WO2024053608A1 - 方向性電磁鋼板 - Google Patents

方向性電磁鋼板 Download PDF

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WO2024053608A1
WO2024053608A1 PCT/JP2023/032247 JP2023032247W WO2024053608A1 WO 2024053608 A1 WO2024053608 A1 WO 2024053608A1 JP 2023032247 W JP2023032247 W JP 2023032247W WO 2024053608 A1 WO2024053608 A1 WO 2024053608A1
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Prior art keywords
mass
less
steel sheet
grain
iron loss
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PCT/JP2023/032247
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English (en)
French (fr)
Japanese (ja)
Inventor
猛 今村
之啓 新垣
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JFE Steel Corp
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JFE Steel Corp
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Priority to JP2024514751A priority Critical patent/JP7601280B2/ja
Priority to EP23863146.9A priority patent/EP4582567A4/en
Priority to KR1020247035291A priority patent/KR20240167855A/ko
Priority to CN202380063616.0A priority patent/CN119836484A/zh
Priority to US18/994,823 priority patent/US20260049381A1/en
Publication of WO2024053608A1 publication Critical patent/WO2024053608A1/ja
Anticipated expiration legal-status Critical
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Definitions

  • the present invention relates to a grain-oriented electrical steel sheet suitable for a core material of a transformer.
  • a grain-oriented electrical steel sheet is a soft magnetic material used as an iron core material for transformers, and has a crystal structure in which the ⁇ 001> orientation, which is the axis of easy magnetization of iron, is highly aligned in the rolling direction of the steel sheet.
  • This type of texture is caused by secondary recrystallization, which causes ⁇ 110 ⁇ 001>-oriented crystal grains, called Goss orientation, to preferentially grow enormously during purification annealing during the manufacturing process of grain-oriented electrical steel sheets. It is formed through a phenomenon called
  • a common technique used is to secondary recrystallize grains with Goss orientation during purification annealing using a precipitate called an inhibitor.
  • a precipitate called an inhibitor.
  • the method using AlN and MnS described in Patent Document 1 and the method using MnS and MnSe described in Patent Document 2 have been put into practical use industrially.
  • the method using these inhibitors is a useful method for stably developing secondary recrystallized grains, but in order to finely disperse the inhibitors in the steel, slab heating at a high temperature of 1300°C or higher is required. , it was essential to once dissolve the inhibitor component in solid solution.
  • Patent Document 3 a technique for developing Goss-oriented crystal grains by secondary recrystallization in a material that does not contain an inhibitor component is disclosed in Patent Document 3 and the like.
  • This is a technique for secondary recrystallization of grains that have texture, and its effect is called the texture inhibition effect.
  • This method does not require fine dispersion of the inhibitor in the steel, so it does not require heating the slab at high temperatures, which was previously essential, and this method has great advantages in terms of cost and maintenance.
  • Grain-oriented electrical steel sheets are mainly used as the core of transformers, and are required to have excellent magnetization properties, especially low iron loss. To this end, it is important to highly align the secondary recrystallized grains in the steel sheet with the Goss orientation and to reduce impurities in the product sheet. Furthermore, a technology has been developed that physically introduces non-uniformity into the surface of a steel plate and subdivides the width of the magnetic domain to reduce iron loss, that is, a magnetic domain refining technology.
  • Patent Document 4 proposes a technique for reducing the iron loss of a steel sheet by irradiating a final product sheet with a laser, introducing a high dislocation density region into the surface layer of the steel sheet, and narrowing the magnetic domain width.
  • Patent Document 5 proposes a technique for controlling the magnetic domain width by irradiation with an electron beam.
  • grain-oriented electrical steel sheets are mainly used as the core of transformers.
  • the transformer core has a larger iron loss.
  • the iron loss ratio between the two (the value obtained by dividing the iron loss of the transformer core by the iron loss value of the material) is called the building factor. In other words, even if the core loss of the material is good, if the building factor is high, the core loss of the transformer core will be large, causing the problem that sufficient performance cannot be achieved.
  • an object of the present invention is to provide a grain-oriented electrical steel sheet that has magnetic properties that can sufficiently reduce the building factor.
  • the present inventors have determined that the amount of Co in the base steel sheet on which a base film containing forsterite as the main component is formed, and the amount of Ti in the grain-oriented electrical steel sheet with the base film formed thereon. It was discovered that grain-oriented electrical steel sheets with a low building factor can be produced by controlling the amounts within certain ranges.
  • the hot rolled sheet was annealed at 1000°C for 30 seconds in a N2 atmosphere.
  • it was cold rolled to a plate thickness of 1.5 mm, and then intermediate annealed at 1000° C. for 100 seconds in a 25% H 2 -75% N 2 atmosphere.
  • it was cold rolled to a thickness of 0.23 mm, and decarburized annealed at 850°C for 150 seconds in a humid atmosphere of 50% H 2 -50% N 2 and a dew point of 50°C.
  • an annealing separator mainly composed of MgO was applied to the surface of the base steel plate after decarburization annealing, and purification annealing was performed by holding at 1200°C for 10 hours.
  • the heating rate up to 1200°C was 20°C/h
  • N 2 atmosphere was used from room temperature to 700°C
  • the mixing ratio of N 2 and H 2 was varied from 700°C to 1100°C.
  • the atmosphere was H 2 atmosphere from 1100°C to 1200°C.
  • the atmosphere was H 2
  • the atmosphere was Ar.
  • a sample was obtained in which a base film containing forsterite as a main component (hereinafter sometimes referred to as a forsterite film) was formed on the surface of the base steel plate.
  • iron loss W 17/50 iron loss when excited to 1.7T at 50Hz
  • W 19/50 iron loss when excited to 1.9T at 50Hz
  • hysteresis loss Wh 17 Hysteresis loss when excited up to 1.7T
  • Wh 19 hysteresis loss when excited up to 1.9T
  • a three-phase tripod model transformer was fabricated, imitating a transformer, with an external shape of 500 mm square and a board width of 100 mm for each leg and each yoke, and the model transformer iron loss WT 17/50 (1.7 at 50 Hz).
  • the transformer iron loss when excited up to T was measured.
  • the number of stacked samples was 50, with two stacked alternately.
  • the building factor F17 of the model transformer was calculated as the value obtained by dividing the model transformer iron loss WT 17/50 by the sample iron loss W 17/50 (WT 17/50 /W 17/50 ).
  • the relationship between the building factor F17 and the amount of Co in the base steel plate is shown in FIG.
  • the material belongs to Group A, that is, has the relationship 0.30 ⁇ R17 ⁇ R19, and exhibits a good building factor of 1.25 or less in the Co content range of 0.005 to 0.050%.
  • ⁇ Experiment 2> Contains C: 0.037%, Si: 3.05%, Mn: 0.18%, Al: 0.009%, N: 0.0036%, Se: 0.007%, Sn: 0.062% and Co: 0.0080% in mass%, the balance being Fe and
  • a steel slab with unavoidable impurities was manufactured by continuous casting, and after heating the slab by soaking it at 1300°C for 30 minutes, it was finished to a thickness of 2.2mm by hot rolling. Thereafter, the hot rolled sheet was annealed at 1100°C for 30 seconds in a N2 atmosphere.
  • the heating rate up to 1220°C was 15°C/h
  • the N 2 atmosphere was used from room temperature to 700°C, and the mixing ratio of N 2 and H 2 was varied from 700°C to 1100°C.
  • the atmosphere was H 2 atmosphere from 1100°C to 1220°C. Further, during holding, an H 2 atmosphere was used, and during cooling, an Ar atmosphere was used. In this way, a sample was obtained in which a base film containing forsterite as a main component (hereinafter sometimes referred to as a forsterite film) was formed on the surface of the base steel plate.
  • a base film containing forsterite as a main component hereinafter sometimes referred to as a forsterite film
  • the amount of Ti in the steel sheet with a forsterite coating was measured using the method specified in JIS G1223.
  • the ratio of the hysteresis loss Wh 17 to the iron loss W 17/50 when excited at 1.7T is R17, Wh 17 /W 17/50 , and the iron loss W 19 when excited at 1.9T.
  • Ratio of hysteresis loss Wh 19 to /50 Wh 19 /W 19/50 is defined as R19, and is divided into group A, which has the relationship of 0.30 ⁇ R17 ⁇ R19, and group B, which has the relationship 0.30 ⁇ R17 ⁇ R19.
  • the relationship between the amount of Ti and whether it belongs to group A or group B is shown in FIG.
  • FIG. 4 shows the relationship between the building factor F17 and the amount of Ti in a steel sheet with a forsterite coating.
  • the building factor F17 is high even if it belongs to Group A.
  • the building factor is low and good when the Ti content in the steel sheet with a forsterite coating is 0.0050 to 0.0200%. In short, this means that it is good for a certain amount of Ti to be present in the forsterite coating.
  • the mechanism by which the building factor of the model transformer is improved by the amount of Co in the base steel sheet and the amount of Ti in the steel sheet with a base film mainly composed of forsterite is not clear, but the invention They think as follows. That is, since the yoke and legs of the transformer have a constant width, the distance of the magnetic path differs between the inside and outside, like an athletics track. Therefore, during excitation, the magnetic flux tends to be biased towards the inside where the magnetic path is short. Even when the entire steel plate is excited to 1.7T, the magnetic flux density on the inside exceeds that. Therefore, it is estimated that the more advantageous the high magnetic field characteristics, the better the transformer characteristics such as the building factor.
  • the first point is the ratio of hysteresis loss Wh 17 to iron loss W 17/50 when excited at 1.7T, Wh 17 /W 17/50 , that is, R17 and iron loss W 19/50 when excited at 1.9T.
  • Wh 17 /W 17/50 that is, R17 and iron loss W 19/50 when excited at 1.9T.
  • the ratio of hysteresis loss Wh 19 to Wh 19 /W 19/50 that is, R19, does not satisfy the relationship 0.30 ⁇ R17 ⁇ R19.
  • R17 was less than 0.30 in most cases.
  • Hysteresis loss has a high correlation with B8 , and if B8 is the same, it is thought that there will be no large fluctuations, so the above case is considered to be a case where the eddy current loss is extremely large.
  • B8 is the same, it is thought that there will be no large fluctuations, so the above case is considered to be a case where the eddy current loss is extremely large.
  • eddy current loss which is highly frequency dependent, increases. Therefore, it is considered that the building factor increases when the eddy current loss ratio is high.
  • the second point is when the amount of Ti in the steel sheet with a forsterite coating is less than 0.0050% by mass or more than 0.0200% by mass.
  • Japanese Patent Publication No. 2021-509149 discloses a manufacturing technology for a grain-oriented electrical steel sheet containing Co.
  • this document mentions a technology for improving the magnetism of the electrical steel sheet itself, and this technology is completely different from the present invention, which uses a technology for containing Ti in a forsterite film to reduce the building factor. It's technology.
  • the present invention is based on the above findings. That is, the gist of the present invention is as follows.
  • a grain-oriented electrical steel sheet having a coating The amount of Ti in the base steel plate and the base coating is 0.0050 to 0.0200% by mass, R17 is the ratio of hysteresis loss Wh 17 to iron loss W 17/50 when excited at 1.7T, Wh 17 /W 17/50 , and hysteresis loss Wh 19 to iron loss W 19/50 when excited at 1.9T.
  • a grain-oriented electrical steel sheet that satisfies the following formula (1) when the ratio Wh 19 /W 19/50 is R19. 0.30 ⁇ R17 ⁇ R19...(1)
  • the base steel plate further contains Sn: 0.500 mass% or less, Cr: 0.500 mass% or less, Cu: 0.50 mass% or less, Ni: 0.50 mass% or less, Bi: 0.500 mass% or less, P: 0.500 mass% or less, Sb : 0.500 mass% or less, Mo: 0.500 mass% or less, B: 25.0 mass ppm or less, Nb: 0.020 mass% or less, V: 0.020 mass% or less, As: 0.0200 mass% or less, Zn: 0.020 mass% or less, Pb: The direction according to any one of 1 to 3 above, containing one or more selected from 0.0100% by mass or less, W: 0.0100% by mass or less, Ga: 0.0050% by mass or less, and Ge: 0.0050% by mass or less. electromagnetic steel sheet.
  • FIG. 2 is a graph showing the relationship between the Co content of the base steel plate and the building factor F17 in Experiment 1.
  • FIG. 2 is a graph showing the relationship between the Co content of the base steel plate and the building factor F17 (only Group A is extracted) regarding Experiment 1.
  • FIG. 2 is a graph showing the relationship between the amount of Ti in a steel plate with a forsterite coating and whether it belongs to Group A or Group B, regarding Experiment 2.
  • 3 is a graph showing the relationship between the Ti content and the building factor F17 of a steel plate with a forsterite coating in Example 2.
  • Si 1.50-8.00%
  • Si is an element necessary to increase the specific resistance of steel and improve iron loss. Further, Si is an element necessary also to form a forsterite film in the steel sheet of the present invention. However, if the amount of Si is less than 1.50%, there is no effect, and if it exceeds 8.00%, the workability of the steel deteriorates and rolling becomes difficult. For this reason, the amount of Si is limited to 1.50 to 8.00%.
  • the amount of Si is desirably 2.50% or more, and desirably 4.50% or less.
  • Mn 0.02-1.00% Mn is an element necessary to improve hot workability. However, if the amount of Mn is less than 0.02%, there is no effect, and if it exceeds 1.00%, the magnetic flux density of the product plate will decrease. Therefore, the amount of Mn is set to 0.02 to 1.00%. The amount of Mn is desirably 0.04% or more, and desirably 0.20% or less.
  • Co 0.005 ⁇ 0.050%
  • the amount of Co is preferably 0.006% or more, more preferably 0.008% or more. Further, the amount of Co is preferably 0.020% or less, and more preferably 0.015% or less.
  • the base steel sheet of the grain-oriented electrical steel sheet of the present invention contains, in addition to the above-mentioned basic components (Si, Mn, and Co), C (e.g., 0.020 to 0.100%), Al (e.g., 0.002 to 0.040%), and N. (for example, 0.002 to 0.015%).
  • the base steel plate may optionally contain S (for example, 0.020% or less) and/or Se (for example, 0.040% or less).
  • the base steel sheet of the grain-oriented electrical steel sheet of the present invention can appropriately contain the components (elements) described below as necessary.
  • the base steel plate contains Sn: (more than 0%) 0.500% or less, Cr: (more than 0%) 0.500% or less, Cu: (more than 0%) 0.50% or less, Ni: (more than 0%) less than or equal to 0.50%, Bi: (more than 0%) less than or equal to 0.500%, P: (more than 0%) less than or equal to 0.500%, Sb: (more than 0%) less than or equal to 0.500%, Mo: (more than 0%) ) 0.500% or less, B: (more than 0ppm) 25.0ppm or less, Nb: (more than 0%) 0.020% or less, V: (more than 0%) 0.020% or less, As: (more than 0%) 0.0200% or less, Zn: (More than 0%) 0.020% or less, Pb: (More than 0%) 0.0100% or less, W: (More than 0%) 0.0100% or less or
  • each of the above-mentioned elements can be contained in the base steel sheet within the above-mentioned upper limit amount in order to further improve the magnetic properties. If the amount (content) of each element exceeds the above upper limit, the development of secondary recrystallized grains may be suppressed and the magnetic properties may deteriorate.
  • the lower limit of each element does not need to be particularly limited, but is preferably in the following range.
  • Sn 0.005% or more, Cr: 0.005% or more, Cu: 0.01% or more, Ni: 0.01% or more, Bi: 0.005% or more, P: 0.005% or more, Sb: 0.005% or more, Mo: 0.005% or more, B: 0.1ppm or more, Nb: 0.001% or more, V: 0.001% or more, As: 0.0010% or more, Zn: 0.001% or more, Pb: 0.0001% or more, W: 0.0010% or more, Ga: 0.0001% or more, and Ge: 0.0001% that's all
  • the remainder other than the above-mentioned components (elements) is Fe and inevitable impurities.
  • the above-mentioned composition is the composition of the base material steel sheet, that is, it does not take into account the base film whose main component is forsterite.
  • the amount of Ti in the steel sheet with the base film containing forsterite as a main component is set to 0.0050 to 0.0200% for the above-mentioned reasons. limited.
  • the amount of Ti in the base steel sheet and the base coating is preferably 0.0060% or more, and preferably 0.0150% or less.
  • the "main component" refers to the component with the largest mass among the components constituting the base coat.
  • the amount of Ti in the base steel sheet is preferably 0.0030% or less. This is because if the amount of Ti in the base steel sheet is 0.0030% or less, significant deterioration of iron loss due to the formation of Ti precipitates in the steel can be suppressed.
  • the amount of Ti in the steel sheet with the base film is 0.0050% or more. This is because, as mentioned above, if a certain amount of Ti is present in the forsterite coating, it is thought that the coating properties can be improved and the eddy current loss can be improved, but if the Ti amount is less than 0.0050%, the This is because it is presumed to be less effective.
  • the hysteresis loss can be a value obtained by multiplying the energy loss of the iron core due to one rotation of the hysteresis loop by 50, which is the excitation frequency.
  • a general method for manufacturing electromagnetic steel sheets can be used.
  • slabs may be manufactured from molten steel with predetermined composition adjustments using the normal ingot-forming method or continuous casting method, or thin slabs with a thickness of 100 mm or less may be manufactured using the direct casting method.
  • Molten steel may be produced by a blast furnace method or an electric furnace method. Since it is difficult to add the above-mentioned various components that can be contained in the base steel plate in the middle of the process, it is desirable to add them in the molten steel stage.
  • the slab may be heated and hot rolled in a conventional manner, or it may be hot rolled immediately after casting without heating.
  • the heating temperature when heating is desirably 1250°C or lower.
  • the temperature for hot-rolled sheet annealing is preferably about 950 to 1150°C. If the temperature is 950°C or higher, the remaining unrecrystallized parts can be sufficiently suppressed, and if the temperature is 1150°C or lower, the excessive coarsening of the grain size after annealing can be suppressed, and the subsequent primary recrystallization texture can be further improved. It can be made into a good one.
  • the temperature for annealing the hot rolled sheet is preferably 1000°C or higher, and preferably 1100°C or lower.
  • a steel plate after hot rolling or hot rolling annealing is cold rolled once or cold rolled two or more times with intermediate annealing in between to obtain a cold rolled plate of the final thickness.
  • the annealing temperature of the intermediate annealing is preferably in the range of 900 to 1200°C. If the temperature is 900°C or higher, it will effectively suppress recrystallized grains from becoming too fine after intermediate annealing, and also suppress the deterioration of the magnetic properties of the product sheet due to the reduction of Goss nuclei in the primary recrystallized structure. be able to. On the other hand, if the temperature is 1200° C. or lower, excessive coarsening of crystal grains can be suppressed and the primary recrystallized structure of regular grains can be made better, as in the case of hot-rolled sheet annealing.
  • the cold-rolled sheet that has reached its final thickness is then subjected to primary recrystallization annealing that also serves as decarburization annealing.
  • the annealing temperature in this primary recrystallization annealing is preferably in the range of 800 to 900°C from the viewpoint of rapidly progressing the decarburization reaction, and the atmosphere is preferably a humid atmosphere. is preferred.
  • mainly containing MgO means containing MgO in an amount of 75% by mass or more.
  • Ti can be effectively caused to exist in the forsterite film.
  • Ti may be present in the forsterite film by other methods.
  • secondary recrystallization annealing (purification annealing) is performed.
  • This purification annealing is desirably carried out at a temperature of 800°C or higher in order to induce secondary recrystallization, and from the viewpoint of purification it is desirable to raise the temperature to a holding temperature of 1100°C or higher.
  • the holding temperature is more preferably 1180°C or higher.
  • After purification annealing it is preferable to perform water washing, brushing, or pickling in order to remove the attached annealing separation agent.
  • an N 2 atmosphere is used up to the first intermediate temperature (for example, a temperature selected from the range of 600 to 800°C), and the first intermediate temperature is It is preferable to use a mixed atmosphere of N 2 and H 2 from the temperature to the second intermediate temperature (for example, a temperature selected from the range of 1050 to 1150° C.), and to use a H 2 atmosphere from the second intermediate temperature to the holding temperature. .
  • a laminated steel plate in order to improve iron loss, it is effective to apply an insulating coating to the surface of the steel plate before or after flattening annealing.
  • This insulating coating is preferably a coating that can apply tension to the steel plate in order to reduce iron loss.
  • Adopting a method of applying a tension coating via a binder, physical vapor deposition, or chemical vapor deposition to form a coating by depositing an inorganic substance on the surface layer of the steel plate has excellent coating adhesion and has a significant iron loss reduction effect. Therefore, it is desirable.
  • Example 1 Steel slab A...C: 0.070%, Si: 3.55%, Mn: 0.07%, Al: 0.0080%, N: 0.0050%, Co: 0.012%, Mo: 0.026%, Ti: 0.025%, the remainder is Fe and inevitable impurities Steel slab B...C: 0.072%, Si: 3.51%, Mn: 0.07%, Al: 0.0080%, N: 0.0047%, Co: 0.011%, Mo: 0.025%, Ti: 0.0025% Contains Fe and the balance is Fe and unavoidable impurities Steel slab C...C: 0.072%, Si: 3.49%, Mn: 0.07%, Al: 0.0090%, N: 0.0051%, Co: 0.002%, Mo: 0.025% , Ti: 0.024%, the balance being Fe and unavoidable impurities Steel slab D...C: 0.068%, Si: 3.48%, Mn: 0.07%, Al: 0.0090%, N: 0.0050%, Co: 0.008% , Mo: 0.022%
  • the hot rolled sheet was annealed at 1000°C for 60 seconds in a N2 atmosphere.
  • it was cold rolled to a plate thickness of 0.23 mm, and further decarburized annealed at 850°C for 90 seconds in a humid atmosphere of 60% H 2 -40% N 2 and a dew point of 60°C.
  • an annealing separator mainly composed of MgO (MgO: 97% by mass) is applied to the surface of the base steel plate after decarburization annealing, and after holding at 1100°C for 25 hours, it is held at 1200°C for 10 hours. Purification annealing was performed.
  • this temperature raising process from room temperature to 700°C is a N2 atmosphere, from 700°C to 1100°C is an atmosphere with various mixing ratios of N2 and H2 , and from 1100°C (retention start) to 1200°C (retention end). Until then, the atmosphere was H2 . Furthermore, an Ar atmosphere was used during cooling.
  • the Ti content (Ti content in the entire base steel plate and base film) was measured according to the method specified in JIS G1223. . The results are also listed in Table 1.
  • a three-phase tripod model transformer was fabricated, imitating a transformer, with an external shape of 500 mm square and a board width of 100 mm for each leg and each yoke, and the model transformer iron loss WT 17/50 (50 Hz The transformer iron loss when excited up to 1.7T was measured. The number of stacked samples was 50, with two stacked alternately. Then, the building factor F17 of the model transformer was calculated as the value obtained by dividing the model transformer iron loss WT 17/50 by the sample iron loss W 17/50 (WT 17/50 /W 17/50 ). The results are also listed in Table 1.
  • Example 2 A steel slab containing the components shown in Table 2, with the remainder being Fe and unavoidable impurities, is produced by continuous casting, subjected to slab heating by soaking at 1410°C for 20 minutes, and then hot rolled to a thickness of 2.4 mm. Finished thick. Thereafter, the hot rolled sheet was annealed at 1100°C for 20 seconds in a N2 atmosphere. Next, it was cold rolled to a plate thickness of 1.5 mm, and then intermediate annealed at 900° C. for 100 seconds in a 25% H 2 -75% N 2 atmosphere. Thereafter, it was cold rolled to a thickness of 0.23 mm, and further decarburized annealed at 825°C for 150 seconds in a humid atmosphere of 40% H 2 -60% N 2 and a dew point of 45°C.
  • an annealing separator mainly composed of MgO (MgO: 88% by mass) was applied to the surface of the base steel plate after decarburization annealing.
  • MgO MgO: 88% by mass
  • 5 parts by mass of superhydrated TiO 2 which was obtained by adding TiO 2 powder to 50° C. hot water and stirring for 24 hours, was added to the powdered MgO.
  • purification annealing was performed at 1200°C for 10 hours.
  • the heating rate up to 1200°C was 15°C/h
  • the N 2 atmosphere was used from room temperature to 700°C, and the mixing ratio of N 2 and H 2 was varied from 700°C to 1100°C.
  • the atmosphere was H 2 atmosphere from 1100°C to 1200°C.
  • the atmosphere was H 2 , and during cooling, the atmosphere was Ar.
  • the Ti content (Ti content in the entire base steel plate and base film) was measured according to the method specified in JIS G1223. .
  • the measurement results are also listed in Table 3.
  • a three-phase tripod model transformer was fabricated, imitating a transformer, with an external shape of 500 mm square and a board width of 100 mm for each leg and each yoke, and the model transformer iron loss WT 17/50 (50 Hz The transformer iron loss when excited up to 1.7T was measured. The number of stacked samples was 50, with two stacked alternately. Then, the building factor F17 of the model transformer was calculated as the value obtained by dividing the model transformer iron loss WT 17/50 by the sample iron loss W 17/50 (WT 17/50 /W 17/50 ). The results are also listed in Table 3.

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