Simplified models including eddy currents for laminated structures (original) (raw)
Eddy-Current Losses in Laminated Cores and the Computation of an Equivalent Conductivity
IEEE Transactions on Magnetics, 2000
This paper deals with the computation of eddy-current losses in laminated cores. In the first part we recall some approximate formulas existing in the literature and implemented in many electromagnetic computer packages. Then we assess their accuracy by making comparisons with the exact loss values obtained by numerical solution of the quasi-static Maxwell equations. In the second part we introduce a definition of an equivalent electric conductivity allowing us to replace the laminated core with a homogeneous isotropic or anisotropic medium. We compare the values of this equivalent conductivity with those obtained from some approximate formulas.
A Linear FEM Benchmark for the Homogenization of the Eddy Currents in Laminated Media in 3D
IFAC Proceedings Volumes, 2012
The simulation of eddy current losses in laminated iron cores by the finite element method is of great interest in designing of electrical machines. Modeling each lamination individually by the finite element method requires many elements and leads to an inappropriately large system of equations. A two-scale finite element method is proposed to efficiently compute the losses in laminated media with linear material properties. The approach for the two-scale finite element method based on the magnetic vector potential A is described. Its accuracy and the computational costs are evaluated by a representative linear finite element benchmark.
MOR for the MSFEM of the Eddy Current Problem in Linear Laminated Media
SNE Simulation Notes Europe
The multiscale finite element method has proven to be a powerful method in the simulation of eddy currents in laminated cores. However, the resulting equation systems of the problems relevant in electrical engineering are still too large to be solved conveniently. The use of model order reduction methods to overcome this shortcoming is obvious. The feasibility to exploit the specific approach of the multiscale finite element method in terms of a structural model order reduction method has been studied in this work. A small numerical example shows satisfactory results.
Journal of Applied Physics, 2010
A theoretical model is presented for the low-frequency magnetoelectric ͑ME͒ effect in three-layered magnetostrictive-piezoelectric laminates. The model considers both the laminate finite size and the detection circuitry loading ͑closed-circuit conditions͒. The model development is based on a system of electroelasticity and magnetoelasticity equations and takes into account the boundary conditions at the inner and outer surfaces of the laminate. An averaging method is used to estimate the effective parameters of the laminate materials. The ME voltage coefficient for transverse fields is obtained theoretically. The obtained solution allows us to set up the laminate equivalent electrical circuits and to find their electrical parameters in terms of the physical properties of the laminate and its geometry.
Comparison of the field methods in homogenization of the laminated magnetic cores
International Journal of Applied Electromagnetics and Mechanics, 2020
The comparison of three field methods for homogenization of the laminated cores has been presented in this work. As a result, the equivalent electrical conductivity and magnetic permeability for the geometry of the core entire body were obtained for magnetic field 3D modelling. The first method is an iterative homogenization method (IHM) connected with the field solution, whereas the two others are based on analytical expressions arising from the Maxwell's equations. For 3D field solution, Finite Element numerical model including eddy currents under various frequency values was used in IHM. The model is based on a combination of the total and the reduced magnetic potentials. For comparison to our IHM, the two analytical approaches for core homogenization were used, as well. To calculate the stray losses in the homogenized laminated C-core these three approaches have been executed, as a case study. Applying suitable simplifications, according the methods of analytical homogenization, between the analytically calculated and measured values of the core losses high differences have been obtained. For the cores from amorphous strip, the analytical methods are inappropriate and our method, though iteratively implicit, gives significantly better equivalent parameters for the laminated C-core.
Alternating electromagnetic field computation in laminated cores
IEEE Transactions on Magnetics, 1983
A finite element method is developed to compute alternating electromagnetic fields in laminated cores. The method is applied to a simplified model problem in order to evaluate power losses in mitered overlap joints. The influence of eddy currents on the magnetic field distribution in the neighborhood of the mitered joints is discussed, The power losses are evaluated for cores with different overlap lengths.
Three-Dimensional–Two-Dimensional Coupled Model for Eddy Currents in Laminated Iron Cores
IEEE Transactions on Magnetics, 2000
Eddy currents due to magnetic flux perpendicular to the sheets of a lamination iron core are represented on a number of 2D slice models, which are embedded in a 3D model of the entire device using a multi-scale technique. The choice of a different spatial resolution enables to attain an advantageous convergence of the discretization error for the eddy-current power losses, compared to a standard modelling technique using an anisotropic surrogate material.
Calculation of eddy currents and associated losses in electrical steel laminations
1999
Starting from the well known analytical formula for the eddy current losses in electrical steel laminations, saturation and edge effects are studied by means of 1D and 2D finite element models of a single lamination. A novel method for directly including the laminated core energy dissipation in a time stepped 2D model of a complete (rotating) machine is proposed. By way of example the method is applied to a tooth model with enforced flux waveforms.
Energies
The following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computational complexity. The verification of the obtained data correctness is based on a detailed balance of energy and power in the investigated system. The correctness of the obtained results was also confirmed by comparing them with the results included in norms that describe the losses in laminated sheets. The presented approach is based on expressing the equivalent permeability of transformer metal sheets by using RC or RL circuits. The impedances of these circuits are treated as the transmittance of Infinite Impulse Response filters (IIR) of the Laplace s variable. In this form they are implemented in direct calculations of the dynamics of electric machines based on field-circuital models, u...
Magnetic Field-Based Eddy-Current Modeling for Multilayered Specimens
IEEE Transactions on Magnetics, 2007
Eddy-current inspection for nondestructive evaluation has traditionally been investigated in terms of coil impedance signals via theoretical and experimental methods. However, advanced eddy-current techniques use solid-state sensors such as Hall devices, giant magnetoresistive sensors, anisotropic magnetoresistive sensors, and superconducting quantum interference devices for magnetic field measurement to achieve better sensitivity and high temporal and spatial resolution in material evaluation and characterization. Here, we review the Dodd and Deeds integral model and use the truncated region eigenfunction expansion (TREE) method for computation of the magnetic field. This results in series expressions instead of integral ones. Thus, the computation is both simplified and speeded up so that it becomes convenient for solving one-dimensional eddy-current inverse problems. We compare the theoretical results from the analytical model with the results from a numerical simulation based on the finite-element method in terms of accuracy and computation time.
MSFEM for the Eddy Current Problem in a Laminated Core Including Hysteresis
IEEE Transactions on Magnetics, 2019
A multiscale finite element method is extended to allow for materials with hysteresis. The method is developed for an eddy current problem, coupled with a network. As an example, a laminated toroidal transformer core is considered. Utilizing the symmetry of the domain, the problem can be rewritten as a two-dimensional one. The multiscale method shows good results compared to the reference solutions for both the nonlinear problem with magnetization curve and with the inclusion of hysteresis by the Preisach model, while preserving its main advantages of drastically reducing the number of degrees of freedom by utilizing a coarse mesh that does not resolve each single iron sheet. Both the multiscale solution and the reference solution are compared to measurement data. It is demonstrated that the inclusion of hysteresis is necessary in order to achieve a good approximation of the measurement data, which is used to identify both the magnetization curve and the parameters for the Preisach model.
Inclusion of Eddy Currents in Laminations in Two-Dimensional Finite Element Analysis
IEEE Transactions on Magnetics, 2000
The inclusion of eddy currents in electrical steel sheets in a two-dimensional (2-D) finite element analysis is studied. For the eddycurrent modeling of the sheets a so-called one-dimensional (1-D) approach is applied. Two different techniques for representing the 1-D eddy-current solution within the 2-D field equations are shown. The properties of the two techniques are analyzed by utilizing two simple example geometries. The implementations of the computational algorithm of the coupled 2-D-1-D method are verified by analytical equations. A proper coupling method that accords with the computation results is suggested.
3-D Eddy Current Modelling of Steel Laminations to Analyze Edge Effects
2016
The correct estimation of iron losses is still a challenging task in the numerical analysis of electrical machines. For estimation of eddy current losses, various formulations based on 1D and 2-D models are mentioned in literature which neglect effect of current density at the edges of steel laminations. This paper compares such simplified 1-D/2-D eddy current loss model with a 3-D model to analyze the effect of edges on eddy current loss calculation. Thickness of the lamination along with frequency of field excitation were determined where considerable deviation in eddy current losses among loss models is observed due to edge assumption.
Progress In Electromagnetics Research M, 2021
The aim of this paper is to develop a hybrid modeling approach based on direct coupling between the finite element method (FEM) and the partial element equivalent circuits method (PEEC). Through this FEM-PEEC approach, we can efficiently compute the three-dimensional eddy current distribution created by a rectangular coil (exciting coil) in conductive and magnetic structures having heterogeneous dimensions. Magnetic field created by the rectangular coil is given by calculating quasistatic Green’s function integrals. In goal to construct rectangular coil, the calculation is made for elementary parallelepipedic conductors oriented respectively in x and y directions. By this manner, three possible configurations are proposed and compared to show errors, especially in corners. By only meshing the active parts of the domain (without air region), we confirm through the issued results that the proposed methodology contributes to accelerate the execution time while maintaining the precision...
Modeling of Losses Due to Inter-Laminar Short-Circuit Currents in Lamination Stacks
Electrical, Control and Communication Engineering
ABSTRACT The cores of electrical machines are generally punched and laminated to reduce the eddy current losses. These manufacturing processes such as punching and cutting deform the electrical sheets and deteriorate its magnetic properties. Burrs are formed due to plastic deformation of electrical sheets. Burr formed due to punching on the edges of laminated sheets impairs the insulation of adjacent sheet and make random galvanic contacts during the pressing of stacked sheets. The effect of circulating current occurs if the burrs occur on the opposite edges of the stacks of laminated sheets and incase of bolted or wielded sheets, induced current return through it. This induced current causes the additional losses in electrical machine. The existence of surface current on the boundary between two insulated regions causes discontinuity of tangential component of magnetic field. Hence, based on this principle, the boundary layer model was developed to study the additional losses due to galvanic contacts formed by burred edges. The boundary layer model was then coupled with 2-D finite element vector potential formulation and compared with fine mesh layer model. Fine mesh layer model consists of finely space discretized 950028 second order triangular elements. The losses were computed from two models and were obtained similar at 50 Hz. The developed boundary layer model can be further used in electrical machines to study additional losses due to galvanic contacts at the edges of stator cores.
2021
This paper presents a new integro-differential coupling between partial equivalent electrical circuits (PEEC) and finite difference method (FDM) taking into account the magnetization effect. This coupling is intended for thin plates having simultaneously significant conductive and magnetic properties in the presence of exciting coils of complex topologies. These cases exist in eddy current nondestructive testing (ECNDT), eddy current separation, induction or levitation melting devices, and more other applications. The choice of FDM, is in relation with rectangular surfaces generated by numerical meshes leading to mathematical integrations of magnetic and electrical quantities with independent variables, unlike more complicated forms of surfaces generated by finite element method (FEM) or others. Fully successful analytical expressions have been realized and implemented in overall coupling process. The PEEC method is mainly used to calculate the magnetic field applied to the nodes of...
Eddy current simulation in thick cylinders of finite length induced by coils of arbitrary geometry
Journal of Magnetic Resonance, 2010
Eddy currents are inevitably induced when time-varying magnetic field gradients interact with the metallic structures of a magnetic resonance imaging (MRI) scanner. The secondary magnetic field produced by this induced current degrades the spatial and temporal performance of the primary field generated by the gradient coils. Although this undesired effect can be minimized by using actively and/or passively shielded gradient coils and current pre-emphasis techniques, a residual eddy current still remains in the MRI scanner structure. Accurate simulation of these eddy currents is important in the successful design of gradient coils and magnet cryostat vessels. Efficient methods for simulating eddy currents are currently restricted to cylindrical-symmetry. The approach presented in this paper divides thick conducting cylinders into thin layers (thinner than the skin depth) and expresses the current density on each as a Fourier series. The coupling between each mode of the Fourier series with every other is modeled with an inductive network method. In this way, the eddy currents induced in realistic cryostat surfaces by coils of arbitrary geometry can be simulated. The new method was validated by simulating a canonical problem and comparing the results against a commercially available software package. An accurate skin depth of 2.76 mm was calculated in 6 min with the new method. The currents induced by an actively shielded x-gradient coil were simulated assuming a finite length cylindrical cryostat consisting of three different conducting materials. Details of the temporal-spatial induced current diffusion process were simulated through all cryostat layers, which could not be efficiently simulated with any other method. With this data, all quantities that depend on the current density, such as the secondary magnetic field, are simply evaluated.
Journal of Applied Physics, 2000
In this article, the diffusion of electromagnetic fields into a ferromagnetic lamination is numerically studied by means of an error-based numerical method. This technique has been developed so far only for the case of nonhysteretic constitutive relations. The generalization to the hysteretic case requires a modification of the technique in order to take into account the evolution of the ''magnetization state'' of the media. Numerical computations obtained by using this approach are reported and discussed.