Magnetic Charge Model Research Articles

The magneto-elastoplastic coupling effect on the magnetic flux leakage signal

This paper introduces an experimental progress of the magneto-elastoplastic coupling phenomenon on magnetic flux leakage signal for ferromagnetic materials. The magnetic flux leakage signal on the surface of medium carbon steel was measured under the combined action of elastic load and plastic deformation. Based on the experimental results, the influences of elastic load and plastic deformation on the magnetic flux leakage signal and their coupling effects were analyzed. A theoretical mechanism of experimental phenomena was explained by the magneto-elastoplastic coupling model and magnetic charge model. The results show that the magnetic flux leakage signal increases with the increase of the elastic load, and the magnetic flux leakage signal increases first and then decreases with the increase of plastic deformation. As the elastic load increases, the effect of plastic deformation on the magnetic flux leakage signal gradually increases. The work in this paper provides a vigorous support for the safety evaluation of engineering structures caused by the combination of plastic deformation and residual stress through magnetic flux leakage signal.

Considering Operating Point Variation in 3-D Analytical Charge Model Used for Design of Low-Stiffness Permanent Magnet Vibration Isolator

Vibration isolators are a key technology in ultraprecision machining and ultraprecision measurements. The increasing performance requirements of magnetic vibration isolation systems (MVISs) continue to demand improvements in the accuracy on which these devices are modeled. However, a serious constraint exists in designing MVISs, as high stiffnesses will be introduced by nonlinear force–displacement characteristics. The traditional analytic magnetic charge model assumes that the relative magnetic permeability $\mu _{r} = 1$ , which causes the accuracy of the magnetic analytic model of the MVIS to decrease. To solve this defect, in this article, low-stiffness MVISs are designed by using the three-dimensional analytic magnetic charge model while considering the variations of the operating point. The optimized parameters of the MVIS are then obtained by combining the genetic algorithm. The feasibility of the proposed analytical charge method is verified from the results of experimental measurements and finite-element methods. The results of this article provide a powerful tool for the design of a high-performance MVIS and provide important support for the ultimate goal of ultraprecision machining and measurements.

Stress-Dependent Magnetic Charge Model for Micro-Defects of Steel Wire Based on the Magnetic Memory Method

ABSTRACTMagnetic memory method (MMM) is widely used for diagnosing ferromagnetic material on early stage as a nondestructive technology, but no clear description exists for the influence of stress on MMM signals at the micro-defect position on the surface of steel wire yet. Hence, based on traditional magnetic charge model, a stress-dependent magnetic charge model that combined the Jiles magneto-mechanical constitutive relation was intended to calculate the MMM signals around micro-defect on surface of steel wire. Meanwhile, the Hp(y) signals on surface of steel wire with different defects were measured during the whole tension test. By comparing the results of theoretical model and experiment, some conclusions can be drawn. First, the position of vale-peak on Hp(y) signals curves can be used to determine the micro-defect on steel wire. Secondly, the vale-peak amplitude (Sv-p) and vale-peak width (Lv-p) of Hp(y) signals curves, as two characteristic parameters of magnetic signals, not only can reflect the variations of defect depth and defect width, but also judge the load subjected by specimen. Sv-p has an approximate growth with the increase of defect depth as a whole, but decreases with the increase of loads. And the effect of load on Sv-p increases with defect depth. Lv-p has an approximate growth with the increase of defect width as a whole, but does not change with the increase of loads. Finally, the stress-dependent magnetic charge model can be better to reflect the changing laws of Hp(y) signals around defect and can be used for the numerical analysis of MMM signals on surface of steel wire.

Integral definition method to solve magnetic force of axial permanent magnetic bearing

In the design process of the permanent magnetic bearing, the calculation of the magnetic force between the magnetic rings is an important element. Transforming complicated physical problems into mathematical problems by establishing the mathematical model of the magnetic ring is a common method when calculating the magnetic force. In this paper, the equivalent magnetic charge model of a permanent magnet bearing is established by the former’s magnetic charge viewpoint, and the quadratic integral based on this model is solved by the integral definition method. This paper compares the results of integral definition method with those obtained by Monte Carlo method and ANSYS in order to verify the correctness.

Study on Magnetic Force Calculation of Spherical Permanent Magnets

This paper presents three approaches to calculate the interacting magnetic force about spherical permanent magnet, respectively based on magnetic dipole-dipole model, equivalent magnetic charge model and equivalent magnetizing current model. We use all of three models to fully calculate and study the behaviors of lateral and axial forces with respect to the related positions between a pair of spherical magnets. The accuracies of the calculation results are compared with the experimental data. In conclusion, the magnetic dipole-dipole model has the most advantageous accuracy and efficiency for the magnetic force calculation about spherical permanent magnets on account of the particularity of sphere. Our study provides an important criterion for choosing a proper method to calculate magnetic force about spherical permanent magnet.

Modeling and Optimization of Air-Core Monopole Linear Motor Based on Multiphysical Fields

The key technology of the air-core monopole linear motor (AMLM), a core component of precision motion systems, is the distribution of the electromagnetic structure and cooling structure. Thus, AMLM can achieve small thrust fluctuation, high thrust density, and low surface temperature rise. Consequently, the multiobjective optimal design of AMLM under the multiphysical fields has become the key technology of AMLM. Consideration of the strict requirements of AMLM model calculational accuracy will cause an excessively long computation time for the finite-element analysis (FEA) software three-dimensional (3-D) model, and it is not convenient for an optimal computation of the multiphysical fields model. Therefore, a surface magnetic charge model and an image method are proposed in the paper to establish an air gap magnetic field model of AMLM. The saturation characteristic of magnetic materials can be reflected through saturation coefficient of the model. In addition, the air gap field distribution status of AMLM can be better predicted. An AMLM thermal field model is established by adopting the thermal network method. In the model, the heat transfer coefficient of cooling water is calculated based on the current curve obtained from the FEA software. Parametric modeling was performed on the AMLM electromagnetic and cooling structure through definition of 7-D proportionality coefficients. Based on the aforementioned electromagnetic field and the thermal field model, genetic algorithm (GA) was adopted for AMLM optimization design by setting cooling capacity and size as constrain conditions as well as by setting thrust density, thrust fluctuation, mover's mass, and motor constants as optimization objects. The AMLM electromagnetic field, the accuracy of thermal field model, and the validity of the AMLM optimization method were verified through simulation and tests. The method proposed has significantly improved the efficiency of optimization calculation.

基于磁荷模型的全极化质子对撞结果预测

基于磁荷模型的全极化质子对撞结果预测

Modeling of the Electromagnetic Drive Torque on the Permanent Magnet in a Novel Drive Mechanism

Analytical models of vibration exciters and shakers are of great importance to their dynamic analysis and control. Furthermore, the modeling of the drive torque/force of the driving principle plays a key role in the modeling of an entire driving system. This paper aims to find a more detailed analytical model of the electromagnetic drive torque on the permanent magnet with a new shape in a novel driving mechanism. The proposed model contains all the related parameters instead of treating them as only one variable. Two methods of the permanent magnet installation are firstly introduced and compared. Based on the magnetic charge model, torque models of the bipolar cylindrical permanent magnet and partial bipolar cylindrical permanent magnet are then obtained. Thereupon then the final model with a composite shape is gained by combining the cylindrical and partial cylindrical ones. Moreover, all analytical models are verified by finite element method and it is found the final detailed model can characterize the electromagnetic drive torque in a high accuracy.

Toward Accurate Design of a Transverse Flux Machine Using an Analytical 3-D Magnetic Charge Model

Low-speed high-torque applications, e.g., wind energy generation, favor high number of pole solutions. This usually results in a dominating leakage flux in traditionally radial or axial field machines, while the output power remains constant. Within transverse flux machines (TFMs), an increase in output power proportional to the number of poles is achieved by traversing the flux direction. However, TFMs still suffer from a relatively large leakage, reducing their application in present industries. In order to research this leakage, fast and relatively accurate 3-D models are essential. To date, finite-element models (FEMs) have been dominantly used to calculate these 3-D magnetic fields. However, the FEM requires a large number of elements, hence it is very time consuming (hours for a single solution). A fast and more accurate parameterized model is essential to maximize the power factor while maintaining a high torque density. In this paper, the validity of a 3-D analytical magnetic charge model is used to investigate its applicability to model TFM topologies. As such, an automated parametric search has been undertaken to minimize machine volume, i.e., without considering power factor although with fixed constraints on magnetic flux density and slot leakage. Although this does not provide a global optimized minimum, it is surely interesting for the experienced machine designer who wants to further understand the physics of this machine. To illustrate the accuracy of the magnetic charge model, the error of the final result of such a parametric search is compared with a 3-D FEM, which shows an error in force prediction of only 8.9%.

Comparison of Harmonic and Magnetic Charge Model for Spherical Magnetic Structures With a Neumann Boundary

This paper includes the Neumann boundary conditions in the magnetic charge modeling method for spherical magnetic structures. In the spherical coordinate system, the geometry and the magnetic properties of the imaged magnetic structure are obtained with the method of inversion. This method is applied to a spherical permanent magnet array, and the results are compared with the harmonic modeling and finite-element analysis. In addition to this validation, the modeling methods are compared on their limitations and accuracy.

Magnetic charge model for 3D MMM signals

Stress concentration is a major cause of metal structure failures. Based on the metal magnetic memory (MMM) technique, detailed information of stress concentration or defects on ferromagnetic materials can be obtained from the changed magnetic signals. The magnetic charge model of MMM signal is described, and simulations based on this model are performed for a sample with stress-concentration zone or a long elliptical defect. Some basic characteristics produced by present model are coincident with existed experimental measurements. The agreements between simulations and experimental results confirm that the present magnetic charge model can be used as an MMM signal forward technique.

Analytical Force, Stiffness, and Resonance Frequency Calculations of a Magnetic Vibration Isolator for a Microbalance

The accuracy of a microbalance is highly dependent on the level of floor vibrations. One strategy to reduce floor vibrations is a magnetic vibration isolator. Magnetic vibration isolators have the possibility to obtain a zero-stiffness region, which is beneficial for attenuating vibrations. In this paper, a 3-D analytical magnetic surface charge model is used to calculate the spring characteristics of a cone-shaped magnetic vibration isolator for different angles.

Design and development of a novel bi-directional piezoelectric energy harvester

In this paper, a novel bi-directional piezoelectric energy harvester which can harvest vibration energy bi-directionally is introduced and investigated theoretically and experimentally. The proposed harvester is composed of two sub-systems: a main beam to generate electricity and a spring–mass oscillator to trigger the vibration of the main beam from an additional direction by using magnets to couple the two sub-systems. The theoretical model is built on the basis of the Euler–Bernoulli beam theory and the magnetic charge model. A prototype is fabricated to test the performance of the harvester experimentally. Linear upward and downward frequency sweeps are used to obtain the frequency responses. The experimental results show good agreement with the theoretical model under frequency sweeps. A comparison with a beam–beam bi-directional piezoelectric energy harvester is also performed experimentally. Although both bi-directional piezoelectric energy harvesters exhibit the capability of harvesting vibration energy in two orthogonal directions, the beam–spring energy harvester shows a more consistent performance in both directions as regards the bandwidth and amplitude of the frequency responses.

Novel Universal Multistable Mechanism Based on Magnetic–Mechanical–Inertial Coupling Effects

Different from multistable mechanisms incorporating multiple bistable elements, a novel universal multistable mechanism possessing the capability of being triggered in all in-plane directions was first designed and fabricated by using symmetric 3-D magnetic structures, which mainly consists of one magnetic ring supported by a elastic rod and one axially magnetized pillar fixed on the aluminum case. The in-plane isotropic multistability was originated from the nonlinear interactions among the inertial force, the elastic force, and the magnetic force. According to the pseudo-rigid-body model and magnetic charge model theories, an accurate mathematical model was established for precisely analyzing the nonlinear magnetic-mechanical-inertial coupling mechanics. By considering the influence of the translational motion and the inclination angle of the magnetic ring on the magnetic field distribution and strength, the nonlinear force versus displacement relationship was obtained numerically and experimentally. The numerical results are in good accordance with those obtained by experiments, thus validating the design methodology for isotropic multistable mechanism.

Indirect Fault Detection Method for an Onboard Degaussing Coil System Exploiting Underwater Magnetic Signals

This paper proposes an indirect fault detection method for an onboard degaussing coil system, installed to reduce the underwater magnetic field from the ferromagnetic hull. The method utilizes underwater field signals measured at specific magnetic treatment facilities instead of using time-consuming numerical field solutions in a three-dimensional space. An equivalent magnetic charge model combined with a material sensitivity formula is adopted to predict fault coil locations. The purpose of the proposed method is to yield reliable data on the location and type of a coil breakdown even without information on individual degaussing coils, such as dimension, location and number of turns. Under several fault conditions, the method is tested with a model ship equipped with 20 degaussing coils.

Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness

Abstract The vibration isolator using a novel magnetic spring with negative stiffness (MS-NS) is proposed in this paper. The proposed isolator which combines a positive stiffness spring with the MS-NS in parallel possesses the characteristic of high-static–low-dynamic stiffness. The MS-NS is composed of three cuboidal magnets configured in repulsive interaction. An analytical expression of the stiffness of the MS-NS is derived by using the magnetic charge model, and the approximation to the exact analytical expression is sought. Then, the nonlinearity of the stiffness is analyzed, and it is shown that the MS-NS is approximately linear for small oscillations. In order to validate the correctness and effectiveness of the MS-NS, the vibration transmissibility of the proposed isolator with and without the MS-NS is measured. The experimental results demonstrate that combining a vibration isolator with the MS-NS in parallel can lower the natural frequency of the isolator; and the analytical calculations and experimental results show a good consistency.

Calculation of the Sensitive Region of a U-shaped Permanent Magnet for a Single-Sided NMR Spectrometer

With a conventional NMR (Nuclear Magnetic Resonance) spectrometer, the study sample is placed inside the magnet. In contrast, with a single-sided NMR spectrometer, the study sample is outside, but close to the magnet. Single- sided spectrometers can thus be used with a large sample and made portable. A high magnetic field can be achieved without the need for a high-current, DC power supply when using neodymium (NdFeB) magnets. The system is, therefore, relatively low cost, as well. The U-shaped magnet developed here consists of two permanent magnets of size 50x50x25 mm 3 (with a measured surface magnetic field of 0.35 T) placed on a piece of thick steel with opposite poles upward, giving a magnetic field parallel to the surface of the magnets. The magnetic charge model was used to calculate the magnetic field in planes at different distances from the magnets' surface and the size of the NMR sensitive region with 10 3 ppm homogeneity was obtained. Calculated field values and values measured using a tesla meter allowed the values of the surface magnetic charge density σ m to be determined. Magnets positioned with a gap of one-half the width of the magnet face produced the largest sensitive region. In this case, the sensitive region was 12 x 2.5 x 1 mm and located 15 mm above the magnet surface with a central field of 0.23 T.

Modeling of Spherical Magnet Arrays Using the Magnetic Charge Model

This paper presents an analytical method for evaluating the magnetic flux density produced by spherical permanent magnet arrays used in spherical actuators. To investigate the performances of magnetic arrays, analytical models are used due to their lower computational time compared to 3-D finite element analysis. This paper presents an analytical model for the calculation of the magnetic field produced by a spherical permanent magnet array using magnetic charge modeling. To obtain the total magnetic field solution, first the magnetic field produced by a single spherical tile is considered. By means of superposition, the magnetic field produced by the array is obtained. Two magnet array topologies are modeled and the analytical results are validated using finite element analysis.

Analysis and Optimization of Ironless Permanent-Magnet Linear Motor for Improving Thrust

As known, improving launcher thrust is the goal that the mankind is pursuing. There is no saturation phenomenon in the ironless permanent-magnet linear motor (IPMLM); hence, the thrust of IPMLM has a linear relationship with current through windings to provide larger thrust. The topology of IPMLM determines that its thrust fluctuation is smaller than that of an iron permanent-magnet linear motor. In this paper, the model of an air-gap magnetic field is established by the magnetic charge model and the image method for global optimization of IPMLM thrust. All dimensions of IPMLM are described by motor thickness and three ratio coefficients (i.e., α, β , and γ). The cooling power of the cooling system under different temperature gradients, which determines current density of winding, is calculated by Comsol software. Different values of α, β, and γ mean that each dimension of IPMLM is different, the current density in different windings being subject to constraint condition <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cu</sub> ≤ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> . Therefore, we can obtain the variation of current density with dimension and the variation of thrust with dimension. For obtaining maximum thrust in the same volume, the size ratio among magnetic structure, winding structure, and cooling structure is derived by the thrust analytical expression. The distribution of the IPMLM thermal field is analyzed by a 3-D finite-element method, and this optimization method of IPMLM thrust density is proved by experiment.

A Bidirectional Acceleration Switch Incorporating Magnetic-Fields-Based Tristable Mechanism

In order to fulfill the requirements of low energy consumption and two sensing directions, a novel bidirectional acceleration switch is proposed by utilizing the magnetic-fields-based tristable mechanism that can maintain the three stable states without input power and with high position accuracy and repeatability. The bidirectional acceleration switch mainly consists of an inertial mass supported by two parallel elastic beams, two metal contact points, and four permanent magnets with one imbedded in the inertial mass and the other three fixed in the case along the vertical direction. Based on the magnetic charge model, the nonlinear magnetic force is analyzed, and then, a static design model of the bidirectional switch is established by considering the elastic force, the magnetic force, the contact force, and the inertial force. To validate the feasibility of the design method, a miniature sample of the switch is fabricated. The results of the centrifugal experiment show that the threshold accelerations in two directions are 53.0 and -52.0 g, respectively, which are close to the design values of 55.0 and -50.0 g, correspondingly. In addition, the threshold values can be adjusted by changing the relative distances among the four magnets.