EP4786626A1

EP4786626A1 - Grain-oriented electrical steel sheet and manufacturing method therefor

Info

Publication number: EP4786626A1
Application number: EP24872573.1A
Authority: EP
Inventors: Ryo Matsubara; Yusuke Kawamura; Rei Honma; Toshiyuki Suzuma
Original assignee: Nippon Steel Corp
Current assignee: Nippon Steel Corp
Priority date: 2023-09-27
Filing date: 2024-09-27
Publication date: 2026-08-05
Also published as: KR20260057119A; WO2025070793A1; CN121889526A; JPWO2025070793A1

Abstract

This grain-oriented electrical steel sheet includes a plurality of magnetic domain control treatment lines extending in a direction intersecting a rolling direction on a surface, in a case where a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction is set on the surface, and further, imaginary lines parallel to the rolling direction and having a length of 50 mm are set inside the evaluation region at intervals of 5 mm in a direction perpendicular to the rolling direction, in at least one of the imaginary lines, among the plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines, the absolute maximum value of an interval between adjacent intersection points in the rolling direction is more than 20 mm, and the average value of spacings of magnetic domain walls measured along the imaginary line is 600 µm or less, and the plurality of magnetic domain control treatment lines are tensile stress introduction lines in which a tensile stress of 40 MPa or more is introduced.

Description

TECHNICAL FIELD

The present invention relates to a grain-oriented electrical steel sheet and a method for manufacturing the same.
The present application claims priority based on Japanese Patent Application No. 2023-166093 filed in Japan on September 27, 2023 , the contents of which are incorporated herein by reference.

BACKGROUND ART

The grain-oriented electrical steel sheet is a steel sheet containing 7 mass% or less of Si and having a secondary recrystallization texture in which secondary recrystallized grains are accumulated in a {110}<001> orientation (Goss orientation) in which an easy axis of magnetization <001> is oriented in a rolling direction. Grain-oriented electrical steel sheets are mainly used as iron cores of power transformers. Grain-oriented electrical steel sheets are required to reduce energy loss (iron loss).
A technique of narrowing a spacing of magnetic domain walls of a grain-oriented electrical steel sheet (magnetic domain refinement technique by magnetic domain control treatment) for reducing iron loss has been known. The spacing of magnetic domain walls can be narrowed by irradiating the surface of the grain-oriented electrical steel sheet with a laser or an electron beam in a direction intersecting the rolling direction to introduce a thermal strain. The spacing of magnetic domain walls can also be narrowed by forming a groove in the direction intersecting the rolling direction on the surface of the grain-oriented electrical steel sheet. Examples of a method of forming the groove include a method of irradiating a laser or an electron beam, a method by mechanical processing such as gear, and a method by chemical processing such as etching.
In recent years, in order to provide a grain-oriented electrical steel sheet having good iron loss characteristics, various improved techniques related to magnetic domain refinement have been proposed (see, for example, Patent Documents 1 to 3.).

Citation List

Patent Documents

Patent Document 1: Japanese Unexamined Patent Application, First Publication No. 2012-57219
Patent Document 2: Japanese Unexamined Patent Application, First Publication No. 2012-12664
Patent Document 3: Japanese Unexamined Patent Application, First Publication No. 2012-57218

SUMMARY OF INVENTION

Technical Problem

When the magnetic domain control treatment is applied to the grain-oriented electrical steel sheet, the magnetostrictive characteristic of the grain-oriented electrical steel sheet changes depending on the flux closure domain. As a result, noise characteristics of the grain-oriented electrical steel sheet deteriorate. The noise characteristic is a degree of noise generated by an electrical product (for example, a transformer, a motor, and the like) manufactured using a grain-oriented electrical steel sheet as a material. Magnetostriction is a phenomenon in which an outer shape is slightly deformed when a ferromagnetic material is magnetized. When the grain-oriented electrical steel sheet is excited by alternating current, the magnitude of the magnetostriction changes with a change in the strength of magnetization, and thus vibration occurs. The magnitude of the magnetostriction is very small on the order of 10^-6, but the magnetostriction generates vibration in the iron core, and the vibration propagates to an external structure such as a tank of a transformer to become noise. That is, the magnetic domain control treatment is effective for reducing iron loss of the grain-oriented electrical steel sheet, but deteriorates noise characteristics of the grain-oriented electrical steel sheet.
In recent years, there is an increasing demand for not only a reduction in iron loss but also a reduction in noise for grain-oriented electrical steel sheets. However, no magnetic domain refinement technique capable of sufficiently achieving both noise reduction and iron loss reduction has been proposed so far.
An object of the present disclosure is to provide a grain-oriented electrical steel sheet having a low iron loss (low iron loss) and a low noise (excellent noise characteristics) when the grain-oriented electrical steel sheet is made into an electrical product, and a method for manufacturing the grain-oriented electrical steel sheet. Solution to Problem
The present inventors have studied a method for suppressing deterioration of noise characteristics while reducing iron loss.
As a result, the present inventors have found that when a magnetic domain control treatment using tensile stress is performed, an interval of the magnetic domain control treatment is widened in at least a part of a specific region, whereby a grain-oriented electrical steel sheet having a low iron loss and excellent noise characteristics can be obtained.
The present disclosure has been made in view of the above findings. The gist of the present disclosure is as follows.

[1] A grain-oriented electrical steel sheet according to one aspect of the present disclosure includes a plurality of magnetic domain control treatment lines extending in a direction intersecting a rolling direction on a surface, in a case where a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction is set on the surface, and further, imaginary lines parallel to the rolling direction and having a length of 50 mm are set inside the evaluation region at intervals of 5 mm in a direction perpendicular to the rolling direction, in at least one of the imaginary lines, among a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines, an absolute maximum value of an interval between adjacent intersection points in the rolling direction is more than 20 mm, and an average value of spacings of magnetic domain walls measured along the imaginary line is 600 µm or less, and the plurality of magnetic domain control treatment lines are tensile stress introduction lines in which a tensile stress of 40 MPa or more is introduced.
[2] In the grain-oriented electrical steel sheet according to [1], the average value of the spacings of magnetic domain walls measured along the imaginary line may be 500 µm or less.
[3] In the grain-oriented electrical steel sheet according to [1], the average value of spacings of magnetic domain walls measured along the imaginary line may be 600 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
[4] In the grain-oriented electrical steel sheet according to [3], the average value of the spacings of magnetic domain walls measured along the imaginary line may be 500 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
[5] A grain-oriented electrical steel sheet according to another aspect of the present disclosure includes a plurality of magnetic domain control treatment lines extending in a direction intersecting a rolling direction on a surface, in a case where a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction is set on the surface, and further, imaginary lines parallel to the rolling direction and having a length of 50 mm are set inside the evaluation region at intervals of 5 mm in a direction perpendicular to the rolling direction, in at least one of the imaginary lines, among a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines, an absolute maximum value of an interval between adjacent intersection points in the rolling direction is more than 20 mm, and an absolute maximum value of a spacing of magnetic domain walls measured along the imaginary line is 1200 µm or less.
[6] In the grain-oriented electrical steel sheet according to [5], the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line may be 800 µm or less.
[7] In the grain-oriented electrical steel sheet according to [5], the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line may be 1200 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
[8] In the grain-oriented electrical steel sheet according to [7], the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line may be 800 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
[9] In the grain-oriented electrical steel sheet according to any one of [1] to [8], the plurality of magnetic domain control treatment lines may be thermal strains.
[10] In the grain-oriented electrical steel sheet according to [9], the absolute maximum value of the tensile stress introduced into the thermal strain in the magnetic domain control treatment line may be non-uniform at each measurement point of the tensile stress.
[11] In the grain-oriented electrical steel sheet according to [10], when each of a plurality of intersection points between the imaginary line and the plurality of magnetic domain control treatment lines is a magnetic domain refinement point, the absolute maximum value of the tensile stress in a unit of MPa introduced into the thermal strain measured at each of the magnetic domain refinement points is TS_m, and the variance of TS_m is σ(TS_m)², σ(TS_m)² > 5.0 may be satisfied.
[12] In the grain-oriented electrical steel sheet according to [10], when each of a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines is defined as a magnetic domain refinement point, an arithmetical mean value of absolute maximum values of the tensile stresses in a unit of MPa introduced into the thermal strain measured at each of magnetic domain refinement points having a β angle of less than 2° among the magnetic domain refinement points is defined as TS_{m(β < 2)}, and an arithmetical mean value of absolute maximum values of the tensile stresses in a unit of MPa introduced into the thermal strain measured at each of magnetic domain refinement points having a β angle of 2° or more among the magnetic domain refinement points is defined as TS_{m(β ≥ 2)}, TS_{m(β < 2)} > TS_{m(β ≥ 2)} may be satisfied.
[13] In the grain-oriented electrical steel sheet according to [11], when TS_{m(β < 2)} is an arithmetical mean value of absolute maximum values of the tensile stress in a unit of MPa introduced into the thermal strain, the absolute maximum values being measured at each of magnetic domain refinement points having a β angle of less than 2° among the magnetic domain refinement points, and TS_{m(β ≥ 2)} is an arithmetical mean value of absolute maximum values of the tensile stress in a unit of MPa introduced into the thermal strain, the absolute maximum values being measured at each of magnetic domain refinement points having a β angle of 2° or more among the magnetic domain refinement points, TS_{m(β < 2)} > TS_{m(β ≥ 2)} may be satisfied.
[14] A method for manufacturing the grain-oriented electrical steel sheet according to another aspect of the present disclosure is a method for manufacturing the grain-oriented electrical steel sheet according to any one of [1] to [8] includes: a magnetic domain image acquisition step of acquiring a magnetic domain image of a surface of the grain-oriented electrical steel sheet; a region specification step of specifying a region having a spacing of magnetic domain walls of more than 500 µm in the grain-oriented electrical steel sheet based on the magnetic domain image obtained in the magnetic domain image acquisition step; and a magnetic domain control treatment line forming step of forming a magnetic domain control treatment line on a surface of the grain-oriented electrical steel sheet after the region specification step, in the magnetic domain control treatment line forming step, the magnetic domain control treatment line is formed in the region where the spacing of magnetic domain walls is more than 500 µm.
[15] In the method for manufacturing a grain-oriented electrical steel sheet according to [14], in the magnetic domain control treatment line forming step, the magnetic domain control treatment line may be formed by irradiation with a laser or an electron beam.

Advantageous Effects of Invention

According to the above aspect of the present disclosure, it is possible to provide a grain-oriented electrical steel sheet having a low iron loss (low iron loss) and having a low noise (excellent noise characteristics) when the grain-oriented electrical steel sheet is made into an electrical product, and a method for manufacturing the grain-oriented electrical steel sheet.

BRIEF DESCRIPTION OF DRAWINGS

[FIG. 1A] A schematic view illustrating an example of a grain-oriented electrical steel sheet according to the present embodiment.
[FIG. 1B] A schematic view illustrating an example of a grain-oriented electrical steel sheet according to the present embodiment.
[FIG. 1C] A schematic view illustrating an example of a grain-oriented electrical steel sheet according to the present embodiment.
[FIG. 2] A graph showing a relationship between the spacing of magnetic domain walls before laser irradiation and the spacing of magnetic domain walls after laser irradiation.
[FIG. 3A] A diagram illustrating an example of distribution of a spacing of magnetic domain walls of a grain-oriented electrical steel sheet before a magnetic domain refinement treatment.
[FIG. 3B] A diagram illustrating an example of distribution of a spacing of magnetic domain walls of a grain-oriented electrical steel sheet after a magnetic domain refinement treatment.
[FIG. 3C] A view illustrating an example of a magnetic domain image acquired by the image acquisition device.
[FIG. 3D] A view schematically illustrating FIG. 3C.
[FIG. 4] A block diagram illustrating an example of a hardware constitution of the image acquisition device.
[FIG. 5] A block diagram illustrating an example of a hardware constitution of an analysis device.
[FIG. 6] A schematic diagram illustrating an example of a constitution of a laser irradiation device.
[FIG. 7] A schematic view showing a method of cutting out a plurality of partial regions from a magnetic domain image of a grain-oriented electrical steel sheet.
[FIG. 8] An example of a plurality of partial Fourier images obtained by applying two-dimensional Fourier transform to each of a plurality of partial regions cut out from a magnetic domain image of a grain-oriented electrical steel sheet.
[FIG. 9] A schematic cross-sectional view of a grain-oriented electrical steel sheet in which a magnetic domain control treatment line is a thermal strain.
[FIG. 10] A schematic plan view showing a method of measuring a magnetic domain control strength at an intersection point of the magnetic domain control treatment line and the imaginary line.
[FIG. 11] A graph schematically showing a relationship between the size of spacing of magnetic domain walls and the magnetic domain control saturation strength.
[FIG. 12] A graph schematically showing a relationship between the magnitude of β angle and the magnetic domain control saturation strength.

DESCRIPTION OF EMBODIMENTS

A grain-oriented electrical steel sheet according to an embodiment of the present disclosure (grain-oriented electrical steel sheet according to the present embodiment) and a method for manufacturing the same will be described.
As shown in FIG. 1A, a plurality of magnetic domain control treatment lines 11 extending in a direction intersecting a rolling direction RD are provided on a surface of a grain-oriented electrical steel sheet 1 according to the present embodiment. In addition, in the present embodiment, in a case where a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction RD is set on the surface, and further, an imaginary line VL parallel to the rolling direction RD and having a length of 50 mm is set inside the evaluation region at an interval of 5 mm in a direction perpendicular to the rolling direction RD, in at least one imaginary line VL, an absolute maximum value (dmax) of an interval (d1 to d7) in the rolling direction RD between adjacent intersection points among a plurality of intersection points VP of the imaginary line VL and the plurality of magnetic domain control treatment lines 11 is more than 20 mm, and, the average value of the spacings of magnetic domain walls measured along the imaginary line VL is 600 µm or less, or the absolute maximum value of the spacings of magnetic domain walls is 1200 µm or less.
The magnetic domain control treatment line 11 is a tensile stress introduction line into which a tensile stress of 40 MPa or more is introduced.
As described later, the grain-oriented electrical steel sheet according to the present embodiment may have a forsterite film and/or an insulating coating on the surface of a steel sheet to become a base steel sheet.
Each will be described below. However, in a case where the grain-oriented electrical steel sheet includes a base steel sheet and a forsterite film and/or an insulating coating, the following provisions regarding the chemical composition, the magnetic domain control treatment line, the interval between intersection points, and the spacing of magnetic domain walls are provisions regarding the base steel sheet. However, the provision regarding the sheet thickness is a provision regarding the entire grain-oriented electrical steel sheet including the base steel sheet, and the forsterite film and/or the insulating coating.

[Grain-Oriented Electrical Steel Sheet]

(Chemical Composition)

The chemical composition of the grain-oriented electrical steel sheet 1 is not limited as long as it is equivalent to that of the known grain-oriented electrical steel sheet 1. For example, the grain-oriented electrical steel sheet 1 can contain, as a chemical composition, Si: 2.50 to 7.00%, Mn: 0 to 1.00%, C: 0 to 0.085%, acid-soluble Al: 0 to 0.065%, N: 0 to 0.012%, Cr: 0 to 0.300%, Cu: 0 to 0.400%, P: 0 to 0.500%, Sn: 0 to 0.300%, Sb: 0 to 0.300%, Ni: 0 to 1.000%, S: 0 to 0.015%, Se: 0 to 0.015%, Bi: 0 to 0.020%, Nb: 0 to 0.030%, V: 0 to 0.030%, Mo: 0 to 0.030%, Ta: 0 to 0.030%, W: 0 to 0.030%, B: 0 to 0.080%, and Ti: 0 to 0.015% in mass%. The balance of the chemical composition includes Fe and impurities.
The chemical compositions of the grain-oriented electrical steel sheet 1 may be measured by a general analysis method of steel. For example, the chemical component may be measured using inductively coupled plasma-atomic emission spectrometry (ICP-AES). Specifically, the chemical composition of the grain-oriented electrical steel sheet 1 can be measured by collecting a test piece from the center portion in the thickness direction of the sample, and measuring the test piece under a condition based on a calibration curve prepared in advance using ICPS-8100 manufactured by Shimadzu Corporation or the like (measuring device). The amounts of C and S, which are difficult to measure by ICP-AES, may be measured using a combustion-infrared light absorption method. The amount of N may be measured using an inert gas fusion-thermal conductivity method.
In a case where the forsterite film and/or the insulating coating are/is formed on the grain-oriented electrical steel sheet 1, the chemical composition of the grain-oriented electrical steel sheet 1 (that is, the chemical composition of the base steel sheet) may be analyzed after removing the forsterite film and/or the insulating coating from the grain-oriented electrical steel sheet 1.
The insulating coating can be removed, for example, by immersing the sample in a sodium hydroxide solution and then immersing the sample in dilute sulfuric acid and nitric acid. Conditions such as the temperature and concentration of sodium hydroxide, dilute sulfuric acid, and nitric acid solution, and the time for immersion are appropriately adjusted so that the base metal of the sample is not excessively dissolved. An example of the conditions of the removal operation of the insulating coating is as follows. First, the sample is immersed in a sodium hydroxide solution having a concentration of 20% at 80°C for 15 minutes. Thereafter, the sample is dried. Then, the sample is immersed in diluted sulfuric acid having a concentration of 10% at 80°C for 4 minutes. Thereafter, the sludge adhering to the surface of the sample is removed with a waste cloth or the like. Further, the sample is immersed in nitric acid having a concentration of 10% at room temperature while being stirred for about 10 seconds.
The forsterite film can be removed, for example, by immersing the sample in sulfuric acid followed by immersion in nitric acid. Conditions such as the temperature and concentration of sulfuric acid and nitric acid and the time for immersion are appropriately adjusted so that the base metal of the sample is not excessively dissolved. An example of conditions of the removal operation of the forsterite film is as follows. First, the sample is immersed in sulfuric acid having a concentration of 10% at 80°C for 3 minutes. Thereafter, the surface of the sample is washed with water using a waste cloth or the like to remove the sludge adhering to the surface. Thereafter, the sample is dried. Further, the sample is immersed in nitric acid having a concentration of 10% at room temperature while being stirred for about 5 seconds.
The sheet thickness of the grain-oriented electrical steel sheet 1 is not limited, but is preferably 0.15 mm to 0.30 mm, for example. When the thickness is 0.30 mm or less, classical eddy-current loss can be suppressed, and iron loss can be further reduced. On the other hand, when the sheet thickness is 0.15 mm or more, rolling efficiency can be improved to improve productivity.

(Magnetic domain control treatment line 11)

A plurality of the magnetic domain control treatment lines 11 provided on the surface of the grain-oriented electrical steel sheet 1 have a function of refining a 180° magnetic domain. By refining the magnetic domain, the iron loss of the grain-oriented electrical steel sheet 1 can be reduced. The magnetic domain is a collection of magnetic dipoles existing inside a ferromagnetic material, and is a small region where magnetic moments are aligned in one direction. The 180° magnetic domain is a magnetic domain in which the magnetization direction is the <100> orientation of the crystal and which is sandwiched between two 180° magnetic walls substantially parallel to the rolling direction RD. A distance (domain wall interval) between adjacent domain walls of the 180° magnetic domain is referred to as a spacing of the 180° magnetic domain walls. Hereinafter, unless otherwise specified, the spacing of the 180° magnetic domain walls is simply referred to as "spacing of magnetic domain walls".
The extending direction of the magnetic domain control treatment line 11 is not particularly limited as long as it is a direction intersecting the rolling direction (as long as it is not parallel to the rolling direction). The magnetic domain control treatment line 11 and the rolling direction RD may be substantially perpendicular (substantially parallel to the transverse direction TD). That is, the angle formed by the magnetic domain control treatment line 11 and the transverse direction TD may be substantially 0°. On the other hand, as illustrated in FIG. 1A, the angle formed by the magnetic domain control treatment line 11 and the transverse direction TD may be more than 0°. For example, the angle formed by the magnetic domain control treatment line 11 and the transverse direction TD may be an arbitrary value within the range of 0 to 45°. The angle formed by the magnetic domain control treatment line 11 and the transverse direction TD may be 1° or more, 3° or more, or 5° or more. The angle formed by the magnetic domain control treatment line 11 and the transverse direction TD may be 40° or less, 35° or less, or 30° or less.
As illustrated in FIG. 1A, the angles formed by all the magnetic domain control treatment lines 11 and the transverse direction TD may be the same. That is, all the magnetic domain control treatment lines 11 may extend in parallel to each other. On the other hand, the angle formed by the magnetic domain control treatment line 11 and the transverse direction TD may vary. That is, some or all of a plurality of the magnetic domain control treatment lines 11 may extend non-parallel to each other. The average value of the angles formed by the magnetic domain control treatment line 11 and the transverse direction TD may be 1° or more, 3° or more, or 5° or more. The average value of the angles formed by the magnetic domain control treatment line 11 and the transverse direction TD may be 40° or less, 35° or less, or 30° or less. The average value of the angles may be calculated by measuring an angle formed with the transverse direction TD at a plurality of positions with respect to one magnetic domain control treatment line, or by measuring an angle formed with the transverse direction TD by a plurality of magnetic domain control treatment lines at one point or a plurality of positions.
When dmax (an absolute maximum value of an interval in a rolling direction between adjacent intersection points among a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines) is more than 20 mm, as shown in FIG. 1B, the magnetic domain control treatment line 11 may not be interrupted in the middle (that is, all the magnetic domain control treatment lines may be formed over the entire width direction of the steel sheet), and as shown in FIG. 1C, the magnetic domain control treatment line 11 may include a curved portion (that is, may not be formed only of a straight line).
The type of the magnetic domain control treatment line 11 is not particularly limited as long as the magnetic domain control treatment line is a tensile stress introduction line into which a tensile stress of 40 MPa or more is introduced, but a preferred example is the thermal strain. The thermal strain can be formed using means such as laser irradiation, electron beam irradiation, or ion implantation.
As the tensile stress is higher, the effect of reducing the iron loss is enhanced. On the other hand, the lower the tensile stress is, the more noise characteristics are improved. Tensile stress according to characteristics required for the grain-oriented electrical steel sheet 1 can be appropriately selected.
Regarding the magnitude of the tensile stress, in at least a part of the magnetic domain control treatment line 11, the tensile stress in any direction is 40 MPa or more, preferably 60 MPa or more, and more preferably 80 MPa or more. In a case where the tensile stress in at least one direction is 40 MPa or more, it is considered that the requirement that "the tensile stress in any direction is 40 MPa or more" is satisfied, and the requirement that "The plurality of magnetic domain control treatment lines are tensile stress introduction lines into which a tensile stress of 40 MPa or more is introduced." of the present embodiment is satisfied. For example, in at least a part of the magnetic domain control treatment line 11, the tensile stress in an arbitrary direction is preferably 300 MPa or less, 200 MPa or less, 180 MPa or less, or 150 MPa or less. The tensile stress in an arbitrary direction in the magnetic domain control treatment line 11 may be uniform or may vary.
The magnitude of the tensile stress introduced in the thermal strain is measured by the EBSD Wilkinson method and Cross Court manufactured by BLG Vantage. The EBSD Wilkinson method is described in detail in A. J. Wilkinson, et al. "High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity" Ultramicroscopy Vol 106, No. 4-5, March 2006, P. 307-313.
When the magnitude of the tensile stress introduced in the thermal strain is measured by the EBSD Wilkinson method and the Cross Court manufactured by BLG Vantage, first, the magnetic domain control treatment line 11 is specified by the above-described procedure. Next, the grain-oriented electrical steel sheet 1 is cut through the magnetic domain control treatment line 11 and perpendicularly to the magnetic domain control treatment line 11. This cut cross section is used as a measurement surface. The cross section of the magnetic domain control treatment line 11 included in the measurement surface is analyzed by the EBSD Wilkinson method and Cross Court manufactured by BLG Vantage, and a tensile stress component in an arbitrary direction is extracted and the magnitude thereof is measured. For example, it is possible to extract a tensile stress component in a rolling surface normal direction ND, a direction parallel to the magnetic domain control treatment line 11, and a direction perpendicular to the rolling surface normal direction ND and the magnetic domain control treatment line 11.
The number of measurement points is, for example, 10. In a case where the tensile stress in an any direction is 40 MPa or more (that is, in a case where the tensile stress in at least one direction is 40 MPa or more,) in at least one portion of the grain-oriented electrical steel sheet 1, the absolute maximum value of the tensile stress in an any direction in the plurality of magnetic domain control treatment lines included in the grain-oriented electrical steel sheet 1 is determined to be 40 MPa or more. Therefore, for the purpose of determining whether the absolute maximum value of the tensile stress is 40 MPa or more, the measurement of the tensile stress may be stopped when a measurement point at which the tensile stress in an arbitrary direction is 40 MPa or more is found. However, in a case where σ(TS_m)², TS_{m(β < 2)}, or TS_{m(β ≥ 2)} to be described later is obtained, the measurement is not stopped, and the tensile stress at each measurement point is obtained.
In a case where the magnetic domain control treatment line 11 is a thermal strain, the magnetic domain control treatment line 11 may not be visually identified. In this case, for example, the position of a thermal strain can be identified by photographing a magnetic domain image and observing the photographed magnetic domain image using the image acquisition device 30 having a constitution shown as an exemplary example in FIG. 4. At the time of photographing, as necessary, a magnetic domain image is photographed while a DC magnetic field is applied along the rolling surface normal direction ND of the grain-oriented electrical steel sheet 1.

(Interval between intersection points of imaginary line parallel to rolling direction and magnetic domain control treatment line)

(Spacing of magnetic domain walls)

As described above, the magnetic domain control treatment line 11 provided on the surface of the grain-oriented electrical steel sheet 1 has a function of refining the 180° magnetic domain. In addition, the effect of reducing the iron loss is enhanced as the interval between the magnetic domain control treatment lines is smaller. Therefore, in the general magnetic domain control treatment, each interval of the magnetic domain control treatment lines is formed so as not to be more than 20 mm.
On the other hand, in the grain-oriented electrical steel sheet according to the present embodiment, in a case where a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction RD is set on the surface, and further, imaginary lines VL parallel to the rolling direction RD and having a length of 50 mm are set inside the evaluation region at intervals of 5 mm in the direction perpendicular to the rolling direction, in at least one imaginary line VL, the absolute maximum value of the interval in the rolling direction RD between adjacent intersection points among the plurality of intersection points VP of the imaginary line VL and the plurality of magnetic domain control treatment lines 11 is more than 20 mm. That is, in at least a part, the interval between the magnetic domain control treatment lines in the rolling direction is more than 20 mm. FIG. 1A illustrates a state in which only one imaginary line VL is drawn as an example. In a case where a plurality of imaginary lines VL is set, the required number of other imaginary lines can be set in parallel to the imaginary line VL of FIG. 1A.
In addition, the grain-oriented electrical steel sheet according to the present embodiment satisfies at least one of the following requirements at the imaginary line VL having an absolute maximum value of the interval in the rolling direction RD of more than 20 mm.

(1) The average value of the spacings of magnetic domain walls measured along the imaginary line VL is 600 µm or less.
(2) The absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line VL is 1200 µm or less.

Both of the above requirements (1) and (2) may be satisfied. That is, the average value of the spacings of magnetic domain walls measured along the imaginary line VL may be 600 µm or less, and the absolute maximum value may be 1200 µm or less.
As described above, the magnetic domain control treatment is effective for reducing the iron loss of the grain-oriented electrical steel sheet, but deteriorates noise characteristics of the grain-oriented electrical steel sheet. Therefore, deterioration of noise characteristics can be suppressed by reducing the density of the magnetic domain control treatment lines. That is, both noise reduction and iron loss reduction can be achieved in a well-balanced manner.
That the absolute maximum value of the interval between the intersection points is more than 20 mm means that there is a region where the interval in the rolling direction of the magnetic domain control treatment line is more than 20 mm in the steel sheet, which is more preferable from the viewpoint of low noise.
The present inventors have further conducted studies and analyzed changes in the magnetic domains of the grain-oriented electrical steel sheets before and after the magnetic domain control, and as a result, it has become clear that there are portions where the spacing of magnetic domain walls is reduced and portions where the spacing of magnetic domain walls is hardly reduced by the magnetic domain control. That is, the present inventors have found that the magnetic domain refinement effect when the magnetic domain control treatment is performed differs depending on the spacing of magnetic domain walls before the magnetic domain control. More specifically, it has been found that the magnetic domain refinement effect by the magnetic domain control treatment is less likely to appear in a region having a narrow spacing of magnetic domain walls.
According to the above findings, it is found that it is extremely effective to preferentially perform a magnetic domain control treatment in a region having a wide spacing of magnetic domain walls in order to achieve both iron loss reduction and noise reduction. Magnetic domain control treatment in a region having a wide spacing of magnetic domain walls can reduce iron loss. A magnetic domain control treatment line formed in a region having a narrow spacing of magnetic domain walls is considered to cause deterioration of noise characteristics due to a flux closure domain. Therefore, deterioration of noise characteristics can be prevented by minimizing magnetic domain control treatment in a region having a narrow spacing of magnetic domain walls.
Therefore, in order to obtain the effect of reducing iron loss while minimizing deterioration of noise characteristics, the magnetic domain control treatment is mainly performed in a region having a wide spacing of magnetic domain walls and having a large magnetic domain refinement effect. It is preferable to perform the magnetic domain control treatment only in a region having a wide spacing of magnetic domain walls, but it is allowable to perform the magnetic domain control treatment in a region having a narrow spacing of magnetic domain walls since the deterioration of noise characteristics is small if the ratio is small. In addition, it is preferable to perform the magnetic domain control treatment on all the regions with a wide spacing of magnetic domain walls, but a region where the magnetic domain control treatment is not performed may be included within a range where the iron loss reduction effect can be sufficiently obtained.
As a result of further studies by the present inventors on the magnetic domain refinement effect, as shown in FIG. 2, in the region where the spacing of magnetic domain walls is about 500 µm or less, the spacing of magnetic domain walls were substantially the same before and after the magnetic domain control treatment. That is, in the region where the spacing of magnetic domain walls is about 500 µm or less, it is considered that the effect of the magnetic domain refinement by the magnetic domain control is hardly obtained. Therefore, in the grain-oriented electrical steel sheet according to the present embodiment, in a case where the effect of reducing the iron loss is sufficiently obtained while lowering the density of the magnetic domain control treatment lines, the magnetic domain control is not intentionally performed in such a region where the spacing of magnetic domain walls is 500 µm or less, and the magnetic domain control treatment lines are mainly formed in a region where the spacing of magnetic domain walls is more than 500 µm. As a result, in the grain-oriented electrical steel sheet according to the present embodiment, in the imaginary line VL where the absolute maximum value of the interval in the rolling direction RD is more than 20 mm, the spacing of magnetic domain walls measured along the imaginary line has an average value of 600 µm or less, or an absolute maximum value of 1200 µm or less. That is, in the grain-oriented electrical steel sheet 1 satisfying at least one of the requirement (1) and the requirement (2), the spacing of magnetic domain walls is set to a small value over the entire imaginary line VL. Therefore, both noise reduction and iron loss reduction can be achieved in a well-balanced manner.
In the grain-oriented electrical steel sheet according to the present embodiment, in the two or more imaginary lines VL, the absolute maximum value of the interval in the rolling direction between adjacent intersection points among the plurality of intersection points VP is preferably more than 20 mm, and at least one of the following requirements is preferably satisfied.

(1) The average value of the spacings of magnetic domain walls measured along each of the imaginary lines VL is 600 µm or less.
(2)The absolute maximum value of the spacings of magnetic domain walls measured along each of the imaginary lines VL is 1200 µm or less.

Both of the above requirements (1) and (2) may be satisfied. That is, the average value of the spacings of magnetic domain walls measured along the imaginary line VL may be 600 µm or less, and the absolute maximum value may be 1200 µm or less.
The fact that there is a region where the absolute maximum value of the interval between the intersection points is more than 20 mm in the plurality of imaginary lines means that there is a region where the interval between the magnetic domain control treatment lines in the rolling direction is more than 20 mm at a plurality of positions of the steel sheet, which is more preferable from the viewpoint of low noise.
The average value of the spacings of magnetic domain walls described above is still more preferably 500 µm or less, 450 µm or less, 400 µm or less, 380 µm or less, 350 µm or less, or 300 µm or less. The absolute maximum value of the spacings of magnetic domain walls is more preferably 1000 µm or less, 800 µm or less, 600 µm or less, 500 µm or less, 450 µm or less, or 400 µm or less.
The interval between the intersection points of the imaginary line and the plurality of magnetic domain control treatment lines in the rolling direction, and the average value and the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line are obtained by the following methods.
For example, a rectangular sample having both sides of 100 mm (or 100 mm or more) in length can be cut out from the grain-oriented electrical steel sheet 1 and subjected to measurement. In a case where the grain-oriented electrical steel sheet 1 is a coil, a sample may be collected from an arbitrary position of the coil. In a case where the grain-oriented electrical steel sheet 1 is a component incorporated in an electrical product such as a transformer or a motor, a sample may be collected from any place of the component. In a case where the size of the component is small, if the length of one side of the sample is 50 mm or more, the length of one side of the sample may be less than 100 mm. At that time, it is desirable to collect a sample by a method such as wire cutting in order to minimize the influence of mechanical strain or the like on the sample.
For this sample, a magnetic domain image is acquired by an image acquisition device including a light source unit, a magneto-optical sensor (MO sensor), an image sensor, and a signal processing unit.
In this magnetic domain image, a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction is set, and further, imaginary lines VL parallel to the rolling direction and having a length of 50 mm are set at intervals of 5 mm in a direction perpendicular to the rolling direction inside the evaluation region.
The interval between intersection points of the imaginary line VL and the plurality of magnetic domain control treatment lines 11 is measured, and the absolute maximum value thereof is set as the absolute maximum value of the interval between adjacent intersection points in the rolling direction.
The average value and the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line are set by a plurality of sub imaginary lines perpendicular to the sheet surface vertical direction (thickness direction) and perpendicular to the imaginary line VL. The length of the sub imaginary line is set to 5 mm, and is set at intervals of 2 mm in the rolling direction. The sub imaginary line is set to intersect the imaginary line VL at the center thereof. The number of magnetic domains included in each of the sub imaginary lines is measured, and a value obtained by dividing the length of the sub imaginary line by the number of magnetic domains included in the sub imaginary line is regarded as a spacing of magnetic domain walls on the sub imaginary line. An average value of the spacings of magnetic domain walls on the sub imaginary line is an average value of the spacings of magnetic domain walls measured along the imaginary line, and an absolute maximum value of the spacings of magnetic domain walls on the sub imaginary line is an absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line.
That is, in the present embodiment, "along the imaginary line VL" means that the centers of the sub imaginary lines are located on the imaginary line at equal intervals.
The place where the evaluation region and the imaginary line VL are set is not limited. The evaluation region and the imaginary line VL may be set at an any place where the imaginary line VL in which the absolute maximum value of the interval in the rolling direction between the adjacent intersection points among the plurality of intersection points VP can be set. For example, the imaginary line VL may be set so as to pass through the region where the magnetic domain control treatment line 11 is not provided. On the other hand, in a case where it is not possible to find a place where the imaginary line VL can be set such that the absolute maximum value of the interval between the adjacent intersection points falls within the range of the present disclosure, it is estimated that the requirements of the present disclosure are not satisfied.
In addition, the magnetic domain image is output to an analysis device, which is a computer device such as a personal computer (PC) including a calculation unit, a memory, a display unit, an input unit, and a communication I/F, via a cable or by wireless communication. In the calculation unit, the magnetic domain structure is analyzed from the magnetic domain image using the line segment method.
An example of measurement by the line segment method will be described. FIG. 3C is a magnetic domain image acquired by CMOS-MagView manufactured by Matesy GmbH. FIG. 3D is a diagram schematically illustrating FIG. 3C showing measurement.
In the line segment method, evaluation is performed by drawing a line segment Ls perpendicular to the magnetic domain. The interval between the line segments is drawn so as to be three per 1 cm in the rolling direction RD. The spacing of magnetic domain walls is derived based on the interval w of the intersection point Ip between the 180° magnetic domain wall and the line segment Ls. However, in a case where there are the flux closure domain 301 and the noise 302, these are not counted as domain walls. In a case where the average value of the spacings of magnetic domain walls is obtained, the average interval is obtained from the length of each line segment Ls and the number of intersection points Ip.
In the grain-oriented electrical steel sheet according to the present disclosure, the absolute maximum value of the tensile stress introduced into the thermal strain, which is an index of the strength of the magnetic domain control, in the magnetic domain control treatment line is preferably non-uniform at each measurement point of the tensile stress.
The higher the strength of magnetic domain control is, the higher the effect of magnetic domain refinement is, on the other hand, the higher the strength of the magnetic domain control is, the more easily the hysteresis loss is increased and the noise characteristics are deteriorated. According to the new findings of the present inventors, a grain-oriented electrical steel sheet has a non-uniform magnetic domain control saturation strength. Therefore, it is preferable to make the magnetic domain control strength non-uniform according to the magnetic domain control saturation strength.
The magnetic domain control saturation strength means a magnetic domain control strength at which the effect of magnetic domain refinement treatment is substantially saturated. In a case where the magnetic domain control strength is equal to or lower than the magnetic domain control saturation strength, a higher magnetic domain control strength leads to reduced iron loss. However, in a case where the magnetic domain control strength is more than the magnetic domain control saturation strength, the iron loss reduction effect is hardly enhanced even if the magnetic domain control strength is increased. On the other hand, even in a case where the magnetic domain control strength is more than the magnetic domain control saturation strength, a higher magnetic domain control strength leads to increased hysteresis loss and worsened noise characteristics. Therefore, it is extremely preferable that the magnetic domain control strength is within the range not exceeding the magnetic domain control saturation strength.
More preferably, when each of a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines is defined as a magnetic domain refinement point, the absolute maximum value of the tensile stress in a unit of MPa introduced into the thermal strain measured at each of the magnetic domain refinement points is TS_m, and the variance of the TS_m is σ(TS_m)², σ(TS_m)² > 5.0 is satisfied.
The "absolute maximum value of the tensile stress introduced into the thermal strain" is an absolute maximum value of the tensile stress measured in one arbitrary cross section for measurement. The tensile stress varies in one measurement cross section, and thus one "absolute maximum value of the tensile stress introduced into the thermal strain" is specified for one measurement cross section. As schematically illustrated in FIG. 9, the thermal strain 541 has a certain degree of spread in the cross section. The tensile stress is the highest at a site directly irradiated with the laser beam, and the tensile stress is low at a site away from the site. That is, the measured value of the tensile stress differs for each measurement site in the cross section. According to the method for measuring tensile stress as described later, the distribution and the absolute maximum value of tensile stress in the cross section can be derived.
In a case where the magnetic domain control strength is uniform, the absolute maximum value of the tensile stress introduced into the thermal strain 541 is a constant value over the entire magnetic domain control treatment line 11. On the other hand, in a case where the magnetic domain control strength is non-uniform, the absolute maximum value of the tensile stress introduced into the thermal strain in the magnetic domain control treatment line is non-uniform at each measurement point of the tensile stress. Hereinafter, the absolute maximum value of tensile stress introduced into a thermal strain may be simply referred to as "tensile stress".
In addition, the present inventors have found that the magnetic domain control saturation strength has a strong relationship with the β angle. The β angle is a deviation angle of grains from the Goss orientation around the axis of the transverse direction (TD). In a point where the β angle is small, the magnetic domain control saturation strength is high. In the grain-oriented electrical steel sheet before the magnetic domain control treatment, there is a relationship also between the β angle and the spacing of magnetic domain walls. In the grain-oriented electrical steel sheet before the magnetic domain control treatment, the larger the β angle is, the smaller the spacing of magnetic domain walls is. However, in the grain-oriented electrical steel sheet after the magnetic domain control treatment, the relationship between the spacing of magnetic domain walls and the β angle becomes small. This is because the magnetic domain control treatment changes the spacing of magnetic domain walls, but does not change the β angle.
Therefore, it is preferable to select the optimum magnetic domain control strength according to the size of the spacing of magnetic domain walls or the β angle. For example, it is preferable that the magnetic domain refinement treatment is performed with a large magnetic domain control strength at a portion where the spacing of magnetic domain walls is large and the β angle is small; and the magnetic domain refinement treatment is performed with a small magnetic domain control strength at a portion where the spacing of magnetic domain walls is small and the β angle is large. As described above, the magnetic domain refinement treatment is not performed on a region where the original spacing of magnetic domain walls is narrow.
Specifically, it is preferable that when TS_{m(β < 2)} is an arithmetical mean value of absolute maximum values of the tensile stress in a unit of MPa introduced into the thermal strain, measured at each of the magnetic domain refinement points having a β angle of less than 2° among the magnetic domain refinement points, and TS_{m(β ≥ 2)} is an arithmetical mean value of absolute maximum values of the tensile stress in a unit of MPa introduced into the thermal strain, measured at each of the magnetic domain refinement points having a β angle of 2° or more among the magnetic domain refinement points, TS_{m(β < 2)} > TS_{m(β ≥ 2)} is satisfied.
In this case, the iron loss of the grain-oriented electrical steel sheet after magnetic domain control is further reduced. On the other hand, in the grain-oriented electrical steel sheet after magnetic domain control, an increase in hysteresis loss and deterioration in noise characteristics are further suppressed.
An example of a method of measuring TS_m and σ(TS_m)² will be described with reference to FIG. 10. A broken line in FIG. 10 is a plurality of imaginary lines VL set at intervals of 5 mm in parallel along the rolling direction RD of the grain-oriented electrical steel sheet. An X mark and an O mark in FIG. 10 are intersection points of the imaginary line VL and the thermal strain 541 which is a magnetic domain control treatment line. The β angle is 2° or more at the point marked with the × mark, and the β angle is less than 2° at the point marked with the O mark. However, there is no need to consider the β angle at the intersection point for calculating σ(TS_m)².
First, the rolling direction RD of the grain-oriented electrical steel sheet is specified. The rolling direction RD can be specified by a method described later. Next, imaginary lines VL are set at intervals of 5 mm in parallel along the rolling direction RD of the grain-oriented electrical steel sheet. Then, an intersection point of the imaginary line VL and the thermal strain 541 which is the magnetic domain control treatment line is specified. In a case where the thermal strain 541 cannot be visually recognized with the naked eye, the thermal strain 541 is specified based on a magnetic domain image. The shape of the sample is preferably a rectangle whose size along the rolling direction RD is 100 mm or more and whose size along the transverse direction TD is 100 mm or more. One side of the rectangle is preferably parallel to the rolling direction RD.
Then, TS_m is measured at all the intersection points in the measurement region, and the variance σ(TS_m)² of TS_m is calculated. The tensile stress TS_m introduced in the thermal strain is measured by an EBSD Wilkinson method and a Cross Court manufactured by BLG Vantage. The EBSD Wilkinson method is described in detail in A. J. Wilkinson, et al. "High-resolution elastic strain measurement from electron backscatter diffraction patterns: New levels of sensitivity" Ultramicroscopy Vol 106, No. 4-5, March 2006, P. 307-313.
When the magnitude of tensile stress introduced into the thermal strain is measured by the EBSD Wilkinson method and Cross Court manufactured by BLG Vantage, first, the thermal strain 541 as the magnetic domain control treatment line is specified by the above-described procedure. Next, the grain-oriented electrical steel sheet 1 is cut through the magnetic domain control treatment line and perpendicularly to the magnetic domain control treatment line. This cut cross section is used as a measurement surface. The cross section of the magnetic domain control treatment line included in the measurement surface is analyzed by the EBSD Wilkinson method and Cross Court manufactured by BLG Vantage, and a tensile stress component in an arbitrary direction is extracted and the magnitude thereof is measured. For example, it is possible to extract tensile stress components in the rolling surface normal direction, in the direction parallel to the magnetic domain control treatment line, and in the direction perpendicular to the rolling surface normal direction and the magnetic domain control treatment line.
The variance σ(TS_M)² of the absolute maximum values TS_M of tensile stress specified at each of a plurality of the measurement points is derived in accordance with the method for deriving a population variance described in the paragraph 2.36 of JIS Z 8101-1:2015 "Statistics-Vocabulary and symbols-Part 1: General statistical terms and terms used in probability".
TS_{m(β < 2)} and TS_{m(β ≥ 2)} are measured by the following method.
First, the β angle is measured at each intersection point to specify the intersection points where the β angle is 2° or more and the intersection points where the β angle is less than 2°. The β angle in the grain-oriented electrical steel sheet is measured by the side surface reflection Laue method. The side surface reflection Laue method is widely known as a method for measuring a crystal orientation.
Next, the absolute maximum value TS_m of tensile stress is specified for each of all the intersection points where the β angle is 2° or more, and the arithmetical mean value of these values is calculated. The value is regarded as TS_m(β≥2).
Furthermore, the absolute maximum value TS_m of the tensile stress is specified at each of all intersection points where the β angle is less than 2°, and the arithmetical mean value of these values is calculated. The value is regarded as TS_{m(β < 2)}. The method for measuring the absolute maximum value TS_m of the tensile stress introduced into the thermal strain 541 at the intersection point is as described above.
In the plurality of magnetic domain control treatment lines 11, the interval along the rolling direction RD between the magnetic domain control treatment lines 11 adjacent along the rolling direction RD is not particularly limited. The effect of reducing the iron loss is enhanced as the interval is smaller. On the other hand, the larger the interval is, the more the noise characteristics are improved. The interval can be appropriately selected according to the characteristics required for the grain-oriented electrical steel sheet 1. For example, the interval along the rolling direction RD between the magnetic domain control treatment lines 11 adjacent to each other along the rolling direction RD may be 1.0 mm or more, 2.0 mm or more, 3.0 mm or more, or 5.0 mm or more. The interval along the rolling direction RD between the magnetic domain control treatment lines 11 adjacent along the rolling direction RD may be 10.0 mm or less, 9.0 mm or less, 8.0 mm or less, or 7.0 mm or less.
The interval of the adjacent magnetic domain control treatment lines 11 along the rolling direction RD may be constant or may vary (may fluctuate). In the case that variation is present, the average value of the intervals P along the rolling direction RD between the magnetic domain control treatment lines 11 adjacent to each other along the rolling direction RD may be 1.0 mm or more, 2.0 mm or more, 3.0 mm or more, or 5.0 mm or more. The average value of the intervals along the rolling direction RD between the magnetic domain control treatment lines 11 adjacent along the rolling direction RD may be 10.0 mm or less, 9.0 mm or less, 8.0 mm or less, or 7.0 mm or less. The interval may be obtained by drawing one or more straight lines L along the rolling direction RD and measuring the distance between two adjacent points LP at the intersection point LP of the straight line L and the magnetic domain control treatment line. In the case of calculating the average value of the intervals, a plurality of distances between two adjacent points LP may be measured and averaged.
In the grain-oriented electrical steel sheet 1 according to the present embodiment, the intervals of VP vary at the imaginary line VL, which is the measurement position of the spacing of magnetic domain walls. That is, even when the average of the intervals of the magnetic domain control treatment lines 11 is in the above range, the imaginary line VL, which is the measurement position of the spacing of magnetic domain walls, passes through the region where the magnetic domain control treatment line 11 is not provided, so that the absolute maximum value of the interval in the rolling direction at the intersection point of the imaginary line VL and the magnetic domain control treatment line 11 is more than 20 mm.
The angle formed by the magnetic domain control treatment line 11 and the transverse direction TD can be measured using a known angle measuring means after the magnetic domain control treatment line 11 and the transverse direction TD are specified by the above-described and later-described procedures.
The interval of the magnetic domain control treatment line 11 along the rolling direction RD can be measured using a known length measuring means after the magnetic domain control treatment line 11 and the rolling direction RD are specified by the above-described and later-described procedures.
Here, the interval of the magnetic domain control treatment line 11 along the rolling direction RD is a distance from the center of the width of the magnetic domain control treatment line in the rolling direction RD to the center of the width of the adjacent magnetic domain control treatment line in the rolling direction RD.

(Method for specifying rolling direction RD and transverse direction TD)

The rolling direction RD and the transverse direction (sheet width direction) TD of the grain-oriented electrical steel sheet 1 are specified by the following means.

(1) In a case where the sample is cut out from the coil-shaped grain-oriented electrical steel sheet 1, the width direction of the coil is regarded as the transverse direction TD. A direction perpendicular to the transverse direction TD and the rolling surface normal direction ND is regarded as the rolling direction RD.
(2) In a case where the sample is cut out from a part or the like of an electrical product, the rolling direction RD and the transverse direction TD are specified from rolling defects on the surface of the grain-oriented electrical steel sheet 1. The extending direction of the rolling defect is regarded as a rolling direction RD. A direction perpendicular to the rolling direction RD and the rolling surface normal direction ND is regarded as a transverse direction TD.
(3) In a case where it is difficult to specify the rolling direction RD and the transverse direction TD from a rolling defect on the surface of the grain-oriented electrical steel sheet 1, the rolling direction RD and the transverse direction TD are specified from the crystal orientation of the grain-oriented electrical steel sheet 1. Specifically, the crystal orientation of the grain-oriented electrical steel sheet 1 to be evaluated is measured at a plurality of points. Then, the direction in which the deviation angle from the easy axis of magnetization <001> at which the angle formed by the crystal orientation at the measurement point with the rolling surface normal direction ND (sheet thickness direction) is the closest to the right angle is minimized is regarded as the rolling direction RD, and the direction perpendicular to the rolling direction RD and the rolling surface normal direction ND is regarded as the transverse direction (sheet width direction) TD.

(Coating)

The grain-oriented electrical steel sheet 1 may have a forsterite film on its surface (That is, the grain-oriented electrical steel sheet may be composed of a base steel sheet and a forsterite film formed on the surface of the base steel sheet.). Further, the grain-oriented electrical steel sheet 1 may have an insulating coating on the surface of the base steel sheet or the surface of the forsterite film (That is, the grain-oriented electrical steel sheet may be composed of a base steel sheet, a forsterite film formed on the surface of the base steel sheet, and an insulating coating formed on the surface of the forsterite film, or may be composed of a base steel sheet and an insulating coating formed on the surface of the base steel sheet.).
The forsterite film and the insulating coating may be formed on one surface or both surfaces of the grain-oriented electrical steel sheet 1.
The forsterite film is, for example, an inorganic coating film containing magnesium silicate as a main component. The forsterite film is formed, for example, by a reaction between an annealing separator containing magnesia (MgO) applied to the surface of the base steel sheet and a component of the surface of the base steel sheet in final annealing. The forsterite film has, for example, a composition (more specifically, a composition containing Mg₂SiO₄ as a main component) derived from the components of the annealing separator and the base steel sheet. On the other hand, in a case where an annealing separator mainly containing Al₂O₃ is used in final annealing, a forsterite film may not be formed.
The insulating coating has a function of applying electrical insulation properties and tension to the grain-oriented electrical steel sheet 1. The tension is applied to the grain-oriented electrical steel sheet 1 to facilitate domain wall movement in the grain-oriented electrical steel sheet 1, and thus, the iron loss of the grain-oriented electrical steel sheet 1 can be reduced. In addition, according to the insulating coating, various characteristics such as corrosion resistance, heat resistance, and slippage can be provided to the grain-oriented electrical steel sheet 1. The insulating coating may be, for example, a known coating formed by applying a coating solution containing phosphate and colloidal silica as main components to the surface of the forsterite film and baking the coating solution.

[Manufacturing Method]

The grain-oriented electrical steel sheet according to the embodiment exhibits its advantageous effects as long as it has the above characteristics, regardless of the manufacturing method therefor. However, according to the following method, it is preferable because it can be stably manufactured.
That is, the grain-oriented electrical steel sheet according to the present embodiment can be manufactured by a manufacturing method including the following steps (1) to (III). In a case where the distribution of the spacings of magnetic domain walls is clear, such as in a case where the distribution of the spacings of magnetic domain walls is estimated by a method other than image acquisition, the steps (I) and (II) may be omitted.

(I) A magnetic domain image acquisition step of acquiring a magnetic domain image of the grain-oriented electrical steel sheet.
(II) A region specification step of specifying a region having a spacing of magnetic domain walls of more than 500 µm in the grain-oriented electrical steel sheet based on the magnetic domain image obtained in the magnetic domain image acquisition step.
(III) A magnetic domain control treatment line forming step of forming a magnetic domain control treatment line on the surface of the grain-oriented electrical steel sheet after the region specification step.

Each step will be described.
First, the grain-oriented electrical steel sheet (original sheet) to be subjected to the magnetic domain image acquisition step or to be subjected to the magnetic domain control treatment line forming step in a case where the magnetic domain image acquisition step or the magnetic domain image acquisition step and the region specification step are not performed may be a known grain-oriented electrical steel sheet.
For example, the original sheet can contain, as a chemical composition, Si: 2.50 to 7.00%, Mn: 0 to 1.00%, C: 0 to 0.085%, acid-soluble Al: 0 to 0.065%, N: 0 to 0.012%, Cr: 0 to 0.300%, Cu: 0 to 0.400%, P: 0 to 0.500%, Sn: 0 to 0.300%, Sb: 0 to 0.300%, Ni: 0 to 1.000%, S: 0 to 0.015%, Se: 0 to 0.015%, Bi: 0 to 0.020%, Nb: 0 to 0.030%, V: 0 to 0.030%, Mo: 0 to 0.030%, Ta: 0 to 0.030%, W: 0 to 0.030%, B: 0 to 0.080%, and Ti: 0 to 0.015% in mass%. The balance of the chemical composition includes Fe and impurities.
A forsterite film may be formed on the surface of the grain-oriented electrical steel sheet serving as the original sheet.

(Magnetic domain image acquisition step)

(Region specification step)

In the magnetic domain image acquisition step, a magnetic domain image of the surface of the grain-oriented electrical steel sheet is acquired before the magnetic domain control treatment line forming step. In the region specification step, a region having a spacing of magnetic domain walls of more than 500 µm in the grain-oriented electrical steel sheet is specified based on the magnetic domain image obtained in the magnetic domain image acquisition step.
As described above, it is considered that the effect of magnetic domain refinement is small in a region having a small spacing of magnetic domain walls, and the effect of magnetic domain refinement by magnetic domain control is hardly obtained in a region having a spacing of magnetic domain walls of about 500 µm or less. Therefore, it is preferable not to perform magnetic domain control in this region.
In the magnetic domain treatment line forming step, which is a subsequent step, the magnetic domain control treatment is mainly performed in a region having a spacing of magnetic domain walls of more than 500 µm, so that the magnetic domain control treatment lines can be reduced, and iron loss can be reduced while deterioration of noise characteristics is suppressed.

(Magnetic domain control treatment line forming step)

In the magnetic domain control treatment line forming step, a plurality of magnetic domain control treatment lines extending in a direction intersecting the rolling direction are formed on the surface of the grain-oriented electrical steel sheet by mainly forming the magnetic domain control treatment lines in the region having the spacing of magnetic domain walls of more than 500 µm specified in the region specification step. At that time, the magnetic domain control treatment line is formed such that there is a region where the interval in the rolling direction is more than 20 mm.
Examples of the method include a method of forming a magnetic domain control treatment line in a direction intersecting a rolling direction at a position more than 20 mm moved in the rolling direction with respect to an adjacent magnetic domain control treatment line on the basis of a distribution of a spacing of magnetic domain walls obtained in the region specification step, and a method of forming a magnetic domain control treatment line such that an interval between adjacent intersection points is more than 20 mm in the rolling direction at a certain position by not forming the magnetic domain control treatment line in a partial range even when a start point is within 20 mm in the rolling direction from the adjacent magnetic domain control treatment line as shown in FIG. 1A.
Preferably, the magnetic domain control strength is determined according to the spacing of magnetic domain walls and the size of the β angle of the grain-oriented electrical steel sheet before the magnetic domain refinement treatment. The magnetic domain control strength is an amount of the thermal strain. In this case, the absolute maximum value of the tensile stress introduced into the thermal strain in the magnetic domain control treatment line becomes non-uniform at each measurement point of the tensile stress.
The higher the strength of magnetic domain control is, the higher the effect of magnetic domain refinement is. On the other hand, the higher the strength of magnetic domain control is, the more easily the hysteresis loss is increased and the noise characteristics are deteriorated. According to the new findings of the present inventors, a grain-oriented electrical steel sheet has a non-uniform magnetic domain control saturation strength.
The magnetic domain control saturation strength means a magnetic domain control strength at which the effect of magnetic domain refinement treatment is saturated. In a case where the magnetic domain control strength is equal to or lower than the magnetic domain control saturation strength, a higher magnetic domain control strength leads to reduced iron loss. However, in a case where the magnetic domain control strength exceeds the magnetic domain control saturation strength, the iron loss reduction effect cannot be enhanced even if the magnetic domain control strength is increased. However, even in a case where the magnetic domain control strength is more than the magnetic domain control saturation strength, the higher the magnetic domain control strength is, the more hysteresis loss increases and noise characteristics deteriorate. Therefore, it is extremely preferable that the magnetic domain control strength is within the range not exceeding the magnetic domain control saturation strength.
Specifically, it is preferable that the magnetic domain refinement treatment is performed with a high magnetic domain control strength at a portion where the spacing of magnetic domain walls is large and the β angle is small; and the magnetic domain refinement treatment is performed with a low magnetic domain control strength at a portion where the spacing of magnetic domain walls is small and the β angle is large. In the region where the β angle is large, the magnetic domain control effect cannot be obtained, and thus the magnetic domain control saturation strength is 0. In the region where the β angle is smaller than a predetermined value, the magnetic domain control effect is obtained. For example, it is estimated that the magnetic domain control effect can be obtained in a case where the β angle is 2° or less. In the region where the β angle is smaller than a predetermined value, as the β angle increases, the magnetic domain control saturation strength also increases. In the region where the β angle is still smaller, the magnetic domain control saturation strength is substantially constant.
FIG. 11 is a graph schematically showing a method for determining the magnetic domain control strength based on the spacing of magnetic domain walls. In FIG. 11, the vertical axis represents the magnetic domain control strength, and the horizontal axis represents the size of the spacing of magnetic domain walls. In FIG. 11, the solid line graph indicates the magnetic domain control saturation strength. In the region where the spacing of magnetic domain walls is small, the effect of magnetic domain control cannot be obtained, and thus the magnetic domain control saturation strength is 0. In the region where the spacing of magnetic domain walls is more than 500 µm, the effect of magnetic domain control is obtained. In the region where the spacing of magnetic domain walls exceeds 500 µm, as the spacing of magnetic domain walls increases, the magnetic domain control saturation strength also increases. In the region where the spacing of magnetic domain walls is more than about 1200 µm, the magnetic domain control saturation strength is substantially constant.
FIG. 12 is a graph schematically showing a method for determining the magnetic domain control strength based on the β angle. In FIG. 12, the vertical axis represents the magnetic domain control strength, and the horizontal axis represents the magnitude of the β angle. In FIG. 12, the solid line graph indicates the magnetic domain control saturation strength. In the region where the β angle is large, the magnetic domain control effect cannot be obtained, and thus the magnetic domain control saturation strength is 0. In the region where the β angle is smaller than a predetermined value, the magnetic domain control effect is obtained. For example, it is estimated that the magnetic domain control effect can be obtained in a case where the β angle is 2° or less. In the region where the β angle is smaller than a predetermined value, as the β angle increases, the magnetic domain control saturation strength also increases. In the region where the β angle is still smaller, the magnetic domain control saturation strength is substantially constant.
It is most preferable that the relationship between the spacing of magnetic domain walls of the point where the magnetic domain control is performed and the magnetic domain control strength is on the solid line graph in FIG. 11. Alternatively, it is most preferable that the relationship between the β angle of the point where the magnetic domain control is performed and the magnetic domain control strength is on the solid line graph in FIG. 12. The magnetic domain control saturation strength can be used as a target value of the magnetic domain control strength.
Furthermore, there is a magnetic domain control minimum strength, which is the minimum strength at which the magnetic domain control effect is exhibited. In a case where the magnetic domain control is performed, the magnetic domain control strength is more preferably equal to or more than the magnetic domain control minimum strength.
However, the magnetic domain control strength may slightly vary with respect to the magnetic domain control saturation strength as a target value. In FIGS. 11 and 12, the region equal to or higher than the magnetic domain control minimum strength and within a certain range from the graph of the magnetic domain control saturation strength is referred to as a target range of the magnetic domain control strength. The magnetic domain control strength and the spacing of magnetic domain walls of the part to be subjected to the magnetic domain control are preferably within the shaded region surrounded by broken lines in FIGS. 11 and 12. In a case where the absolute maximum value of the tensile stress introduced into the thermal strain in the magnetic domain control treatment line is made non-uniform at each measurement point of the tensile stress, it is preferable to change the magnetic domain control strength. In this case, it is preferable to change the magnetic domain control strength inside a shaded region surrounded by a broken line.
The magnetic domain control strength can be changed according to irradiation conditions of a laser or an electron beam. Specifically, the power, irradiation time, irradiation interval, and the like of the laser or electron beam may be changed to change the average irradiation energy density Ua (mJ/mm²) per unit area. Even if the Ua is the same, the thermal strain introduced into the steel sheet is slightly different depending on the combination of the power of the laser or electron beam, the irradiation time, the irradiation interval, and the like.
The magnetic domain control treatment line may be formed by irradiation with a laser or an electron beam. Irradiation conditions may be in a known range.
The interval in the forming direction of the magnetic domain control treatment line (the scanning direction in the case of a laser or the like) and the rolling direction RD of the magnetic domain control treatment line may be controlled by a known method so as to be in the range of the grain-oriented electrical steel sheet according to the present embodiment described above.

(Specific methods in magnetic domain image acquisition step to each magnetic domain control treatment line forming step)

Acquisition of a magnetic domain image and identification of a region having a spacing of magnetic domain walls of more than 500 µm can be performed by the following method.
The magnetic domain image can be acquired by, for example, the image acquisition device. Next, the distribution of the width (spacing of magnetic domain walls) of the 180° magnetic domain is derived from the magnetic domain image. The distribution of the spacings of magnetic domain walls in the original sheet can be derived by using, for example, an analysis device.
A region having a spacing of magnetic domain walls of a predetermined value or more (for example, more than about 500 µm) is determined as a region where a magnetic domain control treatment is to be performed (hereinafter, simply referred to as a treatment region in some cases).
The treatment region may be determined by visually observing the magnetic domain image displayed on the display unit of the analysis device by the operator.
FIG. 4 illustrates an example of a hardware constitution of the image acquisition device 30 that acquires a magnetic domain image of an original sheet (grain-oriented electrical steel sheet 1 before magnetic domain control treatment). The image acquisition device 30 includes a light source unit 31, a magneto-optical sensor (MO sensor 33), an image sensor 35, and a signal processing unit 37.
The light source unit 31 includes a light source including a light emitting diode (LED), and irradiates the MO sensor 33 with light having a uniform polarization plane.
The MO sensor 33 is a device that measures a magnetic domain structure of a magnetic material. The MO sensor 33 has an observed section on which a magnetic sample to be measured is placed. The light irradiated from the light source unit 31 passes through the inside of the MO sensor 33 and is reflected by the reflection layer. The reflected light passes through the inside of the MO sensor 33 again and is output to the outside of the MO sensor 33. When the original sheet as a magnetic sample is placed on the observed section of the MO sensor 33, a leakage magnetic field corresponding to the direction of spontaneous magnetization of the original sheet is generated inside the MO sensor 33. This leakage magnetic field rotates the polarization plane of the reflected light.
The image sensor 35 is a Complementary Metal-Oxide-Semiconductor (CMOS) image sensor. The image sensor 35 forms an image of the reflected light from the MO sensor 33 on the light receiving surface to perform photoelectric conversion, and outputs an analog signal after the photoelectric conversion to the signal processing unit 37. The distribution of the leakage magnetic field can be obtained by detecting the reflected light in which the polarization plane is rotated by the image sensor 35, and the magnetic domain structure of the original sheet becomes clear.
The signal processing unit 37 includes an amplifier, an AD converter, a Digital Signal Processor (DSP), and the like. The analog signal output from the image sensor 35 is amplified by an amplifier. Then, the analog signal is converted into a digital signal by an AD converter. The digital signal is subjected to predetermined digital processing using a DSP to generate an image signal. The image signal generated by the signal processing unit 37 is output to the analysis device 40 (see FIG. 5) via a cable or by wireless communication.
FIG. 5 illustrates a hardware constitution of an analysis device 40 that analyzes the magnetic domain structure of the original sheet. The analysis device 40 is a computer device such as a personal computer (PC). The analysis device 40 includes a calculation unit 41, a memory 43, a display unit 45, an input unit 47, and a communication I/F 49.
The calculation unit 41 includes a Central Processing Unit (CPU). The calculation unit 41 analyzes the magnetic domain structure from the magnetic domain image of the original sheet according to the program stored in the memory 43. Then, the calculation unit 41 determines a treatment region to which the magnetic domain control treatment is applied. The processing executed by the calculation unit 41 is described in detail later.
The memory 43 includes a Read Only Memory (ROM) and a Random Access Memory (RAM). The ROM stores programs executed by the CPU of the calculation unit 41 and data required for executing these programs. The program and data stored in the ROM are loaded into the RAM and executed.
The memory 43 may include a magnetic memory such as a hard disk drive (HDD) or an optical memory such as an optical disk. Alternatively, the memory 43 may be detachable from the analysis device 40 and store programs and data in a computer-readable recording medium. Alternatively, the memory 43 may receive the program executed by the calculation unit 41 from the network via the communication I/F 49.
The display unit 45 includes a display such as a liquid crystal display (LCD), a plasma display, or an organic electroluminescence (EL) display. The display unit 45 displays an image on the basis of the image signal output from the image acquisition device 30. In addition, the display unit 45 displays the analysis result of the magnetic domain structure by the calculation unit 41.
The input unit 47 includes an input device such as a mouse or a keyboard. The communication I/F 49 is an interface for transmitting and receiving data to and from an external device via a network such as a Local Area Network (LAN), a Wide Area Network (WAN), or the Internet.
Instead of general-purpose hardware such as a CPU, dedicated hardware specialized for analyzing a magnetic domain structure, such as an application specific integrated circuit (ASIC) or a Field Programmable Gate Array (FPGA), may be adopted as the calculation unit 41.
FIGS. 4 and 5 illustrate a case where the image acquisition device 30 and the analysis device 40 are separate devices, but a system in which the image acquisition device 30 and the analysis device 40 are integrated may be adopted.
As means for introducing the thermal strain into the surface of the original sheet, known means such as laser irradiation, electron beam irradiation, and ion implantation can be adopted. Hereinafter, a constitution of the laser irradiation device 500 that introduces the thermal strain by laser irradiation will be described.
FIG. 6 illustrates a constitution of the laser irradiation device 500. The laser irradiation device 500 includes a polygon mirror 501, a light source device 503, a collimator 505, a condenser lens 507, a motor 509, a sensor 511, a control unit 513, and a sheet passing device 515.
The sheet passing device 515 passes the original sheet in the rolling direction RD.
The polygon mirror 501 has, for example, a regular polygonal prism shape. A plurality of the plane mirrors is provided on each of a plurality of side surfaces constituting the polygon mirror 501 having a regular polygonal prism shape. The laser beam LB enters the plane mirror of the polygon mirror 501 in one direction (horizontal direction) from the light source device 503 via the collimator 505 and is reflected by the plane mirror.
The polygon mirror 501 is rotatable about the rotary shaft O1 by driving from the motor 509. The incident angle of the laser beam LB with respect to the plane mirror sequentially changes according to the rotation angle of the polygon mirror 501. As a result, the reflection direction of the laser beam LB is sequentially changed, and the surface of the original sheet can be scanned. A Reference Sign P in FIG. 6 represents an interval between the adjacent magnetic domain control treatment lines 11, that is, an irradiation pitch of the laser beam LB.
The light source device 503 outputs the laser beam LB by a predetermined irradiation system (for example, a continuous irradiation system or a pulse irradiation system) under the control of the control unit 513.
The condenser lens 507 is provided on the optical path of the laser beam LB reflected from the polygon mirror 501. The condenser lens 507 constitutes a condenser optical system having a predetermined focal distance. The laser beam LB reflected from the polygon mirror 501 is condensed on the surface of the original sheet via the condenser lens 507, whereby the thermal strain is introduced into the surface of the original sheet.
The motor 509 is coupled to the polygon mirror 501. The motor 509 rotationally drives the polygon mirror 501 under the control of the control unit 513.
The sensor 511 is connected to a drive shaft of the motor 509. The sensor 511 detects a rotation angle of the polygon mirror 501 rotated by the motor 509. Furthermore, the sensor 511 outputs a signal (Hereinafter, the rotation angle signal is referred to as a rotation angle signal.) indicating the detected rotation angle to the control unit 513.
The control unit 513 includes a processor. The control unit 513 is connected to the light source device 503, the motor 509, the sensor 511, and the sheet passing device 515. The control unit 513 receives an input of a speed signal from the sheet passing device 515. Further, the control unit 513 outputs a signal instructing the motor 509 to rotationally drive the polygon mirror 501.
In addition, the control unit 513 controls on and off of the power of the laser beam LB output from the light source device 503 based on the stress introduction signal representing the treatment region and the rotation angle signal output from the sensor 511. In a case where the laser irradiation device 500 is electrically connected to the analysis device 40, the stress introduction signal is input from the analysis device 40 to the laser irradiation device 500. The stress introduction signal may be input to the laser irradiation device 500 by an operator.
Next, an example of a method of determining the treatment region will be described in detail. The processing for specifying the treatment region is executed by, for example, the calculation unit 41 of the analysis device 40.
The calculation unit 41 derives the distribution of the spacings of magnetic domain walls of the original sheet using, for example, a line segment method. Then, the calculation unit 41 determines a region where the spacing of magnetic domain walls is a predetermined value or more (for example, more than about 500 µm) as a portion to which the magnetic domain control treatment is preferentially applied.
In the line segment method, evaluation is performed by drawing a line segment perpendicular to the magnetic domain. The line segments are drawn at intervals of three lines per 1 cm in a direction parallel to the magnetic domain. A spacing of magnetic domain walls is derived based on an interval between the intersection points of 180° magnetic domain walls and line segments.
FIG. 3A illustrates an example of distribution of the spacings of magnetic domain walls of the grain-oriented electrical steel sheet 1 before the magnetic domain control treatment, which is obtained by further analyzing the magnetic domain image acquired by CMOS-MagView manufactured by Matesy GmbH by two-dimensional Fourier transform. FIG. 3B shows the distribution of the spacings of magnetic domain walls after the surface of the grain-oriented electrical steel sheet 1 of FIG. 3A is subjected to the magnetic domain control treatment, which is obtained in the same manner as in FIG. 3A. The magnetic domain control treatment here is performed by applying continuous wave laser irradiation along a direction substantially perpendicular to the rolling direction RD. In FIGS. 3A to 3B, the unit of the numerical value is µm.
As an example of analysis using the two-dimensional Fourier transform, a method for deriving a distribution of a spacings of magnetic domain walls is described using a short-interval two-dimensional Fourier transform (Hereinafter, it is referred to as "ST2DFT".) obtained by expanding a short-term Fourier transform, which is one of signal processing methods that have been used for time-frequency analysis of audio signals for a long time, to a two-dimensional region.
An image (magnetic domain image) represented by an image signal acquired by the image acquisition device 30 is expressed as x (k, l) as a data column of two-dimensional coordinates (k-l coordinates). In the present embodiment, the magnetic domain image to be analyzed is an image binarized with two types of colors or an image expressed in three or more gradations (multiple gradations) such as gray scale.
In order to derive the distribution of the spacings of magnetic domain walls of the original sheet 2, the calculation unit 41 executes the following processes (A-1), (A-2), and (A-3).

(A-1) Treatment of cutting out a plurality of partial regions from magnetic domain image
(A-2) Treatment of performing ST2DFT
(A-3) Treatment of deriving distribution of spacings of magnetic domain walls

Hereinafter, the treatment of A-1 to A-3 will be described in detail.

(A-1) Treatment of cutting out a plurality of partial regions from magnetic domain image

In order to cut out a plurality of partial regions from a magnetic domain image and analyze each frequency structure, a window function Wa (k, l) of a rectangular window in which a range in the k direction set to 0 ≤ k ≤ N_k-1 and a range in the l direction set to 0 ≤ l ≤ N_l-1 is used (N_k and N_l are natural numbers). As the window function Wa (k, l), a Hamming window, a Hanning window, a Blackman window, or the like can be applied.
When the observation position in the data column x (k, l) of the magnetic domain image is expressed by an index (n, m), and the shift amounts of the window function Wa (k, l) in the k direction and the l direction are expressed as S_k and S_l, respectively (n, m, S_k, and S_l are integers.), a data column x_nm (k-nS_k, l-mS_l) of a partial region obtained by cutting out a range of nS_k ≤ k ≤ nS_k + N_k-1 and mS_l ≤ l ≤ mS_l + N_l-1 from the magnetic domain image is obtained as in Expression (1).
[Mathematical Formula 1] $x_{nm} (k - {nS}_{k}, l - {mS}_{l}) = W_{a} (k - {nS}_{k}, l - {mS}_{l}) x (k, l)$
FIG. 7 illustrates an example in which partial regions respectively corresponding to the observation positions (n, m) = (1, 1), (2, 2), (3, 3),..., and (P, Q) (P and Q are natural numbers) are cut out from the magnetic domain image G.
In the present embodiment, N_k and N_l that define the range of the window function Wa (k, l) are parameters corresponding to the number of pixels in the k direction and the number of pixels in the l direction in the partial region, respectively.

(A-2) Treatment of performing ST2DFT

When the data column of the partial region is defined as x_nm (n', m') = x_nm (k-nS_k, l-mS_l), and the two-dimensional Fourier transform is performed on x_nm (n', m'), a partial Fourier image X (f_k, f_l, n, m) corresponding to the partial region of the observation position (n, m) is obtained as in Expression (2).
[Mathematical Formula 2] $X (f_{k}, f_{l}, n, m) = \sum_{n' = 0}^{N_{k} - 1} \sum_{m' = 0}^{N_{l} - 1} x_{nm} (n', m') \exp \{- 2 πj (\frac{f_{k} n'}{N_{k}} + \frac{f_{l} m'}{N_{l}})\}$
Here, f_k and f_l are space frequencies.
When the resolution of the space frequency f_k is denoted by Δf_k and the resolution of the space frequency f_l is denoted by Δf_l, Δf_k and Δf_l are defined as in Expression (3).
[Mathematical Formula 3] $\{\begin{matrix} Δ f_{k} = \frac{2}{N_{k} Δ k} \\ Δ f_{l} = \frac{2}{N_{l} Δ l} \end{matrix}$
Δk and Δl are the space resolution in the k direction and the space resolution in the l direction in the magnetic domain image, respectively.
For example, when the two-dimensional Fourier transform is performed on the data column x_nm (k-nS_k, l-mS_l) of each partial region illustrated in FIG. 7, a partial Fourier image X (f_k, f_l, n, m) is obtained for each observation position (n, m) as illustrated in FIG. 8.

(A-3) Treatment of deriving distribution of spacings of magnetic domain walls

When the partial Fourier image X (f_k, f_l, n, m) is obtained, the coordinates (k component f_k ^max (n, m) and l component f_l ^max (n, m)) of the peak position of the spot of the partial Fourier image X (f_k, f_l, n, m) are obtained. Note that, regarding the derivation of the peak position, a region in the vicinity of k = 0 and l = 0 is a part that greatly depends on the contrast of the image, and thus is excluded.
Then, the distribution L (n, m) of the spacings of magnetic domain walls is derived as in Expression (4) from the resolution of the space frequency defined by Expression (3) and the peak position of the spot of the partial Fourier image.
[Mathematical Formula 4] $L (n, m) = \frac{1}{\sqrt{{(Δ f_{k} f_{k}^{\max} (n, m))}^{2} + {(Δ f_{l} f_{l}^{\max} (n, m))}^{2}}}$
As described above, by using ST2DFT, it is possible to quantitatively derive the distribution L (n, m) of the spacing of magnetic domain walls while maintaining the position information of the magnetic domain image.
When the calculation unit 41 derives the distribution of the spacings of magnetic domain walls, the calculation unit 41 determines the region where the spacings of magnetic domain walls are the predetermined value or more as the treatment region (that is, a region to which the magnetic domain control treatment is applied). The control unit 513 of the laser irradiation device 500 controls to turn on the power of the laser beam LB with respect to the treatment region, and preferably to turn off the power of the laser beam LB with respect to the region other than the treatment region. As a result, the magnetic domain control treatment line 11 is introduced into the treatment region of the original sheet. In the other regions, introduction of the magnetic domain control treatment line 11 is suppressed.
The magnetic domain image of the grain-oriented electrical steel sheet 1 after the magnetic domain control treatment can also be obtained by the above-described procedure. In the magnetic domain image of the grain-oriented electrical steel sheet 1, the magnetic domain control treatment line 11 may be unclear. In this case, the observation conditions may be adjusted so that the magnetic domain control treatment line 11 can be clearly confirmed. For example, the magnetic domain control treatment line 11 can be clarified by applying a DC magnetic field along the sheet surface perpendicular direction (thickness direction) of the grain-oriented electrical steel sheet 1.

(Insulating Coating Forming Step)

In a case where an insulating coating is formed on the surface of the grain-oriented electrical steel sheet, an insulating coating forming step of forming an insulating coating by a known method after final annealing may be included. The insulating coating forming step may be performed before the magnetic domain control treatment line forming step or may be performed after the magnetic domain control treatment line forming step as long as the step is performed after the final annealing. However, when the insulating coating is formed before the magnetic domain control treatment line forming step, the insulating coating may be peeled off in the magnetic domain control treatment line 11. Therefore, the step is preferably performed after the magnetic domain control treatment line forming step. In a case where the insulating coating forming step is performed before the magnetic domain control treatment line forming step, the insulating coating is preferably formed again on the magnetic domain control treatment line 11 after the magnetic domain control treatment line forming step. Examples
The effects of the aspects of the present invention will be described more specifically with reference to Examples. However, the conditions in the examples are merely one condition example adopted to confirm the operability and effects of the present invention. The present invention is not limited to this one condition example. The present invention can adopt various conditions as long as the object of the present invention is achieved without departing from the gist of the present invention.

(Example 1)

Grain-oriented electrical steel sheets in the same lot having a sheet thickness of 0.23 mm and classified into 23P085 in the table 2 of JIS C 2553:2019 "Cold-rolled grain-oriented electrical steel strip and sheet delivered in the fully-processed state" were used as original sheets. The magnetic domain control treatment was performed on the original sheet so as to have the shape of the magnetic domain control treatment line shown in Table 1. Here, the shapes A to E and A-2 of the magnetic domain control treatment lines in the table are as follows.

A: A magnetic domain control treatment line with a straight linear shape was formed in a region where the spacing of magnetic domain walls was more than a predetermined value (500 µm).
B: A magnetic domain control treatment line was straight linearly formed over the entire width of the original sheet.
C: A magnetic domain control treatment line with an ordered broken linear shape was formed.
D: A magnetic domain control treatment line with a random broken linear shape was formed.
E: A magnetic domain control treatment line having an interval of 4 mm was formed only in a region within ±4 mm from the center of each crystal grain in the rolling direction RD. The radius of curvature of the steel sheet at the position where the grains were present during the final annealing was 250 mm.
A-2: A linear magnetic domain control treatment line including a curve was formed in a region where the spacing of magnetic domain walls is more than a predetermined value (500 µm).

The region having a spacing of magnetic domain walls of more than 500 µm was identified by the above-described method.
In addition, the magnetic domain control treatment line was a tensile stress introduction line due to the thermal strain.
The magnetic domain control treatment was performed by laser irradiation. At the time of laser irradiation, the average irradiation energy density Ua (mJ/mm²) was changed to 0.5 to 2.0 mJ/mm², and the irradiation pitches PL (mm) were all 4 mm.
The magnitude of the tensile stress introduced in each magnetic domain control treatment line was measured by the above-described method. The tensile stress was measured at 10 points of each magnetic domain control treatment line, and the absolute maximum value of the entire tensile stress was described in Table 2.
The noise and iron loss of the grain-oriented electrical steel sheets subjected to the magnetic domain control treatment obtained as a result are evaluated and described in Table 2.
The methods for evaluating noise and iron loss were as follows. First, 180 grain-oriented electrical steel sheets having a sheet thickness of 0.23 mm were laminated to form a three-phase transformer core. The widths of the leg and the yoke of the three-phase transformer core were both 150 mm. The height and width of the outer shape of the three-phase transformer core were both 750 mm. Noise and iron loss of these three-phase transformer cores were measured. The measurement conditions were a frequency of 60 Hz and an excitation magnetic flux density of 1.8 T.
In measuring the noise, microphones were arranged at equal intervals at eight points around the transformer in which the three-phase transformer core was incorporated. The distance between the transformer and the microphone was 30 cm. The values obtained by correcting the A characteristics to the noise measurement results by the microphones and averaging the results are described in Table 2 as the noise evaluation results (unit: dBA) of the grain-oriented electrical steel sheets. An example in which the evaluation result of noise was 50.55 dBA or less was determined to be an example in which noise reduction was achieved. The noise evaluation result determined to be unacceptable was underlined.
The iron loss was obtained by measuring voltages and currents on the primary side and the secondary side with a power analyzer when excitation was performed at a frequency of 60 Hz and an excitation magnetic flux density of 1.8 T as described above. The obtained iron loss is described in Table 2 as an iron loss evaluation result (unit: W/kg) of the grain-oriented electrical steel sheet. An example in which the evaluation result of the iron loss was 1.360 W/kg or less was determined to be an example in which iron loss reduction was achieved. The noise evaluation result determined to be unacceptable was underlined.
Further, a rectangular sample having both sides of 100 mm in length was cut out from a three-phase transformer core for measuring noise and iron loss.
In this rectangular sample, a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction was set, and imaginary lines VL parallel to the rolling direction and having a length of 50 mm were set at intervals of 5 mm in a direction perpendicular to the rolling direction inside the evaluation region. The number of imaginary lines was nine.
In each of the nine imaginary lines VL, among the magnetic domain control treatment lines and the intersection points, the absolute maximum value of the intervals (interval between intersection points) in the rolling direction between the adjacent intersection points, the average value of the spacings of magnetic domain walls measured along the imaginary line, and the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line were measured in the manner described above.

In Table 1, among the plurality of imaginary lines, the number of imaginary lines in which the absolute maximum value of the intervals between the intersection points is more than 20 mm, and among the imaginary lines in which the absolute maximum value of the intervals between the intersection points is more than 20 mm, the number of imaginary lines in which the average value and the maximum value of the spacings of magnetic domain walls were equal to or less than a predetermined value was determined.

[Table 1]

Sample No.	Average irradiation energy density Ua (mJ/mm²)	Absolute maximum value of tensile stress introduced in magnetic	The number of imaginary lines in which the absolute maximum value of the	Number of lines whose average value of spacings of magnetic	Number of lines whose average value of spacings of magnetic	Number of lines whose absolute maximum value of spacings of	Number of lines whose absolute maximum value of spacings of	Shape of magnetic domain control treatment line
		domain control treatment line (MPa)	interval between the intersection points is more than 20 mm among the plurality of imaginary lines (lines)	domain walls is 600 µm or less (lines)	domain walls is 500 µm or less (lines)	magnetic domain walls is 1200 µm or less (lines)	magnetic domain walls is 800 µm or less (lines)
1	1.7	225	1	1	0	0	0	A
2	1.5	211	1	1	0	0	0	A
3	1.6	217	1	1	0	0	0	A
4	1.5	215	1	1	1	0	0	A
5	1.7	220	1	0	0	1	0	A
6	1.7	224	1	1	0	1	0	A
7	0.5	85	1	0	0	1	1	A
8	2.0	279	2	2	0	0	0	A
9	1.6	218	4	4	2	0	0	A
10	1.5	215	3	3	2	0	0	A
11	1.3	189	5	5	4	0	0	A
12	1.5	220	2	0	0	2	0	A
13	1.0	151	4	0	0	4	0	A
14	1.5	219	3	0	0	3	2	A
15	1.5	217	4	0	0	4	3	A
16	1.5	217	0	0	0	0	0	B
17	1.5	219	0	0	0	0	0	C
18	1.5	222	0	0	0	0	0	D
19	1.5	217	0	0	0	0	0	E
20	1.5	211	2	3	2	0	0	A-2
21	1.5	211	3	0	0	2	1	A-2

[Table 2]

Sample No.	Iron loss (W/Kg)	Noise (dBA)	Remarks
1	1.330	50.35	Invention Example
2	1.341	49.14	Invention Example
3	1.351	48.74	Invention Example
4	1.301	49.95	Invention Example
5	1.334	49.95	Invention Example
6	1.326	49.75	Invention Example
7	1.327	49.24	Invention Example
8	1.322	48.94	Invention Example
9	1.313	48.54	Invention Example
10	1.315	47.73	Invention Example
11	1.315	47.33	Invention Example
12	1.318	48.74	Invention Example
13	1.318	48.13	Invention Example
14	1.318	47.53	Invention Example
15	1.318	47.33	Invention Example
16	1.299	53.11	Comparative Example
17	1.382	50.75	Comparative Example
18	1.411	47.53	Comparative Example
19	1.324	52.43	Comparative Example
20	1.308	47.39	Invention Example
21	1.318	47.14	Invention Example

As can be seen from Tables 1 and 2, in a case where a magnetic domain control treatment line that is a tensile stress introduction line in which a tensile stress of 40 MPa or more is introduced is formed into a region where a spacing of magnetic domain walls is more than a predetermined value (500 µm) (samples No.1 to 15, 20, and 21), in at least one imaginary line, an absolute maximum value of the interval in a rolling direction between adjacent intersection points among a plurality of intersection points of the imaginary line and the magnetic domain control treatment line is more than 20 mm, and an average value of spacings of magnetic domain walls measured along the imaginary line is 600 µm or less, or an absolute maximum value is 1200 µm or less. As a result, the iron loss was low and the noise was small.
On the other hand, in a case where the magnetic domain control treatment line is a magnetic domain control treatment line with an ordered broken linear shape or a random broken linear shape, the absolute maximum value of the interval in the rolling direction between adjacent intersection points among the plurality of intersection points of the imaginary line and the magnetic domain control treatment line, or the average value and the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line are out of the scope of the present invention. As a result, one or both of the iron loss characteristics and the noise characteristics were poor.

(Example 2)

Grain-oriented electrical steel sheets in the same lot having a sheet thickness of 0.23 mm and classified into 23P085 in the table 2 of JIS C 2553:2019 "Cold-rolled grain-oriented electrical steel strip and sheet delivered in the fully-processed state" were used as original sheets. The magnetic domain control treatment was performed on the original sheet so as to have the shape of the magnetic domain control treatment line shown in Table 3. Here, the shapes A-3 to A-6 of the magnetic domain control treatment lines in the table are as follows.
A-3: The average irradiation energy density Ua was changed within a range of 0.75 to 1.75 mJ/mm².
A-4: The average irradiation energy density Ua was changed within a range of 0.5 to 2.0 mJ/mm².
A-5: The average irradiation energy density Ua was changed within a range of 0.75 to 1.75 mJ/mm², and the adjustment of the magnetic domain control strength described with reference to FIGS. 10 to 12 was applied.
A-6: The average irradiation energy density Ua was changed within a range of 0.5 to 2.0 mJ/mm², and the adjustment of the magnetic domain control strength described with reference to FIGS. 10 to 12 was applied.
Uniformity of the absolute maximum value of the tensile stress, σ(TS_m)², TS_{m(β < 2)}, and TS_{m(β < 2)} obtained in this manner were measured by the above-described method. The results are shown in Table 4.

In addition, the noise and iron loss of the grain-oriented electrical steel sheets subjected to the magnetic domain control treatment obtained in this manner were evaluated in the same manner as in Example 1 and described in Table 5.

[Table 3]

Sample No.	Average irradiation energy density Ua (mJ/mm²)	Absolute maximum value of tensile stress introduced in magnetic domain control treatment line (MPa)	The number of imaginary lines in which the absolute maximum value of the interval between the intersection points is more than 20 mm among the plurality of	Number of lines whose average value of spacings of magnetic domain walls is 600 µm or less (lines)	Number of lines whose average value of spacings of magnetic domain walls is 500 µm or less (lines)	Number of lines whose absolute maximum value of spacings of magnetic domain walls is 1200 µm or less (lines)	Number of lines whose absolute maximum value of spacings of magnetic domain walls is 800 µm or less (lines)
			imaginary lines (lines)
22	0.75 to 1.75	232	4	3	3	0	0
23	0.75 to 1.75	231	3	0	0	3	2
24	0.50 to 2.00	279	3	1	1	0	0
25	0.50 to 2.00	278	3	3	1	0	0
26	0.50 to 2.00	280	5	3	3	0	0
27	0.50 to 2.00	279	2	0	0	1	1
28	0.50 to 2.00	278	3	0	0	2	1
29	0.50 to 2.00	279	5	0	0	4	3
30	0.75 to 1.75	233	3	1	1	0	0
31	0.75 to 1.75	232	2	2	1	0	0
32	0.75 to 1.75	231	4	3	2	0	0
33	0.75 to 1.75	233	2	0	0	1	1
34	0.75 to 1.75	232	3	0	0	3	1
35	0.75 to 1.75	231	5	0	0	4	2
36	0.50 to 2.00	280	5	4	2	0	0
37	0.50 to 2.00	281	4	0	0	3	2

[Table 4]

Sample No.	Whether the absolute maximum value of the tensile strength is uniform at each measurement point of the tensile strength	σ(TS_m)²	TS_{m(β < 2)}	TS_m(β≥=2)	Shape of magnetic domain control treatment line
22	Non-uniform	4.5	162	182	A-3
23	Non-uniform	4.7	161	184	A-3
24	Non-uniform	5.6	145	193	A-4
25	Non-uniform	5.3	144	194	A-4
26	Non-uniform	6.0	141	190	A-4
27	Non-uniform	5.9	140	192	A-4
28	Non-uniform	5.1	143	190	A-4
29	Non-uniform	5.2	144	197	A-4
30	Non-uniform	4.1	195	143	A-5
31	Non-uniform	4.4	197	141	A-5
32	Non-uniform	4.3	192	146	A-5
33	Non-uniform	4.8	196	147	A-5
34	Non-uniform	4.9	197	143	A-5
35	Non-uniform	4.3	197	141	A-5
36	Non-uniform	5.6	224	110	A-6
37	Non-uniform	6.4	246	104	A-6

[Table 5]

Sample No.	Iron loss (W/Kg)	Noise (dBA)	Remarks
22	1.297	46.97	Invention Example
23	1.298	46.94	Invention Example
24	1.289	46.42	Invention Example
25	1.288	46.36	Invention Example
26	1.287	46.24	Invention Example
27	1.283	46.81	Invention Example
28	1.282	46.73	Invention Example
29	1.281	46.64	Invention Example
30	1.299	45.40	Invention Example
31	1.298	45.31	Invention Example
32	1.297	45.22	Invention Example
33	1.294	45.88	Invention Example
34	1.293	45.77	Invention Example
35	1.292	45.63	Invention Example
36	1.288	45.24	Invention Example
37	1.286	45.41	Invention Example

As can be seen from Tables 3 to 5, in any example, the iron loss was low and the noise was also low. In addition, in a case where one or both of σ(TS_m)² > 5.0 and TS_{m(β < 2)} > TS_{m(β ≥ 2)} are satisfied, the iron loss is lower or the noise is smaller.

INDUSTRIAL APPLICABILITY

According to the present disclosure, it is possible to provide a grain-oriented electrical steel sheet having a low iron loss (low iron loss) and having a low noise (excellent noise characteristics) when the grain-oriented electrical steel sheet is made into an electrical product, and a method for manufacturing the grain-oriented electrical steel sheet. Therefore, industrial applicability is high.

REFERENCE SIGNS LIST

1 Grain-oriented electrical steel sheet
11 Magnetic domain control treatment line (tensile stress introduction line)
RD Rolling direction
TD Transverse direction (sheet width direction)
ND Rolling surface normal direction
VL Imaginary line
VP Intersection point
30 Image acquisition device
31 Light source unit
33 MO sensor
35 Image sensor
37 Signal processing unit
40 Analysis device
41 Calculation unit
43 Memory
45 Display unit
47 Input unit
49 Communication I/F
301 Flux closure domain
302 Noise
Ls Line segment
Ip Intersection point
500 Laser irradiation device
501 Polygon mirror
503 light source device
505 Collimator
507 Condenser lens
509 Motor
511 Sensor
513 Control unit
515 Sheet passing device

Claims

A grain-oriented electrical steel sheet comprising
a plurality of magnetic domain control treatment lines extending in a direction intersecting a rolling direction on a surface,

wherein

in a case where a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction is set on the surface, and further, imaginary lines parallel to the rolling direction and having a length of 50 mm are set inside the evaluation region at intervals of 5 mm in a direction perpendicular to the rolling direction,

in at least one of the imaginary lines, among a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines, an absolute maximum value of an interval between adjacent intersection points in the rolling direction is more than 20 mm, and an average value of spacings of magnetic domain walls measured along the imaginary line is 600 µm or less, and

the plurality of magnetic domain control treatment lines are tensile stress introduction lines in which a tensile stress of 40 MPa or more is introduced.
The grain-oriented electrical steel sheet according to claim 1, wherein
the average value of the spacings of magnetic domain walls measured along the imaginary line is 500 µm or less.
The grain-oriented electrical steel sheet according to claim 1, wherein
an average value of spacings of magnetic domain walls measured along the imaginary line is 600 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
The grain-oriented electrical steel sheet according to claim 3, wherein
the average value of the spacings of magnetic domain walls measured along the imaginary line is 500 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
A grain-oriented electrical steel sheet comprising
a plurality of magnetic domain control treatment lines extending in a direction intersecting a rolling direction on a surface,

wherein

in a case where a square evaluation region having a side length of 50 mm and a side parallel to the rolling direction is set on the surface, and further, imaginary lines parallel to the rolling direction and having a length of 50 mm are set inside the evaluation region at intervals of 5 mm in a direction perpendicular to the rolling direction,

in at least one of the imaginary lines, among a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines, an absolute maximum value of an interval between adjacent intersection points in the rolling direction is more than 20 mm, and an absolute maximum value of a spacing of magnetic domain walls measured along the imaginary line is 1200 µm or less.
The grain-oriented electrical steel sheet according to claim 5, wherein
the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line is 800 µm or less.
The grain-oriented electrical steel sheet according to claim 5, wherein
the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line is 1200 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
The grain-oriented electrical steel sheet according to claim 7, wherein
the absolute maximum value of the spacings of magnetic domain walls measured along the imaginary line is 800 µm or less in each of the two or more imaginary lines in which the absolute maximum value of the interval in the rolling direction is more than 20 mm.
The grain-oriented electrical steel sheet according to any one of claims 1 to 8, wherein
the plurality of magnetic domain control treatment lines are thermal strains.
The grain-oriented electrical steel sheet according to claim 9, wherein
the absolute maximum value of the tensile stress introduced into the thermal strain in the magnetic domain control treatment line is non-uniform at each measurement point of the tensile stress.
The grain-oriented electrical steel sheet according to claim 10, wherein
when each of a plurality of intersection points between the imaginary line and the plurality of magnetic domain control treatment lines is a magnetic domain refinement point, the absolute maximum value of the tensile stress in a unit of MPa introduced into the thermal strain measured at each of the magnetic domain refinement points is TS_m, and the variance of TS_m is σ(TS_m)², $σ {({TS}_{m})}^{2} > 5.0$ is satisfied.
The grain-oriented electrical steel sheet according to claim 10, wherein
when each of a plurality of intersection points of the imaginary line and the plurality of magnetic domain control treatment lines is defined as a magnetic domain refinement point, an arithmetical mean value of absolute maximum values of the tensile stresses in a unit of MPa introduced into the thermal strain measured at each of magnetic domain refinement points having a β angle of less than 2° among the magnetic domain refinement points is defined as TS_{m(β < 2)}, and an arithmetical mean value of absolute maximum values of the tensile stresses in a unit of MPa introduced into the thermal strain measured at each of magnetic domain refinement points having a β angle of 2° or more among the magnetic domain refinement points is defined as TS_{m(β ≥ 2)}, ${TS}_{m (β < 2)} > {TS}_{m (β \geq 2)}$ is satisfied.
The grain-oriented electrical steel sheet according to claim 11, wherein
when TS_{m(β < 2)} is an arithmetical mean value of absolute maximum values of the tensile stress in a unit of MPa introduced into the thermal strain, the absolute maximum values being measured at each of magnetic domain refinement points having a β angle of less than 2° among the magnetic domain refinement points, and TS_{m(β ≥ 2)} is an arithmetical mean value of absolute maximum values of the tensile stress in a unit of MPa introduced into the thermal strain, the absolute maximum values being measured at each of magnetic domain refinement points having a β angle of 2° or more among the magnetic domain refinement points, ${TS}_{m (β < 2)} > {TS}_{m (β \geq 2)}$ is satisfied.
A method for manufacturing the grain-oriented electrical steel sheet according to any one of claims 1 to 8, the method comprising:
a magnetic domain image acquisition step of acquiring a magnetic domain image of a surface of the grain-oriented electrical steel sheet;

a region specification step of specifying a region having a spacing of magnetic domain walls of more than 500 µm in the grain-oriented electrical steel sheet based on the magnetic domain image obtained in the magnetic domain image acquisition step; and

a magnetic domain control treatment line forming step of forming a magnetic domain control treatment line on a surface of the grain-oriented electrical steel sheet after the region specification step,

wherein in the magnetic domain control treatment line forming step, the magnetic domain control treatment line is formed in the region where the spacing of magnetic domain walls is more than 500 µm.
The method for manufacturing a grain-oriented electrical steel sheet according to claim 14, wherein
in the magnetic domain control treatment line forming step, the magnetic domain control treatment line is formed by irradiation with a laser or an electron beam.