Linear Permanent Magnet Vernier Machine Research Articles

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.

Novel Virtual Winding Current Controller for Suppression of Linear Permanent Magnet Machine Electromagnetic Thrust Ripple

Thrust force ripple, including no-load detent force and electromagnetic thrust ripple, worsens the precision of linear permanent magnet machine (LPMM) control system. Asymmetrical current injection algorithm has been proposed for the suppression of electromagnetic thrust ripple, and the key point of the algorithm is positive- and negative-sequence (PNS) current closed-loop control. To achieve better steady-state and dynamic performance, a novel high-bandwidth current controller is proposed in this paper. A dual three-phase control system composed of three-phase virtual winding and the three-phase LPMM is introduced. According to the dual three-phase topology, PNS components are decoupled by a novel coordinate transformation, and the proposed controller avoids the use of filters or sophisticated algorithms for extraction of PNS currents. Experimental results based on a linear vernier permanent magnet machine (LVPMM) are presented. It verifies that the asymmetrical current control strategy based on the novel PNS current controller reduces electromagnetic thrust ripple by more than 60% compared with symmetrical three-phase current control.

Performance Improvement in a Linear Primary Permanent Magnet Vernier Machine by Modular Unit Shift Effect

This article investigates the effects of modular unit shift on the detent force and mutual to self-inductance ratio in the modular linear primary permanent magnet vernier (MLPPMV) machine. First, the winding connection and slot/pole combinations for the modular design is discussed. Then, the relationship of the phase shift and modular unit spacing is given. The operation principle of the MLPPMV machine is analyzed from the perspective of the air-gap field modulation theory. Moreover, the analytical expressions of the modular unit shift and phase shift angle for the MLPPMV machine are derived. Afterwards, the back EMFs, detent forces and inductances are comparatively analyzed. The investigation reveals that the reasonable modular unit shift has significance to improve the electromagnetic performances. Furthermore, the finite element method is adopted to evaluate. Finally, a prototype of MLPPMV machine is built. Experiments are carried out on a linear test bench, verifying the theoretical analysis.

Quantitative Comparison of Modular Linear Permanent Magnet Vernier Machines with and Without Partitioned Primary

Quantitative Comparison of Modular Linear Permanent Magnet Vernier Machines with and Without Partitioned Primary

Thrust Ripple Reduction of Dual-Side Toroidal-Winding Linear Permanent Magnet Vernier Machine by Unequal End-Teeth Width

The linear permanent magnet vernier machines have attracted more and more attention last several years due to its high thrust density at low speed, which is very suitable for the direct-drive applications. A dual-side toroidal-winding linear permanent magnet vernier machine (DSTWLPMVM) with the unequal end-teeth width is proposed in this paper to reduce the detent force and thrust ripple. The low detent force in DSTWLPMVM is achieved by combination of two single-side detent forces with the opposite phase angle, which is obtained by optimizing the unequal end-teeth width of the primary two-sides. In the proposed machine, the symmetry three-phase flux linkage of the toroidal winding also can be obtained by optimizing the unequal end-teeth width. Therefore, the low thrust ripple of DSTWLPMVM is achieved by optimizing the unequal end-teeth width for obtaining the low detent force and symmetry three-phase flux linkage. The vertical magnetic force in the proposed LPMVM is also considered by finite element analysis (FEA) in this paper. Via optimizing the unequal end-teeth width, the detent force is reduced by 90% while the peak-to-peak thrust ripple is reduced by 69% than that of DSTWLPMVM with the equal end-teeth width, respectively. In this paper, the thermal and PM demagnetization behavior of the proposed machine are also analyzed by FEA.

Design and Evaluation of Linear Primary Permanent Magnet Vernier Machines for Urban Railway Transportation

Linear induction machine (LIM) is used as a driving machine in urban railway transportation because of its simple structure and mature technology. However, low thrust force and efficiency have always been a difficult problem to be solved. In the last decade, linear primary permanent magnet vernier machine termed as LVM in this paper has been extensively investigated owing to its potential application prospect in urban railway transportation. However, there is a lack of investigation on the feasibility of rendering the LVM the same size as existing LIM used in urban railway transportation. Therefore, in this paper, a large-sized LVM is designed and evaluated according to the requirement. Firstly, the LIM used in practical urban railway transportation are introduced. Secondly, the LVMs with the same size as the LIM counterpart are established by finite element method. Then, effects of consequent-pole Halbach permanent magnet structure, secondary tooth number and primary slot shape on performances are investigated. Thirdly, a LVM is optimized and compared with the LIM. The results revealed that the LVM exhibits higher thrust force and efficiency. Finally, a small-sized prototype of LVM is constructed to validate the simulation.

A Mesh Design Technique for Double Stator Linear PM Vernier Machine Based on Equivalent Magnetic Network Modeling

Linear permanent magnet Vernier machines (LPMVMs) is an attractive solution for stroke and direct-drive applications. Several LPMVM topologies have been presented for different applications that operate based on magnetic flux modulation. LPMVMs have some advantages including high force, and torque density at low speeds. This paper introduces a double-excited linear Vernier machine for wave energy conversion. To model the machine, finite element analysis and nonlinear equivalent network model are used. To improve the accuracy of the model and compact the network, a new meshing method is proposed. For better continuity in the output waveforms of the machine, special positioning is utilized. The end-effect is modeled using two separate networks. Finally, the modeling and simulation results are compared with each other and validated experimentally.

Performance analysis of linear permanent magnet Vernier machine using mixed subdomain and magnetic equivalent circuit techniques including end‐effect

Performance analysis of a linear permanent magnet Vernier machine (LPMVM), which has a complex structure, is mostly based on the finite element methods, while for its optimisation or sensitivity analysis a quick mathematical technique is desirable. This paper introduces an LPMVM and its principles of operation. Then, a mixed subdomain and magnetic equivalent circuit are applied to extract magnetic field equations in various parts of the machine, in which the end-effect in included. Besides, the electromotive force, thrust force, normal force and electric equivalent circuit are determined. An LPMVM was prototyped and tested to verify the accuracy of the proposed method.

A Novel Consequent-Pole Modular-Mover Linear Permanent Magnet Vernier Machine for Thrust Ripple and Cost Reduction

Recently, linear permanent magnet vernier machine (LPMVM) is attracting more and more attention due to its high thrust density, high efficiency, and simple structure at low-speed operation, which makes it a preferable solution for direct-drive linear motion applications. In order to further reduce the thrust ripple and the cost of LPMVM, a novel consequent-pole modular-mover LPMVM (CM-LPMVM) is proposed and analyzed in this article. Due to the dual-flux-modulation effect, the proposed CM-LPMVM can exhibit a low thrust ripple (∼3.2% of the average thrust) and high thrust density (∼387 kN/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) at a low current density of 3 A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , as well as reduce nearly half of the PM usage at the same time. The performance improvement of the proposed CM-LPMVM is verified by the comparison to a regular modular-mover LPMVMs, using the finite-element method. Finally, three prototypes are built and tested. The experimental results match well with the analytical data, showing the superiority of the proposed CM-LPMVM.

Design and Analysis of Fractional Pole-Pair Linear Permanent Magnet Machine

A novel concept of fractional pole-pair linear permanent magnet machine (FP-LPM) has been proposed recently. It is found that using fractional pole-pair number in linear permanent magnet machine(LPM) could effectively reduce slot cogging force as well as back EMF unbalance. Thus thrust ripple is curtailed which improves its thrust quality and enhances its application potential. However, some issues of FP-LPM still remain unsolved, such as phase split, current phase adjustment, plus structure optimization is different from the traditional topology due to extra auxiliary tooth, etc. This paper contributes to giving a detailed designing methodology including winding arrangement, regulations of choosing slot/pole combination and effective end optimization method of FP-LPM. Thus, this paper can give helpful guidance in designing FP-LPM to satisfy different application demands. Finally, an 18slots/29poles fractional pole-pair linear permanent magnet vernier machine (FP-LPMVM) is designed and constructed using the proposed method and the test results verifies the research conclusions.

Evaluation of Linear Permanent Magnet Vernier Machine Topologies for Wave Energy Converters

Today, the importance of using vernier machines in wave energy converters has increased because of its simple structure and ability to generate a lot of thrust force at low speeds due to the magnetic gear effect. The linear vernier permanent magnet machine has been designed in various structures. Proper design and selection of the main parameters of the machine will improve performance and increase the efficiency of the linear vernier machine. One of these parameters is the shape of the permanent magnets and how they are magnetically oriented. The novelty of this paper is the reduction of leakage flux, achieved by changing the shape and orientation of the permanent magnet. Three types of linear permanent magnet vernier machines with different permanent magnet structures and orientation, including V-shape, Halbach array and consequent-pole are presented. The considered machines have been compared to each other and to the existing machine in terms of airgap flux density, back EMF, PM flux, Inductance, thrust force, detent force, loss, efficiency, power factor, flux density and flux line, using the finite element method in the same conditions and with the same volume of permanent magnets. The results show that the magnetic orientation and shape of the permanent magnet have a considerable effect on the leakage flux, and all the proposed models have a lower leakage flux and better performance compared to the existing model.

Analysis of the Fractional Pole-Pair Linear PM Vernier Machine for Force Ripple Reduction

Linear permanent magnet Vernier machine (LPMVM) is attracting more and more attentions recently due to its simple structure, high efficiency, and high thrust density at low speed. In this article, a novel fractional pole-pair linear permanent magnet Vernier machine (FP-LPMVM) is proposed, which gives more freedom in the design of the LPMVM to reduce the force ripple of the machine. The operation and force ripple reduction principles of the FP-LPMVM are also given in this article with the help of analytical equations. It is found that some of the proposed FP-LPMVM exhibit inherent good performances such as high EMF symmetry and low thrust ripple due to the combining of the flux modulation effect and the FP-LPMVM. In order to verify the theoretical analysis in this article, two LPMVM prototypes (i.e., 12 slots 20 poles integer pole-pair LPMVM and 18 slots 29 poles fractional pole-pair LPMVM) are manufactured, tested, and compared with each other. The experimental results are consistent with the FEA results, and the validity of the analysis and the superiorities of the proposed FP-LPMVM are verified.

Development of Linear Vernier Hybrid Permanent Magnet Machine for Wave Energy Converter

Today, due to the limited supply and rapid consumption of fossil fuels, transitioning towards renewable energy supplies has become more important than ever.. The purpose of this paper is to present a new linear permanent magnet vernier machine structure which is designed to capture wave energy and improve the performance of the prototype vernier machine. By halving the proposed vernier machine, amending gear ratio and changing the shape of permanent magnet (PM) and teeth, the performance of the proposed vernier machine increases compared to the prototype vernier machine. This novelty causes the proposed vernier machine to be lighter, more economical and more efficient than the prototype vernier machine. Moreover, the main parameters of the proposed vernier machine compared to the prototype vernier machine are improved, so that in the proposed vernier machine, induced voltage, PM flux and thrust force are increased by 30, 68 and 27% respectively. In addition, the ripple of thrust force is reduced by 5%, and the self-inductance is diminished by 55%. All analyses have been performed in the same conditions with the finite element method using Ansys Maxwell software.

Multi-Objective Optimization Design of a Modular Linear Permanent-Magnet Vernier Machine by Combined Approximation Models and Differential Evolution

In this article, a modular linear permanent-magnet (PM) vernier machine is presented and optimized for high-precision and safety-critical direct-drive applications. The novelty of this article is to not only propose a multi-objective optimization method, but also present a modular linear PM vernier machine. The presented machine has the merit of desired fault-tolerant capability and improved force performances by mainly adopting the modular mover structure. And, the design principle of modular mover structure is introduced in detail in this article. To realize low detent force, high thrust force, low force ripple, and good fault tolerance, modular mover structure, PM array with flux-intensifying effect and six-phase structure are adopted in machine design. Furthermore, a new multi-objective optimization method is proposed to obtain a set of tradeoff solutions among multiple optimization objectives in machine optimization. First, to decompose the high dimension design space, the design variables are stratified into nonsensitive and sensitive levels by utilizing a comprehensive sensitivity analysis. Second, combined approximation models are implemented to decrease the large amount of computations. Then, to enhance the efficiencies of two multi-objective optimization processes, multi-objective differential evolution algorithm with ranking-based mutation operator is employed. After the optimization by the proposed multi-objective optimization method, the desired comprehensive performances with high optimization efficiency and accuracy can be obtained. Finally, to verify the results of theoretical analysis, a prototype machine is fabricated.

Mechanism Investigation of Ring Type Winding in Linear Permanent Magnet Vernier Machine for Improving Force Density

The linear permanent magnet vernier (LPMV) machines have been paid more attention in railway vehicles because of its simple structure and low cost. In this paper, the ring type winding (RTW) is adopted in both non-modular and modular LPMV machines to improve force density. The configuration and operating principle of two LPMV-RTW machines are presented. The coil connection and mechanism of RTW are explained and compared with conventional distributed winding (DW) and concentrated winding (CW). The back electromotive force and thrust force are investigated by the time-stepping finite-element method. It is found that non-modular LPMV-RTW machine possesses larger force density than non-modular LPMV-DW machine while modular LPMV-RTW machine has higher force density and utilization ratio of winding than modular LPMV-CW machines under the constant copper loss. Finally, the experiment result is obtained on the prototype, verifying the theoretical analysis.

Analysis and Evaluation of a Linear Primary Permanent Magnet Vernier Machine With Multiharmonics

This article investigates a multiharmonics linear primary permanent magnet vernier machine. With the adoption of nonuniformly distributed PM arrays along the air gap, richer harmonics are achieved and make its performance superior to the conventional linear primary permanent magnet vernier machine. First, the structures are described and compared. Then, their operation principles are analyzed by the flux modulation theory. The electromagnetic performances of two machines are analyzed and compared through the finite element method and theoretical analysis. The results show that the multiharmonics linear primary permanent magnet vernier machine offers 15% higher thrust force density compared with the conventional linear primary permanent magnet vernier machine. Finally, the experiments on a prototype of the multiharmonics linear primary permanent magnet vernier machine are carried out for validation.

A new HTS dual stator linear permanent magnet Vernier machine with Halbach array for wave energy conversion

In this paper, a high-temperature superconductor-dual stator linear permanent magnet Vernier machine (HTS-DSLPMVM) with Halbach array has been proposed for wave energy conversion. In order to better investigate, this machine has been compared to the prototype double stator linear permanent magnet Vernier machine (DSLPMVM). Both of the machines operate based on magnetic gear effect. At lower speeds they have the ability to produce a high thrust force. DSLPMVM and HTS-DSLPMVM have the same structure. So that, DSLPMVM and HTS-DSLPMVM consist of two stators and one translator with a three-phase concentrated winding. Each phase has been located independently on the translator. Also, permanent magnet (PM) Halbach array with appropriate magnetic direction mounted among the slot of the translator. The innovation of the proposed machine is that HTS-Bulk is located between the slot of the stators to shield the leakage flux. The operation of the two machines has been compared and analysed using the finite element method (FEM). Results show that, HTS-Bulk makes back-EMF, air gap flux density, power factor and thrust force to increase significantly and inductance to decrease, which effectively improves the machine operation.

Modeling and Analyzing a Novel Dual-Flux-Modulation Consequent-Pole Linear Permanent-Magnet Machine

A novel dual-flux-modulation consequent-pole linear permanent-magnet (DFM-CP-LPM) machine is proposed in this paper, which can be regarded as the combination of a linear flux-switching PM machine and a linear vernier PM machine. Via two sets of interoperable PMs mounted on both the primary and the secondary, the proposed machine can work in a dual-flux-modulation mode, achieving higher thrust density. Meanwhile, the consequent-pole structure is introduced, reducing approximately half of the PM usage compared to a conventional surface-mounted linear PM vernier machine (LPMVM), which will greatly reduce the cost. In this paper, the configuration and the operation principle of the novel DFM-CP-LPM are presented. Then the optimization and several thrust ripple reduction methods are introduced to improve the performance of the machine. Thermal analysis is also carried out to check the demagnetization risk of primary PMs, due to the heat from coils. Finally, the proposed machine is compared to a conventional LPMVM and a consequent-pole linear vernier permanent magnet machine with only PMs set on the secondary. The results verify the superiority of the proposed DFM-CP-LPM.

Influence of Armature Windings Pole Numbers on Performances of Linear Permanent-Magnet Vernier Machines

Linear permanent-magnet vernier (LPMV) machine has attracted more and more attention for several advantages including high power density and low cost. Both magnets and windings are located on the short mover, while the long stator is only consisting of iron, which is very suitable for long stroke applications. This paper investigates the influence of armature windings pole-pair numbers on the electromagnetic performances of LPMV machine by using an analytical method based on the finite element. The aim of this paper is to make a comprehensive comparative study of the machine with different armature windings pole-pair numbers while keeping slot number as a constant, select the topology of high performances and recommend suitable application areas. The performances of machines with the armature windings pole-pair numbers $P_{\mathrm {w}}= 1$ , 3, 6 are analyzed in detail. Finally, a new modular LPMV machine with $P_{\mathrm {w}} = 6$ , which possess higher thrust force, lower thrust force ripple, and high fault-tolerant capability, is prototyped and experiments are conducted for validation.