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.

Elliptical Halbach magnet and gradient modules for low-field portable magnetic resonance imaging.

This study aims to develop methods to design the complete magnetic system for a truly portable MRI scanner for neurological and musculoskeletal (MSK) applications, optimized for field homogeneity, field of view (FoV), and gradient performance compared to existing low-weight configurations. We explore optimal elliptic-bore Halbach configurations based on discrete arrays of permanent magnets. In this way, we seek to improve the field homogeneity and remove constraints to the extent of the gradient coils typical of Halbach magnets. Specifically, we have optimized a tightly packed distribution of magnetic Nd2Fe14B cubes with differential evolution algorithms and a second array of shimming magnets with interior point and differential evolution methods. We have also designed and constructed an elliptical set of gradient coils that extend over the whole magnet length, maximizing the distance between the lobe centers. These are optimized with a target field method minimizing a cost function that considers also heat dissipation. We have employed the new toolbox to build the main magnet and gradient modules for a portable MRI scanner designed for point-of-care and residential use. The elliptical Halbach bore has semi-axes of 10 and 14& cm, and the magnet generates a field of 87& mT homogeneous down to 5700& ppm (parts per million) in a 20-cm diameter FoV; it weighs 216& kg and has a width of 65& cm and a height of 72& cm. Gradient efficiencies go up to around 0.8& mT/m/A, for a maximum of 12& mT/m within 0.5& ms with 15& A and 15& V amplifier. The distance between lobes is 28& cm, significantly increased with respect to other Halbach-based scanners. Heat dissipation is around 25& W at maximum power, and gradient deviations from linearity are below 20% in a 20-cm sphere. Elliptic-bore Halbach magnets enhance the ergonomicity and field distribution of low-cost portable MRI scanners, while allowing for full-length gradient support to increase the FoV. This geometry can be potentially adapted for a prospective low-cost whole-body technology.

Design of Planar Permanent Magnet Array for Remotely Actuated Magnetic Micro Robots

Design of Planar Permanent Magnet Array for Remotely Actuated Magnetic Micro Robots

An analytical model for a coaxial electromagnetic recuperator considering end effect

A coaxial electromagnetic recuperator (CER), leveraging the principle of tubular permanent magnet linear synchronous motor, has been introduced to mitigate the shortcomings of the traditional recuperator, including low reliability and uncontrollable counter-recoil motion. Firstly, the layout and structural scheme of the CER are presented, with the maximum recuperator force determined through a force analysis of the recoil process. Subsequently, by incorporating a virtual permanent magnet area at both ends of the permanent magnet array, a precise CER analysis model is developed. This model adeptly accounts for the end effect due to magnet length limitations and formulates expressions for air gap flux density, back electromotive force, and electromagnetic thrust. The analytical model’s accuracy is then validated against a finite element model. Finally, the key parameters influencing CER performance were improved, and the overall structure of the CER was refined, significantly enhancing its thrust capabilities.

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.

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.

Production of High-Power Nitrogen Sputtering Plasma for TiN Film Preparation

High-density nitrogen plasma was produced using a high-power pulsed power modulator to sputter titanium targets for the preparation of titanium nitride film. The high-power pulsed sputtering discharge unit consisted of two targets facing each other with the same electrical potential. The titanium target plates were used as target materials with dimensions of 60 mm length, 20 mm height, and 5 mm thickness. The gap length was set to be 10 mm. The magnetic field was created with a permanent magnet array behind the targets. The magnetic field strength at the gap between the target plates was 70 mT. The electrons were trapped by the magnetic and electric fields to enhance the ionization in the gap. The nitrogen and argon gases were injected into the chamber with 4 Pa gas pressure. The applied voltage to the target plates had an amplitude from −600 V to −1000 V with 600 μs in pulse width. The target current was approximately 10 A with the consumed power of 13 kW. The discharge sustaining voltage was almost constant and independent of the applied voltage, in the same manner as the conventional normal glow discharge. The ion density and electron temperature at the surface of the ionization region were obtained as 1.7 × 1019 m−3 and 3.4 eV, respectively, by the double probe measurements. The vertical distribution of ion density and electron temperature ranged from 1.1 × 1017 m−3 (at 6 cm from the target edge) to 1.7 × 1019 m−3 and from 2.4 eV (at 6 cm from the target edge) to 3.4 eV, respectively. From the emission spectra, the intensities of titanium atoms (Ti I), titanium ions (Ti II), and nitrogen ions (N2+) increased with increasing input power. However, the intensities ratio of Ti II to Ti I was not affected by the intensities from N2+.

Design of guided wave magnetostrictive patch transducer with vertical static bias magnetic field for pipe inspection

Compared with electromagnetic acoustic transducer (EMAT), magnetostrictive patch transducer (MPT) has higher energy conversion efficiency. MPT is often used to excite and receive long-distance ultrasonic guided waves for defect detection or structural health monitoring of large industrial equipment. In this work, a new design method of permanent magnet MPT using the vertical static bias magnetic field to excite shear horizontal (SH) guided waves is proposed. First, the mathematical model of exciting ultrasonic guided waves by a vertical static bias magnetic field MPT is established, and the equivalent surface stress in the magnetostrictive patch is calculated. It is shown that the vertical static bias magnetic field MPT can excite SH guided waves in plates. Then, the influence of static bias magnetic field intensity on the amplitude of guided wave signal is analyzed. Compared with other traditional MPTs, the amplitude of SH guided wave signal excited by the vertical static bias magnetic field MPT is increased. Finally, a periodic permanent magnet (PPM)-MPT with a central frequency of 120 kHz is designed. The proposed PPM-MPT improves the energy conversion efficiency compared to the circumferential alternating permanent magnet array type MPT. The PPM-MPT can detect defects in a steel pipe with a wall thickness of 3.5 mm and an inner diameter of 100 mm. The results show that the PPM-MPT designed in this paper successfully detects the through hole with a diameter of 2 mm, and the cross-section loss rate of the defect is about 0.6 %.

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.

Evaluation of stress-loaded ferromagnetic structures using the magnetic recording method and extended signal analysis

This paper presents a new method of analysis of results obtained using the Magnetic Recording Method (MRM), which was applied to inspect tensile stress-loaded ferromagnetic samples. The MRM method comprised a two-step procedure. In the first step, a strictly defined magnetic pattern is recorded on the samples using an array of permanent magnets, and then the original residual magnetization is measured. Next, the samples are subjected to static stress. In the second step, the residual magnetization measurement is repeated. Comparative analysis of the measurement results allows for an accurate and unambiguous assessment of applied stress in steel components. Moreover, the magnetization was measured again after three years to investigate the effect of time on magnetization patterns. The study confirms that the method is stable and has a negligible time dependence.

Calculation of the parameters of an axial flux motor as an actuator of automotive systems

Problem. Axial flux electric motors offer several significant advantages compared to electric motors of traditional design. Currently, scientific periodicals contain numerous publications regarding the development and use of axial flux electric motors with printed windings across various fields. These include applications such as HDD-drives in computer technology, fans and pumps of various capacities, propulsion systems for bicycles and motorcycles, including in-wheel motors, manipulator drives for machine tools and industrial robots, and even within space technologies. Research confirms the high efficiency and size-to-weight ratios of axial flux motors when modern technologies are employed. However, there is little information available regarding the application of such motors in automotive electromechanical equipment. A distinctive feature of automotive electrical systems is their predominantly 12 V onboard power supply, along with high demands on size-to-weight ratios and reliability in conditions of elevated vibrations and wide temperature ranges. In this context, the development of an axial flux motor for automotive applications becomes relevant, particularly as an actuating mechanism for auxiliary systems such as window lifters, windshield wipers, air conditioning, and cooling fans, etc. Goal. The goal of the article is to determine the feasibility of using an axial flux electric motor as an actuator for automotive auxiliary systems by comparing its calculated parameters with the parameters of motors of traditional design using modern technologies and materials. Methodology. The methods and algorithms used for the calculation of electric machines take into account the characteristics and physical processes specific to axial flux machines with printed windings and permanent magnet arrays. Results. A comparison of the obtained characteristics of the designed motor with the characteristics of a modern prototype of traditional design was conducted. Based on the comparison, it was determined that the designed motor has better size-to-weight ratios while maintaining energy performance. Consequently, a conclusion was drawn about the feasibility of using electric motors with axial flux as actuators for automotive auxiliary systems. Originality. The prototype of the designed motor is considered to be a 250 W DC motor with a supply voltage of 12 V. The imposed constraint on the external diameter of the designed motor is set to 100 mm. Practical value. At the same output power and nearly identical torque, the calculated motor exhibits higher size-to-weight ratios. The weight of the calculated motor is 46% of the weight of the prototype. With an external diameter 54% larger than the prototype, the axial length of the calculated motor is 73% smaller. The mass of the calculated motor is 2.34 times smaller than the mass of the prototype.

Weft insertion guideway design based on high-temperature superconducting levitation

Abstract Wide-width weaving machines typically employ the method of increasing the shuttle’s initial speed to achieve a broader weft insertion. However, this approach not only leads to issues such as significant equipment vibrations, high noise levels, increased energy consumption, and reduced lifespan but also has limitations in achieving substantial increases in the fabric width. The article proposes a wide-width weft insertion method based on high-temperature superconducting magnetic levitation technology. It utilizes the levitation characteristics of high-temperature superconducting shuttles in a permanent magnet array’s magnetic field to levitate the shuttle. The shuttle is then propelled by a traveling wave magnetic field generated by an array of electromagnetic coils, enabling wide-width weft insertion. Based on the required thrust values and weaving speed for the shuttle insertion process, the structural parameters of the weft insertion guideway were calculated. A superconducting suspended weft insertion structure was designed, and a mathematical model between the weft insertion guideway and the shuttle was established. Subsequently, a simulation model of the weft insertion guideway was created using Simulink, and the model was simulated, verified, and analyzed using the field-oriented control algorithm. The simulation results indicate that the operating speed of the levitated shuttle and the driving force for weft insertion meet the requirements for high-speed wide-width weaving.

Mixed convection by buoyancy and magnetothermal forces

The magnetic force in the paramagnetic fluid depends on the local gradient of magnetic flux density and the temperature-dependent magnetic susceptibility. In the presence of the gravity, the buoyant force due to the temperature difference additionally overlaps, and the resultant flow becomes a mixed convection. In this study, the effect of the temperature-dependent magnetic force (magnetothermal force) on the natural convection was numerically investigated. The magnetic field formed by the permanent-magnet array was employed and effective one was discussed in terms of the heat transfer. A three-dimensional Rayleigh-Benard convection simulation was conducted with the magnet array below the bottom hot wall. It was found that the magnetothermal force enhances the convection not only where the magnet locates but also away from the magnet due to the force profile.

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.

Rapid Measurement of Magnetic Particle Concentrations in Wildland–Urban Interface Fire Ashes and Runoff Using Compact NMR

Wildfires are increasing in size, frequency, and intensity, releasing increased amounts of contaminants, including magnetic particles, into the surrounding environment. The aim of this paper is to develop a sensing method for the detection and quantification of magnetic particles (MPs) in fire ash and fire runoff using a compact Time-Domain Nuclear Magnetic Resonance (TD-NMR) system. The system is made up of custom NMR electronics with a compact and rugged permanent magnet array designed to enable future deployment as an in situ sensor. A signal-to-noise ratio of 25 dB was measured for a single scan, and sufficient data can be acquired in one minute. A linear relationship with an R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> value of 0.9699 was established between transverse relaxation rates and MP concentrations in ash samples. This was validated by testing known dilutions of pure magnetite particles and showing that they fit within the same linear curve. The developed approach was then applied to detect MPs in surface water, where changes in the relaxation rates as high as 400% were observed before and after a wildfire event. MPs were removed from the surface water using a magnetic particle separator to confirm that observed changes were solely due to the presence of MPs. The compact NMR system can be used as a simple and rapid approach to track and quantify the concentrations of magnetic particles released from fire ashes and also from other sources such as discharges from coal ash and other combustion ashes.

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.

Compact remanence-free permanent magnet-based variable magnetic field source.

We demonstrate a simple and compact variable magnetic field source based on the permanent cube magnet array approximating a Halbach cylinder. The large air gap area accommodates standard cryostat tails while providing a high uniformity and magnetic field stability of up to 0.5T over regions of up to about a centimeter. It eliminates magnetic remanence effects and produces reproducible fields without the need for feedback. Thanks to the low cost and exceptional energy efficiency, it provides an accessible solution for modest magnetic field requirements in a wide range of research applications.

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.

Single-sided magnetic resonance-based sensor for point-of-care evaluation of muscle

Magnetic resonance imaging is a widespread clinical tool for the detection of soft tissue morphology and pathology. However, the clinical deployment of magnetic resonance imaging scanners is ultimately limited by size, cost, and space constraints. Here, we discuss the design and performance of a low-field single-sided magnetic resonance sensor intended for point-of-care evaluation of skeletal muscle in vivo. The 11 kg sensor has a penetration depth of >8 mm, which allows for an accurate analysis of muscle tissue and can avoid signal from more proximal layers, including subcutaneous adipose tissue. Low operational power and shielding requirements are achieved through the design of a permanent magnet array and surface transceiver coil. The sensor can acquire high signal-to-noise measurements in minutes, making it practical as a point-of-care tool for many quantitative diagnostic measurements, including T2 relaxometry. In this work, we present the in vitro and human in vivo performance of the device for muscle tissue evaluation.