Anouar Belahcen, Katarzyna Fonteyn, Reijo Kouhia, Paavo Rasilo and Antero Arkkio
– The purpose is to implement and compare different approaches for modelling the magnetostriction phenomenon in iron sheet used in rotating electrical machines.
Abstract
Purpose
The purpose is to implement and compare different approaches for modelling the magnetostriction phenomenon in iron sheet used in rotating electrical machines.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
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.
Originality/value
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.
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A. Belahcen and A. Arkkio
The purpose of this paper is to find out how to model the effect of mechanical stresses on the magnetic properties of electrical steel used in electromagnetic devices and…
Abstract
Purpose
The purpose of this paper is to find out how to model the effect of mechanical stresses on the magnetic properties of electrical steel used in electromagnetic devices and especially in electrical machines. Further, the effect of these stresses on the operation of the machines should be studied.
Design/methodology/approach
The constitutive equation of the electrical steel is usually modeled as a non linear relation between the magnetic flux density and the magnetic field strength. In this research, this constitutive equation is developed to account for the mechanical stresses through a parametric relationship, the parameters of which are estimated from measurements. Further, the constitutive equation is used in a magnetomechanically coupled numerical simulation of an induction machine.
Findings
The mechanical stresses degrade the properties of the electrical steel and increase the magnetization current in electrical machines. This leads to a decrease in the efficiency of these machines.
Research limitations/implications
The effect of mechanical stresses is studied from the point of view of magnetization properties. This work does not model the effect of stresses on the specific losses of the material. Such a research is still going on.
Originality/value
The effect of mechanical stress on the magnetic properties of the materials used in electrical machines is modeled in an easy and original way, which allow for its application in numerical simulation and analysis of these machines.
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Brijesh Upadhaya, Paavo Rasilo, Lauri Perkkiö, Paul Handgruber, Anouar Belahcen and Antero Arkkio
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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A. Belahcen, E. Dlala, K. Fonteyn and M. Belkasim
The purpose of this paper is to find out how to model iron losses in electrical machines accurately and efficiently.
Abstract
Purpose
The purpose of this paper is to find out how to model iron losses in electrical machines accurately and efficiently.
Design/methodology/approach
The starting point was a previously developed vector hysteresis model that was designed and incorporated into the 2D time‐stepping finite‐element (FE) simulation of induction machines. The developed approach here is a decoupling between the vector hysteresis model and the 2D FE model of the machine. The huge time consumption of the incorporated hysteresis model required some new approach to make the model computationally efficient. This is dealt with through an a posteriori use of the vector hysteresis model.
Findings
In this research, it was found that the vector hysteresis model, although used in an a posteriori scheme is able to accurately predict the iron losses as far as these losses are small enough not to affect the other operation characteristics of the machine.
Research limitations/implications
The research methods reported in this paper deal mainly with induction machines. The methods should be applied for transient operations of the induction machines as well as for other types of machines. The fact that the iron losses do not affect very much the operation characteristics of the machine is based on the fact that the air gap field plays a major role in these machines. The method cannot be applied to other magnetic devices where the iron losses are the main loss component.
Originality/value
The paper is of practical value for designers of electrical machines, who use FE programs. The methods presented here allow them to use a different FE package to simulate the machine and own routines (based on the presented methods) to predict the iron losses without loss of accuracy and in a reasonably short time.
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Anouar Belahcen, Paavo Rasilo, Thu-Trang Nguyen and Stephane Clénet
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
The method does not account for uncertainties related to the manufacturing process, which might result in even larger variability.
Practical implications
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.
Originality/value
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.
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Martin Marco Nell, Benedikt Schauerte, Tim Brimmers and Kay Hameyer
Various iron loss models can be used for the simulation of electrical machines. In particular, the effect of rotating magnetic flux density at certain geometric locations in a…
Abstract
Purpose
Various iron loss models can be used for the simulation of electrical machines. In particular, the effect of rotating magnetic flux density at certain geometric locations in a machine is often neglected by conventional iron loss models. The purpose of this paper is to compare the adapted IEM loss model for rotational magnetization that is developed within the context of this work with other existing models in the framework of a finite element simulation of an exemplary induction machine.
Design/methodology/approach
In this paper, an adapted IEM loss model for rotational magnetization, developed within the context of the paper, is implemented in a finite element method simulation and used to calculate the iron losses of an exemplary induction machine. The resulting iron losses are compared with the iron losses simulated using three other already existing iron loss models that do not consider the effects of rotational flux densities. The used iron loss models are the modified Bertotti model, the IEM-5 parameter model and a dynamic core loss model. For the analysis, different operating points and different locations within the machine are examined, leading to the analysis of different shapes and amplitudes of the flux density curves.
Findings
The modified Bertotti model, the IEM-5 parameter model and the dynamic core loss model underestimate the hysteresis and excess losses in locations of rotational magnetizations and low-flux densities, while they overestimate the losses for rotational magnetization and high-flux densities. The error is reduced by the adapted IEM loss model for rotational magnetization. Furthermore, it is shown that the dynamic core loss model results in significant higher hysteresis losses for magnetizations with a high amount of harmonics.
Originality/value
The simulation results show that the adapted IEM loss model for rotational magnetization provides very similar results to existing iron loss models in the case of unidirectional magnetization. Furthermore, it is able to reproduce the effects of rotational flux densities on iron losses within a machine simulation.
Details
Keywords
Brijesh Upadhaya, Floran Martin, Paavo Rasilo, Paul Handgruber, Anouar Belahcen and Antero Arkkio
Non-oriented electrical steel presents anisotropic behaviour. Modelling such anisotropic behaviour has become a necessity for accurate design of electrical machines. The main aim…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Andreas Gschwentner, Manfred Kaltenbacher, Barbara Kaltenbacher and Klaus Roppert
Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various…
Abstract
Purpose
Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.
Design/methodology/approach
The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.
Findings
The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.
Originality/value
The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.
Details
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Jan Karthaus, Benedikt Groschup, Robin Krüger and Kay Hameyer
Due to the increasing amount of high power density high-speed electrical machines, a detailed understanding of the consequences for the machine’s operational behaviour and…
Abstract
Purpose
Due to the increasing amount of high power density high-speed electrical machines, a detailed understanding of the consequences for the machine’s operational behaviour and efficiency is necessary. Magnetic materials are prone to mechanical stress. Therefore, this paper aims to study the relation between the local mechanical stress distribution and magnetic properties such as magnetic flux density and iron losses.
Design/methodology/approach
In this paper, different approaches for equivalent mechanical stress criteria are analysed with focus on their applicability in electrical machines. Resulting machine characteristics such as magnetic flux density distribution or iron are compared.
Findings
The study shows a strong influence on the magnetic flux density distribution when considering the magneto-elastic effect for all analysed models. The influence on the iron loss is smaller due to a high amount of stress-independent eddy current loss component.
Originality/value
The understanding of the influence of mechanical stress on dimensions of electrical machines is important to obtain an accurate machine design. In this paper, the discussion on different equivalent stress approaches allows a new perspective for considering the magneto-elastic effect.
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Paul Handgruber, Simon Schernthanner, Oszkár Bíró, Andrej Stermecki and Georg Ofner
The purpose of this paper is to study the effects of inverter supply on the iron loss characteristics of slip-ring induction machines. Pulse width modulated (PWM) voltage supply…
Abstract
Purpose
The purpose of this paper is to study the effects of inverter supply on the iron loss characteristics of slip-ring induction machines. Pulse width modulated (PWM) voltage supply on the stator side, as well as a doubly fed operation mode with rotor-sided inverter, are investigated.
Design/methodology/approach
An inverter fed machine model is coupled to previously developed eddy current and hysteresis loss models. The eddy current model is based on a finite element method and considers the three-dimensional (3D) eddy current distribution in the steel sheets. The hysteresis losses are computed by a static Preisach vector model.
Findings
It is found that under stator-sided inverter supply the eddy current losses do significantly increase when compared to sinusoidal feeding, contributing to a total loss increase of 10-15 percent. In doubly fed operation, the additional losses are generally lower owing to the winding topology of the studied machine.
Research limitations/implications
The analyses presented are restricted to single PWM pattern only. The influences of different PWM parameters remain to be investigated in future.
Practical implications
Regarding practical applications, the reduced additional losses in doubly fed configurations can be considered as a further advantage when competing against other topologies available.
Originality/value
The 3D eddy current model is applied for the first time to quantify the effects of inverter supply. Furthermore, the presented studies on the iron losses in doubly fed operation are original and of practical value for designers and researches.