Air-gap Flux Research Articles

An Improved Magnetic Equivalent Circuit Method for Segmented-Halbach Axial-Flux Permanent Magnet Machines

Much attention is paid to axial-flux permanent magnet (AFPM) machines thanks to the compactness and high torque density. However, the finite element method (FEM) for AFPM machines will cause a large computational burden during simulation. Thus, this paper proposes an improved magnetic equivalent circuit method (MECM) to predict the performances of segmented-Halbach AFPM machines, which can consider the different magnetization directions of Halbach PMs. Magnetic circuit is built in the whole machine. Besides, the air gap is treated as a slide layer to avoid the additional models for position-dependent permeances. Then, the predicted performances are compared with those calculated by FEM and measured in an experiment. As a quasi 3D analytical method, it predicts the same air-gap flux density as the FEM. The only errors are due to the serious flux leakage caused by opening slots. The predicted back EMF is consistent with the measurement in the experiment. The electromagnetic torque is affected by the errors of air-gap flux density, which results in large ripples. However, the trend of torque with current coincides with the measurement. It means the proposed MECM is effective for the segmented-Halbach AFPM machine.

A New Technique for the Subdomain Method in Predicting Electromagnetic Performance of Surface-Mounted Permanent Magnet Motors With Shaped Magnets and a Quasi-Regular Polygon Rotor Core

Surface-mounted permanent magnet (SPM) motors with shaped magnets and a quasi-regular polygon rotor core (QPRC) are challenging to analyze in terms of accuracy and speed because of the special structure. This article proposes a new technique for the subdomain method which can accurately predict the electromagnetic performance of this kind of motor. The proposed new technique deals with the shaped magnet based on the method of magnet symmetrical segmentation, and it can solve the magnetic field generated by a pair of symmetrical segments together at each time. Especially, for the QPRC, the idea of variable rotor core radius is used in the new technique to analyze different segments. Furthermore, the new technique adopts a periodic boundary condition, which can quickly predict the electromagnetic performance of the motor, such as air-gap flux density, cogging torque, no-load back-EMF, winding inductance, electromagnetic torque and unbalanced magnetic force (UMF). This proposed new technique is applied to a 12-pole/3-phase SPM motor with shaped magnets and a QPRC, and its correctness is verified by finite-element analysis and experiment. The new technique can analyze the motor accurately, and its calculation speed is two orders of magnitude faster than that of the finite-element method.

Torque Capability Comparison of Induction and Interior Permanent Magnet Machines for Traction Applications

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.

Analytical modeling and performance evaluation of an adjustable permanent magnet linear eddy current brake with mechanical magnetic adjuster

A novel mechanical flux-adjusting permanent magnet linear eddy current brake with high performance and its nonlinear analytical model are proposed. The innovative point lies in attaching an additional mechanical magnetic adjuster directly above the interior permanent magnet bar, which can achieve flexible adjustment of the air-gap flux and improve the generation capacity of the braking force and its regulation range. Considering the importance of the analytic model in practical design, the average air-gap flux density and eddy current density are estimated based on the equivalent magnetic circuit method and Ampere’s law, where the critical flux-weakening effect and leakage flux effect are calculated quantitatively. Then a practical theoretical model of braking force is derived based on the energy conversion and verified by the 3D finite-element method. Through analysis of the magnitude and regulation range of the braking force in a given range of speed, the advantages of the device and the electromagnetic force model are proved separately. Moreover, design suggestions for selecting the key geometrical parameters are further given, which offer useful information for pre-design and optimization.

Bearing Fault Numerical Model for the Closed-slot Rotor Submersible Motor

This study proposes a numerical model of the bearing fault of a motor with a closed-slot rotor using the finite element method (FEM). The rotor's radial motion can be regarded as static eccentric at the defect time points and healthy at other time points. The frequency of the harmonic component is analyzed corresponding to bearing fault in stator current according to the radial movement of the motor shaft. Moreover, the relative permeability variation region is established to achieve the radial motion of the rotor with bearing fault. Firstly, the relative permeability variation region is established in the health and static eccentric models. Then, the defect time points are estimated and the static eccentricity model by transient field is analyzed. Finally, the relative permeability of the variable region in the static eccentric model is imported into the variable region of the health model at the defect time points. The simulation results show that the air gap flux density of the bearing fault model is different from that of the health model and static eccentric models. In addition, the stator current contains harmonic components of the bearing fault. The analysis results prove the applicability of the proposed model.

Analysis and Compensation of Hysteresis Effect on Electromagnetic Force in Axial Magnetic Bearings

Magnetic bearings (MBs) enable the rotor to run at high speed without lubrication due to no mechanical contact. However, the inherent hysteresis of ferromagnetic materials affects the support characteristics, reducing the design performance and stability margin of MBs, especially for axial MBs using materials with high coercive force. To analyze and compensate for the hysteresis effect on the electromagnetic force in axial MBs, an efficient method is proposed in this paper. Firstly, the hysteresis properties of the ferromagnetic materials are simulated by the Preisach model, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> relationships under any external magnetic field can be determined. Taking into account the non-ideal factors such as hysteresis and saturation effects, the nonlinear magnetic circuit model of the axial MBs is established. The magnetic flux density working point under different control currents and eccentric displacements can be determined through iterative calculation, and then the air gap flux density distribution and electromagnetic force of the axial MBs are calculated. On this basis, the adverse effects of hysteresis on the bearing capacity and system stability of axial MBs are analyzed. A compensation algorithm is designed based on the inverse model to reduce the hysteresis effect. The inverse model is approximated modeled by the Lissajous curve. Finally, the proposed analysis and control methods are verified by the finite element method (FEM) or experiments. The results show that the proposed analysis method is capable of accomplishing good accuracy and requires less computation time than FEM, it can be applied to arbitrary current variation processes. In addition, the phase lag of the system is effectively improved with the compensation algorithm.

Design of Rotor Magnetic Barrier Structure of Built-in Permanent Magnet Motor Based on Taguchi Method

In this paper, a 20kW vehicle built-in permanent magnet synchronous motor is taken as an example, and a magnetic barrier structure is added to the rotor of the motor to solve the uneven saturation problem of the rotor side magnetic bridge. This structure improves the air-gap flux density waveform of the motor by influencing the internal magnetic flux path of the motor rotor, thus improving the sine of the no-load back EMF waveform of the motor and reducing the torque ripple of the motor. At the same time, Taguchi method is used to optimize the structural parameters of the added magnetic barrier. In order to facilitate the analysis of its uneven saturation phenomenon and improve the optimization effect, a simple equivalent magnetic network (EMN) model considering the uneven saturation of rotor magnetic bridge is established in this paper, and the initial values of optimization factors are selected based on this model. Finally, the no-load back EMF waveform distortion rate, torque ripple and output torque of the optimized motor are compared and analyzed, and the influence of magnetic barrier structure parameters on the electromagnetic performance of the motor is also analyzed. The results show that the optimized motor can not change the output torque of the motor as much as possible on the basis of reducing the waveform distortion rate of no-load back EMF and torque ripple.

Analytical Modeling of Open-Circuit Air-Gap Flux Density in Interior Permanent Magnet Machine

In this paper, a general analytical model suitable for the magnetic analysis of the interior permanent magnet (IPM) machine is proposed by coupling the equivalent model and Maxwell’s equations based 3-D analytical model. In the proposed analytical model, to reduce boundary conditions, the IPM topology is transformed into the surface-mounted permanent magnet (SPM) topology through the equivalent model with universality. Meanwhile, Maxwell’s equations based 3-D analytical model is established to conduct magnetic analysis and then gives a unified expression of air-gap flux density of the IPM machine. Then, the saliency effect is taken into account using the saliency coefficient, which is deduced by the magnetomotive force and flux-path permeance model. Additionally, the slotting effect is considered by conformal mapping. The saliency and slotting effect act on additional functions in the analytical model. Finally, the accuracy of the analytical method is validated by the finite element method (FEM) in the IPM machine condition.

Permanent Magnet Assisted Synchronous Reluctance Motor with Asymmetric Rotor for High Torque Performance

Permanent magnet assisted synchronous reluctance motor (PMA-SynRM) is a kind of high torque density energy conversion device widely used in modern industry. In this paper, based on the basic topology of PMA-SynRM, a novel PMA-SynRM of asymmetric rotor with position-biased magnet is proposed. The asymmetric rotor design with position-biased magnet realizes the concentration of magnetic field lines in the motor air gap to obtain higher electromagnetic torque, and makes both of magnetic and reluctance torque obtain the peak value at the same current phase angle. The asymmetric rotor configuration is theoretically illustrated by space vector diagram, and the feasibility of high torque performance of the motor is verified. Through the finite element simulation, the effect of the side barrier on output torque and the Mises stress under the rotor asymmetrical design are analyzed. Then the motor characteristics including airgap flux density, back EMF, magnetic torque, reluctance torque, torque ripple, losses, and efficiency are calculated for both the basic and proposed PMA-SynRMs. The results show that the proposed PMA-SynRM has higher torque and efficiency than the basic topology. Moreover, the torque ripple of the proposed PMA-SynRM is reduced by the method with harmonic current injection, and the torque characteristics in the whole current cycle are analyzed. Finally, the endurance to avoid PM demagnetization is confirmed based on the PM remanence calculation.

Analytical Calculation of Air Gap Magnetic Field of SPMSM with Eccentrically Cut Poles Based on Magnetic Pole Division

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.

Performance Evaluation of Stator/Rotor-PM Flux-Switching Machines and Interior Rotor-PM Machine for Hybrid Electric Vehicles

A three-phase interior permanent magnet (IPM) machine with 18-stator-slots/12-rotor-poles and concentrated armature winding is commercially employed as a 10 kW integrated-starter-generator in a commercial hybrid electric vehicle. For comprehensive and fair evaluation, a pair of flux-switching permanent magnet (FSPM) brushless machines, namely one stator permanent magnet flux-switching (SPM-FS) machine, and one rotor permanent magnet flux-switching (RPM-FS) machine, are designed and compared under the same DC-link voltage and armature current density. Firstly, a SPM-FS machine is designed and compared with an IPM machine under the same torque requirement, and the performance indicates that they exhibit similar torque density; however, the former suffers from magnetic saturation and low utilization of permanent magnets (PMs). Thus, to eliminate significant stator iron saturation and improve the ratio of torque per PM mass, an RPM-machine is designed with the same overall volume of the IPM machine, where the PMs are moved from stator to rotor and a multi-objective optimization algorithm is applied in the machine optimization. Then, the electromagnetic performance of the three machines, considering end-effect, is compared, including air-gap flux density, torque ripple, overload capacity and flux-weakening ability. The predicted results indicate that the RPM-FS machine exhibits the best performance as a promising candidate for hybrid electric vehicles. Experimental results of both the IPM and SPM-FS machines are provided for validation.

Design advantages and analysis of a novel five-phase doubly-fed induction generator

PurposeThe purpose of this paper is to provide an analysis of the performance of a new five-phase doubly fed induction generator (DFIG).Design/methodology/approachThis paper presents the results of a research work related to five-phase DFIG framing, including the development of an analytical model, FEM analysis as well as the results of laboratory tests of the prototype. The proposed behavioral level analytical model is based on the winding function approach. The developed DFIG model was used at the design stage to simulate the generator’s no-load and load state. Then, the results of the FEM analysis were shown and compared with the results of laboratory tests of selected DFIG operating states.FindingsThe paper provides the results of analytical and FEM simulation and measurement tests of the new five-phase dual-feed induction generator. The use of the MATLAB Simscape modeling language allows for easy and quick implementation of the model. Design assumptions and analytical model-based analysis have been verified using FEM analysis and measurements performed on the prototype. The results of the presented research validate the design process as well as show the five-phase winding design advantage over the three-phase solution regarding the control winding power quality.Research limitations/implicationsThe main disadvantage of the winding function approach-based model development is the simplification regarding omitting the tangential airgap flux density component. However, this fault only applies to large airgap machines and is insignificant in induction machines. The results of the DFIG analyses were limited to the basic operating states of the generator, i.e. the no-load state, the inductive and resistive load.Practical implicationsThe novel DFIG with five phase rotor control winding can operate as a regular three-phase machine in an electric power generation system and allows for improved control winding power quality of the proposed electrical energy generation system. This increase in power quality is due to the rotor control windings inverter-based PWM supply voltage, which operates with a wider per-phase supply voltage range than a three-phase system. This phenomenon was quantified using control winding current harmonic analysis.Originality/valueThe paper provides the results of analytical and FEM simulation and measurement tests of the new five-phase dual-feed induction generator.

Research on Electromagnetic Vibration Characteristics of a Permanent Magnet Synchronous Motor Based on Multi-Physical Field Coupling

Background and Purpose: The stator vibration characteristics are comprehensively mastered by considering the influence of winding and the housing structure on the stator modes. This effect is neglected in the research field of electromagnetic vibration of permanent magnet synchronous motors (PMSMs). Methods: The radial air-gap flux density equations and PMSM’s electromagnetic force density are derived, and then the harmonic characteristics of electromagnetic force density are studied. An equivalent finite element model of the stator is proposed that investigates the impacts of the winding and stator housing rules on the stator modal frequency. Finally, the harmonic response and acoustic analyses of electromagnetic vibration are carried out based on multi-physics field coupling. Results: The equivalent radiated power distribution laws and acoustic field of motor electromagnetic vibration under transient operating conditions are obtained. The theoretical analysis results are consistent with the experimental results. Conclusion: The obtained results show that the spatial order of the radial electromagnetic force is not equal to the order of the radial mode of the motor stator. The reason for this is that structural resonance is induced when the frequency components of the spatial radial electromagnetic force are coupled with the intrinsic frequency of the stator.

Design and Performance Comparison of Novel Flux-Concentrating IPM Machines for Power Generation System Application of Extended-Range Electric Vehicle

A new spoke-type interior permanent magnet (IPM) machine with enhanced flux-concentrating capability and high saliency ratio rotor is proposed for the extended-range electric vehicles traction applications. The evolution of the proposed flux-concentrating rotor structure from the spoke-type IPM rotor is illustrated to achieve a higher saliency ratio and higher air-gap flux density. Two IPM motors with the same magnets volume are developed and compared with the proposed IPM machine. The rotor configurations are optimized by the multiobjective genetic algorithm to maximize the torque/power and minimize the cogging torque, as well as increasing the saliency ratio. Furthermore, the major electromagnetic performance of the three machines are analyzed and compared by the finite-element analysis (FEA), including the air-gap flux density, cogging torque, saliency ratio, torque-current curves, and field-weakening capability. The results show that the IPM machine with high saliency ratio rotor can achieve higher torque/power, maximum torque per ampere capability, and flux-weakening ability. Finally, a-rated 60-kW PM motor with the proposed rotor is manufactured and experimented to verify the results of the FEA.

Torque Ripple Generation Mechanism of Induction Motors by Time and Space Harmonic Fields

In this article, we investigate the generation mechanism of torque ripples in induction motors by using theoretical expression of torque ripples and finite element analysis, to obtain useful information of motor designs. By analyzing the time and space harmonics included in the air-gap flux densities, it is revealed that the torque ripple generation mechanism of induction motors is quite different from that of synchronous motors. The proper stator/rotor slot combinations to reduce the torque ripple is also clarified.

Design Criterion and Analysis of Hybrid-Excited Vernier Reluctance Linear Machine With Slot Halbach PM Arrays

This paper proposes a hybrid-excited vernier reluctance linear machine (HEVRLM) with slot halbach PM arrays. By utilizing halbach PM arrays, leakage flux that existing in the consequent pole structure can be greatly reduced. Besides, the dc excitation can enhance both the flux regulation capability and force density. First, the machine topology and working principle are introduced. Then, magnetomotive force (MMF)-permeance model is established to analytically calculate the air gap flux density under hybrid excitation. Moreover, the flux regulation capability, thrust force characteristic and PM demagnetization risk of the proposed machine are comparatively studied based on finite element method (FEM). It shows that halbach PM arrays can effectively reduce the leakage flux and further significantly improve the thrust force density by more than 30&#x0025;. In addition, hybrid excitation is a feasible approach to further improve the thrust force density by distributing the optimal dc and ac currents. Moreover, the proposed HEVRLM exhibits high thrust force density compared with other three types of hybrid-excited linear machines. Finally, a prototype of HEVRLM is manufactured and tested for experimental validation.

Model Order Reduction of Cage Induction Motor With Skewed Rotor Slots Using Multiport Cauer Ladder Network Method

A method for efficiently deriving a reduced-order model of a cage induction motor (IM) with skewed rotor slots is proposed based on the multiport Cauer ladder network (CLN) method. This paper presents several formulations of the multiport CLN method for the skewed rotor, in which the continuity of the bar currents and the space harmonics included in the air-gap flux density waveform are treated differently. The effectiveness of the developed methods was verified from the viewpoints of computational accuracy and cost through application to a practical cage IM with skewed rotor slots.

Structural optimizing design of magnetic barrier primary vernier permanent magnet linear motor

In order to behave the advantages of the primary vernier permanent magnet motor in the rail transport industry, this paper proposes a new type of magnetic barrier primary vernier permanent magnet motor. A non-magnetic material is added between the permanent magnet and the pole pieces in the primary of the motor, and a magnetic barrier coupling mechanism is applied in the secondary of the motor. Firstly, this paper expounds the structural features and operating mechanism of the motor. The equivalent magnetic circuit method is used to deduce the formula of the air gap flux density expression suitable for the magnetic barrier type primary vernier permanent magnet linear motor. Comparing the exemplified motor with two kinds of reluctance motors, and optimizing the parameters of the thickness of the permanent magnet material, the thickness of the non-magnetic conductive material and the arc coefficient of the secondary pole, the results of finite element simulation analysis show that after the usage amount of permanent magnets is reduced by 27%, the thrust of the motor is only reduced by 2.7%, and the thrust fluctuation is reduced by 13%.

Research on magnetic field and temperature field of multi-phase SPMSM under winding fault

In order to quickly and accurately calculate fault-tolerant capability of multi-phase surface-mount permanent magnet synchronous motor (SPMSM) at condition of asymmetrical fault, based on subdomain model, an analytical model for multi-phase SPMSM with asymmetric fault is proposed to calculate magnetic field distribution. Firstly, air-gap flux density, no-load back electromotive force (EMF) and electromagnetic torque are obtained accurately. Then, in order to improve the fault-tolerant capability of multi-phase SPMSM, with the minimum phase current as optimization objective, a fault-tolerant control system under the condition of single-phase winding disconnection is established. The performance of electromagnetic torque and torque ripple are used as evaluation indicators. Finally, taking a 12-phase SPMSM prototype with 44-poles 48-slots as an example, the effectiveness of proposed model is proved by 2D finite element model (FEM) and experiment test.

Analytical Investigation of Magnetic Scalar Potentials Oscillation in Spoke PM Flux Modulation Machines

In this paper, the oscillation phenomena of the scalar magnetic potential of iron pieces of spoke permanent magnet (PM) machines are analyzed and the effects of the oscillation on the air gap flux and back electro-motive force (EMF) are deeply investigated, especially for flux modulation machines such as vernier and flux switching PM (FSPM) machines. To these ends, the formula of the scalar magnetic potential is derived for a generalized spoke PM structure. It reveals that the oscillation phenomena depend on the slot/pole combination, consequently resulting in different behavior according to the machine types such as vernier and FSPM machines. Next, each core’s potential given as a discrete function is developed into a continuous function of an air gap magneto-motive force (MMF) rotating and oscillating through Fourier series expansion. Making use of the developed MMF and the specific permeance of air gap, the equations of air gap flux density and back EMF are derived, which enable accurately estimating the suppression of the modulation flux and the back EMF due to the potential oscillation for different types of spoke PM machines. For validation, various magnetic characteristics are quantitatively examined for different type of spoke PM structures, including PM vernier and FSPM machines, and verified by comparing with FEM simulation results.