Floran Martin

Anisotropic and Strain-Dependent Model of Magnetostriction in Electrical Steel Sheets

This paper presents an anisotropic and mechanical strain-dependent model of magnetostriction in electrical steel sheets and its application in finite-element computations. The presented model is bidirectional and the data needed for its derivation is extracted solely from unidirectional measurements under mechanical loading. The model has six parameters that describe the magnetic and strain behavior and two parameters that describe the anisotropy. The validation of the model is carried out through measurements and computations on a single-phase transformer-like device. The comparison between computation and measurement results seems to be reasonable regardless of the fact that the magnetic behavior is modeled as single valued, isotropic, and anhysteretic. Original magnetostriction measurements are also presented and the importance of magnetostriction anisotropy in a priori isotropic electrical steel sheets is demonstrated. The model is easy to implement in existing codes and the anisotropic behavior is straightforward to modify according to a specific material.

Modeling of Hysteresis Losses in Ferromagnetic Laminations Under Mechanical Stress

A novel approach for predicting magnetic hysteresis loops and losses in ferromagnetic laminations under mechanical stress is presented. The model is based on combining a Helmholtz free-energy-based anhysteretic magnetoelastic constitutive law to a vector Jiles-Atherton hysteresis model. This paper focuses only on unidirectional and parallel magnetic fields and stresses, albeit the model is developed in a full 3-D configuration in order to account also for strains perpendicular to the loading direction. The model parameters are fitted to magnetization curve measurements under compressive and tensile stresses. Both the hysteresis loops and the losses are modeled accurately for stresses ranging from -50 to 80 MPa.

Effect of Mechanical Stress on Excess Loss of Electrical Steel Sheets

Effect of mechanical stress on the magnetic loss of electrical steel sheets is analyzed utilizing the statistical loss theory. The focus of this paper is on the variation of the excess loss component with the applied stress and its correlation with the hysteresis loss. The model and its correlation are validated by performing comprehensive measurements at various combinations of induction levels, frequencies, and stresses. It is found that the excess losses can be modeled with sufficient accuracy by their correlation with the hysteresis losses over a wide range of stresses, frequencies, and flux densities.

Model of Magnetic Anisotropy of Non-Oriented Steel Sheets for Finite-Element Method

Even non-oriented steel sheets present a magnetic anisotropic behavior. From rotational flux density measurements at 5 Hz, the model of magnetic anisotropy is derived from two surface basis-cubic splines with the boundary conditions matching with ferromagnetic theory. Furthermore, the investigation of the magnetic anisotropy shows that the H(B) characteristic is not strictly monotonous due to the angle difference between the field and the flux density. Hence, the standard non-linear solvers would either diverge or converge toward the closest local minimum. Thus, we propose two different specific solvers: 1) a combined particle swarm optimization with a relaxed Newton-Raphson and 2) a modified Newton method.

Analytical model for magnetic anisotropy of non-oriented steel sheets

Purpose – Recent investigations on magnetic properties of non-oriented (NO) steel sheets enhance the comprehension of the magnetic anisotropy behaviour of widely employed electrical sheets. The concept of energy/coenergy density can be employed to model these magnetic properties. However, it usually presents an implicit form which requires an iterative process. The purpose of this paper is to develop an analytical model to consider these magnetic properties with an explicit formulation in order to ease the computations. Design/methodology/approach – From rotational measurements, the anhysteretic curves are interpolated in order to extract the magnetic energy density for different directions and amplitudes of the magnetic flux density. Furthermore, the analytical representation of this energy is suggested based on statistical distribution which aims to minimize the intrinsic energy of the material. The model is finally validated by comparing measured and computed values of the magnetic field strength. Find...

Effect of magnet materials on optimal design of a high speed PMSM

In this paper, we investigate the effect of magnet materials on optimal design of a high speed synchronous machine for different rotor speeds. High speed electrical machine tends to lower the magnetic flux density in order to decrease the iron losses. Thus, ferrite magnets should lead to similar performances as rare earth magnets in the optimal design of surface mounted permanent magnet synchronous machines. With this regard, we suggest to analyze the effect of those both magnet materials on the optimal design of these PMSM for different rotor speeds.

Homogenization Technique for Axially Laminated Rotors of Synchronous Reluctance Machines

In this paper, we propose a homogenization technique to model the axially laminated rotor of synchronous reluctance machines. Thus, the computational effort can be significantly reduced by replacing the laminated parts of the rotor by some equivalent anisotropic media. The proposed method is validated in terms of flux density and electromagnetic torque. Some small discrepancies can be noticed due to the air-gap fluctuations caused by the steel sheets and the interlaminar insulation sheets of the rotor. With the test machine, the homogenization method reduces by the number of elements to one-fourth and the computation time to one-third.

Combined FE and Particle Swarm algorithm for optimization of high speed PM synchronous machine

Purpose – The purpose of this paper is to optimize the stator slot geometry of a high-speed electrical machine, which is used as an assist for a turbocharger. Meanwhile, the suitability of the Particle Swarm algorithm for such a problem is to be tested. Design/methodology/approach – The starting point of the optimization is an existing design, for which the Particle Swarm algorithm is applied in conjunction with the transient time-stepping 2D finite element method. Findings – It is found that regardless of its stochastic nature, the Particle Swarm work well for the optimization of electrical machines. The optimized design resulted in an increase of the slot area and increase of the iron loss, which was compensated by a dramatic decrease in the Joule losses. Research limitations/implications – The optimization was concentrated on the stator design whereas the rotor dimensioning was carried out withing the compressor and turbine design. Originality/value – A turbocharger with electric assist is designed opt...

Magnetomechanical Model for Hysteresis in Electrical Steel Sheet

A coupled magnetomechanical model for hysteresis in an electrical steel sheet is presented. The foundation of the model developed is the classical Sablik-Jiles-Atherton (SJA) model. A comprehensive model for the stress-dependent magnetostriction is also proposed and implemented in the SJA model. Improvements in the SJA model as well are proposed and validated with simultaneous measurements of magnetostriction, magnetic field, and flux density. The measurements were performed on a single electrical steel sheet under various levels of stress (-35 to 100 MPa). The proposed model was found to adequately model the permeability change and the local bowing of the B-H-loop due to stress.

Proper orthogonal decomposition for order reduction of permanent magnet machine model

Model order reduction is an approach for reducing size, complexity, and computation cost of mathematical models in numerical simulations. This paper describes the application of proper orthogonal decomposition method, as one of the most efficient model order reduction techniques, in generating lower dimensional model of a permanent magnet machine. In proper orthogonal decomposition, data collected from high-dimensional numerical simulations (called snapshots) are projected onto a set of orthonormal basis functions. Thereafter, these basis functions are combined with the original model equations to build a reduced order model. The comparison of computational results of the original model with the reduced model indicates that the reduced model is able to accurately reproduce both local and global operation quantities of the machine under investigation.