth seems to be strengthening, while in the yoke, the phenomenon of supersaturation has not yet been observed, indicating a good operating state. Furthermore, three random locations (m1, m2, and m3) on the yoke of the motor are marked to analyze the magnetic flux density distribution. After running, the locations of m4, m5, and m6 correspond to m1, m2, and m3, respectively, and the corresponding magnetic flux density is listed in

Table 2. The magnetic flux density of the different stators after operating for different times.

Operation Time	Position	Types of Stator Materials
		420 °C (T)	460 °C (T)	480 °C (T)	50WW270 (T)
5 ms	m1	0.79	0.89	0.79	0.96
	m2	0.80	0.82	0.78	0.86
	m3	0.63	0.66	0.60	0.66
30 ms	m4	0.81	0.85	0.81	0.86
	m5	0.73	0.78	0.72	0.79
	m6	0.68	0.69	0.67	0.75

. A slight difference at the marked points is observed. As the motor starts running (5 ms), the magnetic flux density at these points first increases and then decreases, and the maximum values of B_s are achieved at 460 °C, being the closest to that of the SS motor. This trend is similar to the one observed at 30 ms, indicating that both the amorphous motor at the current temperature and the SS motor exhibit a faster rate of field establishment, which suggests an improved response speed of the motor. To further evaluate the stability of the motor operation, the electromagnetic torque and its fluctuations are studied, as shown in Figure 10. When the motor runs stably, the present amorphous core annealed at 460 °C and the SS exhibit the larger electromagnetic torque in all listed cores, which are 2.16 and 2.17 N·m, respectively, indicating a greater running power and a higher speed of the motor using the present amorphous core and SS. Nevertheless, the lower torque fluctuation of 3.41% for the present amorphous core than that of 3.7% for the SS is achieved. From the stator perspective, smaller fluctuations may reduce the noise and vibration generated during motor operation, thereby improving the operational stability of the motor. All the above experimental and finite-element simulation studies reveal the importance of stator material optimization and provide a theoretical basis for the design and development of amorphous/nanocrystalline motors.

4. Conclusions

In this work, the magnetic characteristics of FeSiB amorphous alloys and their influence on motors were systematically investigated via both experiment and finite-element simulation. The main results are summarized as follows.

(1)

The FeSiB amorphous core annealed at 460 °C for 10 min exhibits a high magnetic flux density of 1.54 T and low core loss of 0.11 W/kg at 50 Hz and 5.45 W/kg at 1 kHz at 1 T. These values are essential for ensuring high magnetic response and energy efficiency in motors and other electronic devices.

(2)

Finite-element simulation analysis reveals that the reduced core loss in the FeSiB motor, compared to the 50WW270 silicon steel motor, is primarily attributable to the stator loss, which in turn is ultimately governed by the microstructure and magnetic properties of the soft-magnetic material.

(3)

Both amorphous alloy and silicon steel materials contribute to enhanced motor response speed. The current amorphous motor demonstrates stable electromagnetic torque (2.16 N·m) with reduced torque fluctuation (3.41%), resulting in decreased noise and vibration during motor operation, which improves the motor’s operational stability.