An innovative approach for the evaluation of iron losses in magnetic laminations, applied to the optimization of highly saturated electric motors

Transcription

1 An innovative approach for the evaluation of iron losses in magnetic laminations, applied to the optimization of highly saturated electric motors Lode Vandenbossche 1, Sigrid Jacobs, Raphael Andreux 3, Nicolas Labbe 3, Emmanuel Attrazic 4 1 ArcelorMittal Global R&D Gent, J. Kennedylaan 3, 9060 Zelzate, Belgium ArcelorMittal Global R&D, J. Kennedylaan 51, 904 Gent, Belgium 3 Valeo Electrical Systems, Parc d'activités de Chesnes, Ville Nouvelle de l'isle d'abeau, 3891 St Quentin Fallavier Cedex, France 4 ArcelorMittal St Chély d'apcher, Route du Fau de Peyre, 4800 St Chély d Apcher, France Abstract ArcelorMittal is a key supplier for electrical steels in challenging applications such as high power density automotive traction machines and high speed induction machines for industry and power generation systems. Throughout the years we have focused on understanding the specific needs of each electrical machine type and aimed at developing electrical steels to optimally meet these machine demands. This paper presents a specific example of such a development. As a partner of ArcelorMittal, Valeo is a specialist in the design and manufacturing of electrical machines for automotive applications, and especially innovative e-machines aiming at "green" solutions for traction, like hybrid vehicles as a part of the current tendency in electrifying the power train. After improving its alternators towards the Stop and Start function, as a first step for vehicles hybridisation, Valeo aims to bring a substantial reduction in fuel consumption at a reasonable cost, on the basis of improved starter motors. This paper presents the optimisation potential possible for critical operating conditions of such starter motors, based on the use of a more advanced electrical steel grade. That idea triggered the collaboration between ArcelorMittal and Valeo. In order to properly structure the machine and material optimisation, the work was based on detailed magnetic modelling, using not only commercial modelling software, but also using ArcelorMittal s improved iron loss modelling approach. The results illustrate the improved prediction power of the ArcelorMittal material model. In terms of electrical steel choice, the benefit on machine performance will be shown. Obviously in the end, a commercial evaluation needs to be made in terms of costs versus benefit, but the current study shows that even for a conventional machine, such as a starter motor, a structured optimisation approach can lead to an interesting performance improvement potential. Keywords: Starter motors, stop and start systems, electrical steels, electrical machine design, material optimisation. 1. Introduction A starter motor achieves the cranking of the internal combustion engine (ICE) in order to start the vehicle. It uses the battery energy (at a voltage level of 1V) and converts this electrical energy into mechanical power on the ICE shaft. The development in this application is linked to the recent massive introduction of stop and start systems in cars, in order to avoid fuel consumption during idling. The frequent re-starting operation of the ICE brings new constraints regarding the functioning of the starter motor and justifies the study and an optimisation exercise. Such starter-motor typically is a small brushed DC machine which develops about kw of mechanical power for a typical diesel application (P max on Fig. ) when supplied with a 1V battery. One of the main constraints for starter motors is to be as small as possible in volume, which leads to a highly saturated motor. ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 1

2 Fig. 1 shows a basic layout, where the stator poles have concentrated windings and are subjected to essentially DC fields. The rotor is subjected to AC conditions and therefore needs to be made of laminated electrical steel. Figure 1: Layout sketch of a generic starter motor In the classical single starting mode, the machine functions in cold operating mode. In such conditions it is important to use the maximal power level the motor can develop, to optimise the cranking process. Such starting operation then happens only occasionally and lasts just a few seconds. In a "Stop-Start" mode however, the internal combustion engine is warm so that the starter operates at a lower torque operating point. Figure : Torque, power and speed characteristics of a generic starter motor We consider in this study a generic starter motor designed for a classical cold start near to the maximum power (named P max in Fig. ), that means close to 8000 rpm at the armature shaft (electrical frequency around 00Hz). A "Stop-Start" usage of this starter leads to a displacement of the operating point towards higher speed and also to lower electrical current than the cold start. Thus, the typical range of the armature speed goes from roughly 8000 rpm to almost rpm (as shown on Fig. ) corresponding to an electrical frequency of the fundamental from around 00Hz for a cold cranking to almost 1kHz for the no-load point. ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01)

3 The optimisation process consists in improving the starter performance in the re-start operating points by reducing the armature (i.e. rotor) magnetic losses occurring in the electrical steel laminations. Valeo benefits from ArcelorMittal s loss model which is particularly suitable for highly saturated conditions and elevated electrical frequencies, which is particularly the case for automotive starters. In section of this paper, ArcelorMittal s approach to model magnetic losses in electrical steel parts is highlighted. In section 3, the numerical computations of the rotor magnetic losses are treated. For model validation purposes the numerical results obtained on the generic starter motor with conventional electrical steel grade (material A) are compared in section 4 to the measured total iron losses of both stator and rotor, once the numerically estimated stator iron losses are extracted from these machine measurements. Finally, in section 5, the rotor iron losses of the starter motor are compared for two electrical steel grades, the conventional one (material A) and the one optimised for stop/start applications (material B).. ArcelorMittal s approach to model magnetic losses in electrical steel parts of electrical machines A sufficiently accurate estimation of iron losses occurring in the machine s stator/rotor parts is indispensable to effectively carry out the electromagnetic and thermal design of electric machines. Magnetic losses or iron losses of ferromagnetic materials are usually measured and theoretically described under well-defined, standardised conditions like e.g. the Epstein frame test, carried out under unidirectional, homogeneous and sinusoidal magnetic polarisation conditions. Moreover standardised material sample dimensions are used, resulting in the specific iron losses (in W/kg) of a particular electrical steel grade for a given magnetic induction value and frequency value. To give an example: for a M35-35A grade of 0.35mm gauge, the specific iron loss at 1.5T and 50Hz is less than.35 W/kg. However in rotating electrical machines, the occurring magnetic flux paths, flux waveforms, steel part geometries, lamination manufacturing techniques and mechanical constraints are far more complex than in case of the lab conditions of Epstein measurements. Hence the actual iron core losses (in W) dissipated in electrical machines cannot be related in a simple and straight-forward way to the Epstein loss data. To be more specific, compared to the standardised iron loss measurements there are a lot of additional factors influencing the iron losses in machines: the magnetic flux waveforms occurring in electrical machines are not simply sinusoidal and unidirectional, but contain higher harmonics in time (due to saturation effects, stator slotting, power electronics such as PWM, skin effect); the magnetic fields can become, in some regions of the machine, vector properties (known as rotational magnetisation). These non-unidirectional magnetisation conditions give rise to rotational losses; in some regions of the machines, elevated magnetic induction levels occur; especially for electrical machines utilised in electric vehicles, the machine operates within a wide range of different elevated operating frequencies (DC 1kHz) In this section we will show how we tackle the issue of improving the estimation of the iron losses by numerical methods, by taking into account the above-mentioned aspects. Moreover, also assembly stresses (radial compression applied to the steel lamination when fitting it into the machine housing and/or axial compression when performing stack assembly) [7], lamination punching [3, 7-10] and elevated operational temperatures [1] affect the magnetisation processes in the machines and the resulting machine s iron losses. In order to predict the iron losses more accurately, these effects should be considered as well, and incorporated to some extent in the envisaged improved iron loss models. ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 3

4 In the next paragraphs the current state of the art of the improved iron loss modelling is highlighted: in the framework of a collaboration between ArcelorMittal (R&D Gent) and the IEM (Institute of Electrical Machines of the RWTH Aachen), numerical methods were developed [-3] to improve in relatively wide operational ranges of magnetic polarisation J and frequency f the estimation of iron losses occurring in rotating electrical machines. This improved iron loss model can be seen as a further elaborated Bertotti-based loss-separation model [4]. To recapitulate, the well-known classical iron loss model of Bertotti describes nicely the three different iron loss components under unidirectional and sinusoidal magnetic flux density: the (quasi-) static hysteresis losses, the dynamic classical Foucault losses (also known as eddy current losses), and the dynamic excess losses: P Fe ( J p, f ) = khystj p f + keddyj p f + kexcj p f (1), The eddy current parameter can be computed based on the value for thickness, electrical conductivity and mass density [4]. The other parameters are obtained by fitting the measurement data (as a function of peak magnetic induction J p and frequency f). Nevertheless, Bertotti s original approach does not take into account rotational losses and higher harmonics, so estimated loss values are expected to be smaller than the losses occurring in reality. These limitations underline the need to extend the loss model by describing also these mentioned effects which additionally contribute to the iron losses. On the other hand, the ArcelorMittal improved iron loss model includes the most relevant additional aspects which influence the actual iron losses occurring in rotating machines: elevated magnetic induction levels higher harmonics in time and space nonlinear magnetisation effects spatial vector fields; rotational magnetisation elevated operating frequencies ArcelorMittal s state-of-the-art iron loss description reads as follows: P( J, f ) = s s n= 1 1 J ( 1+ ( r( J ) 1) c) n max s5 ( nf ) + s J ( nf ) + s J f 3 n= 1 n J max f + 4 max (), taking into account the following definitions: s : all five parameters are fitted material parameters (depending on the ES grade) i J max : amplitude of the ground (first) harmonic component of the flux density [T] J n : amplitude of the n-th harmonic component of the flux density, with f : fundamental frequency, in Hertz [Hz] J = ( J + ) n nx J ny J c min : flux distortion factor, c = J max J min : minimum value of flux density amplitude, evaluated over one electrical period [T] r : rotational loss factor (empirically determined) ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 4

5 Equation () is an extension of the physically based loss model of Bertotti; it s a mathematical iron loss description, which results in a good fit between measurements and calculations. Therefore it is a valuable mathematical tool for the estimation of iron losses in electrical machines. The proposed calculation method for the improved estimation of iron losses in electrical machines is shown in Fig. 3. The method consists of using the specific loss W(J,f) characteristics obtained by standardised Epstein measurements, in order to fit the material parameters of the improved iron loss description (Eq. ). As been said, this iron loss description accounts for the presence of the real life conditions occurring in electrical machines such as in some regions of the electrical steels elevated magnetic induction levels, waveforms with higher harmonics and rotational magnetisation patterns. Fig.3: General overview of the numerical scheme of the ArcelorMittal iron loss modelling approach. On the other hand, the magnetisation curves J(H,f), also obtained by the standard Epstein measurements serve as input for the D finite element computations (carried out by Valeo) of the electrical machine under evaluation, identifying the local flux densities for each time step during one electrical period. For one particular working point of the machine, the magnetic polarisation values in every finite element of the machine s stator lamination are retrieved, and this is repeated at different time instants during one electrical period. These magnetic polarisation values (as function of time and finite element index) then serve as input for the postprocessing tool implemented into the numerical environment at ArcelorMittal (R&D Gent), which can run independently from the FEM calculations to calculate the iron losses according to the ArcelorMittal iron loss model of equation. These calculations can then be repeated for different operational points as a function of torque (current) and speed (frequency) and all such results can be combined in so-called efficiency maps. Using these efficiency maps the influence of different electrical steel grades on the performance of rotating electrical machines can be studied. 3. Electromagnetic modelling of Valeo s generic starter motor The starter motor electromagnetic modelling was performed for the generic design using a conventional electrical steel grade (material A), but without current in the rotor conductors (open circuit; brushes removed) This choice is made because the aim is to compare the numerically obtained results with experimental machine measurements of the iron losses, and such methodology to measure the iron losses of the starter motor is based on a topology without rotor currents, as explained in section 4. ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 5

6 3.1 Finite element modelling at Valeo and its validation Using the finite element software FluxD, the two-dimensional magneto-static problem is solved for multiple time points during one electrical period, when only supplying current to the field solenoid (= stator). For each time step, the magnetic polarisation values for every element are extracted and stored in text files for further processing (see section 3.). This operation occurs for every considered mechanical position, which is every degrees in our case (90 points for one electrical period). We show on Fig. 4 the magnetic induction field map of the armature (i.e. the rotor). Note that the entire machine circumference had to be represented because of the lack of symmetry (19 rotor slots in front of 4 poles). Fig.4: Map of the flux density in the armature for a specific armature position One specific characteristic of Valeo s starter motor concerns the important three dimensional effects which had to be taken into account in our D finite element model. This phenomenon is related to the different axial lengths of the ferromagnetic parts of the machine as illustrated in Fig.5. To avoid the risk of under- or over-estimating the magnetic flux through the armature, well-known appropriate methods are applied, so that a two-dimensional model of the stator and the rotor is valid, for the given axial ratios. D middle axial view Yoke Pole shoe Armature Lu = 35mm Fig.5: Sketch of the different axial lengths of ferromagnetic parts This finite element modelling approach is actually validated by measurements: a special test bench at Valeo enables the measurement of the back E.M.F. of one armature section during rotation at permanent speed while a constant current is passing through the field stator winding. Such comparison gives information about the flux which is linked between pole shoe and rotor sections. Results displayed on Fig. 6 show that the final D FE model (in blue) is very close to the measurement (red), also indicating that the air gap distance is correctly ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 6

7 estimated in the modelling. The cyan curve represents a simple D model situated in the middle axial view (see Fig.5) without modification of the reluctances. Fig. 6: Back E.M.F of one turn of an armature coil measured and simulated by a D Finite Element Model at a constant speed (000rpm) and constant field winding current, as a function of mechanical position Then, calculations are performed for 6 different operating points in frequency, from the cold cranking (named f min ) to the no-load point (named f max ). For each calculation, Valeo uses the B vs. H curve corresponding to the electrical fundamental frequency provided and measured by ArcelorMittal (6 typical frequencies are selected, see table 1). The DC current values supplying the field winding only have been chosen regarding the characteristic curve presented on Fig.. In spite of the lack of current in the armature coils, it is important to be aware that the simplified model is relevant enough in terms of induction level distribution in the armature. The main contributor to the magnetic field distribution in the starter motor is the stator winding. Fig. 7: Loci of magnetic induction for two locations (middle of rotor teeth and yoke), for two frequencies (f max and f min ) Figure 7 shows magnetic flux density loci for the two extreme frequency values, considered in the middle of the rotor teeth (in blue) and in the armature rotor yoke (in red). We can see the rotational magnetisation particularly present in the yoke. ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 7

8 Fig. 8 shows the results of the finite element modelling in terms of the histogram of J max (maximum magnetic polarization, evaluated over one electrical period; rotor only), for the lowest and highest fundamental frequencies, resp. f min and f max. When increasing the fundamental frequency, the histogram shifts to lower J values. 1% 10% relative occurrence (%) 8% 6% 4% % 0% magnetic polarization J [T] Fig. 8 : Histograms of the maximum polarization values evaluated over one electrical period on each element of the armature mesh, for two fundamental frequencies: f min (in blue) and f max (in red). 3. Magnetic loss modelling of the rotor electrical steel laminations The output data of the finite element modelling, required for the computation in post-processing mode of the iron losses of the rotor part, is then shared by Valeo with ArcelorMittal, in the form of txt-files (ASCII format). Apart from the axial length of the radial flux electrical machine, it is not essential or necessary to share any particular design/geometry detail whatsoever. 70 Wmax ~ 100W fund freq = f1 (fmin) fund freq = f fund freq = f3 fund freq = f4 fund freq = f5 fund freq = f6 (fmax) Losses [W] Physt Prot PeddyHH Peddy_f0 PexcessHH Pexcess_f0 Psaturation Ptotal Fig.9: Iron losses decomposition (different terms according to equation ; and total losses) for the rotor made from the conventional electrical steel grade (material A), for the six considered operating points of the starter motor (indicated by the corresponding fundamental frequency). ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 8

9 In Fig. 9 the results of the rotor iron loss computations based on equation are visualised for the conventional electrical steel grade (material A) and for all six working points (indicated by the different fundamental frequencies): this equation is split into 7 terms: unidirectional hysteresis loss, rotational part of the hysteresis loss, eddy current losses for fundamental frequency (f0) and for the higher harmonics, excess losses for fundamental frequency (f0) and for the higher harmonics, and the saturation term. At the right hand side, the summation of all terms results in the total magnetic losses. Notice that for low frequencies the total iron losses in the rotor increase more rapidly than for higher frequencies, which is linked to the fact that for higher frequencies, the magnetic polarization amplitude values are less elevated (as can be seen in Fig. 8 showing the J max histograms). 3.3 Iron losses in the stator pole shoes In the considered starter, the stator pole shoes are made of a massive ferromagnetic material which makes possible the flow of eddy currents due to high harmonic components (although of rather low amplitude) in the essentially DC magnetic flux in the stator. The local variation of the magnetic flux in the massive pole shoes leads to eddy currents concentrated close to the air gap surface, consistent with an expected skin effect. These stator eddy current losses are calculated utilizing a transient finite element technique; and compared to the iron losses in the laminated armature (i.e. the rotor), these eddy current losses in the stator can be significant. 4. Model validation by machine measurements 4.1 Approach of machine measurements To isolate the iron losses from other losses such as mechanical ones (which are very important on brushed motors), we must remove the brushes. Magnetic saturation distribution is thus only created by the field solenoid in the stator. Iron losses are determined by observing the slow-down of the armature. A specific test bench whose principle is explained on Fig. 10 has been developed by Valeo for this kind of measurements. It is composed of a driving motor (starter provided by a voltage source), the studied armature, whose field winding can be supplied by a current source, and a mechanical part between the two shafts for the mechanical engagement/disengagement. When both shafts are mechanically decoupled, the studied armature decelerates because of its internal mechanical losses and its iron losses when the stator winding is supplied. The speed measurement is ensured by a sensor situated on the top of the shaft. Fig. 10: Schematic view of the test bench for armature slow-down measurement The iron losses (stator + rotor) for a speed Ω0 and a supplied current I 0 can now be determined from the measurements as presented by equation (3), where J represents the armature inertia in the mechanical loss part (the blue line on Fig. 11) of the global measured losses: kg.m, i.e. by removing ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 9

10 P iron dω dω ( Ω 0, I0) = JΩ0( ) (3) dt dt Ω=Ω 0, I = 0 Ω=Ω 0, The outcome of the treatment of the speed versus time data for the six working points (speed and current) is given in the second column of Table 1. These iron losses both contain values due to losses in the laminated armature as well as iron losses in the stator. In the third column of Table 1, we have removed the stator iron losses contribution. Values of losses are given in per unit. I = I 0 max Fig. 11: Armature speed slow-down measurement for different supplied currents Fundamental frequency (Hz) Total iron losses measured (p.u) Measured rotor iron losses = + total iron losses measured iron losses calculated in stator (p.u) f1 = fmin f f f f f6 = fmax Table 1: Results of iron losses measurements, per unit 4. Comparison of iron loss measurements and calculations Figure 1 compares the measured rotor iron losses (as determined in section 4.1) with the calculated rotor iron losses (see section 3.), for Valeo s generic starter motor with the conventional electrical steel grade, manufactured in a series production environment (hence punched laminations and equilibrated by milling the rotor, thus very likely creating electrical contacts between laminations). As can be seen, the general tendency of rotor iron losses as a function of frequency i.e. the iron losses increase less rapidly with increasing frequency for the elevated frequency values is maintained in both measured and calculated results. Also, the calculated values are roughly 70% of the measured ones. The explanation for this is related to the fact that in the numerical approach not all relevant features are included yet, features that could deteriorate (read increase) the rotor iron losses. For this starter motor application with rather small dimensions of the rotor teeth (total tooth width is only 3mm, tooth tip part is even less than 1mm), the local degradation of the permeability ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 10

11 and also the local increase of losses close to the cut edge due to the material degradation by the lamination punching can be significant, and could explain the 30% difference between measured and calculated rotor iron losses. This can be included in the model but was not done in this exercise Fig. 1: Comparison of measured and calculated rotor iron losses for six different operating points. 5. Optimisation of electrical steel choice With the same approach as described in section and illustrated in section 3, the rotor iron losses of the stator motor are now calculated and compared for two electrical steel grades, being the conventional one (material A) and the one optimized for stop/start applications (material B), again without rotor current supplied (brushes removed). Both materials maintain the high magnetic polarisation / high permeability utilisation, which is essential for starter motor applications. In terms of magnetisation patterns, torque and performance, both materials are comparable, for instance when comparing the histograms of material A (see fig.8) with the histograms obtained for material B, hardly any changes can be noticed (for material B, the magnetic polarisation ranges are T and T, respectively at f min and f max ). Fig. 13: Comparison of calculated rotor iron losses for two different electrical steel grades for the rotor laminations. ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 11

12 The results of the rotor iron loss comparison of both materials A and B are shown in Fig. 13. Relatively speaking, the improvement when shifting to material B is more pronounced at f max (warm start; no-load condition): when comparing material B with material A, the rotor iron losses are 37% less at f min, and are 44% less at f max. 6. Conclusion The improved approach of ArcelorMittal for the more accurate iron losses estimation in electrical steel parts is validated by comparing calculations and measurements on a starter motor of Valeo. The differences between measurement and calculation results are linked to phenomena such as punching, for which we have identified how to incorporate them in the model, so we have made a step forward in model validation and know-how to develop this methodology further. Secondly, this paper shows the optimisation potential possible for critical operating conditions of such starter motors, based on the use of a better electrical steel grade. It is clear from this work that e.g. the justification of using an improved electrical steel grade, depends on the exploitation frequency, so it is strongly linked to the operating points of the machine. Obviously, there s also the commercial evaluation to be made in terms of costs versus benefit, but the point made here is that even for a machine taken for granted, such as a starter motor, a structured optimisation approach can lead to interesting performance improvement potential. It must be clear from this paper that the very interactive process between a machine producer and an electrical steel supplier on both electrical steel choice and machines calculations, presents a win-win situation in the optimisation process of a specific application. Even without integrating key know-how exchange, such synergetic approach clearly brings efficient optimisation processes, which can shorten development times significantly. References [1] L. Vandenbossche, S. Jacobs, D. Van Hoecke, B. Weber, E. Attrazic, Extending the drive range of electric vehicles by higher efficiency and high power density traction motors, via a new generation of Electrical Steels, EVS6 Los Angeles, May 6-9, 01. [] S. Jacobs, D. Hectors, F. Henrotte, Magnetic material optimization for hybrid vehicle PMSM Drives, Inductica 009 Berlin. [3] L. Vandenbossche, S. Jacobs, F. Henrotte, Impact of cut edges on magnetisation curves and iron losses in e-machines for automotive traction, EVS-5 conference 010 in Shenzhen. [4] G. Bertotti, General properties of power losses in soft ferromagnetic materials, IEEE Transactions on Magnetics, 4(1), pp , January [5] EN 10106, Cold rolled non-oriented electrical steel sheet and strip delivered in the fully processed state, AFNOR, CEN, 007. [6] D. Van Hoecke, S. Jacobs, B. Weber, E. Attrazic, Advanced electrical steel characterisation of electrical machines subjected to high levels of mechanical stress: automotive traction, Inductica conference 011 in Berlin. [7] M. De Wulf, E. Hoferlin, L. Dupré, Finite Element Modelling of Induction Machines under No-load Condition taking into account Manufacturing Processes, Proceedings ICEM 004 (Cracow, Poland). [8] F. Ossart, E. Hug, O. Hubert, C. Buvat, R. Billardon, Effect of punching on electrical steels: experimental and numerical coupled analysis, IEEE Trans. on Magn., Vol. 36, no. 5, 000, p [9] P. Baudouin, M. De Wulf, L. Kestens, Y. Houbaert, The effect of guillotine clearance on the magnetic properties of electrical steels, J. of Magn. and Magn. Mater., 56, 003, p [10] G. Crevecoeur, P. Sergeant, L. Dupré, L. Vandenbossche, R. Van de Walle, Analysis of the local material degradation near cutting edges of electrical steel sheets, IEEE Trans. on Magn., vol. 44, no. 11, pp , Nov 008. ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 01) 1