Data set generation method, electromagnetic field analysis method, and computer program

Abstract

This data set generation method is for acquiring two-dimensional magnetic properties, the method comprising: a step for measuring a first magnetic field strength vector generated in an analysis object in accordance with a first elliptical magnetization applied in a clockwise direction; a step for measuring a second magnetic field strength vector generated in the analysis object in accordance with a second elliptical magnetization applied in a counterclockwise direction; a step for averaging the first magnetic field strength vector and the second magnetic field strength vector to calculate a first average magnetic field strength vector; a step for averaging a first magnetic flux density vector corresponding to the first elliptical magnetization and a second magnetic flux density vector corresponding to the second elliptical magnetization to calculate a first average magnetic flux density vector; and a step for generating a data set of two-dimensional magnetic properties associating the first average magnetic field strength vector and the first average magnetic flux density vector with each other.

Description

[Technical field]

[0001] The present disclosure relates to a method for generating a data set used for analyzing the magnetic properties of magnetic materials such as iron cores of electric equipment, mainly transformer iron cores, by treating magnetic field strength and magnetic flux density as vector quantities, a method for analyzing an electromagnetic field, and a computer program. [Background technology]

[0002] The easy axis of magnetization of iron <001> Grain-oriented electrical steel sheets, which have a crystal structure with a highly aligned orientation in the rolling direction of the steel sheet, are used particularly as the core material for power transformers. There are various requirements for transformer cores, but the most important one is low core loss.

[0003] From this perspective, it is important that the iron loss value is small as a characteristic required for grain-oriented electromagnetic steel sheets, which are the core material. Also, in order to reduce the excitation current in the transformer and reduce copper loss, a high magnetic flux density is also necessary. This magnetic flux density is evaluated by the magnetic flux density B8 (T) at a magnetizing force of 800A / m, and generally, the higher the orientation concentration in the Goss orientation, the higher the B8. Magnetic steel sheets with high magnetic flux density generally have low hysteresis loss and are excellent in terms of iron loss characteristics. In order to reduce transformer iron loss, it is generally considered that the iron loss of grain-oriented electromagnetic steel sheets, which are the core material, should be reduced. In fact, in a wound core transformer with single-phase excitation, the material iron loss and the transformer iron loss are almost the same, so the transformer iron loss can be reduced by reducing the material iron loss.

[0004] However, it is known that the iron loss in the transformer is larger than the material iron loss, especially in a three-phase excitation transformer having three or five legs. The ratio of the iron loss value (transformer iron loss) when an electromagnetic steel sheet is used as the iron core of the transformer to the iron loss value of the material obtained by the Epstein test or the like is generally called the building factor (BF) or the distraction factor (DF). In other words, in a three-phase excitation transformer having three or five legs, the BF generally exceeds 1. Furthermore, it has been pointed out that in a three-phase excitation transformer, the reduction in the iron loss of the iron core material does not necessarily lead to the reduction in the iron loss of the transformer. In particular, it is known that in an iron core using a material (highly oriented electromagnetic steel sheet: HGO) with a high concentration in the Goss orientation with B8 of 1.88T or more, the magnetic properties of the transformer itself may be deteriorated even if the magnetic properties of the material are good. This means that even if grain-oriented electrical steel sheets with excellent magnetic properties are manufactured, they are not fully utilized in the actual characteristics of transformers. Also, for material properties other than magnetic flux density B8, BF changes with various changes in properties such as the tension of the steel sheet coating or the presence or absence of magnetic domain refinement processing. In addition, BF changes with the shape of the transformer core or differences in the lamination wrapping method of the steel sheet, and the iron loss of the transformer changes.

[0005] In order to select the core material or design the core shape so as to minimize the core loss in the transformer, it is necessary to predict the resulting transformer core loss. However, as described above, the transformer core loss changes depending on various conditions in the transformer, so it is not easy to predict the iron loss.

[0006] One method for making predictions is to compile a database of iron loss test results for previously manufactured transformers, or iron loss results from tests on model transformers made in a reduced size to simulate actual transformers, and make predictions analytically or empirically.

[0007] For example, Patent Document 1 discloses a method of performing multiple regression and multiple correlation analysis with transformer iron loss as a dependent variable and core width dimension, core window frame dimension, core window length dimension, core stack height dimension, core plate thickness dimension, material iron loss value, and material magnetization characteristic value as independent variables, and estimating transformer iron loss using the multiple regression equation obtained from this analysis.

[0008] Another common method is to estimate transformer iron loss by electromagnetic field numerical simulation. For electromagnetic field numerical simulation that analyzes Maxwell's equations using the finite element method, a series of numerical analysis tools, including the creation of mesh models, time analysis using the finite element method, and analysis of the results, are available commercially as software.

[0009] However, to accurately analyze a transformer core made of grain-oriented magnetic steel sheets, it is necessary to select the appropriate electromagnetic properties to be used in the analysis. In general, electromagnetic field numerical methods use magnetic properties obtained by the single sheet magnetic test method or the Epstein test method, which assumes that the magnetic flux density B and the magnetic field strength H are parallel and measures the magnetic flux density in the same direction as the applied magnetic field. The results obtained by these methods treat the mapping quantity (component) in the measurement direction as a scalar value (one-dimensional magnetic property). On the other hand, when a magnetization with an inclination to the easy axis direction, which often occurs in a transformer core, or a rotational magnetization is applied to a material that is extremely easily magnetized in one direction, such as grain-oriented magnetic steel sheets, a spatial difference in direction occurs between the magnetic flux density and the magnetic field strength vector. This spatial difference in direction between the magnetic flux density and the magnetic field strength vector has a significant effect on the prediction results of iron loss in electromagnetic field analysis. However, as described above, the single sheet magnetic testing method or the Epstein testing method measures the mapping quantity (component) in the measurement direction, and therefore it is not possible to measure the spatial directional difference between the magnetic flux density and the magnetic field strength vector.

[0010] Therefore, a method has been proposed in which the magnetic field strength H and magnetic flux density B are measured as vector quantities using the concept of two-dimensional magnetic properties, and electromagnetic field analysis is performed based on the measured vector quantities. As a model of two-dimensional magnetic properties (a model of vector magnetic properties), for example, E&S modeling has been proposed (see, for example, Patent Document 2). By using such a method, it becomes possible to obtain more accurate transformer iron loss than conventional electromagnetic field analysis based on one-dimensional magnetic properties. [Prior art documents] [Patent documents]

[0011] [Patent Document 1] Japanese Patent Application Publication No. 62-75351 [Patent Document 2] JP 2004-184234 A Summary of the Invention [Problem to be solved by the invention]

[0012] In a two-dimensional magnetic property model that captures magnetic field strength H and magnetic flux density B as vector quantities, as described in Reference 1, a two-dimensional magnetic measurement device is used to measure the material magnetic properties that form the basis of the calculations. Reference 1: Enozono, "Two-dimensional vector magnetic properties," Journal of the Magnetic Society of Japan, vol. 27, No. 2, 2003

[0013] The magnetic field strength H is measured using H coils in two orthogonal directions, and the magnetic flux density B is measured using search coils or a probe method in two orthogonal directions. Measurements are also performed under various elliptical magnetization conditions with different maximum magnetic flux density, ellipticity, or inclination. When performing electromagnetic field analysis, analysis is performed using two-dimensional magnetic properties modeled using the vector magnetic property results of the magnetic field strength H and magnetic flux density B under various elliptical magnetization conditions measured in this way, allowing accurate magnetic measurement of the iron core of a transformer, etc.

[0014] In an electromagnetic field analysis method characterized by treating magnetic field strength H and magnetic flux density B as vector quantities, the accuracy of the results is determined by the accuracy of the measurement results of magnetic field strength H and magnetic flux density B obtained using a two-dimensional magnetic measurement device. However, in measurements under the above-mentioned elliptical magnetization conditions, there was a problem in that the measurement results changed significantly depending on whether the rotation direction when applying the elliptical magnetization was clockwise (CW) or counterclockwise (CCW).

[0015] For example, the following documents 2 and 3 report that when the measurement target is a directional electrical steel sheet, or even when the measurement target is a non-directional electrical steel sheet but with a high excitation magnetic flux density, the measured iron loss value varies greatly depending on whether the excitation is clockwise (CW) or counterclockwise (CCW) when excited with elliptical magnetization. Reference 2: Watanabe, Yanase, Okazaki, "Two-dimensional magnetic properties of grain-oriented electrical steel sheets," Materials for the Magnetics Study Group of the Institute of Electrical Engineers of Japan, MAG-08-80, pp. 19-24, 2008 Reference 3: Maeda, Shimoji, Todaka, and Enozono, "Study on measurement method under CCW / CW condition in high magnetic flux density region", Materials of the Magnetics Study Group of the Institute of Electrical Engineers of Japan, MAG-07-139, P1-4, 2007

[0016] In view of the above problems, the present disclosure proposes a method for generating a data set of two-dimensional magnetic properties used in two-dimensional magnetic modeling in an electromagnetic field analysis method characterized by capturing magnetic field strength H and magnetic flux density B as vector quantities, so as to improve the accuracy of analysis results. It also proposes a method for analyzing an electromagnetic field using the generated data set of two-dimensional magnetic properties. [Means for solving the problem]

[0017] A data set generation method according to an embodiment of the present disclosure includes: A method for acquiring two-dimensional magnetic properties used to analyze an electromagnetic field of an analysis target by capturing magnetic field strength and magnetic flux density as vector quantities, comprising: Measuring a first magnetic field intensity vector generated in the analysis object in response to a first elliptical magnetization applied clockwise along an ellipse having a major axis and a minor axis with a predetermined axial ratio, the major axis of which is inclined at a first angle with respect to the rolling direction of the analysis object; measuring a second magnetic field intensity vector generated in the analysis object in response to a second elliptical magnetization applied counterclockwise along an ellipse having a major axis and a minor axis with the predetermined axial ratio, the major axis of which is inclined by a second angle, the second angle being opposite in sign to the first angle, with respect to the rolling direction of the analysis object; averaging the first magnetic field strength vector and the second magnetic field strength vector to calculate a first average magnetic field strength vector; calculating a first average magnetic flux density vector by averaging a first magnetic flux density vector corresponding to the first elliptical magnetization and a second magnetic flux density vector corresponding to the second elliptical magnetization; generating a data set of the two-dimensional magnetic properties that corresponds to the first average magnetic field strength vector and the first average magnetic flux density vector, the predetermined axial ratio, and the first angle; Includes.

[0018] An electromagnetic field analysis method according to an embodiment of the present disclosure includes: The method includes a step of analyzing the electromagnetic field of an iron core using an analysis object having two-dimensional magnetic properties identified by a dataset of two-dimensional magnetic properties that combine a first average magnetic field strength vector and a first average magnetic flux density vector, the dataset being generated by executing the above dataset generation method.

[0019] A computer program according to an embodiment of the present disclosure causes a computer to execute each step of the data set generation method or the electromagnetic field analysis method. Effect of the Invention

[0020] According to the data set generation method, electromagnetic field analysis method, and computer program of an embodiment of the present disclosure, the accuracy of analysis results of the magnetic properties of magnetic bodies such as electric machine cores, mainly transformer cores, can be improved. [Brief description of the drawings]

[0021] [Figure 1] 1 is a block diagram showing a configuration example of an analysis system according to the present disclosure. [Diagram 2] FIG. 4 is a diagram illustrating an example of a relationship between a magnetic flux density vector and a magnetic field strength vector. [Figure 3A] FIG. 13 is a diagram showing an example of clockwise elliptical magnetization applied to an object to be analyzed. [Figure 3B] 3B is a graph showing an example of the measurement results of magnetic field intensity vectors generated when the elliptical magnetization of FIG. 3A is applied to an analysis object. [Figure 4A] FIG. 13 is a diagram showing a relationship in which the magnetization easy axis and the major axis direction of elliptical magnetization are inclined in opposite directions to the rolling direction of the object to be analyzed. [Figure 4B] 4B is a diagram that is symmetrical with respect to FIG. 4A with respect to the rolling direction of the analysis target as an axis. [Figure 5A] FIG. 13 is a diagram showing the relationship in which the magnetization easy axis and the major axis direction of the elliptical magnetization are inclined in the same direction with respect to the rolling direction of the object to be analyzed. [Figure 5B] 5B is a diagram that is symmetrical to FIG. 5A with respect to the rolling direction of the analysis target. [Figure 6] FIG. 2 is a diagram showing an example of a transformer core to which a steel plate to be analyzed is applied. [Figure 7] 1 is a flowchart illustrating an example of a procedure for a dataset generation method according to the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] Hereinafter, an embodiment of an analysis system 1 (see FIG. 1, etc.) and an analysis method according to the present disclosure will be described with reference to the drawings. Each drawing is schematic and may differ from the actual one. Furthermore, the following embodiments are illustrative of an apparatus or method for embodying the technical idea of ​​the present disclosure, and are not intended to specify the configuration as described below. In other words, the technical idea of ​​the present disclosure can be modified in various ways within the technical scope described in the claims.

[0023] (Example of the configuration of analysis system 1) 1, an analysis system 1 according to one embodiment includes an analysis device 10 and a measurement device 20. The analysis system 1 is configured to be capable of analyzing two-dimensional magnetic properties of an analysis object, such as a grain-oriented electrical steel sheet or a non-oriented electrical steel sheet.

[0024] Two-dimensional magnetic properties are properties that express the relationship between magnetic flux density and magnetic field strength, including not only the relationship in magnitude but also the relationship in direction, by treating each of the magnetic flux density and magnetic field strength as two-dimensional vectors. As illustrated in FIG. 2, the magnetic flux density vector is represented as B. The magnetic field strength vector is represented as H. As illustrated in FIG. 2, in a certain analysis object, the magnetic flux density vector B and the magnetic field strength vector H may face in different directions. The magnetic flux density vector B is assumed to be along the X-axis direction. The magnetic field strength vector H is assumed to face in a different direction from the magnetic flux density vector B. In other words, it is assumed that a spatial directional difference occurs between the magnetic field strength vector H and the magnetic flux density vector B.

[0025] Hx represents the X-axis component of the magnetic field strength vector H. One-dimensional magnetic characteristics represent the relationship between the magnitude of the magnetic flux density vector B facing the X-axis direction and the X-axis component Hx of the magnetic field strength vector H. In other words, one-dimensional magnetic characteristics treat the mapping quantities (components) of the magnetic flux density and magnetic field strength in the measurement direction as scalar values.

[0026] When predicting iron loss by analyzing the electromagnetic field of an analysis target in which a spatial directional difference occurs between the magnetic field strength vector H and the magnetic flux density vector B, the spatial directional difference has a large effect on the predicted results of iron loss. The analysis system 1 according to this embodiment can analyze the electromagnetic field with higher accuracy than methods using one-dimensional magnetic properties (such as the single sheet magnetic testing method or the Epstein testing method) by analyzing the electromagnetic field using two-dimensional magnetic properties.

[0027] As shown in Figures 3A and 3B, the two-dimensional magnetic properties are expressed as data that associates a locus BT drawn by the tip of a magnetic flux density vector B when the magnetic flux density applied to the analysis target is changed with a locus HT drawn by the tip of a magnetic field strength vector H that represents the magnetic field strength generated in the analysis target in response to the application of magnetic flux density. The horizontal and vertical axes of Figure 3A respectively represent the X-axis component (Bx) and Y-axis component (By) of the magnetic flux density. The horizontal and vertical axes of Figure 3B respectively represent the X-axis component (Hx) and Y-axis component (Hy) of the magnetic field strength.

[0028] When the components of the magnetic flux density applied to the analysis target in the X-axis direction and the Y-axis direction are expressed as sine waves, the locus BT of the tip of the magnetic flux density vector B can be an ellipse as illustrated in FIG. 3A. Depending on the amplitude of the components of the magnetic flux density in the X-axis direction and the Y-axis direction, the locus BT can be a circle. Depending on the phase of the components of the magnetic flux density in the X-axis direction and the Y-axis direction, the locus BT can be a straight line. When the locus BT of the tip of the magnetic flux density vector B is a curve such as an ellipse or a circle, the magnetic flux is also called rotating magnetic flux or rotating magnetization. When the locus BT of the tip of the magnetic flux density vector B is a straight line, the magnetic flux is also called alternating magnetic flux or alternating magnetization. Rotational magnetization is specified by the length Bm of the major axis of the ellipse that represents the locus BT, the ratio α of the length of the minor axis to the length of the major axis of the ellipse, the angle θ that the major axis of the ellipse makes with the X-axis direction, and the direction (clockwise (CW) or counterclockwise (CCW)) in which the tip of the magnetic flux density vector B moves along the locus BT. Alternating magnetization corresponds to the case in which α in rotational magnetization becomes 0.

[0029] <Analysis device 10> The analysis device 10 includes a control unit 12, a storage unit 14, and an interface 16. The control unit 12 may include at least one processor, such as a central processing unit (CPU) or a graphics processing unit (GPU), in order to control and manage various functions of the analysis device 10. The control unit 12 may include one processor or multiple processors. The processor constituting the control unit 12 may realize the functions of the analysis device 10 by reading and executing a program stored in the storage unit 14.

[0030] The storage unit 14 stores various information or data. The storage unit 14 may store, for example, a program executed in the control unit 12, or data used in a process executed in the control unit 12, or a result of the process. The storage unit 14 may also function as a work memory for the control unit 12. The storage unit 14 may include, but is not limited to, a semiconductor memory. For example, the storage unit 14 may be configured as an internal memory of a processor used as the control unit 12, or may be configured as a hard disk drive (HDD) accessible from the control unit 12. The storage unit 14 may be configured as a non-transitory readable medium. The storage unit 14 may be configured integrally with the control unit 12, or may be configured separately from the control unit 12.

[0031] The interface 16 may be configured to include a communication interface. The communication interface may be configured to communicate with other devices such as the measurement device 20 by wire or wirelessly. The communication interface may be configured to be able to communicate with other devices such as the measurement device 20 via a network. The communication interface may be configured to include an input / output port for inputting and outputting data to and from other devices such as the measurement device 20. The communication interface may communicate based on a wired communication standard, or may communicate based on a wireless communication standard. For example, the wireless communication standard may include a cellular phone communication standard such as 3G, 4G, or 5G. Also, for example, the wireless communication standard may include IEEE802.11 or Bluetooth (registered trademark), etc. The communication interface may support one or more of these communication standards. The communication interface is not limited to these examples, and may communicate with other devices such as the measurement device 20 or input and output data based on various standards.

[0032] The interface 16 may include a display device. The display device may notify the user of information by outputting visual information such as characters, figures, or images. The display device may include various displays such as a liquid crystal display.

[0033] The interface 16 may include an audio output device such as a speaker, or may include various other output devices. The analysis device 10 may further include an input device that accepts input from a user. The input device may include, for example, a keyboard or physical keys, or may include a touch panel or a touch sensor, or a pointing device such as a mouse. The input device is not limited to these examples and may include various other devices.

[0034] <Measuring device 20> The measurement device 20 includes a magnetic flux application unit that applies rotational magnetization (rotational magnetic flux) to the analysis object, and a magnetic field measurement unit that measures the magnetic field intensity generated in the analysis object to which the rotational magnetization has been applied. The magnetic field measurement unit may be configured to include H coils positioned in two orthogonal directions with respect to the analysis object. The measurement device 20 may directly use the value of the magnetic flux density generated by the magnetic flux application unit. The measurement device 20 may further include a magnetic flux density measurement unit that measures the magnetic flux density actually applied to the analysis object. The magnetic flux density measurement unit may be configured to include search coils positioned in two orthogonal directions with respect to the analysis object, or may be configured to perform measurement by a probe method.

[0035] The measurement device 20 may be controlled by the analysis device 10. The analysis device 10 may control the rotational magnetization applied to the analysis target by the magnetic flux application unit. The analysis device 10 may obtain the measurement results from the magnetic field measurement unit or the magnetic flux density measurement unit.

[0036] (Example of analysis system 1 operation) An example of the operation of the analysis system 1 according to this embodiment will be described below. In the analysis system 1, the control unit 12 of the analysis device 10 acquires data representing the relationship between the magnetic flux density vector B and the magnetic field strength vector H as the two-dimensional magnetic characteristics of the analysis target. The two-dimensional magnetic characteristics of the analysis target are expressed as a combination of at least two directional magnetic flux density vectors B and the magnetic field strength vectors H corresponding to each magnetic flux density vector B. In this embodiment, the two-dimensional magnetic characteristics of the analysis target are expressed such that the magnetic flux density vector B is rotational magnetization. The data representing the combination of the magnetic flux density vector B and the magnetic field strength vector H is also referred to as a data set of the two-dimensional magnetic characteristics.

[0037] As described above, the data set of the two-dimensional magnetic properties of the object to be analyzed is data that combines the magnetic flux density vector B applied to the object to be analyzed and the magnetic field strength vector H generated in response to the application of the magnetic flux density vector B.

[0038] Here, the analysis object is assumed to be a steel plate. The magnetic field strength vector H generated in the analysis object may differ depending on whether the direction of rotational magnetization applied to the analysis object is clockwise (CW) or counterclockwise (CCW). Specifically, when the long axis direction of the ellipse rotational magnetization differs from the magnetization easy direction of the steel plate, it was found that the measurement result of the magnetic field strength vector H when clockwise rotational magnetization is applied is significantly different from the measurement result of the magnetic field strength vector H when counterclockwise rotational magnetization is applied. The difference in the measurement result of the magnetic field strength vector H results in a different value of iron loss calculated by electromagnetic field analysis using a data set of two-dimensional magnetic properties based on the measurement result.

[0039] When the long axis direction of the rotational magnetization is inclined clockwise with respect to the easy magnetization direction of the steel sheet, the iron loss value calculated using the data set of the two-dimensional magnetic properties obtained by applying counterclockwise rotational magnetization is greater than the iron loss value calculated using the data set of the two-dimensional magnetic properties obtained by applying clockwise rotational magnetization. Conversely, when the long axis direction of the rotational magnetization is inclined counterclockwise with respect to the easy magnetization direction of the steel sheet, the iron loss value calculated using the data set of the two-dimensional magnetic properties obtained by applying clockwise rotational magnetization is greater than the iron loss value calculated using the data set of the two-dimensional magnetic properties obtained by applying counterclockwise rotational magnetization.

[0040] The difference in iron loss value depending on the direction of rotational magnetization is due to whether the direction of magnetic flux density vector B passes through the easy magnetization direction of the steel plate while magnetic flux density vector B changes from a direction close to the easy magnetization direction where it is easy to magnetize (long axis direction) to a direction away from the easy magnetization direction where it is difficult to magnetize (short axis direction), or whether the direction of magnetic flux density vector B passes through the easy magnetization direction of the steel plate while magnetic flux density vector B changes from a direction away from the easy magnetization direction where it is difficult to magnetize (short axis direction) to a direction close to the easy magnetization direction where it is easy to magnetize (long axis direction). In other words, when turning from a direction close to the easy magnetization direction where it is easy to magnetize (long axis direction) to a direction away from the easy magnetization direction where it is difficult to magnetize (short axis direction), the magnetic field strength generated according to the application of magnetization differs depending on whether it first passes through the easy magnetization direction or turns to the short axis direction and then passes through the easy magnetization direction.

[0041] One of the reasons why the magnetic field strength generated by the rotational magnetization (rotating magnetic flux) differs depending on the direction of rotation is that the magnetic field strength required when the magnetic flux density vector of the rotating magnetization (rotating magnetic flux) moves from the direction close to the easy magnetization direction (long axis direction) where it is easy to magnetize to the direction away from the easy magnetization direction where it is difficult to magnetize (short axis direction). When rotating magnetization (rotating magnetic flux) is applied to a steel plate and the magnetization inside the steel plate is to be directed from the long axis direction to the short axis direction, if the easy magnetization direction exists in that direction, the magnetic field strength in that direction can be small because the magnetic flux density vector passes through the easy magnetization direction at the beginning of the rotation, and there is no need to rotate the magnetic field strength vector H in the short axis direction with a phase difference with respect to the magnetic flux density vector B. As a result, the spatial difference in direction between the magnetic flux density vector B and the magnetic field strength vector H becomes smaller. The iron loss decreases as the spatial difference in direction between the magnetic flux density vector B and the magnetic field strength vector H becomes smaller. This is because iron loss is calculated as the area of ​​the hysteresis loop, and the greater the difference between the magnetic flux density vector B and the magnetic field strength vector H, the greater the iron loss. Conversely, when passing through the easy magnetization direction after facing the short axis direction, the easy magnetization direction is not passed at the start of the rotation, so there is no effect of reducing the spatial directional difference between the magnetic flux density vector B and the magnetic field strength vector H, and it is thought that the iron loss will increase.

[0042] It is difficult to grasp the relationship between the rolling direction of a steel sheet and the direction of easy magnetization in advance. This is because the direction of easy magnetization of the secondary recrystallized grains constituting the grain-oriented electrical steel sheet deviates by several degrees. In addition, because the secondary recrystallized grains are relatively large, there is local variation in the direction of easy magnetization itself.

[0043] Because the magnetization easy direction may differ from the rolling direction, it is difficult to know in advance whether the magnetization easy direction of the steel sheet is inclined clockwise or counterclockwise with respect to the rolling direction. Therefore, in the analysis system 1 according to this embodiment, the control unit 12 of the analysis device 10 acquires the measurement result of the magnetic field intensity vector H when a clockwise rotational magnetization is applied to the analysis object, and the measurement result of the magnetic field intensity vector H when a counterclockwise rotational magnetization is applied to the analysis object. The control unit 12 averages the measurement result of the magnetic field intensity vector H corresponding to the clockwise rotational magnetization and the measurement result of the magnetic field intensity vector H corresponding to the counterclockwise rotational magnetization, and generates the average result as a data set of the two-dimensional magnetic properties of the analysis object. By averaging the clockwise result and the counterclockwise result, the influence of the difference in the rotation direction of the rotational magnetization on the measurement result of the magnetic field intensity vector can be reduced.

[0044] Specifically, the control unit 12 may apply a clockwise (CW) or counterclockwise (CCW) rotational magnetization to the analysis object along a locus BT of an ellipse having a major axis EL and a minor axis ES, as illustrated in Figs. 4A and 4B and Figs. 5A and 5B, by the measurement device 20. The horizontal axis of Figs. 4A and 4B and Figs. 5A and 5B represents the X-axis component (Bx) of the magnetic flux density vector B applied as a rotational magnetization to the analysis object. The vertical axis represents the Y-axis component (By). In the measurement device 20, it is assumed that the steel sheet is arranged so that the rolling direction coincides with the X-axis direction. In Fig. 4A, it is assumed that the magnetization easy direction ME of the steel sheet is inclined in the clockwise direction from the rolling direction (X-axis direction). It is assumed that the direction EL of the major axis is inclined at an angle θ with respect to the rolling direction (X-axis direction) of the steel sheet. In Fig. 4B, it is assumed that the magnetization easy direction ME of the steel sheet is inclined in the counterclockwise direction from the rolling direction (X-axis direction). The long axis direction EL is inclined at an angle -θ with respect to the rolling direction (X-axis direction) of the steel plate. In FIG. 5A, the easy magnetization direction ME of the steel plate is inclined clockwise from the rolling direction (X-axis direction). The long axis direction EL is inclined at an angle -θ with respect to the rolling direction (X-axis direction) of the steel plate. In FIG. 5B, the easy magnetization direction ME of the steel plate is inclined counterclockwise from the rolling direction (X-axis direction). The long axis direction EL is inclined at an angle θ with respect to the rolling direction (X-axis direction) of the steel plate.

[0045] In the locus BT of the rotational magnetization illustrated in Figures 4A and 4B, the direction in which the long axis EL is tilted from the X-axis direction and the direction in which the easy magnetization axis is tilted from the X-axis direction are opposite to each other. The configuration illustrated in Figure 4A and the configuration illustrated in Figure 4B are in a line-symmetrical relationship with respect to the X-axis. Therefore, the case where clockwise (CW) rotational magnetization is applied in the configuration illustrated in Figure 4A is equivalent to the case where counterclockwise (CCW) rotational magnetization is applied in the configuration illustrated in Figure 4B.

[0046] On the other hand, in the locus BT of the rotational magnetization illustrated in Figures 5A and 5B, the direction in which the long axis EL is tilted from the X-axis direction is the same as the direction in which the easy magnetization axis is tilted from the X-axis direction. The configuration illustrated in Figure 5A and the configuration illustrated in Figure 5B are in a line-symmetrical relationship with respect to the X-axis. Therefore, the case where clockwise (CW) rotational magnetization is applied in the configuration illustrated in Figure 5A is equivalent to the case where counterclockwise (CCW) rotational magnetization is applied in the configuration illustrated in Figure 5B.

[0047] As described above, it is difficult to know in advance how the magnetization easy direction is inclined with respect to the rolling direction. Even if the relationship between the magnetization easy direction and the rolling direction is known, the relationship between the long axis direction of the rotational magnetization and the magnetization easy direction may become unclear due to an angle misalignment when the analysis target is set in the measurement device 20. However, regardless of whether the magnetization easy direction is inclined clockwise or counterclockwise with respect to the rolling direction, the influence of the rotational direction on the measurement result of the magnetic field intensity vector H is reduced by applying two types of rotational magnetization that are line-symmetric with respect to the X-axis and averaging the measurement results of the magnetic field intensity vector H generated by each of them. Specifically, the control unit 12 averages the measurement result of the magnetic field intensity vector H obtained by applying the rotational magnetization clockwise (CW) along the locus BT described in FIG. 4A and the measurement result of the magnetic field intensity vector H obtained by applying the rotational magnetization counterclockwise (CCW) along the locus BT described in FIG. 5A. The magnetic field intensity vector calculated by averaging is also called the average magnetic field intensity vector.

[0048] 4A and 5A, the magnetization easy direction is inclined clockwise with respect to the X-axis direction. Therefore, the average magnetic field strength vector when the magnetization easy direction is inclined clockwise with respect to the X-axis direction is H CW4A, the angle when the long axis direction is tilted counterclockwise with respect to the X-axis direction is represented by θ. The measurement result of the magnetic field strength vector H obtained by applying rotational magnetization in a clockwise (CW) direction along the locus BT illustrated in FIG. 4A is represented by H(Bm,α,θ,CW). Here, Bm is the maximum magnetic flux density. Also, as illustrated in FIG. 5A, the angle when the long axis direction is tilted clockwise with respect to the X-axis direction is represented by -θ. The measurement result of the magnetic field strength vector H obtained by applying rotational magnetization in a counterclockwise (CCW) direction along the locus BT illustrated in FIG. 5A is represented by H(Bm,α,-θ,CCW). H CW is calculated as the average of H(Bm,α,θ,CW) and H(Bm,α,-θ,CCW). The averaging reduces the influence of clockwise (CW) and counterclockwise (CCW) rotations, so H CW is H CW It is expressed as (Bm,α,θ).α is also referred to as a predetermined axial ratio.θ is also referred to as a first angle.-θ is also referred to as a second angle. The first angle and the second angle have a positive and negative opposite relationship. The rotational magnetization applied clockwise (CW) along the locus BT illustrated in FIG. 4A is also referred to as a first elliptical magnetization. The rotational magnetization applied counterclockwise (CCW) along the locus BT illustrated in FIG. 5A is also referred to as a second elliptical magnetization. The magnetic field strength vector H when the first elliptical magnetization is applied is also referred to as a first magnetic field strength vector. The magnetic field strength vector H when the second elliptical magnetization is applied is also referred to as a second magnetic field strength vector.

[0049] H CW The X-axis and Y-axis components of H x-CW and H y-CW The X-axis and Y-axis components of H(Bm,α,θ,CW) are expressed as H x (Bm,α,θ,CW) and H y (Bm,α,θ,CW). The X-axis component and Y-axis component of H(Bm,α,-θ,CCW) are H x (Bm,α,-θ,CCW) and H y Let it be expressed as (Bm,α,-θ,CCW). H x-CWand H y-CW The calculation result is expressed by the following formula (1): H x-CW For H, the signs are the same along the X axis, so the average is calculated by adding them together and dividing by 2. y-CW Since the values ​​of are linearly symmetric, the signs are reversed along the Y axis, so the average is calculated by subtracting and dividing by 2.

number

[0050] The control unit 12 may calculate the magnetic flux density vector B applied to the analysis target based on the rotational magnetization (rotational magnetic flux) applied to the analysis target. The control unit 12 may acquire the measurement result of the magnetic flux density vector B from the measurement device 20. The control unit 12 may average the measurement results of the magnetic flux density vector B corresponding to the first elliptical magnetization and the second elliptical magnetization used to calculate the average magnetic field strength vector, and calculate the average magnetic flux density vector. The control unit 12 may generate a data set of two-dimensional magnetic properties by associating the average magnetic field strength vector with the average magnetic flux density vector. The magnetic flux density vector B corresponding to the first elliptical magnetization is also referred to as the first magnetic flux density vector. The magnetic flux density vector B corresponding to the second elliptical magnetization is also referred to as the second magnetic flux density vector.

[0051] The measurement result of the magnetic flux density vector B when a rotational magnetization is applied clockwise (CW) along the locus BT illustrated in FIG. 4A is expressed as B(Bm, α, θ, CW). The measurement result of the magnetic flux density vector B when a rotational magnetization is applied counterclockwise (CCW) along the locus BT illustrated in FIG. 5A is expressed as B(Bm, α, -θ, CCW). The average magnetic field strength vector H CW The corresponding average magnetic field strength vector B CW is calculated as the average of B(Bm,α,θ,CW) and B(Bm,α,-θ,CCW). CW The X-axis and Y-axis components of x-CW and B. y-CW The X-axis and Y-axis components of B(Bm,α,θ,CW) are expressed as follows: x(Bm,α,θ,CW) and B y Let B(Bm,α,θ,CW) be the X-axis component and Y-axis component of B(Bm,α,-θ,CCW), respectively. x (Bm,α,-θ,CCW) and B y Let it be expressed as (Bm,α,-θ,CCW). B x-CW and B. y-CW The calculation result is expressed by the following formula (2). x-CW Since the signs of the x-axis directions are the same, the average is calculated by adding them and dividing by 2. y-CW Since the values ​​of are linearly symmetric, the signs are reversed along the Y axis, so the average is calculated by subtracting and dividing by 2.

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[0052] The control unit 12 may calculate the average magnetic field strength vector and the average magnetic flux density vector based on the measurement results obtained when the rotational magnetization exemplified in FIG. 4B and FIG. 5B is applied.

[0053] 4B and 5B, the magnetization easy direction is inclined counterclockwise with respect to the X-axis direction. Therefore, when the magnetization easy direction is inclined clockwise with respect to the X-axis direction, the average magnetic field strength vector is H CCW As illustrated in FIG. 5B, the angle when the long axis direction is tilted counterclockwise with respect to the X-axis direction is represented by θ. The measurement result of the magnetic field strength vector H obtained by applying rotational magnetization counterclockwise (CCW) along the locus BT illustrated in FIG. 5B is represented by H(Bm, α, θ, CCW). As illustrated in FIG. 4B, the angle when the long axis direction is tilted clockwise with respect to the X-axis direction is represented by -θ. The measurement result of the magnetic field strength vector H obtained by applying rotational magnetization clockwise (CW) along the locus BT illustrated in FIG. 4B is represented by H(Bm, α, -θ, CW). H CCWis calculated as the average of H(Bm,α,θ,CCW) and H(Bm,α,-θ,CW). The averaging reduces the influence of clockwise (CW) and counterclockwise (CCW) rotations, so H CCW is H CCW (Bm,α,θ). The rotational magnetization applied counterclockwise (CCW) along the locus BT illustrated in FIG. 5B is also referred to as the third elliptical magnetization. The rotational magnetization applied clockwise (CW) along the locus BT illustrated in FIG. 4B is also referred to as the fourth elliptical magnetization. The magnetic field strength vector H when the third elliptical magnetization is applied is also referred to as the third magnetic field strength vector. The magnetic field strength vector H when the fourth elliptical magnetization is applied is also referred to as the fourth magnetic field strength vector.

[0054] H CCW The X-axis and Y-axis components of H x-CCW and H y-CCW The X-axis and Y-axis components of H(Bm,α,θ,CCW) are respectively expressed as H x (Bm, α, θ, CCW) and H y (Bm,α,θ,CCW). The X-axis component and Y-axis component of H(Bm,α,-θ,CW) are H x (Bm,α,-θ,CW) and H y Let it be expressed as (Bm,α,-θ,CW). H x-CCW and H y-CCW The calculation result is expressed by the following formula (3): H x-CCW For H, the signs are the same along the X axis, so the average is calculated by adding them together and dividing by 2. y-CCW Since the values ​​of are linearly symmetric, the signs are reversed along the Y axis, so the average is calculated by subtracting and dividing by 2.

number

[0055] The control unit 12 may average the measurement results of the magnetic flux density vector B corresponding to the third elliptical magnetization and the fourth elliptical magnetization used to calculate the average magnetic field strength vector, and calculate the average magnetic flux density vector. The control unit 12 may generate a data set of two-dimensional magnetic properties by associating the average magnetic field strength vector with the average magnetic flux density vector. The magnetic flux density vector B corresponding to the third elliptical magnetization is also referred to as the third magnetic flux density vector. The magnetic flux density vector B corresponding to the fourth elliptical magnetization is also referred to as the fourth magnetic flux density vector.

[0056] The measurement result of the magnetic flux density vector B when a rotational magnetization is applied counterclockwise (CCW) along the locus BT illustrated in FIG. 5B is expressed as B(Bm, α, θ, CCW). The measurement result of the magnetic flux density vector B when a rotational magnetization is applied clockwise (CW) along the locus BT illustrated in FIG. 4B is expressed as B(Bm, α, -θ, CW). The average magnetic field strength vector H CCW The average magnetic flux density vector B CCW is calculated as the average of B(Bm,α,θ,CCW) and B(Bm,α,-θ,CW). CCW The X-axis and Y-axis components of x-CCW and B. y-CCW The X-axis and Y-axis components of B(Bm,α,θ,CCW) are respectively B x (Bm,α,θ,CCW) and B y Let B(Bm,α,θ,CCW) be the X-axis component and Y-axis component of B(Bm,α,-θ,CW), respectively. x (Bm,α,-θ,CW) and B y Let it be expressed as (Bm,α,-θ,CW). B x-CCW and B. y-CCW The calculation result is expressed by the following formula (4). x-CCW Since the signs of the x-axis directions are the same, the average is calculated by adding them and dividing by 2. y-CCW Since the values ​​of are linearly symmetric, the signs are reversed along the Y axis, so the average is calculated by subtracting and dividing by 2.

number

[0057] The combination of the first elliptical magnetization and the second elliptical magnetization may be replaced by a combination of the third elliptical magnetization and the fourth elliptical magnetization. The control unit 12 may obtain measurement results when the first elliptical magnetization, the second elliptical magnetization, the third elliptical magnetization, and the fourth elliptical magnetization are applied, respectively. The control unit 12 may calculate an average magnetic field intensity vector by averaging the measurement results of the first magnetic field intensity vector, the second magnetic field intensity vector, the third magnetic field intensity vector, and the fourth magnetic field intensity vector. In this way, the influence of the rotation direction of the rotational magnetization can be further reduced.

[0058] The control unit 12 may calculate the average magnetic field strength vector and the average magnetic flux density vector for various combinations of Bm, α, and θ, and generate a data set of two-dimensional magnetic properties in which the average magnetic field strength vector and the average magnetic flux density vector correspond to each other. The control unit 12 can obtain data on alternating magnetization (alternating magnetic flux) by setting the value of α to 0.

[0059] The control unit 12 may generate a data set of the two-dimensional magnetic properties including the case where the value of θ is 0. When the value of θ is 0, the first elliptical magnetization and the fourth elliptical magnetization are equivalent to each other. Also, the second elliptical magnetization and the third elliptical magnetization are equivalent to each other.

[0060] The control unit 12 may set a first angle, represented by θ, to at least two different values, calculate an average magnetic field strength vector and an average magnetic flux density vector for each setting of the first angle, and add these combinations to the data set of the two-dimensional magnetic properties.

[0061] The control unit 12 performs electromagnetic field analysis based on the data set of two-dimensional magnetic properties of the object to be analyzed, generated as described above, thereby making it possible to predict the excitation characteristics of an iron core when the object to be analyzed is used as a material for the iron core.

[0062] The control unit 12 may perform an analysis based on a data set combining an average magnetic field strength vector and an average magnetic flux density vector calculated based on the first elliptical magnetization and the second elliptical magnetization, and an analysis based on a data set combining an average magnetic field strength vector and an average magnetic flux density vector calculated based on the third elliptical magnetization and the fourth elliptical magnetization. The average magnetic field strength vector and the average magnetic flux density vector calculated based on the first elliptical magnetization and the second elliptical magnetization are also referred to as the first average magnetic field strength vector and the first average magnetic flux density vector, respectively. The average magnetic field strength vector and the average magnetic flux density vector calculated based on the third elliptical magnetization and the fourth elliptical magnetization are also referred to as the second average magnetic field strength vector and the second average magnetic flux density vector, respectively. The control unit 12 may obtain a result of the analysis based on the data set combining the first average magnetic field strength vector and the first average magnetic flux density vector as a first analysis result. The control unit 12 may obtain a result of the analysis based on the data set combining the second average magnetic field strength vector and the second average magnetic flux density vector as a second analysis result. The control unit 12 may obtain an average analysis result by averaging the first analysis result and the second analysis result, thereby improving the accuracy of the electromagnetic field analysis.

[0063] (Example) As an electromagnetic field analysis method, for example, an E&S model or an E&SS model can be used. In this embodiment, an electromagnetic field analysis using the E&S model is described. In the E&S model, in order to express magnetic properties in one dimension (alternating condition) and two dimensions (rotating magnetic flux condition) taking hysteresis into account, the magnetic field strength H is modeled by the following equations (5) and (6) in relation to not only the magnetic flux density B but also the derivative of the magnetic flux density B that represents an increase or decrease in the magnetic flux density B.

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[0064] In the above formula, the magnetic resistance coefficient v xr ,v xi,v yr and v yi is determined based on the measurement results of the BH loop (two-dimensional magnetic property data set) obtained by the measurement device 20. Specifically, the magnetic resistance coefficient is determined under conditions in which the maximum magnetic flux density Bm, the ellipticity α (axial ratio), and the inclination angle θ are changed to various values ​​and combined. The range and measurement increment of the maximum magnetic flux density Bm, the ellipticity α, and the inclination angle θ are changed depending on the design of the target electric device (transformer, motor, etc.), so they are not particularly specified. In general, it is preferable to measure the maximum magnetic flux density between 0.5 and 2.0 T (tesla) in increments of 0.1 T, the ellipticity between 0 and 1 in increments of 0.05, and the inclination angle between -180 degrees and +180 degrees (-90 degrees to +90 degrees when symmetry is taken into account) in increments of 5 degrees.

[0065] From the results of the above measurements, the average magnetic field strength vector and the average magnetic flux density vector are calculated as described above, and the magnetic resistance coefficient v xr ,v xi ,v yr and v yi is determined.

[0066] The obtained magnetoresistance coefficient v xr ,v xi ,v yr and v yi The data set is the average magnetic field strength vector H CW and the average magnetic flux density vector B CW and the average magnetic field strength vector H CCW and the average magnetic flux density vector B CCWand a data set determined from a combination of the above. The control unit 12 executes an electromagnetic field analysis based on the relationship between the vector quantities of the magnetic field strength H and the magnetic flux density B modeled by the data set of each magnetic reluctance coefficient. In this case, except for the condition where data exists by performing magnetic measurement, the relationship between the vector quantities of the magnetic field strength H and the magnetic flux density B is obtained by coefficient interpolation of the magnetic reluctance coefficient. In this embodiment, the method of electromagnetic field analysis may be, but is not limited to, a method of analyzing Maxwell's equations by the finite element method. In addition to the finite element method, other discretization analysis methods such as the boundary element method may be used. A method that can perform analysis by referring to detailed shape information is suitable.

[0067] The magnetic property results (such as iron loss) obtained from each of the two sets of data, CW and CCW, can be further averaged to obtain accurate results.

[0068] The accuracy of the electromagnetic field analysis was verified using a three-phase, three-legged transformer core. First, as shown in Fig. 6 and Table 1, five three-phase, three-legged model transformer cores with core shapes P1 to P5 were fabricated using four types of grain-oriented electrical steel sheets Q1 to Q4 shown in Table 2. [Table 1] [Table 2]

[0069] The legs of the core were wound with 60 turns, and three-phase excitation was performed with a maximum magnetic flux density of 1.7 T (tesla) and a frequency of 50 Hz (hertz), and the transformer iron loss was measured using the wattmeter method. The results are shown in Table 3.

[0070] From the grain-oriented electromagnetic steel sheet used to make the transformer core, a sample for two-dimensional magnetic measurement measuring 80 mm square was prepared as the steel sheet to be analyzed. The maximum magnetic flux density of the sample was measured from 0.5 to 1.95 T (tesla) in increments of 0.05 T, the ellipticity from 0 to 0.8 in increments of 0.05, and the inclination angle from -180 degrees to +180 degrees in increments of 5 degrees. From the results, the magnetic reluctance coefficient v xr ,v xi ,v yr and v yi In this case, the magnetoresistance coefficient v was calculated in each of the cases where the results of applying clockwise and counterclockwise rotational magnetization were averaged and where the averaging process was not performed. xr ,v xi ,v yr and v yi The magnetic resistance coefficient v xr ,v xi ,v yr and v yi Based on the relationship between the vector quantities of magnetic field strength H and magnetic flux density B modeled using the above, an electromagnetic field analysis was performed, and the above transformer iron loss was actually measured, and the transformer iron loss of the three-phase three-leg model transformer iron core was calculated. The calculation results are shown in Table 3. [Table 3]

[0071] The transformer iron loss calculated using the method according to this embodiment (a method of averaging the results of applying clockwise rotational magnetization and the results of applying counterclockwise rotational magnetization) could be calculated with an accuracy of within 2% of the actually measured transformer iron loss. The average of the actual measurement difference was 0.7%. In contrast, when the averaging process was not performed, the calculation accuracy was significantly worse than when the method according to this embodiment was applied under all conditions. The average of the actual measurement difference was 13.6%.

[0072] (Example of analysis procedure) In the analysis system 1 according to this embodiment, an example of the procedure of a dataset generation method for generating a dataset as an analysis method executed by the control unit 12 of the analysis device 10 will be described based on the procedure of the flowchart illustrated in Fig. 7. The dataset generation method may be realized as a dataset generation program or a computer program executed by a processor constituting the control unit 12 or a computer constituting the analysis device 10. The dataset generation program or the computer program may be stored in a non-transitory computer-readable medium.

[0073] The control unit 12 applies a first elliptical magnetization to the analysis object by using the measurement device 20 (step S1). The control unit 12 measures a first magnetic field strength vector and a first magnetic flux density vector by using the measurement device 20 (step S2).

[0074] The control unit 12 applies a second elliptical magnetization to the analysis object by using the measurement device 20 (step S3). The control unit 12 measures a second magnetic field strength vector and a second magnetic flux density vector by using the measurement device 20 (step S4).

[0075] The control unit 12 calculates the average magnetic field strength vector and the average magnetic flux density vector (step S5). The control unit 12 adds data combining the calculation results of the average magnetic field strength vector and the average magnetic flux density vector to update the data set of the two-dimensional magnetic properties (step S6). After executing the procedure of step S6, the control unit 12 ends the execution of the procedure of the flowchart in FIG. 7.

[0076] The control unit 12 may execute, as the analysis method, an electromagnetic field analysis method for analyzing an electromagnetic field using a data set generated by the data set generation method. The electromagnetic field analysis method may be realized as an electromagnetic field analysis program or a computer program executed by a processor constituting the control unit 12 or a computer constituting the analysis device 10. The electromagnetic field analysis program or the computer program may be stored in a non-transitory computer-readable medium.

[0077] As described above, the analysis system 1, the analysis device 10, and the analysis method according to the present embodiment can reduce the influence of the rotation direction of the rotational magnetization in the electromagnetic field analysis using the two-dimensional magnetic properties, thereby improving the accuracy of the electromagnetic field analysis.

[0078] Although the embodiments of the present disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art can make various modifications or alterations based on the present disclosure. Therefore, it should be noted that these modifications or alterations are included in the scope of the present disclosure. For example, the functions included in each component or each step can be rearranged so as not to be logically inconsistent, and multiple components or steps can be combined into one or divided. The embodiments of the present disclosure can also be realized as a program executed by a processor included in the device or a storage medium on which a program is recorded. It should be understood that these are also included in the scope of the present disclosure. [Explanation of symbols]

[0079] 1 Analysis system 10 Analysis device (12: control unit, 14: memory unit, 16: interface) 20 Measuring Equipment

Claims

1. A method for acquiring two-dimensional magnetic properties used to analyze an electromagnetic field of an analysis target by capturing magnetic field strength and magnetic flux density as vector quantities, comprising: Measuring a first magnetic field intensity vector generated in the analysis object in response to a first elliptical magnetization applied clockwise along an ellipse having a major axis and a minor axis with a predetermined axial ratio, the major axis of which is inclined at a first angle with respect to the rolling direction of the analysis object; measuring a second magnetic field intensity vector generated in the analysis object in response to a second elliptical magnetization applied counterclockwise along an ellipse having a major axis and a minor axis with the predetermined axial ratio, the major axis of which is inclined by a second angle, the second angle being opposite in sign to the first angle, with respect to the rolling direction of the analysis object; averaging the first magnetic field strength vector and the second magnetic field strength vector to calculate a first average magnetic field strength vector; calculating a first average magnetic flux density vector by averaging a first magnetic flux density vector corresponding to the first elliptical magnetization and a second magnetic flux density vector corresponding to the second elliptical magnetization; generating a data set of the two-dimensional magnetic properties that corresponds to the first average magnetic field strength vector and the first average magnetic flux density vector, the predetermined axial ratio, and the first angle; Dataset generation methods including:

2. The method of claim 1 , wherein calculating the first average magnetic flux density vector comprises measuring the first magnetic flux density vector and the second magnetic flux density vector.

3. measuring a third magnetic field intensity vector generated in the analysis object in response to a third elliptical magnetization applied counterclockwise along an ellipse having a major axis and a minor axis with the predetermined axial ratio and whose major axis is inclined by the first angle with respect to the rolling direction of the analysis object; measuring a fourth magnetic field intensity vector generated in the analysis object in response to a fourth elliptical magnetization applied clockwise along an ellipse having a major axis and a minor axis with the predetermined axial ratio and whose major axis is inclined by the second angle with respect to the rolling direction of the analysis object; calculating a second average magnetic field strength vector by averaging the third magnetic field strength vector and the fourth magnetic field strength vector; calculating a second average magnetic flux density vector by averaging a third magnetic flux density vector corresponding to the third elliptical magnetization and a fourth magnetic flux density vector corresponding to the fourth elliptical magnetization; generating a data set of the two-dimensional magnetic properties that corresponds to the second average magnetic field strength vector and the second average magnetic flux density vector, the predetermined axial ratio, and the first angle; The data set generation method of claim 1 , further comprising:

4. The method of claim 3 , wherein calculating the second average magnetic flux density vector comprises measuring the third magnetic flux density vector and the fourth magnetic flux density vector.

5. setting the first angle to at least two different values; the step of generating a data set of the two-dimensional magnetic characteristics includes a step of adding the first average magnetic field strength vector and the first average magnetic flux density vector calculated for each set value of the first angle to the data set of the two-dimensional magnetic characteristics in association with each set value. The data set generating method according to claim 1 or 2.

6. The method further comprising the step of setting the first angle to at least two different values; the step of generating a data set of the two-dimensional magnetic characteristics includes a step of adding the first average magnetic field strength vector, the first average magnetic flux density vector, and the second average magnetic field strength vector, and the second average magnetic flux density vector, which are calculated for each set value of the first angle, to the data set of the two-dimensional magnetic characteristics in association with each set value. The data set generating method according to claim 3 or 4.

7. 3. An electromagnetic field analysis method comprising a step of analyzing an electromagnetic field of an iron core using an analysis object having two-dimensional magnetic properties specified by a dataset of two-dimensional magnetic properties combining a first average magnetic field strength vector and a first average magnetic flux density vector, the dataset being generated by executing the dataset generation method according to claim 1 or 2.

8. 5. An electromagnetic field analysis method comprising a step of analyzing an electromagnetic field of an iron core using an analysis object having two-dimensional magnetic properties specified by a dataset of two-dimensional magnetic properties combining a second average magnetic field strength vector and a second average magnetic flux density vector, the dataset being generated by executing the dataset generation method according to claim 3 or 4.

9. a step of acquiring a first analysis result by analyzing an electromagnetic field of an iron core using an analysis object having two-dimensional magnetic characteristics specified by a data set of two-dimensional magnetic characteristics that combines a first average magnetic field strength vector and a first average magnetic flux density vector generated by executing the data set generation method according to claim 1 or 2; a step of analyzing an electromagnetic field of an iron core using an analysis object having two-dimensional magnetic properties specified by the data set, the data set being generated by executing the data set generation method according to claim 3 or 4, and acquiring a second analysis result; averaging the first analysis result and the second analysis result to obtain an average analysis result; An electromagnetic field analysis method including:

10. A computer program that causes a computer to execute each step of the data set generation method according to any one of claims 1 to 4.

11. A computer program that causes a computer to execute each step of the data set generation method according to claim 5.

12. A computer program that causes a computer to execute each step of the electromagnetic field analysis method according to claim 6.

13. A computer program that causes a computer to execute each step of the electromagnetic field analysis method according to claim 7.

14. A computer program that causes a computer to execute each step of the electromagnetic field analysis method according to claim 8.

15. A computer program that causes a computer to execute each step in the electromagnetic field analysis method described in claim 9.

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