Halbach Array Research Articles

Analytical modelling with experimental validation of electromagnetic Halbach arrays in wireless power transfer systems

AbstractA mathematical model is presented for the optimisation of an Electromagnetic Halbach Array (EHA) for wireless power transfer. The mathematical model is based on Biot‐Savart's law of magnetic field in a current‐carrying square loop. The model is validated through static electromagnetic simulations in ANSYS Maxwell and found to be accurate and effective when predicting the magnetic field within the EHA box. To verify the analytical and simulation results, an EHA was fabricated, and experimental verification was carried out. The results show that the mathematical model can be widely used in the analysis and design optimisation of EHAs of any size and with diverse parameters in the case of single‐layer square spiral planar coils.

Investigating magnetization of permanent magnets by magnetic flux viewing film

Permanent magnets are used in many current industrial as well as home appliances today. Frequently, kitchen plastic magnets could be found at the refrigerators at home. However, the magnetic domain structure of such permanent plastic foils is not known and understood to the users at all. The purpose of this paper is to explain the magnetic domain structure of plastic magnets with Halbach array and ferrite or neodymium magnet polarization orientation. Principles of magnetic field visualization foils (magnetic flux detector and colour changing viewing film) is explained and demonstrated on multipole magnetic structures. Experiments with magnetic polarization reversal by the strong neodymium magnet in weaker ferrite magnetic material is demonstrated. All presented principles are collected in the simple magnetic set and suggested for education of school children of different ages. Elementary school children below 10 years age are mostly interested only in making hidden pictures in magnetic paper and ferrite magnet. Older school children of 11–12 years are able to absorb more knowledge about behaviour and properties of magnets.

Design and Research of Novel Consequent-Pole Dual PM Vernier Machines with Spoke and Halbach Array

Design and Research of Novel Consequent-Pole Dual PM Vernier Machines with Spoke and Halbach Array

Design and Analysis of a Novel Electromagnetic-Propulsion Rotary Machine With External Blending-Shaped Tessellation Magnet Pattern

One major challenge for the design of rotary machine of electric propulsion aircraft is how to improve its torque output and power density. The objective of this paper is to propose a novel external blending-shaped tessellation (EBT) magnet pattern for electromagnetic rotary machine. It can offer several advantages. First, it helps to increase the magnetic flux density in the airgap, and thus the torque output of the rotary machine is increased. Second, it enhances the self-shielding effect greatly, and thus the back iron can be removed completely and replaced with low-density materials. As a result, the rotor mass can be reduced and the system dynamics could be improved. Third, the improved torque and the reduced mass may contribute to the high power density as well. The design concept and operating principle of the proposed external blending-shaped tessellation magnet pattern are presented. Following that, the magnetic field distribution is formulated analytically through Laplace's and Poisson's equations. Then the torque generation of the rotary machine is modeled mathematically. Subsequently, the numerical simulation is conducted to validate the analytical models of the magnetic field distribution and torque output. The magnetic flux density and torque output of the proposed magnet pattern are compared with those of conventional magnet arrays. A research prototype of the electric rotary machine with the EBT magnet pattern is developed, and an experimental test platform is constructed. Experiments are conducted on the magnetic flux density and torque output to verify the proposed design and analytical models. The experimental results validate the derived analytical model of magnetic field and the output torque, and the effectiveness of the magnet array in improving the output characteristic. It shows that the output torque generated by the proposed design is larger than that of conventional Halbach array by 27 percent.

A Novel Field-Free Line Generator for Mechanically Scanned Magnetic Particle Imaging

In this study, we propose an efficient field-free line (FFL) generator for mechanically driven FFL magnetic particle imaging (MPI) applications. The novel FFL generator comprises pairs of Halbach arrays and bar magnets. The proposed design generates high-gradient FFLs with low-mass permanent magnets, realizing fine spatial resolutions in MPI. We investigate the magnetic field generated using simulations and experiments. Our results show that the FFL generator yields a high gradient of 4.76 T/m at a cylindrical field of view of 30 mm diameter and a 70 mm open bore. A spatial resolution of less than 3.5 mm was obtained in the mechanically driven FFL-MPI.

How the Magnetization Angle of a Linear Halbach Array Influences Particle Steering in Magnetic Drug Targeting—A Systematic Evaluation and Optimization

The main challenge in magnetic drug targeting lies in steering the magnetic particles, especially in deeper body layers. For this purpose, linear Halbach arrays are currently in focus. However, to the best of the authors’ knowledge, the impact of the magnetization angle between two neighboring magnets in Halbach arrays has not been investigated for particle steering so far. Therefore, in this paper, a systematic numerical parameter study of varying the magnetization angle of linear Halbach arrays is conducted. This is completed by undertaking a typical magnetic drug targeting scenario, where magnetic particles have to be steered in an optimized manner. This includes the calculation of the magnetic flux density, its gradient, the total magnetic energy, and the resulting magnetic force based on a fitting function for the different Halbach constellations in the context of examining their potential for predicting the particle distribution. In general, increased magnetization angles result in an increased effective range of the magnetic force. However, as there is a trade-off between a weak force on the weak side of the array and a simple manufacturing process, a magnetization angle of 90∘ is recommended. For evaluating the steering performance, a numerical or experimental evaluation of the particle distribution is mandatory.

Nonlinear electromagnetic vibration energy harvester comprising dual helical-plane springs and multiple Halbach arrays for low-frequency and small-amplitude vibrations

Electromagnetic vibration energy harvesters are widely investigated for self-powered wireless sensors and nonlinearity has been introduced for low-frequency and broadband vibration energy harvesting. But how to realize the nonlinearity with small amplitudes, high reliability and few complexities is still a challenge in real-world applications. In this paper, a novel electromagnetic vibration energy harvester comprising dual helical-plane springs and multiple Halbach arrays is proposed. The structural characteristics are analyzed, which indicate that the helical-plane springs can have nonlinear stiffness under small-amplitude vibrations and multiple Halbach arrays can greatly enhance the magnetic field. Then a magnet-electro-mechanical model is built by combining mechanical dynamics &electrodynamics, which is numerically solved by using the Runge-Kutta algorithm. Finally, the feasibility of the nonlinear electromagnetic vibration energy harvester is validated both numerically and experimentally. The results show that it has a nonlinear stiffness, a resonance bandwidth of 3 Hz and a peak power of 14 mW when the excitation amplitude is only 0.5 g. In particular, the resonance frequency range depends on the excitation amplitude. Furthermore, the prototype of a self-powered wireless temperature sensor is constructed and testified. The results of this study indicate that the proposed structure can be utilized and extended to build compact, reliable and nonlinear electromagnetic vibration energy harvesters for low-frequency, small-amplitude and broadband vibrations in real-world applications.

Design and analysis of a passive adaptive wall-climbing robot on variable curvature ship facades

To improve the adaptive motion performance of traditional wall-climbing robots on variable-curvature facades, a crawler-type wall-climbing robot suitable for ship wall features is proposed by utilizing the advantages of passive mechanisms in realizing autonomous robots. The robot consists of two passive adaptive crawler mechanisms and a connecting module. Each track structure contains multiple permanent magnets that can passively adapt to concave and convex facades of different curvatures. A static failure model is established according to the characteristics of the triangular distributed load, and the minimum adsorption force required for the robot to achieve safe motion is determined. The Halbach Array magnetic circuit design method was used to construct a gap-type permanent magnet adsorption model for lightweight design. The influence of wall thickness and air gap distance on the adsorption force is analyzed by parametric simulation. The prototype platform test shows that the robot can realize adaptive variable curvature motion through passive adjustment of the mobile mechanism attitude and has a certain load capacity.

Design of a rotor with a starter-generator integrated into an aero car

The Halbach array structure rotor of the aero motor can satisfy the requirements of high power density and high air-gap flux for aeronautical motors. The size parameters of the rotor are determined by the power rating of the motor based on an analytic method. Producing a Halbach array structure is difficult. Comparison and analysis of the structure of the aero motor show that the overall structure of the rotor adopts a three-axial-section classic Halbach-array hollow structure, and the rotor magnetic steel adopts a discrete structure of 4 blocks per pole and a single 45 degrees magnetisation mode, which reduces the processing difficulty of the rotor magnetic steel. The finite element method was used to analyse the magnetic flux density distribution of the aeronautical motor under various working conditions. The results show that the motor can produce uniform air-gap flux density at various working conditions and present good sinusoidal periodicity. Furthermore, the axial segment did not produce obvious magnetic flux leakage. Finally, considering the eddy current loss of the stator under the rated power-generation condition with high-frequency magnetic field, we conducted coupling analysis of electromagnetic and heat flows to verify that the thermal characteristics of the rotor magnetic steel material could meet the requirements for the aero motor.

Design and Optimization of Halbach Magnetic Gear

This article proposes a new structure to enhance the torque and torque density of permanent magnet gears. The outer magnet is designed with a dual-layer permanent magnet configuration, where the first layer adopts a Halbach array, and the other layer utilizes a conventional radial magnetization structure. With the optimization objectives defined as maximum torque and torque density, and guided by parameter sensitivity, optimization analysis was conducted using response surface method and multi-objective genetic algorithm. The optimized parameters were determined, and finite element simulations were performed to validate the optimization results. The result indicate a 22.22% increase in torque and a 27.42% increase in torque density compared to the previous the traditional magnet gear. The performance of the proposed new structure of magnetic gear has shown significant improvement.

Design and Analysis of Halbach Array PM Inner Rotor Slotted Stator Compensated Pulsed Alternator

Design and Analysis of Halbach Array PM Inner Rotor Slotted Stator Compensated Pulsed Alternator

Linear Actuators for High-Speed Reciprocating Motion with Dual Halbach Arrays (Fundamental Consideration of the Effect of Magnet Arrangement on Thrust Characteristics)

Linear Actuators for High-Speed Reciprocating Motion with Dual Halbach Arrays (Fundamental Consideration of the Effect of Magnet Arrangement on Thrust Characteristics)

Permanent magnet systems to study the interaction between magnetic nanoparticles and cells in microslide channels

We optimized designs of permanent magnet systems to study the effect of magnetic nanoparticles on cell cultures in microslide channels. This produced two designs, one of which is based on a large cylindrical magnet that applies a uniform force density of 6MN/m3 on soft magnetic iron-oxide spherical nanoparticles at a field strength of over 300mT. We achieved a force uniformity of better than 14% over the channel area, leading to a concentration variation that was below our measurement resolution. The second design was aimed at maximizing the force by using a Halbach array. We indeed increased the force by more than one order of magnitude at force density values over 400MN/m3, but at the cost of uniformity. However, the latter system can be used to trap magnetic nanoparticles efficiently and to create concentration gradients. We demonstrated both designs by analyzing the effect of magnetic forces on the cell viability of human hepatoma HepG2 cells in the presence of bare Fe2O3 and cross-linked dextran iron-oxide cluster-type particles (MicroMod). Python scripts for magnetic force calculations and particle trajectory modeling as well as source files for 3D prints have been made available so these designs can be easily adapted and optimized for other geometries.

Design and Optimization of Coaxial Magnetic Gear With Double-Layer PMs and Spoke Structure for Tidal Power Generation

A coaxial magnetic gear (CMG) with double-layer permanent magnets (PMs) and Spoke structure is proposed to replace the mechanical gearbox in tidal power generation system. For the inner rotor PMs, the distributions of PMs are the spoke structure with different sizes, and the magnetization direction is Halbach array. The outer rotor PMs have two layers, one is Halbach array, and the other is radial magnetization. According to the sensitivity of parameters, the response surface method and multiobjective genetic algorithm are used for optimization analysis to determine the optimal structural dimension parameters of CMG. A CMG topology with 4 inner poles and 17 outer poles is established. Compared with the conventional CMG, the output torque of the proposed CMG is increased by 33.42%. Finally, a prototype was made and a test platform was built. The experimental results show that the transmission ratio of the proposed model is consistent with the theoretical value, the no-load loss is relatively small, and the efficiency is high.

A study on the production of low-viscosity bio-oil from rapeseed by magnetic field pyrolysis

In order to investigate the biomass pyrolysis mechanism of rapeseed under magnetic field for their conversion to bio-oil, a technical study was carried out for reducing the bio-oil viscosity to enhance its quality. Rapeseed were used as the raw material, and pyrolysis experiments were conducted at the final temperature of 500 ℃ under four different conditions: no magnetic field, three normal magnetic fields with different magnetic induction intensities (3000 GS, 6000 GS, and 9000 Gs), and a Halbach array magnetic field with 6000 GS. An analysis was conducted on the yield of pyrolysis products, as well as the physicochemical properties and composition of bio-oil. The results indicated that, compared to pyrolysis in the absence of magnetic field, the pyrolysis under magnetic field accelerated the heating process of rapeseeds and affected the pyrolysis reaction. Compared to the pyrolysis without magnetic field, the yield of pyrolysis gas increased from 19.09% to 20.23%, 20.83%, and 21.41% for the magnetic induction intensities of 3000, 6000 and 9000 Gs, respectively. Additionally, with the change in the magnetic induction intensities through values of 3000, 6000 and 9000 Gs, the viscosity of bio-oil decreased from 17.21 mPa·s to 13.99 mPa·s, 11.45 mPa·s, and 10.09 mPa·s, respectively. This suggests that the magnetic field significantly reduced the viscosity of bio-oil derived from rapeseeds, and slightly promoted the conversion of pyrolysis products into pyrolysis gas. When the volume of the magnet decreased by 53.69%, the proportion of pyrolysis bio-oil increased by 8.99%, while the viscosity of the oil decreased by 23.47%, indicating a significant optimization effect. Physicochemical analysis reveals that the moisture content of the pyrolysis oil as well as the hydrophilic groups in the oil obtained under magnetic field conditions increased, which is the main reason for the reduction in the viscosity of the oil. Combined with the in-depth mechanism analysis of magnetic field pyrolysis using simulations in the software package COMSOL, it is concluded that magnetic field pyrolysis enhances heat transfer through magnetoconvection and alters the pyrolysis reaction pathway by affecting the combinations of free radicals.

Analytical Model of Air‐Gap Magnetic Field for Eccentric Harmonic Magnetic Gear with Halbach Array

The eccentric harmonic magnetic gear (EHMG) has the characteristics of high torque density, high transmission ratio and high efficiency. The EHMG with Halbach array has better performance than the EHMG with traditional radial magnetization. Accurate calculation of its air‐gap magnetic field is of great significance for design and optimization. Based on the boundary perturbation method, a 2D analytical model of the air‐gap magnetic field of EHMG with Halbach array is established in this paper. The eccentric air‐gap magnetic field is calculated due to the permanent magnets of the eccentric rotor and the stator acting alone, and then the air‐gap magnetic field of the EHMG is obtained according to the superposition principle. The results of the air‐gap magnetic field are compared and evaluated by the regression evaluation indexes. The analytical results are consistent with the finite element results, which verifies the validity and accuracy of the analytical model. Comparing the EHMG with Halbach array and radial magnetization, the maximum static and dynamic electromagnetic torques of EHMG with Halbach array are increased by 59.1% and 55.6% compared with the EHMG with radial magnetization, which verifies the superior performance of EHMG with Halbach array. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Footstep-powered floor tile: Design and evaluation of an electromagnetic frequency up-converted energy harvesting system enhanced by a cylindrical Halbach array

Energy harvesting floor systems use the mechanical energy generated by human weight to produce electrical energy, providing sustainable power sources for low-power systems at pedestrian crossings. They also have the potential to serve as renewable energy solutions on a larger scale. This study evaluates the design and performance of a kinetic energy harvester floor tile. The system design employs a frequency up-conversion technique to utilize the force exerted by the weight of humans for creating vibrational movement. In addition, the use of the cylindrical Halbach array improves the magnetic flux gradient, leading to an increased power output. A semi-analytical model is presented to evaluate the system performance, which is then validated through available experimental analysis and finite element simulations. A sensitivity analysis is performed to assess the impact of various factors on system performance, ultimately determining the optimal configuration. The optimal modular system is then used to create a 30 × 30 cm2 tile. This tile is capable of generating energy while walking, running, jogging, slow running, and fast running, with power outputs of 0.57, 0.85, 1.11, and 1.42 W (0.57, 0.86, 1.11, and 1.58 mW/cm2) respectively. Additionally, it is estimated that 511 mJ (568 mJ/cm2) of energy is generated per step. Additionally, an assessment is conducted on the energy production capabilities and environmental advantages of a specific site, such as a subway station.

Force and Torque Model of Magnetically Levitated System with 2D Halbach Array and Printed Circuit Board Coils

Precision machining fields often require worktables with different stroke sizes. To address the need for scalability and facilitate manufacturing, this study proposes a novel infinite expansion magnetically levitated planar motor (MLPM) based on PCB stator coils. Different from existing magnetic levitation systems that use PCB coils, the design presented in this paper utilizes smaller coil units, with each coil being independent of one another. The coils are structured in a spiral pattern on a 16-layer PCB, comprising 15 layers of coils, while the last layer is dedicated to wiring and other circuits. Magnetic field modeling is conducted for both the stator coil and the 2D Halbach array structure employed in the system. A simple table lookup method is employed to accurately account for the prevalent end effects observed during system motion. Additionally, the decoupling effect of magnetic force and torque is evaluated by solving for the current vector at different points along a specific trajectory. To verify the accuracy of the proposed system’s modeling, a prototype is developed and tested. Experimental results demonstrate that compared to traditional harmonic model methods, the proposed approach improves the calculation accuracy of magnetic force by 50.31% and torque by 70.65%. This study presents a new MLPM system with vast potential applications in precision manufacturing and robotics. The innovative design and improved performance characteristics make it a promising technology for enhancing the capabilities of worktables in precision machining fields.

Optimal design of a new Halbach array magnetic roller with axial eddy current force

Non-ferrous metal recovery is of great significance to the sustainable development of resources. Small-sized nonferrous metal particles account for a large proportion of nonferrous metals in solid waste, but the recovery efficiency is low. Eddy current separation is an important technology for physical recovery of non-ferrous metals. Optimizing its magnetic roller is extremely important for improving the recovery efficiency and economy of small-sized non-ferrous metals. In this study, COMSOL Multiphysics is used to establish a three-dimensional transient simulation model of the vertical rotary-drum ECS. On the basis of the two-dimensional Halbach array magnetic roll, the magnetic system of the magnetic roll is designed in the axial direction, so that the particles are subjected to the axial eddy current force opposite to the direction of gravity for the first time. This force can slow down the falling velocity of particles, increase the difference in falling trajectory and repulsion distance, improve recovery efficiency. In addition, due to the generation of axial eddy current force, the interlayer dislocation type magnetic roller can achieve the same recovery effect by only using 1/3 of the length of the basic type magnetic roller. Based on the electromagnetic theory and particle dynamics, by comparing the axial magnetic density distribution of different magnetic rollers, the axial eddy current force and the trajectory of non-ferrous metal particles, the generation mechanism of the axial eddy current force and the magnetic system structure that can generate the axial eddy current force are clarified.

Predictor-based model predictive control for maglev planar motor with a 2D Halbach array mover

Magnetic levitated planar motors are widely employed in flexible manufacturing and photolithography due to their characteristics of high precision, high acceleration, and low maintenance. In this paper, a novel predictor-based model predictive control is proposed to improve the tracking performance of a maglev planar motor which consists of a 2D Halbach array mover and stationary square coils. A Kalman filter and finite spectrum assignment based on an augmented system model are employed to forecast mover’s location by compensating for the system delay due to data transmission and processing. The predicted location is fed back to model predictive control for control optimization under the limit of coil currents. Hildreth’s quadratic algorithm is then applied to solve for the optimal control effort within the constraints. Comparative experiments demonstrate the effectiveness of the proposed control strategy, the total tracking error of which is much smaller than the result of a proportional–integral–derivative controller and standard model predictive control in all tests. Additionally, experimental results show that the proposed predictor-based model predictive control can tolerate higher speeds of the mover while retaining mover’s steadiness. The experimental results suggest the proposed predictor-based model predictive control is an effective path-tracking strategy for magnetic levitated planar motors subject to delays.