Epstein Frame Measurement Based Determination of Original Non-Degraded and Fully Degraded Magnetic...

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Epstein Frame Measurement Based Determination

of Original Non-Degraded and Fully Degraded

Magnetic Characteristics of Material Submitted to

Laser CuttingMadeleine Bali1, Student Member, IEEE , Herbert De Gersem2, Annette Muetze1, Senior Member, IEEE

1 Graz University of Technology, Electric Drives and Machines Institute

Inffeldgasse 18/I, A-8010 Graz, Austria2 Technische Universität Darmstadt, Institut f ̈ur Theorie Elektromagnetischer Felder

Schlossgartenstraße 8, D-64289 Darmstadt, Germany

[email protected], [email protected], [email protected]

Abstract—The degrading effect of laser cutting on steel sheetmaterial, and thus on the material’s magnetic characteristics, ismuch less understood than that of mechanical cutting. Further-

more, the estimated degrading influence on magnetic propertiesis still difficult to determine and not sufficiently known. Inthis paper, the magnetic characteristics of the degraded andnon-degraded zones are computed from data obtained by twoEpstein frame measurements using sample strips of differentwidths. Subsequently, these new characteristics are inserted intoa finite-element model, which accounts for arbitrary geometries.The simulation results for the influence of laser cutting onthe magnetic characteristics of the stator lamination stacks areverified by measurements.

Index Terms—Electrical steel sheets, ferromagnetic material,

finite element method, laser cutting, magnetostatics, manufactur-

ing, material degradation.

I. INTRODUCTION

To date, the electromagnetic characteristics of electrical

steel sheets used in electrical machines are implemented in

finite element simulations by magnetization and loss curves

obtained from Epstein frame measurements [1] and/or pro-

vided by manufacturers. The literature generally agrees that

these data sets differ from those of the finished machine (e.g.

[2]), as the magnetic deterioration due to the manufacturing

steps is not taken into account. Commonly, these differences

are considered, for example, by correction or building factors

[3]–[5], which generally do not include the variabilities be-

tween different materials, machine designs (stator and rotor

cross sectional areas), and manufacturing techniques.

This paper focuses on modeling the degrading effect of laser

cutting, in particular solid state laser cutting, in contrast to

the majority of works that have focused on the degradation

effect due to mechanical cutting [6]–[9]. It reviews a method

to estimate the losses for different geometries and applies this

method to samples of solid state laser-cut stator lamination

stacks, thereby further investigating possible differences bet-

ween the modeling of mechanical and laser cutting.

Fig. 1. Arrangement of steel strips in the Epstein frame, based on [1].

I I . PERFORMED M EASUREMENTS

The BH - and specific loss curves of two samples with thesame length, y , and thickness, wz , but with different widths(w1= 30mm and w2 = 7.5mm) are determined by Epsteinframe measurements (Fig. 2). The Epstein frame measure-

ments have been based on the standards IEC 60404-2 [1] and

IEC 60404-10 [10], and the setup has been presented in detail

in [6].

In the case of the ‘wide’ samples (width of w1) 16 electricalsteel sheet strips, in the case of the ‘small’ samples (width

of w2) 64 strips are placed into the frame (Fig. 2). Note thatthe transversely-cut and longitudinally-cut samples are placed

in two opposite coils (Fig. 1) [1].

All samples of one material are taken from the same mother

coil (MC) since material deviations from MC to MC may be

larger than the influence of the manufacturing process [11].

978-1-4673-7151-3/15/$31.00 ©2015 IEEE 6096


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Fig. 2. Correlation between measurements and identification procedure.

III. REVIEW: IDENTIFICATION OF N ON-D EGRADED ANDFULLY D EGRADED BH -C HARACTERISTICS

A. Assumptions and simplifications

The following assumptions and simplifications have been

made:

• The laser cutting process induces equal degradation pro-

files on both sides of the sample.

• The degradation zone is homogeneous and has a specified

depth, d (Fig. 2).• The deteriorated zones on the short sides of the Epstein

samples is neglected as d y (Fig. 2).

The fractions of degraded material in samples 1 and 2 are

denoted as γ 1 (2d / w1) and γ 2 (8d / w2) respectively.Only very few results have been published on the degra-

dation depth of laser cutting, for example in [12]. This is,

among other reasons, also due to a lack of understanding of

the detailed deterioration of the material which is caused by

the laser cutting technique. In contrast to mechanically-cut

samples, laser cutting induces thermal stresses due to the fast

heating followed by a rapid cooling [13], [14]. Thus, not every

measurement method used to identify the degradation depth

Fig. 3. Identifying the non-degraded and degraded BH -curves with the BH -curves of small and wide samples [6].

known from mechanically-cut samples may be applicable

to laser-cut samples. For example, the determination of the

changed grain sizes is not suitable, as according to [15] laser

cutting does not change the grain size of the material. Further-

more, the laser technique and the laser settings influence the

degree, and thus, the depth of deterioration.

In the presented modeling approach, a non-degraded area in

the middle of the sheet and a homogeneously degraded zone

with a deterioration depth of 2.1mm from the cut edge isassumed. Thus, a better comparison with the results presented

in [6], in which mechanically-cut samples are investigated,

is possible, when the same degradation depth is used. Note

that the proposed technique also allows to set other degrada-

tion depths, and the computed material characteristics result

accordingly.

B. Basic identification procedure

The identification procedure has been discussed at length

in [6] and is reviewed here briefly for comprehensiveness.

The basic idea of this procedure is presented in (Fig. 3).

The measurement series (H 1, B1) and (H 2, B2) are obtainedindependently from the ‘wide’ and ‘small’ samples in the

Epstein frame (see also Fig. 2). Of course, it is ensured that

these samples result from the same material and MC.

Subsequently, data points (H, Bnd) and (H, Bdg) are calcu-

lated from 1− γ 1 γ 11− γ 2 γ 2

BndBdg

=

B1B2

. (1)

The subscripts 1 and 2 label the measured data of the twosamples with different widths (see also Section II). Eq. (1)

presents the parallel connection of the flux paths through the

non-degraded (nd) and degraded (dg) zones. Note, the values

B1, B2, Bnd and Bdg all correspond to the same magnetic fieldstrength H .

A few generalizations are implemented to improve the

applicability in practice:

1) Interpolation and sampling,

2) Rayleigh region,3) Full-saturation region.

A more detailed explanation is reviewed from [6] in Ap-

pendix A.

The obtained curves (H, Bnd) and (H, Bdg) can easily beintegrated into a finite element calculation of, for example, a

machine consisting of a material with a fully degraded zone

at the cut edge and a non-degraded zone in the middle of the

sample.

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IV. RESULTS

In the following, the identification procedure is applied to

three different materials

• M270-35A,

• M400-50A,

• M800-65A,

commonly used in electric machine design, at three different

frequencies• 50Hz• 250Hz• 500Hz.

Thus, an extensive verification of this method is possible.

The permeability of sample 1 is substantially better than that

of sample 2, because w1 > w2. Thus, the relative degradedvolume (V degraded/V total sample volume) in sample 2 is larger thanin sample 1 (Fig. 2).

As already shown in [6], piecewise cubic splines in com-

bination with a repairing procedure of the Rayleigh and full

saturation regions represent the measured curves accurately

(see Fig. 4). This, along with the basic identification procedure,

provides the results presented in Fig. 5. The sampling pointsfor the magnetic field strength are taken from the measure-

ments of the first sample (see Appendix A).

0 2000 4000 6000 8000 10000 12000 140000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

22

Magnetic field strength (A/m)

M a g n e t i c f l u x d e n s i t y ( T )

BH1 (measured)

BH1 (calculated)

BH2 (measured)

BH2 (calculated)

Fig. 4. Measured and identified BH -curves, M270-35A at 50 Hz.

0 2000 4000 6000 8000 10000 12000 140000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Magnetic field strength (A/m)

M a g n e t i c f l u x d e n s i t y ( T )

first sample

second sample

nondegraded

degraded

Fig. 5. Identified BH -curves for the degraded and non-degraded materialzone, M270-35A at 50Hz.

As expected, the BH -curves are stacked such that for allvalues H of the magnetic field strength holds, Bnd(H ) >B1(H ) > B2(H ) > Bdg(H ), in all regions of the charac-teristic (Fig. 5).

Note that the model may produce unusual (unphysical)

behavior in the knee point area of the identified non-degraded

BH -curve by producing an extrema (see Fig. 5). This mayoccur when the difference of the magnetic induction or the

relative permeability of both measured samples is very largeat a respective magnetic field strength H : In contrast tomechanically-cut samples (see [16]), the relative permeabil-

ity of the small laser-cut samples is more degraded at the

small magnetic field strength area (see Fig. 6). Addition-

ally, the relative permeability of laser-cut samples at small

magnetic field strengths is, with decreasing sample width or

increasing deteriorated zone, degraded to a plateau (see e.g.

Fig. 6 and [16]). Hence, the difference of relative permeabil-

ities of samples 1 and 2 is significantly larger for laser-cutsamples. Therefore, such artificial extrema may result if the

method is applied to laser-cut samples of significantly different

widths.

200 400 600 800 1000 1200

1000

2000

3000

4000

5000

6000

7000

Magnetic field strength in A/m

R e l a t i v e p e r m e a b i l i t y

M27035A_30_250Hz_mc

M27035A_75_250Hz_mc

M27035A_30_250Hz_lc

M27035A_75_250Hz_lc

Fig. 6. The difference in relative permeability due to the different used samplesizes is larger for laser-cut (lc) than for mechanically-cut (mc) samples at smallmagnetic field strengths.

V. REVIEW: IDENTIFICATION OF L OS S C URVES FOR

NON-D EGRADED AND F ULLY D EGRADED M ATERIAL

A. Loss model

The loss model used in this identification procedure is

described by

ploss = |c1|B + c2B2 , (2)

with ploss the loss density and c1 and c2 the parameters which

need to be identified by regression. The expression is quitesimple but approximates the loss density very accurately.

B. Basic identification procedure

The identification of the loss curves for the non-degraded

and degraded material requires several steps and depends on

the previously obtained BH -curves, Bnd(H ), and Bdg(H ).With this procedure, including both the loss model and the

measurement data, the parameters for the loss model for

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the degraded and the non-degraded material zones can be

determined.

Fig. 7. Identifying the non-degraded and degraded loss curves from the losscurves of small and wide samples [6].

The identification procedure is reviewed from [6]:

1) Choose a set of sampling points for the magnetic field

strength H sample.2) Evaluate the (H, B∗nd)- and (H, B

∗

dg) curves.

3) Calculate the corresponding averaged magnetic flux den-sities, B∗1 and B∗

2 , in both samples, using eq. (1).

4) Evaluate the measured loss curves for B∗1 and B∗

2 , leading

to p1 and p2.5) Evaluate the loss model for a set of model parameters

and for the points B∗nd and B∗

dg.

6) Calculate the corresponding averaged loss densities p∗1and p∗2 in both samples, using:

1− γ 1 γ 11− γ 2 γ 2

pnd pdg

=

p∗1 p∗2

. (3)

7) Compare p∗1 and p∗

2 with p1 and p2.

Steps 1 to 4 are carried out in advance. Steps 5 to 6 are

implemented in a procedure which is given as an input toan optimization routine minimizing the error in step 7.

VI. RESULTS

The loss identification procedure is applied to the measure-

ment results for ‘wide’ and ‘small’ samples of all investigated

material samples. The modeled curves approximate the mea-

sured ones sufficiently well (as illustrated in Fig. 8).

The resulting loss densities for the same magnetic flux

density are ordered as pnd < p1 < p2 < pdg (Fig. 9). Thisapplies to all investigated samples.

VII. APPLYING THE I DENTIFIED C URVES TO A

LASER-C UT S TATOR G EOMETRY

A. Stator measurement setup

The laminations of the investigated stator stack are derived

from the same MC as the investigated Epstein samples and

have been cut by the same laser cutting method. This has been

done to avoid possible additional deviations due to different

production batches.

0 0.5 1 1.50

5

10

15

20

25

30

35

40

45

50

Magnetic flux density (T)

L o s s d e n s i t y ( W / k g )

sample 1: measurement

sample 1: approximation

sample 2: measurement

sample 2: approximation

Fig. 8. Measured and identified loss curves for laser-cut samples, M400-50Aat 250Hz supply frequency.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

10

20

30

40

50

60

70

80


L o s s d e n s i t y ( W / k g )

sample 1

sample 2

nondegraded

degraded

Fig. 9. Measured and computed loss curves for laser-cut samples, M400-50Aat 250Hz supply frequency.

As for the mechanically-cut stator samples in [6], a pri-

mary and secondary coil are wound around the stator yoke

(yoke height = 12mm). Hence, the magnetic flux is onlyconsidered in the yoke; and an alternating field, similar to

the Epstein samples, can be assumed. Similar to the Epstein

frame measurements (see Section II), the form factor of the

secondary voltage is controlled to be in the range 1.111±1%.Additionally, the same power amplifier and power analyzer as

for the Epstein frame measurements are used (see Section II).

The lamination stacks are demagnetized before any readings

are taken.

B. Simulation

The obtained BH -curves for the fully degraded and non-degraded zones of the Epstein samples are applied to the

stator geometry implemented in a finite element simulation(FEMM [17] coupled with Matlab [18]), see Fig. 10. The same

degradation depth, d, is set at the cut edges as for the Epsteinsamples (see Section III).

In contrast to the Epstein samples, the stator lamination

stacks have been pressed (around 4MPa) and glued. Thisinfluence of pressing and gluing is added to the computed

values, so that the computed and measured loss data are

comparable. The increase of specific losses due to the pressing

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Fig. 10. Application of computed magnetic characteristics to arbitrarygeometries.

and gluing is in the range of experimentally determined values

that have been presented in the literature which consider the

pressing of steel sheets into the thickness direction and is based

on [19]. A more detailed explanation of this has been given

in [6].

C. Results

Selected computed and measured results of the investigated

stator samples are presented in Figs. 11-13. In all cases, the

measured and computed specific losses of the investigatedstator lamination stacks are in good agreement, for different

materials as well as different frequencies. Thus, the proposed

identification procedure for laser-cut laminations can also

serve as a good tool in the design process of electrical

machines to obtain more accurate data of changed magnetic

characteristics of electric steel sheets due to cutting.

VIII. SUMMARY

A method which considers the influence of cutting that

had been proposed for mechanically-cut samples [6] has also

been applied to laser-cut samples. This method is verified

by measurements on several stator lamination stacks withdifferent materials and at different frequencies. The computed

specific losses for the stator lamination stacks correspond

with the measured ones. This method has been validated for

frequencies up to 500Hz.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

10

20

30

40

50

60

70

80

90


P o w e r l o s s d e n s i t y ( W / k g )

measured

computed excl. pressing

computed incl. pressing

Fig. 11. Measured and computed loss curves of the investigated statorlamination stack at 50Hz, material M270-35A.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

10

20

30

40

50

60


P o w e r l o s s d e n s

i t y ( W / k g )

measured




0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

3

4

5

6

7

8


P o w e r l o s s d e n s i t y ( W / k g )

measured




ACKNOWLEDGEMENT

The authors would like to thank Dr. M. Braun of Dr.-Ing.

Ernst Braun GmbH and Mr. A. Peter of Kienle & Spiess

GmbH for making the measurement equipment and material

samples available.

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APPENDIX A

Generalizations implemented in the basic identification pro-

cedure, reviewed from [6]:

1) Interpolation and sampling. For the identification proce-

dure there is the need to obtain matching values for H 1

and H 2. This is achieved by interpolating the samplingpoints. As shown in [6], cubic splines provide the best re-

sults with regard to accuracy respecting all magnetization

curve characteristics. This is in contrast to other well-

known fitting functions as e.g., the Brauer curve [20],

the Bertotti curve [21] or the Langevin curve [22]. The

sampling points for the magnetic field strength H aretaken from the measurements of the first sample.

2) Rayleigh region. The measurements for small fields may

lack accuracy. As a consequence, the Rayleigh effect is

only marginally represented in the measurement curves.

Under these circumstances, eq. (1) may lead to invalid

results, e.g., Bdg may become negative. Two remedies

were already shown in [6].Note, even when the (H 1, B1)-curves and (H 2, B2)-curves are “cleaned” to correctly represent the Rayleigh

region, this quality is not carried over by the identification

procedure represented by eq. (1) to the (H, Bnd)- and(H, Bdg)-curves. There, the clean-up procedure shouldbe repeated. In fact, it makes more sense to align the

Rayleigh region for the (H, Bnd)- and (H, Bdg)-curves,because these are assumed to correspond to individual

materials, whereas the (H, B1)- and (H, B2)-curves areparticularly averaged material properties.

3) Full-saturation region. It is necessary to clearly define the

extrapolation of the BH -characteristics for large fields.

• Extrapolating from the last measurement point witha differential permeability, µ0, is based on physicalunderstanding, but may introduce a discontinuity in

the differential permeability which may hamper the

convergence of the Newton method applied later on.

As long as the (H 1, B1)-curve lies above the (H 2, B2)-curve, this procedure guarantees consistent results for

(H, Bnd) and (H, Bdg).• Another technique extends the BH -curves according

to the slope determined by the two last measurement

points. This approach may be inappropriate when the

small variations of the magnetic flux density are not

sufficiently resolved by the measurements. Moreover,

it should be verified that the final slope for (H 1, B1)is larger or equal to that of (H 2, B2).

REFERENCES

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[6] M. Bali, H. De Gersem, A. Muetze, “Epstein Frame Measurement BasedDetermination of Original Non-Degraded and Fully Degraded MagneticProperties of Material Submitted to Mechanical Cutting,” Electric Ma-chines Drives Conference (IEMDC), 2015 IEEE International , pp. 1184-1189, 2015.

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[12] R. Siebert, J. Schneider, E. Beyer “Laser cutting and mechanical cuttingof electrical steels and its effect on the magnetic properties,” IEEE Transactions on Magnetics 50(4), pp.1-4, 2014.

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[16] M. Bali, A. Muetze, “Influences of CO2 and FKL-laser cutting as wellas mechanical cutting on the magnetic properties of electric steel sheetsdetermined by Epstein frame and stator lamination stack measurements,” Energy Conversion Congress and Exposition (ECCE), 2014 IEEE , pp.1443-1450, 2014.

[17] “Finite Element Method Magnetics (FEMM),” [Online]. Available:http://www.femm.info , accessed on 2015-03-19.

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