Analytical Calculation Of Magnetic Field Research Articles

Analytical Calculation of Magnetic Field and Analysis of Rotor Permeability Effects on Permanent Magnet Synchronous Motor with Fractional Slot Concentrated Winding

Accurate calculation of the flux and the magnetic field distribution of fractional slot concentrated winding permanent magnet synchronous motor (FSCW PMSM) is the basis for motor performance analysis, and rapid calculation is key. In this paper, to solve the problem of difficult modeling and accuracy guarantee of the flux linkage differential method, a method is proposed to calculate the flux and the no-load back EMF by the slotless subdomain model. By introducing the leakage flux calculation link, the calculation accuracy is improved, the analytical method results are compared with the finite element method results, and the effectiveness of the proposed method is verified. On this basis, the nonlinear variations of the magnetic field and the no-load back EMF with rotor permeability are determined, and the influence mechanism of rotor length and rotor permeability on the main magnetic circuit is revealed. Finally, an experiment of the prototype is carried out, and the correctness and accuracy of the analytical method and the finite element method is verified by comparing with the experimental results.

Analytical Calculation of Magnetic Field and Electromagnetic Performance for Permanent Magnet Assisted Synchronous Reluctance Motors Considering Saturation Effect

Analytical Calculation of Magnetic Field and Electromagnetic Performance for Permanent Magnet Assisted Synchronous Reluctance Motors Considering Saturation Effect

Analytical calculation of magnetic field in surface-mounted permanent-magnet vernier motors

This paper proposes an analytical method to calculate the on-load magnetic field, Back electromotive force (BEMF) and torque of the surface-mounted permanent-magnet vernier machine (SMPMVM) accounting for slots, tooth-tips, flux modulation pole slots (FMPS) and the shape of magnet. The on-load magnetic field is predicted according to the surface-current method of permanent magnet, subdomain model and the superposition principle. BEMF and torque are calculated based on the magnetic field. The results show that THD of open-circuit and on-load radial flux density in the SMPMVM with concentric magnet poles is smaller than that in the conventional SMPMVM with eccentric magnet poles. 30th and 50th harmonic orders are obvious between two motors. Moreover, the peak cogging torque of the motor with concentric magnet poles is almost six times of the peak cogging torque of motor with eccentric magnet poles. The finite-element and experimental results confirm that the developed analytical method has high accuracy for predicting the magnetic field, BEMF, cogging torque and on-load electro-magnetic torque of SMPMVM with different shape of magnet.

Analytical calculation of magnetic field of double‐stator permanent magnet spherical motor considering cogging effect and edge effect

A new type of double-stator permanent magnet spherical motor (DSSRPMSM) is proposed. Compared with most existing spherical motors, this motor uses a large number of stator iron cores, which can generate larger magnetic flux density and significantly improve torque capacity. The proposed DSSRPMSM can continuously rotate, swing and spiral, and can be used in the multi-degree-of-freedom motion fields of industrial robot joints, moment gyroscopes, panoramic photography tables and so on. Because the motor has the dual characteristics of rotary motor and arc linear motor, the comprehensive effects of stator slotting and stator iron core breaking should be considered. Cylindrical and trapezoidal PM poles are equivalent to dihedral PM poles, and stator coils are equivalent to PM pole models. Analytical models of PM pole magnetic field and stator magnetic field in a spherical coordinate system are established, and the air gap magnetic flux density under unequal magnetic potential boundary conditions is calculated by conformal transformation. The analytical calculation method proposed is consistent with the results of finite element method (FEM) simulation, and the experimental test further verifies the effectiveness and accuracy of this method.

Semi-Analytical Calculation of the Unsaturated Magnetic Field Distribution of a Slotted Spoke-Type Interior Permanent Magnet Machine With Conformal Mapping Method

The performances of an electric machine are closely related to magnetic field, and the magnetic field calculation is the basic work of machine design and optimization. In slotted spoke-type interior permanent magnet (IPM) machines, the analytical calculation of magnetic field is complicated because the boundary of machine is difficult to model. Therefore, this article introduces a conformal mapping (CM) method to calculate the magnetic field semi-analytically. First, the interior magnet is transformed into the surface-mounted magnet to reduce the complexity of boundary conditions. The air-gap magnetic field of the slotless spoke-type IPM machine is calculated by using the boundary conditions of the transformed surface-mounted permanent magnet machine. Then, based on the magnetic field of the slotless air gap, the magnetic fields of the slotted air gap and teeth are also calculated by the CM method. All the semi-analytically calculated magnetic fields are directly verified by the FEM simulation and indirectly verified by the comparison of torque and back EMF. In addition, the comparison of computation time between the semi-analytical method and the FEM shows that the semi-analytical method is time-saving.

Rapid Analytical Calculation of Magnetic Field and Critical Current Distributions in HTS Magnets

For the design of superconducting magnets, the magnetic field and critical current distributions are usually calculated based on finite element software such as COMSOL, ANSYS, etc. These software are necessary for accurate structure modeling and field calculation, but they occupy large memory space and comsume long simulation time. Furthermore, they are not easy to use. To achieve an easy-to-implement solution for rapid magnet field and critical current calculations, this paper investigates three types of analytical calculating methods, and builds an autonomously-operated calculating application program (APP) for the uses in various superconducting magnets.

Analytical magnetic field calculation for flat permanent-magnet linear machines with dual-rotor by using improved two-dimensional hybrid analytical method

PurposeThis paper aims to propose an improved two-dimensional hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain technique and the magnetic equivalent circuit (MEC).Design/methodology/approachThe magnetic field solution is obtained by coupling an exact analytical model (AM), calculated in all regions having relative permeability equal to unity, with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff’s current law) in ferromagnetic regions. The AM and MEC are connected in both axes (x, y) of the (non-)periodicity direction (i.e. in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead of the MEC characterized by an equivalent magnetomotive force (MMF) located in slots, teeth and yokes.FindingsIt is found that whatever the iron core relative permeability, the developed HAM gives accurate results for no- and on-load conditions. The finite-element analysis demonstrates excellent results of the developed technique.Originality/valueThe main objective of this paper is to make a direct coupling between the AM and MEC in both directions (i.e. x- and y-edges). The current density distribution is modeled by using Maxwell’s equations instead of the MEC and characterized by an MMF.

Calculation, design and test results of 3 kW fully HTS electric machine

Superconducting (SC) electrical machines could affect different industries due to their high power density. The most promising of them are fully superconducting machines. In the paper whole cycle of development of fully high temperature superconducting electrical machine is described: analytical calculation of magnetic field in the active zone of the machine, finite element modeling, some design features and experimental research of small-scale prototype. It is shown that theoretical and experimental results are in good correlation. Developed approaches could be used to develop high-power machines.

2-D and 3-D Analytical Calculation of the Magnetic Field and Levitation Force Between Two Halbach Permanent Magnet Arrays

As we know, the analytical calculation of magnetic field and magnetic force has important guiding significance for the optimal design of the size and structure of a magnet. At present, the magnetic field and magnetic force between two permanent magnet (PM) monomers have been described by effective analytical models. However, the magnetic field strength and magnetic force generated by two PM monomers are limited and cannot meet the requirements of a PM levitation system with high magnetic field strength and large levitation force. To this end, this article establishes analytical calculation models of magnetic field and levitation force between two Halbach PM arrays. First, on the basis of Ampere molecular circulation hypothesis, the 2-D analytical model of magnetic field was established based on the surface current method; on the basis of magnetic charge theory, the 3-D analytical model of magnetic field was established based on the magnetic charge method. Second, based on the analytical models of magnetic field, the 2-D and 3-D analytic models of levitation force were derived by virtual work method, respectively. Numerically, the results of two analytical models of magnetic field and two analytical models of levitation force have been compared to verify the accuracy of the models. At the same time, the 2-D and 3-D finite element simulation models of magnetic field and levitation force were established, respectively, and the accuracy of the analytical models were verified again. The results show that the analytical models established in this article is effective and can be used to guide the design and optimization of the magnet composed of two Halbach arrays.

Analytical Calculation of Magnetic Field in Fractional-Slot Windings Linear Phase-Shifting Transformer Based on Exact Subdomain Model

Fractional-slot windings linear phase-shifting transformers (FW-LPSTs) are a new type of transformer that can be used as an important component of multi-rectifier and multi-inverter systems. The FW-LPSTs are proposed for the first time, and few scholars have studied their magnetic field. However, accurate calculation of magnetic field distribution of the FW-LPSTs is the premise of the optimal design of the ontology, and the establishment of an accurate analytical model which remains a challenging task is the key to solving the magnetic field distribution. In view of the limitation of traditional analytical theory in solving the magnetic field, the FW-LPST model based on the exact subdomain method is proposed to obtain the exact magnetic field distribution. Considering the influences of the permeability and the structural parameters of the slot subdomain and the interaction of all slots on the distribution of the magnetic field, the governing equations of the air gap and slot subdomains are established using magnetic vector potential as the variable. According to the boundary conditions of each subdomain, all equations of the boundary condition are listed based on the Fourier series method. Finally, the vector magnetic potential and open-circuit magnetic flux density distribution of each subdomain are solved. The model accurately analyzes the influence of the cogging effect on the magnetic field distribution. The inductances of the primary side and the induced potentials of the secondary side are solved using the magnetic flux linkage method. The accuracy of the proposed analytical model is verified by comparison of the results obtained with those obtained by the finite element method.

Analytical calculation of magnetic field of bearingless flux‐switching permanent‐magnet machine based on doubly‐salient relative permeance method

A doubly-salient relative permeance method is presented herein to predict the magnetic field of bearingless flux-switching permanent-magnet machines (BFSPMMs). Firstly, the subdomain model method is used to compute the magnetic field of slotless BFSPMMs. Then, the slotting effect of the stator and rotor is obtained by the doubly-salient relative permeance method. By combining the two above, the air-gap magnetic field of slotted BFSPMMs can be obtained. The doubly-salient relative permeance method is based on the theory of the subdomain model method. The whole doubly-salient structure is divided into several subdomains, and the Laplace equations for subdomains are established. Then, according to the boundary conditions between subdomains and the core, and the continuity conditions between adjacent subdomains, the equations are solved to calculate the slotting effect. Based on the proposed analytical model, the flux density and electromagnetic performances including back-electromotive force (EMF), torque, and suspension force are predicted and compared with the finite element method results. Furthermore, the back-EMF of the prototype motor is measured and the suspension experiments are carried out based on the analytical method. The comparison results and experiment results verify the validity of the analytical method.

A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

Analytical Modeling of 3-D Magnetic Field and Performance in Magnetic Lead Screws Accounting for Magnetization Pattern

Mounted with helical magnets, the magnetic lead screw (MLS) could realize contactless conversion between rotation and linear motion. Since the magnetic field in the MLS is essentially three dimensional (3-D), previous 2-D analytical magnetic field calculation methods fail to behave well in the accuracy, while 3-D numerical methods suffer from poorer efficiency in computation time. In this article, an analytical model is developed to predict the 3-D magnetic field distribution and the electromagnetic performance of the MLS. Both radial and parallel magnetizations of the helical magnets are considered. It is shown that the air-gap magnetic field distribution is closely dependent on the magnetization pattern of helical magnets. Both 3-D finite-element (FE) simulation and prototype experiment are performed to validate the accuracy of the proposed analytical model. The analytical results are in good agreement with those by FE analysis and experiment, respectively. And it is highlighted that the magnets magnetized in parallel result in the deformation of thrust force and torque characteristics. Finally, the impact of the number of parallel magnetized magnets on the distortion of MLS performance is discussed. The work can be served as a valuable tool for precise and fast optimization design of the MLS.

Analytical calculation of magnetic field in surface-mounted permanent-magnet machines with air-gap eccentricity

PurposeThis paper aims to present an analytical method, which combines the complex permeance (CP) and the superposition concept, to predict the air-gap magnetic field distribution in surface-mounted permanent-magnet (SMPM) machines with eccentric air-gap.Design/methodology/approachThe superposition concept is used twice; first, to predict the magnetic field distribution in slot-less machine with eccentric air-gap, the machine is divided into a number of sections. Then, for each section, an equivalent air-gap length is determined, and the magnetic field distribution is predicted as a concentric machine model. The air-gap field in the slot-less machine with eccentricity can be combined from these concentric models. Second, the superposition concept is used to find the CP under eccentricity fault. At this end, the original machine is divided into a number of sections which may be different from the one for slot-less magnetic field prediction, and for each section, the CP is obtained by equivalent air-gap length of that section. Finally, the air-gap magnetic field distribution is predicted by multiplying the slot-less magnetic field distribution and the obtained CP.FindingsThe radial and tangential components of the air-gap magnetic flux density are obtained using the proposed method analytically. The finite element analysis is used to validate the proposed method results, showing good agreements with the analytical results.Originality/valueThis paper addresses the eccentricity fault impact upon the air-gap magnetic field distribution of SMPM machines. This is done by a combined analysis of the complex permeance (CP) method and the superposition concept. This contrasts to previous studies which have instead focused on the subdomain method.

Semi-Three-Dimensional Analytical Torque Calculation and Experimental Testing of an Eddy Current Brake With Permanent Magnets

This paper presents torque analysis and testing of an eddy current brake with permanent magnets using semi-three-dimensional (3-D) analytical magnetic field calculations. The magnetic field solutions are obtained by considering the eddy current reaction using a 2-D magnetic vector potential and 3-D case by a simple and effective axial dependence modeling. The magnetic torque is also determined from these solutions. A finite-element method (FEM) is employed to validate the analytical magnetic calculations. The braking torque measurement is experimentally verified to validate the analytical study. From the experimental study, we obtain analytical and 3-D FEM results of braking torque with thermal behavior, and these are in good agreement with the experimental results.

DETERMINATION OF ANALYTICAL CALCULATION ERROR OF MAGNETIC FIELD OF HIGH-VOLTAGE CABLE LINES WITH TWO-POINT BONDED CABLE SHIELDS CAUSED BY NON-UNIFORM CURRENT DISTRIBUTION IN THE SHIELDS

This paper deals with the determination of analytical calculation error of magnetic field of high-voltage cable lines in two-point bonded cable shields caused by non-uniformity of the current distribution in the shields. The relative error is determined by comparing numerical calculation of magnetic field obtained in the COMSOL Multiphysics software with the analytical one. It is shown that the maximum value of relative error does not exceed 8 %. The obtained error values are verified by testing the numerical calculation and confirmed by results of experiment. In paper proves the correctness of the analytical calculation of magnetic field of cable lines at the points of its normalization, which is carried out without taking into account the non-uniform current distribution in the cable shields.

ANALYTICAL CALCULATIONS OF ELECTROMAGNETIC QUANTITIES FOR SLOTTED BRUSHLESS MACHINES WITH SURFACE-INSET MAGNETS

In this paper, two-dimensional (2-D) analytical magnetic field calculations are used to compute crucial quantities of Brushless permanent-magnet (PM) machines with surface-inset PMs. The analytical magnetic field distribution is based on the subdomain technique in which the slotting and tooth-tip effects have been considered. It includes both different magnetization patterns (e.g., radial, parallel and Halbach) and different spatial distribution of winding (e.g., concentrated and distributed with one or more layers). The saturation effect of the magnetic circuit is neglected. In this investigation, the phase and line induced back electromotive force (EMF) waveforms, electromagnetic/cogging/reluctance torques, self-/mutual-inductances and unbalanced magnetic forces (UMFs) have been analytically calculated. The analytical expressions can be used for Brushless machines having surface-inset PMs with any radius-independent magnetization pattern. In this study, two slotted Brushless PM machines with surface-inset PMs have been selected to evaluate the efficacy of the analytical expressions by comparing the results with those obtained by the finite-element method (FEM). One of the case studies is a 9-slots/8-poles Brushless DC (BLDC) machine with radially magnetized PMs, non-overlapping all teeth wound winding and six-step rectangular armature current waveforms. The other is a 15-slots/4-poles Brushless AC (BLAC) machine with Halbach magnetization PMs, double-layer overlapping winding and sinusoidal armature current waveforms.

Analysis on the Pitching Moment in Permanent-Magnet Linear Synchronous Motor for Linear Motion Stage Systems

This paper presents the characteristic analysis and experiment of pitching moment in a high-precision permanent-magnet linear synchronous motor. The pitching moment is analyzed according to suggested strategy; therefore, analytical solutions for magnetic fields generated by PMs are derived based on the analytical magnetic field calculation in terms of a 2-D polar coordinate system. The analytical solution of each subdomain (PM, air gap, slot, slot opening, and end region) is derived, and the field solution is obtained by applying the boundary and interface conditions between the subdomains. The magnetic force is determined based on the magnetic field analysis results. Finally, the predictions are compared with the measured data to confirm the validity of the analysis methods presented in this paper.

Analytical Magnetic Field Calculation of Coaxial Magnetic Gear With Flux Concentrating Rotor

In this paper, the analytical model for coaxial magnetic gear (CMG) having a flux concentrating rotor is presented using 2-D space harmonic analysis (SHA). Comparing the conventional CMG with surface-mounted permanent magnet (SPM) on both rotors, the differences are described in terms of governing equations, magnetizations of PMs, general solutions, and boundary conditions. To apply the superposition principle, the analytical model is divided into two cases, such as model for SPM rotor and model for flux concentrating rotor with inset PM. Based on the proposed SHA, the radial and tangential components of flux densities at both air-gap regions are calculated, and the pull-out torques of both rotors are also determined by the Maxwell stress tensor. The results of SHA are in good agreement with the results obtained from finite-element analysis.

Characteristic Analysis of Tubular-Type Permanent-Magnet Linear Magnetic Coupling Based on Analytical Magnetic Field Calculations

This paper presents a characteristic analysis of a tubular-type permanent-magnet (PM) linear magnetic coupling (TLMC) based on analytical magnetic field calculations. First, the analytical solutions for magnetic fields generated by PM are derived on the basis of a magnetic vector potential and a 2-D polar coordinate system. Next, the magnetic force is also determined on the basis of these solutions. The magnetic field and force obtained by the analytical method are compared with those obtained by the finite-element analysis and experiment, which validates the analysis methods presented in this paper.