Magnetic Flux Distribution Research Articles

Process optimization and finite element modeling in magnetorheological abrasive finishing of SS-316L with surface characterization

This study explores the potential of Magnetorheological Abrasive Finishing (MRAF) for ultra-precision finishing of SS-316L using a high-performance Nd-Fe-B (N-35 grade) magnetic tool. Key parameters, including the relationship between normal force (Fn) and working gap, magnetic flux distribution, and finishing spot area, were analyzed using ANSYS 2020 R1® Magnetostatic module simulations. Material removal rate (MRR) and surface roughness (Ra) were optimized through response surface methodology (RSM) using a central composite design (CCD) with two primary input factors: SiC abrasive volume fraction (5%, 10%, 15%) and abrasive mesh size (800, 1000, 1200). Statistical analysis via ANOVA revealed a significant influence of process variables, achieving a remarkable surface finish with a minimum Ra of 52 nm in just 60 min, utilizing an MR fluid with 10% SiC abrasives. Microscopic and spectroscopic evaluations confirmed enhanced surface morphology and microstructural refinement. Moreover, bioactivity studies in simulated body fluid highlighted improved hydroxyapatite layer formation on the finished SS-316L samples, underscoring the process’s potential for biomedical applications.

Analysis of the air gap magnetic field in cylindrical magnetic couplings based on mathematical and finite element approach

The air gap magnetic field of a magnetic coupling plays a crucial role in the examination of its static torque and eddy current losses. Precise characterization of the air gap magnetic field is essential for ensuring the accuracy of performance assessments of the magnetic coupling. This study focuses on the cylindrical magnetic coupling as the subject of investigation, employing mathematical analysis and finite element methods to evaluate and quantify the magnetic field properties. The study establishes a mathematical model of the magnetic field of a magnetic coupling based on electromagnetic field principles and the superposition theorem. An analytical formula for the magnetic flux density distribution of the air-gap magnetic field is derived. Subsequently, a three-dimensional magnetic field finite element model is created using the finite element method to numerically calculate the air gap magnetic field and validate the analytical formula. The research also explores the periodic distribution characteristics of the magnetic field in the air gap, analyzing axial differences in magnetic flux density value and direction distribution influenced by end effects.

Unraveling Magnet Structural Defects in Permanent Magnet Synchronous Machines—Harmonic Diagnosis and Performance Signatures

Rare-earth-based permanent magnets (PMs) have a vital role in numerous sustainable energy systems, such as electrical machines (EMs). However, their production can greatly harm the environment and their supply chain monopoly presents economic threats. Alternative materials are emerging, but the use of rare-earth PMs remains dominant due to their exceptional performance. Damage to magnet structure can cause loss of performance and efficiency, and propagation of cracks in PMs can result in breaking. In this context, prolonging the service life of PMs and ensuring that they remain damage-free and suitable for re-use is important both for sustainability reasons and cost management. This paper presents a new harmonic content diagnosis and motor performance analysis caused by various magnet structure defects or faults, such as cracked or broken magnets. The proposed method is used for modeling the successive physical failure of the magnet structure in the form of crack formation, crack growth, and magnet breakage. A surface-mounted permanent magnet synchronous motor (PMSM) is studied using simulation in Ansys Maxwell software (Version 2023), and different cracks and PM faults are modeled using the two-dimensional finite element method (FEM). The frequency domain simulation results demonstrate the influence of magnet cracks and their propagation on EM performance measures, such as stator current, distribution of magnetic flux density, back EMF, flux linkage, losses, and efficiency. The results show strong potential for application in health monitoring systems, which could be used to reduce the occurrence of in-service failures, thus reducing the usage of rare-earth magnet materials as well as cost.

Critical current characteristics and ampere force distribution of a novel HTS cable with different transposition lengths

Abstract Distribution characteristics of the current, ampere force and magnetic flux density (B [T]) of a novel high temperature superconducting (HTS) cable woven by transposed REBCO tapes under different transposition lengths are proposed, and these characteristics of the cable stacked with 3 REBCO tapes are also carried out in this paper for comparison. The objective is to enhance the current density and the compactness of the HTS tapes combination, and uniform the current, ampere force and magnetic flux density (B [T]) distributions. A 3D finite element model (FEM), based on Maxwell's equations without consideration of the displacement current, is established to describe the state of the system in the liquid nitrogen condition. The distributions characteristics, maximum and minimum values of current, ampere force and magnetic flux density (B [T]) show significant differences in the simulation results between the novel HTS cable woven by 3 transposed REBCO tapes and the cable stacked with 3 REBCO tapes. The simulated results show that the distribution characteristics are improved, with a more uniform distribution characteristic than that of the cable stacked with REBCO tapes. This is due to fully transposed REBCO tapes. In addition, the experimental E-I curve was also reached. The experimental results show that using a shorter transposition length in the cable can improve the critical current. However, A too small transposition length can cause significant damage to the HTS tape, resulting in deformation of the HTS tape and a reduction in the electromagnetic properties of the HTS tape. This affects the critical current of the HTS tape and, ultimately, the critical current of the cable. From the point of view of whether the production process is convenient, meets the requirements of economy and reduces costs, we need to find a suitable transposition length. The measured optimal transposition length is 95 mm for the cable woven by 3 REBCO tapes.
Ethical Compliance: All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Real-time equilibrium reconstruction by multi-task learning neural network based on HL-3 tokamak

Abstract A neural network model, EFITNN, has been developed capable of real-time magnetic equilibrium reconstruction based on HL-3 tokamak magnetic measurement signals. The model processes inputs from 68 channels of magnetic measurement data gathered from 1159 HL-3 experimental discharges, including plasmas current, loop voltage, and the poloidal magnetic fields measured by probes. The outputs of the model feature eight key plasmas parameters, alongside high-resolution ( 129 × 129 ) reconstructions of the toroidal current density J P and poloidal magnetic flux distributions Ψ rz . Moreover, the network’s architecture employs a multi-task learning structure, which enables the sharing of weights and mutual correction among different outputs, and leads to increase the model’s accuracy by up to 32%. The performance of EFITNN demonstrates remarkable consistency with the offline EFIT, achieving average R 2 = 0.941, 0.997 and 0.959 for eight plasmas parameters, Ψ rz and J P , respectively. The model’s robust generalization capabilities are particularly evident in its successful predictions of quasi-snowflake (QSF) divertor configurations and its adept handling of data from shot numbers or plasmas current intervals not previously encountered during training. Compared to numerical methods, EFITNN significantly enhances computational efficiency with average computation time ranging from 0.08 ms to 0.45 ms, indicating its potential utility in real-time isoflux control and plasmas profile management.

Self‐Assembling Design Method of Stator Slots for AC Rotating Machines

To maximize the performance of rotating machines, it is essential to establish a design method with minimal arbitrariness. This paper proposes a self‐assembling method to design stator slots for alternating current (AC) rotating machines. First, we develop a line‐current approximation model of the stator winding using pulse‐width modulation technique and realize an ideal spatial magnetic flux density distribution. Subsequently, we design the realistic stator with an acceptable current density of the winding by forming unique slot shapes in a self‐assembling manner under two synthetic conditions using the developed line‐current approximation model as the starting model. The designed stator realizes a rotating magnetic field similar to the conventional design results. Additionally, we perform an analysis of motor rotation characteristics by combining the self‐assembled stator with a surface‐mounted permanent magnet rotor to determine the possibility of a higher output compared to that when using a conventional stator. The self‐assembled motor without relying on empirical rules shows a possibility of further improving the torque characteristics, thereby contributing to designing the AC rotating machines. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

High Output, Biocompatible, Fully Flexible Fiber‐Based Magneto‐Mechano‐Electric Generator for Standalone‐Powered Electronics

AbstractHarvesting magnetic noise fields around power cables emerges as an attractive approach due to its potential as a renewable and ubiquitous energy source for powering wireless sensor networks (WSNs) in IoT applications, miniature electronics, and implantable medical devices. Flexible polymer‐based magneto‐mechano‐electric (MME) generators gain attention for their effectiveness in magnetic energy harvesting owing to their durability and flexibility. In this study, a lead‐free, flexible MME generator is developed by using Polyvinylidene fluoride (PVDF)‐Aluminium nitride (AlN)‐nanofiber composites fabricated via electrospinning with different AlN compositions and integrated with a magnetostrictive Metglas layer that offers self‐bias characteristics. The MME generator is modeled using COMSOL Multiphysics to analyze the magnetic flux density distribution over the Metglas surface and the piezoelectric effect of the nanofiber composites, with the simulation results aligning well with the experimental data. The optimized, flexible MME generator, incorporating 15 wt.% of AlN in the PVDF/Metglas composite, achieves an open‐circuit voltage of 18.5 V and a power density of 0.93 mW‐cm−3 when exposed to an Alternating Current (AC) magnetic noise field of 6 Oe at a resonance frequency of 50 Hz. The generated power is sufficient to operate LEDs and sensor. This newly developed lead‐free, flexible MME generator shows significant promise for advanced applications in self‐powered WSNs.

Axial vibration characteristics analysis of transformer windings based on magnetic‐structural coupling correction model

AbstractDue to the strong coupling effect between the internal magnetic field and the structural field of the transformer, the magnetic‐structural coupling should be considered in axial vibration process of the winding short‐circuit impact. A 110 kV transformer is taken as the research object. Firstly, the vibration modal characteristics of the transformer are calculated using the classical axial vibration model, and the spatial distribution of the leakage magnetic flux density of the iron core window is obtained based on the image method, which is used as the basis for calculating the excitation electromagnetic force. With the consideration of the non‐linear mechanical characteristic of the pad, the dynamic stiffness equation is analysed and established and the magnetic‐structural coupling correction model is constructed. Finally, the winding vibration amplitudes obtained respectively by the classical model, the magnetic‐structural coupling model, and the magnetic‐structural coupling correction model considering the dynamic stiffness are compared. The results show that, compared with the classical model, the vibration amplitude increment with the magnetic‐structural coupling correction model is less. The dynamic stiffness will hinder the vibration intensification. The magnetic‐structural coupling correction model can provide a more accurate calculation scheme for the winding vibration characteristic analysis.

A novel method based on PSO algorithm and ANN for magnetic flux density estimation near overhead transmission lines

Abstract This paper introduces a novel method that leverages artificial neural networks to estimate magnetic flux density in the proximity of overhead transmission lines. The proposed method utilizes an artificial neural network to estimate the parameters of a mathematical model that describes the magnetic flux density distribution along the lateral profile for various configurations of overhead transmission lines. The training target data is acquired using the particle swarm optimization algorithm. A performance comparison between the proposed method and the Biot-Savart law-based method is conducted using an extensive test dataset. The resulting coefficient of determination and mean square error values demonstrate the successful application of the proposed method for a range of different spatial arrangements of phase conductors. Furthermore, the performance of the proposed method is thoroughly assessed on multiple test cases. The practical relevance of the proposed method is highlighted by contrasting its results with the field measurements obtained in the proximity of a 400 kV overhead transmission line.

On-load magnetic field calculation for linear permanent-magnet actuators using hybrid 2-D finite-element method and Maxwell–Fourier analysis

PurposeThe purpose of this study is to present a novel extended hybrid analytical method (HAM) that leverages a two-dimensional (2-D) coupling between the semi-analytical Maxwell–Fourier analysis and the finite element method (FEM) in Cartesian coordinates.Design/methodology/approachThe proposed model is applied to flat permanent-magnet linear electrical machines with rotor-dual. The magnetic field solution across the entire machine is established by coupling an exact analytical model (AM), designed for regions with relative magnetic permeability equal to unity, with a FEM in ferromagnetic regions. The coupling between AM and FEM occurs bidirectionally (x, y) along the edges separating teeth regions and their adjacent regions through applied boundary conditions.FindingsThe developed HAM yields accurate results concerning the magnetic flux density distribution, cogging force and induced voltage under various operating conditions, including magnetic or geometric parameters. A comparison with hybrid finite-difference and hybrid reluctance network methods demonstrates very satisfactory agreement with 2-D FEM.Originality/valueThe original contribution of this paper lies in establishing a direct coupling between the semi-analytical Maxwell–Fourier analysis and the FEM, particularly at the interface between adjacent regions with differing magnetic parameters.

A Folded Coil Design for Cubic Wireless Charging Space Frames With Even Magnetic Flux Density Distribution

A Folded Coil Design for Cubic Wireless Charging Space Frames With Even Magnetic Flux Density Distribution

Vibration and noise mechanism of a 110 kV transformer under DC bias based on finite element method

Global energy and environmental issues are becoming increasingly problematic, and the vibration and noise problem of 110 kV transformers, which are the most widely distributed, have attracted widespread attention from both inside and outside the industry. DC bias is one of the main contributing factors to vibration noise during the normal operation of transformers. To clarify the vibration and noise mechanism of a 110 kV transformer under a DC bias, a multi-field coupling model of a 110 kV transformer was established using the finite element method. The electromagnetic, vibration, and noise characteristics during the DC bias process were compared and quantified through field circuit coupling in parallel with the power frequency of AC, harmonic, and DC power sources. It was found that a DC bias can cause significant distortions in the magnetic flux density, force, and displacement distributions of the core and winding. The contributions of the DC bias effect to the core and winding are different at Kdc = 0.85. At this point, the core approached saturation, and the increase in the core force and displacement slowed. However, the saturation of the core increased the leakage flux, and the stress and displacement of the winding increased faster. The sound field distribution characteristics of the 110 kV transformer under a DC bias are related to the force characteristics. When the DC bias coefficient was 1.25, the noise sound pressure level reached 73.6 dB.

Computational analysis of electromagnetic field exposure in passengers near high- current contact wire environments.

The electromagnetic environment of a railway station is composed of electrical, magnetic, and electromagnetic fields, which are generated by various sources such as traction current, voltage, pantograph-catenary arc, locomotive braking, wheel-rail rolling arc, and communication systems. However, there is public growing concern among the public about the potential negative human health effects of this electromagnetic environment. To analyze the distribution of electromagnetic fields in human tissues, electromagnetic simulation software is used to create a model that includes six track contact wires and four waiting passengers on three platforms. This model is used to analyze the magnetic field environment created by high currents in the contact wires of a multi-track high-speed railway station. By varying the loads on different contact wires, the distribution of electric field and magnetic flux density within human tissues of waiting passengers on different platforms is studied using this model. When the track is unoccupied, the calculation results show that the maximum values of the electric field and magnetic flux density of the passenger's human body tissue at the blind way on the platform and 1m of the blind way are 17.6mVm-1 and 52.7 μT, respectively. These values increase by 9.28mVm-1 and 16.4 μT compared to when the track is occupied. When more contact wires are loaded with currents, the electric field mode and magnetic flux density mode of human tissues increase at the same position on the platform. Specifically, when the contact wires of six tracks are loaded with current at the same time, the maximum values of the electric field mode and magnetic flux density mode of the waiting passengers' human tissues at the blind way on different platforms are 29.6mVm-1 and 88.1 μT, respectively. These maximum values are lower than the public electromagnetic exposure limits that are designated by the International Commission on Non-Ionizing Radiation Protection guidelines. The research results demonstrate that the magnetic field environment generated by the current in the contact wires of a railway station with six tracks does not pose a health risk to human tissues of passengers waiting at the blind way and 1m of the blind way on the platform. These findings can provide valuable data reference for the formulation of relevant standards for the design of electrified rail transit, as well as the suppression of electromagnetic interference and protection of human bioelectromagnetism.

A novel magnet system—which enables uniformity of radial flux density by means of a parabolic yoke—applied in the Planck-Balance

Abstract A uniform magnetic flux density that is effective in the movement range of the coil is essential for accurate Kibble balance experiments. By utilizing Hopkinson’s law and Kirchhoff’s circuit laws, basic formulas have been derived, providing a method to calculate the magnetic flux density distribution in the airgap of a cylindrical magnet system. A parabolic outer contour of the inner yoke has been found to be a suitable solution to achieve uniformity. Experiments show, that this approach results in a relative change of magnetic flux density in the order of 3 ⋅ 10 − 4 per 8 mm movement range, using a magnet system with a mass of only 2.3 kg. Therefore, the system will be integrated into the upgraded version of PTB’s Planck-Balance—a compact variant of a Kibble balance—aiming for sub 1 ⋅ 10 − 6 accuracy level determination of the geometric factor. The solution described provides a comparatively easy means to design a cylindrical magnet system, using only one permanent magnet disc, without the use of complex simulation software.

A Novel Folding Wireless Charging Station Design for Drones

Unmanned aerial vehicles (UAV) have been used in many fields nowadays. In long-term applications, batteries need to be constantly changed by someone due to short battery life. This problem is eliminated with wireless power transfer (WPT). A reliable, effective, and autonomous solution is offered using wireless charging. The most suitable wireless charging technique for UAVs is inductive power transfer (IPT). In this paper, a novel foldable coil and charge station design is proposed for the wireless charging of UAVs. IPT is provided by receiver and transmitter coils placed on the drone legs and the charging station, respectively. Receiver coils are placed on both legs of the UAV in a light and balanced manner to avoid creating imbalance and weight on the UAV. Receiver coils are designed as vertical rectangular planar spirals. A transmitter coil consists of three rectangular planar spiral coils with two movable edge windings and a fixed middle winding. The transmitter’s folding windings provide both alignments for the UAV during landing and increase the magnetic coupling. A folding wireless charge system of the UAV is designed for 100 W output power at a 138.1 kHz frequency. The misalignment tolerance of the proposed design in the vertical axis is examined. The design’s magnetic flux density distribution is analysed. As an experimental result of the study, 97.66% efficiency was reached in the aligned condition. Also, over 85.48% efficiency was achieved for up to 10 cm of vertical alignment misalignment.

Validation of 3D and 2D thermal and electromagnetic models for high-frequency induction heating in crystal growth processes

Induction heating is crucial to various crystal growth techniques, including the Floating Zone (FZ) method, which is used for producing high-quality single silicon crystals. In this work, 3D and 2D axisymmetric numerical models for the high-frequency induction heating in the FZ process are implemented in open-source software tools Elmer and OpenFOAM. The models are compared and validated with in-situ measurements conducted on a model experiment of the FZ process, consisting of a flat inductor that heats a tin rod. The magnetic flux density distribution around the inductor is measured using a 3D induction coil probe, and the rod’s surface temperature is measured using an infrared camera. Both numerical models were found to be in good agreement with the experimental data, with deviations mainly due to geometric approximations and simplified thermal modeling. The present measurement setup can be used as a benchmark for other numerical models of high-frequency induction processes.

Research on the Relative Placement Angle of the Induction Heater and the Channel in a Four-Channel Induction-Heating Tundish.

In order to optimize the application effect of induction heating (IH) tundishes, a four-channel IH tundish is taken as the research object. Based on numerical simulation methods, the influence of different relative placement angles of induction heaters and channels on the electromagnetic field, flow field and temperature field of the tundish is investigated. We focus on comparing the magnetic flux density (B) and electromagnetic force (EMF) distribution of the channel. The results show that regardless of the relative placement angle between the heater and the channel, the distribution of B in the central circular cross-section of the channel is eccentric. When the heater rotates around channel 1 towards the bottom of the tundish, the distribution of B in the central circular cross-section of the channel changes from a horizontal eccentricity to a vertical one. Through the analysis of the B contour in the longitudinal section of the channel, the difference in effective magnetic flux density area (ΔAB) between the upper and lower parts of the channel can be obtained, thereby quantitatively analyzing the distribution of B in this section. The distribution pattern of ΔAB is consistent with the distribution pattern of the electromagnetic force in the vertical direction (FZ) of the channel centerline. The ΔAB and FZ of channel 1 gradually increase as the heater rotates downwards, while those of channel 2 reach their maximum value at a rotation angle of 60°. Compared to the conventional placement, when the heater rotation angle is 60°, the outlet flow velocities at channel 1 and channel 2 decrease by 15% and 12%, respectively. However, the outlet temperature at channel 2 increases by 1.96 K, and the molten steel flow at the outlet of channel 1 and channel 2 no longer exhibits significant downward flow. This shows that when the heater rotation angle is 60°, it has a dual advantage. On the one hand, it is helpful to reduce the erosion of the molten steel on the channel and the bottom of the discharging chamber, and on the other hand, it can more effectively exert the heating effect of the induction heater on the molten steel in the channel. This presents a new approach to enhance the application effectiveness of IH tundish.

Vector magnetic circuit analysis of silicon steel sheet parameters under different frequencies for electrical machines

AbstractSilicon steel sheets (SSSs), serving as the principal constituent of the magnetic circuit in electric machines, necessitates precise modelling and accurate computation using magnetic circuit theory as a prerequisite for analysing the characteristics of electric machines. Nevertheless, the conventional magnetic circuit theory, limited to a single reluctance component, fails to address the phase relationship between magnetomotive force and magnetic flux, and inadequately represents the magnetic flux distribution observed under high‐frequency conditions. Consequently, the existing magnetic circuit model for SSSs remains imperfect in its current state. Fortuitously, the advent of magductance has effectively addressed these challenges. Building upon magductance, this study deduces the fundamental laws and theorem within the vector magnetic circuit theory. Subsequently, a distributed parameter vector magnetic circuit model for the SSSs is constructed, accompanied by the derivation of expressions pertaining to its reluctance and magductance. The authors propose the transfer function composed of reluctance and magductance parameters, successfully resolving the phase between the magnetic circuit vectors, the magnetic flux distribution, and the magnetic circuit loss under different frequencies for SSSs. Finally, experimental findings affirm the efficacy and validity of the distributed parameter vector magnetic circuit model for SSSs. The proposal of vector magnetic circuit theory opens a whole new door for the analysis, computation, and optimisation of electric machines.

Optimized coil and current flow designs for wireless charging containers with improved even magnetic flux density distribution

AbstractThis paper introduces three different shapes of wireless charging containers (i.e. quadrangular prism, octagonal prism, and hexagonal prism) and presents optimal current flow designs for the coils to enhance the uniformity of magnetic flux distribution inside the containers. Additionally, the concept of folded coil design is introduced to further improve the even distribution of magnetic flux density within the containers. The performance of these designs is evaluated through simulations and practical experiments.

Development of soft magnetic composites for magnetized pavement to improve the efficiency of electric vehicle's wireless power transfer

Integrating the wireless power transfer (WPT) system into the pavement is an effective way to solve the inconvenience of electric vehicles (EVs)’ charging, accelerating the growth of ownership of EVs to achieve net carbon zero in transportation. However, the existence of a cement paving layer between coils was a negative impact factor. Here, two types of ferrite powders were separately mixed into the cement to prepare soft magnetic composite (SMC) material to enhance the coupling degree of coils. The magnetic and mechanical performance of the composite were tested by a vibrating sample magnetometer and compressive and flexural strength tester. Furthermore, to explore the optimal layout of the magnetized pavement structure, nine pavement layouts were designed based on the distribution of magnetic flux. Finally, the effect of SMC material on improving the charging performance was verified by WPT system test platform. Results showed that the Ni–Zn ferrite powder exhibited superior magnetic permeability due to its stronger magnetic moments and lower magnetic domain wall energy compared to Mn–Zn ferrite powder. The peak relative permeability of SMC materials reached 14.370 with an equal mass ratio of Ni–Zn ferrite powder to cement. Conversely, optimal strength was attained with a Mn–Zn ferrite to cement ratio of 0.2, resulting in a compressive strength of 36.0 MPa and a flexural strength of 4.0 MPa. Strategically placing SMC within the pavement, both in the core's interior and exterior to the coil, enhanced the coupling coefficient of coils, thereby improving the transmission efficiency of the WPT system. The incorporation of Ni–Zn ferrite powder in a 1:1 mass ratio to cement materialized the highest efficiency. Nonetheless, considering the mechanical performance, the SMC material with a 0.6 mass ratio of Mn–Zn ferrite powder to cement was recommended for magnetized pavements. The WPT system test results showed a transmission efficiency of 89.78% when utilizing magnetized pavement, surpassing the efficiency with the whole pavement material by 1.36%, which indicated great value and potential in energy conservation and carbon reduction of employing magnetized pavement in WPT technology.