Rectangular Permanent Magnets Research Articles

Physics-informed neural network for simulating magnetic field of permanent magnet

Abstract With the rapid development of deep learning, its application in physical field simulation has been widely concerned, and it has begun to lead a new model of meshless simulation. In this paper, research based on physics-informed neural networks is carried out to solve partial differential equations related to the physical laws of electromagnetism. Then the magnetic field simulation is realized. In this method, the governing equation and the boundary conditions containing physical information are embedded into the neural network loss function as constraints, and the backpropagation of neural networks is realized based on automatic differentiation to solve partial differential equations. The high-precision simulation of tile-shaped and rectangular permanent magnet magnetic fields of permanent magnet motors based on physical information neural network is studied, and the error is within 5%. We consider the simulation of magnetic field in two coordinate systems, and realize the joint training of multiple neural networks in multiple sub-domains and different media.

Research on the backpressure and backflow of a ferrofluid linear pump

Fluid transportation is a critical element in the performance of fluid machinery devices. This paper proposes a ferrofluid linear pump in response to the demand for fluid control without mechanical moving parts inside tubes. The pump includes two rectangular permanent magnets, ferrofluid, tubes, four one-way valves, and a linear actuator. The ferrofluid is bound in the tube by a strong gradient magnetic field generated by two rectangular permanent magnets, forming a liquid plunger. Under the cooperation of four one-way valves on and off, the reciprocating motion of the permanent magnet makes the ferrofluid plunger drive fluid to flow directionally. The maximum backpressure of the ferrofluid plunger under static and dynamic conditions is thoroughly analyzed by theory and experiments. Experiments of the interface profile and backpressure are consistent with the theoretical results in the static condition. The maximum backpressure reaches 8.3kPa in the static condition when the volume of the ferrofluid plunger is 19ul. However, the dynamic test under a reciprocating speed of 10–50 mm/s has a significant backflow phenomenon, and the theory for calculating the backpressure is no longer applicable. The mechanism of the backflow is explored. There is a layer of water film between the ferrofluid plunger and the tube wall. With the increase of the backpressure and reciprocating speed, the thickness of the water film and the velocity gradient may enlarge, which increases the backflow and reduces the volume flow rate. Ultimately, failure occurs when the backpressure exceeds the sealing threshold during the ferrofluid plunger reciprocating process. The critical pressure difference for the pump failure fluctuates around 7.4 kPa.

Magnetic Field Prediction in Cubic Spoke-Type Permanent-Magnet Machine Considering Magnetic Saturation

In this article, a nonlinear semi-analytical model (SAM) is presented to predict the magnetic field distribution (MFD) and electromagnetic performances (EPs) in the cubic spoke-type permanent magnet (PM) machine. To model the rectangular PMs, the rectangular PM is simplified as a combination of fan-shaped regions with different arc angles. Then, the MFD and EPs of the cubic spoke-type machines can be obtained by the harmonic modeling (HM) technique. Particularly, the saturation of the magnetic bridges is considered by the nonlinear iterative algorithm. The proposed nonlinear SAM is studied on a 12-slot/8-pole cubic PM prototype, and the nonlinear finite element (FE) model and experiment verify its correctness. The main contribution of this article is to present a general analytical modeling method for cubic spoke-type PM machines and consider the magnetic saturation of magnetic bridges.

Micro-structural and optical properties of diamond-like carbon films grown by magnetic field-assisted laser deposition

Inhomogeneous magnetic field is introduced into pulsed laser deposition process, in order to find new properties of diamond-like carbon film grown under magnetic field, thereby offering the theoretical and experimental basis for further enhancing sp<sup>3</sup>-bond content in this film. Distribution of the magnetic strength and flux lines induced by a rectangular permanent magnet is calculated. And then, flying trace of the carbon ions in the magnetic field is also simulated by the iterative method, which indicates that the carbon ions cannot expand freely and they are confined and accumulate around the center region of the magnet source. Beside the surface interference, the measurement and the fitted results of ellipsometry parameters show that magnetic field exerts an important influence on layer-thickness distribution and optical constant of the pulsed laser deposition-grown diamond-like carbon film. Meanwhile, it is indicated that the inhomogeneity of the layer-thickness distribution and optical constant increase when the magnetic strength is higher. Micro-structure of diamond-like carbon film is affected seriously by magnetic field, which is indicated by Raman spectra. Magnetic field can enhance the local stress in the carbon matrix net, increasing the sp<sup>3</sup>-bond content. Theoretical research and experimental research both show that a suitable magnetic strength can excite micro-structure of diamond-like carbon film significantly, and the high-quality diamond-like carbon coating with practical application value will be obtained by technological adjustment.

A magnetic field model of rectangular permanent magnets in a magnetic pendulum array

The magnetic pendulum array (MPA) is a novel mechanical antenna for efficient and portable ultra-low-frequency transmission. Its natural frequency is affected by the magnetic field of its rectangular permanent magnets. In this work, the influence of the magnetization of a permanent magnet on the demagnetizing field and the magnetic field of other permanent magnets is analyzed to accurately calculate the natural frequency, and a magnetic field model of the rectangular permanent magnets in an MPA is established to improve the calculation accuracy. The consistency of the theoretical model results is verified through experiments and simulations. Finally, the effect of sizes and distances of the permanent magnets on the natural frequency of an MPA is analyzed, providing theoretical guidance for the dynamic analysis of “A Mechanically Based Antenna (AMEBA).” This research has significance and practical application value in the optimization of the magnetic field characteristics and natural frequency calculation methods for AMEBA.

Study of the Tribological Properties of Magnetic Fluid under the Surface Effects with Magnetic-pole Magnetic-groups

The tribological characteristics of the magnetic fluid are studied with the change of multi-pole distribution in this paper. The maximum magnetic field strength and its gradient on the surface of the magnetic-group are analyzed by the finite element analysis of the magnetic field strength distribution at the same magnetic-group with the area ratio of 30%. The research results show that the matching distribution among N-S magnetic-pole groups at the same pole area ratio of 30% has less influence on the magnetic specimen surface, but the magnetic field distribution of magnetic-pole with the rectangular permanent magnet in the annular friction surface has the optimal range of magnetic field distribution design for specific magnetic fluid lubrication, in which pole group specimen 5 is the best magnetic-pole magnetic-group combination for friction reduction, and specimen 1 is the second best.

Study of irregular electron beam correcting permanent-magnet-quadrupole doublet lens for irradiation accelerator.

In this paper, a permanent-magnet-quadrupole doublet lens with strong-focusing is designed and manufactured. Such an instrument could solve the problem of irregular beam spots produced by the weak focusing of conventional solenoid-focusing systems in low-energy electron irradiation accelerators. It could provide a better and more appropriate initial beam spot before the beam enters the subsequent magnetic spreading system or magnetic scanning system, thus, improving the irradiation uniformity. The association of the parameters of the rectangular permanent magnet with the quadrupole magnetic field is investigated. Focusing results, obtained using irregular beam spots with different profiles and different energies, and magnetic field measurement results, both from the instrument, verify the engineering feasibility of this permanent-magnet-quadrupole doublet lens.

A Fine Modified Calculation Model with Experimental Verification for the Holding Force of the Permanent Magnet

For the common technical applications of permanent magnets such as cylindrical and rectangular permanent magnets, the formula of the holding force, which is based on the idea of equivalent current source and associated with Lorentz force, is fine modified with introducing two parameters, the chamfer size of the magnet and the thickness of the outer protective film. Furthermore, the model is verified by external experimental data. The accuracy of our proposed model has been significantly improved compared to the base model, with an average improvement of 6.3 %. With external data, the average error of the refined model is within 6 %. Compared to other currently available online calculators, our calculation model offers superior calculation accuracy.

Flux‐adjusting characteristic analysis and optimization design of variable‐leakage‐flux interior permanent magnet motor

In this paper, a novel variable-leakage-flux interior permanent magnet (VLF-IPM) motor is proposed, which is a kind of mechanical flux-adjusting PM motor. The VLF-IPM motor can obtain the advantages of the IPM motor and overcome the difficulty to adjust PM airgap flux by locating a self-activating device that is introduced in this paper on the rotor. The effect of the flux barriers on the flux leakage circuit is analysed by establishing a rotor parametric model to clarify the influence of flux barriers of the VLF-IPM motor on flux-adjusting performance. Then, the electromagnetic performance of VLF-IPM motors with different volume ratios of cylindrical permanent magnets (CPMs) and rectangular permanent magnets (RPMs) are compared by using the finite element analysis (FEA) method, and the experiment results show that VLF-IPM motor with characteristics of 0 < κrc < 1 has more advantages comprehensively. Moreover, a multi-objective optimization process is adopted based on sensitivity analysis which can reflect the influences of geometric parameters on the optimization objectives including average torque, torque ripple and cogging torque. Then, the Non-dominated Sorting Genetic Algorithm II(NSGA-II) is utilised to determine the optimal model. Finally, a prototype is manufactured and tested, and the effectiveness of the novel VLF-IPM motor and the self-activating device are verified by the simulation and experiments.

Stability Evaluation of Superconducting Magnetic Levitation with Additional Rectangular Magnets

In order to improve stability of magnetic levitation using superconductors, a hybrid stator with two rectangular permanent magnets (additional magnets) added to the bottom of the superconducting stator was devised, and stability of the levitating magnet was evaluated from magnetic force and magnetic stiffness due to difference in dimensions and spacing of additional magnets and levitation height of the levitating magnet. Magnetic stiffness of the stator with additional magnets was improved compared to that of the conventional simple superconducting stator, and magnetic stiffness increased as width of additional magnets increased. Magnetic stiffness of the stator with additional magnets was also improved by lowering the levitation height of the levitating magnet. Magnetic stiffness was not improved when the distance between additional magnets was increased.

Design and Analysis of a Novel Linear Oscillating Actuator with Dual Stator Rectangular Geometry

This paper proposes a new design of a linear oscillating actuator (LOA) with rectangular topology of stator and mover. The shape of a permanent magnet (PM) has a major impact on cost, mechanical strength and generation of magnetic flux density. This design uses rectangular PMs that are relatively cheaper than tubular PMs. Proposed LOA operates on single phase AC loading source. All the design parameters are optimized by using parametric sweep and the response of the LOA in terms of thrust force is compared. The Electromagnetic (EM) force received by the mover is investigated at various mover positions as well as at different values of the current. Motor constant is examined toward both directions of the force. Resonance phenomena is analyzed using input and output power of the LOA, which is the unique advantage of the LOA. Compared to the conventional LOA designs, the output parameters of the LOA, such as EM force, stroke, operating frequency and power, show great improvement with regards of volume of the proposed LOA. This topology shows significant development in terms of thrust force, motor constant, easy manufacturing and cost. Moreover, range of the stroke of proposed LOA is feasible for linear refrigeration system.

Design of a New 1D Halbach Magnet Array with Good Sinusoidal Magnetic Field by Analyzing the Curved Surface.

In the linear and planar motors, the 1D Halbach magnet array is extensively used. The sinusoidal property of the magnetic field deteriorates by analyzing the magnetic field at a small air gap. Therefore, a new 1D Halbach magnet array is proposed, in which the permanent magnet with a curved surface is applied. Based on the superposition of principle and Fourier series, the magnetic flux density distribution is derived. The optimized curved surface is obtained and fitted by a polynomial. The sinusoidal magnetic field is verified by comparing it with the magnetic flux density of the finite element model. Through the analysis of different dimensions of the permanent magnet array, the optimization result has good applicability. The force ripple can be significantly reduced by the new magnet array. The effect on the mass and air gap is investigated compared with a conventional magnet array with rectangular permanent magnets. In conclusion, the new magnet array design has the scalability to be extended to various sizes of motor and is especially suitable for small air gap applications.

Lateral magnetic stiffness under different parameters in a high-temperature superconductor levitation system* *Project supported by the National Natural Science Foundation of China (Grant No. 11572232).

Magnetic stiffness determines the stability of a high-temperature superconductor (HTS) magnetic levitation system. The quantitative properties of the physical and geometrical parameters that affect the stiffness of HTS levitation systems should be identified for improving the stiffness by some effective methods. The magnetic stiffness is directly related to the first-order derivative of the magnetic force with respect to the corresponding displacement, which indicates that the effects of the parameters on the stiffness should be different from the relationships between the forces and the same parameters. In this paper, we study the influences of some physical and geometrical parameters, including the strength of the external magnetic field (B 0) produced by a rectangular permanent magnet (PM), critical current density (J c), the PM-to-HTS area ratio (α), and thickness ratio (β), on the lateral stiffness by using a numerical approach under zero-field cooling (ZFC) and field cooling (FC) conditions. In the first and second passes of the PM, the lateral stiffness at most of lateral positions essentially increases with B 0 increasing and decreases with β increasing in ZFC and FC. The largest lateral stiffness at every lateral position is almost produced by the minimum value of J c, which is obviously different from the lateral force–J c relation. The α-dependent lateral stiffness changes with some parameters, which include the cooling conditions of the bulk HTS, lateral displacement, and movement history of the PM. These findings can provide some suggestions for improving the lateral stiffness of the HTS levitation system.

Hand-held piezoelectric energy harvesting structure: Design, dynamic analysis, and experimental validation

This research proposes a hand-held piezoelectric energy-harvesting structure for portable human-motion energy harvesting. The proposed structure is composed of a square support frame with two hand shanks, a rotation disk with four identical rectangular permanent magnets, and a 33-Mode piezoelectric patch with a rectangular permanent magnet attached. Piezoelectric materials with good d33 piezoelectric properties and high rigidity can be applied to the proposed structure. The dynamic changes of the proposed structure in the electric and magnetic fields during rotation are simulated and analyzed in detail. Treadmill experiments were also conducted to validate the simulation results. The results showed that the maximum peak-to-peak alternating piezoelectric voltage yields 3.5 V at 8 km/h and 0 degrees. Within 6.7 min, the 100 μF capacitor can be charged to 1.2 V, and the corresponding average power is equal to 0.18 μW at 6 km/h and 0 degrees.

The Design of Linear Magnetic Negative Stiffness Element for Engineering Application using Rectangular Permanent Magnets

Negative stiffness element (NSE) has extensive uses in engineering applications, such as vibration isolation, energy harvesting, and mechanical metamaterial. However, to realize a linear negative stiffness characteristic is still a challenging task. In this paper, we present a compact magnetic negative stiffness element (MNSE) that composed of three rectangular permanent magnets and configured as repelling configuration in horizontal to realize linear negative stiffness characteristic. The effects of the MNSE configuration parameters on the negative stiffness characteristic are analyzed in detail. The results demonstrate that the magnitude of the negative stiffness characteristic can be adjusted by changing the height ratio and width ratio between the central and outer magnets. The height difference between the central and outer magnets can be used to tune the degree of nonlinearity of the negative stiffness characteristic and to get the uniformity stiffness characteristic in the equilibrium position. The procedure to realize the linear negative stiffness characteristic with the expected magnitude and displacement range is developed and confirmed. The proposed MNSE and the design procedure offer an engineering application foundation for the magnetic linear negative stiffness.

Mathematic Modelling and Numerical Analysis for a Novel Inner-Type Nutation Magnetic Drive

This paper presents an inner-type of magnetic gears for non-contact driving, based on the nutation gearing principle. An improved three-dimensional analytical model, based on the magnetic vector potential of rectangular permanent magnets, via the equivalent current, is deduced for the proposed nutation magnetic gears. The transformation of coordinates is applied for a global field solution. The analytical model and the finite element model have analyzed the output torque of the nutation magnetic drive, respectively. The results show that the values calculated by the two models are consistent. The proposed analytical model can provide a reference for the design and optimization of nutation magnetic gears and other permanent magnetic mechanisms with rectangular magnets.

Development of 1.2-GHz ECR ion source and Wien filter for inexpensive ion beam processing system.

A desktop-sized ion beam processing system with an inexpensive electron cyclotron resonance (ECR) ion source has been developed for industrial applications at the National Institute of Technology, Toyama College. A commercially available 1.2- to 1.3-GHz transceiver is adopted as a microwave source to generate the ECR plasma. The minimum-B magnetic field is formed by arranging small rectangular permanent magnets. A Wien filter with orthogonal electric and magnetic fields is employed as a beam separator. At the end of the beam line, a processing chamber with a substrate stage for ion beam applications, such as ion implantation and microfabrication, is installed. Here, we report the results of the first experiment. Ar ion beams with a current of approximately 62 µA were obtained at an extraction voltage of 4 kV. In addition, we demonstrate that Ar and Xe ions can be separated by the Wien filter.

Analysis and Experiment of Vibration Isolation Performance of a Magnetic Levitation Vibration Isolator with Rectangular Permanent Magnets

Magnetic levitation vibration isolator (MLVI) is an efficient method to suppress the external oscillations transmitted to some small instruments in the laboratories. This paper first presents a basic configuration of a kind of MLVI with four sets of the repulsive rectangular permanent magnets. Then, the parametric studies are carried out to discuss how the structure and air gap parameters influence the magnetic force, stiffness, and natural frequency of the MLVI. Moreover, as an MLVI case study, an operating point is set and the size dimensions of the MLVI are determined based on the parametric studies. The transmissibility of the MLVI is calculated by the dynamic equation at the operating point. An experimental table is constructed for the analytical validation. The experimental results proved the validity of the theoretical analysis and showed that there are good consistencies between the experiment results and the theoretical calculation, which obtains that the natural frequency of the MLVI is 4.75 Hz and the initial cut-off frequency of the MLVI is approximately 6 Hz at the operating point. When the frequency of the external oscillations reaches 16 Hz, the attenuation amplitude becomes − 20 dB. All of these show ability of the proposed MLVI to attain low-frequency vibration isolation, and provide a new type of basic passive MLVI to exploit an active MLVI for practical applications.

Obliquely incident EMAT for high-order Lamb wave mode generation based on inclined static magnetic field

Lamb waves have the characteristics of long propagation distance, and they can be used to realize rapid and wide-scale nondestructive testing of plates. The detection sensitivity can be improved by using a high-order Lamb wave mode with a short wavelength. However, Lamb waves have multimode characteristics. The number of Lamb wave modes greatly increases at high frequencies, and it is difficult to obtain a pure single high-order Lamb wave mode with electromagnetic acoustic transducers (EMATs); this increases the difficulty of signal processing and analysis. In this study, an obliquely incident EMAT based on the inclined static magnetic field was designed to solve this problem. The mode selectivity of the proposed obliquely incident EMAT is superior to that of the traditional EMAT. A new parameter is proposed to improve the mode selectivity of EMATs: the polarization angle of the permanent magnet. The incident angle of incident ultrasonic waves is controlled by selecting the polarization angle of permanent magnet. A rectangular permanent magnet is obliquely polarized to provide a biased inclined static magnetic field. The obliquely incident Lorentz force is formed through the coupling between the eddy current and the inclined static magnetic field by an obliquely polarized permanent magnet. The obliquely incident Lorentz force is the source of the obliquely incident ultrasonic wave. Simulation and experimental results show that the developed obliquely incident EMAT can reduce the amplitude of the unwanted modes and enhance the mode selectivity. It was also verified that the developed obliquely incident EMAT had better frequency-response characteristics and sound-field directivity.

Ferro hydro dynamic analysis of heat transfer and biomagnetic fluid flow in channel under the effect of two inclined permanent magnets

Abstract Peripheral vascular diseases is one of the main causes of death in the world. It is disorders that cause the blood vessels to narrow, block, or spasm. Here, effects of two inclined rectangular permanent magnets field on heat transfer and flow characteristics of blood fluid in a channel, as a model of straight part of the aorta, has been investigated using FerroHydroDynamics (FHD) principles. Thermally and hydrodynamically fully developed flow is considered at the inlet of the vessel. Governing equations have been discretized using the finite volume method and the SIMPLE algorithm. Simulations have been carried out for different inclination angles of magnets and saturated magnetization. From the results, the magnetic field of two inclined magnets leads to increase heat transfer of blood fluid flow toward the walls. Moreover, major energy loss, arising from mean wall shear stress, is decreased but local or minor energy loss, arising from generated vortices, is increased. Furthermore, the formation of recirculation zones near the wall, where the magnetic drug can be trapped there for uptake to tissue, is observed.