Air-gap Field Distribution Research Articles

Design and analysis of concave‐core stator direct‐drive permanent magnet motor

AbstractTo solve the problems mechanically caused by parallel direct‐drive permanent magnet motors (DD‐PMSM). This paper proposes a concave‐core stator direct‐drive permanent magnet motor (CCSDD‐PMSM) structure. In this study, an auxiliary yoke structure is proposed to optimise the magnetic circuit and analyse the cogging torque to achieve the minimum detent force. Based on the unit motor and combined with the magnetomotive force to analyse the symmetry of different winding distributions, the stability characteristics of the motor are studied. The magnetic field distribution of the motor load air gap is calculated using the finite element method. The contribution of different spatial order harmonics to the motor output torque is calculated using the Maxwell tensor method. The torque calculation expression of the CCSDD‐PMSM is given. Finally, an experimental prototype is made to verify the accuracy of the analysis in this paper.

Analytical Modeling of Magnetic Air-Gap Field Distribution Due to Armature Reaction

The following paper presents an analytical study of the air-gap magnetic field distribution produced by the armature reaction of a linear machine. Based on the method of images, the magnetic field generated by a current carrying conductor inside the air-gap between two smooth infinitely permeable iron surfaces is modeled as a complex 2D function. The conductor model then becomes a current sheet model and horizontally oriented current sheets are used to model the magnetic field produced by the armature reaction for smooth ferromagnetic surfaces. Focus will be given to the study of the slot opening function in front of energized slots in comparison to the not energized ones of the classical theory pointing out some remarkable differences. Later, the model is extended to slotted geometries using a complex slotting function adapted for energized slots. At last, the Maxwell tensor expressed in complex formulation will be integrated to obtain the force components acting on the machine tooth tips, quantities that will be compared with FEM simulations in order to validate the proposed analytical model.

Precise Control of Flat-Topped Air-Gap Magnetic Field in a Five-Phase Induction Machine Powered by Third-Harmonic-Injected Sinusoidal Supply

The third-harmonic-injected sinusoidal supply (THISS) can help make an innovative breakthrough to improve the power density of multiphase induction machines. However, the existing typical control approaches cannot guarantee the machine to precisely generate the expected flat-topped air-gap magnetic field under all operating conditions, which restricts the popularization of THISS. This article first converts the control objective from generating a flat-topped air-gap field to air-gap flux linkage alignment. In conventional approaches, the rotor leakage flux linkage is not fully considered, and subjective hypothesis is proposed, resulting in the misalignment between air-gap flux linkages components with different harmonic orders. Based on avoidance of exposed flaws and correct theoretical derivation, this article focuses on the spatial distribution of air-gap field and gives priority to the alignment of the air-gap flux linkage by means of harmonic air-gap field-oriented vector control. The required third-harmonic field can be calculated in real time through the fundamental field. Therefore, the flat-topped air-gap field is ensured by fundamental and harmonic current loops. Furthermore, the controllers in fundamental and harmonic current loops are decoupling with each other. The theoretical analysis and the proposed control approach are validated by simulation and experimental results in a five-phase induction machine (FPIM) powered by THISS.

Analytical Model of Electromagnetic Performance for Permanent-Magnet Vernier Machines Using Nonlinear Exact Conformal Model

This paper investigates the air-gap field distribution of the permanent-magnet vernier machine (PMVM) using nonlinear exact conformal model (NECM) to account for slotting effect, flux modulation effect and iron nonlinearity. The exact conformal model based on the region of one-slot and one-flux-modulation-pole (OSECM) are introduced to show the effectiveness of linear analytical model for PMVM. It can keep high calculation accuracy and significantly reduce the computational burden. Then, the NECM is developed from OSECM by introducing the equivalent saturation current into the air region and coil region. The lumped parameter magnetic circuit model (LPMCM) model is used to obtain the magnetic potential of iron region and therefore calculate the equivalent saturation current. The NECM which combines LPMCM and OSECM can essentially improve the accuracy of linear analytical model. The harmonic analysis of air-gap field is performed to theoretically explain the component of electromagnetic torque. Both finite element model (FEM) simulation and test results are presented to validate the NECM.

Synthesis of Application-Optimized Air Gap Field Distributions in Synchronous Machines

This paper deals with the method of shaping the magnetic field distribution in the air gap of a synchronous machine. The main goal is to obtain a specific distribution of the magnetic field in the machine’s air gap to enable easier powering, to increase the torque and power density, or to limit the content of higher harmonics in the induced voltage and torque. This method can be applied for both the electrically excited machines and permanent magnets excited machines. The problem has been reduced to solving a modified system of algebraic equations obtained by the finite element method. The presented examples show the effectiveness of the proposed method both in shaping the contours of the air gap and the magnetization of permanent magnets placed on the rotor. The method can particularly be used in the design of the high-speed synchronous machines.

Analytical Modeling of High-Torque-Density Spoke-Type Permanent Magnet In-Wheel Motor Accounting for Rotor Slot and Eccentric Magnetic Pole

In this article, a hybrid analytical model combining the subdomain method and the lumped-parameter magnetic circuit method (LMCM) is presented for the analysis of a high-torque-density spoke-type permanent magnet in-wheel motor considering rotor slot and eccentric magnetic pole. In the proposed model, the air-gap field distribution is derived using the subdomain method, while the saturation and the axial flux leakage of the iron core are considered by LMCM. The rectangular-shaped spoke magnets, eccentric magnetic poles, and rotor slots are approximated by multiple layers of arc-shaped subdomains. The magnetic equivalent circuit (MEC) of the stator and rotor is established, and the nonlinearity of the iron core is taken into account. Based on the developed hybrid analytical model, electromagnetic performance, such as cogging torque, electromagnetic torque, flux linkage, and back electromotive force, are obtained. The analytical results are verified by the finite-element method, and its application in the optimization process is investigated. Finally, a 1800-Nm high-torque prototype machine is manufactured and tested, and the results validate the accuracy and efficiency of the analytical method.

Analytical Modeling of Air Gap Magnetic Fields and Bearing Force of a Novel Hybrid Magnetic Thrust Bearing

In this article, an analytical method is presented for modeling the complex air gap field distribution and the magnetic force of a novel permanent magnet (PM) bias hybrid magnetic thrust bearing (HMTB). This bearing has a very compact structure and is proposed to replace the traditional magnetic thrust bearings (MTBs) for high-speed rotor systems. The proposed method introduces the notion of the complicated air gap field, calculated from the Schwarz–Christoffel transformation of the air gap geometry, to take into account the effect of slot fringing and leakage. As a result, accurate solutions of the flux distribution and the bearing force can be obtained, which shows good agreement with the results of the finite-element method (FEM). The prototype of the HMTB is designed, analyzed, and tested. The results of the analytical model are compared with experimental data.

Self-Powered Diagnostic System for AC Machines Based on Inhomogeneity of Magnetic Field Distribution in Air Gap

This article presents a self-powered system for supplying rotor measurement equipment and detecting stator winding inter-turn short circuit, and broken rotor bar faults in AC Machines. This system uses harvesting coils to harvest air-gap magnetic field pulsation and generate energy for powering equipment installed on the rotor. Furthermore, installing this system on the stator or rotor of AC machines provides a voltage signal appropriate for fault detection purposes. To determine specifications of the harvesting coils – coils turn numbers, and their optimal mounting positions – numerous finite element simulations have been carried out. In addition, a fault detection method has been proposed to detect broken rotor bar and inter-turn short circuit faults using induced voltage in the harvesting coils. To verify the performance of the proposed system, some experimental and simulation tests have been performed on various AC machines. The results have confirmed the applicability of this system in self-powering applications and fault detection purposes.

Analytical Model of Open-Circuit Air-Gap Field Distribution in Interior Permanent Magnet Machines Based on Magnetic Equivalent Circuit Method and Boundary Conditions of Macroscopic Equations

To accurately and quickly predict the open-circuit air-gap magnetic field in interior permanent magnet synchronous machines (IPMSMs), an analytical model based on magnetic equivalent circuit (MEC) method is proposed. The analytical model can provide radial and tangential components of open-circuit magnetic field in the slotless air gap. The radial component is obtained from the MEC model, and the tangential component is obtained from boundary conditions of macroscopic equations. Then, a complex relative air-gap permeance is applied to take the effect of slots into account. As a result, an accurate solution of both radial and tangential components of the flux density in the slotted air gap is obtained. Additionally, the no-load back electromotive force (EMF) and cogging torque are calculated based on the open-circuit air-gap magnetic field. All the analytical results are verified by the finite element (FE) analysis and they are well matched. In the end, a direct measurement experiment of open-circuit air-gap magnetic field is proposed to verify the validity of both radial and tangential open-circuit air-gap magnetic fields.

Modeling of airgap flux density for the study of stator core vibration in low speed synchronous machines

Purpose This paper aims to develop models and simulations focused on the prediction of electromagnetic forces acting on the stator core of a synchronous machine. It contributes to the study of stator core vibrations. Design/methodology/approach An analytical model based on the rotating fields’ theory including the damper winding contribution was developed. Such model allows the comprehension of airgap magnetic field distribution and the consequent pressure distribution. Focus was given to the pressure sub-harmonics due to the usual fractional winding configuration of low speed machines. A comparative numerical model was also developed and applied to an example laboratory machine. Partial validation measurements were performed. Findings The paper provides the predicted electromagnetic forces and the relative influences of damper winding and teeth tangential forces on each pressure harmonic. It is shown by how much such effects can influence the amplitude of pressure sub-harmonics from a fractional stator winding. Research limitations/implications The performed validation measurements were based on the airgap field distribution, but the resulting core vibration at load was not measured. Therefore, researchers are encouraged to perform additional tests for improved validation. Practical implications The obtained models and results are of great importance for the design phase of new generators and for the diagnosis process of existing machines with core vibration problems. Originality/value As a contribution of this paper, the magnitude of indirect effect of tangential forces and the effect of damper winding are comparatively quantified for each pressure harmonic. The given approach contributes to the relative evaluation of these effects especially on the sub-harmonics from the fractional stator winding.

Analytical Model of Air-Gap Field in Hybrid Excitation and Interior Permanent Magnet Machine for Electric Logistics Vehicles

With the increasing energy shortages and environmental degradation, electric logistics vehicle (ELVs) with energy conservation and environmental protection has become a research hotspot. The design of machine is the key to develop ELVs. Magnetic field analysis is the most critical issue since its accuracy affects the calculation of motor torque, loss, and other characteristics. To provide a calculation method for the field and performance analysis of the machine for ELVs, this paper presents an analytical model of air-gap field for hybrid excitation and interior permanent magnet machine. In the proposed model, it is taken into account for the shape of the stator and rotor teeth. The flux density on the rotor side is derived by equivalent magnetic circuit (EMC) with leakage magnetic flux. Taking the calculated flux density as one of the second boundary conditions, the air-gap field distribution is calculated by magnetic potential model with the eccentricity of the rotor. To verify the analytical method, we adopted the finite element method. The simulation results of the air-gap flux, back electromotive force, and cogging torque are in good agreement with the analytical results. Besides, applying the analytical model, the machine can be optimized for obtaining the optimal air-gap flux density distribution. The hybrid excitation machine with salient pole and interior magnets can provide a good flux density waveform. The study offers a helpful analytical method for design and optimization of the type of machine for ELVs.

Analysis of rotor slot width influence on a bearingless induction motor

A bearingless induction motor (BIM) is a new type of motor with non-contact rotor suspension and negligible friction loss. One major imperfection of this motor is that its performance highly depends on the rotor slot width. This paper attempts to solve this problem by using a combined analytical method and finite element analysis method (FEM). Firstly, the influence on the motor starting characteristics is revealed by analytical method and verified by finite element simulation. Secondly, using the fast Fourier transform (FFT), the effect on the radial harmonic magnetic field distribution of air gap is analyzed. Meanwhile, the impact on the motor load performance is calculated. Thirdly, the relationship among the rotor slot width, the suspension force and the unbalanced magnetic pull force is explored. Finally, the simulation and experimental results show that the BIM designed by the combined analytical method and finite element calculation can not only obtain good torque characteristics and suspension performance but also has less load loss and a better accuracy in its mathematical model. This paper provides a theoretical basis and means for further design optimization of this type of motor.

Analytical calculation and analysis of air gap magnetic field for electromechanical integrated toroidal drive

This article introduces the operating principle and structural characteristics of the electromechanical integrated toroidal drive system. For its inner and outer toroidal double-stator structure, the equivalent current method is applied to calculate its spatial magnetic field, which is produced by the sector cylindrical magnetic teeth and the helical variable cross-section magnetic beam. For the application of the equivalent current method in the modeling of the magnetic field, an effective correction method is proposed. The flux density calculation models for the main magnetic field in the inner and outer air gaps are established under the unified coordinate system, and the analytical expression of magnetic field distribution in spatial air gap is deduced. Finally, the feasibility of the mathematical analytical model is verified by comparing the analytical calculation results with the finite element simulation results. The influences of the main structural parameters on the distribution of the air gap magnetic field and the torque are analyzed, which lay a theoretical foundation for the optimal design of the electromechanical integrated toroidal drive system.

Comparative Study of Stator-Consequent-Pole Permanent Magnet Machines With Different Stator-Slot Configurations

This paper presents a comparative study of the stator-consequent-pole permanent magnet (SCPPM) machines with different stator-slot configurations, i.e., semi-closed slot (SCS) and closed slot (CS). The machine topologies and working mechanism are introduced first. The air-gap field distributions and dominant harmonics contributing to the torque generation corresponding to different stator-slot-opening ratios are evaluated. Then, the six-stator-slot SCS and CS configurations with different rotor-pole pair combinations are optimized by the multi-objective genetic algorithm. In addition, the major electromagnetic characteristics of the optimized 6-/11-pole SCPPM machines having SCS and CS structures are comparatively investigated by the finite-element (FE) analysis. Finally, an SCPPM machine prototype is manufactured and tested to verify the FE analyses.

Analysis of Consequent-Pole Flux Reversal Permanent Magnet Machine With Biased Flux Modulation Theory

This paper proposes a consequent-pole flux reversal machine (CP-FRM) with biased flux modulation theory, which employs homopolar permanent magnets (PMs) placed between the adjacent stator poles. The machine topology is introduced from the perspective of FRM with a shifted magnet position and CP arrangement, and the performance comparison between the proposed CP-FRM and its original surface-mounted PM (SPM) counterpart is presented to highlight the torque improvement of the CP structure. Then, a simplified permeance model is applied to the CP-FRM to identify the principal effective air-gap field harmonics engaging in the torque productions. It shows that the CP-FRM works based on a biased flux modulation effect due to its asymmetric air-gap field distribution caused by the CP configuration, which unveils its underlying torque improvement mechanism over its SPM-FRM counterpart. In order to obtain the highest torque capability, the key design parameters are analytically optimized by analyzing the winding configuration, which aids the establishment of a general design guideline for the CP-FRM. The analytical and FE results are validated by experiments.

Characteristics Analysis of the Motions of the Two-Degree-of-Freedom Direct Drive Induction Motor

The 2-degree-of-freedom direct drive induction motor (2DoFDDIM) is capable of implementing rotary linear or helical motion, which has the definite advantages of integrated structure, high material utilization, and so on. In this paper, the characteristics analysis of the three kinds of motions is presented. The air-gap magnetic field distributions and mechanical characteristics of the 2DoFDDIM with three motions are derived respectively. The results show that there is super synchronous speed or velocity phenomenon for rotary or linear motion. Moreover, the coupling effects between the rotating and travelling wave magnetic fields and that between the two mechanical motions will deteriorate the performance of the three-dimensional (3-D) helical motion compared with the two-dimensional (2-D) motion (rotary or linear). The expressions of the resistant torque and force caused by the coupling effect are derived, which are verified by 3-D finite-element models (FEMs). The results regarding the weakening of the output torque of helical motion and interacting magnetic field obtained from FEMs are then verified by experimental tests. Finally, the skewed slot method is applied to 2DoFDDIM, which successfully improves the performance of helical motion aiming to compensate the coupling resistant torque and force.

Consequent Pole Permanent Magnet Vernier Machine With Asymmetric Air-Gap Field Distribution

In recent years, permanent magnet vernier (PMV) machines have been attracting more and more attention due to the inherently exhibited advantages such as high torque density and simple mechanical structure. In this paper, a consequent pole (CP) PMV machine with single-layer concentrated winding is proposed. The novelty is that the asymmetric air-gap field distribution is introduced to improve its working harmonics and to reduce the PM consumption. By employing a CP structure, the flux density amplitude can be enhanced. Moreover, due to uneven distribution of modulator poles on the armature teeth and fault tolerant teeth, the number of periods of modulator poles is only half of that of the stator teeth. Then, significant improvement in flux density working harmonics can be achieved. Furthermore, the superior electromagnetic decoupling capability can be achieved by introducing the fault-tolerant teeth. The relevant electromagnetic performance such as flux density, back electromotive forces, cogging torque and on-load torque have been calculated by using finite-element analyses, which have also been validated by experiments.

No-load iron loss model for a fractional-slot surface-mounted permanent magnet motor based on magnetic field analytical calculation

The common analytical models for the no-load iron loss of permanent magnet(PM) motors usually neglect the iron loss caused by the rotating magnetic field in the tooth tips and the harmonics of the magnetic fields in the teeth and yokes. This paper presents an analytical model for no-load iron loss of a fractional-slot surface-mounted permanent magnet motor. According to the existing analytical model of the magnetic field distribution in the slotted air gap, the magnetic flux densities considering the harmonics of the stator tooth and yoke are both derived based on the continuity of magnetic flux. Due to the complexity of the magnetic field in the tooth tip, the tangential flux density of the tooth tip is approximated by an equivalent sine wave and the radial component is regarded to be the same as that of the corresponding tooth. After obtaining the magnetic fields in stator different regions, the analytical iron loss is calculated by using the Bertotti model and the orthogonal decomposition model. A 20-pole/24-slot PM synchronous motor is taken as an example. The maximum error between the analytical model and finite element model(FEM) is 5.46%, which verifies the validity of the proposed method.

Modeling and Optimization of Air-Core Monopole Linear Motor Based on Multiphysical Fields

The key technology of the air-core monopole linear motor (AMLM), a core component of precision motion systems, is the distribution of the electromagnetic structure and cooling structure. Thus, AMLM can achieve small thrust fluctuation, high thrust density, and low surface temperature rise. Consequently, the multiobjective optimal design of AMLM under the multiphysical fields has become the key technology of AMLM. Consideration of the strict requirements of AMLM model calculational accuracy will cause an excessively long computation time for the finite-element analysis (FEA) software three-dimensional (3-D) model, and it is not convenient for an optimal computation of the multiphysical fields model. Therefore, a surface magnetic charge model and an image method are proposed in the paper to establish an air gap magnetic field model of AMLM. The saturation characteristic of magnetic materials can be reflected through saturation coefficient of the model. In addition, the air gap field distribution status of AMLM can be better predicted. An AMLM thermal field model is established by adopting the thermal network method. In the model, the heat transfer coefficient of cooling water is calculated based on the current curve obtained from the FEA software. Parametric modeling was performed on the AMLM electromagnetic and cooling structure through definition of 7-D proportionality coefficients. Based on the aforementioned electromagnetic field and the thermal field model, genetic algorithm (GA) was adopted for AMLM optimization design by setting cooling capacity and size as constrain conditions as well as by setting thrust density, thrust fluctuation, mover's mass, and motor constants as optimization objects. The AMLM electromagnetic field, the accuracy of thermal field model, and the validity of the AMLM optimization method were verified through simulation and tests. The method proposed has significantly improved the efficiency of optimization calculation.

Electromagnetic Performance Comparison of Multi-Layered Interior Permanent Magnet Machines for EV Traction Applications

Electromagnetic performance of three multi-layered interior permanent magnet (IPM) machines are investigated and compared for electric vehicle applications in this paper. The rotor structure, air-gap field distribution, torque density, torque ripple, core loss, magnet eddy-current loss, and output power are studied with finite-element analysis. It is demonstrated that the two-layered rotor structure with magnets buried deeply has the lower torque density and magnet eddy-current loss due to the utilization of magnets and the block effects of the armature-reaction flux is lower. The three-layered IPM machine has the lower torque ripple and core loss than two-layered IPM machines because the harmonics of air-gap density are reduce by the increase of magnet layers. Finally, an IPM machine with three-layered magnets rotor is prototyped to verify the analysis.