Research Status and Latest Progress of Magnetic Field Modulation Motors

Abstract

Thanks to the magnetic field modulation effect, the magnetic field modulation motor (MFMM) significantly improves torque density and magnetic field harmonic utilization by breaking the constraints of traditional motor excitation and armature pole number matching. This advantage enhances its development potential in fields such as new energy vehicles, aerospace, power generation, and the military. This article first starts with the basic principle of magnetic field modulation, and adopts the excitation unit position classification method to systematically summarize the evolution laws of major MFMM topology structures such as the permanent magnet synchronous motor, switch magnetic flux motor, and flux reversal motor in recent years. It also analyzes the research progress of key performance such as the torque characteristics and power factor of these motors. Research has pointed out that the MFMM still faces core challenges such as high torque ripple, complex structure, low power factor, and multiple losses. Based on a review of the main achievements in the field, the future development direction of MFMMs is proposed to promote its development in the fields of precision drive and efficient energy conversion.

1. Introduction

As the core equipment for electromechanical energy conversion, motors are widely used in industries, transportation, and other fields. Due to global attention to climate change, they are gradually replacing traditional machinery and hydraulic devices and becoming the core power source in key fields such as national defense, new energy, and aerospace [1]. As the application fields of motors expand, higher requirements have been put forward for their torque density, vibration, control, and heat dissipation performance, which has made structural and principle innovation a research focus [2].

The MFMM is based on the “magnetic field modulation effect” and achieves full utilization of magnetic field harmonics through unequal pole logarithmic armatures, excitation units, and newly added modulation units [3]. This effect endows the motor with a torque amplification function similar to a gearbox, known as the “pole ratio”, thereby providing higher torque density under the same material and demonstrating broad application potential.

Compared with traditional permanent magnet synchronous motors (PMSMs), the core advantage of MFMMs lies in its unique magnetic field modulation mechanism: PMSMs rely on direct magnetic field coupling between the PM and armature winding, with fixed pole pairs and strict matching of power supply frequency, while MFMMs actively regulate magnetic field harmonics through modulation units and use asymmetric pole pair design to achieve torque amplification, significantly improving the torque density. At the same time, the pole ratio of an MFMM can be flexibly designed, breaking through the traditional limit of pole pairs, adapting to a wide range of variable speed requirements, and reducing losses through magnetic field optimization under partial loads. This enables the MFMM to demonstrate higher material utilization and dynamic control capabilities in low-speed, high torque applications (such as electric vehicles, wind power drives), or space limited scenarios.

However, MFMMs face many challenges due to the introduction of modulation units such as complex harmonic coupling mechanisms and performance optimization difficulties caused by diverse structures [4,5]. In recent years, scholars in China and abroad have conducted in-depth explorations of the basic principles, topological structures, and other aspects, enriching the research on MFMMs.

In recent years, multiple reference reviews have been conducted on MFMMs, but most have focused on permanent magnet vernier motors (PMVMs) and flux reversal permanent magnet motors (FRPMs), and have not reflected the latest technological advances in MFMMs [2,6,7,8]. Another reference focused on the study of MFMM losses and did not address the structure and other properties [9]. However, the summary provided by that article is very comprehensive, so we will not repeat the relevant research. Reference [2] summarizes the principle and future applications of MFMMs, which mainly classifies the motor topology based on the relative motion relationship between the MFMM excitation unit and modulation unit. Although it analyzed performance such as torque and power factor, it is still not comprehensive. This article aims to comprehensively review the innovative topology structures and key performance achievements in the field of MFMMs by using the excitation unit position classification method to deeply explore the dominant types of MFMMs and focusing on key indicators such as the torque characteristics and power factor (PF). Finally, we analyze the application, advantages, and limitations of MFMMs to provide theoretical and practical guidance for future motor design optimization and promote technological progress.

2. Basic Principles of Magnetic Field Modulation

The working principle of various MFMMs can be uniformly expressed as follows: the excitation magnetic potential harmonics corresponding to the excitation unit are modulated by the air gap magnetic flux harmonics corresponding to the modulation unit, generating excitation magnetic density harmonics with the same number of pole pairs, rotation speed, and rotation direction as the armature magnetic potential harmonics. The excitation magnetic density harmonics are interlocked with the armature winding, thereby contributing to the average torque. The difference between the working principle of MFMMs and traditional motors is that their armature and excitation magnetic field need to be modulated by a magnetic field modulation unit to generate torque. Therefore, analyzing the modulation process of magnetic field modulation motors is the key to understanding the working principle of magnetic field modulation motors. Figure 1 is a schematic diagram of the qualitative analysis of the magnetic field modulation process, which shows that the process is guided by the modulation unit and plays a role in harmonic polarization. As shown in the figure, an excitation magnetic force of 11 pole pairs generated by an excitation unit was modulated by 12 modulation teeth to produce a magnetic field with 1 pole pair.

In order to further quantitatively analyze the MFMM, the effect of the magnetic field modulation unit on the magnetic field needs to be expressed mathematically. Assuming that at the initial moment, the peak positions of the magnetic potential and magnetic flux are both at the origin position of the stator coordinate system, the equation for the no-load air gap flux density of the MFMM can be expressed as:

$$\begin{array}{ll}B\left(\theta ,t\right)& =F\mathsf{\Lambda }\\ & =F_m{\mathsf{\Lambda }}_0\cos (p_e\theta -p_e{\mathsf{\Omega }}_{e}t)+{\displaystyle \frac{1}{2}}{F}_e{\mathsf{\Lambda }}_1\cos \left[(p_e\pm p_m)\theta -(p_e{\mathsf{\Omega }}_e\pm p_m{\mathsf{\Omega }}_m)t\right]\end{array}$$

(1)

From the magnetic field expression, it can be seen that stable torque can only be generated when the number of harmonic poles of two magnetic fields and the rotational speed satisfy the following relationship:

$$j{p}_a=\left|i{p}_e\pm k{p}_m\right|,i=1,3,\cdots ,\infty ;k=0,1,\cdots ,\infty$$

(2)

$${\omega }_a=j{p}_a{\mathsf{\Omega }}_{j{p}_a}=\left|i{p}_e{\mathsf{\Omega }}_e\pm k{p}_m{\mathsf{\Omega }}_m\right|$$

(3)

For the sake of simplicity and intuitive expression of the principle of magnetic field modulation, Formula (1) only selects the fundamental waves of excitation electromotive force and air gap magnetic flux for derivation. In the formula, $p_e$, $p_m$, and $p_a$ represent the fundamental pole pairs of the excitation magnetic potential, air gap magnetic flux, and armature magnetic potential, respectively. i, j, and k are the harmonic orders corresponding to the excitation magnetic potential, air gap magnetic flux, and armature magnetic potential, respectively. ${\mathsf{\Omega }}_e$ and ${\mathsf{\Omega }}_m$ are the mechanical speeds of the excitation unit and modulation unit, respectively. ${\mathsf{\Omega }}_{j{p}_a}$ is the mechanical speed of the harmonic of the magnetic electromotive force of the opposite pole armature for $j{p}_a$. ${\omega }_a$ is the electrical angular velocity of the harmonic of the armature magnetomotive force. $F$ is the excitation magnetic potential function, $\mathsf{\Lambda }$ is the air gap magnetic permeability function, $F_m$ is the amplitude of the excitation magnetic potential function, ${\mathsf{\Lambda }}_0$ is the constant term of the air gap magnetic permeability function, and ${\mathsf{\Lambda }}_1$ is the fundamental amplitude of the air gap magnetic permeability function.

For MFMMs, they generally contain multiple excitation flux density harmonics that satisfy Equations (2) and (3), which means that this type of motor can use multiple excitation flux density harmonics with different pole pairs to participate in electromechanical energy conversion. In addition, the mechanical speed of each excitation flux density harmonic is often lower than the rotor mechanical speed, which introduces an additional deceleration amplification torque coefficient “pole ratio” in the average torque. Its physical meaning is the ratio of the number of pole pairs of the motor rotor to the number of pole pairs of the motor armature winding. It should be noted that in an MFMM, the rotor may not necessarily be the excitation unit, but also the modulation unit. Taking Figure 1 as an example, the excitation electromotive force of 11 pairs of poles was modulated by the modulation unit, and the harmonic of the working magnetic field was 1 pair of poles. As is well-known, at the same frequency, the larger the number of pole pairs, the lower the speed. Therefore, the pole ratio of this motor is 11.

3. Research on Motor Topology

3.1. Rotor Permanent Magnet Type (Permanent Magnet Vernier Motor)

PMVMs introduce modulation poles on the stator teeth of traditional permanent magnet synchronous motors (PMSMs) to modulate the magnetic field of the low pole number stator armature winding, thereby obtaining harmonic magnetic field components that can match and interact with the high pole number permanent magnet (PM) magnetic field. This can achieve low-speed high torque without increasing the motor volume and slot number.

The PMVM developed from a magnetic gear and belongs to the rotor excitation type of MFMM. The PM pole pairs, armature winding pole pairs, and the number of modulation teeth of a motor with this structure need to meet the following relationship:

$$p_r=k_{FMP}Z\pm p_w$$

(4)

In the formula, p_r, k_FMP, Z, and p_w are the number of PM poles, modulation poles on the stator teeth, stator teeth, and armature winding poles, respectively. The corresponding harmonic rotation speed is:

$${\omega }_{m,n}={\displaystyle \frac{m{p}_r}{m{p}_r+nZ}}{\omega }_r,m=1,3,\cdots ,\infty ;n=0,\pm 1,\cdots ,\pm \infty$$

(5)

Equation (5) shows that when the pole number of the air gap harmonic magnetic field is less than the pole number of the rotor PM, the sub harmonic rotation speed is higher than the rotor speed; on the contrary, when the pole number of the air gap harmonic magnetic field is greater than the pole number of the rotor PM, the sub harmonic rotation speed is lower than the rotor speed. For example, ${\omega }_{1,-1}$ corresponds to the rational speed of $p_r-Z$ in the polar harmonic magnetic fields. From here, it can also be seen that the number of rotor poles in PMVMs will be much greater than the number of stator teeth.

In recent years, the research team has proposed a focused magnetic PMVM (FMPMVM) structure [10], which uses tangential magnetization PM (spoke type) and the principle of magnetic pole repulsion to enhance the magnetic load and achieve high torque output. In addition, V-type and consequent pole arrangement also have a magnetic focusing effect [11,12,13]. However, the magnetic barrier effect in high pole ratio motors limits the effect of magnetic field modulation. For this, the authors of [14] proposed the continuous pole integrated rotor structure of an inverted T-type PM (Figure 2). The magnetization directions of the adjacent PM are the same, and the directions of the auxiliary PM at the bottom are the opposite, in order to avoid the closure of magnetic lines of force, ensure the stable output torque of the motor, and overcome the influence of the magnetic barrier effect. Reference [15] studied a type of PMVM with a magnetic barrier at the bottom of a V-shaped PM, and their results indicated that the introduction of a magnetic barrier could effectively regulate the original magnetic flux path, which is equivalent to generating a secondary modulation effect, thus increasing the effective magnetic flux circuit and improving the torque density.

From the structure of a magnetic circuit, the Halbach motor has a similar structure to a spoke motor, so the magnetic field is the same as the spoke type [16,17]. Compared with other rotor structures, the Halbach array exhibits better internal and external magnetic field strength. Wang proposed a novel Halbach PMVM (Figure 3). This structure inherited the advantage of the low torque ripple of the Halbach structure, but with an increase in PM dosage, the torque density increased by 40.8~69.01% on the basis of a 20% increase in dosage, and the torque ripple decreased by 11.74% [18].

Reference [19] proposed a hybrid split tooth PMVM structure (Figure 4), which improved the optimization of the air gap magnetic field harmonics through a hybrid teeth design, increased the PF from 0.63 to 0.84, increased torque by 37%, and enhanced fault tolerance. The coding tooth structure was introduced in Reference [20] (Figure 5), which introduced specific harmonics through a special tooth profile to modulate multiple magnetic fields and induce in-phase counter potentials, effectively increasing torque and reducing pulsation. Reference [21] showed a variable pole PMVM (Figure 6), whose permanent magnet magnetic field was modulated by teeth to generate harmonics of different pole numbers and phasor diagrams, coupled with A and B type permanent magnet harmonics. By changing the number of armature poles, dual-mode operation was achieved, expanding the motor speed range by at least twice and improving the operational flexibility.

Reference [22] studied a non-uniformly arranged modulation pole PMVM, which is characterized by grouping modulation teeth with two or more teeth in each group. By adjusting the duty cycle of the modulating teeth or the relative position within the group, the reluctance can be reduced, the operating sub-harmonic amplitude can be increased, and the torque density can be enhanced to optimize the motor performance. The reference study showed that the torque performance of the non-uniform split tooth PMVM was slightly superior to the uniform tooth design, which benefits from the optimization of the motor slot vector [23]. Reference [24] proposed a novel hourglass shaped magnetic isolation structure for the primary and secondary tooth type PMVM (Figure 7), which could effectively adjust the air gap magnetic resistance and improve the harmonic characteristics. The hourglass shaped magnetic isolation bridge not only solved the problem of inter pole leakage, but also served to fix the PM.

In the PMVM, in order to achieve low speed and high torque, the number of rotor PM is usually more than the number of stator winding pole pairs, which leads to the increase in PM consumption with the increase in motor capacity. Therefore, a double-layer air gap structure (DLAG-PMVM) was proposed to improve the torque density. The Huazhong University of Science and Technology innovatively designed a consequent pole tangential excitation PMVM with connection bridge, which effectively enhanced the torque [25]. Dr. Zhang found that DLAG-PMVM was most suitable for MW level power generation and had the best torque performance. He proposed a rotor iron core with a bidirectional connection bridge structure (Figure 8) that completely eliminated the convex pole magnetic resistance introduced when the stator and rotor were slotted, making the amplitude of magnetic potential fluctuations between adjacent ferromagnetic poles equal and reducing magnetic potential fluctuations [26]. A double-stator PMVM without a rotor yoke was proposed in Reference [27]. Thanks to the increase in the inductance of the yoke structure, the high-speed operation was realized. Reference [28] proposed a dual stator, single winding axial PMVM. Compared with conventional axial motors, this motor reduced the axial length of the motor while ensuring constant torque, thereby improving the torque density. Reference [29] designed a new built-in saddle-type PM topology on the basis of double stators (Figure 9), with higher torque and lower vibration.

In the fault tolerant design of a PMVM, the modular design of the stator and rotor is increasingly emerging [30]. Reference [31] described a high-tolerance linear PMVM (PMVLM). The motor adopted the best aligned PM array, six-phase winding, and modular mover design, which strengthened the thrust and reduced the phase coupling, and improved the fault tolerance and thrust performance. The motor could also operate under different phase conditions.

Superconducting permanent magnetic materials have been emerging in motor applications, and scholars are exploring superconducting PMVMs (SPMVMs) [32] with the aim to enhance the torque output by replacing PM or the nonconductive material in the modulation structure as the superconducting material. Reference [33] showed that when a high temperature superconducting material was applied to wind turbines and linear motors, the torque performance was improved, but the short circuit current was increased. At present, there are many studies on the application of high temperature superconducting materials for PMVLMs and DLAG-PMVMs [34,35,36].

In order to better quantitatively analyze the impact of the proposed new structure on PMVM performance, based on data analysis in the reference, this paper compared them with traditional PMVMs under the same volume through the following table, and the conclusions are as follows. The ‘-’ in the

Table 1. Comparison of the PMVM performance among different structures.

References		Torque	Torque Ripple	Power Factor	Efficiency
[10]		36%	\	\	30.8%
[14]		13%	−31.5%	\	−2%
[15]		27.9%	−7%	\	\
[18]		40.8~69.01%	−11.74%	\	\
[19]		37%	\	0.21	\
[20]		30%	−62%	\	\
[21]	High speed	−47.5%	−6.9%	\	\
	Low speed	43.3%	−4%	\	\
[22,23]		35.4%	−0.1%	\	\
[24]		7%	−5%	\	\
[26]		83%	\	\	\
[28]		37.5%	\	\	−0.9%
[29]		3.2%	−0.6%	\	\
[31]		6.7%	−4.7%	\	\
[32,33]		36%	\	0.38–0.58	\

represents a decrease.

In order to facilitate readers in selecting the appropriate PMVM architecture based on the application scenario, this article summarizes the corresponding relationship and recommended solutions between typical application scenarios and PMVM performance structures in

Table 2. Relationship between PMVM structure performance characteristics and typical application scenarios.

Application Scenarios/Technical Requirements	References	Advantages	Application Area
Magnetic field modulation and magnetic circuit optimization	[14,15,22,23,24]	Increase torque density, reduce magnetic reluctance and leakage	Industrial high torque equipment, wind power generation
High torque density design	[18,25,26,29]	Increased torque density and reduced vibration, suitable for MW level loads	Electric vehicles, large generator sets
Reliability and fault-tolerant design	[19,31]	Improved power factor, enhanced fault tolerance, and reduced thrust fluctuations	Industrial servo, rail transit drive
Compact and axial integration	[28]	Shortened axial length and increased torque density	Ship propulsion and aviation actuation systems
Exploring cutting-edge technologies	[21,33]	Expansion of speed range ≥ 1 times, significant increase in superconducting torque	Wide speed domain drive and superconducting motor pre research

.

The development of PMVMs has always faced a profound contradiction between performance breakthroughs and engineering practicality. This special motor, which achieves low-speed high torque through harmonic coupling, has to bear multiple design costs while pursuing a high power density.

The core contradiction is reflected in the Halbach array, spoke type, and other magnetic gathering structures used to improve the torque density, which can achieve improved torque performance but require PM incremental costs; the carefully designed hybrid split tooth structure can optimize motor harmonics, but at the cost of complex manufacturing processes. Innovative topologies such as the dual stator and double-layer air gap significantly increase the assembly accuracy requirements and manufacturing costs while improving the torque output. More importantly, these structural innovations often constrain each other—designs that reduce the torque ripple may sacrifice power density, while solutions that improve reliability may affect the efficiency.

This design dilemma essentially stems from the physical limitations of the PMVM: the principle of magnetic field modulation dictates a positive correlation between its torque performance and vibration noise, so an increase in PM usage inevitably drives up costs, and the simplification of topology may weaken its core advantages. There is a tendency in current research to excessively pursue the optimization of individual indicators while neglecting the balance of cost-effectiveness in systems engineering. The introduction of new technologies such as superconducting materials may seem promising, but their feasibility for industrialization remains questionable.

The future of PMVMs does not lie in endless structural complexity, but should shift toward: (1) establishing a precise “performance cost” quantitative evaluation system; (2) developing a compromise design solution that balances electromagnetic performance and manufacturability; and (3) exploring new control strategies to overcome hardware limitations. Only by facing these design trade-offs can PMVMs truly move from the laboratory to industrialization.

3.2. Stator Permanent Magnet Type

3.2.1. Switched Flux Linkage Permanent Magnet Motor

As a kind of stator permanent magnet motor, the switched flux linkage permanent magnet motor (SFPM) has the outstanding advantages of high torque density, simple rotor structure, strong anti-demagnetization ability, etc., and has gradually become a research hotspot in the motor industry. Related products have been successfully applied to transportation, intelligent manufacturing, industrial control, and other fields [37].

The PM of SFPM is a tangential excitation structure, which is placed in the middle of the stator teeth and runs through the whole stator core. The polarity of two adjacent PMs is the opposite. Both the stator and the rotor are laminated by silicon steel sheets. The rotor is a simple reluctance structure. The stator winding is mostly a centralized winding structure, and there is also a distributed winding structure. The magnetic line of the force distribution of the SFPM is shown in Figure 10. Because the polarity of two adjacent PMs is the opposite, the magnetic line of force is squeezed into the stator teeth, passes through the adjacent rotor teeth with the winding turn chain, and returns from the other stator teeth to form a closed loop. Furthermore, as the relative position of the rotor teeth and PM changes, the direction of the flux linkage through the winding also changes, where the winding flux linkage reaches the maximum in the positive direction (Figure 10a) and the winding flux linkage reaches the maximum in the negative direction (Figure 10b), therefore, the winding flux linkage of the SFPM is bipolar, which can produce high back potential and torque.

The SFPM is mainly divided into the V type and E type, of which the V type is mature and common; the E type adds intermediate teeth to each stator tooth for thermal isolation and reduced heat effects. Figure 11 and Figure 12 show these two configurations, and the reference comparison shows that the E type has better torque performance. A series of improved topologies have been developed based on this [38].

Reference [39] explored the reluctance torque and pulsation causes of SFPM, pointing out that the reluctance torque is invalid under the control of id = 0, and put forward the torque suppression pulsation by stator and rotor chamfering method. Reference [40] designed a new structure of a cosine-reduced rotor based on the air gap magnetic field modulation theory to effectively suppress torque ripple. Reference [41] proposed that the partitioned stator multi-excited SFPM (Figure 13) is provided with an auxiliary excitation winding in the stator to enhance the flux-weakening capability. Reference [42] showed a tubular linear SFPM with no end winding where the efficiency was high and the net radial force was zero (Figure 14). Axial SFPM outperformed radial SFPM in terms of length and torque density. The axial SFPM for the yoke less dual rotor presented in [43] used segmented armatures with a higher torque density and lower slot torque.

The switched flux linkage linear motor (SFLM) often improves the thrust density by means of a primary modular design [44]. However, the air gap magnetic flux of SFLPM is difficult to adjust due to PM excitation, and it is difficult to meet the wide speed constant power operation, which limits the wide speed change application [45]. References [46,47,48] further studied the bilateral magnetic circuit complementary modular electrical excitation SFLM (ESFLM) and optimized the design parameters globally. Reference [49] conducted a comparative analysis of the ESFLM for convex pole and segmented rotor structures, and found that the power and torque of segmented rotor structures were 3.1 times and 2.1 times higher than those of convex pole structures, respectively. Reference [50] suggested that the two-side ESFLM of non-overlapping winding had a higher thrust density, higher efficiency, and better heat dissipation. The innovative set in Reference [51] overlapped the armature winding with the asymmetric stator pole over the ESFLM, reducing the magnetic saturation and improving the torque density. Reference [52] suggested that an octane modular stator structure improved the torque density of the ESFLM. Reference [53] proposed an HTS modular SFLM. The motor adopted a low-cost salient pole iron core stator, short moving sub-armature, and HTS excitation winding with low torque pulsation and strong fault tolerance. Reference [54] proposed a method of improving the phase-locked loop by combining a primary dislocation bilateral SFLPM with a second-order notch filter to improve the accuracy of position and velocity estimation. Reference [55] suggested that the secondary core transverse flux SFLPM (Figure 15), unlike conventional linear motors, produces thrust in each phase of the structure with an independent magnetic circuit.

The quantitative analysis of the relevant literature is shown in

Table 3. Comparison of the SFPM performance among different structures.

Reference	Torque	Torque Ripple	Power Factor	Efficiency
[39]	−4.2%	−20%	\	\
[40]	−3.6%	−91.4%	\	\
[41]	28.2%	−71.8%	\	2.8%
[42]	21%	−7.2%	\	\
[43]	18.7%	−92.1%	\	1.23%
[49]	210%	\	\	−12.8%
[50]	40%	5.71%	−0.01	2.39%
[51]	25.7%	−21.27%	\	\
[52]	80%	−38.7%	\	\
[53]	7.5%	−76%	\	\
[55]	140%	−24%	\	\

.

This article summarizes the corresponding relationship and recommended solutions between typical application scenarios and SFPM performance structures in

Table 4. Relationship between SFPM structure performance characteristics and typical application scenarios.

Application Scenarios/Technical Requirements	References	Advantages	Application Area
Torque pulsation suppression and structural optimization	[39,40,42,43]	Reduced torque ripple, improved efficiency, and reduced cogging torque	High precision servo system, linear drive
High torque density and excitation enhancement	[41,44,49,51,52]	Torque density improvement, heat dissipation optimization, magnetic saturation suppression	Industrial heavy-duty equipment, rail transit
High temperature superconductivity and new excitation technology	[53]	Low torque ripple, strong fault tolerance, and cost reduction	Superconducting motor, high reliability drive
Control strategy and improvement of operational accuracy	[54,55]	Improved position/velocity estimation accuracy, homogenized thrust, and enhanced phase independence	Precision positioning system, CNC machine tool

.

SFPM combines the advantages of high power density and robustness through the fusion of stator permanent magnets and doubly salient structures. Its design with both permanent magnets and windings placed in the stator improves heat dissipation and ensures that the rotor is suitable for high-speed operation, making it particularly suitable for high-performance applications such as aerospace servos. However, the main contradiction between torque performance optimization and vibration suppression lies in the fact that although the fixed rotor taper method and cosine taper structure can effectively suppress torque pulsation, such geometric optimization often comes at the cost of sacrificing some output capability. The multi-excitation design of partitioned stator improves the weak magnetic performance by adding auxiliary windings but inevitably increases the system complexity and manufacturing costs. The advantage of axial topology over radial structure in torque density is accompanied by new challenges in mechanical strength and heat dissipation. Although the modular design significantly improves the thrust density, the difficulty in adjusting the air gap magnetic field due to the permanent magnet excitation characteristics severely restricts the ability to operate in a wide speed range. The electric excitation scheme achieves torque multiplication through innovative structures such as segmented rotors, but its non-overlapping winding and special pole design significantly increase the complexity of the manufacturing process. It is worth noting that the second-order notch filter and other strategies used to improve control accuracy essentially trade algorithm complexity for performance improvement, and this compensation at the control level in turn puts higher demands on processor performance.

3.2.2. Flux Reversal Permanent Machine

The basic topology of a flux reversal permanent machine (FRPM) is shown in Figure 16, and two pieces of PM with opposite magnetizing directions are mounted on the surface of each stator tooth facing the air gap side. FRPM can be subdivided into two structures according to the magnetizing modes of the two adjacent PM: in magnetizing mode 1, defined in Figure 16a, the PM magnetizing directions on both sides of the stator slot are the opposite; in magnetizing mode 2, defined in Figure 16b, the PM magnetizing directions on both sides of the stator slot are the same. Figure 17 shows the working principle of the FRPM under the two magnetizing modes, that is, at the initial position, the magnetic flux of each pole provided by the PM enters the coil along the air gap. When the rotor turns a certain angle, the permanent magnetic flux is just reversed, so the magnetic flux leaves the coil and enters the rotor along the air gap. It can be seen that regardless of the kind of magnetizing mode, when the rotor rotates, it will cause a permanent magnetic flux change on the turn chain in the coil, generating a no-load induced electromotive force [8]. Reference [56] comprehensively compared the influence of different magnetizing modes and PM quantity on the electromagnetic torque of an FRPM. The research showed that the arrangement of NSNS-SNSN could obtain a larger electromagnetic torque.

Reference [57] proposed a new type of FRPM, with a PM affixed on the stator teeth, which effectively counteracts invalid harmonics through a special winding design and current sequence. Reference [58] compared symmetric and asymmetric rotor structures and confirmed that asymmetric rotors can flexibly adjust the air gap magnetic permeability function, optimize the harmonic characteristics, and significantly reduce the torque ripple. References [59,60] designed an I-type stator transverse flux reverse permanent magnet linear motor (FRLPM) (Figure 18) that adopted a transverse magnetic circuit structure to achieve the complete decoupling of electrical and magnetic loads. Reference [61] used the grey relational Taguchi method to optimize the variable tooth width FRPM vibrating mirror motor to improve the torque density and dynamic performance. An asymmetric stator pole FRPM was proposed in Reference [62] to solve the problem of flux leakage between adjacent PM poles. Reference [63] adopted a double stator FRPM with the same inner and outer stator structures. The topology can be regarded as a simple superposition of two FRPMs, and the torque density was improved. Reference [64] investigated the double-sided unstopped asymmetric FRPLM (Figure 19), which is suitable for long distance applications with a high thrust density. In Reference [65], an axially stacked polyphase FRPM (Figure 20) was proposed, which was based on the multilayer design method. Each layer was a single-phase FRPM, and each layer had a mechanical angle of 120°. This structure effectively reduced the torque ripple. In Reference [66], a reverse-flux claw pole motor with soft magnetic composite magnetic core was proposed based on the advantages of the claw pole motor and FRPM, and a higher torque coefficient was found in the research. Reference [67] proposed a new partitioned stator FRPM (Figure 21) that was equivalent to the combination of two groups of FRPM, and the two groups of PM were respectively placed in the stator teeth and the rotor slot, reducing the risk of electric excitation pressure and stator saturation. Reference [68] proposed a synthetic slot type FRPM, which combined radial and tangential PM and had excellent torque performance. Reference [69] proposed an axial field double-rotor FRPM (AF-DR FRPM) for use in a magnetic differential system (Figure 22) that decoupled the magnetic flux between two rotors by means of a surface-mounted PM, so that the two rotors could rotate independently. Reference [70] introduced a new dual rotor FRPM topology with a hollow stator, high-temperature superconducting excitation coil, and superconducting magnetic shielding structure. References [71,72] optimized the design of the transverse pole stator, greatly reducing the PM eddy current loss and improving the motor efficiency. Reference [73] proposed that the “Fe/N-Fe/N-Fe/Fe/Fe” asymmetric stator alternate pole FRPM had better counter electromotive force and torque density than traditional alternate pole FRPMs and asymmetric stator FRPMs.

In order to enhance the torque capacity of the motor, the excitation winding is sometimes added to the FRPM to form a hybrid excitation motor, but the simultaneous presence of the armature and the excitation winding in the stator will cause interference in their spatial positions. For this reason, zero-sequence current technology has been proposed to solve this problem [74,75], which integrates excitation and armature winding. Thanks to zero-sequence current technology, the stator MFMM offers improved flux control and torque.

The quantitative analysis of the relevant literature is shown in

Table 5. Comparison of FRPM performance among different structures.

References	Torque	Torque Ripple	Power Factor	Efficiency
[57]	0.6%	21.9%	0.17	−23.5%
[58]	−20%	−27%	\	2.7%
[59,60]	40.6%	−50%	\	\
[61]	28.4%	−29.56%	\	2.8%
[63]	0.3%	−5.9%	\	\
[64]	59%	−2.5%	0.14	\
[66]	0	−7.1%	0.1	0
[67]	257%	\	\	\
[68]	48.7%	\	\	\
[69]	2.8%	\	\	\
[70]	100%	\	\	1.17%
[71,72]	16%	\	\	12%
[73]	55.7%	40%	\	16.4%
[74,75]	69.4%	\	−0.7	12.3%

.

This article summarizes the corresponding relationship and recommended solutions between typical application scenarios and FRPM performance structures in

Table 6. Relationship between FRPM structure performance characteristics and typical application scenarios.

Application Scenarios/Technical Requirements	References	Advantages	Application Area
Torque pulsation suppression and harmonic optimization	[57,58,65,73]	Reduced torque ripple and increased back electromotive force	High precision servo system, CNC machine tool
High torque density and structural innovation	[59,60,63,66,68,69]	Torque density increase, thrust density increase, dynamic response optimization	Industrial heavy-duty equipment, magnetic differential system
Long distance and high thrust applications	[64,70]	Enhanced thrust density, suitable for long travel, and improved high-temperature resistance performance	Rail transit, long-distance transportation system
Efficiency improvement and loss reduction	[61,71,72]	PM eddy current loss reduction, efficiency improvement	Energy saving motor, high-frequency drive system
Hybrid excitation and advanced control	[67,74,75]	Improved flexibility of magnetic flux regulation and reduced risk of stator saturation	Hybrid drive, intelligent demagnetization system

.

The FRPM is a stator permanent magnet doubly salient motor that drives the rotor by reversing the direction of the magnetic field through periodic switching of the stator tooth magnetic poles. Its main advantage is that the rotor structure is extremely simple and sturdy, and does not require permanent magnets, making it particularly suitable for high-speed operation and harsh environments. The stator PM has excellent heat dissipation conditions, and when combined with centralized windings, it can increase the power density. By optimizing the slot matching, the torque ripple can be effectively suppressed.

However, in terms of torque optimization, although asymmetric rotor structures and stator pole designs can effectively reduce the torque ripple and leakage problems, they often come with an increase in manufacturing process complexity. Although the special winding design and current timing control can offset ineffective harmonics, they pose higher requirements for control algorithms. Innovative topologies such as multilayer design and partitioned stator enhance torque density through spatial combinations (such as axial stacking and dual rotor structures), but this performance gain comes at the cost of sacrificing structural compactness and increasing assembly difficulty.

Although the introduction of excitation windings in the hybrid excitation scheme can enhance the torque regulation capability, the spatial competition between the armature and excitation windings leads to a more complex magnetic circuit design. Although zero-sequence current technology alleviates this contradiction through winding integration, it may affect the efficiency of current utilization. It is worth noting that non-traditional structures such as the transverse magnetic flux and axial magnetic field not only increase the thrust density, but also make magnetic circuit analysis and optimization more difficult.

3.3. Double Permanent Magnet Type

In order to further improve the torque density, a kind of double permanent magnet field modulation motor (DPMFMM) with PMs placed at the stator and rotor side at the same time is proposed. Such a motor can effectively improve the torque output capacity of the motor by relying on the “bidirectional field modulation effect” [76]. Its typical structure is shown in Figure 23.

Reference [77] proposed a DPMFMM with a “U” type PM embedded in the stator teeth and studied its torque generation mechanism. Reference [78] proposed a dual PM MFMM with a “T” shaped PM rotor and demonstrated an 8% improvement in torque density over conventional motors. Reference [79] proposed an N/S PM offset structure to reduce the cogging torque of DPMFMM. References [80,81] proposed the structure of a double PM flux reversal motor (Figure 24) and analyzed the working principle of the motor from the field modulation and flux linkage change, where the results showed that the motor had higher torque density and PF than the traditional FRPM and PMVM. Reference [82] proposed a hybrid excitation DPMFMM using the DC bias sinusoidal current. The motor realizes flux regulation by using a DC component in the current, which can combine high torque density with good field regulation capacity. References [83,84] introduced the concept of double PM into the design of the transverse flux motor, proposed transverse flux rotation DPMFMM, and linear DPMFMM, respectively, and proved that the performance of both types of motors was improved. Reference [85] proposed a mixed PM double stator DPMFMM (Figure 25) with ferrite and Nd-Fe-B placed at the outer stator slot and rotor, respectively, introducing a “bidirectional field modulation effect” by using a double alternating pole PM arrangement.

Compared with the single excitation MFMM, the quantitative comparison of the relevant performance in the above reference is shown in

Table 7. Comparison of the DPMFMM performance among different structures.

References	Torque	Torque Ripple	Power Factor	Efficiency
[77]	40.4%	\	\	2.04%
[78]	12%	\	\	\
[79]	−7%	−97%	\	\
[80,81]	80%	0.09	0.12	0.03%
[82]	10.6%%	\	\	0.2%
[83,84]	−7.2%	−2.45%	0.07	\
[85]	168%%	−0.87%	0.03	3.05%

.

This article summarizes the corresponding relationship and recommended solutions between typical application scenarios and DPMFMM performance structures in

Table 8. Relationship between DPMFMM structure performance characteristics and typical application scenarios.

Application Scenarios/Technical Requirements	References	Advantages	Application Area
High torque density and magnetic field modulation optimization	[77,78,80,81,85]	Increased torque density, improved power factor, and enhanced bidirectional magnetic field modulation effect	Electric vehicle drive, industrial heavy-duty equipment
Low cogging torque and vibration suppression	[79]	Reduced cogging torque and improved operational stability	Precision servo system, medical equipment
Hybrid excitation and flexible adjustment of magnetic flux	[82,85]	Expanded magnetic flux regulation range, combining high torque density and dynamic magnetization capability	Hybrid power system, intelligent demagnetization drive
Lateral magnetic flux and special topology applications	[83,84]	Rotating motor torque increases, linear motor thrust density increases, suitable for compact space layout	Aerospace actuators, linear propulsion systems

.

The bilateral excitation MFMM significantly improves torque density and magnetic field control flexibility through stator rotor cooperative excitation, demonstrating potential in high demand fields such as aerospace. However, its complex dual excitation structure leads to increased manufacturing costs, doubled control difficulty, and inherent contradictions between copper and iron consumption in efficiency optimization. Despite its superior theoretical performance, it is still necessary to be cautious of the risk of “over design” in practical applications—if topology innovation (such as hybrid excitation integration) or intelligent control cannot break through the constraints of cost and complexity, such motors may be trapped in the laboratory stage, and optimizing the cost-effectiveness of single-sided excitation schemes is more practical in engineering.

4. Motor Characteristics Study

4.1. Torque Capacity

MFMMs operate based on the field modulation principle. Due to the flexible design of the modulation pole, excitation pole, winding, etc., a “self-increasing” effect can be realized by selecting the proper low pole logarithm operating sub-harmonics and utilizing the field modulation effect. Without increasing the number of pole slots of the motor, the torque density of the motor is improved, which has attracted extensive attention in the field of low speed and large torque. With the development of various industrial fields, the requirements for space intensification and system lightweight have increased sharply, so the requirements for motor structure and torque density are higher.

4.1.1. Torque Density Improvement

The air gap magnetic field of a field-modulated motor contains abundant harmonics, and its utilization rate for harmonics is higher than that of a common PMSM with a higher torque density. Therefore, the design of an MFMM harmonic magnetic field has become one of the magic weapons to improve the torque density of the motor.

Harmonic Optimization

Reference [86] analyzed the air gap permeability function in depth and pointed out that the harmonic component was mainly generated by the permeability change caused by the slotting of the stator and rotor, which lays a theoretical foundation for optimizing the motor performance from the harmonic angle. Reference [87], using Maxwell’s stress tensor method, defined the contribution of dominant operating harmonics to the dominant PMVM torque and explained its high torque density mechanism. Reference [88] discussed the winding phase shift technology of PMVMs and found that an appropriate phase shift angle could not only eliminate the non-operating sub-magnetomotive force harmonics, but also enhance the operating sub-harmonic winding factor, thus improving the torque density. Reference [89] systematically summarized the air gap harmonic characteristics of the MFMM under different excitation sources. Reference [90] proposed a multiharmonic layering method, which realized the accurate layering of harmonic contribution based on the relationship between the optimization target and air gap harmonic. The results showed that the optimization of the target harmonic of each layer significantly improved the motor performance. In Reference [91], the energy method was used to calculate the harmonic contribution and accurately characterize the harmonic counter-electrical potential and harmonic torque. Reference [92] innovatively proposed improving the torque by air gap magnetic field compensation. This method introduces a harmonic factor and torque compensation factor, which effectively reflect the torque compensation effect.

Control Strategies

Many researchers have used advanced algorithms and control technologies to further optimize the motor torque performance and calculation accuracy. Reference [93] successfully improved the output torque of internal, external, and double-stator PMVMs and effectively reduced the torque ripple by using the nondominant sorting genetic algorithm. In Reference [94], an automatic nonlinear equivalent magnetic circuit modeling method was proposed to optimize the ESFPM design and maximize the torque output by parametrizing the motor split ratio and stator core yoke height. Reference [95] constructed a mixed analysis model, combined with the sub-domain model and the conformal transformation, which accurately considered the stator and rotor slotting effect, and found that the rotor slotting had a more significant impact on the air gap magnetic field.

In recent years, the maximum torque per ampere (MTPA) has been widely used in brushless double-fed motors (BDFMs) [96,97]. References [98,99] studied the maximum torque per total ampere (MTPTA) control strategy of the BDFM drive, which considered the iron loss and used the mathematical curve to determine the minimum total current amplitude approximately, with fast response and high accuracy. Reference [100] improved the FRPM torque by using the third harmonic injection method, while Reference [101] proposed the ESFPM vector control mechanism based on PWM technology to maximize the torque by controlling the stator field direction. Meanwhile, MFMM has significant potential in high-frequency performance compared with PMSM. Its magnetic field modulation mechanism can effectively suppress PWM harmonics, reduce the voltage ripple, and minimize electromagnetic interference by optimizing the magnetic circuit design. However, this advantage highly relies on precise modulation algorithms and magnetic circuit optimization. If not controlled properly, it may lead to increased iron loss or the introduction of new high-frequency harmonics due to multiple magnetic circuit structures.

The quantitative description of torque density enhancement using optimization methods in the relevant literature is shown in

Table 9. Comparison of different optimization methods for torque density enhancement.

References	Torque Density
[88]	6.6%
[90]	13.2%
[91]	39%
[92]	34%
[93]	11.5%
[94]	14.9%
[95]	3.8%
[96]	33%
[98,99]	13.02%
[100]	7.2%
[101]	15%

. The typical application scenarios of each literature are shown in

Table 10. Comparison of torque density enhancement strategies and recommended application scenarios.

Application Scenarios/Technical Requirements	References	Advantages	Application Area
Harmonic optimization and magnetic field design	[86,87,88,89,90,91,92]	Optimization of harmonic utilization efficiency and enhancement of back electromotive force	High torque industrial equipment, wind turbines
Intelligent control and algorithm optimization	[93,94,95,98,99,100,101]	Improved computational accuracy and accelerated dynamic response speed	Electric vehicle drive, precision servo system
High frequency performance and electromagnetic compatibility	[100,101]	Reduced electromagnetic interference and controllable high-frequency losses	High frequency power supply system, aerospace equipment
Torque density and efficiency improvement	[96,97,98,99]	Improved efficiency and reduced iron loss	Industrial energy-saving motors, hybrid power systems

.

4.1.2. Torque Ripple Reduction

The MFMM has the advantages of low-speed high-torque operation, direct drive, etc., and the main objective of this kind of motor optimization is to reduce the torque ripple while ensuring the torque density. In recent years, there has been a number of references on the generation mechanism, motor structure, and control models to reduce the torque ripple of MFMMs.

Harmonic Optimization

For the generation mechanism of the MFMM torque ripple, Reference [102] defined the coupling harmonic group factor starting from the analysis and research on the modulation principle considering magnetic coupling, and its novelty lies in the concept of the positive coupling harmonic and negative coupling harmonic. Reference [103] explained the influence of motor modulation teeth on the air gap magnetic density waveform and harmonic distribution based on the modulation process of a PM magnetic field and armature reaction magnetic field, and analyzed the change rule of air gap harmonic distribution with the opening angle of the stator slot on this basis to provide design guidance for reducing the cogging torque. Reference [104] showed that negative-contribution harmonics were the main source of torque ripple, and the torque ripple of the motor could be effectively reduced by optimizing these harmonics.

Control Strategies

From the perspective of control strategy, a system-level robust design optimization method was proposed in Reference [105], which effectively reduced the torque ripple of the driving system of the switched reluctance motor and improved the comprehensive performance. Reference [106] improved the torque tracking accuracy at a low modulation ratio by improving the accurate dead band predictive flux linkage control. Reference [107] combined sensitivity analysis, adopting multi-objective orthogonal optimization and particle swarm optimization, proposed the orthogonal particle swarm optimization algorithm, solved the optimization accuracy and computational quantity problems, and significantly improved the motor performance.

The comparison of different optimization methods for reducing the torque ripple in MFMMs is shown in

Table 11. Comparison of different optimization methods for reducing torque ripple in MFMMs.

Reference	Torque Density
[102]	−57%
[103]	−4.88%
[104]	−59.94%
[105]	−60%
[106]	−39.3%
[107]	−8.23%

. The typical application scenarios of each literature are shown in

Table 12. Comparison of torque ripple reduction strategies and recommended application scenarios.

Application Scenarios/Technical Requirements	References	Advantages	Application Area
Harmonic mechanism analysis and optimization	[102,103,104]	Quantify harmonic contributions and establish a ‘harmonic—torque’ model	Electric vehicle drive, industrial robots
Intelligent optimization and control strategy	[105,106,107]	Improved low-speed torque accuracy and shortened comprehensive performance optimization cycle	New generation motor prototype design, military special motor

.

Through a systematic analysis of the existing literature, it can be concluded that current optimization research on the torque characteristics of MFMMs mainly focuses on two key directions: firstly, improving the magnetic field harmonic characteristics by optimizing the motor body design (such as pole slot matching, magnetic barrier structure, etc.), thereby enhancing torque output performance; and secondly, developing advanced control strategies (such as harmonic current injection, direct torque control, etc.) based on modern control theory to fully unleash the potential of the motor. Future research can continue to deepen the exploration of these two directions, while paying attention to the collaborative optimization between them, in order to further improve the torque performance of magnetic flux modulation motors.

4.2. Power Factor

The low PF problem of MFMMs has plagued their popularity because it needs to be matched with a converter with a higher power capacity in practical application. Therefore, in recent years, improving the PF of MFMMs has become a research hotspot. Although the high torque density characteristics of MFMMs have been proven, a low PF remains an inherent disadvantage of this type of motor due to the serious leakage of the motor itself [108].

4.2.1. Air Gap Magnetic Flux

The low effective flux density of the air gap excited by the PM is often the main reason for a low PF. Changes in the PM topology affect the air gap flux and hence the PF, indicating that some PM designs can improve the PF of the MFMM. This is because the machine’s magnetomotive force and permeability are critical to the air gap flux density [109,110]. The magnetomotive force harmonics have a profound influence on MFMMs. Reference [111] proposed the method of the synergetic optimization of PMs and armature air gap harmonics, and defined the relationship between harmonic order and PF and torque. Reference [112] optimized the load air gap harmonic with a linear weighting method to improve the PMVM PF. Reference [113] compared and analyzed the influence of the magnetic source topology effect on PF and found that the PF of the surface embedded PM structure was better. Reference [19] studied the PF of the fault tolerant MFMM and proposed a design strategy to improve torque and PF through the magnetic field coupling analysis. Reference [114] pointed out that it is difficult to improve the MFMM PF by adjusting the PM parameters, and the slot leakage inductance had a greater impact. Reference [115] put forward a modeling method based on conformal mapping, which could accurately calculate the motor magnetic load, consider magnetic leakage, analyze the influence of the slot effect on the air gap magnetic density and armature winding function, and obtain an accurate calculation formula of the torque and PF.

4.2.2. Winding Inductance

In addition, the winding has an impact on the motor’s PF, mainly acting through the winding inductance. Reference [116] pointed out that the PF of a double stator MFMM is affected by the inductance of inner and outer windings. When the inductance of a single coil is close to or equal to each other, the maximum PF can be obtained when the number of turns is equal; on the contrary, it is optimal when the number of turns is different. Reference [117] re-modeled the relationship between the armature and PM harmonics and their relationship with the inductance and counter electromotive force, and identified the key factors affecting the power factor. Reference [118] calculated each inductance component, extracted the intrinsic coefficient of PF, and guided the initial design. Reference [119] adopted the hierarchical optimization to deduce and optimize the PM flux linkage and synchronous inductance layer, respectively, to improve the PF of the motor.

The comparison of the improvement in the MFMM power factor by different optimization methods is shown in

Table 13. Comparison of different optimization methods for improving the power factor of MFMMs.

Reference	Power Factor
[111]	0.16
[112]	0.14
[113]	0.03
[19]	0.21
[114]	0.2
[115]	0.23
[116]	0.06
[117]	0.07
[119]	0.13

. The typical application scenarios of each literature are shown in

Table 14. Comparison of power factor strategies and recommended application scenarios.

Application Scenarios/Technical Requirements	References	Advantages	Application Area
Optimization of air gap magnetic flux harmonics	[19,111,112,113]	Topology optimization of magnetic sources and analysis of magnetic field coupling	Industrial variable frequency drive, new energy generation system
Magnetic leakage suppression and precise modeling	[114,115]	Slot leakage sensing control, conformal mapping modeling	High precision servo motors, aerospace actuation systems
Collaborative design of winding inductance	[116,117,118,119]	Harmonic inductance relationship modeling, layered optimization	Electric vehicle drive, military special motor

.

The low power factor problem of the MFMM has become the main bottleneck restricting its engineering application, which is essentially due to its special electromagnetic mechanism. From the perspective of electromagnetic design, this type of motor has two inherent characteristics: first, the effective air gap magnetic density generated by permanent magnet excitation is relatively low, and there is a significant leakage effect in the magnetic circuit; the second issue is the insufficient matching between the inductance parameters of the winding and the magnetic circuit structure, resulting in an excessive proportion of reactive power. In response to these issues, the current research mainly seeks breakthroughs from three dimensions: in terms of magnetic circuit optimization, improving the PM topology structure and modulation pole design to enhance the air gap magnetic density; in terms of harmonic management, harmonic suppression and utilization techniques are used to improve the quality of magnetic field waveforms; and in terms of the winding design, reactive power losses are reduced by optimizing the inductance parameters and winding configuration. Although these technological paths have achieved certain results, the improvement in the power factor still faces dual challenges in theory and technology due to the unique working principle of the MFMM. The future breakthrough direction should focus on the collaborative optimization of electromagnetic thermal mechanical multiphysics fields and systematically solve this key technical problem by combining new magnetic materials and intelligent control strategies.

4.3. MFMM Characteristic Analytical Method

In the torque harmonic analysis of MFMMs, commonly used modeling methods mainly include the energy method and Maxwell tensor method. Reference [120] classified the contribution of the air gap magnetic field harmonic torque of a flux concentration MFMM using the Maxwell tensor method and verified the applicability of this method in magnetic field modulation motors. Research has shown that the 14th, 32nd, and 42nd harmonics generate forward driving torque, while the 4th harmonic manifests as braking torque, and the 30th harmonic dominates torque ripple. Reference [121] verified the motor torque using Maxwell’s tensor method, but there is a theoretical contradiction in this method: during motor operation, there is no relative motion between the permanent magnet on the stator side and the winding, so the stator permanent magnet itself does not generate back electromotive force. However, the calculation results of Maxwell’s tensor method showed that it contributed to the effective torque. In contrast, the energy method had more systematic advantages in magnetic field harmonic analysis, and is especially suitable for optimizing the performance of magnetic field modulation motors with unilateral excitation. For example, Reference [20] used the energy method to verify the encoded tooth shaped magnetic field modulation motor, successfully achieving torque enhancement and torque ripple suppression. Reference [122] analyzed the phase relationship between the working harmonics of the winding magnetomotive force and the permanent magnet magnetomotive force using the energy method and directionally derived the optimized parameters of the stator magnetic flux, significantly improving the power factor of the motor. In addition, Reference [123] established a quantitative method for the contribution of harmonics to back electromotive force and torque based on the energy method. By identifying the harmonic orders with negative contributions in differential modulation motors, innovative reuse of these harmonics was achieved. It is worth noting that DPMFMM introduces ineffective harmonics while increasing the effective operating harmonics [124]. In response to this issue, Reference [125] proposed a DPMFMM air gap harmonic contribution analysis method, which confirmed that some air gap harmonics can have a negative impact on the back electromotive force and torque. Research has shown that guided by the energy method, by suppressing or converting these negative contribution harmonics, the torque density of the motor can be effectively improved. Reference [91] was based on a new DPMFMM structure optimized by the energy method. By adjusting the position of the permanent magnet and modulating the tooth parameters, the reuse of negative contribution harmonics was achieved, and the torque density was increased by 60%. The accuracy of the energy method in analyzing complex modulation relationships was experimentally verified.

5. Development Trend and Application Prospect of MFMM

The concept of the MFMM subverts the traditional motor theory, breaks the restriction that excitation and armature pole pairs are equal, and expands the motor structure evolution. The MFMM makes full use of the magnetomotive force harmonics to significantly improve the motor output torque and has a variety of topologies that can be flexibly applied to different fields. Compared with traditional motors, the MFMM torque is greatly improved, showing wide application prospects in the new energy power generation, electric vehicles, ship propulsion, and military fields, and opening up a new space for motor performance improvement. In the field of new energy generation, the MFMM is particularly suitable for direct drive wind turbines. Its high torque characteristics can effectively cope with low wind speed conditions, and the modulated magnetic field design can adapt to a wide speed range of operations, significantly improving the power generation efficiency. In terms of electric vehicle applications, the high power density characteristics of the MFMM can reduce the motor volume and weight, providing greater flexibility for vehicle layout. Its excellent low-speed high torque performance is particularly suitable for heavy-duty commercial vehicles and off-road vehicles. In ship propulsion systems, MFMMs achieve torque amplification through magnetic field modulation, which can replace some gear transmission devices and improve the reliability and energy efficiency of the propulsion system. In the field of military equipment, MFMMs perform well in scenarios such as electric armored vehicles and shipborne electromagnetic catapult systems as their fast dynamic response and anti-demagnetization capabilities meet the requirements of harsh combat environments. In addition, MFMM’s advantages of high-precision torque control and compact structure are creating new application possibilities in high-end equipment fields such as industrial robot joint drives, aerospace actuation systems, and oil drilling and production equipment. However, at present, MFMMs still have the following problems that need to be solved:

(1)

Excessive torque ripple. MFMMs have a stronger ability to utilize field harmonics than ordinary motors, but we should not ignore the fact that the motor is completed on the basis of increasing all sub-harmonics. How to improve the effective working sub-harmonics and reduce non-working sub-harmonics will always be the focus of research on MFMMs. In terms of motor structure, in the future, the sinusoidal nature of the air gap magnetic field can be optimized, and harmonic torque can be reduced by improving the magnetic barrier structure of the rotor/stator (such as layered magnetic barriers, asymmetric magnetic pole design) or adopting a multipole logarithmic combination. Alternatively, a hybrid excitation structure can be used to dynamically adjust the magnetic field strength to suppress torque pulsation. Advanced motor control strategies can also be adopted, such as the harmonic current injection method and intelligent algorithms, that apply deep reinforcement learning to optimize the current waveform and switching frequency in real-time and adaptively suppress pulsation.

(2)

Complicated motor structure. The introduction of the “field modulation” principle has already increased the complexity of the MFMM structure compared with conventional machines. In recent years, MFMM structural models of more and more complex structures have been proposed in order to improve the motor performance. Although these motors have excellent performance, their structure is extremely complex, and their processing and maintenance are extremely difficult, which is not conducive to large-scale popularization and application. In the future, modular design and symmetry optimization may be adopted to solve motor design problems. For example, using standardized functional modules (such as interchangeable magnetic pole units and integrated windings) can reduce the assembly complexity while maintaining modulation performance. the magnetic field modulation structure can be simplified through symmetrical magnetic circuits or quasi uniform air gap design while meeting the torque requirements. In the field of motor manufacturing, 3D printing can be used to achieve complex topologies that are difficult to process with traditional techniques, while reducing the number of parts.

(3)

The PF is generally low, particularly in high pole ratio designs. Although the torque output is large, most of the energy is consumed by reactive power, limiting its application in the high-precision field. In the future, dynamic adjustable electromagnetic modulation units, such as auxiliary excitation windings, can be introduced to optimize the air gap magnetic field distribution in real-time and reduce reactive current demand. Alternatively, a bidirectional magnetic field modulation structure of the rotor/stator can be used to offset the inductive reactive power component through phase compensation. At the same time, advanced intelligent control strategies can be adopted to detect the harmonic reactive power in real-time, inject high-frequency currents of specific phases (similar to active filtering), and offset the reactive power components of low-order harmonics. In terms of material innovation, gradient magnetic materials and programmable magnetic materials can be used to achieve a natural sinusoidal magnetic field and reduce the reactive magnetization current.

(4)

Large loss. Limited by material performance, hysteresis and eddy current loss are difficult to break through, resulting in low energy efficiency and high operation costs, which limits its application in the high-precision and high-efficiency fields. Therefore, reducing loss and improving efficiency has become a key issue in the field of MFMMs. Whether this problem can be solved will directly affect the development prospect and market potential of MFMMs. In the future, various composite materials, such as nanocrystalline soft magnetic alloys and amorphous alloy graphene composite magnetic cores, can be utilized to achieve the self-suppression of eddy current losses and block eddy current paths under high-frequency magnetic fields. In terms of winding technology, superconducting materials can be used in key areas to achieve zero resistance electrification.

(5)

Fault diagnosis faces new challenges. The unique magnetic field modulation mechanism of MFMMs has resulted in significant differences in its fault characteristics compared with traditional motors, mainly manifested in three aspects. Firstly, the failure of the modulation unit (such as modulation pole deformation or demagnetization) will generate special harmonic characteristics, requiring the development of dedicated modulation harmonic analysis algorithms. Secondly, the coupling effect of multiple physical fields makes it difficult for single sensor data to accurately reflect the nature of the fault. Therefore, multisource information fusion technology is needed such as combining high frequency current signals, vibration spectra, and infrared thermography for comprehensive diagnosis. Thirdly, the dynamic modulation process leads to time varying fault characteristics, and traditional threshold detection methods are prone to misjudgment. The latest solution includes building a deep learning based digital twin model to achieve early fault warning by comparing the difference in magnetic field distribution between the measured data and health benchmarks, developing adaptive resonance demodulation technology to effectively extract the characteristic frequencies of mechanical damage in modulation units; and applying transfer learning algorithms to solve the problem of fault feature drift under different operating conditions. These innovative methods provide new ideas for the intelligent operation and maintenance of MFMMs.

6. Conclusions

Based on the basic operating principle of MFMMs and the location of the excitation unit, this paper summarized the topological studies of PMVMs, SFPMs, FRPMs, and DPMFMMs in recent years. Subsequently, the relatively valuable references to MFMMs in recent years were analyzed from the urgently needed characterization problems. In general, MFMMs have made great progress in basic theory, topology structure, and performance optimization, and have been widely used in many fields. Through this article, we hope to provide a reference for the research and application of this kind of motor in the future.