No-load back-EMF Research Articles

An improved subdomain modeling technique for surface-mounted permanent magnet Vernier motor

This work aims to provide a unique analytical model designed for calculating the magnetic field of a surface-mounted permanent magnet Vernier motor (SPMVM). The model is created utilizing the separation variable method to solve Laplace or Poisson equations of the vector magnetic potential in a quasi-Cartesian coordinate system subdomain model. The theoretical justifications for the final analytical equations of electromagnetic torque, no-load back-EMF, stator inductance, and magnetic flux density distribution are given in detail. Then the solution of the equation is expressed in the form of a hyperbolic function. Furthermore, the improved analytical method in the study is generic and can be applied to estimating the parameters of machines with different design concepts. Finally, FEM is employed as the reference for comparison between other models. Compared to the original subdomain model, the calculation results of the improved analytical model are more time-efficient and closer to those of FEM. In addition, the improved analytical method can reduce the dimension of the coefficient matrix and improve the calculation speed. The SPMVM prototype is then built to demonstrate the validity and feasibility of the improved subdomain method and serves as a guide for future SPMVM development.

Analytical Calculation of Magnetic Field and Analysis of Rotor Permeability Effects on Permanent Magnet Synchronous Motor with Fractional Slot Concentrated Winding

Accurate calculation of the flux and the magnetic field distribution of fractional slot concentrated winding permanent magnet synchronous motor (FSCW PMSM) is the basis for motor performance analysis, and rapid calculation is key. In this paper, to solve the problem of difficult modeling and accuracy guarantee of the flux linkage differential method, a method is proposed to calculate the flux and the no-load back EMF by the slotless subdomain model. By introducing the leakage flux calculation link, the calculation accuracy is improved, the analytical method results are compared with the finite element method results, and the effectiveness of the proposed method is verified. On this basis, the nonlinear variations of the magnetic field and the no-load back EMF with rotor permeability are determined, and the influence mechanism of rotor length and rotor permeability on the main magnetic circuit is revealed. Finally, an experiment of the prototype is carried out, and the correctness and accuracy of the analytical method and the finite element method is verified by comparing with the experimental results.

Multi-Objective Optimization Design of 40 MW High-Temperature Superconducting Motor

Abstract To reduce the length of the superconducting wire of the superconducting motor, the no-load back EMF E and the magnetic field component perpendicular to the wire B⊥ were selected as the optimization goals. Therefore, a multi-objective optimization method based on the Response Surface Method (RSM) and Genetic Algorithm (GA) was proposed by taking a high-temperature superconducting motor (HTSM) with a rated power of 40 MW as the research object. Firstly, the overall structure, mathematical model, and output characteristics of HTSM were introduced. Secondly, the sample points required for constructing the RSM equation were obtained by Finite Element Analysis (FEA), and the multi-objective optimization of the RSM equations was performed by applying GA to obtain the Pareto optimal frontier. Finally, the calculated optimal design was simulated and verified. Compared with the initial design, the E of the optimized HTSM was increased by 4.47%, and the B⊥ was reduced by 4.83%. Based on the motor parameters obtained by multi-objective optimization, the final optimized design of HTSM was obtained. The length of the superconducting wire used in the motor has been reduced by 10.2%, which greatly reduces the cost.

Analysis of an Axial-Flux Slotted Limited-Angle Torque Motor with Quasi-Halbach Array for Torque Performance Improvement

Better torque performance and higher reliability have long been the focus of research for slotted limited-angle torque motors (LATMs), which are primarily used to position first-stage valves in electrohydraulic servosystems. This paper presents a high reliability axial-flux slotted LATM with quasi-Halbach array for torque performance improvement including constant torque range (CTR) and output torque. Firstly, the structure with two sets of windings and the operation principle of the proposed slotted LATM is analyzed. Secondly, a brief design procedure is presented, the structure selections of open slot and double-stator single-rotor (DSSR) interior rotor with surface mounted quasi-Halbach permanent magnet (PM) array are illustrated, and the geometric parameters are optimized to obtain the optimal design of the proposed slotted LATM. Then, 3-D finite-element method (FEM) is employed to compare the proposed slotted LATM with the conventional surface mounted PM slotted LATM in terms of cogging torque, no-load back EMF, and output torque, and the results show that the proposed LATM with quasi-Halbach array has a 10% improvement in output torque and a 25% improvement in CTR. Meanwhile, the flux linkages and torque performance of the two sets of windings under various conditions verify good magnetic isolation. Finally, prototypes of two different rotor types are manufactured and a series of experiments are performed to validate the analysis.

Demagnetization Modeling and Analysis for a Six-Phase Surface-Mounted Field-Modulated Permanent-Magnet Machine Based on Equivalent Magnetic Network

Demagnetization Modeling and Analysis for a Six-Phase Surface-Mounted Field-Modulated Permanent-Magnet Machine Based on Equivalent Magnetic Network

Design and Optimization of PMSM for Injection Molding Machine

With the implementation of the “dual carbon policy”, the traditional injection molding machine transmission system pays more and more attention to improving the energy efficiency for the drive motor, and the PM motor has obvious advantages in injection molding machine drive motor because of its high efficiency and high-power density. A permanent magnet servo motor (PMSM) for an injection molding machine with a rated power of 7 kW is designed based on the theory of PMSM in this paper. The 2D finite element analysis (FEA) model of the motor is set up. The electromagnetic performance parameters are obtained, including cogging torque, torque ripple, output torque, and no-load back EMF. The cogging torque of the motor is optimized and analyzed. The results show that the optimized motor has reduced the cogging torque and torque ripple without affecting the output capacity, which is more suitable for the application in the drive system of the injection molding machine.

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.

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.

Magnetic Field Analysis of Surface-Mounted Permanent Magnet Motors Based on an Improved Conformal Mapping Method

In this article, an improved conformal mapping (ICM) method based on a complex potential function is proposed. It can improve the calculation speed and accuracy of magnetic fields for surface-mounted permanent magnet synchronous motors (SPMSMs). The eccentric-shaped poles are replaced by equivalent currents, and the improved conformal mapping method is adopted to transform an actual slotted motor air gap to an equivalent rectangular regular slotless air gap. The ICM method improves the speed of calculation because its number of mapping times is less than the traditional conformal mapping (TCM) method. By solving the complex potential generated by the equivalent current in the rectangular regular air-gap region, the air-gap magnetic field of the SPMSM under no-load, armature reaction and loaded conditions can be solved. Then, the no-load back-EMF and loaded torque performance under different load conditions are calculated. The accuracy of the ICM method is verified by finite-element simulation. In addition, the fast speed and high accuracy of the proposed ICM method incorporating the complex potential function for solving the air-gap magnetic field has been demonstrated in comparison to the TCM method with the Hague equation. An eccentric-shaped-pole permanent magnet motor prototype is also built and tested in experiment and the results agree with those calculated by the proposed ICM method.

Accurate sub-domain model for magnetic field computation in electrical machines with HTS materials

The primary aim of this study was to develop and validate an accurate sub-domain analytical model to estimate the magnetic field of electric machines with high-temperature superconducting (HTS) excitation and armature windings. The model was developed by utilizing the separation variable and harmonic analysis methods to solve Laplace’s or Poisson’s equations of the vector magnetic potential in two-dimensional polar coordinates. The theoretical derivations of the final analytical equations for the magnetic flux density distribution in the air-gap and in permanent magnets, electromagnetic torque, and no-load back-electromotive force (back-EMF) are explained in detail. Finally, the magnetic vector potential, flux density distribution of each sub-domain, no-load back-EMF, and inductive reactance of the armature winding were solved by considering the critical parameters of the superconducting materials, and the influence of higher harmonics. The finite-element method (FEM) was used to validate the accuracy of the developed analytical method for the investigated HTS generator. The results show the developed analytical method is accurate and time-saving.

Harmonic Magnetic Field Analysis Method and Modeling of Double-Sided Air-Cored Superconducting Linear Synchronous Motor for EDS Train

This study introduces a novel methodology based on the idea of double Fourier series and coil segmentation, performed based on governing equations, with harmonic magnetic field analysis of a double-sided air-cored superconducting linear synchronous motor for electrodynamic suspension train. This method can solve the harmonic magnetic field generated by arbitrarily shaped coils. First, with rectangular-shaped coils and race-track-shaped coils as examples, the process of calculating harmonic magnetic field using the proposed method is introduced comprehensively, and the influence of the end effect is also considered. Second, based on the solution results of the harmonic magnetic field, a modeling method that can quickly solve no-load superconducting flux linkage, no-load back EMF, and three-dimensional (3-D) electromagnetic forces without losing accuracy is presented, which is verified by finite element simulation. Finally, two static tests are designed. The effectiveness of the proposed method is verified by the test results of static thrust and static normal force.

PMSM Demagnetization Fault Diagnosis Based on Back-EMF Signal

To study the irreversible demagnetization fault of the permanent magnets (PMs) in the permanent magnet synchronous motor (PMSM), a two-dimensional Finite Element (FE) model of the PMSM is built by the Finite Element Method (FEM). Analysis of demagnetization faulty mechanism of the electric and magnetic signals under local demagnetization conditions is conducted. The no-load Back-EMF signal is adopted as the indicator of the demagnetization faults of PMSM. In this paper, the faults of uniform demagnetization and single magnet demagnetization are studied through FEA. Therefore, the relationship between the amplitude of the back EMF and the degree of demagnetization is obtained. Moreover, the fitting curve is obtained by using the least squares method from multiple sets of FEA results. The results show that the method can effectively diagnose the demagnetization fault of the PMs of the PMSM, and could provide the guideline for online health monitoring of the PMSM in future research works.

Multi-Objective Optimization of an Axial Flux Permanent Magnet Brushless DC Motor with Arc-Shaped Magnets

To get a better electromagnetic performance of an axial flux permanent magnet brushless DC motor (AFPMBLDC), an AFPMBLDC with arc-shaped magnets and its multi-objective optimization design are researched. Firstly, the main design parameters of the AFPMBLDC are proposed, and the initial designs are carried out according to the given requirements. Furthermore, the pole arc coefficient, permanent magnet thickness, permanent magnet arc radius, and air-gap length are selected as optimization factors. Then, an orthogonal experiment table is established, in which the flux density, no-load back EMF, harmonic distortion rate, and output torque ripple are selected as optimization targets. The Taguchi optimization method is adopted to optimize the performance indexes and the optimal parameters are obtained. Finally, the optimized model is constructed, and some simulations are carried out to verify the optimal design. The research results have shown that the air-gap flux density of the optimized AFPMBLDC is reduced to 31.8%, the total harmonic distortion rate of no-load back EMF is less than 7.5%, and the torque ripple is reduced to 4.3%.

SPMSM 설계를 위한 Slotless SPM 모델의 무부하 역기전력 해석

In SPMSM design according to the existing method, some empirical values were used in the calculation of the airgap flux density and the back EMF, so there was a difference from the design result. In order to minimize the dependence on these empirical values and to obtain an accurate back EMF, a method to calculate the no-load back EMF using an analytical method is proposed in this paper. The proposed method combines the airgap flux density distribution and the winding function and is verified using the FEM analysis results. Although this method is for a slotless model, according to the validation, the method proposed in this paper can be applied to perform a slotted model design.

Comparison and analysis of different rotor structures of double‐stator permanent magnet synchronous motor

Compared with the single-stator permanent magnet synchronous motor(SS-PMSM), the double-stator permanent magnet synchronous motor(DS-PMSM) can make full use of the space in the motor cavity to make it have higher torque density, so it is more suitable for direct-drive occasions with low-speed and high-torque. This paper aims to design and compare the parameters and performances of DS-PMSMs with four different rotor structures: 1)Series magnetic circuit of radial magnetised single-layer permanent magnet(type Ⅰ), 2)Series magnetic circuit of radial magnetised double-layer permanent magnet(type Ⅱ), 3)Parallel magnetic circuit of radial magnetised double-layer permanent magnet(type Ⅲ), 4)Parallel magnetic circuit of tangential magnetised permanent magnet(type Ⅳ). Firstly, the equivalent magnetic circuit method is used to analyse the magnetic circuits of the four DS-PMSMs. Next, the finite element analysis tool is used to compare the performances of the four DS-PMSMs with the same volume. Their air-gap flux density, no-load back-EMF, cogging torque, torque characteristics, moment of inertia, rotor loss and efficiency are quantitatively analysed and compared. Finally, this paper provides guidance and suggestions for the selection of the rotor structure of DS-PMSM.

A novel spoke‐type PM motor with asymmetric rotor for low torque pulsation under MTPA control condition

This article presents a novel asymmetric spoke-type rotor structure. It is used to reduce rotor magnetic flux leakage, torque ripple and no-load back-EMF distortion rate while increasing the motor output torque. The traditional method of optimizing torque pulsation is the inverse cosine function, which gives a sinusoidal distribution of the air-gap magnetic field under no-load conditions of the motor. The fundamental wave magnetic field of the air-gap synthetic magnetic field under the load is offset from the no-load air-gap magnetic field. This paper presents the design theory and method of the new type of the asymmetric rotor. Asymmetric spatial harmonics are introduced to the rotor so that the motor has a sinusoidal distribution of the rated load air-gap field under MTPA control. In order to verify the superiority of the new rotor, the performance of four different spoke-type rotor structure motors under the same pole-slot combination was compared. Finally, an experimental prototype is built to verify the theoretical reliability against the design of this paper.

Development of Dual Armature-Winding Four-Phase Variable Flux Reluctance Generator for Fault-Tolerant Capability Improvement

In this paper, a four-phase 8/10-pole dual armature-winding variable flux reluctance generator (DAW-VFRG) with double-redundant rectifier circuit is proposed for onboard generator. The proposed generator integrating four-phase VFRG and dual armature winding structure improves fault-tolerant capability and power density. Based on the airgap field harmonics analysis and winding function theory, the no-load back-EMF model and winding inductance model are deduced for determining the optimal stator/rotor pole combination. In addition, based on magnetic energy comparison, the influence of the connection categories between two sets of armature windings and rectifier circuits on output capability is also investigated when the saturation effect is considered. The key design parameters are globally optimized to improve the output capability and fault-tolerant capability simultaneously. Moreover, the electromagnetic performance of the proposed DAW-VFRG under both normal and fault condition is evaluated and compared with single armature-winding VFRG with half bridge rectifier. Finally, two prototypes are manufactured and tested to validate the finite-element predictions.

Performance analysis of asymmetrical less‐rare‐earth permanent magnet motor for electric vehicle

To reduce the manufacturing cost, the cogging torque and the torque ripple of the traditional V-shaped permanent magnet motor (TPMM), an asymmetrical less-rare-earth permanent magnet motor (ALREPMM) is proposed. An equivalent air-gap flux density model is established, the model is employed to calculate the analytical expression of the no-load back-EMF, and the multiple objectives optimisation are carried out for the motor parameters based on the Taguchi algorithm. Electromagnetic performance of the TPMM structure and the ALREPMM structure is compared by finite element method-based simulation. It is shown that the ALREPMM structure can reduce the amount of rare-earth materials by 19%, and the cogging torque and the THD values of no-load back-EMF are reduced by 77.3% and 26.8%, respectively. Finally, a prototype is manufactured, thus verifying the rationality of the design of the ALREPMM structure through experiments.

Winding MMF and PM MMF Analysis of Axial-Flux Machine with Multi-Phase and Multi-Layer Winding

According to star graph and winding distribution, winding MMFs of three kinds of 12-slot/10-pole multi-phase and multi-layer winding layout are analyzed by the improved winding function method. Analysis results show that multi-phase and multi-layer winding can suppress even order and (12n ± 1) order harmonics, thereby reducing the eddy-current loss in PMs. Based on the unfolded LPMSM model, rotor MMF, air gap flux density, and no-load back-EMF are analyzed by the analytical permeance function method, which is validated by Teslameter and no-load experiment. Winding MMF is validated by FEM. An axial-flux integrated starting/generator (ISG) with double-three-phase four-layer (DTP-FL) winding, segmented armature and PM, and centrifugal fan is designed and manufactured. The no-load and load test with two groups of resistance established has validated the reasonability of the mentioned method. Experiments show that the axial-flux ISG prototype can run at a relative temperature rise.

Comparative performance analysis of bearingless switched reluctance motor

To solve the magnetic field coupling problem in the traditional bearingless permanent-magnet motor, which has magnets on the rotor, we propose two topologies of bearingless switched reluctance motors (BLSRMs) with magnets on the stator yoke. The first is a six/four-pole BLSRM with three pairs of permanent magnets on the stator and the second is a six/four-pole BLSRM with one pair of stator yoke magnets. First, the working principle of BLSRMs is introduced, including the structure and winding configuration, and the mechanism of generating levitation force is analyzed in detail. Based on 2D finite element analysis, the electromagnetic characteristics of the prototype are compared, including torque, suspension force, no-load back EMF, and no-load permanent magnet linkage. The calculation results show that at high speeds, the coupling between the levitation force winding and the torque winding of the BLSRM with one magnet pair is low, which allows for better decoupling performance and greater levitation force. In addition, although the motor with three pairs of permanent magnets in the stator yoke shows better torque performance, the loss of the motor is higher at a high speed. The research results lay a theoretical foundation for further research on a new type of bearingless motors.