Halbach Magnet Array Research Articles

Design and experimental validation of Unilateral Linear Halbach magnet arrays for single-sided magnetic resonance

Single-sided NMR has the potential for broad utility and has found applications in healthcare, materials analysis, food quality assurance, and the oil and gas industry. These sensors require a remote, strong, uniform magnetic field to perform high sensitivity measurements. We demonstrate a new permanent magnet geometry, the Unilateral Linear Halbach, that combines design principles from “sweet-spot” and linear Halbach magnets to achieve this goal through more efficient use of magnetic flux. We perform sensitivity analysis using numerical simulations to produce a framework for Unilateral Linear Halbach design and assess tradeoffs between design parameters. Additionally, the use of hundreds of small, discrete magnets within the assembly allows for a tunable design, improved robustness to variability in magnetization strength, and increased safety during construction. Experimental validation using a prototype magnet shows close agreement with the simulated magnetic field. The Unilateral Linear Halbach magnet increases the sensitivity, portability, and versatility of single-sided NMR.

Design of High Power Density TVC Driving Motor for Space Launch Vehicle Using Halbach Magnet Array Structure

This paper presents a high power density motor design process of a thrust vector control (TVC) system to modify the thrust vector of the gimbal engine of a space launch vehicle. For this system, the high power density motor designing requires computation of the maximum current density by considering the driving environment, operating conditions, and electromagnetic optimum design process. This paper describes the computation of the maximum allowable current density in vacuum, which is the driving environment of a TVC drive motor. In addition, a Halbach magnet array structure is applied as a high output density design method for a surface-mounted synchronous motor. The characteristics of the output and loss of this structure are compared with those of an existing design. Moreover, we highlight the advantages of applying a Halbach magnet array in terms of the demagnetization resistance.

End-Effect Magnetic Field Analysis of the Halbach Array Permanent Magnet Spherical Motor

The Halbach array permanent magnet (PM) spherical motor (PMSM) consists of a spherical rotor and a spherical-shell stator. The magnetic field distribution surrounding the rotor PMs is closely related to the spherical structure of the Halbach array PMSM. The Halbach array PM configuration characteristics lead to the end leakage magnetic field in the latitudinal direction of the spherical structure, which is end effect. Establishment of an accurate 3-D magnetic field analytical model containing the end leakage magnetic field of the Halbach array PMSM is the foundation of magnetic field distortion research with its influence on eddy-current loss. The magnetic field distribution of the Halbach array PMs in the air gap is calculated using the scalar magnetic potential. Laplace and Poisson equations of the scalar magnetic potential in the spherical coordinate system are derived. To analyze the end leakage magnetic field of the Halbach array PMSM in the latitudinal direction, concept of mechanical pseudo-cycle in the motor latitudinal direction is proposed, and the cycle of Fourier series is redefined. A completed 3-D analytical expression of the Halbach array PMSM magnetic field distribution is derived by the new Fourier series and spatial integral technology, in which the end leakage magnetic field is contained. The results obtained by the proposed analytical method are compared with the numerical results, i.e., the results obtained by the finite-element method, which verify the effectiveness of the analytical method. Magnetic field distribution containing the end leakage magnetic field in different magnetization methods is compared and analyzed, which shows that the Halbach array magnetization has a larger main air-gap magnetic field and a smaller end leakage magnetic field. The effect of motor structure parameters on the end leakage magnetic field is analyzed, and the effect of end leakage magnetic field on eddy-current loss is preliminarily discussed, which shows that eddy-current loss caused by end effect almost accounts for half of the total eddy-current loss. The research on end effect and the effect of motor parameters on end effect are of great significance. In the end, the leakage magnetic field results obtained by the proposed analytical method are verified by the experimental results.

Analysis and Application of Discrete Halbach Magnet Array With Unequal Arc Lengths and Unequally Changed Magnetization Directions

This paper presents a general process to analyze and optimize the performance for an arbitrary discrete Halbach magnet array which is “unnormal” on magnetization direction and arc length of each segment. Besides the original type, a new arrangement of Halbach array is proposed, which does not have main PM segments. Two-dimensional field analytical models for predicting the air-gap field distribution of both arrangements are offered and validated by an FEA method. Then, a multi-objective optimizer was applied for different requirements, and comparison between normal and optimized 3-segment Halbach array is given to verify the effect of optimization. At last, some potential applications and follow-up study are discussed.

Halbach Effect at the Nanoscale from Chiral Spin Textures

Mallinson's idea that some spin textures in planar magnetic structures could produce an enhancement of the magnetic flux on one side of the plane at the expense of the other gave rise to permanent magnet configurations known as Halbach magnet arrays. Applications range from wiggler magnets in particle accelerators and free electron lasers to motors and magnetic levitation trains, but exploiting Halbach arrays in micro- or nanoscale spintronics devices requires solving the problem of fabrication and field metrology below a 100 μm size. In this work, we show that a Halbach configuration of moments can be obtained over areas as small as 1 μm × 1 μm in sputtered thin films with Néel-type domain walls of unique domain wall chirality, and we measure their stray field at a controlled probe-sample distance of 12.0 ± 0.5 nm. Because here chirality is determined by the interfacial Dyzaloshinkii-Moriya interaction, the field attenuation and amplification is an intrinsic property of this film, allowing for flexibility of design based on an appropriate definition of magnetic domains. Skyrmions (<100 nm wide) illustrate the smallest kind of such structures, for which our measurement of stray magnetic fields and mapping of the spin structure shows they funnel the field toward one specific side of the film given by the sign of the Dyzaloshinkii-Moriya interaction parameter D.

High performance human-induced vibration driven hybrid energy harvester for powering portable electronics

In this work, we demonstrated theoretically and experimentally the use of a dual Halbach magnet array and combined with a magnetically floated electromagnetic–triboelectric energy harvester to convert the mechanical energy of human induced motion into electrical energy. To achieve very high generated powers, the proposed hybrid energy harvester included a Halbach magnet array, nanostructured polytetrafluoroethylene (PTFE), Al nano–grass, and magnetic springs. A prototype of the hybrid energy harvester was fabricated and tested, with either a vibration exciter or human induced motion. Under a vibration exciter test, the fabricated hybrid energy harvester delivered a high output current of 3.74mA and a power of 10.07mW, corresponding to a volume power density of 344W/m3 under a loading resistance of 710Ω at 4.5Hz resonant frequency and 0.6g acceleration. In addition, the hybrid harvester was able to generate output powers of 5.8mW, 2.6mW, and 3.4mW from human induced vibration of handshaking, walking, and slow running, respectively. The fabricated hybrid electromagnetic–triboelectric harvester exhibits a much higher power density than recently reported in similar works. This work takes a significant step toward hybrid energy harvesting from human induced motion and its potential applications in powered portable electronics.

Analysis and Optimization of a Novel 2-D Magnet Array with Gaps and Staggers for a Moving-Magnet Planar Motor.

This paper presents a novel 2-D magnet array with gaps and staggers, which is especially suitable for magnetically levitated planar motor with moving magnets. The magnetic flux density distribution is derived by Fourier analysis and superposition. The influences of gaps and staggers on high-order harmonics and flux density were analyzed, and the optimized design is presented. Compared with the other improved structures based on traditional Halbach magnet arrays, the proposed design has the lowest high-order harmonics percentage, and the characteristics of flux density meet the demand of high acceleration in horizontal directions. It is also lightweight and easy to manufacture. The proposed magnet array was built, and the calculation results have been verified with experiment.

A Hybrid Electromagnetic–Triboelectric Energy Harvester Using a Dual Halbach Magnet Array Powered by Human‐Body‐Induced Motion

AbstractA highly miniaturized hybridization of electromagnetic–triboelectric energy harvesters with different mechanisms in one harvester is proposed using a Halbach magnet array from human‐body‐induced motion, and it is theoretically and experimentally validated. In particular, the proposed dual Halbach array allows the concentrated magnetic flux lines to interact with the same coil in a manner that produces maximum flux linkage. To obtain much higher power generation at low‐amplitude and low‐frequency vibrations, the proposed harvester is comprised of a Halbach magnet array, sandpaper‐based microstructure polydimethylsiloxane (PDMS), a triboelectric, and magnetic springs. A prototype of the hybrid energy harvester is fabricated and tested, both using a vibration exciter test, and by manual handshaking. Under vibration exciter test, the fabricated hybrid harvester prototype delivers a high output current and power of 4.5 mA and 12.51 mW, respectively, corresponding to a volume power density of 411 W m−3 under a loading resistance of 617 Ω at 6.5 Hz resonant frequency and 0.5g acceleration. The hybrid prototype is also capable of delivering output current and power of 3.55 mA and 7.35 mW, respectively, if driven by handshaking vibration. The fabricated hybridized harvester exhibits much higher power density than similar recently reported works.

Modeling and analysis of Halbach magnet array with pyramidal magnet in planar motor

Modeling and analysis of Halbach magnet array with pyramidal magnet in planar motor

Spatial harmonic analysis on a permanent magnet linear generator with Halbach array for direct‐driver wave energy conversion

AbstractA tubular permanent magnet linear generator (TPMLG) with Halbach array magnetization is proposed to extract wave energy. The magnetic field is analyzed by analytical analysis and verified by numerical analysis. The air‐gap flux density of TPMLG with Halbach array magnetization has a better sinusoidal shape than quasi‐Halbach and other magnetization based on the spatial harmonic analysis. The harmonic component of flux density varies with the degree of permanent magnet magnetization, through optimizing the angle α (α is the angle between the z‐axis and orientation of magnetization), and the harmonic component is smallest when the angle α equal to π/4. Meanwhile, the amplitude of Br in air‐gap region reaches maximum. Analytical analysis proves that TPMLG with Halbach array magnetization can improve generator performance and power density. Finally, a prototype is manufactured and applied to a direct‐drive power take‐off system experiment. Simulations and experimental results demonstrate that it is an effective method for direct‐drive wave power take‐off system.

Force characteristic analysis of a magnetic gravity compensator with annular magnet array for magnetic levitation positioning system

Magnetic levitation positioning system (MLPS) is considered to be the state of the art in inspection and manufacturing systems in vacuum. In this paper, a magnetic gravity compensator with annular magnet array (AMA-MGC) for MLPS is proposed. Benefiting from the double-layer annular Halbach magnet array on the stator, the proposed AMA-MGC possesses the advantages of symmetrical force, high force density and small force fluctuation. Firstly, the basic structure and operation principle of the AMA-MGC are introduced. Secondly, the basic characteristics of the AMA-MGC such as magnetic field distribution, levitation force, parasitic force and parasitic torque are analyzed by the three-dimensional finite element analysis (3-D FEA). Thirdly, the influence of structural parameters on force density and force fluctuation is investigated, which is conductive to the design and optimization of the AMA-MGC. Finally, a prototype of the AMA-MGC is constructed, and the experiment shows good agreement with the 3-D FEA results.

Two-Phase Lorentz Coils and Linear Halbach Array for Multiaxis Precision-Positioning Stages With Magnetic Levitation

In this paper, a new framework for linear permanent-magnet (PM) machines with applications in precision motion control is proposed and validated. A single forcer generating two independent force components in two perpendicular directions is the fundamental unit of the framework. Each forcer consists of two planar Lorentz coils separated by a 90° or 270° phase difference and parallel to a Halbach magnet array. Many coil pairs can be assembled to the same platen to move over a common magnet matrix, forming a linear or planar PM motor. Advantages of this framework include a linear system model, the capability to magnetically levitate the mover in multiaxis stages, and that to generate long translational motion range. The framework developed herein is validated by a six-degree-of-freedom magnetically levitated (maglev) stage. The dimension of the moving platen's frame is $\text{14.3}{\,\text{cm}}\times \text{14.3}{\,\text{cm}}$ , and its total mass is 0.75 kg. The achieved positioning resolution in translations along $X,Y$ , and $Z$ is 10 nm. The positioning resolution in out-of-plane rotation is $\text{0.1}\,\mu {\text{rad}}$ , which is a record in the literature. The maximum travel range in $XY$ with laser interferometers is ${\text{56}\,\text{mm}}\times \text{35}\,{\text{mm}}$ , limited by the size of the precision mirrors. With the coils’ total mass of only 0.205 kg, the achieved acceleration is 1.2 m/s2. Experimental results exhibit reduced perturbations in other axes of in-plane motions.

Design and experiment of hybridized electromagnetic-triboelectric energy harvester using Halbach magnet array from handshaking vibration

We have proposed a new design of hybridized electromagnetic-triboelectric energy harvester using Halbach magnet array from handshaking vibration and validated it theoretically and experimentally. The Halbach array helps to enhance the magnetic flux density and reduce the overall volume as well as generate high power at low frequency. In particular, the proposed dual Halbach array allows the concentrated magnetic flux lines to interact with the same coil in a way where maximum flux linkage occurs. To obtain much higher power generation in low amplitude and low frequency vibrations, the proposed harvester was comprised of a Halbach magnet array, sandpaper passed microstructure PDMS, TENG, and magnetic springs. A prototype of the hybridized energy harvester has been fabricated and tested both using a vibration exciter test and by manual handshaking. Under vibration exciter test, the fabricated prototype of hybridized harvester delivered a high output current and power of 2.9mA and 11.75mW, respectively, corresponding to a volume power density of 381W/m3 under a loading resistance of 1.39kΩ at 5Hz resonant frequency and 0.5g acceleration. It is also capable of delivering output current and power of 2.85mA and 8.1mW, respectively, by handshaking vibration. The fabricated hybridized harvester exhibited much higher power density than the recently reported similar works. Our proposed work takes a significant step toward hybrid energy harvesting from human-body-induced motions such as handshaking, walking, running and its potential applications in self powered portable electronics.

3D Analytical model of drag and lift force for a conductive plate moving above a Halbach magnet array

When a conductive plate moves above a Halbach magnetic source, a magnetic field will be created in the air gap. This field induces eddy currents in the plate and creates drag and lift forces simultaneously. This phenomenon may be applied into eddy current brakes, couplings or magnetic levitation systems. In this paper, by utilizing the derived analytical field solutions of the Maxwell equations with magnetic scalar potential and magnetic field strength, the 3D lift and drag forces, and the flux density distribution in the air gap are predicted and analysed in the steady-state condition. Calculation results produced by analytical model are compared with those from the 3D finite element method. A prototype of the disk-type permanent magnetic eddy-current coupling has been manufactured to validate the accuracy of the 3D analytical model. The results confirm that, compared with 2D analytical model from the papers that had already published, the results calculated by the 3D analytical model have a higher accuracy in performance analysis. Finally, the characteristics of different kinds of magnet arrays are compared based on the proposed model, and several main problems are analysed and discussed.

Design of a Control System for a Maglev Planar Motor Based on Two-Dimension Linear Interpolation

In order to realize the high speed and high-precision control of a maglev planar motor, a high-precision electromagnetic model is needed in the first place, which can also contribute to meeting the real-time running requirements. Traditionally, the electromagnetic model is based on analytical calculations. However, this neglects the model simplification and the manufacturing errors, which may bring certain errors to the model. Aiming to handle this inaccuracy, this paper proposes a novel design method for a maglev planar motor control system based on two-dimensional linear interpolation. First, the magnetic field is divided into several regions according to the symmetry of the Halbach magnetic array, and the uniform grid method is adopted to partition one of these regions. Second, targeting this region, it is possible to sample the electromagnetic forces and torques on each node of the grid and obtain the complete electromagnetic model in this region through the two-dimensional linear interpolation method. Third, the whole electromagnetic model of the maglev planar motor can be derived according to the symmetry of the magnetic field. Finally, the decoupling method and controller are designed according to this electromagnetic model, and thereafter, the control model can be established. The designed control system is demonstrated through simulations and experiments to feature better accuracy and meet the requirements of real-time control.

Magnetic Enhancement of Stem Cell–Targeted Delivery into the Brain Following MR-Guided Focused Ultrasound for Opening the Blood–Brain Barrier

Focused ultrasound (FUS)-mediated blood–brain barrier disruption (BBBD) can enable even large therapeutics such as stem cells to enter the brain from the bloodstream. However, the efficiency is relatively low. Our previous study showed that human neural progenitor cells (hNPCs) loaded with superparamagnetic iron oxide nanoparticles (SPIONs) in culture were attracted by an external magnetic field. In vivo, enhanced brain retention was observed near a magnet mounted on the skull in a rat model of traumatic brain injury, where BBBD also occurs. The goal of the current study was to determine whether magnetic attraction of SPION-loaded hNPCs would also enhance their retention in the brain after FUS-mediated BBBD. A small animal magnetic resonance imaging (MRI)-guided FUS system operating at 1.5 MHz was used to treat rats (∼120 g) without tissue damage or hemorrhage. Evidence of successful BBBD was validated with both radiologic enhancement of gadolinium on postsonication TI MRI and whole brain section visualization of Evans blue dye. The procedure was then combined with the application of a powerful magnet to the head directly after intravenous injection of the hNPCs. Validation of cells within the brain was performed by staining with Perls’ Prussian blue for iron and by immunohistochemistry with a human-specific antigen. By injecting equal numbers of iron oxide (SPIONs) and noniron oxide nanoparticles–loaded hNPCs, each labeled with a different fluorophore, we found significantly greater numbers of SPIONs-loaded cells retained in the brain at the site of BBBD as compared to noniron loaded cells. This result was most pronounced in regions of the brain closest to the skull (dorsal cortex) in proximity to the magnet surface. A more powerful magnet and a Halbach magnetic array resulted in more effective retention of SPION-labeled cells in even deeper brain regions such as the striatum and ventral cortex. There, up to 90% of hNPCs observed contained SPIONs compared to 60% to 70% with the less powerful magnet. Fewer cells were observed at 24 h posttreatment compared to 2 h (primarily in the dorsal cortex). These results demonstrate that magnetic attraction can substantially enhance the retention of stem cells after FUS-mediated BBBD. This procedure could provide a safer and less invasive approach for delivering stem cells to the brain, compared to direct intracranial injections, substantially reducing the risk of bleeding and infection.

Optimization study on the magnetic field of superconducting Halbach Array magnet

This paper presents the optimization on the strength and homogeneity of magnetic field from superconducting Halbach Array magnet. Conventional Halbach Array uses a special arrangement of permanent magnets which can generate homogeneous magnetic field. Superconducting Halbach Array utilizes High Temperature Superconductor (HTS) to construct an electromagnet to work below its critical temperature, which performs equivalently to the permanent magnet based Halbach Array. The simulations of superconducting Halbach Array were carried out using H-formulation based on B-dependent critical current density and bulk approximation, with the FEM platform COMSOL Multiphysics. The optimization focused on the coils’ location, as well as the geometry and numbers of coils on the premise of maintaining the total amount of superconductor. Results show Halbach Array configuration based superconducting magnet is able to generate the magnetic field with intensity over 1 Tesla and improved homogeneity using proper optimization methods. Mathematical relation of these optimization parameters with the intensity and homogeneity of magnetic field was developed.

37‐4: A Novel Magnet‐Array Design for Solving Mask Deformation

Design of Halbach magnet array is employed to solve mask deformation due to gravity. Uniform magnetic force exerted on mask can be yielded, which balances the mask gravity. The magnetic force on the mask changes slower when deviating from the Halbach magnet array comparing with conventional magnet array.

An accurate real-time model of maglev planar motor based on compound Simpson numerical integration

To realize the high-speed and precise control of the maglev planar motor, a more accurate real-time electromagnetic model, which considers the influence of the coil corners, is proposed in this paper. Three coordinate systems for the stator, mover and corner coil are established. The coil is divided into two segments, the straight coil segment and the corner coil segment, in order to obtain a complete electromagnetic model. When only take the first harmonic of the flux density distribution of a Halbach magnet array into account, the integration method can be carried out towards the two segments according to Lorenz force law. The force and torque analysis formula of the straight coil segment can be derived directly from Newton-Leibniz formula, however, this is not applicable to the corner coil segment. Therefore, Compound Simpson numerical integration method is proposed in this paper to solve the corner segment. With the validation of simulation and experiment, the proposed model has high accuracy and can realize practical application easily.

Topology optimization of Halbach magnet arrays using isoparametric projection

Topology optimization using isoparametric projection for the design of permanent magnet patterns in Halbach arrays is proposed. Based on isoparametric shape functions used in the finite element analysis, the permanent magnet strength and magnetization directions in a Halbach array are simultaneously optimized for a given design goal. To achieve fabrication feasibility of a designed Halbach magnet array, two design schemes are combined with the isoparametric projection method. First, a penalization scheme is proposed for designing the permanent magnets to have discrete magnetization direction angles. Second, an extrusion scheme is proposed for the shape regularization of the permanent magnet segments. As a result, the method systematically finds the optimal permanent magnet patterns of a Halbach array considering manufacturing feasibility. In two numerical examples, a circular shaped permanent magnet Halbach array is designed to minimize the magnitude of the magnetic flux density and to maximize the upward direction magnetic flux density inside the magnet array. Logical extension of the method to the design of permanent magnet arrays in linear actuators is provided, where the design goal is to maximize the actuator magnetic force.