Permanent Magnet Vernier Machine Research Articles

Comparative Analysis and Design Optimization of Ferrite-Based Surface PM Vernier Machines

This paper presents the results of a comprehensive investigation into the comparative analysis and design optimization of ferrite-based surface permanent magnet vernier machines (SPMVMs). While SPMVMs boast a simple mechanical structure and enhanced torque density attributed to the flux modulation effect, they suffer from a persistent challenge of low power factor. Several factors hinder the adoption of low-cost ferrite magnets in SPMVMs. First, ferrite magnets are prone to irreversible demagnetization, constraining the allowable range of magnet thickness. Second, the reduced residual magnetic flux density of ferrite magnets exacerbates the decrease in power factor and machine efficiency. Thus, achieving optimal performance in ferrite-based SPMVMs necessitates the careful selection of various design parameters. To address these issues, this study employs a surrogate-based metaheuristic optimization algorithm with adaptive sampling to identify the optimal solution. Additionally, the integration of a Halbach array is explored to further enhance the performance of the three-slot/two-pole SPMVM topology. Subsequently, two ferrite-based SPMVM baseline models—one with a conventional SPM structure and another with a Halbach magnet array—are thoroughly designed, optimized, and subjected to detailed performance analysis using the 2D finite element method.

Dual three Phase Operation of Dual Airgap Permanent Magnet Vernier Machine Having a Yokeless Rotor

Dual three Phase Operation of Dual Airgap Permanent Magnet Vernier Machine Having a Yokeless Rotor

Analysis and Comparison of Even-Order Back EMF Harmonics of Fractional-Slot Concentrated-Winding Consequent Pole Permanent Magnet Vernier Machines

Fractional-slot concentrated-winding (FSCW) consequent pole (CP) permanent magnet vernier (PMV) machines have received increasing attention due to their less magnet consumption but larger torque capability. However, the PM magnetomotive force (MMF) distribution is asymmetric in the CP structure. Thus, even-order air-gap flux density and back-electromotive force (back-EMF) harmonics are generated, which increases torque ripples. In this paper, to eliminate the even-order back-EMF harmonics and the resulting torque ripples, a comprehensive investigation on even-order flux density and back-EMF harmonics of five-phase FSCW CP PMV machines was presented, and then the general design rules without even-order back-EMF harmonics were summarized. Firstly, considering single- and double-layer windings, the effects of slot/pole number combination and flux modulator distribution on even-order flux density and back-EMF harmonics were analyzed. Secondly, the optimal slot/pole number combinations were selected, and then the rules for eliminating even-order back-EMF harmonics of CP PMV machines were summarized. As an extension, it was revealed that the harmonic elimination mechanism of CP PMV machines is applicable to CP-Halbach PMV machines. According to the summarized general design rules, the five-phase CP and CP-Halbach PMV machines with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> =20/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_r</i> =21/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_f</i> =10 were proposed. Their detailed performance has been comparatively analyzed and then the optimal one was selected for prototyping. Both finite element analysis (FEA) and experiments were carried out to validate theoretical analyses.

Low Pole-Pair Ratio Integration Design of Permanent Magnet Vernier Machine With Improved Power Factor

Benefited from flux modulation effects, permanent magnet vernier machines (PMVMs) have the advantage of high torque. Generally, the higher pole-pair ratio ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PR</i> ), i.e., PM pole-pair to armature winding pole-pair, the stronger flux modulation effects, as well as the higher torque. However, PMVMs with high <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PR</i> suffer from low power factor due to the parasitic large inductance. This paper is devoted to propose a low <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PR</i> integration design approach of PMVMs to achieve the high average torque and power factor simultaneously. According to exploit multiple working harmonics with low <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PR</i> s, not only the high power factor and low inductance characteristic can be maintained, but also the average torque and flux modulation effects can be strengthened. Further, the stator flux barrier has been added to restrict the parasitic no-working harmonics with high <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PR</i> s. Based on these, two PMVM design examples with different slot/pole combinations are constructed and analyzed to verify the effectiveness of the proposed design approach. Finally, a prototype is manufactured and experimented. It is showed that under electric loading 320 A/cm, the active volume torque density of proposed PMVM can be up to 33.4 Nm/L, which is comparable to regular PMVM with high <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PR</i> 8, while power factor can be improved from 0.63 to 0.8.

Comparative Analysis of Consequent-Pole PM Vernier Machines With Different Rotor Types

Taking advantage of flux modulation effects, consequent-pole PM vernier (CPMV) machines have been widely investigated recently, featuring high torque density and PM utilization ratio. However, the low-order harmonics of modulated flux fields additionally cause high iron saturation, which results in relatively low average torque under overload conditions, especially for the CPMV machines with an interior CPM (ICPM) rotor. Therefore, this paper proposes two hybrid CPM (HCPM) rotors of PMV machines to improve the overload performance by adding SPMs into the conventional ICPM rotor. First, the topologies of the proposed HCPM rotors are presented, named HCPM1 and HCPM2 rotors, respectively. Then the HCPM rotors and a conventional ICPM rotor with the V-shaped PM arrangement are designed and optimized to find out the optimal design parameters. Moreover, the electromagnetic performances including back-EMF, torque performance, efficiency, flux-weakening capability, and end effect are comprehensively investigated and compared. It indicates that the two proposed HCPM rotors both can generate equivalently high average torque, efficiency, and flux-weakening capability, compared to the conventional ICPM rotor. Furthermore, the proposed HCPM2 rotor can produce ≥22.9% higher torque at overload conditions. In addition, due to the bipolar PM arrangement, the unipolar flux leakage of the HCPM2 rotor is significantly reduced and lower than 0.05T. Finally, the prototype of a 12-stator-slot/ 20-rotor-pole CPMV machine with the HCPM2 rotor is manufactured to validate the finite element (FE) results.

Design Principle Considering Structural Mutual Effects of Double-Stator V-Shape-PM Vernier Machines for Electric Ship Propulsion

This paper proposes the design principle considering structural mutual effects of double-stator V-shape permanent-magnet (DS-V-PM) vernier machines for electric ship propulsion (ESP). Due to the flux concentration effect of the V-PM configuration, the double stators can be divided as a major and a minor stator, considering the different torque generation capability. Cooperation mutual effects between the double stators, V-PM arrangement and vernier machine topology are specifically included in the machine design principle exploration. To illustrate the design principle, first, a unified design principle is deduced, fit for general PM vernier machines. Then, a multi-step optimization strategy with auxiliary of sizing equations is presented, focusing on the parameter cooperation with flux modulation effect. Furthermore, through electromagnetic performance comparison, specific mutual effects of the DS configuration, DS angle shift, V-PMs and barrier structure are clearly summarized. Based on the DS machine design, the multi-mode operation for ESP system is introduced and analyzed. The normal/faulty cruise mode and charging mode are included to realize bi-directional operation. Prototype experiments are carried out for verification of the proposed machine design and operating strategy.

Subdomain Analytical Modeling of a Double-Stator Spoke-Type Permanent Magnet Vernier Machine

This paper proposes an analytical model of the double-stator spoke-type permanent magnet vernier machine (DSSTVM) using the subdomain method (SDM), which can be used to calculate the magnetic field distribution and corresponding electromagnetic parameters of the DSSTVM. The whole field domain is divided into several subdomains according to the magnetic characteristics of each region, within which Laplace’s and Poisson’s equations are solved accordingly in terms of magnetic vector potential (MVP). Then, the corresponding magnetic flux density distribution, back electromotive force (EMF), and electromagnetic torque of the DSSTVM can be obtained. Ultimately, finite element analysis (FEA) is adopted to validate the proposed analytical model’s effectiveness for quickly predicting the no-load and on-load performances of the DSSTVM.

Design and Research of Novel Consequent-Pole Dual PM Vernier Machines with Spoke and Halbach Array

Design and Research of Novel Consequent-Pole Dual PM Vernier Machines with Spoke and Halbach Array

Analytical calculation of magnetic field in surface-mounted permanent-magnet vernier motors

This paper proposes an analytical method to calculate the on-load magnetic field, Back electromotive force (BEMF) and torque of the surface-mounted permanent-magnet vernier machine (SMPMVM) accounting for slots, tooth-tips, flux modulation pole slots (FMPS) and the shape of magnet. The on-load magnetic field is predicted according to the surface-current method of permanent magnet, subdomain model and the superposition principle. BEMF and torque are calculated based on the magnetic field. The results show that THD of open-circuit and on-load radial flux density in the SMPMVM with concentric magnet poles is smaller than that in the conventional SMPMVM with eccentric magnet poles. 30th and 50th harmonic orders are obvious between two motors. Moreover, the peak cogging torque of the motor with concentric magnet poles is almost six times of the peak cogging torque of motor with eccentric magnet poles. The finite-element and experimental results confirm that the developed analytical method has high accuracy for predicting the magnetic field, BEMF, cogging torque and on-load electro-magnetic torque of SMPMVM with different shape of magnet.

A High Power Factor PM Vernier Machine with Segmented-Stator

A High Power Factor PM Vernier Machine with Segmented-Stator

Design of an L-Shaped Array Vernier Permanent Magnet Machine for Unmanned Aerial Vehicle Propulsion Using a Schwarz–Christoffel Mapping-Based Equivalent Magnetic Network Model

The Vernier permanent magnet (VPM) machines supersede conventional permanent magnet synchronous machine (PMSM) topologies in terms of torque-density and cogging torque. This paper presents a fractional-slot L-shaped magnet VPM machine, including peculiar designs for permanent magnet (PM) housing and rotor core construction for small-scale EVs such as unmanned aerial vehicles (UAVs). The idea for selecting the PM arrangement is based on combining the V-shaped and spoke-array PM topologies for achieving a higher torque-density than V-shaped PM machines and a lower cogging torque than spoke-array PM machines. The rotor core is created from non-integrated segments to form the flux-barriers in end-portions of PM housings. In this way, the leakage flux lines in the end-portion of the PMs reduce, resulting in enhanced flux linkage and power factor. A 630 W, 12-slot/8-pole motor is designed and prototyped for model validation purposes. An innovative equivalent magnetic network (EMN) model is established for analytical prediction of the performance of the machine. The Schwarz-Christoffel mapping is used to create the rotor core permeance network due to its special shaping. Two innovative pentagonal-shaped mesh cells are used in the air-gap region for more accurate capturing of flux behavior. The model is validated by comparing the results with the finite element results and experimental measurements.

Investigation of A Novel Phase-Unit Axial-Modular Permanent Magnet Vernier Machine With Integral-Slot Non-Overlapping Concentrated Windings

Investigation of A Novel Phase-Unit Axial-Modular Permanent Magnet Vernier Machine With Integral-Slot Non-Overlapping Concentrated Windings

Synthesis of Consequent Pole Vernier Permanent Magnet Machine Based on Oscillating Magnetic Potential Difference Model

Synthesis of Consequent Pole Vernier Permanent Magnet Machine Based on Oscillating Magnetic Potential Difference Model

Investigation of Permanent-Magnet Vernier Machine with Fractional-Slot Nonoverlapping Windings for Direct-Drive Application

Investigation of Permanent-Magnet Vernier Machine with Fractional-Slot Nonoverlapping Windings for Direct-Drive Application

Unequal Stator Modulated Teeth Structure to Reduce Electromagnetic Vibration in Permanent Magnet Vernier Machine

This paper focuses on electromagnetic vibration analysis of the permanent magnet vernier machine (PMVM) and aims to reduce electromagnetic vibration of the PMVM. Firstly, we analyze the magnetic field and radial force of the PMVM by FEM and analytical method. The results show that the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> radial force at 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> can generate serious electromagnetic vibration. Then, an unequal stator modulated teeth structure is proposed to reduce the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> radial force to reduce the electromagnetic vibration. And we compare the electromagnetic performance of the proposed PMVM with that of the original PMVM. The results show that the electromagnetic performance of the proposed PMVM is not influenced. What is more, we adopt the modal and the electromagnetic vibration analysis of the original PMVM and the proposed PMVM. The results indicate that the proposed PMVM can reduce electromagnetic vibration. Finally, we manufacture the prototype to verify the previous analysis results, the results of theoretical analysis and finite-element method are verified by the prototype test.

Stator Core Loss Analysis and Suppression of Permanent Magnet Vernier Machines

Permanent magnet vernier machine is a new type of permanent magnet machine, which is operated based on flux modulation effect. In this paper, the stator core loss of the permanent magnet vernier machine is investigated based on the relationship of the stator core loss to harmonic components of the airgap magnetic flux density crossing airgap and leakage flux not crossing airgap. In this manner, the stator core loss can be analyzed with consideration of flux modulation effect and flux modulation pole structure. First, stator core losses generated by magnetic fields of permanent magnet and armature winding are analyzed. Then, stator tooth fluxes coming from airgap magnetic flux and leakage flux are derived. Also, non-working stator tooth flux contributing stator core loss but not contributing torque is identified. Based on this, two approaches to suppress the stator core loss of the permanent magnet vernier machine are proposed. Finally, the effectiveness of the stator core loss analysis and suppression is verified by finite element analysis and experiments.

Reduction of Nonworking Armature Harmonics in Vernier Permanent Magnet Machines

Reduction of Nonworking Armature Harmonics in Vernier Permanent Magnet Machines

Torque Improvement of Vernier Permanent Magnet Machine With Larger Rotor Pole Pairs Than Stator Teeth Number

Vernier permanent magnet machines (VPMM) have attracted extensive interest owing to high torque density. However, VPMM with larger rotor pole pair <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_r</i> than stator teeth number <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z_s</i> has weak torque capability due to the opposite phase of fundamental back EMF <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> induced by the fundamental and modulated flux density i.e. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_Pr</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_Pa</i> . Thus, the pole ratio (PR, defined as the ratio of rotor pole pair <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_r</i> to winding pole pair <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_a</i> ) of VPMM with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_r</i> > <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z_s</i> is labelled as “bad”, and has long been abandoned. This paper puts forward two novel design tools i.e. Unequal Element Coil (UEC) and Stator Teeth Unit (STU), via which the torque-improvement method of VPMM with “bad” PR is proposed. Firstly, constructing the winding via UEC, in which both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_Pr</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_Pa</i> induce <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> of the same phase, meanwhile the total <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> is maximized. Secondly, designing the stator teeth structure via STU, so that multiple flux density harmonics are exploited and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> can be further enhanced. A VPMM with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_r</i> = 10, PR = 10 is designed by the proposed method. The FEA and experimental results prove that at current density 7.5A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , the torque density of the proposed VPMM is improved to 18.3Nm/L while the regular counterpart is only 13Nm/L.

Optimal gear ratio selection of linear primary permanent magnet vernier machines for wave energy applications

AbstractLinear permanent magnet vernier generators offer a high capability of force density, making them appealing configurations for wave energy harvesting systems. In absolute terms, the performance of these machines is significantly influenced by the selection of slot/pole combinations based on the magnetic gearing effect. For the first time, this paper aims to investigate the impact of different gear ratios on a wide array of linear primary permanent magnet vernier machines (LPPMVMs) with different slot/pole combinations based on fair criteria to offer a more comprehensive understanding of gear ratio selection. To find the optimal number of slots and poles, the response surface methodology is adopted to obtain a robust design and make a fair comparison among LPPMVMs with optimum design characteristics using a cost‐effective approach for the fast and reliable optimisation process. The higher gear ratios result in higher thrust force capability. This will help establishing a new route toward faster develpment of advanced LPPMVMs. The power loss models of LPPMVMs are studied to predict their steady‐state and transient thermal behaviours, verifying their stability and safety, while a simple external forced convection method can be utilised. To verify the model, finite element analysis is exploited to confirm the electromagnetic and thermal analysis results and provide a more exhaustive investigation.

Asymmetric air gap fault detection in linear permanent magnet Vernier machines

PurposeThe aim of this paper is to introduce an accurate asymmetric fault index for the diagnosis of the faulty linear permanent magnet Vernier machine (LPMVM).Design/methodology/approachThree-dimensional finite element method is applied to model the LPMVM. The geometrical and physical properties of the machine, the effect of stator and translator teeth, magnetic saturation of core and nonuniform air gap due to asymmetric fault are taken into account in the simulation. The air gap asymmetric fault is proposed. This analytical method estimates the air gap flux density of an LPMVM.FindingsThis paper presents an analytical method to predict the performance of a healthy and faulty LPMVM. The introduced index is based on the frequency patterns of the stator current. Besides, the robustness of the index in different loads and fault severity is addressed.Originality/valueIntroducing index for air gap asymmetry fault diagnosis of LPMVM.