Halbach Permanent Magnet Array Research Articles

The influence mechanism of Halbach array magnetic field control on discharge channels in EDM

The use of magnetic field to actively control Electrical Discharge Machining(EDM) can effectively improve the problems of low material removal rate and poor surface quality, but due to the limitation of materials, the magnetic induction intensity of permanent magnets after magnetization is not high, and the magnetic induction lines of permanent magnets are too concentrated and difficult to control. In order to overcome the above shortcomings, this study applied the Halbach array magnetic field to the field of EDM for the first time, established a model of the trajectory of the charged particle beam in the discharge channel, analyzed the influence of the Halbach array magnetic field on the discharge channel, and clarified the improvement mechanism of the Halbacch array magnetic field in EDM. In addition, several sets of experiments were carried out by controlling the distance between the workpiece and the working surface of the Halbach array permanent magnets. The experimental results show that when the distance between the workpiece and the working surface of the Halbach array permanent magnet is less than 10mm, the material erosion rate of the workpiece increases significantly, and the electrode loss rate and surface roughness decrease significantly. When the workpiece is 0mm away from the working surface, the material removal rate is increased by 18.18%, from 0.4513mm3/min to 0.5333mm3/min, the tool wear ratio is reduced by 46.87%, from 0.2587 to 0.13745 mm3/min, and the surface roughness is reduced by 39.56%, from 4.186 μm to 2.53 μm.

Equivalent Analytical Model of Magnetic Field in Parallel Magnetic Circuit Axial Flux Permanent Magnet Machines

The axial flux permanent magnet (AFPM) machines with the parallel magnetic circuit (PMC) rotor can effectively improve its torque density. The PMC rotor consists of two sub‐rotors, radial Halbach array permanent magnet (PM) and tangential PM. The magnetic fields generated by two sub‐rotors are not in the same 2‐D analytical planes. In this paper, an equivalent analytical model of PMC‐AFPM machines is proposed to solve this problem. The radial Halbach array PM rotor is equated to the axial Halbach array PM rotor based on the equivalent transformation principle. The exact subdomain models of equivalent axial Halbach array PM rotor and tangential PM rotor are built respectively and then superimposed to obtain the magnetic field distribution. The electromagnetic characteristics of the PMC‐AFPM machine under no‐load and load conditions are calculated by the proposed analytical model and compared with calculations of the finite element model (FEM). The results verify the accuracy of the equivalent analytical model. The comparative analysis of the AFPM machines with PMC rotor and tangential PM rotor verifies the advantage of PMC rotor configuration to improve the torque density. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Enhancing levitation force of superconductors through wavelength optimization in Halbach permanent magnet arrays

Optimizing the wavelength (γ) of the Halbach array permanent magnet guideway (PMG) in superconducting maglev systems can improve levitation performance without consuming additional materials. The value of γ impacts the external field intensity He and gradient ∇He generated by the PMG. The total amount of magnetic field energy is fixed, and the γ essentially regulates the distribution of this energy. Reducing γ concentrates more magnetic field on the PMG surface, resulting in larger force and stiffness when the levitation height approaches zero. To validate this conclusion, experiments, approximate calculations and numerical simulations have been in all employed. However, excessive reducing γ at higher heights is not ideal as it tends to distribute most of the field energy below the desired height. The approximate method in this paper indicates that the levitation force is positively correlated with (He22Hp−He)∇He . Therefore, the objective is to determine the optimal γ that maximizes this index. Optimal values for γ at different heights have been identified, offering guidance for PMG design. Additionally, applying these findings to two existing PMGs results in 18% and 8.6% augmentation in levitation force respectively. Furthermore, a fully optimized PMG design has the potential to achieve a levitation force of nearly 10 kN m−1, while keeping the cross-sectional areas of the PMG and SC restricted to 4450 mm2 and 2500 mm2, respectively.

Surrogate-Based Multi-Objective Optimization of Flux-Focusing Halbach Coaxial Magnetic Gear

Due to their contact-free and low-maintenance features, magnetic gears (MGs) have been increasingly investigated to amplify the torque of electric motors in electric vehicles (EVs). In order to meet the requirements of propelling EVs, it is essential to design an MG with a high torque density. In this paper, a novel flux-focusing Halbach coaxial MG (FFH-CMG) is proposed, which combines the advantages of flux focusing and Halbach permanent magnet (PM) arrays. The proposed structure has a higher torque performance and greater efficiency than conventional structures. A multi-objective design optimization based on a surrogate model is implemented to achieve the maximum volumetric torque density (VTD), torque-per-PM volume (TPMV), and efficiency, as well as the minimum torque ripple, in the proposed FFH-CMG. The employed optimization approach has a higher accuracy and is less time-consuming compared to the conventional optimization methods based on direct finite-element analysis (FEA). The performance of the proposed FFH-CMG is then investigated through 2D-FEA. According to the simulation results, the optimized FFH-CMG can achieve a VTD of 411 kNm/m3, and a TPMV of 830 kNm/m3, which are significantly larger than those of the existing MGs and make the proposed FFH-CMG very suitable for EV applications.

Comprehensive Analysis of Dual-Rotor Yokeless Axial-Flux Motor with Surface-Mounted and Halbach Permanent Magnet Array for Urban Air Mobility

A dual-rotor yokeless and segmented armature (YASA)-type axial-flux permanent magnet (AFPM) motor with a surface-mounted permanent magnet (SPM) array type was developed for urban air mobility (UAM) aircraft in this work. The proposed AFPM motor had rated and peak output powers of 75.5 and 104 kW, respectively, with rated and peak rotational speeds of 1800 rpm. To achieve a high torque, a cobalt–iron alloy core material was used for the stator core. The prototype AFPM motor, developed by KSEP in the Republic of Korea, was successfully manufactured and verified through experimentation. Additionally, the thermal stability of the winding and permanent magnets (PMs) was confirmed with a water-cooling system. A structure analysis of the proposed AFPM motor was conducted due to the detachment of an uneven air-gap length in the prototype AFPM motor. An output performance comparison based on core materials for the stator and rotor was carried out to explore the material cost reduction. Subsequently, the design for performance improvement by applying a Halbach permanent magnet (HPM) array type was investigated for further research.

Analysis and Suppression of Thrust Fluctuations in Halbach-type Permanent Magnet Synchronous Linear Motors

To address the thrust fluctuation problem of a bilateral type permanent magnet synchronous linear motor (DSPMSLM) with a Halbach permanent magnet array, a DSPMLSM with Halbach permanent magnet array structure is designed using ANSYS software. And based on this motor, the thrust fluctuations of the DSPMLSM are suppressed by using methods such as changing the end tooth height of the armature core, the tooth slot structure, and the opening of an auxiliary slot in the primary yoke. Firstly, the causes of thrust fluctuations in these areas were analyzed. Secondly, MAXWELL simulations were used to demonstrate that the selection of a suitable end tooth height could suppress end forces and that the use of a suitable-sized half-open slot and an auxiliary slot in the primary yoke could effectively reduce slot forces. All three methods can be used to suppress motor thrust fluctuations, reducing the thrust fluctuations of the DSPMLSM from 11.4% to 3.28% and increasing the average output thrust, which provides a reference for further optimization of the output performance of the linear motor.

A Novel Analytical Formulation of the Magnetic Field Generated by Halbach Permanent Magnet Arrays

This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement.

An efficient multi-objective optimization strategy for Halbach array permanent magnet synchronous machines based on nonlinear semi-analytical model

In this article, an efficient multi-objective optimization strategy for the Halbach array permanent magnet synchronous machine (PMSM) is developed by taking into consideration the nonlinear B-H behavior of soft magnetic materials. Based on the harmonic modeling (HM) technology, the electromagnetic performances (EPs) of the Halbach array PMSM can be computed. To specifically model the local magnetic saturation, the stator teeth are separated into several annular layers, and each tooth is further divided into several regions along the tangential direction. Then, the parameters of the Halbach array PMSM are optimized utilizing combined nonlinear semi-analytical model (SAM) and non-dominated sorting genetic algorithm II (NSGA-II). To validate the effectiveness and accuracy of the developed optimization scheme, a Halbach array prototype is then manufactured in accordance with the optimization results. The multi-objective rapid optimization strategy developed in this article, which includes but is not limited to Halbach array permanent magnet (PM) machines, serves as a reference for the design and optimization of various PM machines.

Effect of the passive damping plate on the vertical stability of permanent magnet electrodynamic suspension system

AbstractThe vertical stability of permanent magnet (PM) electrodynamic suspension (EDS) system with a passive damping plate is studied because of the well‐known under‐damped nature of the EDS suspension system. The passive damping plate is installed under the Halbach permanent magnet array. When the vehicle‐mounted Halbach array and passive damping plate move to cut the track conductive plate, the 2D eddy current force is derived by establishing equations of magnetic vector potentials and using the Maxwell stress tensor method. And a 2D finite‐element model (FEM) is built to validate the accuracy of the derived levitation force equation. Based on the derived levitation force equation, the vertical stability of the PM EDS system with a passive damping plate and the effects of the main parameters on the damping ratio are analysed.

Toward Reducing Undesired Rotation Torque in Maglev Permanent Magnet Synchronous Linear Motor

The dq current transformation method can be used to achieve the drive control of the maglev permanent magnet synchronous linear motor (MPMSLM). Specifically, the control of the suspension force Fz can be achieved by controlling the d-axis current, and the control of the thrust force Fx can be achieved by controlling the q-axis current. However, the direct use of the dq current transformation method on traditional MPMSLM structures produces an additional rotation torque around the y-axis. In order to reduce this additional torque, a new MPMSLM structure is proposed in this work. First, the characteristics of additional torque through finite element analysis are analyzed. Second, the Halbach permanent magnet array and coil size are optimized, and the topology of the MPMSLM coil is designed to reduce the additional torque. The decoupling performance and current of the proposed MPMSLM are experimentally verified through open-loop experiments using finite element simulation software. Finally, the decoupling algorithm of the generalized inverse matrix is used to achieve the decoupling between forces Fx and Fz and torque Ty and the d-axis and q-axis currents in each drive unit. Based on this, a three-degree-of-freedom closed-loop control system of the MPMSLM is designed. The LabVIEW 2018 software is used for the simulation analysis of the three-degree-of-freedom MPMSLM motion control system, and the results show that the proposed motor structure has superior closed-loop control performance.

Eddy Current Braking Force Analysis of a Water-Cooled Ironless Linear Permanent Magnet Synchronous Motor

The ironless linear permanent magnet synchronous motor (ILPMSM) is highly compact, easy to control, and exhibits minimal thrust fluctuations, making it an ideal choice for direct loading applications requiring precise positioning accuracy in linear motor test rigs. To address the issue of temperature rise resulting from increased primary winding current and to simultaneously enhance thrust density while minimizing thrust fluctuations, this paper introduces a bilateral-type ILPMSM with a cooling water jacket integrated between the dual-layer windings of the primary movers. The primary winding of the motor adopts a dual-layer coreless structure where the upper and lower windings are closely spaced and cooled by a non-conductive metal cooling water jacket, while the dual-sided secondary employs a Halbach permanent magnet array. The motor’s overall braking force is a combination of the electromagnetic braking force generated by the energized windings and the eddy current braking force induced on the cooling water jacket. This paper specifically focuses on the analysis of the eddy current braking force. Initially, the motor’s geometry and working principle are presented. Subsequently, the equivalent magnetization intensity method is employed to determine the no-load air gap magnetic density resulting from the Halbach array. An analytical model is then developed to derive expressions for the eddy current density and braking force induced in the water-cooling jacket. The accuracy of the analytical method is validated through finite element analysis. Then, a comparative analysis of the braking forces in two primary cooling structures, namely the inter-cooled type and the two-side cooled type ILPMSM, is conducted. Moreover, the characteristics of the eddy current braking force are thoroughly examined concerning motor size parameters and operating conditions. This paper provides a solid theoretical foundation for the subsequent optimization design of the proposed motor.

Accurate Modeling and Optimization of Electromagnetic Forces in an Ironless Halbach-Type Permanent Magnet Synchronous Linear Motor

In order to solve the electromagnetic force optimization problem of a high-power-density ironless Halbach-type permanent magnet synchronous linear motor, this paper adopts an electromagnetic force optimization method based on magnetic field analysis, electromagnetic force modeling, and genetic algorithm optimization: Firstly, the magnetic field of the Halbach permanent magnet array is solved by the combination of the equivalent magnetization strength method and the pseudo-periodic method, which takes into account the influence of the edge effect of the secondary magnetic field, and the magnetic field of the primary winding is solved by Fourier series expansion method. Secondly, the Maxwell tensor method is used to establish the functional relationship between the electromagnetic thrust and the main structural parameters of the unilateral motor. Finally, based on the parameter sensitivity analysis of the optimized variables and the response surface calculation, the optimal combination of the optimized variables to meet the optimization objective is found by a genetic algorithm. This method of the accurate modeling and optimization of an electromagnetic force can accurately calculate the motor air gap magnetic field and electromagnetic thrust, and the optimization speed is fast, which can greatly save time. The optimization results show that, under the premise of constant input power, the unilateral average thrust of the motor is increased by 18.75%, the peak value of thrust fluctuation is decreased by 30.27%, and the results match well with the finite element results, which verifies the correctness of the optimization results of the electromagnetic force and the reasonableness of the optimization method.

Sliding mode control of an outer-rotor magnetic-gear-integrated motor with a Halbach array

In this paper, the magnetic-gear-integrated motor with a Halbach array is analyzed. The combination of coaxial magnetic gear and permanent magnet synchronous motor (PMSM) replaces the role of mechanical gear in transmission structure and realizes the transmission characteristics of low-speed and high torque. Halbach permanent magnet array has the effect of good unilateral magnetic shielding, which can make the waveform closer to the sine wave. Aiming at the problem that the position sensor limits the control accuracy during the operation of the motor, founded on the analysis of the mathematical model of the magnetic-gear-integrated motor, an improved sliding mode observer is proposed. Also, the sliding mode controller (SMC) replaces the PI regulation in the speed loop to increase the robustness of the system. Lyapunov is utilized to prove the stability of the system, and the simulation is built in MATLAB/ Simulink. A 3.6 kW prototype is manufactured and tested. The feasibility of the sensorless-driven system is proven by simulation and experiments.

High-Performance Vernier Machines with Halbach Array Permanent Magnets for Direct Drive Applications

This paper investigates the performance enhancements of permanent magnet Vernier machines (PMVMs) that can be achieved using a new structure of Halbach array permanent magnets (HAPMs) for a direct-drive motorcycle application. To start with, size and design specifications of the electric machine are determined based on the assumed acceleration and drive cycle performance of a motorcycle. Then, five-segment Halbach array permanent magnet Vernier machines (HAPMVMs) with two different slot/pole combinations (24 s/44 p and 12 s/20 p) are suggested and optimized to achieve a high torque density with an acceptable power factor while maintaining a low torque ripple. Two selected designs from optimizations are investigated in the full speed range considering power factor and efficiency maps. Consequently, in order to demonstrate the effectiveness of the proposed five-HAPM structure, the same optimization methods are repeated with three-segment HAPMs as well as with single-piece PMs. The comparisons show a great enhancement in torque and power factor achieved with the use of five HAPMs. For instance, for 22 s/44 p topology, generated torque doubles with the use of five-segment PMs compared to single-segment PMs. Finally, the harmonics of magnetic flux density in the airgap of PMVMs and HAPMVMs are compared and investigated to reveal the reasons behind the superiority of VMs with HAPMs.

Design and Optimization of Synchronous Motor Using PM Halbach Arrays for Rim-Driven Counter-Rotating Pump

This document deals with the design of a Permanent Magnet Synchronous Motor (PMSM) to peripherally drive a counter-rotating pump inducer. The motor/pump is associated using a rim-driven principle where the motor’s active parts are located at the periphery of the inducer blades. It proposes using a Halbach array of permanent magnets for the active rotor of the motor. This solution allows the generation of a Sinusoidal Electromotive Force (EMF). Therefore, a more stable electromagnetic torque is reached. An optimum geometry suitable for the inducer specifications while respecting operational constraints is determined. The obtained geometry is then simulated using the Finite Element Method. The results are satisfactory in terms of average torque and EMF waveform. Use of the Halbach array allows a significant improvement of the flux density in the air gap compared to a designed surface-mounted machine. The experimental validation will be performed once the prototype is realized in the Laboratory of Fluid Engineering and Energy systems (LISFE).

Research on the torque performance for two multi-pole bilayer magnetorheological fluid couplings

This paper studies on the permanent magnets configuration on the transmission torque of the multi-pole bilayer magnetorheological (MR) coupling. Based on the electromagnetic field theory, the magnetic circuit models of traditional permanent magnet array (TPMA) and Halbach permanent magnet array (HPMA) are established, and the magnetic flux density within the MR fluid working gaps has been derived in order to evaluate the merits of the designed MR coupling. A 3D FE magnetic-fluid analysis has been necessary following the initial conceptual analysis, in order to study the influence of key parameters on the transmission torque. The results show that the transmission torque of the MR coupling with Halbach permanent magnet array is 33.45% higher than that of the ordinary permanent magnet array, with a same structure size. For the MR coupling with Halbach permanent magnet array, the unilateral magnetic focusing effect is better with the increase of the residual flux density of the secondary magnetic pole as well as the radial length of magnetic pole. And the single side magnetic focusing effect is the best when the main magnetic pole is 15°. The influence of the magnetic pole angle on the transmission torque has been further studied.

Detailed Design and Prototyping of a High Power Density Slotless PMSM

This article describes the detailed design and development of a 300 kW permanent magnet (PM) synchronous motor for electric aircraft propulsion, taking into consideration manufacturability, balancing ease, and cost of high-volume production with motor performance. The motor consists of a slotless stator structure with custom litz wire and an outer rotor with a Halbach PM array. The design of the proposed motor is based on multi-physics performance including electromagnetic field, thermal and mechanical analysis. For ease of manufacturing and economies of scale, the detailed design is refined by altering the PM segment number, PM shape and litz wire construction. The impacts of changing these parameters are evaluated in detail using analytical and finite element methods. The simulation results are compared with experimental results in terms of torque production, back electromotive force, and current level.

Novel Bearingless Motor Topology With Diamagnetic Salient-Pole Rotor

This article proposes a novel bearingless motor topology with diamagnetic salient-pole rotor. The material of the rotor is pyrolytic graphite (PG) so that five degrees of freedom of the rotor are passively stabilized above a permanent magnet array. The stator consists of two components: a Halbach permanent magnet array and an axial-flux stator core with twelve teeth holding the eight-pole three-phase winding. Passive levitation forces are generated between the permanent magnet unit and the PG rotor. Rotating torque is generated between the stator core and the PG rotor. In this paper, the principle of the five-axis passively stabilized bearingless motor with the PG rotor is outlined. In experiments, passive axial forces and an acceleration process are measured. In the test, open-loop speed control is used. The proof-of-concept successfully achieves stable passive levitation, and allows acceleration up to 200 r/min.

Design of a Single-Sided, Coreless, Flat-Type Linear Voice Coil Motor

A voice coil motor is a type of permanent magnet linear motor, which is based on the Ampere force theorem. It has the following advantages: a simple structure, a small size, no cogging force, and a fast response time. In this study, a voice coil motor was designed to provide x-directional thrust in the magnetically levitated cable table of a lithography machine. The voice coil motor designed in this study was based on the Halbach permanent magnet array, and adopted a single-sided, coreless, flat-type structure. First, the magnetic field distribution was analyzed based on the magnetic charge method to obtain an expression for the magnetic field and the thrust. The results of this analysis agreed very well with the finite element simulation results. Next, the main parameters of the motor, including the number of turns made by the coil, the size of the wire, and the size of the permanent magnets, were selected and optimized to increase the force density. Finally, two double-layer, serpentine waterway water-cooling plate configurations were designed for this voice coil motor. The validity of this water-cooling structure was verified for two different winding equivalent models. This provided feasibility to further upgrade the windings’ current density.

Design of Multilayer Winding-Based Halbach Array PM Compulsator

Compulsator provides higher energy density and comparable power density for pulse power supply than capacitor-based sources. With the added feature of natural current, zero-crossing capabilities make compulsator the ideal choice for pulse power supply to electromagnetic launch applications. A multilayer Halbach array permanent magnet (PM) compulsator is designed to achieve the desired performance. The multilayer winding arrangement is considered to minimize the self-inductance and to maximize the short-circuit current capability of the compulsator. Thus, different winding configurations with series and parallel connections in the compulsator are presented in detail. The mathematical modeling of the designed compulsator is also presented in brief. The designed compulsator is simulated by considering temperature rise, PM demagnetization effect, and so on. The designed compulsator performance in a dead short circuit of all phases and with single-phase short-circuit condition is presented. The obtained results show that the designed compulsator achieves the target objective.