Halbach Permanent Magnet Array Research Articles

Study on the Accurate Magnetic Field Analytical Model of an Inertial Magnetic Levitation Actuator Considering End Effects

To address the demand for low noise and high stealthiness in ships and other vessels, this paper innovatively proposes an inertial magnetic levitation actuator based on non-uniform-sized Halbach permanent magnet arrays. To improve control accuracy, it is necessary to establish an accurate analytical model of the magnetic field and then obtain an accurate electromagnetic force model. However, the distortion of the magnetic field at the ends produces end effects, resulting in thrust fluctuations that affect the actuator’s control accuracy. Therefore, considering the end effects is necessary to establish an accurate analytical model of the magnetic field. To analyze the end leakage magnetic field of the Halbach array, the concept of a mechanical pseudo-cycle in the actuator is proposed, and the cycle of a Fourier series is redefined. A completed analytical expression of the Halbach array magnetic field distribution is derived by the new Fourier series, in which the end leakage magnetic field is contained. The accuracy of the proposed method is verified by solving the analytical model of the magnetic field, and the analytical results are compared with finite element simulations and experimental tests.

Enhancing the magnetic field gradient between two superconductors with rotational motion under a background DC field

The ability of bulk high-temperature superconductors to trap magnetic flux densities up to one order of magnitude larger than the saturation magnetization of conventional ferromagnetic materials offers the prospect of generating large magnetic flux density gradients. Combining multiple superconductors, akin to assembling a Halbach array of permanent magnets, may increase the generated gradient even further. The associated challenge is that superconductors are prone to demagnetization when exposed to field components perpendicular to their main magnetization direction. In the present work, we investigate the magnetic flux density gradient achieved with a pair of cubic, bulk, large-grain melt-textured superconductors in the presence of a background DC magnetic field at 77 K. We investigate the increase of the performance when decreasing the temperature down to 59 K. The studied configuration consists in two facing cubic YBa2Cu3O 7−x superconductors of 6 mm side with anti-parallel magnetization directions. It is obtained after the simultaneous magnetization of the samples followed by a rotation of 180∘ of the top superconductor. Although the background field reduces the trapped field ability of individual samples, it is shown that this phenomenon is significantly mitigated at 65 K and at 59 K compared to 77 K. The results reveal that a sample-to-sample distance ( ∼16 mm) of the order of their size is sufficient to avoid any mutual demagnetization effect during the rotational motion. Furthermore, it is shown that decreasing the temperature is not only beneficial in increasing the field and field gradient achieved but also in extending the range of background fields in which the superconductor can be rotated without demagnetization. This superconducting assembly yields a magnetic flux density gradient exceeding that of an isolated superconductor and has the potential to surpass the capabilities of permanent magnets.

A compact and portable gamma-ray spectrometer (GRASP) for inertial confinement fusion and basic science experiments.

A compact and portable gamma-ray spectrometer has been designed to diagnose different components of the inertial confinement fusion-relevant γ-ray spectrum with energies between ∼3.7-17.9MeV. The system is designed to be as compact as possible for convenient transportation and fielding in diagnostic ports on the OMEGA laser, the National Ignition Facility, and other photon-source facilities. The system consists of a conversion foil for Compton scattering in front of four magnetic spectrometer "arms," each covering a different energy range and constructed out of cylindrical permanent magnet Halbach arrays. Monte Carlo simulations have been used to optimize and assess the performance of the conversion foil, and COSY INFINITY ion-optical simulations have been used to optimize the spectrometer magnets. The performance of the design is assessed for a simulated direct-drive γ-ray spectrum. Spanning its total γ-ray energy bandwidth and using a 1.7mm thick boron conversion foil, the system's total energy resolution and efficiency are ∼15.8%-4.5% and 5.4 × 10-7-3.7 × 10-7e-/γ, respectively, with room for improvement. Spectral γ-ray measurements will provide guidance to the inertial confinement fusion program toward achieving high-energy gain relevant to inertial fusion energy and enable new measurement capabilities for basic discovery science.

Design of a large energy acceptance beamline using fixed field accelerator optics

Large energy acceptance arcs have been proposed for applications such as cancer therapy, muon accelerators, and recirculating linacs. The efficacy of hadron therapy can be improved by reducing the energy layer switching time, however this is currently limited by the small momentum acceptance of the beam delivery system (<±1%). A “closed-dispersion arc” with a large momentum acceptance has the potential to remove this bottleneck, however such a beamline has not yet been constructed. We have developed a design methodology for large momentum acceptance arcs with Fixed Field Accelerator optics, applying it to a demonstrator beam delivery system for protons at 0.5–3.0 MeV (±42% momentum acceptance) as part of the Technology for Ultra-Rapid Beam Operation project at the University of Melbourne. Using realistic magnetic fields, a beamline has been designed with zero dispersion at either end. An algorithm has been devised for the construction of permanent magnet Halbach arrays for this beamline with multipole error below one part in 104, using commercially available magnets. The sensitivity to errors has been investigated, finding that the delivered beam is robust in realistic conditions. This study demonstrates that a closed-dispersion arc with fixed fields can achieve a large momentum acceptance, and we outline future work required to develop these ideas into a complete proof-of-principle beam delivery system that can be scaled up for a medical facility. Published by the American Physical Society 2024

Enhancing unilateral EMAT performance through topological optimization of Halbach permanent Magnet arrays

A novel unilaterally excited electromagnetic acoustic transducer (EMAT) is proposed as a solution to address the challenge of weak electromagnetic ultrasonic detection signals being susceptible to interference from clutter noise signals. EMAT employs Halbach permanent magnet array (HPMA) structure and a coil designed based on Huygens superposition principle. This design enables the generation and reception of highly directive Rayleigh surface waves in aluminum plates. To enhance the operational efficiency of EMAT while maintaining a high level of directivity for surface waves, a penalty function is implemented in COMSOL Multiphysics for the topological optimization of EMAT. The objective function in this optimization process is based on covariance (COV) of the magnetic induction intensity. The research results suggest that the homogeneity of the magnetic induction intensity within the coil region is enhanced by 50 % following topological optimization compared to the original design. The energy conversion efficiency of EMAT is enhanced by 5 times compared to traditional designs. The surface wave speed was determined to be 2631 m/s when measured at a frequency of 400 kHz. The value indicates a relative error of 6.37 % in comparison to the theoretical speed. The results indicate that EMAT has the capability to generate high-directional and pure Rayleigh waves.

Maglev train high-precision positioning technology based on FBG array time division multiplexing

The positioning system is crucial in operating, controlling and monitoring maglev trains. This study proposes a maglev train positioning technology based on weak Fiber Bragg Grating (wFBG) sensing array time division multiplexing (TDM). The onboard Halbach permanent magnet array generates a traveling wave magnetic field that follows the train movement. The wFBG magnetic sensor array fixed on the track senses the magnetic field changes which cause periodical variation in sensors’ center wavelength. The relative position of the onboard Halbach array and the sensors on the track can be determined with the changes in center wavelength. Therefore, train positioning can be achieved. A rotating motor equipped with a circumferentially arranged magnet array is utilized for simulation experiment to verify the frequency response characteristics of the magnetic sensor. The result is that the operating frequency range of the sensor is at most 160 Hz so the sensor can be applied to positioning under the theoretical speed of 23 km/h. A small-scale experiment containing nine sensors is also conducted, which achieves relative positioning accuracy of 20 mm and absolute positioning accuracy of 540 mm, demonstrating the feasibility of the positioning technology. This study introduces the FBG TDM technology into maglev train positioning and provides new ideas about maglev train positioning.

A novel Halbach array permanent magnet flowmeter for liquid metal flow measurement. Part Ⅱ: Impact of velocity distribution on measurement signals and optimization design for electrodes

In this paper, the principles of Halbach array permanent magnet flowmeter (HA-PMFM) in reducing the sensitivity of measurement signals to velocity distribution by using arc-shaped electrodes and multi-electrodes, respectively, are analyzed. The impact laws of disturbance amplitudes of three velocity distribution forms (waterfall, skewed, and blockage types) on the measurement signals acquired by HA-PMFM with point electrodes, arc-shaped electrodes, and multiple electrodes, respectively, were investigated by COMSOL Multiphysics software. The results show that, in comparison to HA-PMFM with point electrodes, HA-PMFM with arc-shaped electrodes mitigates the unevenness of the weight function from 0.68 to 0.12. Under strong velocity distribution disturbances at constant flow velocity, optimized arc-shaped electrodes can reduce the measurement error from a maximum of 15 % to within 7 %, and multi- electrodes can reduce the measurement error from a maximum of 15 % to within 5 % compared to the point electrodes. However, when the uniform incoming flow rate is varied, the optimized arc-shaped electrodes can reduce the measurement error from 2 % to within 1 %, and the multi-electrodes can reduce the error from 2 % to within 1.5 %. This study offers valuable insights for enhancing the measurement accuracy of HA-PMFM in engineering applications and provides guidance for the design of liquid metal electromagnetic flowmeters in various fields, particularly for those compact systems using liquid metal as flow medium in which the flowmeter has to be installed on the flow passage with strongly distorted velocity distribution.

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.