No-load Back Electromotive Force Research Articles

A Quasi-Sinusoidal Concentrated Winding Used in an Integrated Magnetic-Field-Modulated Brushless Compound-Structure Machine

As a promising candidate of the electrical continuously variable transmission (ECVT), the integrated magnetic-field-modulated brushless compound-structure machine (IMFM-BCSM) has advantages of compact structure and no brush. The IMFM-BCSM is composed of a stator with two sets of windings, a permanent-magnet (PM) rotor and a modulation rotor. Due to its special operating principle, i.e., the magnetic field modulation principle, the back electromotive force (EMF) waveform distortion of the IMFM-BCSM is more serious than that of the conventional PM machine. To solve the above problem, a quasi-sinusoidal concentrated winding (QSCW) configuration is proposed and corresponding design method is further introduced. In order to observe the filtering ability of the QSCW, comparisons between QSCW configuration and fractional-slot concentrated winding configuration are carried out. The results show that when the QSCW configuration is employed, the no-load back EMF of the regular winding is more sinusoidal; the distortion degree is less affected by the rotor speeds; and the torque ripple is much smaller. Finally, a prototype is manufactured to verify the theoretical analysis.

Analysis and Reduction Methods of Cogging Torque in Dual PM Vernier Machines With Unevenly Distributed Split Teeth

This article investigates the source and reduction methods of cogging torque in dual PM Vernier machines (DPVMs), especially for the ones with unevenly distributed split teeth (UDST). At first, the increase of no-load back electromotive force in DPVMs with UDST is illustrated through the analysis of airgap working flux harmonics. The reason for largely increased cogging torque of DPVMs with UDST is then analyzed, and main flux harmonics that contribute to cogging torque are identified. To reduce cogging torque and torque ripple, several effective methods are introduced in this article, which are mainly based on the reduction or offset of corresponding airgap flux harmonics. The cogging torque reduction effects and torque performances of these methods are compared. Among them, newly proposed N/S-parts offset method is proved to be superior to other methods in DPVMs. A new DPVM prototype with UDST and N/S-parts offset structure is built and tested. Experimental results show that through the N/S-parts offset method, cogging torque of the machine is largely decreased from 9 to 0.3 N·m, which validates the analysis and simulation results.

Research on a Limit Analytical Method for a Low-Speed Micro Permanent Magnet Torque Motor with Back Winding

The conventional permanent magnet torque motor (PMTM) is slotted on the inner surface of the stator core. When the size of the stator core is small, the winding coils are difficult to embed into the slots. To solve the problem, a novel PMTM is presented, which is slotted on the outer surface of the stator core. As a result, the winding coils can be conveniently embedded into the slots from the outer surface of the stator core. The novel structure of the PMTM with back winding (BWPMTM) is introduced, and the advantage of the novel structure is analyzed. Furthermore, this paper proposes a limit analytical method to solve the optimal parameters of the motor which comprehensively considers four constraints: no-load back electromotive force (EMF), torque, temperature and slot space factor. The optimal parameters of the motor are directly solved to maximize torque density within the constrained range. This method avoids repeated iterative processes and greatly reduces the amount of calculation for PMTM design. Electromagnetic performance and thermal performance are analyzed based on the finite element model (FEM). Finally, the building of a prototype and the experimental results obtained with it are discussed. The rationality of the novel structure and the limit analytical method are verified.

Analysis of Permanent Magnet-assisted Synchronous Reluctance Motor Based on Equivalent Reluctance Network Model

In this paper, the equivalent reluctance network model (ERNM) is used to calculate the magnetic circuit of a permanent magnet-assisted synchronous reluctance motor (PMASynRM) and calculate no-load air-gap magnetic field and electromagnetic torque. Iteration method is used to solve the relative permeability of iron core. A novel reluctance network model based on actual distribution of the magnetic flux inside the motor is established. The magnetomotive force (MMF) generated by armature winding affects the relative permeability of iron core, which is considered in the calculation of ERNM to improve the accuracy when the motor is under load. ERNM can be used to measure air-gap flux density, no-load back electromotive force (EMF), the average value of motor torque, the armature winding voltage under load, and power factor. The method of calculating the motor performance is proposed. The results of calculation are consistent with finite element method (FEM) and the computational complexity is much less than that of the FEM. The results of ERNM has been verified, which will provide a simple method for motor design and analysis.

Magnetic Field Analysis of an Inner-Mounted Permanent Magnet Synchronous Motor for New Energy Vehicles

The motor is an important component that affects the output performance of new energy vehicles (using new energy sources such as electric energy and hydrogen fuel energy to drive the motor and provide kinetic energy). Motors with high power and low noise can effectively improve the dynamic performance, passability and smoothness of new energy vehicles and bring a comfortable experience to driver and passengers. The magnetic field analytical model of the inner-mounted permanent magnet synchronous motor (IPMSM) is studied to improve its output quality. The motor is divided into four subdomains: the stator slot subdomain, the stator slot notch subdomain, the air-gap subdomain, and the permanent magnet (PM) subdomain. The general solution of the vector magnetic potential of each subdomain is solved, and the expression of magnetic flux density of each subdomain is derived. Meanwhile, the analytical model of the non-uniform air gap is established according to the uniform air-gap model. The model’s accuracy is verified by finite element analysis and prototype tests. The results show that the calculation results of the analytical model are effective. The model can be applied to predict the no-load back electromotive force (EMF) and cogging torque of the motor under different main air gaps. It also provides an effective and fast analysis method for the design and optimization of IPMSM for new energy vehicles.

An analytical model for stator yokeless radial flux dual rotor permanent magnet synchronous machine

PurposeThe purpose of this study is to propose an analytical model with consideration of the permeability of soft-magnetic materials, which can predict the magnetic field distribution more accurately and facilitate the initial design and parameter optimization of the machine.Design/methodology/approachThis paper proposes an analytical model of stator yokeless radial flux dual rotor permanent magnet synchronous machine (SYRFDR-PMSM) with the consideration of magnetic saturation of soft-magnetic material. The analytical model of SYRFDR-PMSM is divided into seven regions along the radial direction according to the different excitation source and magnetic medium, and the iron permeability in each region is considered based on the Maxwell–Fourier method and Cauchy’s product theorem. The magnetic vector potential of each region is obtained by the Laplace’s or Poisson’s equation, and the magnetic field solution is determined using the boundary conditions of adjacent regions.FindingsThe inner and outer air-gap flux density, flux linkage, output torque, etc., of SYRFDR-PMSM are predicted by analytical model, resulting in good agreement with that of finite element model. Additionally, the SYRFDR-PMSM prototype is manufactured and the correctness of analytical model is further verified by experiments on no-load back electromotive force and current–torque curve. Reasonable design of the slot opening width and pole arc coefficient can improve the average output torque and reduce output torque ripple.Research limitations/implicationsThe analytical model proposed in this paper assumes that the permeability of soft-magnetic material is a fixed value. However, the actual iron’s permeability varies nonlinearly; thus, the prediction results of the analytical model will have some deviations from the actual machine.Originality/valueThe main contribution of this paper is to propose an accurate magnetic field analytical model of SYRFDR-PMSM. It takes into account the permeability of soft-magnetic material and slot opening, which can quickly and accurately predict the electromagnetic performance of SYRFDR-PMSM. It can provide assistance for the initial design and optimization of SYRFDR-PMSM.

Design of a New Consequent-Pole Segmented Dual-Stator Permanent Magnet Machine

In this article, a new consequent-pole segmented dual-stator permanent magnet (CPSDSPM) machine, which is used for some high-torque and low-speed applications, is proposed. This proposed machine adopts two stators, in which the external stator is segmented into three parts. The intermediate rotor is sandwiched between the internal stator and the external stator. Due to a particular coupling effect between the internal stator and the external stator, the CPSDSPM machine can inherently exhibit excellent flux-enhancing ability and output capability. The configuration of this proposed machine is introduced. The working mechanism especially the coupling effect is discussed by analytical models. The electromagnetic properties, such as the no-load back electromotive force (back EMF), the cogging torque, the output capability, and the torque ripple, are all calculated and analyzed by the finite element (FE) method. It can be seen that the simulating results can verify the correctness of the theoretical analysis and the superiority of the proposed CPSDSPM machine. A prototype machine is fabricated and tested to validate the results of the FE analysis.

Optimization and Simulation of Auxiliary Magnetic Barrier Permanent Magnet Synchronous Machine for Wind Turbine

The auxiliary magnetic barrier permanent magnet synchronous motor(AMBPMSG) has not only the advantages of high power density and highefficiency of permanent magnet synchronous generator, but also the advan-tages of high temperature non-demagnetization and low cost of the reluctancemotor. It has a broad application prospect in the field of wind power gen-eration. Statement is presented in this paper, on the basis of structure andoperation principle of the motor, the magnetic barrier surrounding the shape,shape of magnetic bridge, magnetic barrier layer and a permanent magnet isoptimized, by means of two-dimensional finite element simulation softwareanalysis of air-gap magnetic field, the counter electromotive force, reduce no-load back electromotive force harmonic content, in order to obtain the optimalelectromagnetic performance, and develop the visual design and simulationplatform software. The research of this paper has a certain reference value forthe popularization and application of AMBPMSG.

Open-Circuit Air-Gap Magnetic Field Calculation of Interior Permanent Magnet Synchronous Motor With V-Shaped Segmented Skewed Poles Using Hybrid Analytical Method

Due to the local inhomogeneous magnetic saturation of the core of the interior permanent magnet synchronous motor (IPMSM), the magnetic field changes nonlinearly, which makes the analytical calculation of the magnetic field difficult. Therefore, the calculation of the magnetic field mostly relies on the finite element method (FEM). However, the high computation cost of FEM restricts the efficiency of the design and analysis of IPMSM. In this article, an analytical model (AM) of slotless open-circuit air-gap magnetic field (OC-AG-MF) of IPMSM with V-shaped segmented skewed poles is derived by combining the subdomain method (SDM) and the magnetic equivalent circuit (MEC) method, and then, the AM of slotted OC-AG-MF of IPMSM with V-shaped segmented skewed poles is obtained by introducing the complex relative permeance. To show the effectiveness of the novel AM, the OC-AG-MF and cogging torque of an IPMSM with V-shaped segmented skewed poles for electric vehicles are calculated by the AM and FEM, respectively. The spatial order, amplitude–frequency characteristics, and the 3-D spatial distribution of the OC-AG-MF are analyzed. Finally, the accuracy of the AM is experimentally verified by direct measurement of OC-AG-MF and no-load back electromotive force (EMF) of the motor. The AM proposed in this article is shown to accurately calculate the radial and tangential components of OC-AG-MF of IPMSM with V-shaped segmented skewed poles considering rotor magnetic bridge saturation effect and stator slotting effect. Meanwhile, the efficiency of the design and analysis of the motor is expected to be improved due to the reduced computational effort compared to the prevalent FEM.

Study on the performance of multi‐branch modular permanent magnet motor affected by magnetic pole segmentation

To better address the requirements of integrated equipment, here, a multi-branch modular permanent magnet motor using a toroidal winding with reverse turn coils is proposed. High-speed motors have a large winding span, and the use of a toroidal winding with reverse turn coils in place of lap windings can effectively shorten the length of the motor end. Motor modularisation can improve production, assembly efficiency, and the maintenance economy. To innovate the windings from a basic toroidal winding, a modularised toroidal winding with reverse turn coil is proposed which enables the motor to be decoupled in electrical and mechanical structures. The inductance parameter calculation and finite element simulation verification are carried out on the new winding structure and the lap windings. The feasibility of the 60-degree phase toroidal winding with a reverse turn coil structure with reverse turns is also assessed. The no-load back electromotive force of the new winding structure is a square wave, which will bring certain torque fluctuations. To improve the performance of the motor, the method of radial magnetic pole segmentation is used, and the new magnetic pole is analysed and verified by the segmented magnetic circuit. Finally, the combination of magnetic pole segmentation is explored, and the effect of different segmentation methods on the performance of the motor is compared.

Comparative Study of Winding Configuration on a Multitooth Flux-Switching Permanent Magnet Machine

In this paper, based on a 6-stator-coil/17-rotor-tooth (6/17) conventional concentrated-winding multi-tooth flux-switching permanent magnet (C-MFSPM) machine, a novel full-pitch multi-tooth FSPM (FP-MFSPM) machine is proposed by changing winding configurations. Then, the electromagnetic performance of six FP-MFSPM topologies sharing the same 6-stator-coil but with different rotor teeth combinations, namely 6/13, 6/15, 6/17, 6/19, 6/21, and 6/23, is compared by using finite element analysis (FEA). The results show that 6/17 and 6/19 are the optimal stator-coil/rotor-tooth combinations for FP-MFSPM machines, which exhibit better electromagnetic performance, such as more enormous torque and smaller torque ripple. Thereafter, the existing C-MFSPM and the proposed FP-MFSPM machines with 6/17 and 6/19 structures are quantitatively compared in terms of no-load back electro-motive force (back-EMF), air-gap flux density, cogging torque, electromagnetic torque, torque ripple, etc. The FEA-predicted results validate that the proposed FP-MFSPM machines have more sinusoidal back EMF, larger torque output, and smaller torque ripple, which are superior to the C-MFSPM topologies.

Improvement in Torque Density by Ferrofluid Injection into Magnet Tolerance of Interior Permanent Magnet Synchronous Motor

In an interior permanent magnet synchronous motor, an adhesive such as bond is generally injected into the magnet tolerance to prevent vibration of the permanent magnet within the insertion space. In this case, a disadvantage is that the magnet tolerance does not contribute to the performance. In this paper, ferrofluid is inserted to improve the torque density, utilizing the magnet tolerance. When inserting ferrofluid into the magnet tolerance, it is important to fix the magnet because conventional adhesives are not used, and it is important that the ferrofluid does not act as a leakage path within the insertion space. In this study, a new rotor configuration using a plastic barrier that satisfies these considerations was introduced. The analysis was conducted through finite element analysis (FEA), and this technique was verified by comparing the simulation results and the experimental results through a dynamo test. It was confirmed that the no-load back electromotive force in the final model increased through ferrofluid injection.

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.

Research on the Non-Magnetic Conductor of a PMSM Based on the Principle of Variable Exciting Magnetic Reluctance

A permanent magnet synchronous motor (PMSM) based on the principle of variable exciting magnetic reluctance (VMRPMSM) is presented. The motor is equipped with symmetrical non-magnetic conductors on both sides of the tangential magnetized permanent magnets (PMs). By placing the non-magnetic conductor (NMC), the magnetic reluctance in the exciting circuit is adjusted, and the flux weakening (FW) of the motor is realized. Hence, the NMC is studied comprehensively. On the basis of introducing the motor structure, the FW principle of this PMSM is described. The shape of the NMC is determined by analyzing and calculating the electromagnetic force (EF) acting on the PMs. We calculate the magnetic reluctance of the NMC and research on the effects of the NMC on electromagnetic force, d-axis and q-axis inductance and FW performance. The critical speeds from the test of the no-load back electromotive force (EMF) verify the correctness of the NMC design. The analysis is corresponding to the test result which lays the foundation of design for this kind of new PMSM.

Investigation and Analysis of Novel Skewing in a 140 kW Traction Motor of Railway Cars That Accommodate Limited Inverter Switching Frequency and Totally Enclosed Cooling System

This study facilitated the improvement of no-load back electromotive force (back-EMF) wave form, total harmonic distortion (THD) of back-EMF, and torque ripple using a novel skew angle formula, considering the specific order of a no-load THD. In real usage environments, it is taken into consideration for the fully enclosed cooling system and limited inverter switching frequency of urban railway car traction motors. Since the most railway car traction motors use high-withstand voltage rectangular wires in slot-open structure, a no-load back EMF waveform includes large space slot harmonics, which should be smaller as possible. For 6-step control, the no-load back EMF waveform is important because switching for motor control is performed once after the rotor position is determined. To improve the no-load back EMF waveform and THD, two-dimensional and three-dimensional finite element analysis (FEA) were performed using a novel skew angle formula considering specific harmonic order reduction, while the fundamental amplitude was minimally reduced. A prototype with the novel skew was fabricated and verified. In addition, it was designed by calculating a low current density for a fully enclosed cooling system. A temperature saturation experiment was also performed, and successfully verified. Therefore, we suggest that the no-load back EMF characteristics and torque ripple are improved by applying the novel skew angle instead of a traditional skew angle.

Performance Analysis of a Coreless Axial-Flux PMSM by an Improved Magnetic Equivalent Circuit Model

In this paper, an improved magnetic equivalent circuit (MEC) model of a coreless axial-flux permanent-magnet synchronous machine (AFPMSM) with printed circuit board (PCB) winding is presented, which considers the curvature effect, fringing effect, leakage flux, and rotor yoke's magnetic saturation. The axial air-gap flux density distribution, no-load back electromotive force, winding inductances, and electromagnetic torque are predicted by the proposed MEC model. The steady-state performances of the machine under heavy load, as well as the dynamic response of the machine with a connected voltage source and mechanical load, are calculated. All the results obtained from the proposed model are in good agreement with those issued from the 3D finite element method (FEM). The computation time of the proposed model is greatly reduced compared to 3D FEM. Finally, a coreless AFPMSM prototype with a PCB stator is manufactured, and experiments are carried out to verify the predicted results.

An Improved Subdomain Model for Magnetic Field Calculation of SPMSM Considering No-load Leakage Flux

Due to big leakage flux, the performance of permanent magnet (PM) motor will be much reduced. Especially for surface-mounted permanent magnet synchronous motor (SPMSM) with similar number of poles and slots, because the zigzag leakage flux is big and varies with the relative positions between stator and rotor, selecting no-load leakage flux coefficient with experience may cause a big calculation error to electromagnetic parameters by equivalent magnetic circuit model. Finite-element method (FEM) can directly calculate the coefficient, but entire process is time-consuming. Focusing on this problem, an analytical model of no-load leakage flux coefficient is proposed including air-gap leakage flux model and zigzag leakage flux model. Then, an improved subdomain model for magnetic field calculation of SPMSM is established, and the air-gap magnetic flux density, inducing flux linkage and line no-load back electromotive force (EMF) are calculated considering no-load leakage flux. To verify the improved model, an external rotor type SPMSM with 20-poles and 24-slots for bridge crane is designed and manufactured. Finally, the validity of improved model is verified by experimental test.

Optimized design and performance analysis of a magnetic-field modulated brushless dual-mechanical port motor with Halbach array permanent magnets

In order to develop an electrical continuously variable transmission (E-CVT) to replace mechanical power coupling equipment applied in series-parallel hybrid electric vehicle (HEV), this paper proposes a magnetic-field modulated brushless dual-mechanical port motor with Halbach array permanent magnets, which has a more compact structure. The operating characteristics are analyzed by the lever analogy. It is concluded that the motor can realize the speed and torque decoupling between the engine and the wheel, which meet multi-mode operation requirements for HEV. To realize the multi-objective design of torque output, torque ripple and usage amount of permanent magnets, an optimization scheme combined parameter sensitivity with response surface methodology is adopted. The trade-offs among the optimization objectives are considered, then the key structural parameters and its optimal values are efficiently determined. Based on a two-dimensional model, the electromagnetic performances are simulated and analyzed. The results show that, after the parameters optimization, the no-load back electromotive force (EMF) has better sinusoidal characteristic, and the torque ripples and cogging torque peaks of the motor have been significantly reduced. Furthermore, a prototype motor is tested. The experimental results are consistent with the simulation results, which demonstrates the validity of the proposed structure and parameter optimization method.

Characteristic analysis and direct measurement for air gap magnetic field of external rotor permanent magnet synchronous motors in electric vehicles

In this study, the air gap magnetic field characteristics of external rotor permanent magnet synchronous motors (PMSMs) under both the stator and rotor coordinate systems considering low-order current harmonics and high-order sideband current harmonics are analysed. A direct measurement technique (DMT) for air-gap magnetic field is proposed. First, an analytical model of air gap magnetic field of external rotor PMSMs is established. The spatial order and frequency characteristics of stator/rotor air gap magnetic field are revealed. Then, a 24-pole 27-slot external rotor PMSM is taken as an example. The analytical and finite element (FE) results are compared and analysed. The difference of the spatial order and frequency characteristics between the stator and rotor air gap magnetic field are verified. Next, a new DMT is proposed, which can detect the precise distribution and local microscopic characteristics on the order of 10−1 mm with high resolution. The accuracy of analytical and FE model are verified by the DMT and an indirect experimental test of no-load back electromotive force. Finally, the mechanical challenges of in-wheel motors and the practicablility of DMT for eccentricity detection are further discussed.

Analytical model for magnetic field calculation of SPMSM with chamfered pole considering iron core saturation

To effectively optimise pole shape for surface-mounted permanent magnet synchronous machine (SPMSM), an analytical model of SPMSM with the chamfered pole is proposed for no-load and on-load magnetic field calculation. In this model, the pole of SPMSM is approximately segmented into pieces with regular shape and uniform magnet property, and magnetic field parameters can be obtained by subdomain superposition. Meanwhile, iron core saturation is considered to get a correction coefficient to revise air-gap flux density, inducing flux linkage, line no-load back electromotive force (EMF) and electromagnetic torque. Based on this analytical model, the geometry optimisation of PM can be optimised by end thickness of pole, pole-arc coefficient of cutting and remanence, and the waveform total harmonic distortion of air-gap flux density and no-load back EMF are greatly reduced. To verify the analytical model, an outer rotor type SPMSM with 20-poles and 72-slots for tractor application is designed and manufactured. Finally, the effectiveness of the improved method is validated by the finite-element method and experimental test.