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Magnetic properties of laminated steel sheets for normal fluxes
340
Journal
MAGNETIC
PROPERTIES
T. YAGISAWA,
OF LAMINATED
Y. TAKEKOSHI
of Magnetism
and Magnetic Materials 26 (1982) 340-342 North-Holland Publishing Company
STEEL SHEETS FOR NORMAL
FLUXES
and S. WADA
Toshibu Corporution, Heuvy Appumtus Engineering Laboraoty, Jupun
The losses in laminated steel sheets due to normal fluxes have been investigated. The loss is high at the surface layer, and decreases with flux penetration, while the AC permeability increases. After a few layers those reach constant values. The flux distribution and the losses in cores can be calculated using these values.
Laminated cores of electrical machines are often subjected to normal fluxes. Such a case can be seen in the core legs [ 1,2] and the magnetic shields on the tank walls of large transformers, or in the end regions of large generator cores [3,4]. For normal fluxes lamination of thin insulated sheets is not effective in reducing eddy-currents, and losses are very high. To prevent local heating designers have to predict the values of these losses. In this paper, the losses of laminated steel sheets due to normal fluxes have been investigated experimentally. The measurements have been done under the simple condition that only the normal components of the fluxes enter the model cores of laminated sheets uniformly from the air-gaps. Also described is that the flux distribution and the losses in a more complex case can be calculated approximately, using the data, under this simple condition.
2. Experiment The samples of electrical steel sheets were placed with air-gaps between magnetizing yokes, and normal fluxes at 50 Hz were applied to the sample sheets from the yokes. The magnetizing yokes consisted of a pair of U-shaped cores, and primary and secondary coils were wound. The total losses of the yokes with the samples were measured with 0304-8853/82/0000-0000/$02.75
0 1982 North-Holland
a wattmeter, and the difference between the loss measured with 2N sheets and that with 2(N - 1) sheets corresponds to the loss of the Nth sheet from the surface of the lamination. The magnetizing currents and the AC hysteresis loops were also determined in a similar way. Search coils for measuring flux distribution were placed in V-shaped grooves cut on the surface of the sheet and stuck with paraffin.
3. Result and discussion Fig. 1 shows the loss variation from the surface to the inside. The loss is higher in a few sheets near the surface, and decreases towards the inner part. Fig. 2 shows the AC hysteresis loops of the surface and the inside sheet of the sample. These results can be explained as follows; The distribution of normal induction is almost uniform on the surface, while in the inside the flux flows to the edge of the sheets by the eddy-current effect, and the eddy-current loss is lower than that of the surface sheet. Fig. 3 shows the distribution of normal fluxes.
4. Simplified expression and its application Eddy-currents by normal fluxes are similar to those in solid cores. In addition, the permeability in the normal direction can be approximated as
T. Yugisawa
et (11. / Mugnetic
properties
of luminuted
341
steel sheets
3-
Bam0.5T f =50HZ
-7 : 1 \
cz \ m 2-
!,
‘\
--I 7+ 01
I
nA
L 0
IO
20
30
Fig. 1. Loss variation
from surface
of laminations
in a stack.
Table I Measured
0.
W =
52mm
flux distribution
and calculated
..__ across
the core.
losses
inner part
t,
/
B, 0-I
surface
i’\
*
Loss (W) measured
calculated
18 108 320
14 95 285
L-J-
400300200100
0
0.10 0.19 0.28
100200300400
H (A/cm)
Fig. 2. Hysteresis
loops for normal
Fig. 4. Calculated
flux lines for the model core.
fluxes at 50 Hz.
LAMINATED
constant. Then the AC permeability and the eddycurrent loss in the inner sheets are given by simple expressions: l/2 LL (1) PAC =s ( 27rfu1 p =
1 Fig. 3. Normal
3..
.
-i-J
I
k
40
with number
O-6.
.
‘\~ ‘1,
.a_ /x No. of sheet
, \ f
hLlr3/2a’/2p-‘/2f s/2(@/L)2
(2)
SHEi!XS
where L is the peripheral length of the sheet, S the area of the sheet and h the height of the stack. The calculated loss is also shown in fig. 1. The leakage fluxes of electrical machines which entered the laminated sheets perpendicularly change their direction to parallel. In order to prediet the losses, the normal components have to be
342
T. Yagisawa et al. / Magnetic properties
calculated by numerical methods. In many cases th.e width of the sheets is smaller than the length, so the flux distribution in laminated cores can be calculated under 2-dimensional approximation by use of the normal AC permeability. Fig. 4 shows an example of the calculation, and table 1 shows the comparison of the calculated and measured losses. 5. Conclusion
The loss and the AC permeability of laminated steel sheets for normal fluxes have been investi-
of laminated steel sheets
gated experimentally. These values can be given by simple expressions. Using these values, the flux distribution and the losses in the laminated cores of electrical machines can be calculated approximately.
References [I] C.J. Carpenter, Proc. IEE 124 (1977) 659. [2] R.F. Hemmings and G.D. Wale, Proc. IEE 124 (1977) 1064. [3] P.J. Tavner, p. Hammond and J. Penman, Proc. IEE 125 (1978) 1339. [4] P.J. Tavner, Proc. IEE, 127B (1980) 57.
Journal
MAGNETIC
PROPERTIES
T. YAGISAWA,
OF LAMINATED
Y. TAKEKOSHI
of Magnetism
and Magnetic Materials 26 (1982) 340-342 North-Holland Publishing Company
STEEL SHEETS FOR NORMAL
FLUXES
and S. WADA
Toshibu Corporution, Heuvy Appumtus Engineering Laboraoty, Jupun
The losses in laminated steel sheets due to normal fluxes have been investigated. The loss is high at the surface layer, and decreases with flux penetration, while the AC permeability increases. After a few layers those reach constant values. The flux distribution and the losses in cores can be calculated using these values.
Laminated cores of electrical machines are often subjected to normal fluxes. Such a case can be seen in the core legs [ 1,2] and the magnetic shields on the tank walls of large transformers, or in the end regions of large generator cores [3,4]. For normal fluxes lamination of thin insulated sheets is not effective in reducing eddy-currents, and losses are very high. To prevent local heating designers have to predict the values of these losses. In this paper, the losses of laminated steel sheets due to normal fluxes have been investigated experimentally. The measurements have been done under the simple condition that only the normal components of the fluxes enter the model cores of laminated sheets uniformly from the air-gaps. Also described is that the flux distribution and the losses in a more complex case can be calculated approximately, using the data, under this simple condition.
2. Experiment The samples of electrical steel sheets were placed with air-gaps between magnetizing yokes, and normal fluxes at 50 Hz were applied to the sample sheets from the yokes. The magnetizing yokes consisted of a pair of U-shaped cores, and primary and secondary coils were wound. The total losses of the yokes with the samples were measured with 0304-8853/82/0000-0000/$02.75
0 1982 North-Holland
a wattmeter, and the difference between the loss measured with 2N sheets and that with 2(N - 1) sheets corresponds to the loss of the Nth sheet from the surface of the lamination. The magnetizing currents and the AC hysteresis loops were also determined in a similar way. Search coils for measuring flux distribution were placed in V-shaped grooves cut on the surface of the sheet and stuck with paraffin.
3. Result and discussion Fig. 1 shows the loss variation from the surface to the inside. The loss is higher in a few sheets near the surface, and decreases towards the inner part. Fig. 2 shows the AC hysteresis loops of the surface and the inside sheet of the sample. These results can be explained as follows; The distribution of normal induction is almost uniform on the surface, while in the inside the flux flows to the edge of the sheets by the eddy-current effect, and the eddy-current loss is lower than that of the surface sheet. Fig. 3 shows the distribution of normal fluxes.
4. Simplified expression and its application Eddy-currents by normal fluxes are similar to those in solid cores. In addition, the permeability in the normal direction can be approximated as
T. Yugisawa
et (11. / Mugnetic
properties
of luminuted
341
steel sheets
3-
Bam0.5T f =50HZ
-7 : 1 \
cz \ m 2-
!,
‘\
--I 7+ 01
I
nA
L 0
IO
20
30
Fig. 1. Loss variation
from surface
of laminations
in a stack.
Table I Measured
0.
W =
52mm
flux distribution
and calculated
..__ across
the core.
losses
inner part
t,
/
B, 0-I
surface
i’\
*
Loss (W) measured
calculated
18 108 320
14 95 285
L-J-
400300200100
0
0.10 0.19 0.28
100200300400
H (A/cm)
Fig. 2. Hysteresis
loops for normal
Fig. 4. Calculated
flux lines for the model core.
fluxes at 50 Hz.
LAMINATED
constant. Then the AC permeability and the eddycurrent loss in the inner sheets are given by simple expressions: l/2 LL (1) PAC =s ( 27rfu1 p =
1 Fig. 3. Normal
3..
.
-i-J
I
k
40
with number
O-6.
.
‘\~ ‘1,
.a_ /x No. of sheet
, \ f
hLlr3/2a’/2p-‘/2f s/2(@/L)2
(2)
SHEi!XS
where L is the peripheral length of the sheet, S the area of the sheet and h the height of the stack. The calculated loss is also shown in fig. 1. The leakage fluxes of electrical machines which entered the laminated sheets perpendicularly change their direction to parallel. In order to prediet the losses, the normal components have to be
342
T. Yagisawa et al. / Magnetic properties
calculated by numerical methods. In many cases th.e width of the sheets is smaller than the length, so the flux distribution in laminated cores can be calculated under 2-dimensional approximation by use of the normal AC permeability. Fig. 4 shows an example of the calculation, and table 1 shows the comparison of the calculated and measured losses. 5. Conclusion
The loss and the AC permeability of laminated steel sheets for normal fluxes have been investi-
of laminated steel sheets
gated experimentally. These values can be given by simple expressions. Using these values, the flux distribution and the losses in the laminated cores of electrical machines can be calculated approximately.
References [I] C.J. Carpenter, Proc. IEE 124 (1977) 659. [2] R.F. Hemmings and G.D. Wale, Proc. IEE 124 (1977) 1064. [3] P.J. Tavner, p. Hammond and J. Penman, Proc. IEE 125 (1978) 1339. [4] P.J. Tavner, Proc. IEE, 127B (1980) 57.