Air-gap Magnetic Field Research Articles

Winding-MMF-based design and investigation of dual-winding hybrid-tooth vernier permanent magnet motor with reduced torque ripple and improved power factor

In this paper, in order to further reduce torque ripple and improve power factor, a new vernier permanent magnet motor is proposed, in which the design concept of dual-winding hybrid-tooth configuration is incorporated. In order to clarify motor torque ripple and power factor, the winding-magnetomotive-force-based design and analysis method is proposed, in which harmonic characteristics are considered as key factors during the magnetic field modulation process. The relationship between harmonics generated by winding MMF, torque ripple, and power factor are investigated. In addition, the split-tooth vernier permanent magnet motor is also investigated as a referenced motor. Detailed comparisons between the DWHT-VPM motor and ST-VPM motor are carried out, including air gap magnetic field, torque, and power factor. Both theoretical and simulation results verify the reasonability of the proposed DWHT-VPM motor, and the effectiveness of the proposed winding-MMF-based analysis method, which provide a new potential research path for the design and analysis of flux modulation motors.

Characterization of linear motor flux pump using H-formulation

H-formulation is an effective method for electromagnetic simulation analysis of superconductors. This paper innovatively uses H-formulation to simulate and analyze the operation characteristics of magnetic flux pump operating in linear-motor pattern. Via COMSOL Multiphysics, this paper establishes a two-dimensional electrical equipment simulation model that comprehensively compares excitation conditions of triangular and trapezoidal current waves to investigate the effects of the working excitation waveforms’ frequency and amplitude on the operating features of the equipment. The following operation control laws are revealed: the current amplitude has a linear control effect on the mean value of superconductor surface electric field and the average amount of air-slot density of magnetic flux, the current frequency has no effect on the air-gap magnetic field waveform, and the regulation effect of the excitation frequency on the average value of superconductor surface strength of electric field is related to the waveforms. Finally, the equivalent circuit of the pumping model is established, and two interrelated L-R equivalent circuits are designed by quadratic substitution, and the final pumping current reaches 43A.

Thermal analysis and temperature evaluation on a magnetic‐geared dual‐rotor machine

AbstractThe thermal performance of the magnetic‐geared dual‐rotor machine (MGDRM) is investigated. Because the effective component in the outer airgap magnetic field harmonics is low, the torque production of MGDRM cannot match the regular permanent magnetic synchronous machine (PMSM). Although the analysis shows that the torque generation of the MGDRM is weak, this conclusion is limited in the electromagnetic field. The MGDRM outer rotor should also be considered from the thermal aspect, and the effect on the torque generation should be valued in particular. The outer rotor thermal buffer effect blocks the heating flow from the winding to the inner rotor magnets. Thus, the MGDRM can withstand a heavy electrical load in a short period, producing higher torque. With this understanding, the torque production ability of the MGDRM can extend to a higher level, even close to the regular PMSM. To validate the analysis, a MGDRM machine is prototyped, and the dual‐rotor temperature information acquisition is realised by a wireless data collection. The rotor temperature estimation technology on the dual‐rotor is then investigated as an auxiliary function. The estimation error can be limited around 5°C, which is good for warning the thermal risk. And thus the MGDRM overheating can be safely adopted to extend the torque generation.

A hybrid analytical model of open-circuit air gap magnetic field of Interior Permanent Magnet Synchronous Motor with non-uniform air gap structure considering saturation effect

A hybrid analytical model of open-circuit air gap magnetic field of Interior Permanent Magnet Synchronous Motor with non-uniform air gap structure considering saturation effect

Adaptive Control Strategy for Aligned and Synchronous Operation of Harmonic Air-Gap Magnetic Field for Multi- Phase Induction Machine

Adaptive Control Strategy for Aligned and Synchronous Operation of Harmonic Air-Gap Magnetic Field for Multi- Phase Induction Machine

Novel Magnetic Field Modeling Method for a Low-Speed, High-Torque External-Rotor Permanent-Magnet Synchronous Motor

In view of the unstable electromagnetic performance of the air gap magnetic field caused by the torque ripple and harmonic interference of a multi-slot and multi-pole low-speed, high-torque permanent magnet synchronous motor, we propose a simplified model of double-layer permanent magnets. The model is divided into an upper and a lower subdomain, with the upper subdomain being an ideal circular ring and the lower subdomain being a segmented sector ring. Moreover, we develop an exact analytical model of the motor that predicts the magnetic field distribution based on Laplace’s and Poisson’s equations, which is solved using the method of separating variables. Taking a 40p168s low-speed, high-torque permanent magnet synchronous motor as an example, the accuracy of the model is verified by comparison with an ideal circular ring model, a segmented sector ring model, and the finite element method. Based on the proposed simplified model, three combined permanent magnets considering both edge-cutting and polar arc cutting structures are proposed, which are chamfered, rounded, and rectangular combinations. Under the premise of a consistent edge-cutting amount, the electromagnetic characteristics of the three combination types of permanent magnets are compared using the finite element method. The results show that the electromagnetic characteristics of the chamfered combination PM are superior to those of the other two combinations. Finally, a prototype is manufactured and tested to validate the theoretical analysis.

Analysis of Contra-Rotating Brushless Integrated Flux-Modulation Machine With Open-Slot Structure for Wind Power Generation

This paper presents a contra-rotating (CR) brushless integrated flux-modulation (BIFM) machine with open-slot structure for wind power generation, termed CR-BIFM machine. The presented machine employs two contra-rotating rotors coupled with two sets of wind turbine blades, thus being able to capture more wind energy than conventional single-rotor wind turbines. Due to the dual flux-modulation effect and flux-bridge effect, the presented machine exhibits high torque/power density, making it suitable for direct-drive wind power generation without issues related to mechanical gearboxes. As two sets of windings share the same stator slots in the presented machine, the decoupling design of windings is systematically investigated from the perspective of air-gap modulated magnetic field, considering the influence of both stator and rotors. The advantages of the presented machine are comprehensively evaluated compared to the baseline machine, showing that the presented machine exhibits higher torque/power density, higher efficiency, higher power factor, higher PM utilization, and better vibration performance. Finally, a prototype is fabricated and tested to validate the analysis.

Analytical calculation method of a liquid-cooling eddy current brake considering magnetic saturation and skin effect

In this article, a clear and concise analytical method for predicting the performance of a Liquid-cooling eddy current brake (LC-ECB) is proposed. The LC-ECB has a coolant channel in the rotor to allow direct cooling of the inner surface of the stator. The static air-gap magnetic field distribution is obtained by the dynamic magnetic equivalent circuit (MEC) method, and the magnetic flux leakage and global magnetic saturation effects are fully considered. The magnetic field intensity distribution function of the eddy current reaction magnetic field is derived for the first time based on Ampere circuital theorem. Considering the local magnetic saturation and skin effect, a novel double-iteration algorithm based on the conservation principle of magnetic pressure drop is applied to obtain the transient air-gap flux density distribution, and then the brake torque expression is obtained. The finite element method (FEM) and experimental results show that the proposed method is feasible and effective. The new model is easy to program and can be easily used in the initial design and optimization of LC-ECB.

Torsional vibration characteristics analysis and adaptive fixed‐time control of wind turbine drivetrain

AbstractThe drivetrain has an important impact on the stability and reliability of wind turbines operating in complex conditions, which belongs to the electromechanical coupling system. This work studies the two domains of research on drivetrain vibration analysis and control method in detail. The electromechanically coupled torsional vibration model is first established by considering the air gap magnetic field energy of the PMSG. Preliminary analysis in terms of Hamiltonian energy indicates that there is sufficient energy to sustain the exciting oscillation behaviors. Moreover, to reduce the vibration amplitude caused by wind speed or torsional stiffness, a novel adaptive fixed‐time control method is proposed to solve the issue of wind turbine drivetrain chaotic oscillation with uncertainties and disturbances. Furthermore, the proposed method not only can prevent the jumping and bifurcation of torsional vibration from happening, but also there are the advantages of the control scheme with high accuracy, fast convergence rate and strong robustness. For the fair comparison, three different control methods have been used to demonstrate the superiority of the control scheme by the simulation results. The research results can provide a theoretical basis for the parameter design and control of wind turbine drivetrain.

Vibration Characteristics and Vibration Mitigation Analysis of End Cap PM Excitation Homopolar Inductor Machine

Vibration analysis and vibration mitigation are very important to ensure the safe and stable operation of electrical machines applied in flywheel energy storage systems (FESS). In traditional integer slot synchronous machines, it is generally believed that there is only the zeroth-mode vibration caused by odd tooth harmonics. However, the homopolar inductor machine (HIM) adopts the end cap excitation structure, which makes its air-gap magnetic field contain the DC component, odd tooth harmonics and even tooth harmonics. The force density distribution on the slotted stator is analyzed by the magnetomotive force-multiplying permeance method. The results show that there are both zeroth- and pth(pole pairs)-mode vibrations caused by tooth harmonics and DC component of the air-gap flux density. Furthermore, to reduce vibration and resonance, and to improve the electromagnetic performance of HIM, it is best to use the stator skew slot, the magnetic slot wedge (MSW) and the sinusoidal rotor slot at the same time. Finally, a 54-slot/6-pole EPE-HIM is tested to validate the analytical and the finite-element method (FEM) results, and the variation trend of the experimental results and FEM results is the same.

A mathematical analytical modeling method for rotor eccentricity fault of large VSPSU

Aiming at the rotor eccentric fault modeling problem of large VSPSU (VSPSU), a mathematical analytical modeling method based on air gap magnetic field analysis is proposed. This method uses Fourier series decomposition to represent the air gap permeability of static and dynamic eccentricity faults. Then, taking a single coil as a unit, the eccentric self-inductance coefficients between each branch of the windings are derived. Furthermore, the mathematical analytical modeling of the eccentric fault is completed by combining the voltage and flux formulas of each winding branch. The model can reliably reflect the typical fault characteristics of large VSPSUs with eccentric faults, which can provide an analysis basis for subsequent relay protection research.

Investigation on the Influence of Eccentricity on the AC Copper Loss of High-Speed Slotless Permanent Magnet Motor

The armature winding of slotless motor is directly exposed to the air gap magnetic field. During high speed operation, the effective part of the armature winding cuts the flux lines directly, which would inevitably cause large AC copper loss. Moreover, when the rotor is eccentric, appreciable distortions would be appeared in the air gap flux density. The additional flux density would aggravate the AC copper loss. In this paper, the mechanism of AC copper loss of high speed slotless motors is explained firstly. Then the influence of eccentricity on AC copper loss is evaluated. Finally, the difference in the effect of dynamic and static eccentricity on AC copper loss is compared.

Suspension Flux Internal Model Control of Single-Winding Bearingless Flux-Switching Permanent Magnet Motor

A suspension flux internal model control method is proposed to address the problem of the strong coupling of a single-winding bearingless flux-switching permanent magnet motor leading to a significant ripple of the rotor radial displacement. Firstly, based on air-gap magnetic field modulation theory, the stator flux equation considering rotor dynamic eccentricity is established to reveal the relationship between the eccentric rotor and the magnetic field. Secondly, according to the dynamic characteristics of the motor and the variation law of the air-gap magnetic field, the suspension-plane flux is substituted into the rotor dynamic model, and the suspension flux-dynamics internal model and corresponding output are constructed, respectively. Finally, a complete control strategy is established, and the rotor is stably suspended by PWM control. The simulation and experimental results show that the proposed method has better steady-state and dynamic performance than traditional PID control, and the maximum radial displacement ripples of the rotor are reduced by 53% and 50% in steady-state and dynamic operation.

The harmonic resonance and singularity analysis of bifurcation for the magnetized elastic plate with action of time-varying magnetic potential

This paper deals with the superharmonic resonance of a ferromagnetic thin rectangular plate in the air-gap magnetic field excited by armature magnetic potential. Electromagnetic forces applied on the plate by the air-gap magnetic field cause the plate to transversal vibrate, which affects the air-gap magnetic field in turn, resulting the vibration and magnetic field coupling. According to the basic electromagnetic field theory and considering the magnetoelastic coupling effect, the air-gap magnetic field intensity is obtained by solving the Laplace's equation satisfied the air-gap magnetic boundary conditions. The electromagnetic force model of soft ferromagnetic plates is determined based on theories of electromagnetic and elasticity. According to the large deflection theory of plates, basic energy relationships and variational equations of the elastic plate are given. Eventually, the nonlinear magnetoelastic vibration equation of ferromagnetic thin plates is derived using Hamilton's principle and Galerkin method. The multi-scale method is used to solve the superharmonic resonance to obtain the amplitude-frequency response equation and the stability discriminant of solutions. The topological analysis of amplitude-frequency equation is carried out using singularity theory, and the bifurcation characteristics of systems on physical parameter planes in different regions are obtained according to the transition set. The correctness of analytical solutions is verified by comparison with numerical solutions. Through numerical calculations, curves of the static deflection and equivalent magnetic force of plate with parameters are given, and the amplitude curves, dynamic phase plane trajectories and time history diagrams of system response with changes in electromagnetic and structural parameters are plotted. Results show that both the decrease of armature magnetic potential amplitude and the increases of plate thickness and initial air-gap thickness reduce the static deflection. The increase of armature magnetic potential amplitude increases the equivalent magnetic force. As the decrease of initial air-gap thickness and the increases of armature magnetic potential amplitude and excitation force amplitude, the amplitudes of the upper branch and lower branch curves representing stable solutions decrease and increase, respectively, and the single-value solution region increases.

A Novel Analytical Formulation of the Magnetic Field Generated by Halbach Permanent Magnet Arrays

This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement.

A Planar Electromagnetic Actuator With Passive Adsorption for CubeSats Transport in a Weightless Environment

A planar electromagnetic actuator (PEA) with passive adsorption is proposed to transport multiple miniature satellites (CubeSats) in a weightless environment. It can realize reliable mover adsorption to the track and fast 2-Dof translational motion, even under the interference of external acceleration. Compared with the conventional layout of permanent magnets (PMs), the PEA with the structure of Halbach array can achieve higher force density. The magnetic equivalent circuits (MEC) method is applied to reveal the mechanism of electromagnetic performance improvement. An accurate electromagnetic force model is developed by combining the MEC and mirror magnetic charge methods to consider the positive effects of yokes on the PM operating point and airgap magnetic field distribution for PEAs with large airgaps. The influence of main structural parameters on adsorption and driving performances is analyzed. A kinetic model is derived to predict the mover velocity. A PEA prototype has been manufactured and tested to experimentally validate the improved models, electromagnetic performance, and motion characteristics.

Analysis of rotor fatigue characteristics of permanent magnet synchronous motor spindle in eccentric state

In this paper, the distribution of the air gap magnetic field in the motorized spindle is obtained through theoretical derivation, which is verified by comparing with the finite element simulation results. Based on the original calculation of air gap magnetic field, the rotor eccentricity theory is added, and the distribution of air gap magnetic field after rotor eccentricity is obtained. The correctness of the calculation theory of eccentric air gap magnetic field is verified by the finite element simulation results. Through the electromagnetic force calculation and finite element simulation of asymmetric magnetic field in eccentric state, the influence law of unbalanced electromagnetic force on the fatigue life of motorized spindle rotor is summarized.

Optimization of coaxial magnetic gear and its application in wave power generation

The application of coaxial magnetic gear (CMG) in wave generator instead of traditional variable speed gearbox can effectively improve torque density and reduce torque ripple. Thus, the operation principle of CMG from the perspective of magnetic field modulation is firstly analyzed in this paper. Then the air gap magnetic fields induced by high-speed and low-speed rotors are studied. And the radial height, inner diameter angle, and outer diameter angle of the modulating pieces (MPs) are optimized by using the combination of response surface method (RSM) and particle swarm optimization (PSO) algorithm to improve the torque transmission capacity of CMG. The CMG is combined with the permanent magnet synchronous machine to get the magnetic-gear permanent magnet synchronous generator (MG-PMSG). The design feasibility of the MG-PMSG is verified from four aspects: static magnetic field analysis, no-load characteristics, load characteristics and load disturbance analysis.

3D Hybrid Segmented Layer Modeling of On-Load Magnetic Fields and Torques for Coreless Axial-Flux Permanent Magnet Synchronous Motor

This paper presents a novel 3-dimensional hybrid segmented layer model (3D HSLM) for coreless axial-flux permanent magnet synchronous motors (AFPMSMs). In the proposed 3D HSLM, the magnetic field sources are divided into the PM array and current-driven electro-magnets, which are captured by the combination of the magnetic scalar potential and vector potential models. This paper proposes a geometry function and cylindrical harmonic index modulation functions in order to correctly capture the curvature effect by the PMs and coils with arbitrary shapes and also the radial edge effect from the finite lengths of the rotor and the stator. The proposed modeling method also enables accurate estimation of the motor characteristics on the on-load conditions using the magnetic vector potential model. The fidelity of the proposed 3D HSLM is validated against the equivalent FEM models for various cases with different PM and coil shapes, in terms of the airgap magnetic fields, motor torque, and flux linkage. The comparison results show that the proposed 3D HSLM yields a modeling accuracy of more than 98% while significantly reducing the calculation time by two orders of magnitude as compared to the FEM models.

Accurate Modeling and Optimization of Electromagnetic Forces in an Ironless Halbach-Type Permanent Magnet Synchronous Linear Motor

In order to solve the electromagnetic force optimization problem of a high-power-density ironless Halbach-type permanent magnet synchronous linear motor, this paper adopts an electromagnetic force optimization method based on magnetic field analysis, electromagnetic force modeling, and genetic algorithm optimization: Firstly, the magnetic field of the Halbach permanent magnet array is solved by the combination of the equivalent magnetization strength method and the pseudo-periodic method, which takes into account the influence of the edge effect of the secondary magnetic field, and the magnetic field of the primary winding is solved by Fourier series expansion method. Secondly, the Maxwell tensor method is used to establish the functional relationship between the electromagnetic thrust and the main structural parameters of the unilateral motor. Finally, based on the parameter sensitivity analysis of the optimized variables and the response surface calculation, the optimal combination of the optimized variables to meet the optimization objective is found by a genetic algorithm. This method of the accurate modeling and optimization of an electromagnetic force can accurately calculate the motor air gap magnetic field and electromagnetic thrust, and the optimization speed is fast, which can greatly save time. The optimization results show that, under the premise of constant input power, the unilateral average thrust of the motor is increased by 18.75%, the peak value of thrust fluctuation is decreased by 30.27%, and the results match well with the finite element results, which verifies the correctness of the optimization results of the electromagnetic force and the reasonableness of the optimization method.