Investigation of a Micro Two-Phase Flux-Switching Motor

Abstract

This paper presents the world’s smallest two-phase flux-switching motor (FSM), featuring a four-pole stator and a two-pole rotor with a non-uniform air gap design. The FSM offers several advantages, including a compact size, simple structure, and ease of manufacturing, making it suitable for future micromachine applications. The motor has an outer stator diameter of 8 mm, an outer rotor diameter of 4 mm, and a stack length of 5 mm. This research employs a topological method and JMAG-Designer Ver.22.0 electromagnetic analysis software to enhance the rotor design for high output torque and low torque ripple. The final design achieves an average torque of 174 μN-m and a torque ripple of 40%, which is lower than those of any two-phase motor reported in the literature. The two-phase FSM has been fabricated, assembled, and tested to demonstrate its feasibility.

1. Introduction

In recent years, flux-switching motors (FSMs) have garnered significant attention due to their high torque density, high-speed capabilities, ease of control, low vibration, and minimal noise. These characteristics make them well suited for applications in transportation, renewable energy, and aerospace [1]. This type of motor is excited on the stator and can be implemented using three excitation methods: permanent magnet, coil excitation, and hybrid excitation [2]. These methods facilitate effective heat dissipation and result in a simple yet robust rotor design. Among these options, stator coil excitation does not require permanent magnets, which simplifies the design and reduces manufacturing costs [3]. In 1955, Rauch and Johnson [4] first proposed the conceptual design of a single-phase flux-switching motor featuring a four-pole stator and a two-pole rotor. This design incorporated two permanent magnets and a set of alternating current (AC) coils in the stator. In 1999, Pollock and Wallace [5] introduced a two-phase flux-switching motor, also with a four-pole stator and a two-pole rotor. This motor eliminated the need for permanent magnets; instead, the stator comprised excitation and armature windings, and its feasibility was experimentally validated. In 2003, C. Pollock and H. Brackley [6] conducted a comparison between two-phase flux-switching motors and switched reluctance motors, utilizing an eight-pole stator and a four-pole rotor with an exterior rotor design. The stator structure was asymmetrical, and the study demonstrated that flux-switching motors could reduce radial forces during operation, thereby improving noise and vibration levels. In 2005, Yi Cheng and colleagues [7] proposed a two-phase permanent magnet flux-switching motor featuring an eight-pole stator and a four-pole rotor, utilizing four permanent magnets in the stator, specifically designed for low-energy consumption axial fans. In 2006, Y. Chen and colleagues [8] introduced a single-phase permanent magnet flux-switching motor with a four-pole stator and a two-pole rotor, which incorporated two permanent magnets in the stator and a non-uniform air gap rotor design, enabling self-starting unidirectional rotation. In the same year, Pollock and Pollock [9] presented a flux-switching motor tailored for automotive applications, equipped with an eight-pole stator and a four-pole rotor. This rotor also featured a non-uniform air gap design, and its simple yet robust structure ensured longevity and high reliability, while maintaining extremely low costs for large-scale applications. Their findings indicated that the torque ripple exceeded 90%. In 2006, Bangura [10] derived design equations for a two-phase flux-switching motor featuring an eight-pole stator and a four-pole rotor, utilizing 2D finite element analysis and experimental validation. In 2008, Chen et al. [11] developed a lumped-parameter magnetic circuit model for a single-phase flux-switching motor with a four-pole stator and a two-pole rotor, comparing the magnetic circuit model with finite element analysis and experimental results. Their findings indicated that this motor design could produce negative torque. In 2014, Zhang et al. [12] introduced a novel flux-switching motor with a composite rotor design, employing two stacked rotor structures in the axial direction to achieve a non-uniform air gap effect, which enabled self-starting capabilities. This motor was designed with an eight-pole stator and a four-pole rotor, relying solely on finite element analysis without actual motor implementation. In 2017, You et al. [13] proposed a two-phase flux-switching motor with an eight-pole stator and a four-pole rotor, utilizing two axially stacked rotor structures. One of the rotor structures features a non-uniform air gap, achieving high starting torque; however, this composite rotor design produces approximately 13% lower torque output compared to conventional rotors. In 2017, Omar et al. [14] introduced a novel flux-switching motor featuring a segmented rotor and non-overlapping windings. The stator consists of 12 poles, while the rotor has 6 poles. The non-overlapping armature coils minimize coil end length and copper losses, whereas the segmented rotor shortens the magnetic flux path, thereby reducing magnetic reluctance and generating higher torque output. In 2019, Rahman et al. [15] compared three flux-switching motors with stator and rotor pole configurations of 6/3, 8/4, and 8/6. Utilizing finite element analysis for design, the 6/3 configuration was unable to self-start, the 8/4 design employed a non-uniform air gap rotor, and the 8/6 configuration incorporated a segmented rotor and non-overlapping windings. Among the three, the 8/6 design demonstrated the lowest copper and iron losses, as well as the highest efficiency, making it suitable for applications in pedestal fans. In 2020, You and Yang [16] proposed a 50 mm diameter two-phase flux-switching motor along with a new speed control system featuring an eight-pole stator and a four-pole rotor. By increasing the excitation current near the commutation position to enhance the reluctance torque, they significantly reduced torque ripple from over 100% to 56%. In 2023, Wang et al. [17] introduced a new single-phase flux-switching motor with an eight-pole stator and a four-pole rotor, which axially stacks two rotor structures. The stator contains 12 permanent magnets and utilizes low-cost ferrite to replace DC winding coils, achieving higher efficiency and torque density. In 2024, Zhang and Guo [18] presented a flux-switching motor with an eight-pole stator and a four-pole rotor, employing axially stacked rotor structures to create a non-uniform air gap effect. This motor incorporates an optical sensor to detect rotor position and utilizes iterative learning control (ILC) for driving rotation.

Topology optimization is a mathematical technique that optimizes the layout of structures within specified design constraints, aiming to maximize performance. C. Midha [19] asserted that topology optimization can facilitate the innovative design of electromagnetic devices without depending on prior experiences. There are three optimization methods: homogenization, density, and discrete (on/off) methods. This research employs the homogenization method due to its simplicity, allowing for the creation of straightforward continuous 2D electromagnetic structures. In 2022, E. Andriushchenko et al. [20] applied a topology optimization method to solve the torque ripple problem in switched reluctance motors. Since the on–off topology optimization method was selected, the final motor design is quite complex and can only be produced using additive manufacturing techniques, such as 3D printing.

The two-phase flux-switching motor provides numerous advantages, including high torque density, a simple and robust design, the absence of permanent magnets, high reliability, and low cost. Additionally, these motors must generate continuous positive torque for forward rotation to prevent reverse rotation caused by resistive torque. This requirement is especially critical for micromotors with low output torque, which are commonly used in applications such as fluid pumps and toys. Consequently, both average torque and torque ripple are established as design objectives for this research.

According to the literature [16], the minimum diameter for such motors is 50 mm; however, with speed feedback control, the torque ripple can be reduced to as low as 56%. This study proposes the world’s smallest two-phase flux-switching motor, featuring a diameter of just 8 mm and a stack length of 5 mm, to demonstrate the feasibility of miniaturization. Topology optimization methods and JMAG electromagnetic analysis software are employed to achieve high average torque and low torque ripple. This research aims to pave the way for future applications in micromechanical power output.

2. Design and Analysis of a Miniature Two-Phase Flux Switching Motor

2.1. Design of a Two-Phase Flux-Switching Motor

This paper presents a two-phase flux-switching motor with a stator outer diameter of 8 mm, an air gap of 0.2 mm, and a length of 5 mm. The rotor features a two-pole asymmetrical salient pole design, with a rotor outer diameter of 4 mm and a length of 5 mm. The motor is equipped with a DC excitation winding and an AC armature winding, allowing for both DC and AC inputs for operation.

Table 1. Specifications of a micro axial flux two-phase flux-switching motor.

Mechanical Specifications
Stator	Poles	4	Rotor	Poles	2
	External diameter	8.00 mm		External diameter	4.00 mm
	Internal diameter	4.40 mm		Root diameter	2.20 mm
	Yoke width	0.60 mm		Internal diameter	1.00 mm
	Tooth width	1.45 mm		Air gap	0.20 mm
	Stack length	5.00 mm		Stack length	5.00 mm
Electrical Specifications
Phase	2		Step angle	90°
Number of turns of coil	40		Diameter of coil	0.07 mm
Maximum Current	1 A		Resistance of coil	3.6 Ω

provides the specifications of the two-phase flux-switching motor, while Figure 1 illustrates the 3D assembly and exploded views of the motor.

2.2. Rotor Design of the Two-Phase Flux-Switching Motor

The two-phase flux-switching motor features a stator with four poles and a rotor with two asymmetrical salient poles. The stator is equipped with direct current (DC) field windings and alternating current (AC) excitation windings. The motor operates using a DC and a square-wave AC of 1 ampere. The rotor design is optimized within fixed stator structural dimensions to achieve high output torque and minimal torque ripple. The following section will detail the mechanical design of the motor and the steps involved in the topology optimization of the rotor.

Topology design is a method that simultaneously optimizes the shape and size specifications of structures. This design approach involves defining a design area, subdividing it into multiple small finite element mesh structures, and determining the presence and density of these meshes based on design parameters or algorithms to achieve an optimized structural design. The objective is to conduct a global search using the topology method to ascertain the distribution of the optimized design. The design parameters define the rotor’s geometric shape as variable design parameters, while the stator shape, rotor outer diameter, and shaft hole diameter are established as invariant design parameters.

Ripple torque is defined as

$$T_{ripple}={\displaystyle \frac{T_{max}-T_{min}}{T_{max}+T_{min}}}\times 100\%$$

(1)

The constraints stipulate that the average torque must exceed 160 μN-m, while the torque ripple must remain below 70%. The optimization objective is to maximize the average torque while minimizing the torque ripple.

The objective function is defined as

$$\mathit{Objective} \mathit{function}={\displaystyle \frac{T-T_C}{T_C}}\times 100\%+(T_{rippleC}-T_{ripple})$$

(2)

$T$ is average torque and $T_C$ is constrained to 160 μN-m, while the torque ripple $T_{ripple}$ is limited to 70%. The minimum value of the objective function will be chosen as the geometric shape for rotor optimization.

2.2.1. Step 1: Design of Rotor Pole Width and Diameter for Two-Phase Flux-Switching Motors

The topology design of the magnetic pole width for the two-phase flux-switching motor rotor varies the magnetic pole width from 1.2 mm to 2.0 mm, increasing along the X-axis in increments of 0.1 mm. At a magnetic pole width of 2.0 mm, the motor demonstrates improved output performance. The inner diameter of the topology magnetic pole is reduced from 2.8 mm to 2.2 mm in intervals of 0.2 mm. Figure 2 illustrates the design process for the rotor’s magnetic pole width. The optimal magnetic pole width is identified as step 1-6, yielding an average torque of 219.91 μN·m, a torque ripple of 159.76%, and an objective function value of −52.32, which is the maximum value for this step. Figure 3 and

Table 2. Step 1: torque characteristic comparison table for each step.

Step	1-1	1-2	1-3	1-4	1-5	1-6
Maximum Torque (μN-m)	325.53	327.00	326.86	337.82	345.90	351.33
Minimum Torque (μN-m)	0.0004	−0.0024	−0.0011	−0.0010	−0.0007	−0.0015
Average Torque (μN-m)	157.35	189.39	208.84	211.85	216.76	219.91
Torque Ripple (%)	206.86	172.66	159.57	159.47	159.58	159.76

present the torque–angle curves and torque characteristics associated with the rotor’s magnetic pole width design process for the motor.

2.2.2. Step 2: Preliminary Design of Rotor Topology for Quadrants I and III

The preliminary design of the rotor topology for quadrants I and III of the motor employs a grid size of 0.20 mm × 0.20 mm. The red grids represent additions, while the blue grids indicate reductions. Initially, two layers of additional topology grids are superimposed on the original magnetic pole width, with the outermost layer designated as the first layer and the layer closest to the X-axis identified as the second layer. Figure 4 illustrates the design process for the preliminary rotor topology in quadrants I and III of the two-phase flux-switching motor. In step 2-1, portions of the first and second layers of topology grids are reduced, resulting in an increase in average torque and a decrease in torque ripple. In step 2-2, an additional grid of topology is incorporated into both the first and second layers. In step 2-3, another layer of topology grid is added to the first layer, along with one grid added to the second layer. In step 2-4, sections of the fourth-layer topology grid are reduced, which significantly decreases torque ripple. In step 2-5, portions of the second-layer grids are reduced, leading to a slight increase in average torque and a decrease in torque ripple. In step 2-6, parts of the front of the fourth-layer grids are reduced, further decreasing torque ripple. Ultimately, step 2-6 is identified as the optimal design for quadrants I and III, achieving an average torque of 193.37 μN-m, a torque ripple of 107.33%, and an objective function value of −16.47, which represents the maximum value for this step. Figure 5 and

Table 3. Step 2: torque characteristic comparison table for each step.

Step	2-1	2-2	2-3	2-4	2-5	2-6
Maximum Torque (μN-m)	328.81	327.03	319.58	299.68	300.31	299.67
Minimum Torque (μN-m)	−1.16	−3.14	−6.36	75.92	83.78	97.72
Average Torque (μN-m)	209.97	208.09	200.38	194.50	194.61	193.37
Torque Ripple (%)	157.14	158.63	162.65	115.04	111.05	107.33

illustrate the torque–angle curves and torque characteristics of the preliminary design process for the rotor topology in quadrants I and III.

2.2.3. Step 3: Detailed Design of Rotor Topology in Quadrants I and III

The detailed design of the rotor topology for quadrants I and III of the motor employs a grid size of 0.10 mm × 0.10 mm. The red grids represent additions, while the blue grids indicate reductions. Figure 6 illustrates the detailed design process for the rotor magnetic poles in quadrants I and III. In step 3-2, portions of the eighth-layer topology grids are reduced, resulting in a slight increase in average torque and a decrease in torque ripple. In step 3-3, additional grids are incorporated into the first, second, and ninth layers, further reducing torque ripple. In step 3-4, sections of the back of the second-layer topology grids are reduced, leading to a slight increase in average torque. In steps 3-5, grids are added to the front of the first and second layers, which reduces torque ripple. In step 3-6, topology grids are incorporated at the front of the first layer and the back of the third layer, resulting in a slight decrease in torque ripple. Ultimately, step 3-6 is identified as the optimal design for quadrants I and III, achieving an average torque of 186.29 μN-m, a torque ripple of 97.74%, and an objective function value of −11.31, which represents the maximum value for this step. Figure 7 and

Table 4. Step 3: torque characteristic comparison table for each step.

Step	3-1	3-2	3-3	3-4	3-5	3-6
Maximum Torque (μN-m)	299.03	298.90	282.42	274.73	278.28	273.91
Minimum Torque (μN-m)	101.09	96.54	91.18	94.12	93.18	91.79
Average Torque (μN-m)	193.27	193.52	188.45	189.33	187.42	186.29
Torque Ripple (%)	105.46	104.93	100.41	100.68	98.75	97.74

illustrate the torque–angle curves and torque characteristics of the detailed design process for the rotor topology in quadrants I and III.

2.2.4. Step 4: Contour Design of Rotor Topology for Quadrants I and III

The contour design of the rotor topology for quadrants I and III of the motor employs a grid size of 0.10 mm × 0.10 mm. The red grids represent additions, while the blue grids indicate reductions. Figure 8 illustrates the design process for the rotor magnetic poles in quadrants I and III. In step 4-2, additional topology grids are incorporated into the tenth and eleventh layers, resulting in a decrease in torque ripple. In step 4-3, extra grids are added to the front of the ninth layer, which slightly increases the average torque. In steps 4-4 to 4-6, the topology is delineated using solid lines to define the contour shape. Ultimately, step 4-6 is selected as the optimal contour design for quadrants I and III, achieving an average torque of 170.80 μN-m, a torque ripple of 63.73%, and an objective function value of 13.02, which is the maximum value for this step. Figure 9 and

Table 5. Step 4: torque characteristic comparison table for each step.

Step	4-1	4-2	4-3	4-4	4-5	4-6
Maximum Torque (μN-m)	273.92	257.30	257.45	260.67	255.16	209.13
Minimum Torque (μN-m)	93.17	82.38	82.39	93.59	93.46	100.27
Average Torque (μN-m)	186.30	182.80	180.18	178.63	176.94	170.80
Torque Ripple (%)	97.02	89.08	81.09	79.35	75.85	63.73

present the torque–angle curves and torque characteristics of the contour design process for the rotor topology in quadrants I and III.

2.2.5. Step 5: Preliminary Design of Rotor Topology for Quadrants II and IV

The preliminary design of the rotor topology for quadrants II and IV of the motor employs a grid size of 0.2 mm × 0.2 mm. The red grids indicate additions, while the blue grids signify reductions. Figure 10 illustrates the design process for the rotor magnetic poles in quadrants II and IV. In steps 5-2, one grid of topology is added to the first layer. In step 5-3, another grid is added to the first layer, demonstrating a positive trend. In step 5-4, one grid is added to the first layer, resulting in a slight increase in average torque. In step 5-5, two grids are added to the first layer, again leading to a slight increase in average torque. In step 5-6, portions of the front of the first layer are reduced, which slightly increases average torque while decreasing torque ripple. Ultimately, step 5-6 is selected as the optimal design for quadrants II and IV, achieving an average torque of 172.80 μN-m, a torque ripple of 60.70%, and an objective function value of 17.30, which is the maximum value for this step. Figure 11 and

Table 6. Step 5: torque characteristic comparison table for each step.

Step	5-1	5-2	5-3	5-4	5-5	5-6
Maximum Torque (μN-m)	208.96	208.97	209.39	211.39	215.72	213.48
Minimum Torque (μN-m)	104.85	104.79	104.60	107.09	100.10	108.58
Average Torque (μN-m)	171.10	171.37	171.74	172.30	172.67	172.80
Torque Ripple (%)	60.85	60.97	60.95	60.53	66.96	60.70

present the torque–angle curves and torque characteristics of the preliminary design process for the rotor topology in quadrants II and IV.

2.2.6. Step 6: Detailed Design of Rotor Topology in Quadrants II and IV

The detailed design of the rotor topology for quadrants II and IV of the motor employs a grid size of 0.10 mm × 0.10 mm. The red grids indicate additions, while the blue grids signify reductions. Figure 12 illustrates the design process for the rotor magnetic poles in quadrants II and IV. In step 6-2, portions of the first and second layers of topology grids are reduced, resulting in a slight decrease in torque ripple. In step 6-3, sections of the back of the first layer are reduced, leading to a slight increase in average torque. In step 6-4, additional topology grids are added to the back of the first layer, which slightly increases average torque and decreases torque ripple. In step 6-5, more topology grids are added to the back of the second layer, further increasing average torque. In step 6-6, an additional layer of topology grids is placed above the first layer, significantly reducing torque ripple. Ultimately, step 6-6 is selected as the optimal fine design for quadrants II and IV, achieving an average torque of 172.83 μN-m, a torque ripple of 52.67%, and an objective function value of 25.35, which represents the maximum value for this step. Figure 13 and

Table 7. Step 6: torque characteristic comparison table for each step.

Step	6-1	6-2	6-3	6-4	6-5	6-6
Maximum Torque (μN-m)	214.03	212.54	212.39	212.92	213.21	210.03
Minimum Torque (μN-m)	111.39	112.79	112.80	114.11	115.39	119.00
Average Torque (μN-m)	173.03	172.79	172.75	172.96	173.09	172.83
Torque Ripple (%)	59.32	57.74	57.63	57.13	56.49	52.67

present the torque–angle curves and torque characteristics of the detailed design process for the rotor topology in quadrants II and IV.

2.2.7. Step 7: Contour Design of Rotor Topology for Quadrants II and IV

The contour design of the rotor topology for quadrants II and IV of the motor employs a grid size of 0.10 mm × 0.10 mm. The red grids represent additions, while the blue grids indicate reductions. Figure 14 illustrates the design process for the rotor magnetic poles in quadrants II and IV. In step 7-2, one layer of topology grids is added upward, resulting in a slight decrease in torque ripple. In step 7-3, additional grids are incorporated at the front of the second layer, which slightly increases average torque and reduces torque ripple. Steps 7-4 to 7-6 outline the topology using solid lines to define the contour shape. Ultimately, step 7-6 is selected as the optimal contour design for quadrants II and IV, achieving an average torque of 174.18 μN-m, a torque ripple of 40.37%, and an objective function value of 38.49, which is the maximum value for this step. Figure 15 and

Table 8. Step 7: torque characteristic comparison table for each step.

Step	7-1	7-2	7-3	7-4	7-5	7-6
Maximum Torque (μN-m)	209.30	209.13	209.14	209.13	209.14	209.69
Minimum Torque (μN-m)	133.27	134.45	138.62	138.79	138.75	139.36
Average Torque (μN-m)	173.51	172.80	173.10	173.64	173.55	174.18
Torque Ripple (%)	43.82	43.21	40.74	40.51	40.54	40.37

present the torque–angle curves and torque characteristics of the contour design process for the rotor topology in quadrants II and IV.

This study employs the JMAG electromagnetic analysis software to simulate the results of electromagnetic analysis derived from the topological optimization design, which are presented in 2D plots. Figure 16 illustrates the distribution of magnetic flux density in the motor at angles of 0°, 50°, 64°, and 90°. At an angle of 50°, the motor achieves maximum torque, with a peak magnetic flux density of 1.46 T, as depicted in Figure 16b. At 90°, the motor reaches the final excitation phase before the electromagnetic coil switches, where the maximum magnetic flux density of 1.53 T occurs at the angular position between the stator back iron and the magnetic pole, as shown in Figure 16d.

2.3. Torque Performance Under Different DC and AC Driving Conditions

In this study, the torque performance of a two-phase flux-switching motor was evaluated under various direct current (DC) and alternating current (AC) excitation currents, ranging from 0.5 A to 1 A. Figure 17 illustrates the torque–angle position plot of the motor, indicating that the maximum torque occurs at an angle of approximately 50°.

3. Fabrication, Assembly, and Testing of Two-Phase Flux-Switching Motor

3.1. Manufacturing of Motor Components

The stator and rotor are constructed by stacking silicon steel sheets, each with a thickness of 0.5 mm, using 50CS400 electrical steel manufactured by China Steel Corporation, Kaohsiung, Taiwan for a motor stack length of 5 mm. Wire Electrical Discharge Machining (WEDM) is employed for small-scale customized production, eliminating the need for additional molds while providing high precision and reducing production time. The rotor and stator are illustrated in Figure 18a.

The electromagnetic coils are wound using copper wire with a diameter of 0.07 mm. During the winding process, the copper wires are susceptible to friction with the stator, which can damage the enamel coating or lead to short-circuiting of the coils. To prevent this, insulating materials are placed in the stator slots for protection. Figure 18b illustrates the completed stator winding.

The stator, with its completed winding, is securely mounted on the assembly platform. The shaft and the assembled rotor will be installed on the platform, as illustrated in Figure 18c. Two mechanical bearings, along with nuts and screws, are utilized to ensure the concentricity of the rotor and stator. Figure 18d illustrates the completed assembly of the motor.

3.2. Bearings and Shaft

The bearing selected for this project is the NSK F6S, Tokyo, Japan, which has an outer diameter of 3 mm, an inner diameter of 1 mm, and a thickness of 1 mm. This bearing features low-friction torque and can withstand both axial and radial loads, making it suitable for applications that require low vibration, low noise, and high speed. The shaft is constructed from SUJ2 bearing steel and is precision ground, with an outer diameter of 1 mm and a length of 30 mm.

3.3. Physical Testing of the Motor

In this study, a power supply serves as the voltage source for the two-phase flux-switching motor, while a driver generates a square-wave signal for single-phase excitation. The experiment utilizes an oscilloscope probe connected to the motor’s output terminal to measure phase voltage and phase current at various speeds. Figure 19 illustrates the electrical measurement setup. During the experiment, the motor operates without a load. Figure 20 indicates that the maximum speed of the two-phase flux-switching motor is 14,000 RPM (467 Hz).

3.4. Measurement of Back Electromotive Force (BEMF)

In this experiment, the back electromotive force (BEMF) of a two-phase flux-switching motor is measured at various speeds: 1000, 3000, 6000, 9000, 12,000, and 14,000 RPM. At the maximum speed of 14,000 RPM, the experimental value of the induced electromotive force (EMF) for the motor is 1.59 V. Figure 21 and

Table 9. BEMF measurement at various speeds.

Excitation Frequency (Hz)	Rotational Speed (RPM)	Experiment Value (V)
33	1000	0.83
100	3000	0.95
200	6000	1.12
300	9000	1.30
400	12,000	1.47
467	14,000	1.59

present the voltage–speed curve and BEMF data for the motor.

3.5. Torque Measurement

In this experiment, the maximum starting torque of a two-phase flux-switching motor is measured at currents ranging from 0.5 A to 1 A. The method employed is a weight-hanging approach. First, a standard weight of 50 g is suspended from the motor’s shaft sleeve. This weight is then placed on a Denver Instrument SI-234 precision electronic scale, Göttingen, Germany. Since the objective is to measure the weight lifted by the motor once it begins operating, the electronic scale must be zeroed after placing the standard weight. Next, the power is turned on to activate the motor, and the weight lifted by the motor under operating conditions is recorded. The starting torque is subsequently calculated using the torque formula. The radius of the motor’s shaft sleeve is 2 mm.

When measuring the starting torque, it is essential to consider the static friction torque of the motor, which was determined to be 6.08 μN-m. This value is then incorporated into the measurement data for correction. In this experiment, the maximum torque of the motor was measured at a mechanical angle of 50° and compared with the values obtained from JMAG electromagnetic analysis. Figure 22 and

Table 10. Comparison of theoretical and experimental starting torque for a two-phase flux-switching motor.

DC (A)	AC (A)	Theory (μN-m)	Experiment (μN-m)	Error (%)
0.5	0.5	51.81	47.05	−9.19
0.6	0.6	74.74	71.3	−4.60
0.7	0.7	101.86	95.99	−5.76
0.8	0.8	133.12	121.01	−9.10
0.9	0.9	168.83	145.55	−13.79
1.0	1.0	208.42	168.52	−19.14

present the theoretical and experimental torque–current curves, along with a comparison table for a two-phase flux-switching motor. At both DC and AC excitation currents of 1 A, the experimental starting torque was measured at 168.52 μN-m. The discrepancy between the theoretical and experimental values is 19.14%.

The starting torque calculation formula is shown in Equation (3) as follows:

$$T=mgr$$

(3)

where $T$ is the starting torque, $m$ is the mass of the weight lifted by the motor, $g$ is the gravitational constant, and $r$ is the radius of the shaft sleeve.

3.6. Shaft Runout Measurement

This study employs the Keyence LK-G10 laser displacement sensor, Osaka, Japan, to measure the shaft runout of the motor. The principle involves emitting an infrared beam onto the motor shaft and reflecting it back to the LK-G10 receiver. By measuring the travel time, the runout can be accurately determined. Figure 23 illustrates the shaft runout curves at 1000 RPM and 14,000 RPM. The maximum runouts recorded are 39.7 µm, 11 µm, 9.4 µm, 8.2 µm, 7.8 µm, and 6.5 µm at speeds of 1000 RPM, 3000 RPM, 6000 RPM, 9000 RPM, 12,000 RPM, and 14,000 RPM, respectively.

4. Discussion

This research focuses on the development of a wireless-driven micromotor that operates using a single AC excitation. Since the wireless-driven motor does not require a power connection or battery, it is ideal for applications such as toys, micro-pumps, water tanks, and pressure vessels that do not necessitate feedthrough.

In our earlier work on a wireless-driven single-phase switched reluctance motor [21], permanent magnets were utilized to provide the starting position and rotational torque in the absence of electromagnetic excitation. However, a significant drawback of this motor design is its low average torque and high torque ripple. By replacing the DC field windings of a two-phase flux-switching motor with permanent magnets, the motor can achieve significantly improved torque performance using only AC excitation.

5. Conclusions

This study presents a micro two-phase flux-switching motor, which features a stator equipped with a DC excitation winding and an AC armature winding, eliminating the need for permanent magnets. The rotor is designed with a dual-pole asymmetric geometry that facilitates self-starting, thereby avoiding dead zones, and its integrated design contributes to a simplified structure. This micromotor is easy to manufacture and offers an effective solution for micromechanical power output. The rotor design employs topology optimization methods and JMAG electromagnetic analysis software to achieve high average torque and low torque ripple. When the DC and AC excitation currents are set to 1 A, the analytical results indicate an average torque of 174 μN-m and a torque ripple of 40%. This torque ripple is the lowest reported in the literature for two-phase motors, regardless of whether optimization is achieved through geometric structure or control algorithms. The micro two-phase flux-switching motor has been fabricated, assembled, and tested. At DC and AC excitation currents of 1 A, the motor reaches a maximum speed of 14,000 RPM. The maximum starting torque is measured at 164 μN-m, with a discrepancy of 19% between the experimental and theoretical values.