Halbach Array Research Articles

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.

Design and Multi-Objective Optimization for Improving Torque Performance of a Permanent Magnet-Assisted Synchronous Reluctance Motor

Permanent magnet-assisted synchronous reluctance motors (PMA-SynRMs) are widely used in various industries as a relatively inexpensive and high-performance energy conversion device. The model proposed in this article relies on a magnetic pole-biased permanent magnet synchronous reluctance motor with a magnetic focusing effect. Two types of models with Halbach array and magnetic focusing effect have been proposed, which increase excitation and make the internal magnetic circuit of the rotor more saturated, thereby achieving higher electromagnetic torque. Through finite element simulation analysis and verification, the motor characteristics of the basic and proposed permanent magnet-assisted synchronous reluctance motor were calculated, including the air gap flux density and back electromotive force (EMF) in no-load analysis, as well as the average torque, torque ripple, and efficiency in load analysis. In addition, multi-objective optimization was also conducted on the rotor topology structure of proposed model two, using the uniform Latin hypercube sampling method to uniformly sample the data samples and the Pearson correlation coefficients to perform a sensitivity analysis on the data. The pilOPT multi-objective autonomous optimization algorithm was used to perform multi-objective autonomous optimization on parameters with high correlation, and the best-found solution based on the Pareto front was selected. Compared with proposed model two, the average torque of the optimized model increased by 18.14%, the efficiency increased by 1.05% and the torque ripple decreased by 5.22%. Finally, the anti-demagnetization performance of the optimized model’s permanent magnet was analyzed.

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.

Modeling and analysis of a novel 6-DOF magnetic levitation system with experimental verification

To improve the uniformity of magnetic flux and increase the stroke of the magnetic levitation system, this paper designs a novel 6-DOF magnetic levitation system and proposes an improved novel Halbach array. First, a repulsive passive magnetic bearing is utilized to provide levitation force, leading to a noticeable reduction in levitation power consumption. Then, a magnetic circuit model for the magnetic levitation system is established, and the improved novel Halbach array is optimized based on this model. Next, the stable levitation model and measurement model for the system are established, and the magnetic field distribution and magnetic bearing stiffness are analyzed. Results indicated an increase of 0.1[Formula: see text]T in the maximum magnetic flux density, accompanied by an improvement in the uniformity of magnetic flux. Additionally, there is an enhancement of 10% in magnetic bearing stiffness. Finally, a prototype of the system is constructed, and the stable levitation simulation and experiment of the actuator are conducted with this system. The maximum levitation absolute displacement error obtained by simulation is about 655[Formula: see text]nm, and the experimental results exhibited a maximum levitation absolute displacement error of approximately 750 nm for the system, confirming the effectiveness of the proposed modeling method.

Stochastic evaluation of quasi-zero stiffness magnetic spring using a reluctance-corrected analytical model

—In state of the art high-precision motion systems, which utilize magnetic levitation, a quasi-zero stiffness gravity compensation is one of the essentials to improve dynamic performance, eliminate position dependency and thus simplify controller design. Special configurations of permanent magnets, such as Halbach magnet arrays, can realize magnetic levitation as a form of magnetic spring. However, unlike conventional permanent magnet machines with large stiffness, the quasi-zero stiffness magnetic spring requires higher modeling accuracy for force estimation, which is affected by the nonlinear reluctance effect of permanent magnets. In this study, we propose an accurate magnetic modeling method for the quasi-zero stiffness magnetic spring. By correcting the reluctance effect of magnets, the proposed magnetic model achieves superior accuracy estimating levitation force and stiffness to the conventional surface current model. Using the reluctance-corrected magnetic model, tolerance analysis was performed to identify dominant geometric parameters affecting the uncertainty of the Halbach array magnetic spring performance. A Monte-Carlo simulation was used to estimate the overall tolerance of magnetic forces and stiffness. The experimental results fit in the tolerances.

Magnetic circuit optimisation and actuator suspension experiment of the 6‐DOF magnetic suspension platform for mini/micro LED

AbstractTo improve the speed of mass transfer, a magnetic suspension platform (MSP) is used to transport the display chips. A novel 6‐DOF MSP is proposed in this paper. An improved Halbach array is used to supply the magnetic flux density. Two types of permanent magnets are utilised in the improved Halbach array. The smaller permanent magnet serves to consolidate the magnetic flux density, thereby enhancing the uniformity of the magnetic field. The finite element method is employed to analyse how variations in angle impact both the strength and uniformity of the magnetic flux density. The results show that the magnetisation direction of 45° is the most effective in terms of improving the uniformity and strength of the magnetic density. Finally, a 6‐DOF MSP prototype is manufactured. A magnetic density measurement experiment and a stable suspension experiment for the actuator are conducted. The results indicate an enhancement in the uniformity of the magnetic field within the air gap. Additionally, the maximum suspension positioning accuracy of the actuator is about 750 nm.

Improving the homogeneity of Halbach arrays by optimizing magnet combinations using a genetic algorithm.

The purpose of this study was to test the effectiveness of using a genetic algorithm to find the optimal combination of permutations of permanent magnets in a Halbach magnet array in order to achieve the best magnetic field homogeneity in this work area. The test took place on a simple Halbach magnet array of 32 cubic permanent magnets. The magnetization of these magnets was preliminary assessed. Our calculations demonstrate that it is possible to achieve homogeneity of the magnetic field within the working area comparable to that of ideal identical magnetic blocks. Therefore, our study shows that combinatorics can be used to optimize homogeneity without selecting magnetic blocks, which can significantly reduce the cost of manufacturing the final structure.

Hybrid electromagnetic Halbach array for wireless power transfer (WPT) system using variable and uniform pitch coils

AbstractThe electromagnetic Halbach array (EHA) for wireless power transfer (WPT), designed to improve the transferred power and power transfer distance, has been proven to be effective and can be applied in various consumer applications. This paper presents a hybrid form of the EHA, aimed at improving the quality of power generated and transmitted. The expression for the determination of the magnetic field of a variable pitch flat coil for wireless power transfer and other uses has been derived. The average magnetic field, magnetic flux, and power transfer efficiency are investigated. The power transfer efficiency and the average magnetic field generated by four different design considerations were compared. The hybrid electromagnetic Halbach array wireless power transfer system (HEHA‐WPTS) has also been studied and results are compared with the conventional arrangements. Simulations and experiments were carried out to verify the analytical results obtained. According to the results obtained, the HEHA‐WPTS, with a base coil with variable pitches and uniform side coils, produces a more uniform average magnetic field and a better average power transfer efficiency over a longer power transfer distance.

Torque Calculation and Dynamical Response in Halbach Array Coaxial Magnetic Gears through a Novel Analytical 2D Model

Coaxial magnetic gears have piqued the interest of researchers due to their numerous benefits over mechanical gears. These include reduced noise and vibration, enhanced efficiency, lower maintenance costs, and improved backdrivability. However, their adoption in industry has been limited by drawbacks like lower torque density and slippage at high torque levels. This work presents an analytical 2D model to compute the magnetic potential in Halbach array coaxial magnetic gears for every rotational angle, geometry configuration, and magnet specifications. This model calculates the induced torques and torque ripple in both rotors using the Maxwell Stress Tensor. The results were confirmed through Finite Element Analysis (FEA). Unlike FEA, this analytical model directly produces harmonics values, leading to faster computational times as it avoids torque calculations at each time step. In a case study, a standard coaxial magnetic gear was compared to one with a Halbach array, revealing a 14.3% improvement in torque density and a minor reduction in harmonics that cause torque ripple. Additionally, a case study was conducted to examine slippage in both standard and Halbach array gears during transient operations. The Halbach array coaxial magnetic gear demonstrated a 13.5% lower transmission error than its standard counterpart.

Multiple-degree-of-freedom damping characteristics evaluation of dual halbach array eddy current damper for turbopump in cryogenic environment

Liquid hydrogen turbopumps are used in large high-performance rockets. Stable high-speed rotation is required for rocket turbopumps. The damping mechanism of the pump must suppress vibration not only in the radial direction but also in the axial direction. However, conventional damping elements using oil or rubber cannot be used due to the cryogenic temperature of liquid hydrogen. Therefore, the application of eddy current dampers to liquid hydrogen turbopumps is focused on in this paper. Although various structures of eddy current dampers have been developed, the multi-degree-of-freedom damping characteristics of dual Halbach array type eddy current dampers for liquid hydrogen turbopumps have not yet been investigated. The variation of damping characteristics with temperature has also not yet been verified. In this paper, we propose a novel dual Halbach array type eddy current damper for liquid hydrogen turbopumps. The proposed damper can generate high damping force and can be operated maintenance-free at the cryogenic temperature. The analysis results show that the damping characteristics strongly depend on temperature and that the amplitude reduction effect is greater at low temperatures. It was also found that the proposed damper has a higher damping force density than conventional dampers.

Modelling permanent magnet excited uniform fields with rational approximations

PurposeA novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.Design/methodology/approachFirst, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.FindingsAAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.Research limitations/implicationsAAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.Originality/valueThe authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

Nonlinear control of coaxial double rotor magnetic gear based on high gain observer in wind turbine

AbstractThis paper proposes a nonlinear control law with a dynamic controller based on high gain observer (HGO) for a co‐axial double rotor magnetic gear (CADRMG) based on Halbach array used in wind turbines. The generalized canonical form (GCF) is used to normalize the nonlinear augmented system to achieve the dynamic control signal with a chain of integrator of system output. In addition, a tracking problem is defined to track high speed rotor (HSR) with respect to GCF. On the other hand, the HGO is used to estimate the error tracking at the expense of nonlinear terms. Furthermore, the nonlinear system observability of the augmented system is evaluated. A dynamic control law is used to solve the tracking problem based on HGO. This controller can eliminate the effect of load torque as a constant and unknown disturbance in the closed‐loop system. Moreover, the closed‐loop stability of the system under dynamic signal control is guaranteed. The system states estimation is calculated by recursive equations from tracking error estimations. Finally, numerical simulations are given to illustrate the theoretical results of proposed system.

Novel hybrid chemical magnetorheological fluid for polishing Ti–6Al–4V alloy

ABSTRACT This study presents a highly efficient chemical and magnetorheological fluid (C-MRF) hybrid polishing process established by using an eco-friendly slurry of malic acid, Fe3O4–SiO2 abrasive particles, and hydrogen peroxide (H2O2) as an oxidant, all mixed with purified water, highlighting its efficacy in a wide range of polishing applications. Herein, the polishing processes of Ti–6Al–4V alloy utilizing C-MRF with on Fe3O4–SiO2 abrasives are detailed, and the polishing performance is assessed by investigating the influence of oxidizing agent H2O2 and acid malic to the surface finish of the Ti–6Al–4V alloy. The linear variable magnetic field by improved Halbach array was proposed to improve the material removal rate and surface quality and create a polishing process with a highly efficient magnetic field source. Single-factor and orthogonal experimental analysis methods are applied to provide the technological parameters factors with varying influences on surface quality and material removal ability.

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.

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.

A Novel Two-Stage 3D-Printed Halbach Array-Based Device for Magneto-Mechanical Applications

This research unveils a versatile Halbach array magnetic device with promising biomedical applications, offering innovative solutions for targeted therapy and disease management in evolving biomedical engineering. This paper explores the potential of a novel Halbach array-based device for harnessing magneto-mechanical phenomena in biomedical applications. The study employs computational modeling using COMSOL Multiphysics to define the device’s magnetic properties and validate its operation within the theoretical prediction. The research catalogs the device’s operational modes and assesses crucial parameters related to magneto-mechanical biomedical modalities, including magnetic field strength, gradient, and force. Experimental validation of numerical findings through magnetic field measurements confirms the device’s multifaceted potential, particularly in targeted drug delivery and tissue engineering applications. Finally, the adaptability of the magnetic arrangements for various scenarios is also highlighted. This investigation provides valuable insights into integrating magneto-mechanical principles into biomedical engineering. It paves the way for further research and innovative approaches in theranostics, positioning the presented apparatus as a promising tool with untapped potential for future exploration and discovery in the evolving biomedical field.

Design, scalable construction, and test of optimal linear Halbach arrays for mobile applications

Advancing permanent magnet arrays for linear electric machines is a compelling endeavor with the potential to further improve efficiencies in the fields of power generation or passenger and cargo transportation. Permanent magnets offer an unparalleled advantage by providing a consistent and efficient source of magnetic flux density without the need for external power input. This remarkable property allows for the development of smaller, lighter, and more energy-efficient electric machines, making them ideal for applications in several industries. Here, we present the design of an optimal linear Halbach array with a sinusoidal distribution of the magnetic flux density component Bz perpendicular to the surface of the array. A large scale and easy scalable six-segmented Halbach array has been built without the use of a steel backplate enabling a lightweight and compact design. Numerical results of the magnetic flux density distributions are calculated by relying on finite element methods and are compared with experimental measurements of the magnetic flux density, showing good agreement. The demonstration revealed that, with an optimal magnet configuration, the absence of a backplate does not result in any diminishment of magnetic flux density strength.

Exploring magnetic properties and dynamic performance of magnetic-hydraulic double-floating journal bearing based on offset load

An innovative structural system of magnetic-hydraulic double-floating journal bearing is designed to improve the ability to resist offset loads. By considering the magnetic force to the water-lubricated journal bearing and the magnetic structure design, a force model of the innovative bearing is proposed. The magnetic force and water film force for the bearing are simulated by comparing the load-carry capacity of only water film force. Experimental results showed the load-carry capacity and stability test of the innovative bearing. The design of innovative bearing with the upper suction and lower magnetic repulsion based on the Halbach array can provide a larger supporting magnetic force. The axially non-uniform magnetic structure deployment can manipulate the changes of the magnetic force in the axial direction to hold the offset load. The test found that by comparing the traditional water-lubricated bearing, the bearing has a certain vibration suppression ability in the vertical direction. Under the test speed, the bearing stiffness hardly changes with the change of the speed, which also shows a slightly decreasing trend with the increase of the excitation frequency.

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.

Combination of Measurement Data and Domain Knowledge for Simulation of Halbach Arrays With Bayesian Inference

Combination of Measurement Data and Domain Knowledge for Simulation of Halbach Arrays With Bayesian Inference