Search

The flux-switching permanent magnet (FSPM) machine has aroused wide interest recently due to high-power density, favorable PM cooling capability, and essentially sinusoidal electromotive-force (EMF) waveform per phase. Previously, the phase back-EMF generation mechanism of FSPM machines is exposed from a flux-switching perspective, however, which is rethought from the viewpoint of air-gap modulation magnetic field in Part I as in this article, and electromagnetic torque generation mechanism of FSPM machines will be reported in Part II as another sister paper. With the aid of magnetic field modulation theory, the air-gap PM magnetic field and back-EMF of the FSPM machine are modeled based on modulation and winding functions. Their characteristics are analyzed in detail and consequently, principles concerning FSPM machines on arbitrary stator-slot/ rotor-pole combinations can be obtained, including the basic feature of FSPM machines, the principle and necessary conditions for the back-EMF generation, the fundamental reason of sinusoidal back-EMF waveform, and the contributions of modulation harmonics to phase back-EMF. Finally, experimental verification on a 12s/10p prototyped machine is conducted. [ABSTRACT FROM AUTHOR]

Based on the back electromotive force generation principle in part I of the series papers, the electromagnetic torque generation mechanism of flux-switching permanent magnet (FSPM) machines is rethought in this article as part II from the perspective of air-gap modulation magnetic field. By magnetic field modulation theory, the air-gap armature magnetic field due to winding currents is modeled. Considering the unipolarity of the stator core, a novel concept of ‘fictitious modulation reluctance (FMR) rotor’ for FSPM machines is proposed. Then, by combining with the air-gap permanent magnet (PM) field and the FMR rotor, generation mechanisms of harmonic PM torque and reluctance torque are investigated. The requirements for FSPM machines to produce a stable electromagnetic torque are determined, i.e., |mPw ± vPr| = Ppm, mrvMfm ≠0, and ωe = Prωr. Besides, the harmonics operation states and harmonic torque characteristics of FSPM machines are analyzed and calculated based on the Maxwell stress tensor method. Further, the average torque versus current density predicted by finite element is validated by testing on an exampled 12s/10p FSPM one. [ABSTRACT FROM AUTHOR]

In this paper, an analytical method (AM) based on the air-gap magnetomotive force (MMF) permeance model is proposed to predict the nonlinear instantaneous torque of switched reluctance machines (SRMs). The analytical expression of the air-gap MMF is first obtained from the winding function and current profile, while the air-gap magnetic permeance considering the double-sided slotting effects is also derived. Then, the nonsaturated field distribution along the air-gap circumference is presented based on which the instantaneous torque can be calculated from the Lorentz force law. Furthermore, the model is enhanced with a saturation distribution factor to include the nonlinear characteristics. The proposed method is free from preliminary data or empirical coefficient and benefits from the simplified model and solution. The AM will be validated by the two-dimensional finite-element method based on four SRMs with different structures. Moreover, an SRM prototype is manufactured for experimental verification. [ABSTRACT FROM AUTHOR]

By measuring the open-circuit radial stray magnetic flux density (RSMFD) of three spatial points, a novel diagnostic method for the eccentricity of interior permanent magnetic motors (IPMSMs) in electric vehicles is proposed. Outperforming traditional methods, the proposed method can noninvasively diagnose not only the severities of static eccentricity (SE), dynamic eccentricity (DE), and mixed eccentricity (ME), but also the eccentricity location. In this article, diagnosis results are described through three eccentricity parameters: SE ratio, DE ratio, and SE angle. First, an analytical model of the open-circuit RSMFD of the IPMSM is proposed, with its accuracy validated by experiments. The pattern of the impact of the eccentricity parameters on the open-circuit RSMFD is analyzed to form the basis of the proposed method. Then, an eccentricity prototype motor, which can continuously emulate the eccentricity according to any listed eccentricity parameters, is developed. A test rig is built to collect the open-circuit RSMFD and validate the analytical calculation results. Finally, an eccentricity diagnostic model based on the open-circuit RSMFD is established. The diagnosis results proved the noninvasiveness, effectiveness, and viability of the proposed method. [ABSTRACT FROM AUTHOR]

This article proposes a quantitative analysis model for the electromagnetic forces in rotor-permanent-magnet (rotor-PM) machines, decoupling the air-gap field modulation and the force modulation. First, a unified analytical model of the equivalent concentrated forces (ECFs) is deduced based on the air-gap flux density (AFD) harmonics. Second, the air-gap field modulation and the force modulation are decoupled by the ECF coefficient. Then, to determine the contributions of the modulated AFD harmonics, a quantitative analytical method is proposed. On this basis, the vibration performance of a 12-slot/10-pole (12s/10p) interior PM machine is investigated considering the modulation effect. The results reveal that the influences of rotation speed, PM-excited field, and armature field on the vibration can be clearly represented by the proposed method. Finally, the modal test and the acceleration measurement are conducted to validate the analysis. [ABSTRACT FROM AUTHOR]

This article presents a novel method for enabling energy-efficient and orientation-independent gravity compensation in active vibration isolation systems by taking advantage of the inherent negative stiffness of a hybrid reluctance actuator (HRA). Counteracting the gravitational force acting on the mover of an HRA with the position dependent force of the actuator’s integrated permanent magnet, the gravitational force can be compensated without the need for an additional actuation. An HRA-system with two translational degrees of freedom (DOF) is developed, comprising a permanent magnet for generating a constant biasing flux for both system axes and two actuator coils per axis for actively controlling the position of the mover. The system prototype has an actuation range of $\pm$ 0.7 mm in both DOF, while enabling energy efficient gravity compensation of payloads up to 500 g by an additional current feedback control loop. Experiments demonstrate that the current consumption for compensation of a 500 g payload is reduced from 1.58 A to 10 mA, which corresponds to a reduction of the power consumption by a factor of 25 000. [ABSTRACT FROM AUTHOR]

The magnetic coupling phenomenon widely exists in the type of double rotor motor, which is difficult to be eliminated completely due to the interactions between two layers of air-gap magnetic fields in a compact geometry structure. This article studies magnetic coupling in the perspective of air-gap harmonic groups, where the novelty is to propose the concept of positive coupling harmonics and the negative one. And, a double rotor flux-switching PM machine is chosen as the research subject. Then, the article begins with the analytical investigation of the modulation principle considering magnetic coupling, where the coupling harmonic group factor is defined. According to this factor, the coupling harmonics are analyzed and selected, and the positive and negative coupling harmonic groups are further determined. Next, the influence of coupling harmonic group on the machine performance is investigated in detail, including the back-EMF, torque performances, overload capability, and so on. The results show that the raise of positive coupling harmonic group factor brings the improvement of machine performances. In addition, a prototype machine is manufactured for experimental testing. Overall, theoretical analysis, simulation and test results verify the validation of the whole investigation to a large extent. [ABSTRACT FROM AUTHOR]

Compared with the conventional permanent magnet (PM) machines, the flux-switching permanent magnet (FSPM) machine exhibits higher torque ripple due to its special doubly salient structure and high air-gap flux density, leading to the deterioration of smooth operation. In this article, the output torque ripple suppression methods of FSPM machines from both rotor and stator sides are proposed with the aid of general air-gap field modulation theory. According to harmonic modulation mechanism, air-gap PM field can be modified by revising harmonic content of rotor and stator modulation functions and, consequently, three concepts, including cos-shaped edge rotor (CSER), cos-shaped edge stator, and double cos-shaped edge, are proposed and implemented to suppress the output torque ripple due to the cogging torque and electromagnetic torque ripple of FSPM machines. Finally, finite-element analysis and experiments are conducted to verify the proposed approaches. The results reveal that the CSER method exhibits the most effective suppression effect. [ABSTRACT FROM AUTHOR]

Permanent magnet Vernier motors (PMVMs) possess the advantage of high torque density for high-performance applications. However, the low power factor challenge makes it unacceptable for direct-drive applications. A lack of accurate modeling method based on the motor sizing law, i.e., air-gap flux density, linear current density, and motor geometry parameters, raises difficulties for machine designers to further conduct research on the performance metrics. This article presents a deep investigation into the analytical modeling technique for surface PMVMs (SPMVMs). It can identify an accurate approach to obtain the performance metrics, including electromagnetic torque and power factor. The modeling technique is developed based on the conformal mapping method. By using this, both radial and tangential permeability functions can be calculated to obtain the motor magnetic loading accurately, considering the leakage flux. The slotting effect on both air-gap flux density and armature-winding function is analyzed to achieve a precise formula for torque and power factor computations. The new modeling technique is applied to integral-slot SPMVMs with different slot/pole combinations, gear ratios, slot openings, and magnet thickness to evaluate the impacts of motor parameters on high-power-factor and high-torque-density designs. Finally, an SPMVM with the characteristics of high torque density and power factor is fabricated to verify the analytical model at the power rating of 0.8 kW and the speed of 500 r/min. The experimental results show that the prototype exhibits a high power factor of 0.9 and high torque density 22.5 Nm/L. [ABSTRACT FROM AUTHOR]

Variable reluctance resolvers (VRRs) have been widely used for rotor position detection in harsh working conditions. However, conventional installation of VRRs inevitably occupies the axial space of machine systems, and may weaken the reliability of rotor position detection encountering shock and vibration. In this article, a novel VRR structure with inner stator is investigated, which is radially integrated inside a permanent magnet synchronous machine (PMSM) to construct compact machine topology. The hybrid machine topology is first discussed, and detailed electromagnetic design is carried out. Improved analytical analysis on air gap flux density distribution and inductance evaluation of the integrated VRR is derived based on modified winding function approach, and testified by finite element analysis. A prototype is manufactured from an existing 2.2 kW PMSM, and experiments are conducted to validate the effectiveness of proposed machine topology. [ABSTRACT FROM AUTHOR]

Winding inductance is a crucial parameter of machines, which plays an essential role in flux-weakening capability, reluctance torque, power factor, etc. In this article, winding inductance characteristics of flux-switching permanent magnet (FSPM) machines are investigated from the perspective of air-gap modulation magnetic field. With the aid of the general air-gap field modulation theory, the air-gap magnetic field contributed by an arbitrary energized winding of FSPM machines is modeled and analyzed. Then, an analytical expression of winding inductance is derived based on winding function and single-phase magnetic field, through which the relationship between winding inductance and single-phase magnetic field harmonics is unveiled. It is found that the direct current (dc) and 2nd harmonic components of winding inductances in FSPM machines are caused by the dc and 2nd time-harmonic components of primitive harmonics, respectively, which are essentially different from that of traditional interior permanent magnet or reluctance machines. Finally, experiments on a prototype three-phase 12/10 FSPM machine are conducted to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

A typical flywheel energy storage system (FESS) includes an electrical machine, a flywheel, and magnetic bearings, which are independent of each other. Therefore, the structure of FESS is complicated, which leads to the problems of high cost and low integration. This article presents a novel stator PM excitation solid rotor machine (SPE-SRM) for FESS, which integrates an electrical machine, flywheels, and a magnetic bearing. The design method of the SPE-SRM is presented specifically. First, the structure and operation principle of the SPE-SRM are illustrated. Second, the design and optimization of the flywheel-rotor are presented with considering of power, energy storage, and mechanical strength. Third, the magnetic equivalent circuit of the SPE-SRM is established to simplify the design. Besides, the armature reaction and leakage flux factor are investigated. Fourth, the performance indexes, including torque, suspension force, no-load back electromotive force (back-EMF), losses, and temperature rise are fully analyzed by the finite element analysis. Finally, a 22 kW prototype is manufactured and tested. The rationality of the concept and design is validated by experiments. The SPE-SRM has the merits of high integration, robust structure, and low cost, so it has the potential for wide application in FESS. [ABSTRACT FROM AUTHOR]

Traditional multipoint hybrid maglev systems cannot realize the zero-power horizontal levitation state under eccentric load, which means the steady-state current is zero, and the air gap of each magnet is equal. This article proposes a new maglev system with two rotary magnets to solve this problem. The two magnets can move on an annular guideway to counteract the moment caused by the eccentric load. At first, we established the linear parameter varying model of this maglev system. Then, the control strategy is designed, which consists of a zero-power horizontal levitation controller and rotation controller. The levitation control is realized by introducing feedback of integral current and deviation of air gap in the proportional-derivative control system. The rotation controller employs a centroid observer and centroid Jacobian. It outputs the rotating angle at the demand of the zero-power and horizontal levitation. Experimental results demonstrate that the proposed maglev system has a better zero power and horizontal levitation performance than without rotary magnets. The direction of the air gap variation is opposite to that of the loading direction. The variation size of air gap length depends on the load weight, whereas rotation angle is related to the load weight and loading position. [ABSTRACT FROM AUTHOR]

In this article, considering the influence of iron core saturation and complex boundary conditions, a novel no-load magnetic field analytical method and system multiobjective optimization model for interior permanent magnet synchronous motor (IPMSM) are proposed. First, an analytical method based on magnetic potential permeance method is proposed. The complex cogging effect and equivalent air gap permeability function are fully considered in this method. Furthermore, on the basis of Taguchi optimization design based on Fuzzy theory, an improved optimization model considering multivariable interaction is proposed. Among them, in order to comprehensively consider the performance of electromagnetic, vibration, and temperature rise, five optimization objectives including torque, pulsation, cogging torque, loss, and flux density are optimized. The sensitivity of design variables and the interaction between variables are not ignored. Finally, a 6-pole 36-slot IPMSM is manufactured for prototype experiments. A large number of prototype experiments, finite element, and computational fluid dynamics simulation analysis including no-load magnetic field, back electromotive force, temperature rise, electromagnetic torque, and so on are carried out. The accuracy and rationality of the proposed no-load magnetic field analysis method and global optimization model are well-verified. [ABSTRACT FROM AUTHOR]

The detection and location of eccentricity faults in a permanent magnet synchronous generator (PMSG) become increasingly essential, especially in safety-critical applications. However, the existing approaches for monitoring eccentricity subject to many limitations. In this article, a novel method for online detection and location of the eccentricity fault in a PMSG is proposed based on the external magnetic sensing. The noninvasiveness facilitates installation and maintenance work. In this article, the effect of different eccentricity faults on the external leakage flux density is analyzed theoretically with the magnetic equivalent circuit method first. Then, two indicators are proposed for detecting static eccentricity (SE) and dynamic eccentricity (DE), respectively. The amplitudes of the SE and DE indicators are proportional to the fault degree. The angle of the SE indicator proves to be the direction of SE. Meanwhile, two indicators show excellent robustness and are independent of loads and rotation speed. Moreover, these indicators can be applied in any surface-mounted PMSG with a three-multiple number of slots. Accordingly, an algorithm to diagnose the eccentricity fault is shown based on two indicators from three sensing points outside. The computation of the method is light, which leads to fast detection speed. Finally, the accurate results in multioperating conditions from simulations and experiments verify the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

The mechanism of torque ripple generation by time and space harmonic magnetic fields in permanent magnet synchronous motors is investigated to obtain advanced motor designs. The general expression between the torque ripples and harmonic air-gap flux densities in the motor is derived by using Maxwell stress tensor. Both the numerical and experimental verifications of this expression are carried out. By using this expression, the difference of the torque ripple generation between the surface and interior permanent magnet synchronous motors are discussed. Based on these investigations, the shape of the rotor surface of an interior permanent magnet motor is optimized. It is clarified that specific harmonic components of thetorque ripples in interior permanent magnet synchronous motors can be reduced to be nearly zero by optimizing the rotor surface shape. [ABSTRACT FROM AUTHOR]

As a promising candidate of the electrical continuously variable transmission, 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. [ABSTRACT FROM AUTHOR]

This article presents an analytical method to predict the magnetic field of eccentric surface-mounted permanent magnet synchronous machine (SPMSM) by applying the hybrid magnetic circuit and subdomain method. Taking stator saturation into account, the surface current is appended to the stator coil conductor, which can generate a magnetomotive force (MMF) to compensate the MMF drop across the stator core. The rotor yoke saturation effect is modeled by increasing the air-gap length. To solve the problem resulted from rotor eccentricity in analytical analysis, an equivalent transformation method is given. The transformation principle is that the eccentric machine can be equivalent to a concentric one with redistributed PM remanence and armature current density. On this basis, the subdomain method is adopted to predict the magnetic field of the reestablished machine. The proposed analytical method is implemented and evaluated on the 6p/36s and 8p/12s SPMSM and exhibits good agreement with the FEM and experiment results. [ABSTRACT FROM AUTHOR]

It is well known that permanent magnet Vernier machine (PMVM) has multiple flux field harmonics, which can produce stable torque. However, some flux field harmonics would create torque that undermines the total torque output. Such as the 6 slots 26 poles split-tooth PMVM here, of which modulated flux field outputs torque while fundamental flux field undermines torque output. In this article, a 26 pole PMVM with coding-shaped tooth is proposed. The coding-shaped tooth can introduce permeance harmonics with specific phase and amplitude, thus modulating flux fields that all output torque. Air-gap permeance harmonics of the proposed and the regular split-tooth PMVM are obtained via FEA. Based on MMF-permeance model, flux fields of two machines and their contributions to average torque are investigated, proving that the proposed machine has multiple flux fields that all output torque. Moreover, by optimizing geometric parameters of coding-shaped tooth, the proposed machine could obtain largest average torque and smallest torque ripple simultaneously. Electromagnetic performances of the optimized machines are studied comparatively in semianalytical way and FEA. It is proved that with same overall size, PM usage, and copper loss, the proposed machine could achieve 30% larger torque density, 86% smaller cogging torque, and 62% lower torque ripple than its counterpart. Finally, a 16-N·m (rated) prototype is built and tested. [ABSTRACT FROM AUTHOR]

In this article, the direct current (dc) winding induced voltage in wound-field flux-switching machines is qualitatively analyzed with air-gap field modulation principle. Operation principle and effective harmonics of dc winding induced voltage are modelled and deduced. It is found that only air-gap field harmonics with specific spatial orders, which numerically equals to odd times of half stator poles, can contribute to dc winding induced voltage. Harmonic order of dc winding induced voltages under open-circuit only, armature reaction only, and on-load condition, are predicted for m-phase WFFS machines with any feasible stator/rotor pole number combinations. Different armature winding configurations, including concentrated winding and distributed winding, are also analyzed and compared using the winding factor. Finite element analysis is employed to verify the prediction results. Finally, a prototype is built and tested for validation. [ABSTRACT FROM AUTHOR]

Torque ripple reduction for permanent magnet assisted reluctance (PMAREL) machine has always been concerned by designers. In order to seek the internal factors of torque ripple for PMAREL, this article proposes an effective torque calculation model considering air-gap field time-space harmonics using finite element method (FEM) combined with two-dimensional fast Fourier transform (2D-FFT). It can be used to investigate the contribution of air-gap field time-space harmonics to average torque and torque ripple, and precisely extract the characteristic components of the air-gap field time-space harmonics that contribute to the torque. Besides, the details of time-space harmonic order, movement form, magnitude and initial phase will be obtained from the characteristic components. Hence, the time-space harmonics of air-gap field that mainly contribute to the torque ripple can be found through this model and suppressed by adjusting the angles of the flux-barrier ends for making torque smooth. According to the optimized design, a 36-slot 4-pole PMAREL is manufactured and tested. Both finite element analysis and experimental results confirm the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This article investigates rotor losses in permanent magnet Vernier machines. By analyzing air-gap field, the harmonic distribution and frequency of modulated open-circuit flux density and armature reaction flux density are obtained. Then, rotor losses production principle is revealed and the influence of each harmonic on the loss is analyzed. Meanwhile, the influence of each harmonic on torque is also studied. It is found that some harmonics have no contribution to torque but produce additional losses. On this basis, a new rotor structure is proposed to suppress the rotor losses. Comparison results indicate that by suppressing nonworking harmonics, the rotor losses can be reduced effectively without affecting the effective torque. Finally, the theoretical and finite-element analysis results are verified by prototype tests. [ABSTRACT FROM AUTHOR]

This article proposes a new hybrid analytical model combining subdomain model and equivalent magnetic network for permanent magnet vernier machines, which are easy to get saturated due to the air-gap field modulation effect. The key is representing saturation effect by iterating equivalent surface current as part of interface conditions in the proposed subdomain model. First, five subdomains are divided to calculate magnetic field distribution. The equivalent surface current is utilized as the boundary constraint between subdomains and iron core. Second, the equivalent magnetic network is established based on stator structure, and the fluxes flowing into flux modulation poles are equivalent as the magnetic flux sources. Node magnetic potentials can be achieved with the application of Kirchhoff's law of current. Then, the equivalent surface current is updated for convergence by node magnetic potential to accurately predict saturated performance. Finally, a prototype is manufactured, and the effectiveness of the proposed hybrid model is verified by the finite-element analysis (FEA) and experimental results. The hybrid model combines the subdomain model and the equivalent magnetic network model to complement each other and it is demonstrated to be more efficient than the FEA model while maintaining high accuracy. [ABSTRACT FROM AUTHOR]

This article investigates the effects of phase shift on the inductance and short-circuit current (SCC) in permanent-magnet (PM) machines with dual three-phase winding configurations. First, the relationship between the phase shifts and slot/pole combinations, for the dual three-phase winding configurations, is discussed. Second, analytical expressions of the inductance are derived for the 48-slot/22-pole PM machines with different phase shifts based on the winding function theory. Afterwards, the SCC amplitude of different phase shifts is comparatively analyzed. The investigation reveals that the 7.5° and 30° configurations have great significance to improve the self-inductance value. Thereby, the 30° configuration has comparable SCC amplitude compared to the 7.5° counterpart, while being lower than the 15° configuration one. Moreover, the 30° configuration exhibits lower eddy-current loss and preferable torque performance than its counterparts. Furthermore, the finite-element method is used to calculate electromagnetic performances for evaluation. Finally, some experiments on the prototype machine are carried out for validation. [ABSTRACT FROM AUTHOR]

This article proposes a torque improvement method for dual m-phase synchronous reluctance machines by phase shift technique. The emphasis is put on the relationship of d–q axis inductance harmonics and phase shifts. First, all feasible phase shifts for various slot/pole combinations are discussed in general. Second, the influences of phase shift on reluctance torque performance are investigated based on inductance analysis. It is founded that the first main torque harmonic can be eliminated when phase shift equals to π/2m (m is odd) and π/m (m is even), respectively. This is the optimal phase shift covering all the m cases. Third, the optimal phase shift with torque improvement and ripple reduction is verified by the theoretical analysis and finite element method. Finally, the dual 3-phase 24-slot/10-pole synchronous reluctance machines with 30° and 60° phase shifts are fabricated. The experiments on the prototype machine are carried out for validation. [ABSTRACT FROM AUTHOR]

In this article, we developed an improved hybrid field model (IHFM) to predict the on-load performance of the interior permanent-magnet (IPM) motors considering both iron saturation and slotting effect. It combines the airgap analytical model based on the modified conformal mapping with the reluctance mesh method for stator and rotor. The reluctance mesh method can accurately predict the rotor saturation and tooth-tip saturation even their field distribution is complicated due to the armature reaction. Besides, IHFM will significantly accelerate computation speed using the analytical model for airgap region while keeping high accuracy. The finite-element analysis and experimental results of the flat-type and V-type IPM motors are demonstrated to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]