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Effect of non-metallic precipitates and grain size on core loss of non-oriented electrical silicon steels
Journal of Magnetism and Magnetic Materials 451 (2018) 454–462
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Effect of non-metallic precipitates and grain size on core loss of non-oriented electrical silicon steels Jiayi Wang, Qiang Ren, Yan Luo, Lifeng Zhang ⇑ Beijing Key Laboratory of Green Recycling and Extraction of Metals and School of Metallurgical and Ecological Engineering, University of Science and Technology, Beijing, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 21 August 2017 Received in revised form 14 November 2017 Accepted 17 November 2017 Available online 23 November 2017 Keywords: Non-oriented electrical silicon steel Precipitates Grain size Core loss
a b s t r a c t In the current study, the number density and size of non-metallic precipitates and the size of grains on the core loss of the 50W800 non-oriented electrical silicon steel sheets were investigated. The number density and size of precipitates and grains were statistically analyzed using an automatic scanning electron microscope (ASPEX) and an optical microscope. Hypothesis models were established to reveal the physical feature for the function of grain size and precipitates on the core loss of the steel. Most precipitates in the steel were AlN particles smaller than 1 lm so that were detrimental to the core loss of the steel. These finer AlN particles distributed on the surface of the steel sheet. The relationship between the number density of precipitates (x in number/mm2 steel area) and the core loss (P1.5/50 in W/kg) was regressed as P1.5/50 = 4.150 + 0.002 x. The average grain size was approximately 25–35 lm. The relationship between the core loss and grain size (d in lm) was P1.5/50 = 3.851 + 20.001 d1 + 60.000 d2. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction The non-oriented electrical silicon steel is an essential magnetic material well used as the materials for rotors for different motors and generators, especially in energy, machinery and electricity fields [1–4]. With the increase of the global electricity energy consumption, requirements for high-quality non-oriented electrical silicon steel are becoming serious more and more [5]. Core loss is an important feature to judge the quality of non-oriented electrical silicon steel sheets, and a low value of this parameter leads to a better efficiency of energy utilization, a decrease in heat generation, and leads to downsize motors and improve service life simultaneously [6]. Factors which have influences on the core loss the steel can be classified into two major parts: non-metallic precipitates and properties of the material including crystallographic texture, chemical composition, microstructure and grain size [7–11]. It is an essential way to decrease the core loss by decreasing the number density of non-metallic precipitates and improving the grain size, whose boundaries block the motion of domain wall during magnetization [12]. Studies were reported to investigate the effect of non-metallic precipitates and grain size on the core loss of steel [13–18]. However, only qualitative conclusions were obtained since too many parameters were involved to carry out
⇑ Corresponding author. E-mail address: [email protected] (L. Zhang). https://doi.org/10.1016/j.jmmm.2017.11.072 0304-8853/Ó 2017 Elsevier B.V. All rights reserved.
quantitative analysis. Furthermore, most quantitative analysis on the grain size and core loss are short of theoretical fundamentals and the physical feature of grains on the core loss were hardly revealed. Recently, Pirgazi [2] established a mathematic model showing the relationship between magnetic induction and grain size of the steel. Mathematic equation between grain size and core loss can be obtained using the developed model. Furthermore, it is known that the coercivity is in direct proportion to the core loss and the number density of non-metallic precipitates. Meanwhile, it is in inversely proportion to the size of precipitates, hinting that the relationship between precipitates and core loss can be regressed into a linear equation. In the current study, the effect of non-metallic precipitates and grain size on the core loss of a non-oriented electrical silicon steel were quantitatively investigated using an automatic scanning electron microscope (ASPEX) and optical microscope. The statistical feature of non-metallic precipitates and grain size of the steel were obtained. Furthermore, hypothesis models on the eddy current loss, as well as hysteresis loss, and grains were established.
2. Materials and experiments Eight samples of 50W800 non-oriented electrical silicon steel product sheets fabricated by one-step-cold-rolling technique were the analyzed in this study. The thickness of samples is 0.5 mm. The manufacturing process and parameters of the samples are similar.
J. Wang et al. / Journal of Magnetism and Magnetic Materials 451 (2018) 454–462
The equivalent Si content (Si% + Al%) of these samples are about 1.3 wt%, and their core loss are listed in Table 1. The core loss is measured by MTR-2949 alternating current magnetization characteristic measuring device from METRON Tech Research Corporation, Japan whose accuracy can reach to 0.0001 W/kg with a maximum error of 0.0016%. The main devices in this study are ASPEX SEM and Leica DM 4000 optical microscope (OM). The minimum equivalent size of the detected precipitates can reach to under 0.1 lm by using ASPEX SEM and the optical micrographs of grain were taken by OM. Polished samples were exposed to ASPEX and abundant data including precipitate size, number density can be gained by automatic scanning. Then, the samples were etched by 4%-nitric-acid ethanol solution. The average grain size can be counted using Image-pro plus software (IPPS). Fig. 1 shows the method for counting grain size by IPPS. First of all, the scale of the pictures of grains should be the same. After dealing the picture by graphics software such as PS and inputting the scale into IPPS, the real grain size of each sample can be directly obtained by IPPS. Then, the square mean was computed with the grain size just gained to know the average grain size. To improve the accuracy of the average grain size, more than 10 optical micrographs should be counted for each sample. Eq. (1) shows the formula to calculate the average grain size.
¼ D
rffiffiffiffiffiffiffiffiffiffiffiffiffi P 4 Si pn
ð1Þ
is average gain size of each sample, Si means the area of where D each grain which can be given by IPPS directly, n is the total grain number. 3. Effect of non-metallic precipitates on core loss of the steel The magnetic property can be detrimentally influenced by precipitates through three ways: raising the inner stress induced by lattice distortion caused by precipitates; blocking the motion of domain wall during magnetization; inhibiting grain growth which is an indirect way to affect magnetic property [8]. It was reported that precipitates whose size is close to the thickness of domain wall have the strongest pinning effect on the grain growth and the motion of domain wall during magnetization [18]. The particles with the critical size about 30–100 nm have the strongest pinning effect. However, some studies [15,19] have focused on the effect of larger precipitates (>0.1 lm) on magnetic property, showing that these larger precipitates can also give damage on the motion of domain wall due to the raising of inner stress. In this study, the intersection of rolling direction (RD) and transverse direction (TD) of samples were scanned in order to count the number of precipitates. Fig. 2 shows the distribution of precipitate size and Fig. 3 shows the relationship between average number density of precipitates and core loss. As shown in Fig. 2, most precipitates have a diameter smaller than 1 lm which is considered to be the critical size having detrimental effect on the motion of domain wall during magnetization of these samples. With the number density of these precipitates
Table 1 Core loss (W/kg) of sample steel. Sample
P1.5/50 (W/kg)
Sample
P1.5/50 (W/kg)
A B C D
4.1976 4.7373 4.4534 4.3937
E F G H
4.5666 4.5831 4.6887 4.3941
455
increasing, the core loss grows up obviously. As mentioned above, core loss is in direct proportion to the number density of precipitates and in inversely proportion to precipitate size. Since the average precipitate size can be regarded as 0.3 lm now, the equation of precipitate and core loss can be regression analyzed by the linear equation where the number density of precipitates was assumed as the only variable. Eq. (2) is the regression equation between number density of precipitates (<1lm) and core loss and Fig. 3 shows their graphic relationship.
P1:5=50 ðW=kgÞ ¼ 4:14988 þ 0:002xðnumber=mm2 Þ
ð2Þ
As shown in Fig. 3, if there are 100 more precipitates (<1lm) per mm2, core loss will increase by 0.2 W/kg. Precipitates will raise the dislocation density of grain and hinder the motion of domain wall during magnetization, raising the coercivity and then impact the core loss. To identify the source of finer precipitates, the intersection of rolling direction (RD) and normal direction (ND) of samples were scanned in order to know the distribution of precipitates in ND. Fig. 4 shows the typical distribution of precipitates on RD-ND plane of samples. As shown in Fig. 4, the smaller precipitates whose size are smaller than 1 lm prefer to locate on the layers of samples in normal direction while the larger precipitates tend to distribute in the interior of samples. These layers which contain a plenty of smaller precipitates on the surface of samples are thought to be nitriding layer according to the composition analysis of precipitates shown in Fig. 5. As shown in Fig. 5, smaller precipitates with a diameter smaller than 1 lm are most AlN particles. These nitriding layers may be generated in the final annealing process where the air atmosphere contains nitrogen. Non-oriented electrical silicon steel is a kind of ultra-low sulfur steel which has a close affinity to nitrogen. The nitrogen atoms can be absorbed from the annealing atmosphere into the interior of steel sheet and combine with aluminum atom, resulting in finer AlN precipitates appearing on the surfaces of steel sheet and lead to remarkable rise in hysteresis loss. This nitriding process will be promoted by bringing down the sulfur contain or raising final annealing temperature [20]. Fig. 6 is the typical morphology of finer AlN particles in samples. Most finer AlN particles are rod-like in samples. The flat precipitates have a stronger effect on the motion of domain wall than circular precipitates during magnetization which may be due to the major axis of precipitates having a chief blocking effect on domain wall [21]. Generally, the precipitates with a diameter smaller than 1 lm are thought to have the strongest damage to core loss in these samples. These precipitates are mainly AlN particles and distribute on the surface of steel sheet. The nitriding layers can be prevented by increasing hydrogen partial pressure in final annealing atmosphere or adding surface-enriching elements like P, Sb, Sn that will not affect grain growth [22]. According to Taisei’s work [23], when the mass fraction of AlN particles is lower than 0.0024 wt%, there will be little effects on core loss caused by these precipitates. 4. Effect of grain size on core loss of the steel The final grain size is determined by many factors such as final annealing temperature, soaking time, and precipitates [24,25]. Namely, precipitates degrade the speed of grain growth but don’t determined the final grain size [21], for which the effects of grain size on core loss can be analyzed separated from that of precipitates. By using OM and IPPS, accurate data of grain size of each sample can be gained. Fig. 7 and Table 2 show the volume fraction of grains in different size and the average grain size of the samples.
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Fig. 1. Method for counting grain size (A) Scale chart (B) Optical micrograph of samples (C) paint grain boundaries and fill grains with white (D) count each grain size by IPPS.
Fig. 2. Distribution of precipitate size and number density.
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Fig. 5. Composition triangle of precipitates on RD-ND plane in samples.
As shown in Fig. 8(b), the eddy current system can be seen as a electric circuit, where the grains and grain boundaries can be regarded as resistances. Under the externally applied magnetic field, induced electromotive force appears in steel sheet and lead to eddy current passing through grains and grain boundaries. Besides, the eddy current can also spin in a single grain or among some domains in one grain. Assuming grains are spherical, shown as Fig. 8(c), the resistance of a single grain Rg and its grain boundary Rb can be shown as Eqs. (4) and (5).
Fig. 3. Relationship between number density of precipitates and core loss.
Rg ¼ qg
d0 d0 6 ¼ qg 3 ¼ qg pd0 Seqg pd0
ð4Þ
Dl Dl nDl ¼ qb 2 ¼ qb 2 4pd0 Seqb 4pd0
ð5Þ
6d0
Rb ¼ qb
n
Fig. 4. Typical distribution of precipitates on RD-ND plane in samples.
Eq. (3) shows the formula to calculate the volume fraction of grains in different grain size ranges.
P Sj V j ¼ P 100% Si
ð3Þ
where Vj is volume fraction of grains in different grain size ranges, Sj means the area of grains in different grain size ranges. According to the result of IPPS, the grains whose equivalent diameter are around 30–50 lm predominate in total volume and the average grain size of samples are about 25–35 lm. Core loss comprises eddy current loss and hysteresis loss, and eddy current loss can be divided into classical eddy current loss and anomalous eddy current loss which can be ignored in nonoriented electrical silicon steel [26–28]. To study the relationship between core loss and grain size, hypothesis models and a mathematic model are built. 5. Hypothesis ideal model of eddy current loss and grains Eddy current loss means the energy loss generated by induced eddy current in the interior of the material. Fig. 8 is the hypothesis ideal model of eddy current loss and grains.
where Seqg and Seqb are equivalent area of cross section of grain and grain boundary respectively, qg and qb are their resistivity, n is the number of connected grains, Dl is the thickness of grain boundaries, d0 is the diameter of the grain. So the eddy current loss Pe can be written as Eq. (6).
" k k m X X X 2 2 Pe ¼ i1k R0k þ i2k qgkm 1
1
1
" k m1 X X n Dl 2 i2k qbkm þ 2 p dkm 4 1 1
6 pdkm !#
!#
ð6Þ
where i is the current intensity of each electric circuit, k is the number of electric circuit, R0 is the resistance when the eddy current spins in a single grain or among some domains in one grain rather than pass through grains and grain boundaries, m is the grain number in the electric circuit. Furthermore, as shown in Eq. (6), the relationship between eddy current loss Pe and average diameter of the grain d can be abbreviated to be Eq. (7). 1
Pe ¼ A0 þ B0 d
2
þ C0d
ð7Þ
where A0, B0, C0 are constants and A0 is the energy loss caused by the eddy current when it spins in the interior of a single grain, B0d1 is the energy loss caused when the eddy current pass through the interior of grains, C0d2 is the energy loss caused when the eddy current pass through the grain boundaries.
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Fig. 6. Typical three-dimensional morphology of finer AlN particles by partial extraction on steel matrix (left) and full extraction from steel matrix (right).
Fig. 7. The volume fraction of grains in different size.
6. Hypothesis ideal model of hysteresis loss and grains Hysteresis loss means the energy loss caused by the friction effect of the high-speed rotation of magnetic torque during magnetization. Fig. 9 is the hypothesis ideal model of hysteresis loss and grains.
When silicon steel sheet is magnetized, the wall of domains whose magnetization direction are parallel to applied magnetic field will migrate to both size and result in the expansion of these domains, while at the same time, the domains whose magnetization direction are antiparallel to applied magnetic field will shrink. Furthermore, the domains whose magnetization direction are per-
J. Wang et al. / Journal of Magnetism and Magnetic Materials 451 (2018) 454–462 Table 2 Average grain size of each sample (lm). Sample
Average grain size (lm)
Sample
Average grain size (lm)
A B C D
32.2 27.6 35.3 35.0
E F G H
35.5 31.9 30.2 32.3
pendicular to applied magnetic field will rotate from their original direction to the direction of applied magnetic field. In the end, the domains in a single grain unite as one. If the applied magnetic field intensity is strong enough and the magnetizing time is sufficient, domain walls will pass through grain boundaries and smaller domains will unite as a bigger domain as shown in Fig. 9(d) which can be regarded as the fully magnetized state. The process of the migration of domain walls is similar to the conduction of eddy current, so the relationship between hysteresis loss and grains can refer to hypothesis model of eddy current loss and grains. The resistance of the grains to the motion of the domain walls Tg and the resistance of the grain boundaries to the motion of the domain walls Tb can be given by Eqs. (8) and (9).
Tg ¼ cg
d0 d0 6 ¼ cg 3 ¼ cg pd0 Seqg pd0
ð8Þ
Dl Dl nDl ¼ cb 2 ¼ cb 2 4pd0 Seqb 4pd0
ð9Þ
6d0
Tb ¼ cb
where A1, B1, C1 are constants and A1 is the energy loss caused by the rotation of domains whose magnetization direction are perpendicular to applied magnetic field, B1d1 is the energy loss caused when the domain walls migrate in the grain, C1d2 is the energy loss caused when the domain walls pass through the grain boundaries (However, C1d2 should be ignored because the domain walls can hardly pass through the grain boundaries in practice). 7. Mathematic model In practical application, it’s hard to test the resistivity of each grain and grain boundary, so classical equations are used to analyzed the relationship between core loss and grain size. According to classical eddy current loss formula [29], classical eddy current loss Pce can be given by Eq. (11).
Pce ¼
ðptfBm kÞ 6r q
2
1
Ph ¼ A1 þ B1 d
2
þ C1 d
ð10Þ
ð11Þ
where t is the thickness of sheet, f is the frequency, Bm is the maximum magnetic induction, k means waveform factor, q is the resistivity, r is the density of material. However, the classical eddy current loss Pce is valid when the magnetic permeability is assumed as a constant [30]. In practice, the magnetic permeability will change over time, for which a correction factor ke is introduced into Eq. (11) to amend the effect of the changeable magnetic permeability as Eq. (12).
n
where cg and cb are the hypothesis resistivity to the migration of domain walls, just as qg and qb to Rg and Rb. So the relationship between hypothesis loss Ph and average diameter of the grain d can also be given by Eq. (10).
459
Pe ¼ ke Pce ¼ ke
ðptfBm kÞ 6rq
2
ð12Þ
Eq. (13) is the expression of hysteresis loss Ph [8]
Ph ¼ kh
Af r
Fig. 8. Hypothesis ideal model of eddy current loss and grains (a) Eddy current in non-oriented steel sheet (b) Hypothesis electric circuit (c) Hypothesis grain.
ð13Þ
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Fig. 9. Hypothesis ideal model of hysteresis loss and grains (a) Connected grains and domains in grains (b) Beginning of magnetization (c) Domains in a single grain unite (d) Domain walls pass through grain boundaries and smaller domains unite as a bigger domain.
where kh is the correction factor, A is the area of magnetic hysteresis loop. Refer to Zhu’s work [26], the magnetic hysteresis loop of highmagnetic-induction material can be seen as a parallelogram approximately. So the area of magnetic hysteresis loop can be estimated by Eq. (14).
A 4Bm Hc
ð14Þ
where Hc is the coercivity. Combine Eq. (14) with Eq. (13) and the hysteresis loss Ph can be rewritten as Eq. (15).
Ph ¼ k h
4fBm Hc r
ð15Þ
So the total core loss can be written as Eq. (16).
ðpftBm kÞ 4fBm Hc þ kh 6rq r 2
PT ¼ Pe þ Ph ¼ k e
ð16Þ
H. Pirgazi [2] have built a model of magnetic induction shown as Eq. (17).
B ¼ C0 þ C 1 Sieq þ C 2 Ea þ C 3
1 d
ð17Þ
where Sieq is the equivalent Si contain which can be regarded as Si + Al%, Ea is the average anisotropy energy and d is the grain size, Ci are constants whose value depend on the magnetic field intensity. As shown in Eq. (17), the magnetic induction is influenced by Sieq, Ea and d and so is the core loss. Sieq, and d (Ea isn’t taken into account in this study) can be used as the correction factor taking place of ke and kh to modify Eq. (16) as below.
" # 2 ðpftBm kÞ 4fBm Hc 1 1 PT ¼ þ D0 þ D1 Sieq þ D2 þ D3 2 d 6rq r d 1
¼ A þ Bd " A¼
2
þ Cd
# 2 ðpftBm kÞ 4fBm Hc ðD0 þ D1 Sieq Þ þ 6rq r
" # 2 ðpftBm kÞ 4fBm Hc D2 B¼ þ 6rq r " # 2 ðpftBm kÞ 4fBm Hc þ D3 C¼ 6rq r
ð18Þ ð19Þ
ð20Þ
ð21Þ
Eq. (18) shows the relationship between grain size and core loss. Di are influence coefficients of each factor whose value depend on the frequency f and the maximum magnetic induction Bm, besides, D0 means the influence coefficients of matrix Fe element. When the other factors are certain, A to C can be seen as positive constants. According to hypothesis model of eddy current loss and hysteresis loss, A is the energy loss caused by the eddy current when it spins in the interior of a single grain and the rotation of magnetization direction of domains, Bd1 is the energy loss caused when the eddy currents pass through the interior of grains and the domain walls migrate in the interior of grain, Cd2 is the energy loss caused when the eddy current pass through the grain boundaries. So the relationship between grain size and core loss can be analyzed according to the pattern of Eq. (18). Table 3 shows the value of Di when f and Bm are 50 Hz and 1.5 T, respectively. The ideal equation between grain size and core loss of 1.3% Sieq non-oriented electrical silicon steel sheet in this study is shown as Eq. 22. 1
P1:5=50 ðW=kgÞ ¼ 3:851 þ 20:001d
þ 60:000d ðlmÞ 2
ð22Þ
Fig. 10 shows the comparison between ideal equation (Eq. (22)) and measured value in this study (Table 2) and studies [31,32] whose equivalent Si contain are similar to this study. The goodness of fit R2 of these two fitting curves are about 0.456 and 0.875 respectively. However, Eq. (18) is a simple calculation model which is available for fine-grain material where anomalous eddy current loss can be ignored. In fact, the anomalous eddy current loss, which can be seen as the effect of grain size on the parameter A0 approximately in this study, will increase with the grain growing up and result in the obvious increase of total core loss when it’s big enough [28]. Furthermore, the influence coefficients such as D0, D2 and D3 shall be influenced by Si content and anisotropy energy, and PH and PT should have different influence parameters and different value of these influence parameters. But
Table 3 Value of Di when f and Bm are 50 Hz and 1.5 T.
D0 D1 D2 D3
Value
Unit
1.256 0.098 5.861 17.582
dimensionless /wt% /lm /lm2
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Metallurgical and Ecological Engineering at University of Science and Technology Beijing (USTB), China. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.jmmm.2017.11.072. References
Fig. 10. Comparison between ideal line and measured value on core loss.
the relationship between anomalous eddy current loss and grain size, as well as the effects of Si content and anisotropy energy on the influence coefficient Di, is lack of theoretical study. Further researches are needed to make this calculation model more accurate and complete.
8. Conclusions The diameter of most precipitates in 50W800 non-oriented electrical silicon steel product sheet is smaller than 1 lm which can be regarded as the critical size having effective pinning force on the motion of domain wall during magnetization in this study. These finer precipitates are mainly AlN particles and distribute on the surface of steel sheet. The regression equation between number density of precipitates and core loss is P1.5/50 (W/kg) = 4.14988 + 0.002x (number/mm2) approximately. As shown in the equation, if 100 more these precipitates (<1lm) are contained per mm2, the core loss will increase by 0.2 W/kg. As far as 50 W800 non-oriented electrical silicon steel product sheet samples in this study, the grains with the size of 30–50 lm predominate in total volume. The ideal equation between grain size and core loss of 50W800 non-oriented electrical silicon steel product sheet is shown as P1.5/50 (W/kg) = 3.851 + 20.001d1 + 60.000d2 (lm) whose goodness of fit R2 is about 0.456. Acknowledgements The authors are grateful for support from the National Science Foundation China (Grant No. 51725402, No. 51504020 and No. 51704018), the Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-15-001C2, No. FRF-TP-15-067A1 and No. FRF-TP-17-039A1), Guangxi Key Research and Development Plan (Grant No. AB17129006), National Postdoctoral Program for Innovative Talents (Grant No. BX201700028), Beijing Key Laboratory of Green Recycling and Extraction of Metals (GREM) and the High Quality steel Consortium (HQSC) and the Laboratory of Green Process Metallurgy and Modeling (GPM2) at the School of
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Effect of non-metallic precipitates and grain size on core loss of non-oriented electrical silicon steels Jiayi Wang, Qiang Ren, Yan Luo, Lifeng Zhang ⇑ Beijing Key Laboratory of Green Recycling and Extraction of Metals and School of Metallurgical and Ecological Engineering, University of Science and Technology, Beijing, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 21 August 2017 Received in revised form 14 November 2017 Accepted 17 November 2017 Available online 23 November 2017 Keywords: Non-oriented electrical silicon steel Precipitates Grain size Core loss
a b s t r a c t In the current study, the number density and size of non-metallic precipitates and the size of grains on the core loss of the 50W800 non-oriented electrical silicon steel sheets were investigated. The number density and size of precipitates and grains were statistically analyzed using an automatic scanning electron microscope (ASPEX) and an optical microscope. Hypothesis models were established to reveal the physical feature for the function of grain size and precipitates on the core loss of the steel. Most precipitates in the steel were AlN particles smaller than 1 lm so that were detrimental to the core loss of the steel. These finer AlN particles distributed on the surface of the steel sheet. The relationship between the number density of precipitates (x in number/mm2 steel area) and the core loss (P1.5/50 in W/kg) was regressed as P1.5/50 = 4.150 + 0.002 x. The average grain size was approximately 25–35 lm. The relationship between the core loss and grain size (d in lm) was P1.5/50 = 3.851 + 20.001 d1 + 60.000 d2. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction The non-oriented electrical silicon steel is an essential magnetic material well used as the materials for rotors for different motors and generators, especially in energy, machinery and electricity fields [1–4]. With the increase of the global electricity energy consumption, requirements for high-quality non-oriented electrical silicon steel are becoming serious more and more [5]. Core loss is an important feature to judge the quality of non-oriented electrical silicon steel sheets, and a low value of this parameter leads to a better efficiency of energy utilization, a decrease in heat generation, and leads to downsize motors and improve service life simultaneously [6]. Factors which have influences on the core loss the steel can be classified into two major parts: non-metallic precipitates and properties of the material including crystallographic texture, chemical composition, microstructure and grain size [7–11]. It is an essential way to decrease the core loss by decreasing the number density of non-metallic precipitates and improving the grain size, whose boundaries block the motion of domain wall during magnetization [12]. Studies were reported to investigate the effect of non-metallic precipitates and grain size on the core loss of steel [13–18]. However, only qualitative conclusions were obtained since too many parameters were involved to carry out
⇑ Corresponding author. E-mail address: [email protected] (L. Zhang). https://doi.org/10.1016/j.jmmm.2017.11.072 0304-8853/Ó 2017 Elsevier B.V. All rights reserved.
quantitative analysis. Furthermore, most quantitative analysis on the grain size and core loss are short of theoretical fundamentals and the physical feature of grains on the core loss were hardly revealed. Recently, Pirgazi [2] established a mathematic model showing the relationship between magnetic induction and grain size of the steel. Mathematic equation between grain size and core loss can be obtained using the developed model. Furthermore, it is known that the coercivity is in direct proportion to the core loss and the number density of non-metallic precipitates. Meanwhile, it is in inversely proportion to the size of precipitates, hinting that the relationship between precipitates and core loss can be regressed into a linear equation. In the current study, the effect of non-metallic precipitates and grain size on the core loss of a non-oriented electrical silicon steel were quantitatively investigated using an automatic scanning electron microscope (ASPEX) and optical microscope. The statistical feature of non-metallic precipitates and grain size of the steel were obtained. Furthermore, hypothesis models on the eddy current loss, as well as hysteresis loss, and grains were established.
2. Materials and experiments Eight samples of 50W800 non-oriented electrical silicon steel product sheets fabricated by one-step-cold-rolling technique were the analyzed in this study. The thickness of samples is 0.5 mm. The manufacturing process and parameters of the samples are similar.
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The equivalent Si content (Si% + Al%) of these samples are about 1.3 wt%, and their core loss are listed in Table 1. The core loss is measured by MTR-2949 alternating current magnetization characteristic measuring device from METRON Tech Research Corporation, Japan whose accuracy can reach to 0.0001 W/kg with a maximum error of 0.0016%. The main devices in this study are ASPEX SEM and Leica DM 4000 optical microscope (OM). The minimum equivalent size of the detected precipitates can reach to under 0.1 lm by using ASPEX SEM and the optical micrographs of grain were taken by OM. Polished samples were exposed to ASPEX and abundant data including precipitate size, number density can be gained by automatic scanning. Then, the samples were etched by 4%-nitric-acid ethanol solution. The average grain size can be counted using Image-pro plus software (IPPS). Fig. 1 shows the method for counting grain size by IPPS. First of all, the scale of the pictures of grains should be the same. After dealing the picture by graphics software such as PS and inputting the scale into IPPS, the real grain size of each sample can be directly obtained by IPPS. Then, the square mean was computed with the grain size just gained to know the average grain size. To improve the accuracy of the average grain size, more than 10 optical micrographs should be counted for each sample. Eq. (1) shows the formula to calculate the average grain size.
¼ D
rffiffiffiffiffiffiffiffiffiffiffiffiffi P 4 Si pn
ð1Þ
is average gain size of each sample, Si means the area of where D each grain which can be given by IPPS directly, n is the total grain number. 3. Effect of non-metallic precipitates on core loss of the steel The magnetic property can be detrimentally influenced by precipitates through three ways: raising the inner stress induced by lattice distortion caused by precipitates; blocking the motion of domain wall during magnetization; inhibiting grain growth which is an indirect way to affect magnetic property [8]. It was reported that precipitates whose size is close to the thickness of domain wall have the strongest pinning effect on the grain growth and the motion of domain wall during magnetization [18]. The particles with the critical size about 30–100 nm have the strongest pinning effect. However, some studies [15,19] have focused on the effect of larger precipitates (>0.1 lm) on magnetic property, showing that these larger precipitates can also give damage on the motion of domain wall due to the raising of inner stress. In this study, the intersection of rolling direction (RD) and transverse direction (TD) of samples were scanned in order to count the number of precipitates. Fig. 2 shows the distribution of precipitate size and Fig. 3 shows the relationship between average number density of precipitates and core loss. As shown in Fig. 2, most precipitates have a diameter smaller than 1 lm which is considered to be the critical size having detrimental effect on the motion of domain wall during magnetization of these samples. With the number density of these precipitates
Table 1 Core loss (W/kg) of sample steel. Sample
P1.5/50 (W/kg)
Sample
P1.5/50 (W/kg)
A B C D
4.1976 4.7373 4.4534 4.3937
E F G H
4.5666 4.5831 4.6887 4.3941
455
increasing, the core loss grows up obviously. As mentioned above, core loss is in direct proportion to the number density of precipitates and in inversely proportion to precipitate size. Since the average precipitate size can be regarded as 0.3 lm now, the equation of precipitate and core loss can be regression analyzed by the linear equation where the number density of precipitates was assumed as the only variable. Eq. (2) is the regression equation between number density of precipitates (<1lm) and core loss and Fig. 3 shows their graphic relationship.
P1:5=50 ðW=kgÞ ¼ 4:14988 þ 0:002xðnumber=mm2 Þ
ð2Þ
As shown in Fig. 3, if there are 100 more precipitates (<1lm) per mm2, core loss will increase by 0.2 W/kg. Precipitates will raise the dislocation density of grain and hinder the motion of domain wall during magnetization, raising the coercivity and then impact the core loss. To identify the source of finer precipitates, the intersection of rolling direction (RD) and normal direction (ND) of samples were scanned in order to know the distribution of precipitates in ND. Fig. 4 shows the typical distribution of precipitates on RD-ND plane of samples. As shown in Fig. 4, the smaller precipitates whose size are smaller than 1 lm prefer to locate on the layers of samples in normal direction while the larger precipitates tend to distribute in the interior of samples. These layers which contain a plenty of smaller precipitates on the surface of samples are thought to be nitriding layer according to the composition analysis of precipitates shown in Fig. 5. As shown in Fig. 5, smaller precipitates with a diameter smaller than 1 lm are most AlN particles. These nitriding layers may be generated in the final annealing process where the air atmosphere contains nitrogen. Non-oriented electrical silicon steel is a kind of ultra-low sulfur steel which has a close affinity to nitrogen. The nitrogen atoms can be absorbed from the annealing atmosphere into the interior of steel sheet and combine with aluminum atom, resulting in finer AlN precipitates appearing on the surfaces of steel sheet and lead to remarkable rise in hysteresis loss. This nitriding process will be promoted by bringing down the sulfur contain or raising final annealing temperature [20]. Fig. 6 is the typical morphology of finer AlN particles in samples. Most finer AlN particles are rod-like in samples. The flat precipitates have a stronger effect on the motion of domain wall than circular precipitates during magnetization which may be due to the major axis of precipitates having a chief blocking effect on domain wall [21]. Generally, the precipitates with a diameter smaller than 1 lm are thought to have the strongest damage to core loss in these samples. These precipitates are mainly AlN particles and distribute on the surface of steel sheet. The nitriding layers can be prevented by increasing hydrogen partial pressure in final annealing atmosphere or adding surface-enriching elements like P, Sb, Sn that will not affect grain growth [22]. According to Taisei’s work [23], when the mass fraction of AlN particles is lower than 0.0024 wt%, there will be little effects on core loss caused by these precipitates. 4. Effect of grain size on core loss of the steel The final grain size is determined by many factors such as final annealing temperature, soaking time, and precipitates [24,25]. Namely, precipitates degrade the speed of grain growth but don’t determined the final grain size [21], for which the effects of grain size on core loss can be analyzed separated from that of precipitates. By using OM and IPPS, accurate data of grain size of each sample can be gained. Fig. 7 and Table 2 show the volume fraction of grains in different size and the average grain size of the samples.
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Fig. 1. Method for counting grain size (A) Scale chart (B) Optical micrograph of samples (C) paint grain boundaries and fill grains with white (D) count each grain size by IPPS.
Fig. 2. Distribution of precipitate size and number density.
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Fig. 5. Composition triangle of precipitates on RD-ND plane in samples.
As shown in Fig. 8(b), the eddy current system can be seen as a electric circuit, where the grains and grain boundaries can be regarded as resistances. Under the externally applied magnetic field, induced electromotive force appears in steel sheet and lead to eddy current passing through grains and grain boundaries. Besides, the eddy current can also spin in a single grain or among some domains in one grain. Assuming grains are spherical, shown as Fig. 8(c), the resistance of a single grain Rg and its grain boundary Rb can be shown as Eqs. (4) and (5).
Fig. 3. Relationship between number density of precipitates and core loss.
Rg ¼ qg
d0 d0 6 ¼ qg 3 ¼ qg pd0 Seqg pd0
ð4Þ
Dl Dl nDl ¼ qb 2 ¼ qb 2 4pd0 Seqb 4pd0
ð5Þ
6d0
Rb ¼ qb
n
Fig. 4. Typical distribution of precipitates on RD-ND plane in samples.
Eq. (3) shows the formula to calculate the volume fraction of grains in different grain size ranges.
P Sj V j ¼ P 100% Si
ð3Þ
where Vj is volume fraction of grains in different grain size ranges, Sj means the area of grains in different grain size ranges. According to the result of IPPS, the grains whose equivalent diameter are around 30–50 lm predominate in total volume and the average grain size of samples are about 25–35 lm. Core loss comprises eddy current loss and hysteresis loss, and eddy current loss can be divided into classical eddy current loss and anomalous eddy current loss which can be ignored in nonoriented electrical silicon steel [26–28]. To study the relationship between core loss and grain size, hypothesis models and a mathematic model are built. 5. Hypothesis ideal model of eddy current loss and grains Eddy current loss means the energy loss generated by induced eddy current in the interior of the material. Fig. 8 is the hypothesis ideal model of eddy current loss and grains.
where Seqg and Seqb are equivalent area of cross section of grain and grain boundary respectively, qg and qb are their resistivity, n is the number of connected grains, Dl is the thickness of grain boundaries, d0 is the diameter of the grain. So the eddy current loss Pe can be written as Eq. (6).
" k k m X X X 2 2 Pe ¼ i1k R0k þ i2k qgkm 1
1
1
" k m1 X X n Dl 2 i2k qbkm þ 2 p dkm 4 1 1
6 pdkm !#
!#
ð6Þ
where i is the current intensity of each electric circuit, k is the number of electric circuit, R0 is the resistance when the eddy current spins in a single grain or among some domains in one grain rather than pass through grains and grain boundaries, m is the grain number in the electric circuit. Furthermore, as shown in Eq. (6), the relationship between eddy current loss Pe and average diameter of the grain d can be abbreviated to be Eq. (7). 1
Pe ¼ A0 þ B0 d
2
þ C0d
ð7Þ
where A0, B0, C0 are constants and A0 is the energy loss caused by the eddy current when it spins in the interior of a single grain, B0d1 is the energy loss caused when the eddy current pass through the interior of grains, C0d2 is the energy loss caused when the eddy current pass through the grain boundaries.
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Fig. 6. Typical three-dimensional morphology of finer AlN particles by partial extraction on steel matrix (left) and full extraction from steel matrix (right).
Fig. 7. The volume fraction of grains in different size.
6. Hypothesis ideal model of hysteresis loss and grains Hysteresis loss means the energy loss caused by the friction effect of the high-speed rotation of magnetic torque during magnetization. Fig. 9 is the hypothesis ideal model of hysteresis loss and grains.
When silicon steel sheet is magnetized, the wall of domains whose magnetization direction are parallel to applied magnetic field will migrate to both size and result in the expansion of these domains, while at the same time, the domains whose magnetization direction are antiparallel to applied magnetic field will shrink. Furthermore, the domains whose magnetization direction are per-
J. Wang et al. / Journal of Magnetism and Magnetic Materials 451 (2018) 454–462 Table 2 Average grain size of each sample (lm). Sample
Average grain size (lm)
Sample
Average grain size (lm)
A B C D
32.2 27.6 35.3 35.0
E F G H
35.5 31.9 30.2 32.3
pendicular to applied magnetic field will rotate from their original direction to the direction of applied magnetic field. In the end, the domains in a single grain unite as one. If the applied magnetic field intensity is strong enough and the magnetizing time is sufficient, domain walls will pass through grain boundaries and smaller domains will unite as a bigger domain as shown in Fig. 9(d) which can be regarded as the fully magnetized state. The process of the migration of domain walls is similar to the conduction of eddy current, so the relationship between hysteresis loss and grains can refer to hypothesis model of eddy current loss and grains. The resistance of the grains to the motion of the domain walls Tg and the resistance of the grain boundaries to the motion of the domain walls Tb can be given by Eqs. (8) and (9).
Tg ¼ cg
d0 d0 6 ¼ cg 3 ¼ cg pd0 Seqg pd0
ð8Þ
Dl Dl nDl ¼ cb 2 ¼ cb 2 4pd0 Seqb 4pd0
ð9Þ
6d0
Tb ¼ cb
where A1, B1, C1 are constants and A1 is the energy loss caused by the rotation of domains whose magnetization direction are perpendicular to applied magnetic field, B1d1 is the energy loss caused when the domain walls migrate in the grain, C1d2 is the energy loss caused when the domain walls pass through the grain boundaries (However, C1d2 should be ignored because the domain walls can hardly pass through the grain boundaries in practice). 7. Mathematic model In practical application, it’s hard to test the resistivity of each grain and grain boundary, so classical equations are used to analyzed the relationship between core loss and grain size. According to classical eddy current loss formula [29], classical eddy current loss Pce can be given by Eq. (11).
Pce ¼
ðptfBm kÞ 6r q
2
1
Ph ¼ A1 þ B1 d
2
þ C1 d
ð10Þ
ð11Þ
where t is the thickness of sheet, f is the frequency, Bm is the maximum magnetic induction, k means waveform factor, q is the resistivity, r is the density of material. However, the classical eddy current loss Pce is valid when the magnetic permeability is assumed as a constant [30]. In practice, the magnetic permeability will change over time, for which a correction factor ke is introduced into Eq. (11) to amend the effect of the changeable magnetic permeability as Eq. (12).
n
where cg and cb are the hypothesis resistivity to the migration of domain walls, just as qg and qb to Rg and Rb. So the relationship between hypothesis loss Ph and average diameter of the grain d can also be given by Eq. (10).
459
Pe ¼ ke Pce ¼ ke
ðptfBm kÞ 6rq
2
ð12Þ
Eq. (13) is the expression of hysteresis loss Ph [8]
Ph ¼ kh
Af r
Fig. 8. Hypothesis ideal model of eddy current loss and grains (a) Eddy current in non-oriented steel sheet (b) Hypothesis electric circuit (c) Hypothesis grain.
ð13Þ
460
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Fig. 9. Hypothesis ideal model of hysteresis loss and grains (a) Connected grains and domains in grains (b) Beginning of magnetization (c) Domains in a single grain unite (d) Domain walls pass through grain boundaries and smaller domains unite as a bigger domain.
where kh is the correction factor, A is the area of magnetic hysteresis loop. Refer to Zhu’s work [26], the magnetic hysteresis loop of highmagnetic-induction material can be seen as a parallelogram approximately. So the area of magnetic hysteresis loop can be estimated by Eq. (14).
A 4Bm Hc
ð14Þ
where Hc is the coercivity. Combine Eq. (14) with Eq. (13) and the hysteresis loss Ph can be rewritten as Eq. (15).
Ph ¼ k h
4fBm Hc r
ð15Þ
So the total core loss can be written as Eq. (16).
ðpftBm kÞ 4fBm Hc þ kh 6rq r 2
PT ¼ Pe þ Ph ¼ k e
ð16Þ
H. Pirgazi [2] have built a model of magnetic induction shown as Eq. (17).
B ¼ C0 þ C 1 Sieq þ C 2 Ea þ C 3
1 d
ð17Þ
where Sieq is the equivalent Si contain which can be regarded as Si + Al%, Ea is the average anisotropy energy and d is the grain size, Ci are constants whose value depend on the magnetic field intensity. As shown in Eq. (17), the magnetic induction is influenced by Sieq, Ea and d and so is the core loss. Sieq, and d (Ea isn’t taken into account in this study) can be used as the correction factor taking place of ke and kh to modify Eq. (16) as below.
" # 2 ðpftBm kÞ 4fBm Hc 1 1 PT ¼ þ D0 þ D1 Sieq þ D2 þ D3 2 d 6rq r d 1
¼ A þ Bd " A¼
2
þ Cd
# 2 ðpftBm kÞ 4fBm Hc ðD0 þ D1 Sieq Þ þ 6rq r
" # 2 ðpftBm kÞ 4fBm Hc D2 B¼ þ 6rq r " # 2 ðpftBm kÞ 4fBm Hc þ D3 C¼ 6rq r
ð18Þ ð19Þ
ð20Þ
ð21Þ
Eq. (18) shows the relationship between grain size and core loss. Di are influence coefficients of each factor whose value depend on the frequency f and the maximum magnetic induction Bm, besides, D0 means the influence coefficients of matrix Fe element. When the other factors are certain, A to C can be seen as positive constants. According to hypothesis model of eddy current loss and hysteresis loss, A is the energy loss caused by the eddy current when it spins in the interior of a single grain and the rotation of magnetization direction of domains, Bd1 is the energy loss caused when the eddy currents pass through the interior of grains and the domain walls migrate in the interior of grain, Cd2 is the energy loss caused when the eddy current pass through the grain boundaries. So the relationship between grain size and core loss can be analyzed according to the pattern of Eq. (18). Table 3 shows the value of Di when f and Bm are 50 Hz and 1.5 T, respectively. The ideal equation between grain size and core loss of 1.3% Sieq non-oriented electrical silicon steel sheet in this study is shown as Eq. 22. 1
P1:5=50 ðW=kgÞ ¼ 3:851 þ 20:001d
þ 60:000d ðlmÞ 2
ð22Þ
Fig. 10 shows the comparison between ideal equation (Eq. (22)) and measured value in this study (Table 2) and studies [31,32] whose equivalent Si contain are similar to this study. The goodness of fit R2 of these two fitting curves are about 0.456 and 0.875 respectively. However, Eq. (18) is a simple calculation model which is available for fine-grain material where anomalous eddy current loss can be ignored. In fact, the anomalous eddy current loss, which can be seen as the effect of grain size on the parameter A0 approximately in this study, will increase with the grain growing up and result in the obvious increase of total core loss when it’s big enough [28]. Furthermore, the influence coefficients such as D0, D2 and D3 shall be influenced by Si content and anisotropy energy, and PH and PT should have different influence parameters and different value of these influence parameters. But
Table 3 Value of Di when f and Bm are 50 Hz and 1.5 T.
D0 D1 D2 D3
Value
Unit
1.256 0.098 5.861 17.582
dimensionless /wt% /lm /lm2
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Metallurgical and Ecological Engineering at University of Science and Technology Beijing (USTB), China. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.jmmm.2017.11.072. References
Fig. 10. Comparison between ideal line and measured value on core loss.
the relationship between anomalous eddy current loss and grain size, as well as the effects of Si content and anisotropy energy on the influence coefficient Di, is lack of theoretical study. Further researches are needed to make this calculation model more accurate and complete.
8. Conclusions The diameter of most precipitates in 50W800 non-oriented electrical silicon steel product sheet is smaller than 1 lm which can be regarded as the critical size having effective pinning force on the motion of domain wall during magnetization in this study. These finer precipitates are mainly AlN particles and distribute on the surface of steel sheet. The regression equation between number density of precipitates and core loss is P1.5/50 (W/kg) = 4.14988 + 0.002x (number/mm2) approximately. As shown in the equation, if 100 more these precipitates (<1lm) are contained per mm2, the core loss will increase by 0.2 W/kg. As far as 50 W800 non-oriented electrical silicon steel product sheet samples in this study, the grains with the size of 30–50 lm predominate in total volume. The ideal equation between grain size and core loss of 50W800 non-oriented electrical silicon steel product sheet is shown as P1.5/50 (W/kg) = 3.851 + 20.001d1 + 60.000d2 (lm) whose goodness of fit R2 is about 0.456. Acknowledgements The authors are grateful for support from the National Science Foundation China (Grant No. 51725402, No. 51504020 and No. 51704018), the Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-15-001C2, No. FRF-TP-15-067A1 and No. FRF-TP-17-039A1), Guangxi Key Research and Development Plan (Grant No. AB17129006), National Postdoctoral Program for Innovative Talents (Grant No. BX201700028), Beijing Key Laboratory of Green Recycling and Extraction of Metals (GREM) and the High Quality steel Consortium (HQSC) and the Laboratory of Green Process Metallurgy and Modeling (GPM2) at the School of
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