An innovative approach for the evaluation of iron losses in
magnetic laminations, applied to the optimization of highly
saturated electric motors
Lode Vandenbossche1, Sigrid Jacobs2, Raphael Andreux3,
Nicolas Labbe3, Emmanuel Attrazic4
1
ArcelorMittal Global R&D Gent, J. Kennedylaan 3, 9060 Zelzate, Belgium
2
ArcelorMittal Global R&D, J. Kennedylaan 51, 9042 Gent, Belgium
3
Valeo Electrical Systems, Parc d'Activités de Chesnes, Ville Nouvelle de l'Isle d'Abeau,
38291 St Quentin Fallavier Cedex, France
4
ArcelorMittal St Chély d'Apcher, Route du Fau de Peyre, 48200 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 12V) 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 2kW of mechanical
power for a typical diesel application (Pmax on Fig. 2) when supplied with a 12V 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 2012)
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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 2: 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 Pmax in Fig. 2), that means close to 8000 rpm at the armature shaft (electrical frequency around 200Hz).
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 30000 rpm (as shown on Fig. 2) corresponding to an electrical frequency of the fundamental
from around 200Hz 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 2012)
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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 2 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).
2. 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 M235-35A grade of 0.35mm
gauge, the specific iron loss at 1.5T and 50Hz is less than 2.35 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 2012)
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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 [2-3] 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:
PFe ( J p , f ) = k hyst J p2 f + k eddy J p2 f 2 + k exc J 1p.5 f 1.5
(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 Jp 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 ) = s1 (1 + (r ( J max ) − 1) ⋅ c )J max f +
2
∞
s2
n =1
J n (nf ) + s3
2
2
∞
Jn
1.5
(nf )1.5 + s4 J max s
5
⋅f2
(2),
n =1
taking into account the following definitions:
•
si :
•
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 J n = ( J nx + J ny )
f : fundamental frequency, in Hertz [Hz]
•
c:
•
•
J min : minimum value of flux density amplitude, evaluated over one electrical period [T]
all five parameters are fitted material parameters (depending on the ES grade)
2
flux distortion factor, c =
J min
2
2
J max
r : rotational loss factor (empirically determined)
ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 2012)
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Equation (2) 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. 2). 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 2D 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 2. 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 2012)
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3.1 Finite element modelling at Valeo and its validation
Using the finite element software Flux2D, 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 3.2). This operation occurs for every considered mechanical position, which is every 2
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 2D 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.
2D 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 2D 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 2012)
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estimated in the modelling. The cyan curve represents a simple 2D 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 2D Finite Element Model
at a constant speed (2000rpm) 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
fmin) to the no-load point (named fmax). 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. 2. 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 (fmax and fmin)
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 2012)
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Fig. 8 shows the results of the finite element modelling in terms of the histogram of Jmax (maximum magnetic
polarization, evaluated over one electrical period; rotor only), for the lowest and highest fundamental frequencies,
resp. fmin and fmax. When increasing the fundamental frequency, the histogram shifts to lower J values.
12%
relative occurrence (%)
10%
8%
6%
4%
2%
0%
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
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: fmin (in blue) and fmax (in red).
3.2 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 = f2
fund freq = f3
fund freq = f4
fund freq = f5
fund freq = f6 (fmax)
60
Losses [W]
50
40
30
20
10
0
Physt
Prot
PeddyHH
Peddy_f0
PexcessHH Pexcess_f0 Psaturation
Ptotal
Fig.9: Iron losses decomposition (different terms according to equation 2; 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 2012)
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In Fig. 9 the results of the rotor iron loss computations based on equation 2 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 Jmax 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
Ω 0 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 2 , i.e. by removing
ArcelorMittal-Valeo: Evaluation of iron losses applied to optimization of highly saturated electric motors (Inductica Berlin 2012)
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Piron (Ω 0 , I 0 ) = − JΩ 0 (
dΩ
dΩ
−
)
dt Ω = Ω 0 , I = 0 dt Ω = Ω 0 , I = I 0
(3)
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.
max
Fig. 11: Armature speed slow-down measurement for different supplied currents
Fundamental
frequency (Hz)
f1 = fmin
f2
f3
f4
f5
f6 = fmax
Total iron losses
measured (p.u)
0.61
0.82
0.91
1.00
1.00
0.96
Measured rotor iron losses =
+ total iron losses measured
– iron losses calculated in stator (p.u)
0.37
0.59
0.74
0.86
0.88
0.86
Table 1: Results of iron losses measurements, per unit
4.2 Comparison of iron loss measurements and calculations
Figure 12 compares the measured rotor iron losses (as determined in section 4.1) with the calculated rotor iron
losses (see section 3.2), 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 2012)
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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. 12: 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 2 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 0.8 – 2.06 T and 0.4 – 1.34 T, respectively at fmin and fmax).
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 2012)
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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 fmax (warm start; no-load condition): when
comparing material B with material A, the rotor iron losses are 37% less at fmin, and are 44% less at fmax.
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
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Angeles, May 6-9, 2012.
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