JP6631368B2 - BH curve creation device, electromagnetic field analysis device, BH curve creation method, and computer program - Google Patents

Description

  The present invention relates to a BH curve creation device, an electromagnetic field analysis device, a BH curve creation method, and a computer program, and more particularly, to a BH curve indicating the relationship between magnetic flux density and magnetic field intensity by interpolating measurement data of magnetic flux density and magnetic field intensity. It is suitable for use to create.

  2. Description of the Related Art Conventionally, in order to evaluate iron loss of a magnetic material such as an electromagnetic steel sheet, an electromagnetic field analysis based on Maxwell's equation has been performed. When considering the phenomenon that the magnetic resistivity (reciprocal of magnetic permeability) included in Maxwell's equation used in the electromagnetic field analysis changes according to the magnetic flux density, a BH curve showing the relationship between the magnetic flux density and the magnetic field strength in performing the electromagnetic field analysis Need to give. This is because the measurement of the magnetic flux density and the magnetic field strength is performed under discrete measurement conditions, whereas the electromagnetic field analysis (numerical calculation) requires arbitrary values of the magnetic flux density and the magnetic field strength. For this purpose, a continuous BH curve is created by interpolating discretely measured "magnetic flux density and magnetic field strength measurement data".

  Conventionally, as a method of interpolating the measurement data of the magnetic flux density and the magnetic field strength, a section between two adjacent measurement points is defined as one section, and in each section, the measurement points at both ends are approximated by a predetermined formula. That is, a method such as piecewise linear interpolation, spline interpolation, and Akima interpolation has been adopted (see Non-Patent Document 1).

Japanese Patent No. 3643334

Norio Takahashi, "Three-dimensional finite element method-basics of magnetic field analysis technology-", August 2006, IEEJ, p. 98-102 Richard M. Bozorth, "FERROMAGNETISM", 1951, IEEE PRESS, p. 77 Japanese Industrial Standards Magnetic steel sheet single sheet magnetic test method, Japan Standards Association, published October 31, 1996

  However, in the above-described conventional technique, a curve is created such that the BH curve always passes through the measurement point. Therefore, if the variation in the measurement data becomes large due to the measurement error between the magnetic flux density and the magnetic field strength, in the above-described conventional technique, the magnetic resistance (or the magnetic permeability; hereinafter the same) represented by the ratio between the magnetic flux density and the magnetic field strength. However, there is a problem that the smoothness does not become smooth with respect to the change in the magnetic field strength (the differential coefficient of the curve representing the relationship between the magnetic resistivity (magnetic permeability) and the magnetic field strength changes rapidly). In particular, in a grain-oriented electrical steel sheet having a strong anisotropy of magnetic properties, since the magnetic properties greatly change with a slight change in the angle of the magnetic flux density with respect to the rolling direction, the measurement error of the magnetic flux density and the magnetic field strength tends to increase. However, such a problem becomes remarkable.

  The present invention has been made in view of the above problems, and has as its object to create a BH curve so that the magnetic permeability changes more smoothly with respect to a change in magnetic field strength than in the past.

The BH curve creation device according to the present invention performs a calculation by a computer to obtain a continuous relationship between a magnetic field intensity H acting on a magnetic material and a magnetic flux density B generated in the magnetic material by applying the magnetic field intensity H. A BH curve creating apparatus for creating a BH curve, wherein the magnetic field strength H when a plurality of discrete values of magnetic field strength H are applied to a magnetic material for which the BH curve is created, BH measurement data input means for inputting magnetic property measurement data, which is measurement data of the magnetic flux density B in the magnetic material generated by applying the magnetic field strength H, and saturation of the magnetic material for which the BH curve is created and the magnetic flux density B _s, a saturation magnetic flux density, magnetic field strength inputting section for inputting a saturation magnetic characteristic measurement data is measurement data of the magnetic field intensity H _s which corresponds to the saturation flux density B _s, the BH A magnetic field different from the magnetic field strength H in the magnetic property measurement data, using the magnetic property measurement data input by the constant data input means and the saturation magnetic property measurement data input by the saturation magnetic flux density / magnetic field strength input means. BH interpolation formula setting means for setting a BH interpolation formula representing the BH curve in order to obtain a magnetic flux density B with respect to the intensity H, wherein the BH interpolation formula sets the magnetic field intensity H from 0 to the magnetic characteristic. and BH interpolation formula of the first region to the maximum value of the measured data, the magnetic field intensity H is said from the maximum value of magnetic characteristic measurement data, the second to the magnetic field intensity H _s which corresponds to the saturation flux density B _s and BH interpolation type region, the magnetic field intensity H is, anda BH interpolation formula above magnetic field intensity H _s which corresponds to the saturation flux density B _s of the third region, the BH interpolation equation of the first region Is the first area. The term of the power of the magnetic flux density B representing a dominant magnetic property in a region having a relatively small value, and the dominant magnetic property in a region having a relatively large value of the first region; is a single formula expressing the magnetic field strength H in the linear combination of the power section of the magnetic flux density B, the BH interpolation equation of the third region, the saturated magnetic flux density B _s, corresponding to the saturation flux density B _s From the point represented by the magnetic field strength H _s , and the slope of the increment of the magnetic flux density B with respect to the magnetic field strength H is a linear unitary equation of vacuum permeability μ ₀ , The value and differential coefficient at the starting point of the BH interpolation equation are the same as the value and differential coefficient at the end point of the BH interpolation equation in the first area, and the value and differential coefficient at the end point of the BH interpolation equation in the second area. The coefficient is a value and a value at the starting point of the BH interpolation formula in the third area. Beauty is the same as the differential coefficient, and is a single formula expressing that permeability mu or relative permeability mu _r with increasing magnetic field intensity H decreases monotonically, the BH interpolation formula setting unit, the BH After calculating the undetermined coefficient of the interpolation formula of the first area based on the magnetic property measurement data input by the measurement data input means, and calculating the undetermined coefficient of the BH interpolation formula of the first area, It is characterized in that the undetermined coefficient of the BH interpolation formula of the area 2 is calculated.
The electromagnetic field analysis device of the present invention includes an electromagnetic field analysis unit that performs calculation by a computer using the BH interpolation formula obtained by the BH curve creation device and analyzes the electromagnetic field of the same type of magnetic material as the BH interpolation formula. It is characterized.

According to the BH curve creation method of the present invention, a computer calculates a continuous relationship between a magnetic field intensity H acting on a magnetic material and a magnetic flux density B generated in the magnetic material by applying the magnetic field intensity H. A BH curve creating method for creating a BH curve, wherein a magnetic field strength H of a plurality of discrete values is applied to a magnetic material for which the BH curve is created, A BH measurement data input step of inputting magnetic property measurement data, which is measurement data of a magnetic flux density B in the magnetic material generated by applying the magnetic field strength H, and a saturation of the magnetic material for which the BH curve is created. and the magnetic flux density B _s, a saturation magnetic flux density, magnetic field strength input step of inputting a saturation magnetic characteristic measurement data is measurement data of the magnetic field intensity H _s which corresponds to the saturation flux density B _s, the BH A magnetic field different from the magnetic field strength H in the magnetic property measurement data using the magnetic property measurement data input in the constant data input step and the saturation magnetic property measurement data input in the saturation magnetic flux density / magnetic field strength input step. A BH interpolation formula setting step of setting a BH interpolation formula representing the BH curve, in order to obtain a magnetic flux density B with respect to the intensity H, wherein the BH interpolation formula sets the magnetic field intensity H from 0 to the magnetic characteristic. and BH interpolation formula of the first region to the maximum value of the measured data, the magnetic field intensity H is said from the maximum value of magnetic characteristic measurement data, the second to the magnetic field intensity H _s which corresponds to the saturation flux density B _s and BH interpolation type region, the magnetic field intensity H is, anda BH interpolation formula above magnetic field intensity H _s which corresponds to the saturation flux density B _s of the third region, the BH interpolation equation of the first region Is the first area. The term of the power of the magnetic flux density B representing a dominant magnetic property in a region having a relatively small value, and the dominant magnetic property in a region having a relatively large value of the first region; is a single formula expressing the magnetic field strength H in the linear combination of the power section of the magnetic flux density B, the BH interpolation equation of the third region, the saturated magnetic flux density B _s, corresponding to the saturation flux density B _s From the point represented by the magnetic field strength H _s , and the slope of the increment of the magnetic flux density B with respect to the magnetic field strength H is a linear unitary equation of vacuum permeability μ ₀ , The value and differential coefficient at the starting point of the BH interpolation equation are the same as the value and differential coefficient at the end point of the BH interpolation equation in the first area, and the value and differential coefficient at the end point of the BH interpolation equation in the second area. The coefficient is a value and a value at the starting point of the BH interpolation formula in the third area. Beauty is the same as the differential coefficient, and is a single formula expressing that permeability mu or relative permeability mu _r with increasing magnetic field intensity H decreases monotonically, the BH interpolation equation setting step, the BH After calculating the undetermined coefficient of the interpolation formula of the first area based on the magnetic property measurement data input in the measurement data input step, and calculating the undetermined coefficient of the BH interpolation formula of the first area, It is characterized in that the undetermined coefficient of the BH interpolation formula of the area 2 is calculated.
The electromagnetic field analysis method of the present invention includes an electromagnetic field analysis step of performing calculation by a computer using a BH interpolation formula obtained by a BH curve creation method and analyzing an electromagnetic field of the same type of magnetic material as the BH interpolation formula. It is characterized.

  A computer program according to the present invention causes a computer to function as each unit of the BH curve creation device.

According to the present invention, the BH interpolation formula for the first area from the magnetic field strength H of 0 to the maximum value of the magnetic property measurement data, and the magnetic field strength H are calculated from the maximum value of the magnetic property measurement data. and BH interpolation equation of the second region to the magnetic field intensity H _s which corresponds to the saturation flux density B _s, the magnetic field intensity H is, the saturation magnetic flux density B corresponding magnetic field strength _s H _s or more BH of the third region The BH curve is expressed by the interpolation formula. Then, the BH interpolation formula for each of the first region and the third region is set as a BH interpolation formula reflecting a physical phenomenon in the region. Further, the value and the differential coefficient at the starting point of the BH interpolation equation in the second area are the same as the value and the differential coefficient at the end point of the BH interpolation equation in the first area, and the BH interpolation equation in the second area is different. The value and differential coefficient at the end point are set to be the same as the value and differential coefficient at the start point of the BH interpolation formula in the third area. Therefore, the BH curve can be created so that the magnetic permeability changes more smoothly than before in response to a change in the magnetic field strength.

FIG. 2 is a diagram illustrating a functional configuration of the information processing apparatus. It is a figure which shows an example of a BH curve, and an example of a curve showing the relationship between the magnetic permeability and magnetic field intensity obtained from the said BH interpolation formula. FIG. 4 is a diagram illustrating a schematic shape of a BH curve in a first area. 6 is a flowchart illustrating an example of an operation in a BH curve creation unit. FIG. 4 is a diagram showing a BH curve in the first embodiment. It is a figure which shows the curve which represents the relationship between a relative magnetic permeability and a magnetic field intensity in each of 1st Example and a comparative example. It is a figure which shows an example of the outline of a structure of a single plate magnetic tester. It is a figure explaining an example of a cutting-out method of a sample. It is a figure which shows notionally an example of the BH curve for every angle and every stress. It is a figure showing a BH curve in a 2nd example.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
((First Embodiment))
First, a first embodiment will be described.
FIG. 1 is a diagram illustrating an example of a functional configuration of the information processing apparatus 100. The hardware of the information processing apparatus 100 illustrated in FIG. 1 can be realized by using, for example, a computer system including a CPU, a ROM, a RAM, an HDD, and various interfaces.
In FIG. 1, the information processing device 100 is roughly divided into a BH curve creation unit 110 and an electromagnetic field analysis unit 120. Note that the BH curve creation unit 110 and the electromagnetic field analysis unit 120 may be provided in separate information processing devices.

(BH curve creation unit 110)
The BH curve creation unit 110 has a BH measurement data input unit 111, a saturation magnetic flux density / magnetic field intensity input unit 112, and a BH interpolation formula creation unit 113.

<BH measurement data input unit 111>
The BH measurement data input unit 111 calculates the magnetic field strength H and the magnetic field strength when a plurality of discrete magnetic field strengths H [A / m] are applied to a magnetic material for which a BH curve is created. The measurement data of the magnetic flux density B [T] in the magnetic material generated by the action of H is input and stored in the storage medium. Name). In the present embodiment, an example will be described in which the magnetic material for which the BH curve is created is a grain-oriented electrical steel sheet, which is a type of silicon steel sheet. However, the magnetic material for which the BH curve is to be created is not limited to the grain-oriented electrical steel sheet, but may be another ferromagnetic material such as a non-oriented electrical steel sheet, or a magnetic material (preferably a soft magnetic steel sheet). If it is a magnetic material), it need not be a ferromagnetic material. The BH curve is a curve indicating a continuous relationship between a magnetic field intensity H acting on the magnetic material and a magnetic flux density B generated in the magnetic material by applying the magnetic field intensity H. Creating a BH curve refers to calculating an undetermined coefficient that is a constant other than the magnetic flux density B and the magnetic field strength H among the variables constituting a BH interpolation formula described later.

The magnetic property measurement data can be obtained by using, for example, an SST (Single Strip. Tester; single-plate magnetic tester), an Epstein tester, or the like. In these measuring devices, the magnetic flux density B within the magnetic material, the magnetizing up state to reach the saturation magnetic flux density B _s of the magnetic material, since it is generally difficult, the saturation magnetic flux density B of the magnetic material _s measurement data cannot be obtained. Therefore, the magnetic property measurement data is data of the magnetic flux density B _lower than the saturation magnetic flux density Bs and the magnetic field strength H corresponding to the magnetic flux density B. In this embodiment, the angle θ between the rolling direction RD (Rolling Direction) of the grain-oriented electrical steel sheet and the direction of the magnetic flux density B is 0 [°], and the stress σ applied to the grain-oriented electrical steel sheet is 0 °. In the state of [Pa], the magnetic property measurement data of the grain-oriented electrical steel sheet is obtained.

  The BH measurement data input unit 111 may be, for example, a CPU that acquires magnetic characteristic measurement data and stores it in an HDD or the like based on an operation of a user interface by an operator. This can be realized by acquiring the characteristic measurement data and storing it in the HDD or the like, or by the CPU acquiring the magnetic characteristic measurement data stored in the portable storage medium and storing the data in the HDD or the like.

<Saturation magnetic flux density / magnetic field intensity input unit 112>
The saturation magnetic flux density / magnetic field strength input unit 112 performs a saturation magnetic property measurement, which is measurement data of the saturation magnetic flux density B _s of the magnetic material for which the BH curve is created and the magnetic field strength H _s corresponding to the saturation magnetic flux density B _s. Data is input and stored in a storage medium.
The saturation magnetic flux density B _s and the magnetic field strength H _s corresponding to the saturation magnetic flux density B _s are obtained, for example, using a graph described in Non-Patent Document 2. That is, Non-Patent Document 2 shows the relationship between the saturation magnetic flux density B _{s of the} magnetic steel sheet measured at a certain magnetic field strength H _s and the content of Si (silicon) added to the magnetic steel sheet. A graph is shown. Therefore, the saturation magnetic flux density B _s which corresponds to the content of Si in the BH curve creation subject to magnetic material (magnetic steel sheet) by reading from the graph, the saturation magnetic flux density B _s, to the saturation flux density B _s can be obtained and the corresponding magnetic field intensity H _s.

Incidentally, the saturation magnetic flux density B _s is not necessarily obtained in this way. For example, VSM; may be measured saturation magnetic flux density B _s by (Vibrating Sample Magnetometer vibrating sample magnetometer).
The saturation magnetic flux density / magnetic field strength input unit 112 may be, for example, a CPU that acquires saturation magnetic characteristic measurement data based on an operation of a user interface by an operator and stores the measurement data in an HDD or the like, or a CPU that communicates through a communication interface. Implemented by acquiring saturation magnetic property measurement data from an external device and storing it in an HDD or the like, or by a CPU acquiring saturation magnetic property measurement data stored in a portable storage medium and storing the data in an HDD or the like it can.

<BH interpolation formula creation unit 113>
The BH interpolation formula creation unit 113 sets a BH interpolation formula representing a BH curve in order to obtain a magnetic flux density B for a magnetic field strength H different from the magnetic field strength H in the magnetic property measurement data input by the BH measurement data input unit 111. I do. Here, setting the BH interpolation formula means calculating an undetermined coefficient of the BH interpolation formula described later. The undetermined coefficient is a variable that is not determined at the time of inputting the magnetic characteristic measurement data and the saturation magnetic measurement data, among the variables other than the magnetic flux density B and the magnetic field strength H in the BH interpolation formula.
In the present embodiment, the BH curve is divided into the following three regions (1) to (3), and a BH interpolation formula is set for each of the three divided regions.
(1) An area where the magnetic field strength H is from 0 to the maximum value of the magnetic property measurement data. In the following description, this area will be referred to as a “first area” as necessary.
(2) magnetic field strength H is, the region of the maximum value of the magnetic characteristic measurement data, to the magnetic field intensity H _s which corresponds to the saturation flux density B _s. In the following description, this area will be referred to as a “second area” as necessary.
(3) the magnetic field strength H is the magnetic field strength H _s or more regions corresponding to the saturation flux density B _s. In the following description, this area is referred to as a “third area” as necessary.
The BH interpolation formulas for each of the first to third areas will be described below.

FIG. 2 is an example (FIG. 2A) of a BH curve represented by a BH interpolation formula in the entire region of a magnetic material for which a BH curve is to be created, and a magnetic permeability μ and a magnetic field strength obtained from the BH interpolation formula. FIG. 3 is a diagram illustrating an example of a curve indicating a relationship with H (FIG. 2B).
In FIG. 2A, the BH curve 201 represented by the BH interpolation formula in the entire region of the magnetic material for which the BH curve is to be created is a BH interpolation formula for the first to third regions (formula (1) described later). To (3)). Further, in FIG. 2 (a), the point where the magnetic field strength H is shown in the region of 0~H _max (●) conceptually shows the magnetic characteristic measurement data. The BH interpolation formula in each of the first to third areas is set as follows.

[First area]
In the first area, a “power term of the magnetic flux density B” representing a dominant magnetic characteristic in an area having a relatively small value in the first area, and a relative area of the first area. The expression (BH interpolation formula) representing the BH curve is expressed by a simple expression that is linearly combined with the “power term of the magnetic flux density B” representing the dominant magnetic characteristic in the region where the value is large. Specifically, in the first area, the BH interpolation equation is represented by the following equation (1).

(1) In the _{formula, a m, a n, m} , n are undetermined coefficients - a [].
The measurement range of the magnetic field strength H of the magnetic material for which the BH curve is created is a range from a value where the magnetic field strength H is close to 0 to a maximum value _Hmax of the magnetic field strength H that can be measured by the measuring device. , The magnetic flux density B corresponding to the magnetic field strength H is measured discretely. As described above, the measuring apparatus for performing this measurement, it is generally difficult to obtain measurement data of the saturation flux density B _s of the magnetic material (magnetic characteristic measurement data). Therefore, the maximum value H (maximum value) of the magnetic flux density corresponding to _max B _max of the magnetic field intensity H is a value less than the saturation magnetic flux density B _s.

FIG. 3 is a diagram illustrating an example of the outline of the BH curve in the first region.
When the magnetic characteristic measurement data is graphed with the magnetic field strength H being on the horizontal axis and the magnetic flux density B being on the vertical axis, the outline of the BH curve is S-shaped in the first region as shown in FIG. Is known to be. Therefore, the present inventors have come to the conclusion that in the first region, it is necessary to express the BH curve with a single expression representing the S-shape.

Specifically, assuming that the BH curve shown in FIG. 3A has the horizontal axis of the magnetic flux density B and the vertical axis of the magnetic field strength H, as shown in FIG. In a region where the value of the magnetic flux density B is relatively small, the magnetic field strength H is expressed by a _m ^Bm (0 <m <1). , A _n B ⁿ (n> 1). Therefore, the present inventors have conceived of expressing the BH curve (BH interpolation formula) of the first region by a single formula using these two linear combinations. For the above reasons, the BH interpolation formula for the first area is expressed by the above-described formula (1).

Unknown coefficients a _m in (1), a _n, m, n, for example, a method of determining the known undetermined coefficients proposed in the field of non-linear optimization method (simulated annealing, the non-linear least-squares method, etc.) It can be calculated by using At this time, for example, an error (for example, a sum of squares of the error) between the BH interpolation formula of the first area given the undetermined coefficients a _m , an _n , m, and n and the magnetic characteristic measurement data is reduced (for example, minimized). to) unknown coefficients a _m, can be calculated a _n, m, _n. Incidentally, undetermined coefficients a _m, a method for determining the a _n, m, n are, can be realized by a known technique and will not be described in detail.

[Third area]
The third region is a region where the magnetic flux density B is _{equal to} or higher than the saturation magnetic flux density Bs. Therefore, in the third region, the formula (BH interpolation equation) representing the BH curve, and the saturation flux density B _s, starting from the point represented by the magnetic field intensity H _s which corresponds to the saturation flux density B _s, and , The gradient of the increment of the magnetic flux density B with respect to the magnetic field strength H needs to be expressed by a single linear expression that is the magnetic permeability μ ₀ [H / m] of vacuum. Specifically, in the third area, the BH interpolation equation is represented by the following equation (2).

[Second area]
Since the BH curve needs to have continuous and smooth characteristics in the entire region, the value and differential coefficient at the starting point of the second region are the end points (magnetic characteristics) of the BH interpolation formula in the first region. The value and the differential coefficient at the end point of the second area are the same as the value and the differential coefficient at the point of the maximum value of the measurement data, and the starting point of the BH interpolation formula in the third area (the saturation magnetic characteristic measurement data). It is necessary to express the BH interpolation formula in the second region with a single formula that is the same as the value and the derivative in (point). Specifically, in the second area, the BH interpolation equation is represented by the following equation (3).

In equation (3), p and q are undetermined coefficients [-].
Magnetic characteristic measurement data is typically a data up area where the magnetic saturation occurs, the maximum value of the magnetic characteristics measurement data (the maximum value H _max of the magnetic field strength H), the saturation magnetic characteristic measurement data (saturation magnetic flux density B _s From the corresponding magnetic field strength H _s ), the magnetic permeability μ (= B / H) monotonously decreases as the magnetic field strength H increases. Therefore, as the BH interpolation formula of the second region, a single expression expressing a characteristic in which the magnetic permeability μ or the relative magnetic permeability μ _r [−] monotonously decreases with an increase in the magnetic field strength H is used, so that the magnetic saturation is obtained. from occurs region, the relationship between the magnetic flux density B and the magnetic field strength H in the region up to the saturation flux density B _s can be accurately represented.

Examples of the BH interpolation formula for the second region include an exponential function, a power function of the magnetic field strength H represented by H ^−r (r> 1), a logarithmic function multiplied by a negative value, and a negative value. And a hyperbolic tangent function (tanh) multiplied by Equation (3) shows an example in which an exponential function is used as the BH interpolation equation for the second area. The process of deriving equation (3) will be described below.

  First, a differential formula H ′ (= dH / dB) obtained by differentiating the BH interpolation formula (1) of the first region with the magnetic flux density B is represented by the following formula (4). The differential equation B ′ (= dB / dH), which is the reciprocal of the equation (4), is represented by the following equation (5). Further, a differential formula B ′ (= dB / dH) obtained by differentiating the formula (2), which is an interpolation formula for the third region, with the magnetic field strength H is expressed by the following formula (6).

In (2), the magnetic field intensity H is, when a saturation magnetic flux density B corresponding magnetic field strength _s H _s (H = H _s), the magnetic flux density B, representing the physical phenomena becomes saturated magnetic flux density B _s Equation (6) expresses a physical phenomenon in which the differential coefficient at this time becomes the vacuum magnetic permeability μ ₀ .
In deriving the BH interpolation formula for the second region, the present inventors devised the following formula (7) as the differential formula B ′ (= dB / dH) of the BH interpolation formula for the second region. (7) is a monotonically decreasing function, and the magnetic field strength H is, the value (derivative) when the saturation magnetic flux density B field strength corresponding to the _s H _s (H = H _s) is a vacuum permeability This is an equation that results in a magnetic susceptibility μ ₀ . By determining the equation (7) in this way, the saturation magnetic property measurement data (saturation magnetic flux density B _s , saturation magnetic flux density B _s) can be calculated by using the BH interpolation equation in the second area and the BH interpolation equation in the third area. the differential coefficient in the magnetic field intensity H _s) corresponding to _s may be the same.

In the equation (7), k and q are undetermined coefficients [-].
Next, the magnetic field intensity H is, when a magnetic field intensity H _s which corresponds to the saturation flux density B _s (H = H _s), the magnetic flux density B is determined the constant of integration so that the saturation flux density B _s , (7), the following equation (8) is obtained. By determining the integration constant in this manner, the end point of the BH interpolation formula in the second region and the starting point of the BH interpolation formula in the third region can have the same value.

  The following equation (11) (that is, equation (3)) is obtained by modifying equation (8) using the variable p defined by equation (10) obtained by modifying equation (9) below.

In the equation (11), the undetermined coefficients p and q can be calculated so as to satisfy both the following (A) and (B).
(A) When the magnetic field strength H is the maximum value of the magnetic property measurement data (the maximum value H _max of the magnetic field strength H) (H = H _max ), the magnetic flux density B becomes the maximum value (magnetic flux) of the magnetic property measurement data. The maximum value _Bmax of the density B is obtained (B = _Bmax ).
(B) When the magnetic field strength H is the maximum value of the magnetic property measurement data (the maximum value H _max of the magnetic field strength H) (H = H _max ), the differential equation B obtained by differentiating the equation (11) with the magnetic field strength H The value of '(= dB / dH) becomes the value of the differential expression B' (Expression (5)) corresponding to the interpolation expression (Expression (1)) in the first area (B '= (B ′ in equation (5)).

By (A), the value can be made the same at the starting point of the BH interpolation formula in the second area and the end point of the BH interpolation formula in the first area. Further, according to (B), the maximum value of the magnetic property measurement data (the maximum value B _{max of} the magnetic flux density B and the maximum value of the magnetic field intensity H) are obtained by the BH interpolation formula in the second region and the BH interpolation formula in the first region. The derivative at the value _Hmax ) can be the same.
As is clear from the item (B), in the present embodiment, after calculating the undetermined coefficients a _m , B _n , m, and n of the BH interpolation formula of the first area, the BH interpolation formula of the second area is calculated. Undetermined coefficients p and q are calculated.

  In FIG. 3A, by defining the BH interpolation formulas of the first to third regions as described above, the BH curve 201 represented by the BH interpolation formula is continuous in all regions, and Has smooth properties. Therefore, as shown in FIG. 2B, the “curve 202 representing the relationship between the magnetic permeability μ and the magnetic field strength H” obtained from the BH curve 201 also has continuous and smooth characteristics.

For example, the BH interpolation formula creating unit 113 causes the CPU to read the magnetic property measurement data and the saturation magnetic property measurement data from the HDD or the like, calculate the undetermined coefficients of the equations (1) and (3), and and undetermined coefficients of the input variables and a (saturation magnetic flux density B _s, the magnetic field intensity H _s which corresponds to the saturation flux density B _s) can be realized by storing in the HDD or the like.

(Electromagnetic field analyzer 120)
The electromagnetic field analysis unit 120 analyzes the electromagnetic field of the magnetic material when the magnetic field strength H is externally applied to the magnetic material, using the BH interpolation formula created by the BH interpolation formula creation unit 113. The electromagnetic field is represented by Maxwell's equation, and the electromagnetic field analysis unit 120 can calculate the numerical solution by using, for example, a finite element method. It is assumed that the magnetic material to be analyzed for the electromagnetic field and the magnetic material to be used for creating the BH curve are the same type of material. The magnetic material to be analyzed for the electromagnetic field is formed into a predetermined shape, for example, an electric motor, a generator, and a core of a transformer.

  To briefly explain an example of this calculation method, first, the initial value of the vector potential A is given, the magnetic flux density B in each mesh is obtained, the magnetic field strength H of the mesh is obtained by the BH interpolation formula, and the ratio is obtained from the ratio thereof. Find the magnetic resistivity ν. Such a magnetic resistivity ν is calculated for all the meshes, a Maxwell's equation is created, and an electromagnetic field analysis for obtaining a solution by numerical calculation is performed, whereby the vector potential A is calculated. The difference δA is obtained by subtracting the previously obtained vector potential A from the vector potential A. If the difference δA is not less than the threshold value, the vector potential A is updated by adding the difference δA to the previously obtained vector potential A. Such calculation is repeated until the difference δA becomes smaller than the threshold, and the magnetic flux density B when the difference δA becomes smaller than the threshold is output. Note that the electromagnetic field analysis can be realized by a known technique as described in Non-Patent Document 1 or Patent Document 1, for example, and therefore, detailed description thereof is omitted here.

For example, the electromagnetic field analysis unit 120 reads, from the HDD or the like, a BH interpolation formula in which the undetermined coefficient, the input variable, and the magnetic permeability μ _{0 of the} vacuum are set, and outputs the magnetic field strength H from the outside to the magnetic material to be analyzed. This can be realized by calculating an electromagnetic field (distribution of the magnetic flux density of the magnetic material) when given, storing the calculated result in an HDD or the like, or displaying the result on a computer display.

(Operation flowchart)
Next, an example of the operation of the BH curve creation unit 110 will be described with reference to the flowchart of FIG.
First, in step S401, the BH measurement data input unit 111 inputs magnetic property measurement data of a magnetic material for which a BH curve is to be created and stores the data in a storage medium.
Next, in step S402, the saturation magnetic flux density, magnetic field strength input section 112 stores in the storage medium to input saturation magnetic flux density B _s of the magnetic material will be created interest BH curve.

Next, in step S403, the saturation magnetic flux density, magnetic field strength input unit 112, a magnetic field strength of the magnetic material will be created interest BH curve, the magnetic field strength H which corresponds to the saturation flux density B _s input at step S402 Enter _s and store it in the storage medium.
Next, in step S404, BH interpolation equation creating unit 113 calculates undetermined coefficients a _m of BH interpolation formula of the first region ((1)), a _n, m, and n.
Next, in step S405, the BH interpolation formula creating unit 113 calculates the undetermined coefficients p and q of the BH interpolation formula (formula (3)) in the second area.

Next, in step S406, the BH interpolation formula creation unit 113 sets the undetermined coefficients a _m , an _n , m, n, p, and q calculated in steps S404 and S405 and input variables (saturation magnetic flux density B _s , saturation magnetic flux the magnetic field intensity H _s) which corresponds to the density B _s, stored in the storage medium as the value to be set to BH interpolation formula ((1) to (3) below). Then, the processing according to the flowchart of FIG. 4 ends. The BH interpolation formula (that is, the BH curve) for the entire region of the magnetic material for which the BH curve is to be created is based on these undetermined coefficients a _m , an _n , m, n, p, q, and the input variables (saturation flux The density B _s , the magnetic field strength H _s corresponding to the saturation magnetic flux density B _s ), and the magnetic permeability μ _{0 of the} vacuum are substituted into the equations (1) to (3).

(First embodiment)
Next, examples will be described.
FIG. 5 is a diagram showing a BH curve represented by a BH interpolation formula. FIG. 5B is an enlarged view of the first and second regions of the BH curve 501 shown in FIG. 5A.
In the invention examples, the saturation magnetic flux density B _s is the 2.03 [T], the magnetic field intensity H _s which corresponds to the saturation flux density B _s is the 30000 [A / m], the Si content 3 [wt% And a BH interpolation formula for a grain-oriented electrical steel sheet having a thickness of 0.35 [mm] was obtained, and a BH curve 501 represented by the BH interpolation formula was obtained. The undetermined coefficients were the values shown below.

Then, the relationship between the relative magnetic permeability μ _r and the magnetic field strength H was determined from the BH interpolation formula (BH curve 501). Further, as a comparative example, a BH interpolation formula is created by piecewise linear interpolation using the same magnetic property measurement data as the magnetic property measurement data obtained when the BH interpolation formula (BH curve 501) is obtained. , The relationship between the relative magnetic permeability μ _r and the magnetic field strength H was determined. The piecewise linear interpolation is to linearly interpolate between two magnetic property measurement data adjacent to each other with the two magnetic property measurement data as both end points.

FIG. 6 is a diagram showing curves representing the relationship between the relative magnetic permeability μ _r and the magnetic field strength H in each of the invention example and the comparative example.
As shown in FIG. 6, it can be seen that the curve 601 obtained in the invention example is smoother than the curve 602 obtained in the comparative example.

(Summary)
As described above, in the present embodiment, the first region where the magnetic field strength H is from 0 to the maximum value of the magnetic property measurement data, and the magnetic field strength H is the saturation magnetic flux density B from the maximum value of the magnetic property measurement data a second region to magnetic field intensity H _s corresponding to _s, the magnetic field intensity H is, by dividing the BH curve and the magnetic field intensity H _s or more third region corresponding to the saturation flux density B _s, respectively For the regions, a BH interpolation formula reflecting the physical phenomenon of each region is set using the magnetic characteristic measurement data and the saturation magnetic characteristic measurement data. In the first region, in the region of the first region where the value is relatively small, the term of the power of the magnetic flux density B representing the dominant magnetic property is expressed, and in the region where the first region is relatively large. The BH interpolation formula is represented by a single formula that is linearly combined with a power term of the magnetic flux density B representing the dominant magnetic characteristics. In the third region, and the saturation flux density B _s, the a saturation magnetic flux density starting from the point represented by the magnetic field intensity H _s corresponding to B _s, the increment of the flux density B to the magnetic field strength H inclination of vacuum The BH interpolation formula is represented by a single linear formula having a magnetic permeability μ ₀ . Further, the value of the starting point and the differential coefficient in the second area are the same as the value and the differential coefficient at the end point of the BH interpolation formula in the first area, and the value of the ending point and the differential coefficient in the second area are the third. Is the same as the value and differential coefficient at the starting point of the BH interpolation formula in the region, and the differential expression (= dB / dH) of the magnetic field strength with respect to the magnetic flux density is a monotonically decreasing function. Express the interpolation formula. Therefore, it is possible to create a BH curve such that the magnetic permeability μ changes more smoothly with respect to the change in the magnetic field strength H than in the related art. As a result, it is possible to prevent a BH curve whose differential coefficient changes abruptly from being created like the curve 602 shown in FIG.

  Therefore, for example, in the repetitive calculation in the above-described electromagnetic field analysis, the convergence is caused by the fact that the magnetic resistivity ν obtained from the BH interpolation formula fluctuates greatly with respect to the magnetic resistivity ν obtained in the previous calculation. It is possible to prevent the solution from being unable to be obtained without satisfying the condition (the condition that the difference δA becomes smaller than the threshold value). On the other hand, in the present embodiment, it is possible to create a BH curve whose differential coefficient changes smoothly like the curve 601 shown in FIG. 6, so that the above-mentioned convergence condition is easily satisfied, A solution can be obtained faster and more accurately than in the past.

(Modification)
In the present embodiment, the case where the BH curve 501 (BH interpolation formula) is used for the electromagnetic field analysis has been described as an example, but the BH curve 501 (BH interpolation formula) is not necessarily used for the electromagnetic field analysis. For example, the BH curve 501 (BH interpolation formula) may be displayed on a computer display, and an appropriate BH curve may be presented to the operator.
Further, when the unknown coefficients _{a m, a n, m,} n, p, is stored in the data table the q by type of magnetic material, the type of information of the magnetic material is input through the user interface or the like, the magnetic The undetermined coefficient corresponding to the type of the material may be read and the BH interpolation formula may be set (created).

((Second embodiment))
Next, a second embodiment will be described.
In the first embodiment, the angle θ between the rolling direction RD (Rolling Direction) of the grain-oriented electrical steel sheet and the direction of the magnetic flux density B is 0 [°], and the stress σ applied to the grain-oriented electrical steel sheet is Is described as an example in a case where the magnetic property measurement data of the grain-oriented electrical steel sheet is obtained in a state where is 0 [Pa]. On the other hand, in the present embodiment, the angle θ between the rolling direction RD (Rolling Direction) of the grain-oriented electrical steel sheet and the direction of the magnetic flux density B is different from the stress σ applied to the grain-oriented electrical steel sheet. The case where the magnetic property measurement data of the grain-oriented electrical steel sheet is obtained for each angle θ between the rolling direction RD and the direction of the magnetic flux density B and for each stress σ applied to the grain-oriented electrical steel sheet will be described. As described above, the magnetic property measurement data acquired by the BH measurement data input unit 111 is mainly different between the present embodiment and the first embodiment. Therefore, in the description of the present embodiment, the same portions as those in the first embodiment are denoted by the same reference numerals as those in FIGS.

(Information processing device)
Also in the present embodiment, similarly to the first embodiment, the case where the magnetic material for which the BH curve is created is a grain-oriented electrical steel sheet will be described as an example. However, as described in the first embodiment, the magnetic material for which the BH curve is created is not limited to the grain-oriented electrical steel sheet. In the following description, the angle θ between the rolling direction RD of the grain-oriented electrical steel sheet and the direction of the magnetic flux density B is abbreviated as angle θ as necessary, and the stress σ applied to the grain-oriented electrical steel sheet is required. Accordingly, it is abbreviated as stress σ.

  In the present embodiment, an example will be described in which magnetic property measurement data is obtained for each angle θ and each stress σ according to the magnetic property test method for a single magnetic steel sheet described in Non-Patent Document 3 (JIS C 2556). . FIG. 7 is a diagram illustrating an example of a schematic configuration of a single-plate magnetic tester. Note that the XYZ coordinates shown in FIGS. 7 and 8 indicate the relationship of the orientation in each figure.

  In FIG. 7, the single-plate magnetic tester excites a single grain-oriented electromagnetic steel plate (single plate) and measures the magnetic flux density B and the magnetic field strength H at that time. Is performed for each of the exciting currents, thereby obtaining magnetic property measurement data. The waveforms of the respective magnetic flux densities are all sine waves and have the same frequency.

The single-plate magnetic tester has an upper yoke 71, a lower yoke 72, an exciting coil 73, a B coil 74, and an H coil 75.
The upper yoke 71 and the lower yoke 72 are arranged at positions substantially facing each other via the plate surface of the sample S. The upper yoke 71 and the lower yoke 72 are the same, and differ only in the arrangement position.

  The upper yoke 71 and the lower yoke 72 have two legs and a (one) trunk. The two legs and the trunk are integrally formed using the same magnetic material. In the present embodiment, the case where the upper yoke 71 and the lower yoke 72 are configured by laminating grain-oriented electrical steel sheets will be described as an example.

  The two legs have the same shape and size, and have a generally rectangular parallelepiped shape. The body also has a generally rectangular parallelepiped shape. Both ends of the torso are connected to the proximal ends of the two legs. The tip surfaces of the two legs become pole faces. The upper yoke 71 and the lower yoke 72 are arranged such that the tip surfaces of the two legs contact the plate surface of the sample S, and a region between the two legs is positioned on the plate surface of the sample S. . At this time, the tip surfaces of the two legs of the upper yoke 71 and the tip surfaces of the two legs of the lower yoke 72 are substantially opposed to each other via the plate surface of the sample S.

  In the present embodiment, the planar shape of the sample S is rectangular. One short side Sa of the sample S is fixed so as not to move. Then, a load F is applied to the plate thickness portion of the other short side sb of the sample S in a direction along the long side of the sample S (Y-axis direction). Thereby, a compressive stress is applied to the sample S. By applying a plurality of discrete loads F to the sample S, different compressive stresses corresponding to the loads F are applied to the sample S as the stress σ. As described above, in the present embodiment, the case where the compressive stress in the direction along the long side of the sample S (Y-axis direction) is applied as the stress σ will be described as an example.

The excitation coil 73 is configured by winding a metal wire (for example, a copper wire) around the sample S. The sample S, the upper yoke 71, and the lower yoke 72 are excited when an exciting current flows from the exciting power supply to the exciting coil 73.
The B coil 74 is configured by winding a metal wire (for example, a copper wire) around the sample S inside the excitation coil 72. The B coil 74 is for measuring an induced electromotive force based on a magnetic field generated when the sample S, the upper yoke 71, and the lower yoke 72 are excited. The magnetic flux density B in the sample S is measured based on the induced electromotive force. In the example shown in FIG. 7, the direction of the magnetic flux density B in the sample S is a direction along the long side of the sample S (Y-axis direction).

  The H coil 75 is configured by winding a metal wire (for example, a copper wire), and a surface formed by the wound portion (a so-called coil surface) is opposed to the plate surface of the sample S in a state of being close to the plate surface. It is arranged to be. The H coil 75 is for measuring a magnetic field acting on the sample S when the sample S, the upper yoke 71, and the lower yoke 72 are excited. The magnitude of the magnetic field in the sample S is measured based on the electromotive voltage induced in the H coil 75.

  The upper yoke 71, the lower yoke 72, the excitation coil 73, the B coil 74, and the H coil 75 can be realized by, for example, the same one as described in Non-Patent Document 3. Note that the single-plate magnetic tester is not limited to the configuration shown in FIG. 1 and can be realized in various modes described in Non-Patent Document 3. For example, in the present embodiment, the case where the H coil 75 is used (the case where the H coil method is used) is described as an example, but the exciting current method may be adopted. In this case, the H coil 75 becomes unnecessary. Further, as described in Non-Patent Document 3, two H coils (2H coil method) may be used. FIG. 7 shows an example in which a single-plate magnetic tester is configured by a vertical yoke-structured multi-yoke frame described in Non-Patent Document 3. However, even if a horizontal yoke structure is adopted, A single yoke frame may be employed.

  The magnetic flux density B and the magnetic field strength H of the sample S were measured while changing the effective value of the exciting current while the load F was applied to the sample S as described above. Similarly to the above, the magnetic property measurement data at the stress σ corresponding to the load F is obtained. Then, by performing this measurement while changing the load F (that is, stress σ) applied to the sample S, magnetic property measurement data at each of the plurality of stresses σ is obtained. In this manner, magnetic property measurement data for each stress σ is obtained. Note that the method described in Non-Patent Document 3 can be adopted as a method for measuring the magnetic characteristics in the single-plate magnetic tester, and thus detailed description is omitted here.

FIG. 8 is a diagram illustrating an example of a method of cutting out the sample S. FIG. 8 shows a sheet surface of the grain-oriented electrical steel sheet M, and shows an example of cutting three samples S1, S2, and S3 from the grain-oriented electrical steel sheet M. In FIG. 8, RD is the rolling direction as described above. TD is the direction perpendicular to the rolling direction (transversal direction).
In the example shown in FIG. 8, it is assumed that the samples S1, S2, and S3 are cut from the grain-oriented electrical steel sheet so that the shapes and the sizes are the same.

As described above, in the present embodiment, the samples S1 to S3 are set in the single-plate magnetic tester such that the direction of the magnetic flux density B is along the long side of the samples S1 to S3 (B in FIG. 8). See pointing direction). Therefore, in the present embodiment, the samples S1 to S3 are cut out from the grain-oriented electrical steel sheet M at different angles θ between the direction along the long side and the rolling direction RD of the grain-oriented electrical steel sheet M. By setting the samples S1 to S3 cut out in this manner in a single-plate magnetic tester as described above, the magnetic flux density B and the magnetic field strength H of the samples S having different angles θ can be measured.
By measuring the magnetic property measurement data for each stress σ for each of the samples S1 to S3 as described above, the magnetic property measurement data for each angle θ and each stress σ can be obtained.

  In FIG. 8, the angle θ of the sample S1 is 0 [°]. FIG. 8 shows an example in which three samples S1 to S3 are cut out from the grain-oriented electrical steel sheet M. However, the number of angles θ is not limited to three as long as it is plural, and is three or more. It may be. Further, from the symmetry of the sample S, the range of the angle θ may be a range of 0 ° to 90 °.

The BH measurement data input unit 111 inputs and stores the magnetic characteristic measurement data for each angle θ and each stress σ obtained as described above.
Further, a saturation magnetic flux density B _s, the magnetic field intensity H _s which corresponds to the saturation flux density B _s is not changed by the presence or absence and the size of the angle θ and stress sigma. Therefore, also in this embodiment, the saturation magnetic characteristic measurement data as (the saturation flux density B _s, the measurement data of the magnetic field intensity H _s which corresponds to the saturation flux density B _s), the same as that described in the first embodiment Data can be used. However, it is needless to say that data of the same material as the sample S is used as the saturation magnetic characteristic measurement data. As described above, the saturation magnetic flux density / magnetic field strength input unit 112 inputs and stores the saturation magnetic characteristic measurement data as described in the first embodiment.

Also in the present embodiment, the same formula as in the first embodiment is used as the BH interpolation formula for the first to third regions. For example, equation (1) is used as the BH interpolation equation for the first area, equation (2) is used as the BH interpolation equation for the third area, and equation (3) is used as the BH interpolation equation for the second area.
As described above, in the present embodiment, magnetic property measurement data for each angle θ and each stress σ can be obtained. Therefore, for the magnetic property measurement data of one angle θ and one stress σ, the BH interpolation formula of the first area (the undetermined coefficient of the equation (1)), the BH interpolation formula of the second area, and the third area Are derived one at a time. As described above, since the saturation magnetic property measurement data does not change with the angle θ and the stress σ, the BH interpolation formula in the second region does not change with the angle θ and the stress σ (see the formula (2)). .

The BH interpolation formula creation unit 113 derives and stores one BH interpolation formula for each of the first to third regions for all combinations of the angle θ and the stress σ included in the magnetic characteristic measurement data. In this way, a BH curve for each angle θ and each stress σ is obtained.
FIG. 9 is a diagram conceptually illustrating an example of a BH curve for each angle θ and each stress σ. FIG. 9 is a BH curve represented by a BH interpolation formula in all the regions (first to third regions), similarly to FIG. 2A.

  As described in the first embodiment, the electromagnetic field analysis unit 120 uses the BH interpolation formula created by the BH interpolation formula creation unit 113 to apply the magnetic field strength H to the magnetic material from the outside. Analyze the electromagnetic field. The analysis of the electromagnetic field using the BH curve according to the angle θ and the stress σ can be realized by using, for example, the technique described in Patent Literature 1, and a detailed description thereof will be omitted here. The unmeasured BH curve of the angle θ and the stress σ can be obtained, for example, by performing interpolation or extrapolation (for example, linear interpolation or linear extrapolation) using the measured BH curve.

(Second embodiment)
Next, a second embodiment will be described.
FIG. 10 is a diagram showing a BH curve in the present embodiment. FIG. 10B is an enlarged view of the first and second regions of the BH curves 1001 and 1002 shown in FIG.
In this embodiment, from a grain-oriented electrical steel sheet having a saturation magnetic flux density B _s of 1.989 [T], a Si content of 3 [mass%], and a sheet thickness of 0.35 [mm], The sample S was cut out so that the angle θ was 0 [°]. The sample S was set in the single-plate magnetic tester shown in FIG. 7, a compressive stress of -70 [MPa] was applied, and BH curves were derived by the method of the invention and the method of the comparative example.

  The BH curve 1001 of the invention example is obtained by deriving the BH interpolation formula of the first to third regions by the method of the present embodiment. The BH curve 1002 of the comparative example is generated by the magnetic measurement data (see ● in FIGS. 10A and 10B) input to the BH measurement data input unit 111 and the saturation magnetic flux density / magnetic field intensity input unit 112. It is obtained by interpolating between the input saturation magnetic characteristic measurement data (see ◆ in FIGS. 10A and 10B) by piecewise linear interpolation. In the comparative example, it can be seen that the first area, the third area, and the second area do not change smoothly. On the other hand, in the invention example, the BH curve can be created so that the first area, the third area, and the second area change smoothly even under the condition of applying the stress σ. I understand.

(Summary)
In a magnetic material whose magnetic characteristics change according to the angle θ or a magnetic material to which a stress σ is applied, the magnetic characteristics change with changes in the angle θ and the stress σ. For this reason, the measurement error of the magnetic property measurement data input to the BH measurement data input unit 111 is larger than when the angle θ is 0 [°] and the stress σ is 0 [Pa]. For example, in a magnetic material such as a grain-oriented electrical steel sheet having strong magnetic property anisotropy, the magnetic property greatly changes with a slight change in the angle θ of the magnetic flux density B with respect to the rolling direction RD, and the magnetic specific measurement data In some cases, the influence of the measurement error greatly affects the result of the electromagnetic field analysis. Therefore, if a BH curve for each angle θ and each stress σ is obtained as in the present embodiment, in addition to the effects described in the first embodiment, an electromagnetic field analysis is performed in consideration of the angle θ and the stress σ. Even in this case, the convergence condition described in the first embodiment can be easily satisfied, and a solution can be obtained quickly and accurately.

(Modification)
In the present embodiment, an example has been described in which the angle θ is an angle between the rolling direction RD of the grain-oriented electrical steel sheet and the direction of the magnetic flux density B. However, the angle θ does not necessarily need to be based on the rolling direction RD as long as the angle is between the predetermined direction of the magnetic material and the direction of the magnetic flux density B. For example, an angle between the direction TD perpendicular to the rolling direction RD and the direction of the magnetic flux density B may be used instead of the angle θ.

  Further, in the present embodiment, the case where the device for measuring the magnetic characteristics is a single-plate magnetic tester has been described as an example. However, the device for measuring magnetic properties is not limited to a single-plate magnetic tester. For example, an Epstein tester may be used, but it is preferable to use a device that can apply a stress to the sample as uniformly as possible, such as a single-plate magnetic tester. Since the magnetic properties of the single-plate sample are measured, stress can be applied to the sample as uniformly as possible).

  In this embodiment, the case where the stress σ is a compressive stress in the direction of the magnetic flux density B of the magnetic material has been described as an example. However, the stress σ is not limited to such a compressive stress. For example, in a device for measuring magnetic properties, when a stress determined from a compressive stress, a tensile stress, and a shear stress can be applied to a magnetic material, the stress may be used instead of the stress σ.

Further, in the present embodiment, an example has been described in which a BH curve is obtained for each angle θ and each stress σ. However, this is not necessary. For example, when analyzing an electromagnetic field of an electric device in which no stress is applied to the iron core and the angle θ differs depending on the location of the iron core, a BH curve for each angle θ may be set without applying the stress σ. . Conversely, for example, when analyzing the electromagnetic field of the electrical equipment in a state where the stress σ is different at a constant angle θ, when the electromagnetic field is analyzed at a constant angle θ (for example, the angle θ = 0 [°]). A BH curve for each stress σ may be set.
In addition, in the present embodiment, various modifications described in the first embodiment can be adopted.

The embodiments of the present invention described above can be realized by a computer executing a program. In addition, means for supplying a program to a computer, for example, a computer-readable recording medium such as a CD-ROM on which the program is recorded, or a transmission medium for transmitting the program may be applied as an embodiment of the present invention. it can. Further, a program product such as a computer-readable recording medium on which the program is recorded can also be applied as an embodiment of the present invention. The above-described program, computer-readable recording medium, transmission medium, and program product are included in the scope of the present invention.
In addition, the embodiments of the present invention described above are merely examples of specific embodiments for carrying out the present invention, and the technical scope of the present invention should not be interpreted in a limited manner. Things. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features.

Reference Signs List 100 information processing device 110 BH curve creation unit 111 BH measurement data input unit 112 saturation magnetic flux density / magnetic field intensity input unit 113 BH interpolation formula creation unit 120 electromagnetic field analysis unit 201, 501 BH curve represented by BH interpolation formula 202 Curve 601 showing the relationship between magnetic field strength Curve showing the relationship between relative magnetic permeability and magnetic field strength (Invention example)
602 Curve representing the relationship between relative magnetic permeability and magnetic field strength (comparative example)
1001 BH curve represented by BH interpolation formula (Invention example)
1002 BH curve represented by piecewise linear interpolation (comparative example)

Claims (9)

BH curve for performing a calculation by a computer to create a BH curve which is a continuous relationship between a magnetic field intensity H acting on the magnetic material and a magnetic flux density B generated in the magnetic material by applying the magnetic field intensity H A production device,
The magnetic field strength H when a plurality of discrete values of the magnetic field strength H are applied to the magnetic material for which the BH curve is created, and the magnetic material in the magnetic material generated by applying the magnetic field strength H BH measurement data input means for inputting magnetic property measurement data which is measurement data of magnetic flux density B;
Saturation magnetic flux density B _s and the saturation magnetic flux density, magnetic field intensity to enter the saturation magnetic characteristic measurement data is measurement data of the magnetic field intensity H _s which corresponds to the saturation flux density B _s of the magnetic material to be generation target of the BH curve Input means;
The magnetic field strength H in the magnetic property measurement data is obtained by using the magnetic property measurement data input by the BH measurement data input means and the saturation magnetic property measurement data input by the saturation magnetic flux density / magnetic field strength input means. BH interpolation formula setting means for setting a BH interpolation formula representing the BH curve to obtain a magnetic flux density B for different magnetic field strengths H.
The BH interpolation formula is such that the magnetic field strength H is from 0 to the maximum value of the magnetic property measurement data in the first region, and the magnetic field strength H is the maximum value of the magnetic property measurement data. and BH interpolation equation of the second region to the magnetic field intensity H _s which corresponds to the saturation flux density B _s, the magnetic field intensity H is, the saturation magnetic flux density B corresponding magnetic field strength _s H _s or more BH of the third region An interpolation formula, and
The BH interpolation formula for the first region is obtained by calculating a power of the magnetic flux density B, which represents a dominant magnetic characteristic in a region having a relatively small value in the first region, and a power of the first region. A single expression that expresses the magnetic field strength H in a linear combination with the power of the magnetic flux density B, which represents a dominant magnetic characteristic in a region where the value is relatively large,
The BH interpolation equation of the third region, the starting point the saturated magnetic flux density B _s, the points represented by a magnetic field intensity H _s which corresponds to the saturation flux density B _s, and the magnetic flux density to the magnetic field strength H A linear unitary equation in which the slope of the increment of B is the vacuum permeability μ ₀ ,
The value and differential coefficient at the starting point of the BH interpolation formula in the second area are the same as the value and differential coefficient at the end point of the BH interpolation formula in the first area, and the BH interpolation formula in the second area is used. Are the same as those at the starting point of the BH interpolation formula in the third region, and the permeability μ or the relative permeability μ _r is monotonic with the increase in the magnetic field strength H. It is a single expression that expresses that
The BH interpolation formula setting means calculates an undetermined coefficient of the interpolation formula of the first area based on the magnetic property measurement data input by the BH measurement data input means,
A BH curve creation device, wherein after calculating an undetermined coefficient of a BH interpolation formula of the first area, an undetermined coefficient of a BH interpolation formula of the second area is calculated. The BH curve creating device according to claim 1, wherein the BH interpolation formula for the first area is represented by the following formula (1).
_{Here, a m, a n, m} , n are undetermined coefficients [-] is, H is a magnetic field intensity [A / m], B is a magnetic flux density [T].

3. The BH curve creating device according to claim 1, wherein the BH interpolation formula for the second area is expressed by the following formula (2). 4.
Here, p and q are undetermined coefficients [-], H is a magnetic field intensity [A / m], B is a magnetic flux density [T], and B _s is a saturation magnetic flux density [T]. And H _s is the magnetic field strength [A / m] corresponding to the saturation magnetic flux density B _s .

The BH measurement data input means inputs the magnetic property measurement data measured in a state where the stress σ applied to the magnetic material is different,
4. The BH curve creating device according to claim 1, wherein the BH interpolation formula setting unit sets the BH interpolation formula for each of the plurality of different stresses σ. 5. The BH measurement data input means inputs the magnetic characteristic measurement data measured in a state where the angle θ between the predetermined direction of the magnetic material and the direction of the magnetic flux density is different,
The BH curve creation device according to any one of claims 1 to 4, wherein the BH interpolation formula setting means sets the BH interpolation formula for each of the different angles θ.   The BH curve creation device according to any one of claims 1 to 5, wherein the magnetic material is a silicon steel plate.   An electromagnetic field for performing a calculation by a computer using a BH interpolation formula obtained by the BH curve creating apparatus according to claim 1, and analyzing an electromagnetic field of a magnetic material of the same type as the BH interpolation formula. An electromagnetic field analyzer having an analyzing means. BH curve for performing a calculation by a computer to create a BH curve which is a continuous relationship between a magnetic field intensity H acting on the magnetic material and a magnetic flux density B generated in the magnetic material by applying the magnetic field intensity H The method of creation,
The magnetic field strength H when a plurality of discrete values of the magnetic field strength H are applied to the magnetic material for which the BH curve is created, and the magnetic material in the magnetic material generated by applying the magnetic field strength H A BH measurement data input step of inputting magnetic property measurement data that is measurement data of the magnetic flux density B;
Saturation magnetic flux density B _s and the saturation magnetic flux density, magnetic field intensity to enter the saturation magnetic characteristic measurement data is measurement data of the magnetic field intensity H _s which corresponds to the saturation flux density B _s of the magnetic material to be generation target of the BH curve Input process,
Using the magnetic property measurement data input in the BH measurement data input step and the saturation magnetic property measurement data input in the saturation magnetic flux density / magnetic field strength input step, the magnetic field strength H in the magnetic property measurement data is A BH interpolation formula setting step of setting a BH interpolation formula representing the BH curve to obtain a magnetic flux density B for different magnetic field strengths H,
The BH interpolation formula is such that the magnetic field strength H is from 0 to the maximum value of the magnetic property measurement data in the first region, and the magnetic field strength H is the maximum value of the magnetic property measurement data. and BH interpolation equation of the second region to the magnetic field intensity H _s which corresponds to the saturation flux density B _s, the magnetic field intensity H is, the saturation magnetic flux density B corresponding magnetic field strength _s H _s or more BH of the third region An interpolation formula, and
The BH interpolation formula for the first region is obtained by calculating a power of the magnetic flux density B, which represents a dominant magnetic characteristic in a region having a relatively small value in the first region, and a power of the first region. A single expression that expresses the magnetic field strength H in a linear combination with the power of the magnetic flux density B, which represents a dominant magnetic characteristic in a region where the value is relatively large,
The BH interpolation equation of the third region, the starting point the saturated magnetic flux density B _s, the points represented by a magnetic field intensity H _s which corresponds to the saturation flux density B _s, and the magnetic flux density to the magnetic field strength H A linear unitary equation in which the slope of the increment of B is the vacuum permeability μ ₀ ,
The value and differential coefficient at the starting point of the BH interpolation formula in the second area are the same as the value and differential coefficient at the end point of the BH interpolation formula in the first area, and the BH interpolation formula in the second area is used. Are the same as those at the starting point of the BH interpolation formula in the third region, and the permeability μ or the relative permeability μ _r is monotonic with the increase in the magnetic field strength H. It is a single expression that expresses that
The BH interpolation formula setting step calculates an undetermined coefficient of the interpolation formula of the first area based on the magnetic property measurement data input in the BH measurement data input step,
A BH curve creation method, comprising: calculating an undetermined coefficient of a BH interpolation formula in the first area, and then calculating an undetermined coefficient of a BH interpolation formula in the second area.   A computer program for causing a computer to function as each unit of the BH curve creation device according to claim 1.

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