Analytical Magnetic Field Model Research Articles

Analytical Model of Magnetic Field Generated by Racetrack Superconducting Excitation Winding Within Cylindrical Ferromagnetic Boundary Based on Mirror Method

Analytical Model of Magnetic Field Generated by Racetrack Superconducting Excitation Winding Within Cylindrical Ferromagnetic Boundary Based on Mirror Method

A Hybrid Analytical Model of Open-Circuit Air Gap Magnetic Field of Interior Permanent Magnet Synchronous Motor With Non-Uniform Air Gap Structure Considering Saturation Effect

A Hybrid Analytical Model of Open-Circuit Air Gap Magnetic Field of Interior Permanent Magnet Synchronous Motor With Non-Uniform Air Gap Structure Considering Saturation Effect

Analytical Model for Magnetic Field and Inductance of Toroidal D-Shaped HTS Magnet

Analytical Model for Magnetic Field and Inductance of Toroidal D-Shaped HTS Magnet

Thrust ripple suppression analysis of moving-magnet-type linear synchronous motor based on independent coil

In this paper, a novel thrust ripple suppression method for multi-secondary permanent magnet synchronous linear motor based on independent coil structure is proposed. Independent coil structure can realize independent power supply for each coil by changing the driving mode of the coils. Combined with the new power supply strategy, the detent and electromagnetic force fluctuation can be suppressed. Firstly, the cogging and end force of moving-magnet-type linear motor are separated by periodic and vector boundary conditions and harmonic analysis is carried out. An analytical model of air gap magnetic field based on virtual magnetic poles is established to solve the back EMF and electromagnetic force fluctuation of the motor. The generation mechanism and harmonic of electromagnetic force fluctuation are analyzed. A multi-secondary PMLSM based on independent coil is proposed, the principle of suppressing motor thrust ripple is expounded, and the coupling effect between modules is analyzed. Finally, a zero-crossing power supply strategy is proposed. The simulation and experimental results show that multi-secondary independent coil PMLSM can effectively suppress the detent and electromagnetic force fluctuation.

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

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

Magnetic Model Calibration and Distortion Compensation for Electromagnetic Tracking in a Clinical Environment

Electromagnetic tracking (EMT) of surgical tools is used for image-guided navigation in minimally invasive interventions. Calibration of the tracker position and orientation is a fundamental task to correct systematic errors. This article explores the effect of metallic distortion on the open hardware Anser EMT system and describes a newly developed approach for volume calibration of the magnetic field model. The technique is also applied to effectively map the field in the presence of magnetic shields that can be used to reduce electromagnetic distortions passively. Unlike calibration techniques commonly found in literature, which aim to correct the tracking position error, our method can reconstruct an analytical magnetic field model starting from a reduced amount of scattered data. This way, a faster convergence of the solver algorithm is obtained, and EMT position and orientation errors are inherently corrected. The new modelling technique was applied to generate a new, undistorted magnetic field model for Anser EMT, to demonstrate the effectiveness of passive shielding, and to compensate for the distortion introduced by a commercial fluoroscopy C-arm. Furthermore, the concept of a real-time distortion compensation technique is expressed based on the modelling method presented in this article. For all the experiments, sub-millimeter errors were obtained after calibration, which may meet the needs of most endoscopic and surgical navigation tasks.

Magnetic Field Analysis for the Permanent Magnet Spherical Motor With SMC Core

This paper presents a permanent magnet spherical motor (PMSM) with soft magnetic composite (SMC) core. The analytical model of the no-load air-gap magnetic field of the PMSM with SMC core is obtained based on the Laplace equation with the boundary conditions. When the SMC core is added to the stator teeth, a cogging effect occurs, which makes the three-dimensional magnetic circuit of the entire spherical surface uneven. When the spherical motor completes multi-degree-of-freedom motion, the air-gap magnetic field is severely distorted. In order to solve the above problems, this paper proposes for the first time the method of adding spherical shaped pole shoes to the stator teeth, which perfectly solves the problem of magnetic field distortion in this paper. The air-gap magnetic field distribution is improved by optimizing the structure of the stator tooth pole shoes. Finally, the static torque measurement platform was built to test the rotation energized output torque. The research results of this paper lay a theoretical foundation for the structural optimization design of the PMSM with SMC core.

Equivalent Circuit Element Calculation of Gapped Multiwinding Inductors

Accurate and fast models of the equivalent circuit (EC) elements of gapped multiwinding inductors are essential for the design of galvanically isolated converters, such as Flyback and LLC converters. Typically, the EC elements are acquired from measurements or time-consuming FEM simulations, both of which are disadvantageous for optimizing the design of the magnetic device. This paper proposes a multiwinding magnetic device EC that exclusively uses the impedance matrix elements, i.e., self- and mutual impedances. The advantage of the impedance matrix equivalent circuit (IMEC) is that self- and mutual impedances are directly measurable. Furthermore, the paper presents an analytical 2D magnetic field model to calculate the EC elements. It is quantitatively confirmed that frequency significantly affects the resistances and the inductances of magnetically coupled windings. In particular, eddy currents in windings induced by the fringing field of the air gap play a role besides the well known skin and proximity effect. The proposed model accurately considers all these effects in foil, Litz, and round wire conductors. The model is verified using FEM simulations and measurements.

Optimization of the Wire Diameter Based on the Analytical Model of the Mean Magnetic Field for a Magnetically Driven Actuator

A magnetic field induced by an electromagnetic coil is the key variable that determines the performance of a magnetically driven actuator. The applicability of the empirical models of the coil turns, static resistance, and inductance were discussed. Then, the model of the mean magnetic field induced by the coil was established analytically. Based on the proposed model, the sinusoidal response and square-wave response were calculated with the wire diameter as the decision variable. The amplitude and phase lag of the sinusoidal response, the time-domain response, steady-state value, and the response time of the square-wave response were discussed under different wire diameters. From the experimental and computational results, the model was verified as the relative errors were acceptably low in computing various responses and characteristic variables. Additionally, the optimization on the wire diameter was carried out for the optimal amplitude and response time. The proposed model will be helpful for the analytical analysis of the mean magnetic field, and the optimization result of the wire diameter under limited space can be employed to improve the performance of a magnetically driven actuator.

Study on unbalanced magnetic pull of permanent magnet toroidal motor with planet rotor eccentricity

Permanent magnet toroidal motor (PMTM) is a novel spatial motor that integrates toroidal drive system and permanent magnet synchronous motor. The unbalanced magnetic pull (UMP) with planet rotor eccentricity is the main cause of vibration in PMTM. In this paper, the analytical model of magnetic field with planet rotor eccentricity is established with the consideration of magnetic flux leakage. The calculation results of eccentric magnetic fields are compared with simulation results of finite element model. Based on the Maxwell tensor method, the analytical model of UMP with planet rotor eccentricity is established. The changes of UMP with initial eccentricity are obtained. The UMP is analyzed with the effects of eccentric distance and angle. The transient variations of UMP are discussed with different eccentric situations respectively. In addition, both simulation and calculation results for UMP have a good agreement, which verifies the validity of analytical model.

Torque Analytical Calculation of Formed Winding Permanent Magnet Motor

The development of electrification has put forward higher requirements for the efficiency and power density of permanent magnet motors. The combination of formed flat wire windings and open slots with rectangular cross-sections has been applied in permanent magnet motors, which makes the motor torque fluctuate significantly, and the vibration and noise caused by it seriously influence the stability of operation. Therefore, it is essential to study the torque characteristics for permanent magnet motors with formed windings. The open slot brings rich tooth harmonics to the air-gap magnetomotive force. In this study, an analytical model of the motor magnetic field was established based on magnetic potential and relative permeance theory. According to the Lorentz force law, an analytical model of the instantaneous torque of the permanent magnet motor with a formed winding is derived. The model points out that under the modulation of the relative permeance function, the constant torque and torque fluctuation are generated after the interaction of the stator magnetomotive force and rotor magnetic potential that meet the corresponding harmonic order relationship, and the order of the torque fluctuation is a multiple of 6. According to the analytical model, different torque components of the permanent magnet motor with formed windings are calculated and verified by the finite element method.

Analytical Model for No-Load Magnetic Field, Can Losses, and Temperature of Permanent Magnet Canned Motor

Analytical Model for No-Load Magnetic Field, Can Losses, and Temperature of Permanent Magnet Canned Motor

Research on High Precision Magnetic Positioning Technology Based on Facility Transport Platform

With the continuous development of economic globalization, the research demand for intelligent agricultural machinery equipment in modern agriculture is increasing. This paper, which aims at the positioning problem of mobile robots in agriculture production, proposes a low-cost magnetic positioning scheme for cement ground. First, the analytical magnetic field model of ground magnets was established. Then, by comparing the analytic computing results, simulation results, and measured values, the modified model of magnetic fields was built and the relevant impact factors were calculated. After that, acquisition devices were used to collect the ground magnetic field data for the establishment of a magnetic field matching algorithm. Finally, the result showed that the positioning displacement error was ±1 mm, and the positioning accuracy was higher than the conventional indoor positioning method, which solved the problem of the low indoor positioning accuracy of agriculture mobile robots and contributes to the efficient production and modernization of agricultural machinery equipment.

Analytical Calculation of Air-Gap Magnetic Field Distribution in IPMSMs with Mixed Eccentricity Accounting for Bridge Saturation

This paper presents an analytical model for calculating the detailed air-gap magnetic field distribution in interior permanent magnet synchronous motors (IPMSMs) with mixed eccentricity. In order to improve the efficiency of model solving, a modeling strategy combining the equivalent magnetic circuit network method and the subdomain method was adopted. Specifically, the magnetic field distribution of the rotor was modeled by using the magnetic circuit analysis method, and the magnetic field distributions of the air-gap, slot opening and stator slot along the radial direction were modeled in different regions according to their structure ruler. Then, the influence of bridge saturation was considered. Moreover, based on the analysis of the air-gap geometric structure with mixed eccentricity, a detailed spatiotemporal analytical model of the air-gap magnetic field was established, which provides a more accurate description of the mixed eccentricity composed of static and dynamic rotor eccentricities of different severity. The analytical models were compared with the corresponding models established by the finite element method, which proved the accuracy and validity of the models established in this paper. Finally, some key features related to radial and tangential air-gap flux density were extracted, which can significantly reflect the characteristics of eccentricities. The main findings reported in this paper will be of benefit for developing methods for early identification and diagnosis of eccentricity faults in IPMSMs.

Magnetic field analytical calculation method for radial unite of a combined magnetic bearing

AbstractCombined magnetic bearing with radial and axial unites is an important supporting element for high speed and high energy density motor. Accurate calculation of the magnetic field is a key to design and optimise a Combined Radial and Axial Magnetic Bearing (CRAMB). This study focuses on magnetic field analytical calculation method for radial Unite of CRAMB. The analytical calculation model of magnetic field is based on subdomain method. The Laplace's equations in the air‐gap subdomain are solved by the variable separation method. The magnetic field of magnetic bearing with large diameter rotor is analysed and calculated in Cartesian coordinate system. Considering the influence of curvature the magnetic field distribution of magnetic bearing with small diameter rotor is deduced and calculated analytically in polar coordinate system. The effectiveness of the analytical method is verified by finite element and experimental results.

An efficient analytical model and experiments of 3D electromagnetic force of permanent magnet electrodynamic suspension system

Electrodynamic suspension (EDS) with a linear permanent magnet Halbach array, which can be used in ultrahigh-speed maglev systems, has gained increasing attention in recent years. However, inefficient calculation methods of electromagnetic forces restrict the stability research of EDS systems. Hence, an efficient 3D analytical model of the electromagnetic force is established in the paper based on an improved analytical model of the source magnetic field excited by the Halbach array, and then the application conditions of the model are studied. Finally, the analytical results are compared with the experimental results, which are provided by the experiments carried out on a high-speed rotating experiment platform with a flywheel. The results show that the proposed model can shorten the computation time of electromagnetic force to less than 10 ms and the relative errors of analytical results are around 5% under the conditions ①wp/τ≥2.5, wd/wp≥1.5 or ②wp/τ≥4, wd/wp≥1 (τ is the pole pitch of the Halbach array, wp is the width of the permanent magnet, wd is the width of the conducting plate). The analytical model meets the engineering requirements and can provide a reference for further stability research and experiments on EDS systems.

Analysis and Calculation of the Three-Dimensional Air-Gap Magnetic Field and Electromagnetic Torque of a Multishaft Ring-Plate Magnet Gear

A kind of multishaft ring-plate magnet gear (MRMG) structure is proposed. Because an MRMG has the characteristics of an eccentric permanent magnet gear with a small aspect ratio and large magnetic leakage at the end, there is a large deviation when using traditional 2-D FEM or an analytical method to analyze and calculate field and torque values for an MRMG. In this article, a 3-D mathematical analytical model of the MRMG eccentric air-gap magnetic field and electromagnetic torque is established, which is suitable for computer modeling. First, based on the cylindrical coordinate system of the inner and outer permanent magnet rings, the 3-D analytical models of the air-gap magnetic field of the inner and outer permanent magnet rings are established, respectively, by using the vector magnetic potential method. Then, by analyzing the position relationship between the inner and outer permanent magnet rings and their superposition angles, the radial and tangential air-gap magnetic fields of the inner and outer permanent magnet rings are superimposed according to their included angles, and a 3-D analytical model of the air-gap magnetic field and the electromagnetic torque of an MRMG is established. Because all the calculations are magnetic field integrals along the axial length of the MRMG, the magnetic field’s end effect is included in the established model, and the calculated results are more accurate than those of a 2-D FEM and analytical method (error >13%). A 3-D FEM and static loading experiment show that the model has a good accuracy (error < 2%) with the measured results and finite-element analysis, but the calculation speed of the model is faster than that of the 3-D FEM, which not only greatly shortens the calculation time but is also suitable for computer programming and is easily used to perform the MRMG analysis and optimization of different MRMG structural parameters.

Modeling and Analysis of New Power Devices Based on Linear Phase-Shifting Transformer

With the rapid development of new power systems, various new power devices have also been developed. It is very important to establish analytical models of new power devices to ensure or even improve the reliability and stability of the power system. A linear phase-shifting transformer (LPST) is a new type of power device that mainly relies on air gaps to transfer energy, so establishing an accurate air-gap magnetic field model is very important for improving the efficiency of this system. In this paper, an analytical model of an unequal-pitch linear phase-shifting transformer (UP-LPST) was established by combining the distributed magnetic circuit method (DMCM) and Schwartz–Christopher transformation (SCT). Taking the magnetic field strength as a variable, an accurate magnetic field analysis model for a UP-LPST considering saturation, cogging, and edge was established. Taking a 1 kw UP-LPST as a prototype, the accuracy of the model was verified by the finite element method and experiments. This modeling method could also be used to establish magnetic field models of other similar structures in new energy power systems, especially those with cogging structures.

Analytical Modeling of Open-Circuit Magnetic Field in Permanent Magnet Assisted Synchronous Reluctance Motors Considering Iron Bridge Saturation Effects

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Calculating accurately iron bridge saturation effects of the magnetic field, for Permanent Magnet Assisted Synchronous Reluctance Motors (PMASynRMs), remains to be a knotty problem. This paper presents an analytical modeling method to predict open-circuit magnetic field distributions and electromagnetic performances of PMASynRMs, considering iron bridge saturation effects. This analytical modeling method combines the magnetic equivalent circuit method, superposition principle, the solution of the governing Maxwell’s field equations and a complex relative permeance function. A quadruple-layer PMASynRM are remodeled into four surface-inserted permanent magnet synchronous motors (SPMSMs) which have different surface-inserted permanent magnets. Each layer of the interior permanent magnets of the PMASynRM is transformed into a new equivalent surface-inserted permanent magnet whose equivalent thickness needs to be defined by the magnetic equivalent circuit method due to iron bridge saturation effects. Based on superposition principle and the solution of the Laplace’s or Poisson’s field equation, the distribution characteristics of the radial and tangential magnetic flux density are obtained for PMASynRMs. The slotting effect is considered by a complex relative permeance function. To confirm the accuracy of the proposed analytical modeling method, the analytical solutions of magnetic flux density and cogging torque have been compared with Finite Element Method (FEM) simulation results. The root mean square errors of radial and tangential magnetic flux density between analytical and FEM results are 0.000553 and 0.0000916 respectively. The results indicate that the proposed analytical modeling method can consider iron bridge saturation effects effectively, which is suitable for performance predictions and parametric studies of PMASynRMs.&lt;/div&gt;&lt;/div&gt;

Quasi-3-D Nonlinear Analytical Modeling of Magnetic Field in Axial-Flux Switched Reluctance Motors

Analytical modeling (AM) of the magnetic field for axial-flux switched reluctance motors (AFSRMs), considering three-dimensional (3-D) features and nonlinear saturation effects, remains to be a knotty problem. This paper proposes a quasi-3-D nonlinear AM method to predict magnetic field distributions and electromagnetic performances of an AFSRM. Firstly, the harmonic modeling technique is applied to obtain the spatiotemporal distribution characteristics of the axial and tangential magnetic flux density at the mean radius. Secondly, the nonlinearity of the soft magnetic material in teeth is considered by an adaptive convergence rate algorithm. Finally, a radial dependence function is formulated to extend the solution of the annular section to any point in the 3-D space of the AFSRM. To confirm the accuracy of the proposed method, the analytical solutions of magnetic flux density and electromagnetic torque have been compared with FEM simulation results. Meanwhile, an additional validation has been done for the stability of this nonlinear AM method under severe saturation conditions. At last, the reasonable selection of the harmonic truncation order number has been discussed to reach a good balance between the accuracy and time cost. The quasi-3-D nonlinear AM method can consider the curvature and edge effect as well as the saturation effect effectively, which is suitable for performance predictions and parametric studies of AFSRMs.