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This paper proposes a novel consequent‐pole dual‐stator linear permanent magnet vernier machine (DS‐LPMVM) with PM in the mover slot opening, which has a bi‐directional flux modulation effect. The novelty of the proposed machine consists of consequent‐pole double‐sided topology with toroidal windings placed in the mover slot, as well as PMs both on the stator and mover slot to improve the air gap magnetic field. The dual‐stator adopts misalignment structure to suppress detent force and produce steady thrust. The electromagnetic parameters of the proposed DS‐LPMVM are evaluated and quantitatively compared with the conventional linear permanent magnet vernier machine (C‐LPMVM) in terms of air‐gap flux density, no‐load back EMF, inductance, and thrust. The geometrical parameters are designed to reduce the detent force. By analyzing the optimized structure parameters of the two machines, the good electromagnetic performances of the proposed machine are verified by the finite element method (FEM) and semi‐analytical method, and both results of the two methods are basically the same. It is found that the amount of PMs for the proposed machine is reduced by 20% compared to the C‐LPMVM, but the average thrust is increased by 20.7% and the thrust ripple is reduced to 4.04%. The results show that the proposed DS‐LPMVM has better flux modulation effect and thrust characteristics than C‐LPMCM. Finally, a 12‐slot, 10‐pole pairs prototype was manufactured and tested. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Net zero and electrification targets are continuing to enforce a need for the development of high-performance electrical machines, increasingly based on the use of rare earth permanent magnets. Biased flux motors have the potential to overcome some of the disadvantages associated with more conventional electrical machines. Since their introduction, there has been a consistent trend towards new and improved topologies, all relying on the same principles of operation. In this paper, a new alternative operation is proposed where the magnetic flux density offset of each module is different. The resulting asymmetric biased excitations of the magnets leads to a flux concentration in the air gap. Placement of magnets in the slot-opening area is shown to produce a higher average torque at a higher power factor. It is mathematically shown that the conventional methods used to investigate the effect of each group of magnets separately cannot be used for the explanation of this operation principle. Therefore, it is necessary to simultaneously consider both groups of magnets in the magnetic equivalent circuit. Due to the use of magnets in these motors, thermal conditions are also investigated. Finally, a comprehensive comparison between several stator-situated-magnet motors is presented. The performance of the proposed motor is improved in terms of average torque, torque density, PM torque density, power factor, and overload capability. The torque density specifically has increased by 9%. Moreover, both motors have suitable thermal behaviour which confirms the validity of the demagnetization analysis. [ABSTRACT FROM AUTHOR]

To improve the torque performance of the axial-flux permanent-magnet motor (AFPMM), differential evolution (DE) and cuckoo search (CS) are proposed for optimizing the motor's structural parameters. The object of this research is an AFPMM with a single-rotor and double-stator configuration. Firstly, finite element analysis (FEA) and BP neural network machine learning (ML) were combined to obtain an ML calculator. This calculator is about the relationships between five input structural parameters of the motor and two output torque parameters (i.e., average torque and cogging torque). Then, an optimization objective function was designed to reduce the cogging torque while increasing the average output torque. And motor structural parameters were optimized using the DE and CS algorithms, respectively. Finally, air-gap flux density, average torque, cogging torque, and ripple torque before and after the optimization of the motor structure parameters are compared by FEA. The results show that both algorithms achieved almost the same optimized structural parameters. And the optimized motor has reduced cogging torque while increasing the average output torque and reducing the ripple torque. Compared with the CS, the DE is more advantageous in terms of faster iteration speed, shorter time to obtain the optimal solution, and less resource consumption. [ABSTRACT FROM AUTHOR]

This paper investigates the use of fractional-slot concentrated windings (FSCWs) in large-scale (MW level) offshore wind generators. It focuses specifically on a power rating of 3 MW and uses an existing direct-drive synchronous PM machine (DD-SPM) with 480s/160p and dual three-phase integer-slot winding (ISW) as a baseline. A multiple of the common 12s/10p FSCW machine is used that matches the electrical frequency of the ISW machine, yielding a 192s/160p dual three-phase machine. The hybrid star–delta connection has grown increasingly popular owing to its unique harmonic cancellation properties, which can help reduce rotor and PM eddy current losses in FSCW machines. In this paper, two dual three-phase star–delta-wound machines are scaled to 3 MW and included in the investigation. Specifically, a 384s/160p dual three-phase and dual star–delta winding machine, which is a multiplication of the 24s/10p machine, and a 192s/176p dual three-phase and dual star–delta winding machine, which is a multiplication of the 24s/22p machine, are used. These machines are investigated using finite element analysis (FEA) and compared on the basis of their air-gap flux density harmonics, open-circuit electro-motive force (EMF), torque performance, and losses and power. It is found that the proposed 384s/160p dual star–delta winding machine has the best electromagnetic performance of all, with a stator power that is 1.2% greater than that of the baseline ISW machine. However, this machine has a coil pitch of 2 and so loses the manufacturing and fault-tolerant advantage of having concentrated windings. If concentrated windings are desired, then the proposed 192s/176p dual star–delta winding machine is the best choice, with the stator power only 2.6% less than that of the baseline ISW machine, but unfortunately still has significant rotor and PM eddy current losses. [ABSTRACT FROM AUTHOR]

Axial flux permanent magnet (AFPM) machines are being increasingly used in several applications owing to their outstanding features. Most importantly, they are characterized by a high power-to-weight ratio, compactness, and high efficiency. Designers of AFPM generators seek to achieve the required performance and ensure the proper operation of the machine for the targeted application. Among many other parameters, the performance of the machine is highly dependent on the air gap magnetic flux density and no-load induced voltage. Accurate computation of such parameters helps minimize the overall design process. Therefore, the estimation of flux density plays a vital role in determining many other dependent parameters in AFPM machines. This manuscript provides a robust Correlated Analytical Method (CAM) for calculating the air gap magnetic flux density and no-load induced voltage of Coreless Axial Flux Permanent Magnet Generators (CAFPMG). CAM is an extended version of the Simplified Analytical Method (SAM) that is adjusted using correlated coefficients derived from an experimentally validated Three-Dimensional (3D) Finite Element Model (FEM). A complete procedure for the calculations is provided. The results showed the integrity of the CAM compared to the results obtained from the validated FEM. Such a technique will help designers of CAFPM machines perform parametric analysis and optimization in a fast and reliable manner. [ABSTRACT FROM AUTHOR]

This paper introduces a new spherical motion generator and presents a method for modeling its magnetic field and analyzing its moments. The generator employs an electromagnetic drive of a spherical motor as its driving method and utilizes a spherical parallel manipulator to execute the spherical motion. The combination of these two technologies offers several advantages, including a large workspace and high motion accuracy. The equivalent magnetizing current method is used in the magnetic field modeling and the average air-gap flux density is optimized to achieve a better magnetic field distribution, and the accuracy of the analytical model is verified by finite element simulations and experiments. • The electromagnetic-driven SMG merges the spherical parallel manipulator and motor. • A novel SMG is designed to provide large workspace and unlimited spinning motion. • Modeling the magnetic field of SMG as to optimize the magnetic pole arrangement. • The accuracy of the model is verified by finite element method and experiment. [ABSTRACT FROM AUTHOR]

In this article, rotor designs utilizing assisted-poles are investigated for a high-torque density spoke-type permanent magnet synchronous machine (PMSM) with fractional slot concentrated winding (FSCW) to explore the rich air-gap magnetic field harmonics and torque generation mechanism. Due to their higher average torque output, spoke-type PMSMs with FSCW are increasingly used in high-torque density applications. However, slot harmonics generate torque ripples that are difficult to eliminate in FSCW spoke-type PMSMs. Removing slot harmonics from the stator or winding results in a large drop in torque since their winding factors are identical to those of the main harmonic. Therefore, rotor designs having assisted-poles (symmetrical and asymmetrical) are investigated in this work to mitigate slot harmonics and minimize torque ripples. Firstly, the air-gap flux density is analyzed for the machines having assisted-poles, and a model of interaction between the stator and rotor-MMF harmonics is created and validated through Finite element analysis (FEA) to analyze the torque production mechanism. In addition, an analytical relationship between the assisted-poles' dimensions and the generated torque harmonics is proposed. Furthermore, a generalized torque ripple reduction concept for the FSCW spoke-type PMSM having asymmetrically designed assisted-poles is presented. The proposed design and optimization method are validated through analytical calculations and FEA simulations, and a brief comparative analysis is presented for the analyzed machine prototypes. It has been established that the machine designed by applying the proposed asymmetrical assisted-poles can achieve a reduction in torque ripples while also significantly lowering cogging torque in comparison to the conventional spoke-type PMSMs and other spoke-type PMSMs with rotor having symmetrical assisted-poles. [ABSTRACT FROM AUTHOR]

This paper introduces a novel index for static eccentricity (SE) fault diagnosis in synchronous reluctance motors (SynRMs). Although SynRMs with rotor barriers under SE have been modeled in a few papers, any indices for the fault detection have not yet been reported. The proposed index is a specific frequency pattern in the motor current, which can also determine the fault severity. A novel analytical magnetic field investigation is applied to ascertain the proposed index. An accurate nonlinear numerical method is proposed for the motor inductances calculation. The model considers the rotor flux barriers, magnetic saturation, and the stator slots effect. The air gap flux density and the motor current are then achieved. The fast Fourier transform is exploited as a signal-processing tool to calculate motor current spectra. Then, a two-dimension time-stepping finite element method is used to attest of the proposed numerical model. Effectiveness of the proposed index is verified by simulation and experimental tests. [ABSTRACT FROM AUTHOR]

Cascading rotor and stator in axial flux permanent magnet (AFPM) machine is a beneficial concept to increase the power density without increasing the diameter of the machine. Multi-stage AFPM can provide higher torque capability in applications requiring high power density. In this regard single-stator double- rotor (SSDR) and double-stator single-rotor (DSSR) are efficient machines compared to single -stage AFPM. Since SSDR and DSSR are also considered modular units to make multi-stage AFPM, like single-stage AFPM, this paper makes a comparison with analysis between SSDR and DSSR AFPM machines. Based on 3-D finite element analysis (FEA), the air-gap magnetic flux, voltage, current, torque, torque ripple, power and power density, efficiency are comparatively investigated to evaluate their performance. Results show that fully coreless topology only be achieved in SSDR AFPM machine with a higher power density. Finally, a prototype multi-stage coreless generator has been developed using a single stator double rotor (SSDR) configuration to justify the fully coreless concept. This prototype coreless generator eliminates eddy current losses and reduces weight, making it a suitable option for certain portable applications. [ABSTRACT FROM AUTHOR]

This paper introduces an evaluation of the flux air gaps of Shunt Reactors (SRs) to effectively mitigate fringing and leakage fluxes along the height of the iron core. The assessment of these discretely distributed flux air gaps in SRs is a rigorous and challenging process. To define their exact number, the case of one flux air gap is analyzed and investigated to observe/simulate the influence of the flux density distribution and the leakage flux along the air gaps on the reactive power and the operation conditions of the SR. Based on that, to reduce leakage flux, a large flux air gap is divided into smaller ones. Initially, an analytic model is presented to define the main parameters of the SRs. Then, a finite element method is developed to simulate electromagnetic quantities, such as the magnetic flux density, leakage flux, and electromagnetic force. The obtained results can help manufacturers define the exact number of flux air gaps along the iron core of the SR. From that, a suitable technology can be given in manufacturing high voltage SRs applied to high or super high voltage transmission lines. [ABSTRACT FROM AUTHOR]

In this paper, a novel method to design and optimization of a 1.5 kW, 4-pole, 36-slot salient-pole permanent magnet synchronous machine (SPPMSM) based on a three-step skewed pole shoe method to reduce the output torque ripple and the cogging torque is investigated. In the first step, an initial model of the SPPMSM is designed, simulated, and verified through the Finite-Element method (FEM). The simulation results ensure the electromagnetic performance of the initial model of the machine under any operating conditions. Next, a novel method to re-design and optimize the SPPMSM based on a three-step skewed pole shoe shape is presented.. The significant results obtained from the optimized model of the SPPMSM are as: The output average torque and the air gap flux density are increased approximately by 12.65% and 3.33%, respectively compared to the initial design of the SPPMSM. The torque ripple is an important parameter in the design of the machine, and so, is decreased by about 16.03% which is equal to 10.41% in comparison with the initial model which is equal to 12.41%. The cogging torque in the initial model of the SPPMSM is equal to 0.036 N.m and with a 19.44% reduction, in the optimized model, it is 0.029 N.m. And finally, the back-EMF voltage of the SPPMSM is improved by 1.27% compared to the initial design model. [ABSTRACT FROM AUTHOR]

Cogging torque can affect the performance of permanent magnet (PM) homopolar inductor machines (HIMs). In order to find the reduction methods of the PM HIM cogging torque, it is necessary to investigate its production mechanism and analytical model. In this paper, the production mechanism of the PM HIM cogging torque is revealed from the perspective of air‐gap field modulation principle. It is found that the air‐gap permeance of PM HIMs can modulate their air‐gap magneto‐motive force (MMF) and then a large number of modulated air‐gap magnetic fields are generated. These magnetic fields with identical production condition but different rotation speeds or rotation directions can interact with each other, hence the production of the PM HIM cogging torque. By the combination of energy method and air‐gap field modulation principle, the cogging torque analytical model of PM HIMs is derived. Based on the obtained analytical model, the methods for reducing the PM HIM cogging torque are further analyzed. Finally, a 48‐slot/4‐pole (48S4P) PM HIM is designed and exampled. The air‐gap flux density of the 48S4P PM HIM is simulated by three‐dimensional (3‐D) finite element analysis (FEA). Based on the harmonic analysis for the simulated results, the correctness of the proposed cogging torque production mechanism is validated. In addition, a prototype of the 48S4P PM HIM is manufactured. The cogging torque in the prototype is obtained by the analytical model, 3‐D FEA and experiments, respectively. The simulation and measurement results verify the correctness of the cogging torque analytical model. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

The effect of winding chording on five-phase synchronous reluctance motor (SRM) modelled in phase variables is presented. The stator winding configuration is shifted a pole pitch from a fullpitch configuration to a 54 degrees over-full-pitched configuration incorporating the effect of 3rd harmonic of the air-gap magneto-motive force in the inductance equations. The models are monitored on starting, synchronism, loading, faults and loss of synchronism. These are considered simultaneously with vector potential, rotor speed, air-gap flux linkage and winding current. The phase variable (analytical) models have been simulated by using MATLAB/Simulink software while ANSYS Maxwell software has been used to simulate the finite element model (FEM) of the motor for corresponding chording ranges for comparison on direct online starting (DOL). Under all conditions considered in the work, the detailed results are presented and very close similarity is observed between the analytical and the nearly ideal FEM model for all chording ranges and the similarity is enhanced with increase in chording angle. [ABSTRACT FROM AUTHOR]

A transverse flux linear motor is a special type of linear motor with a high thrust force density, and it has broad application prospects in the field of linear direct-drive systems. In the process of oil production, the vibration of the linear motor poses a significant amount of harm to the system due to its special slender structure. This paper focuses on the electromagnetic vibration of a transverse flux permanent magnet linear submersible motor (TFPMLSM). Firstly, the no-load air gap flux density is calculated based on the field modulation principle. Secondly, the radial electromagnetic force (REF) of the TFPMLSM is calculated, and the finite element method (FEM) is used to analyze the time-space and spectral characteristics of the REF. Then, the influence of secondary eccentricity on the frequency spectrum of the REF is further concluded. Finally, the natural frequencies of each vibration mode are calculated using the modal superposition method and the influence of the REF on the motor vibration is obtained through magnetic-structural coupling analysis. The research results found that the motor does not cause resonance at low speeds, and the fundamental frequency of REF has the greatest impact on electromagnetic vibration. [ABSTRACT FROM AUTHOR]

In this study, a generalized torque estimation method is proposed for synchronous motors, including surface permanent magnet synchronous motors (SPMSMs), synchronous reluctance motors (SynRMs), and interior permanent magnet synchronous motors (IPMSMs) for building the analytical motor model. The average motor torque is estimated using the Lorentz force by the generated flux density in the air gap to determine the relationships among torque, flux density, and injected current. In the proposed method, the generated flux density is derived step by step by considering the effects of magnetic flux saturation, the stator slot, the rotor barrier, and permanent magnets (PMs) to ensure that the generated average torque complies with the operating condition of the motor. To verify the proposed method, the output torque of finite element analysis (FEA), Maxwell 2D, is compared to the proposed method in a SPMSM. Moreover, a phasor diagram is plotted to determine the mechanism through which torque is generated in SynRMs and IPMSMs. A SynRM and an IPMSM with ferrites PMs are analyzed using the proposed method, FEA, and the experimental results of this study indicate the effectiveness. [ABSTRACT FROM AUTHOR]

The aim of this article is to develop a rotor reconstruction method for the V‐shaped interior permanent magnet (IPM) machine so that the subdomain method to analytically calculate the air‐gap flux density can be applied. With the proposed method, the V‐shaped IPM rotor with rectangular magnets, magnetic barriers, and saturated iron bridges can be transformed into a U‐shaped equivalent analytical model. The geometry and material parameters of the magnets in the equivalent U‐shaped model can be determined according to the flux equivalence in the air‐gap of the motor. Then using the subdomain method on the U‐shaped equivalent rotor, the static magnetic field problem can be solved and the flux density distribution in the air‐gap be obtained. The validity of this method and accuracy of the solution is verified by the finite element method with case studies. Compared with existing methods, the improved subdomain method has higher accuracy in calculating flux density including radial and tangential components. The presented rotor reconstruction method is not only limited to single‐layer V‐shaped rotor, it can also be applied to other IPM rotors with more complex structures. It is valuable in the design, optimisation of IPM motors, and even development of new rotor topology. [ABSTRACT FROM AUTHOR]

Background: Axial flux permanent magnet motors (AFPMMs) with single-rotor-single-stator structure (SRSSS) are the main components of new energy vehicles. The vibration characteristic of AFPMM with SRSSS significantly affect the security of new energy vehicles. Axial force is a main factor causing vibration of AFPMM. Due to manufacturing error, assembling error and so on, there is eccentricity between rotor axis and stator axis. Eccentric axial force will be time-varying as AFPMM works. To research the law of eccentricity on the axial force of AFPMM, a new modelling method is needed. Purpose: The eccentricity between rotor axis and stator axis can be divided into three situations: translation error alone, deflection error alone and both. The aim of this study is to obtain the law of translation error and deflection error on the axial force of AFPMM with SRSSS in the three situations. Methods: An analytical method is adopted to build a model of axial flux air gap magnetic field model without eccentricity. Both cogging effect and end effect are taken into consideration. Another analytical method is adopted to build the eccentric models of air gap for three situations: translation error alone, deflection error alone and both. The model of axial force is also established in the analytical way. Finite element models are given to validate the method proposed in this study. Conclusion: According to the results, for AFPMM with SRSSS, the axial force is reduced as the translation error rises when only the translation error exists. If there is only a deflection error existing, the axial force is increased with the growth of deflection error while the axial force is decreased with the increment of g0. The amplitude of axial force fluctuation rises as deflection error is increased. When translation error and deflection error both exist, the tendency of a translation error and deflection error on the axial force is the same as that when either translation error or deflection error exists alone. The FE results have validated all the results. [ABSTRACT FROM AUTHOR]

The pole–slot combination is an important factor affecting the cogging and electromagnetic characteristics of a permanent magnet synchronous motor. Taking a 95 kW direct-drive drilling permanent magnet synchronous motor (DPMSM) as an example, this paper presents an analytical model of the motor's magnetic field based on the ideas of segmental discretization and magnetic vector potential, and considers a case in which the stator slot type is a closed slot. The Laplace or Poisson equations of each solution domain are solved using the separation of variables method, and the undetermined coefficients in the general solution are obtained by combining the boundary or interface conditions, thus completing the construction of the analytical model of the motor. The accuracy of this analytical model is verified with the finite element method (FEM). Based on the analytical model, the effects of the different pole–slot combinations on the electromagnetic performance, such as the air-gap flux density, back-EMF, cogging torque, output torque, etc., are investigated, and a reasonable choice of pole–slot combinations is made. The test results of the prototype are basically consistent with the predictions of the analytical model. The analytical model serves as an accurate and efficient calculation tool for the design of DPMSMs. [ABSTRACT FROM AUTHOR]

Introduction. The drive electric motor is one of the key components in the traction chain of an electric vehicle. Traditional radial flux motors used in electric vehicles, which use permanent magnets or induction motors in an electric field, are experiencing significant development aimed at optimizing their weight and cost. However, it can only go so far, so switching to a completely different type of machine, such as an axial flow, might be a good alternative. The novelty to this item is an axial flux permanent magnet motorization with non-slotted TORUS-NS rotor (single interior stator with two external rotors North-South) type housed in the wheel of the vehicle; this allows power to pass directly from the motor to the wheel, increasing the efficiency of the motor. System complexity is also less, as the transmission, differentials and driveshaft are eliminated. Purpose is to equip the electric car and choose the motor adapted to the application and the available space. The smaller size and weight allows for a lighter vehicle and more batteries, thus increasing range. The focus on customization is because vehicle performance is so dependent on the quality of the vehicle architecture, battery pack and axial flux motor design. The results obtained are in good agreement of accuracy, in particular the flux density at the air gap. The investigation is carried out by the finite element method. Machine model was run on Maxwell 16.0 business code. [ABSTRACT FROM AUTHOR]

Recently, the interest in consequent-pole flux-switching permanent magnet (CP-FSPM) machines has been increasing because of the flux-focusing PM arrangements and the removal of the flux-barrier effect. A simple and rigid outer-rotor salient pole rotor structure can be adopted in CP-FSPM machines, making them applicable for in-wheel direct-drive applications. In this study, three CP-FSPM machines with II-shaped (II-PM), V-shaped (V-PM), and straight U-shaped PM (SU-PM) arrays are analyzed and compared. Moreover, a CP-FSPM machine with inclined U-shaped PM (IU-PM) arrays is proposed to improve the flux-focusing effect and stator slot utilization. The working principles of CP-FSPM machines are analyzed by adopting a semi-analytical model. Combining the finite element analysis (FEA) results of air gap flux density and the analytical model of phase back electromotive force (EMF), the contributions of multiple working harmonics to the back EMF are quantitatively analyzed. Additionally, 6/16 and 6/17 CP-FSPM machines with different PM arrangements are globally optimized. Both the no-load and on-load performance of the optimized machines are included in the performance comparison. The results illustrate that the 6/16 and 6/17 machines exhibit their respective merits, and the IU-PM machine shows the best torque production ability in these CP-FSPM machines with the same design criteria. [ABSTRACT FROM AUTHOR]

Based on the magnetic gear effect, the field-modulated permanent-magnet machine (FMPMM) can realize the unequal pole design of the rotor PM field and the stator armature magnetic field. With the advantages of high torque density and high efficiency, the FMPMM has been widely studied in low-speed direct-drive applications. As a kind of machine excited by PMs, the performance of the FMPMM was affected by the demagnetization state. However, the method for establishing the FMPMM demagnetization model based on a finite element analysis (FEA) presented some problems, including tedious repeated modeling work and long calculation time-consuming under fine subdivision. Therefore, in this paper, a six-phase surface-mounted FMPMM was taken as an example, and an equivalent magnetic network (EMN) model was proposed for evaluating the machine performance under demagnetization. In order to realize the rapid establishing EMN models under diverse demagnetization types, the variable coercivity of PM was introduced. Furthermore, for the purpose of improving the calculation accuracy and shortening the calculation time, the least square method was used in fitting and analyzing the discrete results. Then, in order to verify the validity of the proposed EMN model, a prototype was fabricated and a testing platform was built. The air-gap flux density and the no-load back EMF obtained by the FEA, the proposed EMN model, and the experimental testing were compared. The results showed that the proposed EMN model can realize the rapid modeling and accurate analysis of the six-phase surface-mounted FMPMM under diverse demagnetization types. [ABSTRACT FROM AUTHOR]

An analytical method was proposed for obtaining the magnetic field distribution for surface-mounted permanent magnet machines with the structure of unequal magnetic poles. Firstly, the Laplace equation and Poisson equation were solved using the method of the separation of variables, and then the mathematical model of the motor structure with unequal magnetic poles was obtained. Secondly, according to the design parameters of the two types of prototypes motors, the flux density in the air gap region of the two types of prototypes motors was calculated, respectively. Thirdly, by comparing the results calculated using the analytical method with the results obtained using the finite element method, the analytical method proposed in this paper was proven to be effective. Moreover, the armature reaction field and the effect of the stator slotting were considered in the mathematical model as well. Overall, the analytical method presented in this paper provides a theoretical basis for the analytical calculation of motors with the structure of unequal magnetic poles. [ABSTRACT FROM AUTHOR]

This paper proposes a stator core design to achieve variable-flux characteristics enhanced by magnetic saturation in fractional-slot concentrated winding (FSCW) permanent-magnet (PM) motors without additional excitation systems, complicated structures, or active controls. Magnetic saturation induced at suitable locations can enhance variable-flux characteristics because the PM flux linkage is variable with the magnetic saturation in cores. In distributed winding configurations, magnetic saturation is induced symmetrically for each rotor pole by the fundamental that is dominant in the spatial distribution of the air-gap flux density. The magnetic saturation at each rotor pole can enhance variable-flux characteristics. In FSCW configurations, magnetic saturation is not induced symmetrically for each rotor pole because of several dominant space harmonics. The magnetic saturation at several rotor poles cannot enhance variable-flux characteristics. In the proposed design, the stator core has thin tooth tips for inducing magnetic saturation. The magnetic saturation in the stator core achieves the variable-flux characteristics that are effective for expanding the operating region or decreasing electromotive force and increasing torque. The efficacy of the proposed design is determined by estimating motor performance through a finite element method analysis and demonstrating the actual motor performance of a prototype. [ABSTRACT FROM AUTHOR]

This paper describes the design and modelling of a DC linear stepper motor (DLSM), to investigate the air-gap magnetic flux density and the static features of the thrust force under the DC current excitation condition, while taking the nonlinear properties of iron materials used into account. A Finite Element Method (FEM) study utilizing software called a "MagNet" was employed to model and construct a linear DC motor. The thrust force, air-gap flux density, and static thrust force at various airgaps were compared in simulation and real time. The result showed that the magnetic flux density presents a sinusoidal shape in both the simulation and measurement, where the peak error value was around 7.14%. A comparison was made with thrust force, as the armature current has different values; the results show that the difference between the experimental and computed peak value was 8.07%, while the error between the measured and simulated value was 5.02% when the thrust force was measured at different air gap lengths. [ABSTRACT FROM AUTHOR]

In the design process of surface-mounted permanent magnet motor (SPMSM) for industrial robots and computer numerical control (CNC) machine tools, to pursue the sinusoidal nature of the back electromotive force, the magnetic poles in the form of eccentric pole cutting structure are often used. To analyze the no-load air gap magnetic field of the SPMSM with eccentrically cut poles simply and accurately, a subdomain model magnetic field analytical calculation method based on equal-area integral block processing of permanent magnets is proposed. The problem that the traditional subdomain analysis model cannot be directly applied to the SPMSM with eccentrically cut poles of unequal thickness is solved. The proposed method considers the influence of stator slotting and the actual permeability of permanent magnets, and directly obtains the fundamental wave and harmonic components of the no-load air gap flux density by solving the subdomain model. The finite element method (FEM) is used to directly calculate the air gap magnetic field for verification. The results of the analytical method and the no-load air gap magnetic density calculated by the FEM are consistent, which verifies the accuracy of the proposed analytical method and can quickly guide the design of the SPMSM with eccentrically cut poles. [ABSTRACT FROM AUTHOR]

To improve the performance of low-speed large-torque direct drive systems in limited space, an axial field flux-switching composite machine (AFFSCM) is proposed in this paper. The AFFSCM is composed of an axial field flux-switching permanent magnet machine (AFFSPMM) and magnetic gear. Therefore, it has the advantages of a compact structure, a large power/torque density, and a wide speed regulation range. First, the topology and magnetic modulation mechanism of the AFFSCM are investigated in detail. Then, the harmonic components of the inner/outer air-gap flux density are analyzed before and after the regulation of the rotary magnetic modulation ring. Based on this, the coupling conditions of the inner/outer air-gap magnetic field are deduced. Then the AFFSCM is initially designed, a three-dimensional finite-element model of the AFFSCM is built, and the electromagnetic performances are analyzed by the finite-element method, including the flux density of the inner/outer air-gap, the speed, the static torque, etc. Next, the cogging torque of the AFFSPMM is analyzed and optimized based on the magnetic modulation mechanism to suppress the torque ripple of the AFFSCM. Finally, an 800 W prototype is constructed and related experiments are done to validate the AFFSCM. [ABSTRACT FROM AUTHOR]

This study elaborates upon a new modular split‐tooth permanent magnet‐assisted switched reluctance motor (MSTPM‐SRM). In the proposed topology, the stator comprises six modular E‐cores in which the middle poles are split into two teeth. Two permanent magnets (PMs) are placed between each module's middle and side poles. Primarily, the proposed topology is introduced. Next, the principle of operation of the proposed topology are elucidated, and the magnetic equivalent circuit analysis is adopted in order to validate the operational basics. It is proved that the embedded PMs significantly increase the air‐gap's flux density and adjusts the poles' flux density. The flux density distributions, static, and steady‐state characteristics of the proposed MSTPM‐SRM motor and its PMless counterpart are extracted by utilising 2‐D finite element analysis. It is illustrated that the average torque of the proposed MSTPM‐SRM is dramatically increased compared to its PMless counterpart, especially at high excitation currents. Furthermore, the cogging torque analysis is done and it is shown that the proposed structure has approximately zero cogging torque. Finally, a prototyping version of the proposed motor is fabricated, and the experimental results are elicited. It is shown that the experimental results endorse the simulation results. [ABSTRACT FROM AUTHOR]

This paper deals with the design and analysis of a surface-mounted outer rotor in-wheel motor (IWM) with the aim of reducing cogging torque and torque ripple for electric vehicles. The proposed IWM is equipped with axial sinusoidal surface-mounted permanent magnets (PMs), with the purpose of producing sinusoidal air gap flux density distribution, thus to realize sinusoidal back electromotive force (EMF) and smooth electromagnetic torque. To highlight the advantage of the proposed IWM, the conventional IWM with tile-shaped PMs and the IWM with stepwise-shaped PMs are also studied for comparison. The finite element method in the commercial software package is utilized to analyze the performance of the three motors, including the radial flux density of air gap, back EMF, cogging torque, and electromagnetic torque. Through the quantitative comparison, it is found that the proposed IWM greatly reduces the cogging torque, highly improves the sinusoidality of back EMF, and nearly eliminates the torque ripple. [ABSTRACT FROM AUTHOR]

This paper investigates the torque generating capabilities and performance comparison of induction machines (IM) and interior-permanent magnet (IPM) machines for electric vehicle (EV) traction applications. Electromagnetic performance characteristics, such as torque, torque ripple, air-gap flux density, etc. are quantitatively compared by changing the level of electric loading. Other performance metrics such as saturation factor, power losses, efficiency, and so on, as well as the flux-weakening capability and efficiency map have also been compared. For calculations of the electromagnetic performance characteristics, 2D time-stepping finite element analysis (FEA) has been employed. It has been revealed that due to the reduction in torque components of IPM machine as a consequence of magnet demagnetization, it cannot generate toque as high as IM under overloading operating conditions. A thorough review of the literature on comparative studies on the electrical machines used in EV or Hybrid EV (HEV) applications is also included. [ABSTRACT FROM AUTHOR]

Multiple factors and consequences may lead to a stator winding fault in an external rotor permanent magnet synchronous motor that can unleash a complete system shutdown and impair performance and motor reliability. This type of fault causes disturbances in operation if it is not recognized and detected in time, since it might lead to catastrophic consequences. In particular, an external rotor permanent magnet synchronous motor has disadvantages in terms of fault tolerance. Consequently, the distribution of the air-gap flux density will no longer be uniform, producing fault harmonics. However, a crucial step of diagnosis and controlling the system condition is to develop an accurate model of the machine with a lack of turns in the stator winding. This paper presents an analytical model of the stator winding unbalance fault represented by lack of turns. Here, mathematical approaches are used by introducing a stator winding parameter for the analytical modeling of the faulty machine. This model can be employed to determine the various quantities of the machine under different fault levels, including the magnetomotive force, the flux density in the air-gap, the flux generated by the stator winding, the stator inductances, and the electromagnetic torque. On this basis, a corresponding link between the fault level and its signature is established. The feasibility and efficiency of the analytical approach are validated by finite element analysis and experimental implementation. [ABSTRACT FROM AUTHOR]

This document deals with the design of a Permanent Magnet Synchronous Motor (PMSM) to peripherally drive a counter-rotating pump inducer. The motor/pump is associated using a rim-driven principle where the motor's active parts are located at the periphery of the inducer blades. It proposes using a Halbach array of permanent magnets for the active rotor of the motor. This solution allows the generation of a Sinusoidal Electromotive Force (EMF). Therefore, a more stable electromagnetic torque is reached. An optimum geometry suitable for the inducer specifications while respecting operational constraints is determined. The obtained geometry is then simulated using the Finite Element Method. The results are satisfactory in terms of average torque and EMF waveform. Use of the Halbach array allows a significant improvement of the flux density in the air gap compared to a designed surface-mounted machine. The experimental validation will be performed once the prototype is realized in the Laboratory of Fluid Engineering and Energy systems (LISFE). [ABSTRACT FROM AUTHOR]

In this study, the design parameters of Open Slotted Axial Flux Permanent Magnet (OSAFPM) Generator for wind turbines are presented using Genetic Algorithms (GA), an optimization algorithm based on natural selection and genetic mechanisms. Electromagnetic analysis of Open Slotted Axial Flux Permanent Magnet generator has been performed by using parameters optimized with Genetic Algorithms. The ANSYS Maxwell program, which uses the finite element method (FEM), has been used for electromagnetic analysis. Compared to ANSYS Maxwell, it is observed that the genetic algorithm significantly reduces the computational time required for design optimization. However, initial design and optimization with Genetic Algorithms have resulted by 8.94% increase in power densities. In addition, 12.71%, 38.62%, 62.02%, and 56.39% improvements have been obtained for air gap magnetic flux density, flux linkage, induced voltage, and current waveforms, respectively. This suggests that optimization with a Genetic algorithm improves the Open Slotted Axial Flux Permanent Magnet generator parameters. [ABSTRACT FROM AUTHOR]

In this paper, power-sizing equations of rotor-permanent-magnet flux-switching (RPM-FS) machines are proposed and implemented, where the main decisive factors of the electromagnetic torque, namely electric loading and magnetic loading, are deduced, respectively. Although the topologies of RPM-FS machines are evolved from traditional stator-PM flux-switching machines, there are still seriously flux leakages between poles, and it is hard to derive the peak value of the air-gap flux density directly. Hence, a local simplified magnetic equivalent circuit is utilized to calculate the magnetic loading, which is crucial for the power-sizing equation. The influences of the pole-to-pole flux-leakages and harmonics in back-EMF are considered to improve the calculated accuracy of the power-sizing equation. Consequently, the electromagnetic torque can be predicted with acceptable accuracy. The feasibility of the power-sizing equation is verified by the finite element analysis and experimental results. [ABSTRACT FROM AUTHOR]

Due to the enhanced air gap flux density and eddy currents in the favorable path, eddy current brakes with slotted conductors have attracted more attention in recent years. However, due to the increased difficulty in analytical modeling, there is currently no suitable analytical model available for the optimization design of eddy current brakes with slotted conductor. To solve this problem, an improved analytical model is provided based on the subdomain model and the least squares method in this article. The proposed analytical model considers slotted conductor disk, magnetic saturation of primary core and actual path of eddy currents in the conductor disk. The accuracy of the proposed analytical model is verified by finite-element method (FEM) and experimental measurement. The results show that the improved analytical model has good accuracy in the entire speed range. As the analytical model takes less computational time than three-dimensional FEM, it can be used as an effective tool for the optimization design. [ABSTRACT FROM AUTHOR]

Variable reluctance resolvers (VRRs) have been widely used for rotor position detection in harsh working conditions. However, conventional installation of VRRs inevitably occupies the axial space of machine systems, and may weaken the reliability of rotor position detection encountering shock and vibration. In this article, a novel VRR structure with inner stator is investigated, which is radially integrated inside a permanent magnet synchronous machine (PMSM) to construct compact machine topology. The hybrid machine topology is first discussed, and detailed electromagnetic design is carried out. Improved analytical analysis on air gap flux density distribution and inductance evaluation of the integrated VRR is derived based on modified winding function approach, and testified by finite element analysis. A prototype is manufactured from an existing 2.2 kW PMSM, and experiments are conducted to validate the effectiveness of proposed machine topology. [ABSTRACT FROM AUTHOR]

The double‐sided permanent magnet linear synchronous motor (DS‐PMLSM) is widely used in the industrial field with high precision and long strokes due to simple construction, high instantaneous thrust and high controllability. However, parasitic issues, such as unavoidable manufacturing tolerances, might cause the symmetrical position deviation of primary or secondary components, which results in an asymmetrical air‐gap between components, affecting the motor's electromagnetic characteristics further. In this paper, it is taken into account secondary torsional or offset conditions (the secondary component is displaced sideways from a symmetrical position), and investigates the variations of electromagnetic characteristics on the 12‐solt 14‐pole short‐primary DS‐PMLSM. Based on the finite element method (FEM), the effects of secondary torsion or offset on the air‐gap flux density, the back‐EMF, the detent force, the thrust force, and the normal force are investigated and compared respectively. In addition, the analytical results of the back‐EMF considering lower secondary torsion are verified on a lower secondary torsional prototype. From the analytical results of electromagnetic characteristics, it is revealed that with the torsional angle or offset distance rising, the normal force and detent force in the Y‐axis gradually increase, while the thrust force and the back‐EMF decrease. These theoretical researches can play an important role in the operation and assembly process of the DS‐PMLSM. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Surface-mounted permanent magnet (SPM) machines with skewed slots as vehicle drives are widely used. Due to skewed slots, electromagnetic characteristics are modulated by the skew effect. To analyze the skew effect, Maxwell’s equations-based 3-D analytical model is proposed. Based on differences in 3-D air-gap flux density distribution, the mechanism by which the skew effect modulates cogging torque, flux linkage, and back electromotive force (EMF) is investigated. The effectiveness of the theory about the skew effect is verified by both the finite element method (FEM) and the experimental result. [ABSTRACT FROM AUTHOR]

This paper presents a new topology of an axial flux-switching memory machine with series-type permanent magnets (SPMs) to improve the flux regulation capability. The key idea was to combine low coercive force (LCF) PMs, which can be magnetized and demagnetized readily, with high coercive force (HCF) PMs in series to provide a variable air-gap magnetic flux. The flux regulating principle and the forward magnetization effect of HCF PMs on LCF PMs are presented and discussed. Based on 3D finite element analysis (FEA), the magnetization variation of LCF PMs and the electromagnetic performances of the machine under different magnetization states were investigated. Simulation results showed that the air-gap magnetic flux could be weakened by up to 45% by using a magnetization current impulse, significantly extending the PM motor's flux-weakening speed range. Finally, a prototype machine was built, and experiments were performed to validate the predictions. The basic experimental validation shows that the measured back-EMF and the flux regulating characteristic matched the 3D FEA results well. [ABSTRACT FROM AUTHOR]

Factors such as insufficient heat dissipation and excessively high temperature can easily lead to demagnetization of the PMs in permanent-magnet (PM) motors. As a result, the magnetic field distribution of the motor will not be uniform, producing fault harmonics and lowering the operational performance of the motor. An essential stage in the diagnosis of faults and the monitoring of motor condition is the establishment of an accurate model of motors with demagnetization faults. In this paper, demagnetization faults are modeled by changing the Fourier coefficients in the Fourier expansion of the magnetization of PMs. This model can be used to determine the motor performance under various types of demagnetization, including radial air gap flux density, back electromotive force (EMF), and torque. On this basis, the corresponding relationship between the demagnetization degree and the fault signature is established, to provide a theoretical foundation for the subsequent demagnetization fault diagnosis. The finite element analysis (FEA) verifies the effectiveness and superiority of the proposed analytical model. The modeling method proposed in this paper can be applied to PM motors with PMs having different magnetization directions and shapes because it is based on the demagnetization region of PMs. [ABSTRACT FROM AUTHOR]

This paper presents an analytical model for calculating the detailed air-gap magnetic field distribution in interior permanent magnet synchronous motors (IPMSMs) with mixed eccentricity. In order to improve the efficiency of model solving, a modeling strategy combining the equivalent magnetic circuit network method and the subdomain method was adopted. Specifically, the magnetic field distribution of the rotor was modeled by using the magnetic circuit analysis method, and the magnetic field distributions of the air-gap, slot opening and stator slot along the radial direction were modeled in different regions according to their structure ruler. Then, the influence of bridge saturation was considered. Moreover, based on the analysis of the air-gap geometric structure with mixed eccentricity, a detailed spatiotemporal analytical model of the air-gap magnetic field was established, which provides a more accurate description of the mixed eccentricity composed of static and dynamic rotor eccentricities of different severity. The analytical models were compared with the corresponding models established by the finite element method, which proved the accuracy and validity of the models established in this paper. Finally, some key features related to radial and tangential air-gap flux density were extracted, which can significantly reflect the characteristics of eccentricities. The main findings reported in this paper will be of benefit for developing methods for early identification and diagnosis of eccentricity faults in IPMSMs. [ABSTRACT FROM AUTHOR]

Shaded pole induction motors’ theoretical analysis is quite difficult because of the presence of strong harmonic components and the elliptical rotating field. The change of air gap reluctance is affecting the air gap flux distribution and thus the performance of the motor. In the study, the effect of the change in the SPIM’s stator, rotor and squirrel cage on the performance of the motor is analysed by the Finite Element Method. The flux distributions and torque values of the closed-interpoles type and the stator with different interpoles clearances are obtained. The effects of single and double cage structures in the rotor part and the effects of copper and aluminium cage materials in the squirrel cage were analysed. According to the analyses, it was determined that the single cage motor with aluminium cage material exhibited the best torque performance with a torque value of 132.78 mNm. [ABSTRACT FROM AUTHOR]

An analytical subdomain model is employed in this paper for predicting the magnetic field distributions in a three-phase double-stator permanent magnet synchronous machine (DSPMSM) during open-circuit and onload conditions. Due to the stator cores are located in the outer and inner parts of the motor, the DS-PMSM construction is quite complex. The rotor magnets are positioned between these two stators. The stator inner radius, stator outer radius, slot opening, magnet arc, magnet thickness, inner and outer air-gap thickness and number of windings turns will directly influence the motor performance in DS-PMSM. The analytical subdomain model employed in this paper has a significant advantage as a rapid design tool since it is capable of precisely predicting the performance of DS-PMSM while requiring less computational effort. The analytical model was initially created using the separation of variables technique in four subdomains based on the Poisson’s and Laplace’s equations: inner air-gap, inner magnet, outer magnet and outer air-gap. Applying the appropriate boundary and interface conditions yields the field solutions in each subdomain. Besides, the fractional DSPMSM with different number of slots between outer and inner stators to rotor poles can result in low cogging torque and non-overlapping winding configuration. The analytical results are validated by Finite Element Analysis (FEA). The slotted air-gap flux density, back-emf, and output torque have all been evaluated as electromagnetic performances. The results demonstrate that the suggested analytical model is capable of accurately predicting the DSPMSM performance. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNT), CNT–aluminum (CNT–Al), and CNT–copper (CNT–Cu) composite wires have shown remarkable electrical and mechanical properties for developing windings of single-phase induction motor. A quest has been made that if these advanced carbon nanomaterials can outclass commonly used electrical wire metals to significantly leverage electrical machines. However, these advanced materials are still in laboratory stage and most material properties are not yet experimentally reaching to their expectations. Therefore, there is need to understand the potential of these nanomaterials for electrical machines and the numerical analysis of the performance of electrical machines with various advanced novel carbon nanomaterials is still a challenge. This paper presents a comprehensive study to compare the performance of a single induction motor with its stator and rotor made with different winding materials. In doing so, the traditional copper and aluminum rotor and stator coils have been replaced by windings made of pure CNT yarn, CNT–Al, and CNT–Cu wires. A 2-D induction machine model was developed for the simulation study conducted in COMSOL Multiphysics finite element-based software. General-purpose sizing and power equations were utilized during the computation. The simulated results of flux distribution, air-gap flux density, torque, and corresponding output power were used as criteria to determine the highest quality solution. The simulation results revealed that using CNT–Cu and CNT–Al wires as machine winding can achieve 25.9% and 16.8% higher efficiency, respectively, than using CNT wires. The motor torque from the proposed finite element model was validated against the experimental results under identical speed and input voltage, and an error of 5.9% suggests that the model can be used to predict the motor performance with reasonable accuracy. [ABSTRACT FROM AUTHOR]

In this study, the influence of slot opening on the leakage reactance, power factors, winding current, and air gap flux density, as well as other parameters of the surface-mounted permanent magnet synchronous motor driven by an inverter is analyzed using the two-dimensional time-step finite element method. Thus, the law of permanent magnet power loss caused by slot opening under PWM qa obtained. The results show that the leakage reactance of the motor increased when the slot opening decreased from 7 mm to 2 mm. Then, the armature ripple current caused by the inverter was found to be suppressed well, and the high harmonic current was filtered well. This reduced the amplitude of the high-order harmonic of the air gap flux density, and the permanent magnet power loss was reduced by nearly 75%. Finally, two prototypes with different slot openings were tested for permanent magnet temperature rise, which verified the analysis method and calculation results proven in this paper. [ABSTRACT FROM AUTHOR]

This article proposes a hybrid evaluation method of electromagnetic force and vibration for electrical machines considering high-frequency current harmonics caused by the inverter. First, the permeance and armature magnetomotive force (MMF) is calculated based on the virtual MMF and the slot matrix. Then, the air-gap flux density and electromagnetic force construction process under arbitrary current is thoroughly studied. The vibration transfer function is obtained by utilizing the modal analysis and the modal test. Finally, the vibration can be calculated according to the modal superposition method. By applying this method to an interior permanent magnet machine, it can significantly reduce the computation efforts compared with the multiphysics procedure due to the extensive use of the finite-element method. In addition, the accuracy of this method is validated by conducting an experimental study. [ABSTRACT FROM AUTHOR]

The use of a magnetic adjustable speed drive is a popular choice in industrial settings due to its efficient operation, vibration isolation, low maintenance, and overload protection. Most conventional magnetic adjustable speed drives use various forms of the permanent magnets (PMs). Due to the PMs, this type of machine has continuous free-wheeling losses in the form of hysteresis and induced eddy currents. In recent years, the homopolar-type rotor has been widely used in high-speed machines, superconducting machines, and in the application of flywheel energy storage. This study proposes a new application of the homopolar-type rotor. A novel adjustable speed drive with a homopolar-type rotor (HTR-ASD), which has obvious advantages (no brush, no permanent magnet, and no mechanical flux regulation device), is designed and analyzed in this study. Its speed and torque can be adjusted only by adjusting the excitation current. Firstly, in this study, the structure, operation principles, and flux-modulated mechanism of the HTR-ASD are studied. The homopolar-type rotor has a special three-dimensional magnetic circuit structure with the same pole. The 3D-FEM is usually used to calculate its parameters, which is time consuming. In this study, an analytical method is developed to solve this issue. To analytically calculate the torque characteristics, the air gap magnetic flux density, and the winding inductance parameter, the equivalent circuit and the air gap permeance are researched to simplify the analysis. Then, the key parameters of the HTR-ASD are calculated. Finally, the performance of the HTR-ASD is comparatively studied using the analytical method and finite element method, and a comparison of the results is carried out. The comparison indicates that the analytical method is in good agreement with simulation results, and that it is very helpful for designing homopolar-type rotor machines. According to the analysis, the proposed adjustable speed drive displays a great performance in relation to the operating characteristics of a flexible mechanical speed drive. [ABSTRACT FROM AUTHOR]

As one of the key components, low-speed direct-drive in-wheel machines with high compact volume and high torque density are important for the traction system of electric vehicles (EVs). This paper introduces four different types of outer-rotor permanent magnet motors for EVs, including one five-phase SPM machine, one three-phase IPM machine with V-shaped PMs, one seven-phase axial flux machine (AFM) of sandwich structure and finally one hybrid flux (radial and axial) machine with a third rotor with V-shaped PMs added to the AFM. Firstly, the design criteria and basic operation principle are compared and discussed. Then, the key properties are analyzed using the Finite Element Method (FEM). The electromagnetic properties of the four fractional slot tooth concentrated winding in-wheel motors with similar dimensions are quantitatively compared, including air-gap flux density, electromotive force, field weakening capability, torque density, losses, and fault tolerant capability. The results show that the multi-phase motors have high torque density and high fault tolerance and are suitable for direct drive applications in EVs. [ABSTRACT FROM AUTHOR]

Due to the high power density, short axial size, and wide permanent magnet (PM) flux linkage regulation range, an axial-flux PM memory machine (AFPMMM) with hybrid Halbach array is investigated in this article. To solve the problem of magnetic density variation of Halbach array composed of different types of PMs in asymmetric bilateral air-gap structure, the analytical method for calculating the air-gap flux density of AFPMMM is presented through mathematical analysis, which uses cylindrical coordinate system instead of Cartesian coordinate system and is solved by equivalent method, separated variable method, and boundary conditions. The magnetic field generated by the Halbach array is divided into three directions: radial, circumferential, and axial. The analytical model is compared with the finite element method (FEM) simulation results to verify its effectiveness. In addition, an approximate piecewise linear hysteresis model with parallelogram return line is established based on the analytical expression of magnetic field. By applying different pulse currents to change the residual flux density of PM, the flux regulation characteristics of the motor are studied, and it is found that the air-gap flux density of the motor can be smoothly adjusted by continuously changing the pulse current, which plays a positive role in solving the problem of online magnetic regulation of the motor. [ABSTRACT FROM AUTHOR]