Next Article in Journal
Expanding the Frontiers of Industrial Robots beyond Factories: Design and in the Wild Validation
Previous Article in Journal
Modeling and Optimization of a Micro-Channel Gas Cooler for a Transcritical CO2 Mobile Air-Conditioning System
Previous Article in Special Issue
Analysis and Design of Novel Axial Field Flux-Modulation Permanent Magnet Machines for Direct Drive Application
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Machines
Volume 10
Issue 12
10.3390/machines10121178
machines-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Review

A Review of Axial-Flux Permanent-Magnet Motors: Topological Structures, Design, Optimization and Control Techniques

by
Zhuo Hao
1,†,
Yangyang Ma
2,†,
Pengyu Wang
2,
Geng Luo
1,* and
Yisong Chen
1
1
School of Automobile, Chang’an University, Xi’an 710064, China
2
College of Automotive Engineering, Jilin University, Changchun 130012, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Machines 2022, 10(12), 1178; https://doi.org/10.3390/machines10121178
Submission received: 9 November 2022 / Revised: 30 November 2022 / Accepted: 6 December 2022 / Published: 7 December 2022
(This article belongs to the Special Issue Optimization and Modelling of Synchronous Permanent Magnet, Synchronous Reluctance and Induction Machines)
Browse Figures
Versions Notes

Abstract

:
Axial-flux permanent-magnet (AFPM) motors are a kind of important motor with compact structure, high power density and high torque density. In this review, the progress of AFPM motors and their key technologies are analyzed and described, with emphasis on the topological structures, design and optimization methods and control techniques. Based on these analyses, the main findings of the review are the following: (1) the yokeless and segment armature (YASA)-type motors have great potential for development; (2) the multi-objective optimization design theories can be integrated and applied to optimize the design of AFPM motors; and (3) optimal control and sensorless control have important value in improving system reliability and reducing cost. Finally, highlights and prospects are provided for further advancing AFPM motors.

1. Introduction

Axial-flux permanent-magnet (AFPM) motors are now attractive choices for various applications, such as new energy vehicles [1], aerospace [2], marine [3] and other industrial applications [4,5]. The reason is that AFPM motors have the advantages of compact structure, high torque density and high power density [6]. Compared with the conventional radial-flux permanent-magnet (RFPM) motors, AFPM motors can be made in a smaller volume under the same power demand, which is more suitable for compact applications. Additionally, AFPM motors can obtain better dynamic response performance [7]. In view of the many advantages of AFPM motors, studying the progress of AFPM motors is of great significance.
In order to improve the comprehensive performance of AFPM motors, some studies have presented the novel topological structures, design and optimization methods and control techniques [8,9,10]. In terms of the topological structures, studies mainly focus on the rotor shape optimization, stator design, winding structure and permanent magnet selection and evaluate the air gap flux intensity, back electromotive force, flux linkage, cogging torque and torque ripple performances of the designed topological structure of AFPM motors [11,12,13]. In addition, in terms of the design and optimization methods, cogging torque reduction, flux leakage reduction and torque ripple reduction are important issues which demand attention of designers during design process [14,15], and the size design and electromagnetic model of AFPM motors are the basis of design optimization, which demands attention as well. Furthermore, in terms of the control techniques, the controlled system and control algorithm are proposed to increase torque density and decrease the cogging torque of AFPM motors [16,17,18], and the studies mainly focus on simplifying the structure of controlled system and improving the precision of control algorithm to achieve effective dynamic performance and high reliability. Based on the above, this paper mainly focuses on three aspects: (i) topological structures; (ii) design and optimization; and (iii) control techniques, and Figure 1 depicts a summary of the major points of this paper.

1.1. Literature Survey

In recent years, many studies on key technologies for AFPM motors have been published, which provides references for this paper. The scope, keywords and results of the literature survey in this paper are given in Table 1. A total of 126 related studies were referred to in this review, of which 69.05% were published in the last 5 years (see Figure 2).

1.2. Motivations and Contributions

Based on the abovementioned information and the literature survey, AFPM motors are important and widely used, and certain progress has been made in key technologies. However, to date, only a few reviews on AFPM motors have been published [7,19,20]. In light of this, we review the research progresses of AFPM motors in this paper. We not only summarize the research progresses of AFPM motors in topological structures, design and optimization methods and control techniques but also put forward the prospects in the future development of AFPM motors.
In order to advance the understanding and development of novel high-performance AFPM motors, the research progress of topological structures, design and optimization methods and control techniques of AFPM motors are extensively reviewed in this paper. Specifically, the main contributions of this paper include: (i) a comprehensive summary of the progress of AFPM motors (especially topological structures, design and optimization methods and control techniques) over the past 5 years and (ii) a presentation of the important highlights and prospects regarding the optimization and innovation of AFPM motors. This review can provide better insight into current progress and future directions and provide some reference value for related studies on the optimization and innovation of AFPM motors.

2. Topological Structures of Axial-Flux Permanent-Magnet Motors

Many different topological structures of axial-flux permanent-magnet motors have been proposed. According to the number of stators and rotors in the AFPM motor structure, AFPM motors can be classified as four typical-types [19,21]: single-stator/single-rotor (SSSR), double-stator/single-rotor (DSSR), single-stator/double-rotor (SSDR) and multi-stator/multi-rotor (MSMR), as shown in Figure 3. The SSSR-type AFPM motors are widely used in the servo drive and transportation industry due to their compact structure and high torque capacity. However, the unbalanced axial force between stator and rotor can easily distort the structure and produce vibration noise and reduce the life of the motors [22]. For the DSSR-type AFPM motors, the rotor is located between two stators, and the permanent magnet (PM) can be located on the surface or inside of the rotor, and compared with the structure where the PM is located on the surface, embedding the PM inside the rotor can better protect the PM from impact and corrosion [23]. The SSDR-type AFPM motors with the stator located between two rotors have good symmetry to eliminate the unbalanced axial forces and can improve the vibration and life of the motor during the life cycle [24]. With N stators and (N+1) rotors, the MSMR-type AFPM motors can improve the torque density and power density without increasing the motor diameter and are very suitable for large torque occasions such as ship propulsion [25].
AFPM motors have gradually become the application hotspot in the field of new energy vehicles due to their excellent characteristics [26,27]. Many studies have studied the new topological structures of AFPM motors for new energy vehicles. AFPM motors of external stator/internal rotor (axial flux internal rotor, AFIR)-type and external rotor/internal stator (toroidally wound internal stator, TORUS)-type can be designed to be suitable for the drive system of electric vehicles [28,29]. The topological structures of AFIR- and TORUS-type AFPM motors are shown in Figure 4 [30,31]. References [32,33,34] designed and analyzed the topology of AFIR-type AFPM motors and made some progress in reducing cost and improving efficiency and service life, and references [35,36,37] designed TORUS-type AFPM motors for the drive systems of electric vehicles, hybrid electric vehicles and fuel cell vehicles. Most of the designed AFPM motors used soft magnetic composite (SMC) cores to improve the weak magnetic capacity and reduce the magnetic flux loss.
In order to further improve the efficiency and power density of the AFPM motors, the stator yoke of the TORUS-type AFPM motor is removed, and the stator structure is partitioned by the centralized windings, obtaining a new-type of AFPM motor, the yokeless and segment armature (YASA) topology (see Figure 5, [31,38]). Compared with the TORUS-type AFPM motors, the YASA-type AFPM motors not only reduce the core loss but also reduce the winding copper consumption so that the efficiency and power density of the AFPM motors are improved. Studies on YASA-type AFPM motor mainly focus on improving power and efficiency. Di Gerlando et al. studied and optimized the size of YASA-type AFPM motor to further reduce the additional power loss and improve the working efficiency of the motor [39]. Xu et al. investigated and optimized the cogging torque of the YASA motor with SMC core [40]. Concretely, the structure of YASA motor was with 10 poles and 12 slots, and the stator cores were made of SMC material, while the rotors were made of solid magnetic material. Fard et al. proposed a novel yokeless and segmented armature axial field flux-switching sandwiched permanent-magnet (YASA-AFFSSPM) motor [41]. The YASA-AFFSSPM motor with three-phase 12/19-pole was composed of a single stator and two rotors, which could exhibit higher torque density and lower cogging torque. Reference [42] innovatively designed the 65 kW 18-slot/20-pole YASA-type AFPM motor. The stator and rotor of the AFPM motor were manufactured with SMC to reduce the core loss at high frequency, and the PM was divided into three segments to reduce the magnet loss, and reference [43] studied and compared a double-rotor/single-stator YASA and a single-stator/single-rotor configuration, and the studies showed that YASA configuration exhibited higher efficiencies at higher speeds, while the single-stator/single-rotor was more efficient in high torque cycles. Currently, many motor manufacturers have developed more mature YASA-type AFPM motor products, such as Magnax AXF290 [44], YASA 750 [45], Magelec motor [46] and other motor products, and the peak power is higher than 200 kW and the efficiency is more than 95%, which can be used in the drive systems of new energy vehicles.

3. Design and Optimization of Axial-Flux Permanent-Magnet Motors

The design and analysis of AFPM motors usually starts from performance requirements and size constraints, followed by the matching design and optimization design of parameters and finally the evaluation of the mechanical performance of the overall structure [7,47]. After years of exploration in academia and industry, the unique design and analysis methods of AFPM motors have been established. This section focuses on analyzing and summarizing the recent advances in sizing equation, electromagnetic modeling and optimization design of AFPM motors.

3.1. Sizing Equation

The design starts with estimating the external size of the AFPM motors to meet the power/torque requirements under the given constraints (such as maximum allowable geometric size, rated/peak torque, rated/peak speed, peak voltage/current, etc.) [48,49]. If the stator resistance and leakage inductance of the AFPM motors are negligible, the output power P o u t of the AFPM motors can be calculated by Equation (1) [21,50]:
P o u t = η n p T ∫ 0 T e ( t ) i ( t ) d t = η n p K p E p k I p k
where η is the motor efficiency; n p is the number of motor phases; T is the periodic cycle of the motor electromotive force (EMF); e ( t ) is the phase air-gap EMF; i ( t ) is the phase current; K p is the electrical power waveform factor; E p k and I p k are the peak values of phase air-gap EMF and phase current, respectively, and K p , E p k can be defined from reference [51].
K p = ∫ 0 T e ( t ) i ( t ) E p k I p k d t
E p k = K e N p h B g f p ( 1 − λ 2 ) D o 2
where K e is the EMF factor per unit air-gap area; N p h is the number of winding turns per phase; B g is the flux density in air-gap; f is the converter frequency; p is motor pole pairs; λ is the ratio of the inner diameter D i to the outer diameter D o of the motor.
Based on the above equations, a general-purpose sizing equation for AFPM motors can be obtained, as expressed in Equation (4) [52]:
P o u t = 1 1 + K ϕ n p n 1 π 2 K e K i K p K L η B g A × f p ( 1 − λ 2 ) ( 1 + λ 2 ) D o 2 L e
where K ϕ is the ratio of electrical load on rotor and stator; n 1 is the number of phases of each stator; K i is the current waveform factor; K L is the aspect ratio coefficient related to the motor structure considering such factors as energy consumption loss, temperature rise and demand efficiency; A is the total electrical load; L e is the effective axial length of the motor; and K L = D o / L e .
The diameter ratio λ of AFPM motors is an important design parameter, which has a significant influence on the characteristics of the AFPM motors [53]. Yesilbag et al. pointed out that for a specific number of pole pairs, the power density of AFPM motors only depended on λ and its maximum value is a proper optimum λ value [54]. In practice, the optimal value of diameter ratio λ depends on the optimization objective. Although the optimization criteria are the same for a given electrical load and magnetic flux density, the optimal value of λ varies depending on the rated power demand, pole pairs and motor structure [55,56]. Additionally, reference [57,58,59,60] pointed out that the reasonable definition of parameters such as magnetic flux density, electrical load and current density could achieve a good estimation of the main geometric dimensions of AFPM motor, which was helpful for the parameter matching and design optimization of subsequent design and analysis of AFPM motors.

3.2. Electromagnetic Modeling

The electromagnetic modeling of AFPM motors is the next step of motor analysis after the sizing equation is determined, and the electromagnetic modeling is the basis of AFPM motor optimization design and performance evaluation. The electromagnetic model establishment and electromagnetic performance analysis methods of AFPM motors mainly include two mainstream methods: finite element analysis (FEA) [61] and magnetic equivalent circuit (MEC) [62]. Due to the inherent three-dimensional (3-D) structure and magnetic flux path, the magnetic flux density distributions along the radial and axial directions of AFPM motors show curvature effects and edge effects independently [63]. The 3-D FEA is generally recognized as the most accurate numerical tool for solving Maxwell equations of each volume element under boundary conditions, so the electromagnetic modeling based on FEA are widely used [64,65,66]. Some references [67,68,69] compared the solutions of the proposed new model with the results of 3-D FEA analysis to verify the rationality as well. However, the 3-D FEA method takes a long computational time, which is difficult to adapt to the modeling and analysis of complex AFPM motors’ topological structure. To overcome the drawback of 3-D FEA, several studies have proposed two-dimensional finite element analysis (2-D FEA) modeling and analysis techniques. Gulec and Aydin converted the 3D AFPM motor models into 2D radial flux motor models with inner and outer rotors and 2D linear motor models for several 2D cut planes [70], as shown in Figure 6a. Concretely, the 2D inner rotor modeling approach (IRMA), 2D outer rotor modeling approach (ORMA) and 2D linear motor modeling approach (LMMA) were used to slice a 3D AFPM motor problem into a number of 2D problems considering the topology and motor symmetry. Kim and Woo developed a novel quasi-3-D model for the fast and accurate design of AFPM machines [71], as shown in Figure 6b. In the conventional quasi-3-D FEA, the cylindrical plane is represented as the 2-D analysis plane. However, enough 2-D analysis planes are required to achieve high accuracy. The novel quasi-3-D model used spatial interpolation to obtain the magnetic flux distribution on virtual air-gap sections between 2-D analysis planes, which could simplify the iteration of the optimization process, reducing the overall time cost and provide a reduction of 98.87% compared to 3-D FEA.
The core concept of magnetic equivalent circuit is to simplify and assume the complex magnetic field to be equivalent to a simple circuit. And compared with FEA, MEC is considered as a simpler method to analyze the electromagnetic model and performance of AFPM motors [72]. Tong et al. proposed a quasi-3-D nonlinear MEC model for double-sided AFPM machines with 36 slots and 24 poles [73]. The proposed MEC model can be used to predict the performance of AFPM machines, including the 3-D distribution of air gap flux densities, flux linkage, no-load back EMF and electromagnetic torque, and the no-load magnetic field and armature magnetic field can be obtained as well. Zhao et al. presented an improved MEC model for a coreless AFPM synchronous machine with 16 poles and 12 slots, which was used to calculate the coreless AFPM synchronous machine’s steady-state and transient performances [74]. Zhang et al. presented a 3-D MEC model for the magnetic field calculation in coreless AFPM synchronous generators by considering the magnetic leakage and fringing flux [75], as shown in Figure 7a. The presented 3-D MEC model was applied to a specific AFPM synchronous generators, and the magnetic field distribution, no-load back EMF and torque could be calculated. Due to the large reluctance of the main flux loop in the ironless stator motors, the end leakage fluxes of the ironless stator AFPM motors are serious. In the light of this, an MEC model considering end leakage fluxes was established in [76], and the MEC model diagram is shown in Figure 7b. The established MEC model could obtain the leakage coefficients representing the ratio of end leakage fluxes to main flux and radial coefficients representing effective radial lengths of end leakage fluxes. In order to implement the electromagnetic modeling and electromagnetic performance analysis of AFPM motors more quickly and accurately, some studies comprehensively use FEA and MEC methods. In addition, some studies combine FEA and MEC methods to implement electromagnetic modeling and the electromagnetic performance analysis of AFPM motors more quickly and accurately [77,78,79], which is the trend of modeling and analysis for AFPM motors in the future as well.

3.3. Optimization Design

The design of AFPM motors must comprehensively consider the performance, cost and reliability. Therefore, the optimal design of the motor is a multi-variable and multi-mode problem [80]. For the optimization design of AFPM motors, studies mainly started with the key parameters and used the optimization algorithms to optimize the key parameters, and the common optimization algorithms include least square (LS) [81], genetic algorithms (GA) [82], neural networks (NN) [83], etc. Meo et al. proposed a new hybrid approach obtained combining a multi-objective particle swarm optimization and artificial neural network (ANN) [84]. In order to generate the training dataset and verification dataset of ANN, a preliminary design based on the sizing equations was developed, and then the FEA of the machine for different values was developed as well. As shown in Figure 8a, the numbers of neurons in the input layer, hidden layer and output layer of the ANN model are 5, 15 and 1, respectively. Fard et al. proposed a hybrid algorithm based on ANN and non-sorting genetic algorithm II (NSGA II) to obtain the maximum torque density and minimum cogging torque [85], and the scheme for the ANN is shown in Figure 8b. Patel et al. optimized the design of AFPM motors applied in electric vehicles and proposed using GA to optimize parameters such as diameter ratio, air-gap flux density and current density to obtain the best combination of parameters [86]. The optimization design combination was verified in the 3D-FEA model, and the results showed that the efficiency of AFPM motor was up to 91.5%. Additionally, some studies used hybrid algorithms with GA to optimize the design of AFPM motors, such as a hybrid genetic algorithm (HGA) combining simulated annealing and father-offspring selection [77], the elitist genetic algorithm (EGA) [87], the non-dominated sorting genetic algorithm (NSGA-II) [88], etc.
With the further development of efficient computer system and optimization theory, new multi-objective optimization algorithms such as particle swarm optimization (PSO) [89,90], bat optimization (BO) [91] and the Taguchi algorithm [92] have also been applied to the optimization design of AFPM motors. Rostami optimized an AFPM motor applied in electric vehicles by using multi-objective optimization algorithms of the quasi-3D approach and PSO algorithm and evaluated the influence of the different driving cycles (NEDC and US06) on the obtained machine parameters [93]. Obviously, the AFPM motor design parameters optimized for different driving cycles would be quite different, and the optimized parameters were imported into the 3D finite element model to verify the accuracy. Chakkarapani et al. proposed multi-objective optimization techniques called the weighted sum method (WSM), multi-objective genetic algorithm (MOGA) and niched pareto genetic algorithm (NPGA) for the design optimization and analysis of slot-less permanent magnet brushless DC motor [94]. The rotor radius, stator/rotor axial length, magnet thickness and winding thickness were simultaneously accounted for in the proposed multi-objective optimization algorithms to maximize the output torque and to reduce the total volume and total power loss. A multi-objective design optimization technique using the response surface modeling and a novel multi-objective multi-verse optimization (MOMVO) algorithm was proposed for AFPM brushless DC micromotor in reference [95]. The two objectives of the optimization were to minimize the micromotor volume and improve the joules efficiency with the constraints of minimum required torque and maximum required back EMF. In the optimization design and analysis of AFPM motors applied in the new energy vehicles in addition to the basic design objectives, such as torque and power, limiting torque ripple, reducing power loss and reducing vibration and noise, were important considerations as well. In order to clearly describe the above optimization and design methods, the characteristics of above methods are compared and analyzed in Table 2.

4. Control Techniques of Axial-Flux Permanent-Magnet Motors

Despite the advantages of AFPM motors, the motors are required to provide sufficient torque and wide speed range for practical applications, which requires the motors to be controlled [96]. The main purpose of the AFPM motor control is to obtain the appropriate torque and speed to meet the requirements of the actual working environment and to obtain the efficiency, stability, reliability, speed range and other comprehensive performance improvement as well. In order to comprehensively reflect the control techniques progress of AFPM motors, this section classifies control techniques into traditional control techniques and novel control techniques.

4.1. Classical Control Techniques

4.1.1. Field Oriented Control (FOC)

The field-oriented control (FOC, also known as vector control, VC) is one of the most classical motor control techniques which is widely used in the control of AFPM motors [97,98]. FOC refers to use the frequency converter to control excitation current and torque current, respectively. Liu and Lee proposed a closed-loop field-oriented control realization method [99], and the closed-loop field-oriented control diagram is shown in Figure 9a. Among the outer feedback control loop of the FOC control diagram, the desired stator q-axis current command was calculated to satisfy the input speed command at various loading conditions. However, the FOC control algorithm is sensitive to rotor parameters, and the control network is more complex. Due to sliding mode control possess high performance robustness under parameter variation and load disturbances, Akhil et al. proposed a look-up table (LUT) based FOC with sliding mode control [100]. The inputs of LUT were reference torque and speed, and the outputs of LUT were reference currents i d and i q , and sliding mode control could modify the outputs of the LUT to enable an optimal control effect. The motor control system usually obtained high-precision rotor position and speed information through the position sensor to complete the closed-loop control of the control system [101]. In order to further improve the stability and reliability of the control system, some studies adopted the sensorless vector control algorithms for AFPM motors [102,103]. Luo et al. proposed the sensorless control strategy of the AFPM machine in electrical vehicles [104], including initial rotor position estimation and rotating position estimation, and the sensorless control strategy was convenient for in-wheel application of electric vehicles. Generally, FOC is easy to achieve, but the control effect is not good.

4.1.2. Direct Torque Control (DTC)

Direct torque control (DTC) is another classic technology of AFPM motor control, and DTC refers to the technology of directly controlling the flux and torque obtained by predicting the measured voltage and current [105]. Siami et al. proposed a DTC method for AFPM machines [106], and the block diagram of proposed DTC is shown in Figure 10a. The torque and flux can be calculated by means of machine equations in stationary reference frames, and then the torque and flow were compared with the reference value in the hysteresis controllers to complete the control. However, only six active voltage vectors of inverters in the DTC method were used to control torque and flux. Aiming at the dynamic performance of axial-field flux-switching sandwiched permanent-magnet (AFFSSPM) motor, Fard et al. proposed a direct torque and flux control scheme [107]. The scheme in Figure 10b could improve the torque density and reduce the cogging torque but still needs to match the speed sensor. Nguyen et al. presented a motion sensorless direct torque and flux control algorithm and field-weakening algorithm for dual-airgap axial-flux permanent-magnet machines [108], which could accurately estimate flux and speed information. The proposed algorithm eliminated the rotary encoder, which in turn reduced the cost of the system. And in the above references [41,106], two sensorless DTC algorithms for AFPM motors were proposed to increase the space for windings and torque capability. Generally, DTC is simple to implement and can obtain fast torque response, but there are also the shortcomings of torque ripple and unstable system.

4.1.3. Improved FOC and DTC

Aiming at the shortcomings of FOC and DTC, some studies proposed the improved FOC and DTC schemes to achieve a better control effect. For example, a sliding mode vector control system based on collaborative optimization of axial-flux permanent-magnet synchronous motors (AFPMSM) for electric vehicle was proposed in [109]. The proposed sliding mode vector control algorithm could improve the dynamic performance of electric vehicles, including torque tracking capability, speed limiting characteristics, and operating characteristics. For excitation copper loss and limited speed range, Yang et al. proposed a novel vector control based on three magnetization state (MS) manipulations for axial-field flux-switching memory machines (AFFSMM) [110], and the three MS manipulations and vector control diagram based on the three MS manipulations are illustrated in Figure 11a,b. Compared with the method based on proportional integral (PI) regulator, the improved FOC control algorithm could reduce the speed and torque overshoot and improve the dynamic performances of AFFSMM (see Figure 11c,d). In [111], Zhao et al. took the three-stator/double rotor AFPMSM as research object and proposed the deadbeat current predictive vector control system based on the efficiency optimal torque distribution method. The proposed deadbeat current predictive vector control system could effectively improve the torque tracking characteristics and achieved no torque overshoot and small torque ripple at steady state. Moreover, some studies also proposed the improved control techniques based on extended disturbance observer [112] and sliding mode observer [102,113,114] to further improve the control effect and accuracy of AFPM motors.

4.2. Novel Control Techniques

With the further development of control theory and optimization theory, some studies have proposed novel control techniques for the dynamic response performance of AFPM motors, mainly including model predictive control (MPC) [115] and adaptive robust control (ARC) [116]. MPC is widely used in the field of machine drive and control due to its simple implementation, fast dynamic response and high tracking accuracy [117,118]. Yuan et al. analyzed the topological structure of AFFSPM motor with 13 poles and 6 slots and proposed a model predictive torque control (MPTC) method for AFFSPM motor [119]. The torque reference value was obtained by the PI controller of the speed outer loop, and the reference flux-linkage amplitude is set to a fixed value, ψ s * . Compared with the VC and DTC, the proposed MPTC method could achieve quicker torque response speed and the smallest torque ripple, and the flux-linkage ripple of the MPTC was only about 1.5%, which was far less than the flux-linkage ripple of 15.3% under DTC. In addition, Zhao et al. proposed a continuous-control-set model predictive control (CCS-MPC) method for the AFSFPM machine drive system [120]. In the CCS-MPC method, the maximum torque per ampere and maximum output power flux-weakening strategies were presented in constant torque and constant power regions, respectively. The proposed CCS-MPC method could improve the anti-load disturbance capability and dynamic response.
The adaptive robust control can continuously obtain the input, state, output variables and performance parameters of the controlled system and update the structure of the controller [121,122]. Therefore, ARC can not only keep the system robust but can also achieve the optimal control effect. Wang et al. studied and proposed an adaptive robust drive control system for an AFPMSM of an electric medium-sized bus based on the optimal torque distribution method, focusing on anti-disturbance control [123]. The simulation and experimental results show that the proposed ARC method could improve the control accuracy of the drive system and could effectively suppress the disturbances, and in [124], Zhang et al. studied the speed sensorless control methods based on model reference adaptive system (MRAS) for hybrid excitation axial-field flux-switching permanent-magnet machine (HEAFFSPMM). The MRAS observer of speed was designed based on the FOC strategy, including three speed sensorless control algorithms: stator currents, stator flux linkages, and simplified stator currents. The control block diagrams of HEAFFSPMM with MRAS for stator current speed sensorless control, for stator flux linkage position sensorless control and for simplified stator current position sensorless control are respectively shown in Figure 12a–c. The simulation and experimental results shown that the MRAS algorithm based on simplified stator currents had good control performance and high control accuracy (see Figure 12d).
In order to clearly describe the characteristics of the control techniques, this paper compares the well-established FOC and DTC algorithms with the novel control algorithms (see Table 3). As shown in Table 3, the complexity, response and robustness of algorithms are summarized.

5. Conclusions

In order to improve the size and cost, torque density, dynamic response and other comprehensive performance factors of AFPM motors and expand their applications, it is urgent and meaningful to explore the key technologies of AFPM motors. This paper mainly reviewed the studies on AFPM motors in the past 5 years, which mainly included three categories: topological structures, design and optimization methods and control techniques. At present, some studies have made progress in the structural design and performance improvement of AFPM motors. Despite of this, there is still much room for improvement. The main findings of the review are the following:
  • Topological structures: There are many novel topological structures of AFPM motors, among which the YASA-type AFPM motors have great potential for development due to their advantages of high efficiency and high energy density. At the same time, new materials have also been applied to the design of novel topological structures of AFPM motors. For example, AFPM motors with printed circuit board (PCB) windings have larger air gap flux density and can effectively reduce magnetic flux leakage, which has broad application prospects. In the future, AFPM motor topological structures should be innovatively developed towards simple structures, with light weight and low cost.
  • Design and optimization methods: In the design of AFPM motors, the diameter ratio is regarded as the most important design parameter of AFPM motors, and power loss, torque ripple and vibration noise are important considerations in the design of AFPM motors as well. The three-dimensional model of AFPM motors can be transformed into a quasi-three-dimensional model by comprehensively using the FEA and MEC analysis, and on this basis, the multi-objective optimization design theories are integrated to optimize the design of AFPM motors, which can achieve accurate modeling and efficient analysis of AFPM motors.
  • Control techniques: The AFPM motors have high requirements for the control system, such as simplicity, stability and reliability. With the development of traditional control algorithms (FOC and DTC), the novel control algorithms (such as MPC and ARC) are design and proposed to optimize the control of AFPM motors, and the sensorless control algorithm can improve reliability and reduce cost. In the future, the control techniques of AFPM motors will be further explored and developed around comprehensive aspects such as robust performance, dynamic response ability and intelligence level.
The novel topological structures, the accurate electromagnetic models, the design and optimization methods and the excellent control techniques will promote the rapid development of the overall performance of AFPM motors. In the future, our work will focus on the optimization design and dynamic performance improvement of AFPM motors for new energy vehicles.

Author Contributions

Conception of the structure and research direction of the paper, Z.H. and Y.M.; writing—original draft preparation, Z.H. and Y.M.; methodology, P.W.; investigation, P.W.; writing—review and editing, G.L.; project administration, G.L. and Y.C.; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Shaanxi Provincial Key R&D Program (grant no. 2021LLRH-04-04-02), the Shaanxi Provincial Key Industry Innovation Chain Project (grant no. 2020ZDLGY16-08) and the Fundamental Research Funds for the Central Universities, CHD (grant no. 300102220511).

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Havel, A.; Sobek, M.; Stepanec, L.; Strossa, J. Optimization of Permanent Magnet Parameters in Axial Flux Rotary Converter for HEV Drive. Energies 2022, 15, 724. [Google Scholar] [CrossRef]
  2. Kumar, S.; Lipo, T.A.; Kwon, B.I. A 32,000 r/min Axial Flux Permanent Magnet Machine for Energy Storage with Mechanical Stress Analysis. IEEE Trans. Magn. 2016, 52, 8205004. [Google Scholar] [CrossRef]
  3. Ouldhamrane, H.; Charpentier, J.-F.; Khoucha, F.; Zaoui, A.; Achour, Y.; Benbouzid, M. Optimal Design of Axial Flux Permanent Magnet Motors for Ship RIM-Driven Thruster. Machines 2022, 10, 932. [Google Scholar] [CrossRef]
  4. Di Dio, V.; Cipriani, G.; Manno, D. Axial Flux Permanent Magnet Synchronous Generators for Pico Hydropower Application: A Parametrical Study. Energies 2022, 15, 6893. [Google Scholar] [CrossRef]
  5. Shin, D.-Y.; Jung, M.-J.; Lee, K.-B.; Lee, K.-D.; Kim, W.-H. A Study on the Improvement of Torque Density of an Axial Slot-Less Flux Permanent Magnet Synchronous Motor for Collaborative Robot. Energies 2022, 15, 3464. [Google Scholar] [CrossRef]
  6. Celik, E.; Gor, H.; Ozturk, N.; Kurt, E. Application of artificial neural network to estimate power generation and efficiency of a new axial flux permanent magnet synchronous generator. Int. J. Hydrog. Energy 2017, 42, 17692–17699. [Google Scholar] [CrossRef]
  7. Shao, L.Y.; Navaratne, R.; Popescu, M.; Liu, G.P. Design and Construction of Axial-Flux Permanent Magnet Motors for Electric Propulsion Applications-A Review. IEEE Access 2021, 9, 158998–159017. [Google Scholar] [CrossRef]
  8. Bi, Y.L.; Pei, Y.L.; Chai, F. A Novel Axial Flux Interior Permanent Magnet Motor with High Torque Density. In Proceedings of the 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 11–14 August 2019; pp. 2797–2801. [Google Scholar]
  9. Wang, D.H.; Peng, C.; Xue, D.H.; Zhang, D.X.; Wang, X.H. Performance Assessment and Comparative Study of a Permanent Magnet Machine with Axial Flux Regulator. IEEE Trans. Energy Convers. 2019, 34, 1522–1531. [Google Scholar] [CrossRef]
  10. Mlot, A.; Gonzalez, J. Performance Assessment of Axial-Flux Permanent Magnet Motors from a Manual Manufacturing Process. Energies 2020, 13, 2122. [Google Scholar] [CrossRef]
  11. Hao, L.; Lin, M.Y.; Xu, D.; Fu, X.H.; Zhang, W. Static Characteristics of a Novel Axial Field Flux-Switching Permanent Magnet Motor with Three Stator Structures. IEEE Trans. Magn. 2014, 50, 4002604. [Google Scholar] [CrossRef]
  12. Torkaman, H.; Ghaheri, A.; Keyhani, A. Design of Rotor Excited Axial Flux-Switching Permanent Magnet Machine. IEEE Trans. Energy Convers. 2018, 33, 1175–1183. [Google Scholar] [CrossRef]
  13. Wang, X.G.; Zhao, M.; Zhou, Y.; Wan, Z.W.; Xu, W. Design and Analysis for Multi-Disc Coreless Axial-Flux Permanent-Magnet Synchronous Machine. IEEE Trans. Appl. Supercond. 2022, 31, 5203804. [Google Scholar] [CrossRef]
  14. Hwang, C.-C.; Li, P.-L.; Chuang, F.C.; Liu, C.-T.; Huang, K.-H. Optimization for Reduction of Torque Ripple in an Axial Flux Permanent Magnet Machine. IEEE Trans. Magn. 2009, 45, 1760–1763. [Google Scholar] [CrossRef]
  15. Cetin, E.; Daldaban, F. Reducing Torque Ripples of the Axial Flux PM Motors by Magnet Stepping and Shifting. Eng. Technol. Appl. Sci. 2018, 8, 2385–2388. [Google Scholar] [CrossRef]
  16. Torres, J.; Pena, R.; Riedemann, J.; Tapia, J.; Moncada, R.; Jara, W.; Pesce, C. Direct power control strategy for an axial flux permanent magnet synchronous machine. Electr. Eng. 2020, 102, 481–491. [Google Scholar] [CrossRef]
  17. Bouyahia, O.; Betin, F.; Yazidi, A. Fault-Tolerant Fuzzy Logic Control of a 6-Phase Axial Flux Permanent-Magnet Synchronous Generator. Energies 2022, 15, 1301. [Google Scholar] [CrossRef]
  18. Lu, H.X.; Li, J.; Qu, R.H.; Ye, D.L.; Xiao, L.Y. Reduction of Unbalanced Axial Magnetic Force in Postfault Operation of a Novel Six-Phase Double-Stator Axial-Flux PM Machine Using Model Predictive Control. IEEE Trans. Ind. Appl. 2017, 53, 5461–5469. [Google Scholar] [CrossRef]
  19. Kahourzade, S.; Mahmoudi, A.; Ping, H.W.; Uddin, M.N. A Comprehensive Review of Axial-Flux Permanent-Magnet Machines. Can. J. Elect. Comput. E 2014, 37, 19–33. [Google Scholar] [CrossRef]
  20. Habib, A.; Zainuri, M.A.A.M.; Che, H.S.; Ibrahim, A.A.; Abd Rahim, N.; Alaas, Z.M.; Ahmed, M.M.R. A systematic review on current research and developments on coreless axial-flux permanent-magnet machines. IET Electr. Power. App. 2022, 16, 1095–1116. [Google Scholar] [CrossRef]
  21. Zhao, J.L.; Lu, Z.L.; Han, Q.F.; Wang, L.; Lin, M.Y. An Overview on Development of Axial Flux Permanent Magnet Motor System and the Key Technology. Proc. CSEE 2022, 42, 2744–2764. [Google Scholar]
  22. Tehrani, G.G.; Dardel, M.; Pashaei, M.H. Passive vibration absorbers for vibration reduction in the multi-bladed rotor with rotor and stator contact. Acta Mech 2019, 231, 597–623. [Google Scholar] [CrossRef]
  23. Xia, B.; Shen, J.-X.; Luk, P.C.-K.; Fei, W.Z. Comparative Study of Air-Cored Axial-Flux Permanent-Magnet Machines with Different Stator Winding Configurations. IEEE Trans. Ind. Electron. 2015, 62, 846–856. [Google Scholar] [CrossRef]
  24. Syed, Q.A.S.; Kurtovic, H.; Hahn, I. Double Stator and Single Rotor Type Single-Phase Flux Switching Axial Flux Permanent Magnet Motor. In Proceedings of the 20th IEEE International Conference on Electrical Machines and Systems (ICEMS), Sydney, Australia, 11–17 August 2017. [Google Scholar]
  25. Habib, A.; Che, H.S.; Abd Rahim, N.; Tousizadeh, M.; Sulaiman, E. A fully coreless Multi-Stator Multi-Rotor (MSMR) AFPM generator with combination of conventional and Halbach magnet arrays. Alex. Eng. J. 2020, 59, 589–600. [Google Scholar] [CrossRef]
  26. Polat, M.; Yildiz, A.; Akinci, R. Performance Analysis and Reduction of Torque Ripple of Axial Flux Permanent Magnet Synchronous Motor Manufactured for Electric Vehicles. IEEE Trans. Magn. 2021, 57, 8106809. [Google Scholar] [CrossRef]
  27. Hou, J.; Geng, W.W.; Zhu, T.; Li, Q. Topological Principle and Electromagnetic Performance of a Novel Axial-Flux Hybrid-Excitation In-wheel Motor. In Proceedings of the 2021 23rd European Conference on Power Electronics and Applications, Ghent, Belgium, 6–10 September 2021. [Google Scholar]
  28. Gholamian, S.A.; Ardebili, M.; Abbaszadeh, K. Selecting and Construction of High Power Density Double-Sided Axial Flux Slotted Permanent Magnet Motors for Electric Vehicles. Int. Rev. Electr. Eng.-I. 2009, 4, 477–484. [Google Scholar]
  29. De Donato, G.; Capponi, F.G.; Borocci, G.; Caricchi, F.; Beneduce, L.; Fratelli, L.; Tarantino, A. Omega-Shaped Axial-Flux Permanent-Magnet Machine for Direct-Drive Applications with Constrained Shaft Height. IEEE Trans. Ind. Appl. 2015, 51, 3050–3058. [Google Scholar] [CrossRef]
  30. Aydin, M.; Huang, S.R.; Lipo, T.A. A new axial flux surface mounted permanent magnet machine capable of field control. In Proceedings of the 2002 IEEE Industry Applications Society (IAS), Pittsburgh, PA, USA, 13–18 October 2002; pp. 1250–1257. [Google Scholar]
  31. Mohamed, A.H.; Hemeida, A.; Rashekh, A.; Vansompel, H.; Arkkio, A.; Sergeant, P. A 3D Dynamic Lumped Parameter Thermal Network of Air-Cooled YASA Axial Flux Permanent Magnet Synchronous Machine. Energies 2018, 11, 774. [Google Scholar] [CrossRef] [Green Version]
  32. Benlamine, R.; Dubas, F.; Espanet, C.; Randi, S.-A.; Lhotellier, D. Design of an axial-flux interior permanent-magnet synchronous motor for automotive application: Performance comparison with electric motors used in EVs and HEVs. In Proceedings of the 2014 IEEE Vehicle Power and Propulsion Conference (VPPC), Coimbra, Portugal, 27–30 October 2014. [Google Scholar]
  33. Li, J.; Lu, Y.; Cho, Y.-H.; Qu, R.H. Design, Analysis, and Prototyping of a Water-Cooled Axial-Flux Permanent-Magnet Machine for Large-Power Direct-Driven Applications. IEEE Trans. Ind. Appl. 2019, 55, 3555–3565. [Google Scholar] [CrossRef]
  34. Friedrich, L.A.J.; Bastiaens, K.; Gysen, B.L.J.; Krop, D.C.J.; Lomonova, E.A. Design of an Axial-Flux Permanent Magnet Machine for a Solar-Powered Electric Vehicle. In Proceedings of the 2018 Thirteenth International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte Carlo, Monaco, 10–12 April 2018. [Google Scholar]
  35. Wang, Y.H.; Lu, J.W.; Liu, C.C.; Lei, G.; Guo, Y.G.; Zhu, J.G. Development of a High-Performance Axial Flux PM Machine With SMC Cores for Electric Vehicle Application. IEEE Trans. Magn. 2019, 55, 8105304. [Google Scholar] [CrossRef]
  36. Larbi, B.; Hatti, M.; Koozi, K.; Ghadbane, A. Design and Investigation of Axial Flux Permanent Magnet Synchronous Machine for electric vehicles. In Proceedings of the 2018 International Conference on Communications and Electrical Engineering (ICCEE), Eloued, Algeria, 17–18 December 2018; pp. 180–185. [Google Scholar]
  37. Takahashi, T.; Takemoto, M.; Ogasawara, S.; Ogawa, T.; Arita, H.; Daikoku, A. Development of a Consequent-Pole-PM-Type Axial-Gap Motor with DC Field Winding. IEEE Trans. Ind. Appl. 2021, 57, 4363–4375. [Google Scholar] [CrossRef]
  38. De Bisschop, J.; Abdallh, A.A.E.; Sergeant, P.; Dupre, L. Analysis and selection of harmonics sensitive to demagnetisation faults intended for condition monitoring of double rotor axial flux permanent magnet synchronous machines. IET Electr. Power. Appl. 2018, 12, 486–493. [Google Scholar] [CrossRef] [Green Version]
  39. Di Gerlando, A.; Foglia, G.M.; Iacchetti, M.F.; Perini, R. Parasitic Currents in Stray Paths of Some Topologies of YASA AFPM Machines: Trend with Machine Size. IEEE Trans. Ind. Electron. 2016, 63, 2746–2756. [Google Scholar] [CrossRef]
  40. Xu, L.J.; Xu, Y.L.; Gong, J.L. Analysis and Optimization of Cogging Torque in Yokeless and Segmented Armature Axial-Flux Permanent-Magnet Machine with Soft Magnetic Composite Core. IEEE Trans. Magn. 2018, 54, 8106005. [Google Scholar] [CrossRef]
  41. Fard, J.R.; Ardebili, M. Design and Control of a Novel Yokeless Axial Flux-Switching Permanent-Magnet Motor. IEEE Trans. Energy Convers. 2019, 34, 631–642. [Google Scholar] [CrossRef]
  42. Chang, J.J.; Fan, Y.E.; Wu, J.L.; Zhu, B. A Yokeless and Segmented Armature Axial Flux Machine with Novel Cooling System for In-Wheel Traction Applications. IEEE Trans. Ind. Electron. 2021, 68, 4131–4140. [Google Scholar] [CrossRef]
  43. Taran, N.; Klink, D.; Heins, G.; Rallabandi, V.; Patterson, D.; Ionel, D.M. A Comparative Study of Yokeless and Segmented Armature Versus Single Sided Axial Flux PM Machine Topologies for Electric Traction. IEEE Trans. Ind. Appl. 2022, 58, 325–335. [Google Scholar] [CrossRef]
  44. Axial-flux Designs Rev Up the Future of Electric Motors. Available online: https://www.allaboutcircuits.com/news/axial-flux-designs-rev-up-future-electric-motors/ (accessed on 11 October 2022).
  45. High Power & Torque Axial Flux Electric Motor. Available online: https://www.yasa.com/products/yasa-750/ (accessed on 10 October 2022).
  46. Axial-Flux Permanent-Magnet motors. Available online: http://www.magelec.cn/products/classify (accessed on 11 October 2022).
  47. Si, J.K.; Zhang, T.X.; Hu, Y.H.; Gan, C.; Li, Y.S. An Axial-Flux Dual-Rotor Slotless Permanent Magnet Motor with Novel Equidirectional Toroidal Winding. IEEE Trans. Energy Convers. 2022, 37, 1752–1763. [Google Scholar] [CrossRef]
  48. Kalender, O.; Ege, Y.; Nazlibilek, S. Design and determination of stator geometry for axial flux permanent magnet free rod rotor synchronous motor. Measurement 2011, 44, 1753–1760. [Google Scholar] [CrossRef]
  49. Carpi, T.; Bonnet, M.; Touhami, S.; Lefevre, Y.; Llibre, J.F. Unified Sizing Model Approach for Radial and Axial Flux Permanent Magnet Machines. In Proceedings of the 24th International Conference on Electrical Machines (ICEM), Gothenburg, Sweden, 23–26 August 2020; pp. 359–365. [Google Scholar]
  50. Huang, S.R.; Luo, J.; Leonardi, F.; Lipo, T.A. A general approach to sizing and power density equations for comparison of electrical machines. IEEE Trans. Ind. Appl. 1998, 34, 92–97. [Google Scholar] [CrossRef] [Green Version]
  51. Chen, A.Y.; Nilssen, R.; Nysveen, A. Performance Comparisons Among Radial-Flux, Multistage Axial-Flux, and Three-Phase Transverse-Flux PM Machines for Downhole Applications. IEEE Trans. Ind. Appl. 2010, 46, 779–789. [Google Scholar] [CrossRef]
  52. Huang, S.R.; Luo, J.; Leonardi, F.; Lipo, T.A. A comparison of power density for axial flux machines based on general purpose sizing equations. IEEE Trans. Energy Convers. 1999, 14, 185–191. [Google Scholar] [CrossRef]
  53. Wang, M.Q.; Tong, C.D.; Song, Z.Y.; Liu, J.Q.; Zheng, P. Performance Analysis of an Axial Magnetic-Field-Modulated Brushless Double-Rotor Machine for Hybrid Electric Vehicles. IEEE Trans. Ind. Electron. 2018, 66, 806–817. [Google Scholar] [CrossRef]
  54. Yesilbag, E.; Ertugrul, Y.; Ergene, L. Axial flux PM BLDC motor design methodology and comparison with a radial flux PM BLDC motor. Turk. J. Electr. Eng. Comput. Sci. 2017, 25, 3455–3467. [Google Scholar] [CrossRef]
  55. Kim, J.H.; Choi, W.; Sarlioglu, B. Closed-Form Solution for Axial Flux Permanent-Magnet Machines with a Traction Application Study. IEEE Trans. Ind. Appl. 2016, 52, 1775–1784. [Google Scholar] [CrossRef]
  56. Wang, C.; Zhang, Z.R.; Liu, Y.; Geng, W.W.; Gao, H.M. Effect of Slot-Pole Combination on the Electromagnetic Performance of Ironless Stator AFPM Machine with Concentrated Windings. IEEE Trans. Energy Convers. 2020, 35, 1098–1109. [Google Scholar] [CrossRef]
  57. Yazdan, T.; Kwon, B.I. Electromagnetic design and performance analysis of a two-phase AFPM BLDC motor for the only-pull drive technique. IET Electr. Power Appl. 2018, 12, 999–1005. [Google Scholar] [CrossRef]
  58. Dwivedi, A.; Singh, S.K.; Srivastava, R.K. Analysis and Performance Evaluation of Axial Flux Permanent Magnet Motors. IEEE Trans. Ind. Appl. 2018, 54, 1765–1772. [Google Scholar] [CrossRef]
  59. Huang, Q.; Luo, L.; Zhu, L.W. Design and Research of Axial Flue Permanent Magnet Motor for Electric Vehicle. In Proceedings of the 3rd IEEE International Electrical and Energy Conference (CIEEC), Beijing, China, 7–9 September 2019; pp. 1918–1923. [Google Scholar]
  60. Guney, O.F.; Celik, A.; Bozkurt, A.F.; Erkan, K. Design and analysis of a high speed double-sided axial flux permanent magnet motor suspended vertically by magnetic bearings. Int. J. Appl. Electrom. 2021, 64, S297–S310. [Google Scholar] [CrossRef]
  61. Jung, J.W.; Park, H.I.; Hong, J.P.; Lee, B.H. A Novel Approach for 2-D Electromagnetic Field Analysis of Surface Mounted Permanent Magnet Synchronous Motor Taking into Account Axial End Leakage Flux. IEEE Trans. Magn. 2017, 53, 8208104. [Google Scholar] [CrossRef]
  62. Mahmoudi, A.; Rahim, N.A.; Hew, W.P. An analytical complementary FEA tool for optimizing of axial-flux permanent-magnet machines. Int. J. Appl. Electrom. 2011, 37, 19–34. [Google Scholar] [CrossRef] [Green Version]
  63. Capponi, F.G.; De Donato, G.; Caricchi, F. Recent Advances in Axial-Flux Permanent-Magnet Machine Technology. IEEE Trans. Ind. Appl. 2013, 48, 2190–2205. [Google Scholar] [CrossRef]
  64. Aycicek, E.; Bekiroglu, N.; Ozcira, S. An Experimental Analysis on Cogging Torque of Axial Flux Permanent Magnet Synchronous Machine. P. Natl. A Sci. India A 2016, 86, 95–101. [Google Scholar] [CrossRef]
  65. Kim, J.H.; Li, Y.J.; Cetin, E.; Sarlioglu, B. Influence of Rotor Tooth Shaping on Cogging Torque of Axial Flux-Switching Permanent Magnet Machine. IEEE Trans. Ind. Appl. 2019, 55, 1290–1298. [Google Scholar] [CrossRef]
  66. Huang, R.D.; Liu, C.H.; Song, Z.X.; Zhao, H. Design and Analysis of a Novel Axial-Radial Flux Permanent Magnet Machine with Halbach-Array Permanent Magnets. Energies 2021, 14, 3639. [Google Scholar] [CrossRef]
  67. Carpi, T.; Lefevre, Y.; Henaux, C.; Llibre, J.F.; Harribey, D. 3-D Hybrid Model of the Axial-Flux Motor Accounting Magnet Shape. IEEE Trans. Magn. 2022, 58, 8105004. [Google Scholar] [CrossRef] [Green Version]
  68. Zhu, L.L.; Xu, D.; Li, Q.; Sun, W.; Hu, Y.Q. Analysis and Optimization of Equivalent Magnetic Circuit Model for a Hybrid Axial Field Flux-Switching Permanent Magnet Machine. In Proceedings of the 21st International Conference on Electrical Machines and Systems (ICEMS), Jeju, Korea, 7–10 October 2018; pp. 407–412. [Google Scholar]
  69. Patel, A.N.; Suthar, B.N. Cogging Torque Reduction of Sandwiched Stator Axial Flux Permanent Magnet Brushless DC Motor using Magnet Notching Technique. Int. J. Eng. 2019, 32, 940–946. [Google Scholar]
  70. Gulec, M.; Aydin, M. Implementation of different 2D finite element modelling approaches in axial flux permanent magnet disc machines. IET Electr. Power Appl. 2018, 12, 195–202. [Google Scholar] [CrossRef]
  71. Kim, K.H.; Woo, D.K. Novel Quasi-Three-Dimensional Modeling of Axial Flux In-Wheel Motor with Permanent Magnet Skew. IEEE Access 2022, 10, 98842–98854. [Google Scholar] [CrossRef]
  72. Huang, Y.K.; Zhou, T.; Dong, J.N.; Lin, H.Y.; Yang, H.; Cheng, M. Magnetic Equivalent Circuit Modeling of Yokeless Axial Flux Permanent Magnet Machine with Segmented Armature. IEEE Trans. Magn. 2014, 50, 8104204. [Google Scholar] [CrossRef]
  73. Tong, W.M.; Wang, S.; Dai, S.H.; Wu, S.N.; Tang, R.Y. A Quasi-Three-Dimensional Magnetic Equivalent Circuit Model of a Double-Sided Axial Flux Permanent Magnet Machine Considering Local Saturation. IEEE Trans. Energy Convers. 2018, 33, 2163–2173. [Google Scholar] [CrossRef]
  74. Zhao, J.; Ma, T.K.; Liu, X.D.; Zhao, G.D.; Dong, N. Performance Analysis of a Coreless Axial-Flux PMSM by an Improved Magnetic Equivalent Circuit Model. IEEE Trans. Energy Convers. 2021, 36, 2120–2130. [Google Scholar] [CrossRef]
  75. Zhang, Y.P.; Wang, Y.M.; Gao, S.N. 3-D magnetic equivalent circuit model for a coreless axial flux permanent-magnet synchronous generator. IET Electr. Power App. 2021, 15, 1261–1273. [Google Scholar] [CrossRef]
  76. Gao, H.M.; Zhang, Z.R.; Wang, C.; Geng, W.W.; Liu, Y. Analysis of end effect in ironless stator AFPM machine via MEC model. IET Electr. Power App. 2020, 14, 147–156. [Google Scholar] [CrossRef]
  77. Wang, W.Q.; Zhou, S.Q.; Mi, H.J.; Wen, Y.D.; Liu, H.; Zhang, G.P.; Guo, J.Y. Sensitivity Analysis and Optimal Design of a Stator Coreless Axial Flux Permanent Magnet Synchronous Generator. Sustainability 2019, 11, 1414. [Google Scholar] [CrossRef] [Green Version]
  78. Johnson, M.; Gardner, M.C.; Toliyat, H.A. A Parameterized Linear 3D Magnetic Equivalent Circuit for Analysis and Design of Radial Flux Magnetic Gears-Part II: Evaluation. IEEE Trans. Energy Convers. 2021, 36, 2903–2911. [Google Scholar] [CrossRef]
  79. Benmessaoud, Y.; Ouamara, D.; Dubas, F.; Hilairet, M. Investigation of Volumic Permanent-Magnet Eddy-Current Losses in Multi-Phase Synchronous Machines from Hybrid Multi-Layer Model. Math. Comput. Appl. 2020, 25, 14. [Google Scholar] [CrossRef] [Green Version]
  80. Lim, D.K.; Woo, D.K.; Kim, I.W.; Ro, J.S.; Jung, H.K. Cogging Torque Minimization of a Dual-Type Axial-Flux Permanent Magnet Motor Using a Novel Optimization Algorithm. IEEE Trans. Magn. 2013, 49, 5106–5111. [Google Scholar] [CrossRef]
  81. Verkroost, L.; Vansompel, H.; De Belie, F.; Sergeant, P. Comparison Between Two Fault Tolerant Deadbeat Controllers under Partial Demagnetization Faults in Permanent Magnet Synchronous Machines. In Proceedings of the 24th International Conference on Electrical Machines (ICEM), Gothenburg, Sweden, 23–26 August 2020; pp. 1074–1080. [Google Scholar]
  82. Lok, C.L.; Vengadaesvaran, B.; Ramesh, S. Implementation of hybrid pattern search-genetic algorithm into optimizing axial-flux permanent magnet coreless generator (AFPMG). Electr. Eng. 2017, 99, 751–761. [Google Scholar] [CrossRef]
  83. Fard, J.R.; Ardebili, M. Design and prototyping of the novel axial flux-switching permanent-magnet motor. COMPEL—Int. J. Comput. Math. Electr. Electron. Eng. 2018, 37, 890–910. [Google Scholar] [CrossRef]
  84. Meo, S.; Zohoori, A.; Vahedi, A. Optimal design of permanent magnet flux switching generator for wind applications via artificial neural network and multi-objective particle swarm optimization hybrid approach. Energy Convers. Manag. 2016, 110, 230–239. [Google Scholar] [CrossRef]
  85. Fard, J.R.; Ardebili, M. Optimal Design and Analysis of the Novel Low Cogging Torque Axial Flux-Switching Permanent-Magnet Motor. Electr. Pow. Compo. Sys. 2019, 46, 1330–1339. [Google Scholar] [CrossRef]
  86. Patel, A.N.; Suthar, B.N. Design Optimization of Axial Flux Surface Mounted Permanent Magnet Brushless DC Motor For Electrical Vehicle Based on Genetic Algorithm. Int. J. Eng. 2018, 31, 1050–1056. [Google Scholar]
  87. Shariati, O.; Behnamfar, A.; Potter, B. An Integrated Elitist Approach to the Design of Axial Flux Permanent Magnet Synchronous Wind Generators (AFPMWG). Energies 2022, 15, 3262. [Google Scholar] [CrossRef]
  88. Deng, W.Z.; Zuo, S.G. Noise reduction of axial-flux motors by combining various pole-arc coefficients and circumferential shifting of permanent magnets: Analytical approach. IET Electr. Power Appl. 2019, 13, 951–957. [Google Scholar] [CrossRef]
  89. Gulec, M.; Aydin, M. Design and Optimization of an Axial Flux Permanent Magnet Assisted Eddy Current Brake. In Proceedings of the 12th International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turke, 26–28 November 2020; pp. 64–67. [Google Scholar]
  90. Li, H.F.; Cui, L.F.; Ma, Z.G.; Li, B. Multi-Objective Optimization of the Halbach Array Permanent Magnet Spherical Motor Based on Support Vector Machine. Energies 2020, 13, 5704. [Google Scholar] [CrossRef]
  91. Abd-Rabou, A.S.; Marei, M.I.; Badr, M.A.L.; Basha, M.A. Design Optimization of Axial Flux Permanent Magnet Brushless DC Micromotor Using Response Surface Methodology and Bat Algorithm. In Proceedings of the 44th Annual Conference of the IEEE Industrial-Electronics-Society (IECON), Washington, DC, USA, 20–23 October 2018; pp. 471–476. [Google Scholar]
  92. Zhu, J.; Li, G.H.; Cao, D.; Zhang, Z.Y. Voltage regulation Rate and THD optimization analysis of coreless axial flux PM synchronous generator for wind power generation. IEEJ Trans. Electr. Electron. Eng. 2019, 14, 1485–1493. [Google Scholar]
  93. Rostami, N. Particle swarm optimization approach to optimal design of an AFPM traction machine for different driving conditions. Turk. J. Electr. Eng. Co. 2019, 27, 3234–3246. [Google Scholar] [CrossRef] [Green Version]
  94. Chakkarapani, K.; Thangavelu, T.; Dharmalingam, K.; Thandavarayan, P. Multiobjective design optimization and analysis of magnetic flux distribution for slotless permanent magnet brushless DC motor using evolutionary algorithms. J. Magn. Magn. Mater. 2019, 476, 524–537. [Google Scholar] [CrossRef]
  95. Abd-Rabou, A.S.; Marei, M.I.; El-Sattar, A.A.; Basha, M.A. Multiobjective Design optimization of Axial Flux Permanent Magnet Brushless DC Micromotor Using Response Surface Methodology and Multi-Verse optimization Algorithm. In Proceedings of the IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology (JEEIT), Amman, Jordan, 9–11 April 2019; pp. 13–18. [Google Scholar]
  96. Zhao, S.D.; Liang, J.T.; Zhao, Y.Q. Optimization Design and Direct Torque Control of a Flux Concentrating Axial Flux Permanent Magnet Motor for Direct Driving System. Electr. Pow. Compo. Sys. 2014, 42, 1517–1529. [Google Scholar] [CrossRef]
  97. Zhao, J.L.; Lin, M.Y.; Xu, D.; Hao, L.; Zhang, W. Vector Control of a Hybrid Axial Field Flux-Switching Permanent Magnet Machine Based on Particle Swarm Optimization. IEEE Trans. Magn. 2015, 51, 8204004. [Google Scholar] [CrossRef]
  98. Haddad, R.Z. Iron Loss Analysis in Axial Flux Permanent Magnet Synchronous Motors with Soft Magnetic Composite Core Material. IEEE Trans. Energy Convers. 2022, 37, 295–303. [Google Scholar] [CrossRef]
  99. Liu, C.-T.; Lee, S.C. Magnetic field modeling and optimal operational control of a single-side axial-flux permanent magnet motor with center poles. J. Magn. Magn. Mater. 2006, 304, E454–E456. [Google Scholar] [CrossRef]
  100. Akhil, R.S.; Mini, V.P.; Mayadevi, N.; Harikumar, R. Modified Flux-Weakening Control for Electric Vehicle with PMSM Drive. IFAC-PapersOnLine 2020, 53, 325–331. [Google Scholar]
  101. Zhang, W.; Liang, X.Y.; Yu, F. Fault-Tolerant Control of Hybrid Excitation Axial Field Flux-Switching Permanent Magnet Machines. IEEE Trans. Magn. 2018, 54, 8106305. [Google Scholar] [CrossRef]
  102. Wilson, R.; Gandhi, R.; Kumar, A.; Roy, R. Performance analysis of twin-rotor axial flux permanent magnet synchronous motor for in-wheel electric vehicle applications with sensorless optimized vector control strategy. In Proceedings of the 9th IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES 2020), Jaipur, India, 16–19 December 2020. [Google Scholar]
  103. Neethu, S.; Pal, S.; Wankhede, A.K.; Fernandes, B.G. High Performance Axial Flux Permanent Magnet Synchronous Motor for High Speed Applications. In Proceedings of the 43rd Annual Conference of the IEEE-Industrial-Electronics-Society (IECON), Beijing, China, 29 October–1 November 2017; pp. 5093–5098. [Google Scholar]
  104. Luo, X.; Niu, S.X.; Fu, W.N. Design and Sensorless Control of a Novel Axial-Flux Permanent Magnet Machine for In-Wheel Applications. IEEE Trans. Appl. Supercond. 2016, 26, 0608105. [Google Scholar] [CrossRef]
  105. Malyshev, A.; Ivanov, A. Direct Torque Control of the Axial Flux Permanent Magnet Motor. In Proceedings of the 13th International IEEE Scientific and Technical Conference on Dynamics of Systems, Mechanisms and Machines, Omsk, Russia, 5–7 November 2019. [Google Scholar]
  106. Siami, M.; Gholamian, S.A.; Yousefi, M. A Comparative Study Between Direct Torque Control and Predictive Torque Control for Axial Flux Permanent Magnet Synchronous Machines. J. Electr. Eng. Slovak. 2014, 64, 346–353. [Google Scholar] [CrossRef]
  107. Fard, J.R.; Ardebili, M. Dynamic performance of the novel axial flux-switching permanent magnet motor. COMPEL—Int. J. Comput. Math. Electr. Electron. Eng. 2017, 36, 1270–1286. [Google Scholar]
  108. Nguyen, T.D.; Foo, G.; Tseng, K.J.; Vilathgamuwa, D.M. Modeling and Sensorless Direct Torque and Flux Control of a Dual-Airgap Axial Flux Permanent-Magnet Machine with Field-Weakening Operation. IEEE-Asme Trans. Mech. 2014, 19, 412–422. [Google Scholar] [CrossRef]
  109. Zhao, J.F.; Hua, M.Q.; Liu, T.Z. Research on a Sliding Mode Vector Control System Based on Collaborative Optimization of an Axial Flux Permanent Magnet Synchronous Motor for an Electric Vehicle. Energies 2018, 11, 3116. [Google Scholar] [CrossRef] [Green Version]
  110. Yang, G.D.; Lin, M.Y.; Li, N.; Hao, L. Vector Control of Stator-Permanent Magnet Memory Machine Based on Three Magnetization State Manipulations. J. Electr. Eng. Technol. 2019, 14, 169–177. [Google Scholar] [CrossRef]
  111. Zhao, J.F.; Zheng, L.X.; Wang, S.; Hua, M.Q. Research on Deadbeat Current Prediction Vector Control System of Axial Flux Permanent Magnet Synchronous Motor for Electric Bus Based on Efficiency Optimal Torque Distribution Method. IEEE Access 2019, 7, 128384–128393. [Google Scholar] [CrossRef]
  112. Yang, G.D.; Lin, M.Y.; Li, N.; Fu, X.H.; Liu, K.; Tan, G.Y.; Zhang, B.B.; Kong, Y. Flux-weakening Stage Control of Hybrid Permanent Magnet Axial Field Flux-switching Memory Machines. Proc. CSEE 2017, 37, 6557–6566. [Google Scholar]
  113. Zhai, L.G.; Zhang, W.; Liang, X.Y.; Yang, Z.X.; Wang, J.L.; Zhu, Y.F. Speed Sensorless Control of Axial Field Flux-Switching Permanent Magnet Machine Based on Improved Adaptive Sliding Mode Observer. In Proceedings of the 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 11–14 August 2019; pp. 1475–1479. [Google Scholar]
  114. Yuan, X.Q.; Zhang, W.; Yu, F.; Gu, W.G. Sliding Mode Control of Axial Field Flux-Switching Permanent Magnet Machine. In Proceedings of the 20th IEEE International Conference on Electrical Machines and Systems (ICEMS), Sydney, Australia, 11–17 August 2017. [Google Scholar]
  115. Verkroost, L.; Druant, J.; Vansompel, H.; De Belie, F.; Sergeant, P. Performance Degradation of Surface PMSMs with Demagnetization Defect under Predictive Current Control. Energies 2019, 12, 782. [Google Scholar] [CrossRef] [Green Version]
  116. Zhang, W.; Wang, J.L.; Liang, X.Y.; Yang, Z.X. Position Sensorless Control of a Hybrid Excitation Axial Flux-switching Permanent Magnet Machine in Full Speed Range. Proc. CSEE 2021, 41, 4646–4655. [Google Scholar]
  117. Zhao, J.L.; Quan, X.W.; Lin, M.Y. Model Predictive Torque Control of a Hybrid Excited Axial Field Flux-Switching Permanent Magnet Machine. IEEE Access 2021, 8, 33703–33712. [Google Scholar] [CrossRef]
  118. Ahmed, A.A.; Koh, B.K.; Lee, Y.I. A Comparison of Finite Control Set and Continuous Control Set Model Predictive Control Schemes for Speed Control of Induction Motors. IEEE Trans. Ind. Inform. 2018, 14, 1334–1346. [Google Scholar] [CrossRef]
  119. Yuan, X.Q.; Zhang, W.; Liang, X.Y.; Hao, L.; Liang, Y.W. Research of Control Methods for Axial Field Flux-Switching Permanent Magnet Machine. In Proceedings of the 21st International Conference on Electrical Machines and Systems (ICEMS), Jeju, South Korea, 7–10 October 2018; pp. 1218–1222. [Google Scholar]
  120. Zhao, J.L.; Quan, X.W.; Jing, M.D.; Lin, M.Y.; Li, N.A. Design, Analysis and Model Predictive Control of an Axial Field Switched-Flux Permanent Magnet Machine for Electric Vehicle/Hybrid Electric Vehicle Applications. Energies 2018, 11, 1859. [Google Scholar] [CrossRef] [Green Version]
  121. Yang, G.D.; Lin, M.Y.; Li, N.; Fu, X.H.; Liu, K. Maximum torque output control of hybrid permanent magnet axial field flux-switching memory machine. In Proceedings of the 2017 IEEE Energy Conversion Congress and Exposition (ECCE), Cincinnati, OH, USA, 1–5 October 2017; pp. 1212–1219. [Google Scholar]
  122. Yang, Z.X.; Zhang, W.; Liang, X.Y.; Wang, J.L.; Zhai, L.G.; Zhu, Y.F. Position Sensorless Control of Hybrid Excitation Axial Field Flux-Switching Permanent Magnet Machine Based on Model Reference Adaptive System. In Proceedings of the 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 11–14 August 2019; pp. 1006–1010. [Google Scholar]
  123. Wang, S.; Zhao, J.F.; Liu, T.Z.; Hua, M.Q. Adaptive Robust Control System for Axial Flux Permanent Magnet Synchronous Motor of Electric Medium Bus Based on Torque Optimal Distribution Method. Energies 2020, 12, 4681. [Google Scholar] [CrossRef] [Green Version]
  124. Zhang, W.; Yang, Z.X.; Zhai, L.G.; Wang, J.L. Speed Sensorless Control of Hybrid Excitation Axial Field Flux-Switching Permanent-Magnet Machine Based on Model Reference Adaptive System. IEEE Access 2020, 8, 22013–22024. [Google Scholar] [CrossRef]
  125. Zhang, Y.C.; Xia, B.; Yang, H.T. Performance evaluation of an improved model predictive control with field oriented control as a benchmark. IET Electr. Power Appl. 2017, 11, 677–687. [Google Scholar] [CrossRef]
  126. Geweth, D.; Vollmer, U.; Diehl, M. An Observer based Field Oriented Economic Model Predictive Control Approach for Permanent Magnet Synchronous Motors. In Proceedings of the 30th Mediterranean Conference on Control and Automation (MED), Vouliagmeni, Greece, 28 June–1 July 2022; pp. 145–151. [Google Scholar]
Machines 10 01178 g001 550
Figure 1. The major points of this paper.
Figure 1. The major points of this paper.
Machines 10 01178 g001
Machines 10 01178 g002 550
Figure 2. Analysis of references: (a) classified by year and (b) proportion in past 5 years.
Figure 2. Analysis of references: (a) classified by year and (b) proportion in past 5 years.
Machines 10 01178 g002
Machines 10 01178 g003 550
Figure 3. Four typical types of topological structures of AFPM motors.
Figure 3. Four typical types of topological structures of AFPM motors.
Machines 10 01178 g003
Machines 10 01178 g004 550
Figure 4. The topological structures of AFIR and TORUS: (a) AFIR type; (b) TORUS type. Adapted from Ref. [31]. Copyright 2018 MDPI.
Figure 4. The topological structures of AFIR and TORUS: (a) AFIR type; (b) TORUS type. Adapted from Ref. [31]. Copyright 2018 MDPI.
Machines 10 01178 g004
Machines 10 01178 g005 550
Figure 5. The YASA-type AFPM motors: (a) exploded view. Adapted with permission from Ref. [38]. Copyright 2018 John Wiley and Sons. (b) Profile view. Adapted from Ref. [31]. Copyright 2018 MDPI.
Figure 5. The YASA-type AFPM motors: (a) exploded view. Adapted with permission from Ref. [38]. Copyright 2018 John Wiley and Sons. (b) Profile view. Adapted from Ref. [31]. Copyright 2018 MDPI.
Machines 10 01178 g005
Machines 10 01178 g006 550
Figure 6. Electromagnetic modeling of FEA. (a) Diagram of converting 3D model to 2D model. Adapted with permission from Ref. [70]. Copyright 2017 John Wiley and Sons. (b) Diagram of novel quasi-3-D model. Adapted from Ref. [71].
Figure 6. Electromagnetic modeling of FEA. (a) Diagram of converting 3D model to 2D model. Adapted with permission from Ref. [70]. Copyright 2017 John Wiley and Sons. (b) Diagram of novel quasi-3-D model. Adapted from Ref. [71].
Machines 10 01178 g006
Machines 10 01178 g007 550
Figure 7. Electromagnetic modeling of MEC. (a) 3-D MEC model considering magnetic leakage and fringing flux. Adapted with permission from Ref. [75]. Copyright 2021 John Wiley and Sons. (b) MEC model considering end leakage fluxes. Adapted with permission from Ref. [76]. Copyright 2019 John Wiley and Sons.
Figure 7. Electromagnetic modeling of MEC. (a) 3-D MEC model considering magnetic leakage and fringing flux. Adapted with permission from Ref. [75]. Copyright 2021 John Wiley and Sons. (b) MEC model considering end leakage fluxes. Adapted with permission from Ref. [76]. Copyright 2019 John Wiley and Sons.
Machines 10 01178 g007
Machines 10 01178 g008 550
Figure 8. ANN models. (a) ANN model adapted with permission from Ref. [84]. Copyright 2016 Elsevier. (b) Multi-layered perceptron ANN model. Adapted with permission from Ref. [85]. Copyright 2018 Taylor & Francis.
Figure 8. ANN models. (a) ANN model adapted with permission from Ref. [84]. Copyright 2016 Elsevier. (b) Multi-layered perceptron ANN model. Adapted with permission from Ref. [85]. Copyright 2018 Taylor & Francis.
Machines 10 01178 g008
Machines 10 01178 g009 550
Figure 9. Closed-loop field-oriented control realization method. Adapted with permission from Ref. [99]. Copyright 2006 Elsevier.
Figure 9. Closed-loop field-oriented control realization method. Adapted with permission from Ref. [99]. Copyright 2006 Elsevier.
Machines 10 01178 g009
Machines 10 01178 g010 550
Figure 10. DTC algorithms. (a) DTC algorithm adapted from Ref. [106]. (b) DTFC algorithm adapted with permission from Ref. [107]. Copyright 2017 Emerald Publishing Limited.
Figure 10. DTC algorithms. (a) DTC algorithm adapted from Ref. [106]. (b) DTFC algorithm adapted with permission from Ref. [107]. Copyright 2017 Emerald Publishing Limited.
Machines 10 01178 g010
Machines 10 01178 g011 550
Figure 11. Improved vector control based on three MS manipulations. (a) Three MS manipulations. (b) Vector control diagram based on three MS manipulations. (c) Speed. (d) Torque. Adapted with permission from Ref. [110]. Copyright 2019 Springer Nature.
Figure 11. Improved vector control based on three MS manipulations. (a) Three MS manipulations. (b) Vector control diagram based on three MS manipulations. (c) Speed. (d) Torque. Adapted with permission from Ref. [110]. Copyright 2019 Springer Nature.
Machines 10 01178 g011
Machines 10 01178 g012 550
Figure 12. The diagrams of speed sensorless control methods based on MRAS. (a) MRAS for stator current. (b) MRAS for stator flux linkage. (c) MRAS for simplified stator current. (d) Simulation performances comparison. Adapted from Ref. [124].
Figure 12. The diagrams of speed sensorless control methods based on MRAS. (a) MRAS for stator current. (b) MRAS for stator flux linkage. (c) MRAS for simplified stator current. (d) Simulation performances comparison. Adapted from Ref. [124].
Machines 10 01178 g012
Table
Table 1. List of literature survey.
Table 1. List of literature survey.
ScopeKeywordsResults
Web of Science and
Engineering Village
(Publisher: MDPI, Elsevier, IEEE, etc.)
➢
axial flux permanent magnet
✧
journal articles (100)
✧
conference articles (23)
✧
website reports (3)
➢
topological structure
➢
ovel
➢
design
➢
modeling
➢
optimization
➢
improved
➢
control algorithm
Table
Table 2. Summary of the optimization and design methods.
Table 2. Summary of the optimization and design methods.
MethodsOptimization ObjectivesVerification MethodsRef
EGA
➢
weight of the permanent magnets, efficiency, sinusoidal voltage
✧
3D-FEA
[87]
NSGA-II
➢
air-gap field, electromagnetic noise, 90 times rotation frequency
✧
3D-FEA
[88]
PSO
➢
air gap magnetic density fundamental wave amplitude, waveform distortion rate, rotor moment of inertia
✧
3D-FEA and experiment
[90]
MOMVO
➢
volume, joules efficiency
✧
against NSGA-II
[95]
Table
Table 3. Summary of the improved and novel algorithms.
Table 3. Summary of the improved and novel algorithms.
AlgorithmsComplexityResponseRobustnessRef
improved FOC vs. PIbasically samequicker response than PIbetter robustness[109]
improved FOC vs. PImore complex control than PIquicker response than PIbetter robustness[110]
MPTC vs. DTCmore complex control than DTCquicker response than DTCbetter robustness[119]
ARC vs. PIbasically samebetter response than PIbetter anti-interference ability[123]
MPC vs. FOCmore complex control than FOCquicker response than FOCbetter steady-state performance than FOC[125]
FO-EMPC vs. FOCmore complex control than FOCquicker response than FOCbetter robustness[126]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Hao, Z.; Ma, Y.; Wang, P.; Luo, G.; Chen, Y. A Review of Axial-Flux Permanent-Magnet Motors: Topological Structures, Design, Optimization and Control Techniques. Machines 2022, 10, 1178. https://doi.org/10.3390/machines10121178

AMA Style

Hao Z, Ma Y, Wang P, Luo G, Chen Y. A Review of Axial-Flux Permanent-Magnet Motors: Topological Structures, Design, Optimization and Control Techniques. Machines. 2022; 10(12):1178. https://doi.org/10.3390/machines10121178

Chicago/Turabian Style

Hao, Zhuo, Yangyang Ma, Pengyu Wang, Geng Luo, and Yisong Chen. 2022. "A Review of Axial-Flux Permanent-Magnet Motors: Topological Structures, Design, Optimization and Control Techniques" Machines 10, no. 12: 1178. https://doi.org/10.3390/machines10121178

APA Style

Hao, Z., Ma, Y., Wang, P., Luo, G., & Chen, Y. (2022). A Review of Axial-Flux Permanent-Magnet Motors: Topological Structures, Design, Optimization and Control Techniques. Machines, 10(12), 1178. https://doi.org/10.3390/machines10121178

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop