Analytical Solution For Magnetic Field Research Articles

Analytical Solution of Magnetic Field in High-Speed Permanent Magnet Synchronous Machines With Novel Composite Rotor

Analytical Solution of Magnetic Field in High-Speed Permanent Magnet Synchronous Machines With Novel Composite Rotor

An exact, time-dependent analytical solution for the magnetic field in the inner heliosheath

We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic divergence constraint. To this end, we assume that the magnetic field is frozen into a plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. Furthermore, we make use of the ideal Ohm’s law for the magnetic vector potential and the electric scalar potential. By employing a suitable gauge condition that relates the potentials and working with a characteristic coordinate representation, we thus obtain an inhomogeneous first-order system of ordinary differential equations for the magnetic vector potential. Then, using the general solution of this system, we compute the magnetic field via the magnetic curl relation. Finally, we analyze the well-posedness of the corresponding Dirichlet-type initial-boundary value problem, specify compatibility conditions for the initial-boundary values, and outline the implementation of initial-boundary conditions.

Nonlinear Analytical Solution of Magnetic Field and Performances of a Spoke Array Vernier Permanent Magnet Machine

This article presents a nonlinear analytical (NA) solution based on subdomains for predicting magnetic field and performances of a spoke array vernier permanent magnet (SAVPM) machine which has spoke array type permanent magnet (PM) excitation. On one hand, equivalent current sheets replace tangentially magnetized PMs to make the magnetic vector potential in the region with PMs satisfy a Laplace's equation, which simplifies the problem and reduces the workload of numerical calculation. On the other hand, in contrast to the existing literature, regions of soft-magnetic material such as a tooth and a rotor pole are subdivided into small pieces, and are no longer a whole with a single permeability for considering local magnetic saturation. Poisson's and Laplace's equations with the given permeability of soft-magnetic material are analytically solved by separation technique of variables in seven subdomains, and nonlinear iteration is used to determine the solution of NA and update soft-magnetic material permeability. NA solves the magnetic field and performances of a SAVPM machine. Frozen permeability method (FPM) is used to determine PM flux linkage and d-axis inductance under load. Results from the NA model have been compared with those from FEA and experiments.

Analytical solution for magnetic field of cylindrical defect in eddy current nondestructive testing

In metal components, a defect frequently causes the failure of the components and results in serious accidents consequently. Eddy current nondestructive testing method is one of the most effective testing approaches to quantitatively monitor the defects both in non-ferrite metal and in ferrite metal. Therefore, knowledge of the magnetic field is necessary to deeply understand the mechanism of eddy current nondestructive technique in defect characterization. In this paper, an analytical expression for the magnetic field for a cylindrical defect in metal in eddy current testing system is proposed by solving the partial differential equations. Firstly, a conductive metal plate with a cylindrical defect is modeled for the cylindrical coil with rectangular cross-section, and the analytical expression to the magnetic potential vector is obtained. Then, the series form expressions are extended to calculate the axial component of magnetic induction intensity Bz and is computed on the MATLAB platform. Finally, a finite element model is setup to validate the proposed analytical expression for the magnetic field. The results show that the magnetic field calculated by the analytical method is in good agreement with that calculated by finite element method, and the calculation efficiency of the analytical method is higher than that of FEM. The proposed expressions not only can be readily used to investigate the quantitative relationship of the cylindrical defects in a conductive metal, but also it is expected to be extended to seek the theoretical expression for the elliptic defect and also for the natural defect in key structures (e.g. oil pipe, rail track, iron bridge, oil tank, ocean ship) by using (pulsed) eddy current nondestructive technique.

Slotless tubular PM generator with dual quasi‐Halbach magnetized PM Array: Analytical and numerical magnetic field analysis

AbstractIn this paper, an initial design and analytical electromagnetic field solution for Slotless and Dual Quasi‐Halbach (DQH) Permanent Magnet mover is proposed for reciprocating free piston alternator application. Utilizing presented analytical magnetic field solution, Air‐Gap magnetic flux characteristic, and generated voltage are estimated. Using 3‐D finite‐element method (FEM) proposed structure numerically investigated and obtained numerical results employed to confirm the derived analytical models. The analytical results are compared with FEM and show excellent agreement. In order to determine output voltage and power characteristics, the load testing has been performed by a resistive variable load. The obtained results from FEM analysis and analytical magnetic field solution show an enhancement in the proposed alternator performance compared with the alternator with Halbach magnetized configuration, by improving provided power.

Analytical Solution of Magnetic Field in High Speed Surface Mounted Permanent Magnet Machine With Parallelly Magnetized Magnet Segments

Due to some limitations of permanent-magnet (PM) production and magnetizing technology, it is difficult to construct the large magnetic poles of high-power surface-mounted PM machines by using integral magnets. One simple solving scheme is that the large magnetic poles can be formed by several parallelly magnetized magnet segments. For the surface-mounted PM machines with parallelly magnetized magnet segments, this paper gives an accurate analytical solution of the magnetic field. First, in 2-D polar coordinates, the PM machine model is divided into three subdomains, and the magnetic field governing equations are established in each region. By adopting the theory of Fourier’s series and the method of separating variables, the solutions of the magnetic field are determined according to associated boundary conditions. Then, the proposed analytical model is compared with finite element method, and the results show that they have a good agreement. Based on the obtained magnetic field solution, the induced electromotive force of a designed PM machine is calculated, and the result is verified by experiment.

Energy and Material Efficient Noncircular Bore Bitter Magnets

Resistive Bitter magnets are still widely used to produce very high continuous magnetic fields. There exist a number of experiments/applications where the second dimension of the bore of Bitter magnets is not fully utilized and thus can be minimized accordingly. Evidently, a significant reduction of one of the dimensions of the bore should result in significant decrease in consumed power and/or coil material, typically with no reduction in applicable science. However, no efforts were mounted before to quantify the benefits, likely owing to the problem intricacy. Using an analytical solution for magnetic field and current density in homothetic elliptical bore coils and finite element analysis solutions for other shapes as well, we make up for the deficiency to a degree. Relevant structural mechanical aspects are viewed to complete the picture. In closing, possibilities to enhance the cooling efficiency of Bitter magnets are discussed, albeit very briefly.

Detent Force Minimization of Permanent Magnet Linear Synchronous Machines Using Subdomain Analytical Method Considering Auxiliary Teeth Configuration

This paper presents electromagnetic modeling and analysis of the detent force in a permanent magnet linear synchronous machine (PMLSM) according to auxiliary teeth configuration. Analytical solutions for magnetic fields generated by PMs are derived based on the Maxwell equation in terms of a 2-D Cartesian coordinate system. The magnetic vector potential of each subdomain (PM, air-gap, slot, and end region) is derived, and the field solution is obtained by applying the boundary and interface conditions between the subdomains. Based on the analytical solution, the magnetic force is derived by using the Maxwell stress tensor. All the analytical results were extensively validated using nonlinear finite-element analysis and experimental results. Using the proposed method, we investigated the influence of the machine parameters on the detent force. Therefore, the proposed method can be very useful in the initial design and optimization process of PMLSM for detent force analysis.

An Improved Analytical Model of the Local Interstellar Magnetic Field: The Extension to Compressibility

Abstract A previously published analytical magnetohydrodynamic model for the local interstellar magnetic field in the vicinity of the heliopause (Röken et al. 2015) is extended from incompressible to compressible, yet predominantly subsonic flow, considering both isothermal and adiabatic equations of state. Exact expressions and suitable approximations for the density and the flow velocity are derived and discussed. In addition to the stationary induction equation, these expressions also satisfy the momentum balance equation along stream lines. The practical usefulness of the corresponding, still exact, analytical magnetic field solution is assessed by comparing it quantitatively to results from a fully self-consistent magnetohydrodynamic simulation of the interstellar magnetic field draping around the heliopause.

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.

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.

Analytical Solution of Magnetic Field in Permanent-Magnet Eddy-Current Couplings by Considering the Effects of Slots and Iron-Core Protrusions

In this study, we propose an analytical model for studying magnetic fields in radial-flux permanent-magnet eddy-current couplings by considering the effects of slots and iron-core protrusions on the eddy currents. We focus on the analytical prediction of the air-gap field by considering the influence of eddy currents induced in conducting bars. In the proposed model, the permanent magnet region is treated as the source of a time-varying magnetic field and the moving-conductor eddy current problem is solved based on the resolution of time-harmonic Helmholtz equations. The spatial harmonics in the air gap and in slots, as well as the time harmonics are all considered in the analytical calculation. Based on the proposed field model, the electromagnetic torque is computed by using the Maxwell stress tensor method. Nonlinear finite element analysis is performed to validate the analytical model. The proposed model can be used for permanent-magnet eddy-current couplings with any slot-pole combination.

Coupled magnetic equivalent circuits and the analytical solution in the air-gap of squirrel cage induction machines

In this paper a new method is presented to couple an analytical magnetic field solution of the air-gap of an induction machine with magnetic equivalent circuits method used to model the rest of the machine. The proposed method eliminates the need for complex static and dynamic mesh generation process in the air-gap. Therefore, the modelling of rotor motion becomes simpler and more accurate.

Magnetic Field and Self-Inductance of a Race-Track Coil

In the superconducting magnetic levitation train, the race-track coil is often used for levitation or propulsion. However, it is difficult to analyze the magnetic field produced by the race-track coil which has linear and semicircular parts of exciting current. Therefore, the analytical solution of magnetic field by this coil has not been obtained yet. Then, in this letter, the exact theoretical analysis is carried out on magnetic field and self-inductance of a race-track coil. In addition, the validity of the theory is confirmed by comparing a measured value with a calculated one.

Coupling finite elements and analytical solution in the airgap of electric machines

A method for coupling an analytical magnetic field solution in the airgap of an electric machine with standard finite element equations used to model the rest of the machine is presented. The proposed method eliminates the need for finite elements in the airgap, thereby facilitating the modeling of rotor motion and allowing for higher accuracy in the airgap field solution. An example compares the accuracy of a standard finite element solution with one obtained from the proposed method, using a purely analytical solution as a reference. >