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Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.

A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.

The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.

The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

Non-oriented electrical steel presents anisotropic behaviour. Modelling such anisotropic behaviour has become a necessity for accurate design of electrical machines. The main aim of this study is to model the magnetic anisotropy in the non-oriented electrical steel sheet of grade M400-50A using a phenomenological hysteresis model.

The well-known phenomenological vector Jiles–Atherton hysteresis model is modified to correctly model the typical anisotropic behaviour of the non-oriented electrical steel sheet, which is not described correctly by the original vector Jiles–Atherton model. The modification to the vector model is implemented through the anhysteretic magnetization. Instead of the commonly used classical Langevin function, the authors introduced 2D bi-cubic spline to represent the anhysteretic magnetization for modelling the magnetic anisotropy.

The proposed model is found to yield good agreement with the measurement data. Comparisons are done between the original vector model and the proposed model. Another comparison is also made between the results obtained considering two different modifications to the anhysteretic magnetization.

The paper presents an original method to model the anhysteretic magnetization based on projections of the anhysteretic magnetization in the principal axis, and apply such modification to the vector Jiles–Atherton model to account for the magnetic anisotropy. The replacement of the classical Langevin function with the spline resulted in better fitting. The proposed model could be used in the numerical analysis of magnetic field in an electrical application.

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.

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.

The proposed model is based on an analytical formulation of the energy depending on the components of the magnetic flux density. This formulation is composed of three Gumbel distributions. Every functional parameters of energy density is formulated with only four parameters which are calculated by fitting the energy extracted from measurements. Finally, the proposed model is validated by comparing the computation and the measurements of 9

loci for NO steel sheets at 10 Hz. The proposed analytical model shows good agreements with an average relative error of 27 per cent.

The paper presents an original analytical method to model magnetic anisotropy for NO electrical sheets. With this analytical formulation, the determination of H does not require any iterative process as it is usually the case with this energy method coupled with implicit function. This method can be easily incorporated in finite element method since it does not require any extra iterative process.

The purpose is to implement and compare different approaches for modelling the magnetostriction phenomenon in iron sheet used in rotating electrical machines.

In the force-based approach, the magnetostriction is modelled as a set of equivalent forces, which produce the same deformation of the material as the magnetostriction strains. These forces among other magnetic forces are computed from the solution of the finite element (FE) field computation and used as loads for the displacement-based mechanical FE analysis. In the strain-based approach, the equivalent magnetostrictive forces are not needed and an energy-based model is used to define magnetomechanically coupled constitutive equations of the material. These equations are then space-discretised and solved with the FE method for the magnetic field and the displacements.

It is found that the equivalent forces method can reproduce the displacements and strains of the structure but it results in erroneous stress states. The energy-based method has the ability to reproduce both the stress and strains correctly; thus enabling the analysis of stress-dependent quantities such as the iron losses and the magnetostriction itself.

The investigated methods do not account for hysteresis and other dynamic effects. They also require long computation times. With the available computing resources, the computation time does not present any problem as far as they are not used in everyday design procedures but the modelling of dynamic effect needs to be elaborated.

The developed and implemented methods are verified with measurements and simulation experiments and applied to as complex structure as an electrical machine. The problems related to the different approaches are investigated and explained through simulations.

The purpose of this paper is to find out how uncertainties in the characterization of magnetic materials propagate through identification and numerical simulation to the computation of iron losses in electrical machines.

The probabilistic uncertainties in the iron losses are modelled with the spectral approach using chaos polynomials. The Sobol indices are used for the global sensitivity analysis. The machine is modelled with a 2D finite element method and the iron losses are computed with a previously developed accurate method.

The uncertainties propagate in different ways to the different components of losses, i.e. eddy current, hysteresis, and excess losses. The propagation is also different depending on the investigated region of the machine, i.e. Stator or rotor teeth, yokes, tooth tips.

The method does not account for uncertainties related to the manufacturing process, which might result in even larger variability.

A major implication of the findings is that the identification of iron loss parameters at low frequencies does not affect the loss variability. The identification with high-frequency measurement is very important for the rotor tooth tips. The variability in the excess loss parameters is of low impact.

The presented results are of importance for the magnetic material manufacturers and the electrical machine designers. The manufacturers can plan the measurement and identification procedures as to minimize the output variability of the parameters. The designers of the machine can use the result and the presented procedures to estimate the variability of their design.

Punching of the electrical sheets impair the insulation and make random galvanic contacts between the edges of the sheets. The purpose of this paper is to model the random galvanic contacts at the stator edges of 37 kW induction machine and estimate the additional losses due to these contacts.

The presence of the surface current at the edges of sheets causes the discontinuity in the tangential component of the magnetic field. The surface boundary layer model which is based on this concept is implemented to model the galvanic contacts at the edges of the sheets. Finite element analysis based on magnetic vector potential was done and theoretical statistical study of the random conductivity at the stator edge was performed using brute force method.

Finite element analysis validates the interlaminar current when galvanic contacts are present at the edges of electrical sheets. The case studies show that the rotor and stator losses increases with the thickness of the contacts. Statistical studies show that the mean value of total electromagnetic loss was increased by 7.7 percent due to random contacts at the edges of sheets.

The novel approach for modeling the galvanic contacts at the stator edges of induction machine is discussed in this paper. The hypothesis of interlaminar current due to galvanic contacts is also validated using finite element simulation.