Johan Gyselinck

Calculation of eddy currents and associated losses in electrical steel laminations

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.

Multiphysics NVH Modeling: Simulation of a Switched Reluctance Motor for an Electric Vehicle

This paper presents a multiphysics modeling of a switched reluctance motor (SRM) to simulate the acoustic radiation of the electrical machine. The proposed method uses a 2-D finite-element model of the motor to simulate its magnetic properties and a multiphysics mechatronic model of the motor and controls to simulate operating conditions. Magnetic forces on the stator are calculated using finite-element analysis and are used as the excitation on a forced response analysis that contains a finite-element model of the motor stator structure. Finally, sound power levels are calculated using the boundary element method. Simulation results of the model are shown and compared with experimental measurements for a four-phase 8/6 SRM.

A 3-D magnetic vector potential formulation taking eddy currents in lamination stacks into account

A method is developed to take the eddy currents in lamination stacks into account with the finite-element method using the three-dimensional (3-D) magnetic vector potential magnetodynamic formulation. It consists in converting the stacked laminations into continuums with which terms are associated for considering the eddy-current loops produced by both parallel and perpendicular fluxes. Two levels of accuracy are proposed. The best one is based on an accurate analytical expression of the eddy currents and makes the method adapted to a wide-frequency range, i.e., even for low skin depths in the laminations.

Multi-slice FE modeling of electrical machines with skewed slots-the skew discretization error

The simulation of rotating electrical machines with skewed slots by means of a multi-slice FE model is studied. Particular attention is devoted to the ensuing skew discretization error. As an alternative to the commonly adopted uniform distribution of the cross-sections along the shaft, a Gauss distribution is proposed. The application to a squirrel-cage induction motor under various working conditions shows that the latter distribution produces a considerably smaller discretization error. The calculation results are also compared to experimental data.

A nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models

The authors present a novel nonlinear homogenization technique for laminated iron cores in three-dimensional (3-D) finite-element (FE) models of electromagnetic devices. The technique takes into account the eddy current effects in the stacked core without the need of modeling all laminations separately. A nonlinear constitutive magnetic law is considered. The system of nonlinear algebraic equations obtained after time discretization is solved by means of the Newton-Raphson scheme. By way of validation, the method is applied to a 3-D FE model of a laminated ring core with toroidal coil

Frequency-domain homogenization of bundles of wires in 2-D magnetodynamic FE calculations

A general approach for the frequency-domain homogenization of multiturn windings in two-dimensional (2-D) finite element (FE) calculations is presented. First, a skin and proximity effect characterization of the individual conductors, of arbitrary cross-section and packing, is obtained using a representative 2-D FE model. Herein, three excitation modes are considered, viz current and flux density in two perpendicular directions. In practical cases, the three modes are independent and the obtained frequency-dependent impedance and complex reluctivity tensor can be readily used in a FE model of the complete device. By way of example and validation, the method is applied to an inductor having an airgap and one of three different windings. The homogenized model produces global results (impedance versus frequency) that agree well with those obtained with a more precise FE model. In the latter, each turn of the winding is explicitly modeled and finely discretized.

A time-domain homogenization technique for laminated iron cores in 3-D finite-element models

The authors present a novel time-domain homogenization technique for laminated iron cores in three-dimensional (3-D) FE models of electromagnetic devices when using the magnetic vector potential formulation. The method is based on a polynomial orthogonal decomposition of the variation of the induction throughout the thickness of the laminations. The nonconstant components, due to skin effect, produce additional degrees of freedom and equations for the homogenized core. Insulating layers of finite width between the laminations (fill factor <1) are taken into account as well. A linear 3-D axisymmetric test case is considered. The results agree well with those obtained with the reference model, in which all laminations are finely discretized and the eddy currents are directly modeled.

Harmonic-balance finite-element modeling of electromagnetic devices: a novel approach

In this paper, a novel and easy-to-implement approach to the harmonic-balance finite-element modeling of electromagnetic devices is presented. The governing system of nonlinear algebraic equations is derived assuming an arbitrary (anisotropic) magnetic constitutive law. It is solved by means of the Newton-Raphson (NR) method, the elaboration of which is very simple thanks to the introduction of the differential reluctivity tensor. The method is validated by applying it to a three-dimensional and a two-dimensional voltage-driven model of a three-phase inductor. The convergence of the NR scheme and the accuracy of the obtained harmonic-balance current waveforms are studied.

Incorporation of a Jiles-Atherton vector hysteresis model in 2D FE magnetic field computations: Application of the Newton-Raphson method

This paper deals with the incorporation of a vector hysteresis model in 2D finite‐element (FE) magnetic field calculations. A previously proposed vector extension of the well‐known scalar Jiles‐Atherton model is considered. The vectorised hysteresis model is shown to have the same advantages as the scalar one: a limited number of parameters (which have the same value in both models) and ease of implementation. The classical magnetic vector potential FE formulation is adopted. Particular attention is paid to the resolution of the nonlinear equations by means of the Newton‐Raphson method. It is shown that the application of the latter method naturally leads to the use of the differential reluctivity tensor, i.e. the derivative of the magnetic field vector with respect to the magnetic induction vector. This second rank tensor can be straightforwardly calculated for the considered hysteresis model. By way of example, the vector Jiles‐Atherton is applied to two simple 2D FE models exhibiting rotational flux. The excellent convergence of the Newton‐Raphson method is demonstrated.

Time-Domain Homogenization of Windings in 2-D Finite Element Models

In this paper, the authors propose an original time-domain extension of the frequency-domain homogenization of multiturn windings in finite element (FE) models. For the winding type in hand (e.g., round conductor with hexagonal packing), an elementary FE model is used for determining dimensionless frequency and time-domain coefficients regarding skin and proximity effect. These coefficients are readily utilized for homogenizing the winding in the FE model of the complete device. The method is successfully applied to an axisymmetric 103-turn inductor. The results agree very well with those obtained by an accurate but very expensive FE model in which all turns are finely discretized