JP2005043340A - Electromagnetic field analysis device, electromagnetic field analysis system, electromagnetic field analysis method, computer program, and computer readable recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily and securely analyze an electromagnetic field generated in large-scale facilities. <P>SOLUTION: The electromagnetic field in an analysis region 21 can be analyzed without division into a multitude of elements, by calculating a mean magnetic flux density B<SB>ave</SB>generated at the central part 20e1 of the cross-section of a magnetic body 20e and at the equivalent element 31 occupied by the air at the sides thereof, the mean magnetic field H<SB>ave</SB>, and the angle θ<SB>BH</SB>between the mean magnetic flux density B<SB>ave</SB>and the mean magnetic field H<SB>ave</SB>, by preparing, with the parameter of an angle θ<SB>B</SB>, B-H curves 90-93 expressing the relationship between the calculated mean magnetic flux density B<SB>ave</SB>and the mean magnetic field H<SB>ave</SB>and B-θ curves 100-103 expressing the relationship between the mean magnetic flux density B<SB>ave</SB>and the angle θ<SB>BH</SB>, and by obtaining the magnetic flux line generated in the analysis region 21 using the prepared B-H curves and the B-θ curves. Accordingly, the storage capacity required for analyzing the electromagnetic field can be extremely reduced. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to an electromagnetic field analysis device, an electromagnetic field analysis system, an electromagnetic field analysis method, a computer program, and a computer-readable recording medium, and in particular, analyzes an electromagnetic field generated in a region where a plurality of substances including a magnetic material are present. Therefore, it is suitable for use.

  Generally, when an electric device is used, a magnetic field is generated around it. Therefore, a magnetic shield device is used to prevent the magnetic field generated from the electrical equipment from leaking to the surroundings.

And with the development of technology in recent years, facilities using large electric devices that use large currents are increasing. For such a large electric device, it is necessary to use a large magnetic shield device.
In addition, when a large current flows near the magnetic shield device or there is a magnetic material having a residual magnetic field, a magnetic field is generated therefrom. Such a magnetic field is a hindrance when trying to perform a precise measurement of a precision device within a magnetic shield device. It is also necessary to configure the magnetic shield device so that an external magnetic field does not enter.

  For example, 200 directional electrical steel sheets having a side length of 2 [m] and a thickness of 1 [mm] are prepared, and these 200 directional electrical steel sheets are arranged in a bowl shape at intervals. A large-sized magnetic shield device configured to have a size of 2 [m] square as a whole has been proposed (see, for example, Patent Document 1).

  By the way, in order to verify the usefulness of such a large magnetic shield device, it is desirable to numerically analyze the electromagnetic field generated in the large magnetic shield device. In such a case, conventionally, the finite element method is generally used. In this finite element method, an electromagnetic field is analyzed by dividing a region to be analyzed into a number of regions (cells) having a relatively simple shape.

  As described above, since the magnetic shield device is configured using a steel plate having magnetic anisotropy, when analyzing the electromagnetic field using the finite element method, it is necessary to make the region to be analyzed very fine. There is. More specifically, it is necessary to divide the region to be analyzed into a large number of cells having a size of about 0.2 [mm] square.

JP 2002-164686 A

However, when an electromagnetic field generated in a large-sized magnetic shield device as in the above-described example is analyzed by the conventional finite element method, a cubic region having a side of 2 [m] is converted into a region of 0.2 [mm] square. Must be divided into (cells). Therefore, the number of areas to be analyzed is about 1 trillion.
However, the capacity of the main storage device in the current personal computer is about 4 [GB] at the maximum. Accordingly, the maximum number of regions (cells) that can be analyzed is about one million.

  As described above, when an electromagnetic field in a large-scale magnetic shield device is analyzed using the conventional finite element method, the amount of data necessary for the analysis far exceeds the storage capacity of the personal computer. For this reason, there is a problem that it is extremely difficult to analyze an electromagnetic field generated in a large-scale facility such as the above-described magnetic shield device.

  The present invention has been made in view of the above-described problems, and an object thereof is to easily and reliably analyze an electromagnetic field generated in a large-scale facility.

The electromagnetic field analysis apparatus of the present invention includes an average magnetic field calculation means for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material, the average magnetic flux density, and the average magnetic field. And an electromagnetic field analyzing means for analyzing an electromagnetic field generated in a wider area than the equivalent element.
Another feature of the present invention is that the average magnetic flux density and the average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material are calculated, and the average magnetic flux density and the average magnetic field are calculated. An electromagnetic field generated in a region wider than the equivalent element by using an average magnetic field calculation means for calculating an angle formed by: an average magnetic flux density; an average magnetic field; and an angle formed by the average magnetic flux density and the average magnetic field. And an electromagnetic field analysis means for analyzing.
Another feature of the present invention is that the magnetic property calculating means for calculating the magnetic permeability or magnetic resistivity in an equivalent element occupied by a plurality of substances including a magnetic material, and the magnetic permeability or magnetic resistivity described above. And an electromagnetic field analysis means for analyzing an electromagnetic field generated in an analysis target area wider than the equivalent element, and the magnetic permeability or the magnetic resistivity is a physical quantity that relates an average magnetic flux density and an average magnetic field in the equivalent element. It is characterized by being.
Another feature of the present invention is an electromagnetic field analysis apparatus for analyzing an electromagnetic field generated in an analysis target area where a plurality of magnetic bodies and nonmagnetic bodies are present repeatedly. The magnetic property calculation means for calculating the magnetic permeability or the magnetic resistivity in the equivalent element occupied by a plurality of substances including the body, and the electromagnetic field generated in the analysis target region is analyzed using the magnetic permeability or the magnetic resistivity. And the magnetic permeability or magnetic resistivity is a physical quantity that correlates an average magnetic flux density and an average magnetic field in the equivalent element, and the magnetic property calculation means is filled with the plurality of magnetic bodies. When determining the magnetic permeability or magnetic resistivity in a certain direction, the magnetic permeability or magnetic resistivity of the magnetic substance in the equivalent element and the equivalent element The magnetic permeability or magnetic resistivity of the non-magnetic material in the above-mentioned equivalent element is apportioned according to the cross-sectional area of the magnetic material in the equivalent element and the cross-sectional area of the non-magnetic material in the equivalent element. To do.

The electromagnetic field analysis system of the present invention includes a plurality of electromagnetic field analysis devices having an average magnetic field calculation means for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material, Using the average magnetic flux density calculated by the electromagnetic field analysis apparatus and the average magnetic field, and an overall model analysis apparatus having an electromagnetic field analysis means for analyzing an electromagnetic field generated in a region wider than the equivalent element, Each of the average magnetic field calculation means included in the electromagnetic field analyzer is characterized by calculating an average magnetic flux density and an average magnetic field in different equivalent elements.
Another feature of the present invention is that the average magnetic flux density and the average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material are calculated, and the average magnetic flux density and the average magnetic field are calculated. A plurality of electromagnetic field analyzers having an average magnetic field calculating means for calculating an angle formed by the plurality of electromagnetic field analyzers, an average magnetic flux density calculated by the plurality of electromagnetic field analyzers, an average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field; And an overall model analysis device having an electromagnetic field analysis means for analyzing an electromagnetic field generated in a region wider than the equivalent element, and each of the average magnetic field calculation means possessed by the plurality of electromagnetic field analysis devices, An average magnetic flux density and an average magnetic field in different equivalent elements are calculated.

The electromagnetic field analysis method of the present invention includes an average magnetic field calculation step for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic substance, the average magnetic flux density, and the average magnetic field. And an electromagnetic field analysis step for analyzing an electromagnetic field generated in a wider area than the equivalent element.
Another feature of the present invention is that the average magnetic flux density and the average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material are calculated, and the average magnetic flux density and the average magnetic field are calculated. An electromagnetic field generated in a region wider than the equivalent element by using an average magnetic field calculation step for calculating an angle formed by: the average magnetic flux density, the average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field. And an electromagnetic field analysis step for analyzing.
Another feature of the present invention is that a magnetic property calculating step for calculating a magnetic permeability or a magnetic resistivity in an equivalent element occupied by a plurality of substances including a magnetic material, and the magnetic permeability or the magnetic resistivity described above. And an electromagnetic field analysis step for analyzing an electromagnetic field generated in an analysis target area wider than the equivalent element, and the magnetic permeability or the magnetic resistivity is a physical quantity that relates an average magnetic flux density and an average magnetic field in the equivalent element. It is characterized by being.
Another feature of the present invention is an electromagnetic field analysis method for analyzing an electromagnetic field generated in a region to be analyzed in which a plurality of magnetic bodies and nonmagnetic bodies are present repeatedly, wherein the magnetic body and the nonmagnetic body A magnetic property calculation step for calculating the magnetic permeability or magnetic resistivity of an equivalent element occupied by a plurality of substances including the body, and analyzing the electromagnetic field generated in the analysis target area using the magnetic permeability or magnetic resistivity. An electromagnetic field analyzing step, wherein the magnetic permeability or the magnetic resistivity is a physical quantity that associates an average magnetic flux density and an average magnetic field in the equivalent element, and the magnetic property calculating step is filled with the plurality of magnetic bodies. In determining the magnetic permeability or magnetic resistivity in a direction occupied by the region, the magnetic permeability or magnetic resistivity of the magnetic substance in the equivalent element, The magnetic permeability or magnetic resistivity of the nonmagnetic material in the equivalent element is prorated according to the cross-sectional area of the magnetic material in the equivalent element and the cross-sectional area of the nonmagnetic material in the equivalent element. It is characterized by that.
In addition, another feature of the present invention is that a plurality of electromagnetic field analysis devices include an average magnetic field calculation step for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material. The overall model analyzer performs an electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element using the average magnetic flux density calculated by the plurality of electromagnetic field analyzers and the average magnetic field, Each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analyzers calculates an average magnetic flux density and an average magnetic field in different equivalent elements.
Another feature of the present invention is that the average magnetic flux density and the average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material are calculated, and the average magnetic flux density and the average magnetic field are calculated. A plurality of electromagnetic field analyzers perform an average magnetic field calculation step for calculating an angle formed by the plurality of electromagnetic field analyzers, an average magnetic flux density calculated by the plurality of electromagnetic field analyzers, an average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field The overall model analysis device performs an electromagnetic field analysis step for analyzing an electromagnetic field generated in a region wider than the equivalent element, and each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analysis devices is performed in different equivalent elements. An average magnetic flux density and an average magnetic field are calculated.

The computer program of the present invention includes an average magnetic flux calculation step for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic substance, the average magnetic flux density, the average magnetic field, Using the average magnetic flux density, the computer executes an electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element.
Another feature of the present invention is that the average magnetic flux density and the average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material are calculated, and the average magnetic flux density and the average magnetic field are calculated. An electromagnetic field generated in a region wider than the equivalent element by using an average magnetic field calculation step for calculating an angle formed by: the average magnetic flux density, the average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field. And an electromagnetic field analysis step for analyzing the above.
Another feature of the present invention is that a magnetic property calculating step for calculating a magnetic permeability or a magnetic resistivity in an equivalent element occupied by a plurality of substances including a magnetic material, and the magnetic permeability or the magnetic resistivity described above. The computer executes an electromagnetic field analysis step for analyzing an electromagnetic field generated in an analysis target area wider than the equivalent element, and the magnetic permeability or the magnetic resistivity is obtained by calculating an average magnetic flux density and an average magnetic field in the equivalent element. It is a physical quantity to be related.
Another feature of the present invention is a computer program for causing a computer to analyze an electromagnetic field generated in an analysis target area where a plurality of magnetic bodies and non-magnetic bodies are repeatedly present. A magnetic property calculation step for calculating a magnetic permeability or a magnetic resistivity in an equivalent element occupied by a plurality of substances including the magnetic material and the non-magnetic material, and the analysis using the magnetic permeability or the magnetic resistivity. An electromagnetic field analysis step for analyzing an electromagnetic field generated in a target region is executed by a computer, and the magnetic permeability or the magnetic resistivity is a physical quantity that associates an average magnetic flux density and an average magnetic field in the equivalent element, and the magnetic characteristic calculation step includes And obtaining the magnetic permeability or magnetic resistivity in a direction in which there is a region filled and occupied by the plurality of magnetic bodies. At this time, the magnetic permeability or magnetic resistivity of the magnetic substance in the equivalent element and the magnetic permeability or magnetic resistivity of the non-magnetic substance in the equivalent element are determined by the cross-sectional area of the magnetic substance in the equivalent element. And the cross-sectional area of the nonmagnetic material in the equivalent element.
In addition, another feature of the present invention is that a plurality of electromagnetic field analysis devices include an average magnetic field calculation step for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material. The overall model analyzer performs an electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element using the average magnetic flux density calculated by the plurality of electromagnetic field analyzers and the average magnetic field, Each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analyzers is characterized by causing a computer to calculate an average magnetic flux density and an average magnetic field in different equivalent elements.
Another feature of the present invention is that the average magnetic flux density and the average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material are calculated, and the average magnetic flux density and the average magnetic field are calculated. A plurality of electromagnetic field analyzers perform an average magnetic field calculation step for calculating an angle formed by the plurality of electromagnetic field analyzers, an average magnetic flux density calculated by the plurality of electromagnetic field analyzers, an average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field The overall model analysis device performs an electromagnetic field analysis step for analyzing an electromagnetic field generated in a region wider than the equivalent element, and each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analysis devices is performed in different equivalent elements. The computer is caused to calculate an average magnetic flux density and an average magnetic field.
A computer-readable recording medium according to the present invention records the above-described computer program.

  According to the present invention, an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material are calculated, and the equivalent magnetic flux is calculated using the calculated average magnetic flux density and the average magnetic field. Since the electromagnetic field generated in a region wider than the element is analyzed, the electromagnetic field generated in the analysis region can be analyzed without dividing the analysis region into a number of elements as in the prior art. As a result, the storage capacity required for analyzing the electromagnetic field can be greatly reduced, and the electromagnetic field in a large-scale facility that has been difficult to analyze can be reliably analyzed.

(First embodiment)
Next, a first embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a block diagram showing an example of the configuration of the electromagnetic field analyzer in the present embodiment. In the present embodiment, as shown in FIG. 2, the analysis target region 21 includes five steel plates (magnetic bodies) 20a to 20e arranged in a bowl shape at equal intervals (30 [mm] intervals). The case where the generated electromagnetic field is analyzed will be described as an example. The analysis target area 21 is a rectangular area having a size of 4000 [mm] in the vertical direction and 1155 [mm] in the horizontal direction. Each of the steel plates 20a to 20e has a width of 1000 [mm] and a thickness of 1 [mm], and each of the steel plates 20a to 20e is arranged in parallel at intervals of 30 mm. It shall be.

In FIG. 1, the electromagnetic field analysis device 1 includes an operation unit 2, a display unit 3, and a processing unit 4.
The operation unit 2 is a device configured with a keyboard, a mouse, and the like, and is a device for transmitting the content input by the user (analyzer) to the processing unit 4.

  The display unit 3 is a device configured with a display or the like, and is a device for displaying a processing result or the like executed by the processing unit 4. The user operates the operation unit 2 and inputs desired content while viewing the content displayed on the display unit 3.

  The processing unit 4 is a computer that includes a CPU, a ROM, a RAM, and the like. The processing unit 4 performs a processing operation in the electromagnetic field analysis device 1 by executing a program recorded in the ROM.

Specifically, the processing unit 4 includes an average magnetic field calculation unit 4a, a magnetic characteristic curve creation unit 4b, and a magnetic field distribution calculation unit 4c.
The average magnetic field calculation unit 4a regards a predetermined region 31 in the analysis target region 21 shown in FIG. 2 as an equivalent element, and calculates the average magnetic flux density B _ave and average magnetic field H _ave in the equivalent element. Calculate magnetic properties. In addition, the average magnetic field calculation unit 4a also calculates an angle θ _BH formed by the calculated average magnetic flux density B _ave and average magnetic field H _ave as the magnetic characteristics of the equivalent elements. In the present invention, the above equivalent elements are referred to as equivalent elements. In the above, bold indicates a vector.

As shown in FIG. 2, an equivalent element 31 made up of a magnetic body (steel plate 20) and a non-magnetic body (air) is repeatedly present in the analysis target region 21. That is, in FIG. 2, there are ten equivalent elements 31 in the X direction and five in the Y direction. Therefore, in the present embodiment, the magnetic body 20 in the analysis target region 21 in FIG. 2 is replaced with the equivalent element 31, and the electromagnetic field in the analysis target region 21 is calculated using the magnetic characteristics of the equivalent element 31. In this way, it is not necessary to divide the analysis target area 21 of FIG. 2 into a large number of areas as in the prior art. In the electromagnetic field analysis apparatus 1 of the present embodiment, the portions for obtaining the magnetic characteristics of the equivalent element 31 are the average magnetic field calculation section 4a and the magnetic characteristic curve creation section 4b of the processing section 4 in FIG. The part that analyzes the electromagnetic field in the analysis target region 21 with the number of divisions in the analysis target region 21 significantly reduced by using the characteristics is the magnetic field distribution calculation unit 4 c of the processing unit 4.
Here, the analysis region and equivalent elements in the present embodiment will be described in detail with reference to FIGS. 3 and 4.

3, the magnetic properties of the equivalent elements 31 (e.g., the average magnetic flux density B _ave relationships and the average magnetic field H _ave, the average magnetic flux density B _ave and the average magnetic field H _ave the angle theta _BH of the average magnetic flux density B _ave It is the figure which showed an example of the analysis model for calculating | requiring (relationship). As shown in FIG. 3, the equivalent element 31 is the same as the equivalent element 31 of FIG. 2, and is a two-dimensional region (plane) formed by the central portion 20e1 of the magnetic body 20e and air on its side. Yes, the vertical dimension is 100 [mm] and the horizontal dimension is 31 [mm]. Here, the case where the equivalent element is a part of the magnetic body 20e in FIG. 2 is described as an example. However, even with the other magnetic bodies 20a and 20b in FIG. Since it is the same, the same magnetic characteristic data calculated from FIG. 3 may be used in the analysis of FIG.

  The analysis region 30 is a two-dimensional region (plane) including the equivalent element 31 at the center, and has a size of 200 [mm] in the vertical direction and 200 [mm] in the horizontal direction.

  FIG. 4 is a diagram illustrating a state in which the analysis region 30 is divided into a plurality of square or rectangular regions so that the analysis region 30 of FIG. 3 can be analyzed by electromagnetic field analysis using a finite element method. Each of the plurality of divided areas has an appropriate size that can be calculated by a finite element method (FEM). In the following description, this divided area is referred to as a divided area. In this embodiment, the finite element method is used as an electromagnetic field analysis method. However, even if it is used in other numerical analysis methods such as a difference method, Fourier transform, and Fourier series, it is the same as when using the finite element method. The electromagnetic field can be analyzed.

The average magnetic field calculation unit 4a obtains the magnetic flux density B and the magnetic field H generated in each of the plurality of divided regions when the external magnetic field H _ext is applied to the analysis region 30. The external magnetic field H _ext is expressed as (Formula 1) below.
H _ext = {H _extX , H _extY } (1 set)

Thus, the external magnetic field H _ext is a two-dimensional vector having a value H _EXTx easy axis direction, and a value H _ExtY the hard axis direction. In the present embodiment, the direction of the external magnetic field H _ext is specified by the angle φ formed by the external magnetic field H _ext and the easy axis X (see FIGS. 2 to 4).

When such an external magnetic field H _ext is applied, the magnetic flux density B (i, j) and magnetic field H (i, j) generated in the divided areas shown by the oblique lines in FIG. (Expression 3)

B (i, j) = {B _X (i, j), B _Y (i, j)} (Expression 2)
H (i, j) = {H _X (i, j), H _Y (i, j)} (Expression 3)

In the above, i and j are natural numbers for specifying the location of the divided region.
As described above, the magnetic flux density B (i, j) and the magnetic field H (i, j) generated in each divided region are also expressed as values B _X (i, j) and H _X (i, j) in the easy axis direction. It is a two-dimensional vector having values B _Y (i, j) and H _Y (i, j) in the magnetic field hard axis direction. The magnetic flux density B (i, j) and magnetic field H (i, j) generated in each divided region can be obtained by electromagnetic field analysis by a finite element method based on Maxwell's electromagnetic equations. Specifically, the equation regarding the static magnetic field shown in the following (formula 4) is used.

Here, [μ] ⁻¹ is the reciprocal of the magnetic permeability. A is a vector potential, and this vector potential A is defined as in the following (formula 5).

J ₀ is an applied current excited in the electric device. Based on this equation, using the interpolation function in the spatially discrete division region as shown in FIG. 4, using the variational method or the Galerkin method, the constitutive equation is obtained, and using the Gaussian elimination method or the ICCG method. Thus, the vector potential A in the divided region is obtained, and then the magnetic flux density B (i, j) and the magnetic field H (i, j) there are obtained. The details of the finite element method are described in, for example, “Nakada, Takahashi,“ Fine Element Method of Electrical Engineering, Second Edition ”, Morikita Publishing, 1982”, so only an outline is given here.

  The average magnetic field calculation unit 4a then generates the magnetic flux density generated in the equivalent element 31 from the magnetic flux density B (i, j) generated in each divided region and the magnetic field H (i, j) obtained as described above. B (i, j) and magnetic field H (i, j) are extracted.

Then, the average magnetic flux density B _ave and the average magnetic field H _ave in the equivalent element 31 are obtained from the extracted magnetic flux density B (i, j) and the magnetic field H (i, j). Specifically, it is obtained by the following (formula 6) to (formula 11).

In the above, B _X (i, j) is the value of the magnetic flux density B (i, j) in the easy axis direction. B _Y (i, j) is the value of the magnetic flux density B (i, j) in the hard axis direction.

H _X (i, j) is a value in the direction of the easy axis of the magnetic field H (i, j). H _Y (i, j) is the value of the magnetic field H (i, j) in the hard axis direction.
ΔS (i, j) is the size (area) of the divided region (see FIG. 4).

In this embodiment, the average magnetic flux density _Bave calculated as described above is regarded as the magnetic flux density generated in the equivalent element 31. The average magnetic field H _ave is regarded as a magnetic field generated in the equivalent element 31.

In the present embodiment, the direction of the average magnetic flux density B _ave is specified by the angle θ _B formed by the average magnetic flux density B _ave and the easy axis X. Further, the direction of the average magnetic field H _ave is specified by the angle θ _H formed by the average magnetic field H _ave and the easy magnetization axis X (see FIG. 3).

  Further, when the magnetic flux density B (i, j) and the magnetic field H (i, j) generated in each divided region are obtained as described above, the B of the steel plate 20 measured in advance as shown in FIG. -H curve is used. In FIG. 5, a BH curve 51 plotted with black circles is a BH curve in the easy magnetization axis direction of the magnetic bodies 20 to 24. A BH curve 52 plotted with white squares is a BH curve in the hard axis direction of the steel plate 20.

  From the above, the magnetic characteristics in the equivalent element 31 are obtained by the following (Expression 12) to (Expression 14).

Then, by changing the external magnetic field H _ext magnitude and direction (the external magnetic field H _ext, the angle φ between the magnetization easy axis X), repeating the calculation by the (expression 2) to (12 type).
More specifically, for example, the angle φ formed by the external magnetic field H _ext and the easy magnetization axis X is set to 0, 15, 30, 45, 60, 75, 90 [°], and the external magnetic field at each angle φ. An average magnetic flux density B _ave and an average magnetic field H _ave are obtained when the size of H _ext is 0, 100, 500, 1000, 2000, 5000, 10000 [Gauss].

As described above, the average magnetic field calculation unit 4a according to the present embodiment has the following four relations, respectively, _indicating the magnitude of the external magnetic field H _ext and the angle φ formed by the external magnetic field H _ext and the easy axis X. As a parameter.
1. External magnetic field H _{ext -angle} θ _B
2. External magnetic field H _{ext −average} magnetic flux density B _ave
3. External magnetic field H _{ext -average} magnetic field H _ave
4). External magnetic field H _{ext -angle} θ _BH
In this embodiment, the external magnetic field H _ext, the angle theta _B, the average magnetic flux density B _ave, the average magnetic field H _ave, and was to obtain the relationship between the angle theta _BH, and the external magnetic flux density B _ext, You may make it obtain _| require the relationship with angle (theta) _B , average magnetic flux density _Bave , average magnetic field _Have , and angle (theta) _BH .

The magnetic characteristic curve creation unit 4b creates a BH curve in the equivalent element 31 based on the average magnetic flux density B _ave and the average magnetic field H _ave calculated by the average magnetic field calculation unit 4a. That is, a curve representing the relationship between the average magnetic field H _ave and the average magnetic flux density B _ave is created. Then, the created BH curve is recorded on a recording medium. An example of a specific method for creating the BH curve in the equivalent element 31 will be described with reference to FIGS.

First, as shown in FIG. 6, curves 60 to 66 representing the relationship between the angle θ _B between the average magnetic flux density B _ave and the easy magnetization axis X and the external magnetic field H _ext are represented by the external magnetic field H _ext and the easy magnetization axis. An angle φ formed with X is created as a parameter.

From these curves 60 to 66, the average magnetic flux density B _ave and the average magnetic field H when the angle θ _B formed by the average magnetic flux density B _ave and the easy magnetization axis X is 0, 15, 30, 90 [°]. _Ask for _ave . Needless to say, the angle θ _B formed between the average magnetic flux density B _ave and the easy magnetization axis X used at this time is not limited to 0, 15, 30, 90 [°].

More specifically, for example, as shown in FIG. 7, a line 70 having an angle θ _B of 30 [°] between the average magnetic flux density B _ave and the easy magnetization axis X, and a curve (for example, a curve) shown in FIG. 64) is obtained. Then, the average magnetic flux density B _ave and average magnetic field H _{ave at} the obtained intersection 71 are obtained.

At this time, performs linear interpolation using the average magnetic flux density B _ave before and after the point 72 and 73 of the intersection 71 and the average magnetic field H _ave, computing the the average magnetic flux density B _ave at the intersection 71 and the average magnetic field H _ave Can do.

Then, to create a B-H curve 80-83 representing the relationship between the average magnetic flux density B _ave and the average magnetic field H _ave obtained as described above (see Figure 8). Further, a leveling process is performed on the BH curves 80 to 83. In the present embodiment, the BH curves 90 to 93 that have been subjected to the leveling process are defined as BH curves in the equivalent element 31 (see FIG. 9).

The magnetic characteristic curve creation unit 4b creates a B-θ curve in the equivalent element 31 based on the average magnetic flux density B _ave and the average magnetic field H _ave calculated by the average magnetic field calculation unit 4a. That is, a curve representing the relationship between the angle θ _BH formed by the average magnetic flux density B _ave and the average magnetic field H _ave (see FIG. 3) and the average magnetic flux density B _ave is created. Then, the created B-θ curve is recorded on a recording medium.

More specifically, as shown in FIG. 10, the above-mentioned (10 type) and the average magnetic flux density B _ave and the angle theta _BH between the average magnetic field H _ave obtained using the relationship between the average magnetic flux density B _ave B-θ curves 100 to 103 representing the angle θ _B formed by the average magnetic flux density B _ave and the easy magnetization axis X are created as parameters. In the example shown in FIG. 10, curves 100 to 103 are created when the angle θ _B formed between the average magnetic flux density B _ave and the easy axis X is 0, 15, 30, 90 [°]. The angle θ _B formed between the average magnetic flux density B _ave used as a parameter and the easy axis X is the same value as the angle θ _B used when creating the BH curves 90 to 93 shown in FIG. Use it.

  The magnetic field distribution calculation unit 4c generates magnetic flux lines in the analysis target region 21 based on the BH curves 90 to 93 and the B-θ curves 100 to 103 created by the magnetic characteristic curve creation unit 4b as described above. Ask for. Then, the magnetic flux density at a desired position in the analysis target region 21 is obtained from the obtained magnetic flux lines. Note that the magnetic flux lines generated in the analysis target region 21 are obtained using a finite element method (FEM). The method of electromagnetic field analysis by the finite element method is as described above.

  Further, when using the finite element method, it is preferable to apply the side element finite element method. In this embodiment, a two-dimensional model is used. However, in a three-dimensional model described later, it is particularly important to perform an electromagnetic field analysis by applying side elements. This is because the amount of data used for the analysis is smaller when the edge element is applied than when the node element is applied. More specifically, when a node element is applied, the number (this embodiment) is obtained by multiplying the number of vertices (nodes) in the element (4 in this embodiment) by the number of dimensions (2 in this embodiment). Then, data based on 8) is required. On the other hand, when the side element is applied, there may be data based on the number of sides constituting the element (6 in the present embodiment).

  In addition, the magnetic flux lines can be obtained more accurately when the side element finite element method is applied than when the nodal element finite element method is applied. More specifically, for example, the nodal element finite element method is applied to a rectangular region (element) at the boundary between different materials (in this embodiment, a steel plate and air) on one of two opposing sides. In this case, the physical quantity obtained from each node is a mixture of physical quantities of the different substances. On the other hand, when the side element finite element method is applied, the physical quantity obtained from one of the two opposing sides is a mixture of physical quantities of the different substances, The physical quantity obtained from the other is the physical quantity of one substance. Therefore, in the rectangular region (element) as described above, the magnetic flux lines can be obtained more accurately by applying the side element finite element method than by applying the nodal element finite element method.

In FIG. 3, when an external magnetic field H _ext is applied to the equivalent element 31 to obtain the magnetic characteristics of the equivalent element 31, the magnetic body 20e1 in the equivalent element 31 is magnetized, but the shape and number of the magnetic bodies 20e1 Depending on the case, the influence of a demagnetizing field may appear and predetermined magnetic characteristics may not be obtained. For this reason, in the present embodiment, as shown in FIG. 3, a wide area in which attention is paid to the number and size of magnetic materials to the extent that no demagnetizing field is generated is considered as an area for analyzing the electromagnetic field. preferable.

Next, an example of the processing operation in the electromagnetic field analysis apparatus 1 of the present embodiment will be described with reference to the flowchart of FIG.
First, in the first step S1, the average magnetic field calculation unit 4a sets the magnitude of the external magnetic field H _ext applied to the analysis region 30 to an initial value (0 [Gauss]).

Next, in step S2, the average magnetic field calculation unit 4a sets an angle φ formed by the external magnetic field H _ext and the easy magnetization axis X to an initial value (0 [°]).
Thus, the direction of the external magnetic field H _ext is set by setting the angle φ formed by the external magnetic field H _ext and the easy magnetization axis X.

Next, in step S3, the average magnetic field calculation unit 4a sets the boundary condition of the analysis region 30 according to the external magnetic field _Hext . Specifically, in the present embodiment, when the external magnetic field H _ext is applied, for example, a value corresponding to the external magnetic field H _ext is inserted into the boundary element in the analysis region 30 in FIG. Try to set.

Next, in step S4, the average magnetic field calculation unit 4a calculates the magnetic flux density B (i, j) and the magnetic field H (i, j) generated in the analysis region 30 according to the setting content of the external magnetic field _Hext .
More specifically, the aforementioned finite element method electromagnetic field analysis is performed on the analysis region 30 with the external magnetic field H _ext as a boundary condition.

  Next, in step S5, the average magnetic field calculation unit 4a determines the magnetic flux density generated in the equivalent element 31 from the magnetic flux density B (i, j) and the magnetic field H (i, j) obtained by the processing in step S4. B (i, j) and magnetic field H (i, j) are extracted.

Next, in step S6, the average magnetic field calculation unit 4a uses the magnetic flux density B (i, j) and the magnetic field H (i, j) extracted in step S5 to determine the magnetic characteristics (in the equivalent element 31). the average magnetic flux density B _ave of seeking average the magnetic field H _ave) is stored in the recording medium. Further, an angle θ _BH formed by the obtained average magnetic flux density B _ave and average magnetic field H _ave is obtained and stored in the recording medium.

Next, in step S7, the average magnetic field calculation unit 4a determines whether or not the magnitude of the external magnetic field _Hext is a specified value.
In the present embodiment, the magnitude of the external magnetic field H _ext is increased in the order of 0, 100, 500, 1000, 2000, 5000, and 10000 [Gauss]. Therefore, 10000 [Gauss] is the specified value.

As a result of the determination in step S7, if the magnitude of the external magnetic field H _ext is not a specified value, the process proceeds to step S8 and the set value is changed. For example, when the set value of the magnitude of the external magnetic field H _ext is 0 [Gauss], the set value is changed to 100 [Gauss]. Then, the process returns to step S3.
On the other hand, when the set value of the magnitude of the external magnetic field H _ext is a specified value, the process proceeds to step S9 and the set value is reset to the initial value.

Then, the determination in step S10, the average magnetic field arithmetic section 4a, the set value of the direction of the external magnetic field H _ext (angle between the external magnetic field H _ext magnetization easy axis X phi) is, whether the specified value To do.
In the present embodiment, the angle φ formed by the external magnetic field H _ext and the easy axis X is increased in the order of 0, 15, 30, 45, 60, 75, 90 [°]. Therefore, 90 [°] is the specified value.

Result of judgment at step S10, the set value of the direction of the external magnetic field H _ext (angle between the external magnetic field H _ext magnetization easy axis X phi) is, if not specified value, the setting value proceeds to step S11 change. For example, when the set value of the angle φ formed by the external magnetic field H _ext and the easy axis X is 0 [°], the set value is changed to 15 [°]. Then, the process returns to step S3.

On the other hand, the set value of the direction of the external magnetic field H _ext (angle between the external magnetic field H _ext magnetization easy axis X phi) is, when it is the specified value is reset to the initial value settings proceeds to step S12 .

Next, in step S13, the magnetic characteristic curve creating unit 4b calculates B− in the equivalent element 31 from the average magnetic flux density B _ave (i, j) and the average magnetic field H _ave (i, j) obtained in step S6. Create H curves 90-93.

Next, in step S14, the magnetic characteristic curve creation unit 4b determines from the average magnetic flux density B _ave (i, j) obtained in step S6 and the angle θ _BH formed by the average magnetic flux density B _ave and the average magnetic field H _ave. The B-θ curves 100 to 103 in the equivalent element 31 are created.

  Finally, in step S15, the magnetic field distribution calculation unit 4c uses the BH curves 90 to 93 and the B-θ curves 100 to 103 in the equivalent element 31 created in steps S13 and S14 to analyze the analysis target region. The magnetic flux lines generated at 21 are obtained. Further, the magnetic flux density at a desired position in the analysis target region 21 is obtained from the obtained magnetic flux lines.

Next, an example of processing operation in the electromagnetic field analyzer 1 when creating the BH curve in step S13 in FIG. 11 will be described with reference to the flowchart in FIG.
First, in the first step S21, the magnetic characteristic curve creating unit 4b represents a curve representing the relationship between the external magnetic field H _ext and the angle θ _B formed by the average magnetic flux density B _ave obtained in step S6 and the easy axis X. 60 to 66 are created by performing the linear interpolation described above.

Next, in step S22, the magnetic characteristic curve generator unit 4b, from the curve 60 to 66 obtained in step S21, the angle theta _B between the average magnetic flux density B _ave magnetization easy axis X, 0, 15, 30, The average magnetic flux density B _ave and average magnetic field H _ave at 90 [°] are obtained.
Finally, in step S23, the magnetic characteristic curve generator unit 4b, the B-H curve 90 to 93 representing the relationship between the average magnetic flux density B _ave and the average magnetic field H _ave obtained in step S22, the leveling process described above Create by doing.

Next, an example of the processing operation in the electromagnetic field analyzer 1 when creating the B-θ curve in step S14 in FIG. 11 will be described with reference to the flowchart in FIG.
First, in the first step S31, the magnetic characteristic curve creation unit 4b determines that the angle θ _B formed by the average magnetic flux density _Bave obtained in step S6 and the easy magnetization axis X is 0, 15, 30, 90 [°]. The angle θ _BH formed by the average magnetic flux density B _ave and the average magnetic field H _ave is obtained.

In step S32, the magnetic characteristic curve creating unit 4b determines that the angle θ _B formed by the average magnetic flux density _Bave and the easy axis X obtained in step 22 in FIG. 12 is 0, 15, 30, 90 [°. ] and the average magnetic flux density B _ave of time, determined in step S31, the angle theta _B between the average magnetic flux density B _ave easy magnetization axis X is the average magnetic flux when the 0,15,30,90 [°] B-θ curves 100 to 103 representing the relationship between an angle θ _BH formed by the density B _ave and the average magnetic field H _ave are created.

  The above-described method (equivalent BH method) of the present embodiment for obtaining the electromagnetic field (for example, magnetic flux lines) generated in the analysis target region 21 is summarized as shown in FIG.

Next, the analysis result of the magnetic flux density obtained as described above will be shown.
FIG. 15 is a diagram comparing the result analyzed by the method of the present embodiment with the result analyzed by the conventional method.

Specifically, FIG. 15A is a diagram comparing the relationship between the angle (external magnetic field approach angle) φ formed by the external magnetic field H _ext and the easy magnetization axis X and the magnetic flux density at the point A shown in FIG. It is.

FIG. 15B is a diagram comparing the relationship between the angle (external magnetic field approach angle) φ formed by the external magnetic field H _ext and the easy magnetization axis X and the magnetic flux density at the point B shown in FIG. .
In FIG. 15, the method in the present embodiment is represented as an equivalent BH method. Table 1 below shows these results in a tabular form.

  As shown in FIG. 16A, when the method of the present embodiment (equivalent BH method) is used, the region occupied by the analysis target region 21 shown in FIG. 2 (vertical 4000 [mm], horizontal 1155 [mm]) is divided into 667 areas (elements). On the other hand, as shown in FIG. 16B, when the conventional finite element method is used, the region occupied by the analysis target region 21 is divided into 52488 regions (elements).

  From these facts (Table 1, FIG. 15 and FIG. 16), when analyzed by the method of the present embodiment, even if the number of divided regions (number of elements) is reduced, the analysis is performed by the conventional method. It can be seen that substantially similar results are obtained.

As described above, in the present embodiment, a predetermined area occupied by the central portion 20e1 of the magnetic body 20 that repeatedly exists at a predetermined interval and the air on the side thereof is defined as one equivalent element 31. The average magnetic flux density B _ave generated in the equivalent element 31, the average magnetic field H _ave, and the angle θ _BH formed by the average magnetic flux density B _ave and the average magnetic field H _ave are calculated, and the calculated average magnetic field H _ave and average magnetic flux density are calculated. BH curves 90-93 represent the relationship between the B _ave, and the average magnetic flux density B _ave and the angle theta _BH between the average magnetic field H _ave, B-θ curve 100 representing the relationship between the average magnetic flux density B _ave 103 is created using the angle θ _B as a parameter, and magnetic flux lines generated in the analysis target region 21 are obtained using the created B-H curves 90 to 93 and B-θ curves 100 to 103. Analysis target area 2 even if it is not divided into It is possible to the electromagnetic field generated in the analysis. As a result, the storage capacity required for analyzing the electromagnetic field can be greatly reduced, and the electromagnetic field in a large-scale facility that has been difficult to analyze can be reliably analyzed.
In this way, the electromagnetic field analysis method is called an equivalent BH method in that the electromagnetic field in the analysis target region 21 is analyzed using equivalent magnetic characteristics.

In the present embodiment, the case where the electromagnetic field is analyzed using the average magnetic flux density B _ave as a reference (B center) has been described, but the average magnetic field H _ave may be used as a reference (H center). For example, in this embodiment, the angle theta _B between the average magnetic flux density B _ave easy axis of magnetization X as a parameter, has been to create a B-H curve 90 to 93, easy magnetization average magnetic field H _ave These may be created using the angle θ _H formed with the axis X as a parameter.

Moreover, you may make it obtain | require the iron loss which arises when the external magnetic field _Hext is given. Specifically, for example, the iron loss is obtained based on the BH curves 90 to 93 created by the magnetic characteristic curve creation unit 4b. Further, a curve representing the relationship between the obtained iron loss and the average magnetic flux density B _ave is created using the angle θ _B formed by the average magnetic flux density B _ave and the easy magnetization axis X as a parameter, and the created curve is used as a recording medium. It may be recorded.

  Furthermore, the analysis target area of the equivalent element is not limited to that shown in FIG. 3 as long as it is an area occupied by a plurality of substances including a magnetic material. That is, as long as it is a representative region in the analysis target region 21, the position and size of the equivalent elements are not limited to those shown in FIG. 3, and the range in which the magnetic field distribution in the analysis target region 21 can be appropriately obtained. Can be determined as appropriate.

For example, as shown in FIG. 17, the electromagnetic field analysis device 1 of the present embodiment is also applied when analyzing an electromagnetic field generated in an analysis target region 171 configured using a steel plate 170 processed into a hollow rectangular parallelepiped shape. be able to. In this case, the equivalent element 172 is, for example, a two-dimensional region (plane) formed by a part of the steel plate 170 and air on its side. Then, an external magnetic field H _ext is applied to the equivalent element 172, and the average magnetic flux density B _ave and the average magnetic field H _ave are calculated as described above. Further, the average magnetic flux density B _ave and the angle θ _BH formed by the average magnetic field H _ave are calculated. Then, magnetic flux lines generated in the magnetic shield device (analysis region) 171 are obtained.

Here, the external magnetic field H _ext is given by, for example, an exciter 173 disposed at the center of the hollow region surrounded by the steel plate 170 as shown in FIG. More specifically, an external magnetic field H _{ext is applied} to the equivalent element 172 by causing a current to flow through the coil 173b wound around the core 173a. The magnitude and direction of the external magnetic field H _ext can be changed by changing the magnitude of the current in the coil 173b and the angle φ ′ of the core 173a.

  In addition, the actual shield device is reduced (for example, (1/16) times or (1/8) times) the shield device to be analyzed, and the magnetic flux lines generated in the shield device to be analyzed are You may make it obtain | require as mentioned above.

  Note that the analysis region described above may be composed of a plurality of types of equivalent elements, and in that case, there are a plurality of types of equivalent elements. In this case, since there are a plurality of types of equivalent elements, there are also a plurality of types of equivalent BH curves corresponding to FIG.

  In the present embodiment, the two-dimensional region formed by the central portion 20e1 of the magnetic body 20e and the air on the side thereof is used as the equivalent element 31, but the substance included in the equivalent element is not limited to these. . That is, any region may be used as an equivalent element as long as it is a region occupied by a magnetic body and a non-magnetic body. Here, the magnetic body is not limited to a ferromagnetic body such as iron or cobalt, but may be a magnetic body other than a ferromagnetic body such as a paramagnetic body such as iron oxide. The non-magnetic material is not limited to air but refers to a non-magnetic material such as a copper coil, wood, and resin.

In this embodiment, the angle θ _BH is considered in order to improve the accuracy of the analysis result of the electromagnetic field. However, the angle θ _BH may be ignored depending on the simple formula and the analysis accuracy to be obtained.
In addition, the operation unit 2, the display unit 3, and the processing unit 4 in the electromagnetic field analysis device 1 may be in the same space, or may be coupled via a network.

(Second Embodiment)
Next, a second embodiment of the present invention will be described. In the following description, the same portions as those in the first embodiment described above are denoted by the same reference numerals as those in FIGS. 1 to 17 and detailed description thereof is omitted.

  In the present embodiment, the two-dimensional analysis in the first embodiment described above is simplified, and the electromagnetic field analysis apparatus of the present embodiment replaces the average magnetic field calculation unit 4a and the magnetic characteristic curve creation unit 4b. Has a magnetic characteristic calculation unit. This magnetic characteristic calculation part calculates | requires the magnetic permeability in the equivalent element 31 shown in FIG.

In FIG. 3, the length of the equivalent element 31 in the hard axis (Y axis) direction is 31 mm, and the thickness of the magnetic body 20e in the hard axis (Y axis) direction is 1 mm. Thus, the thickness of the magnetic body 20e in the equivalent element 31 in the hard axis (Y axis) direction is sufficiently thinner than the length of the equivalent element 31 in the hard axis (Y axis) direction. Then, in the analysis model of FIG. 3, the steel plate 20e1 is filled and occupied in the easy axis (X axis) direction, whereas the steel plate 20e1 is filled and occupied in the hard axis (Y axis) direction. It means that you have not. Thereby, the magnetic characteristic calculation unit obtains the magnetic permeability (permeability of the equivalent element 31) μ _aveX and μ _aveY of each axis in the analysis model of FIG. 3 using the following (Expression 15) and (Expression 16). Can do.

In the above, μ _XFe is the magnetic permeability in the easy axis (X axis) direction of the magnetic body in the equivalent element 31. μ _YFe is the magnetic permeability in the hard axis (Y axis) direction of the magnetic body in the equivalent element 31. μ ₀ is the permeability of air (nonmagnetic material). k is a constant that takes into account the influence of the demagnetizing field.

As described above, in the present embodiment, the thickness of the magnetic body 20e in the equivalent element 31 in the hard axis (Y axis) direction is equal to the length of the equivalent element 31 in the hard axis (Y axis) direction. Thin enough. Therefore, as shown in the above (Expression 16), the permeability μ _Y in the hard axis (Y axis) direction of the equivalent element 31 can be approximated to the permeability μ ₀ of air (non-magnetic material).

Magnetic field distribution calculating unit 4c, by using the magnetic permeability mu _avex in the magnetic properties easy axis determined by the calculation unit (X-axis) direction, and a magnetic permeability mu _AveY in the hard magnetization axis (Y-axis) direction, The electromagnetic field analysis of the analysis target area 21 shown in FIG.

As described above, in the present embodiment, the permeability μ _aveX in the easy axis (X axis) direction of the equivalent element 31 is obtained using the equation (15), and the hard axis of magnetization (Y axis) in the equivalent element 31 is obtained. The magnetic permeability μ _{aveY in the} direction is obtained using (Equation 16), and the electromagnetic field in the analysis target region 21 is analyzed using the obtained magnetic permeability μ _aveX and μ _aveY , so that the electromagnetic field is analyzed at higher speed. be able to. The method described in this embodiment is effective when it is required to execute analysis at a higher speed than the analysis accuracy.
In this embodiment, the magnetic permeability is obtained, but a magnetic resistivity that is the reciprocal of the magnetic permeability may be obtained.

(Third embodiment)
Next, a third embodiment of the present invention will be described. In the first and second embodiments described above, the case where a two-dimensional electromagnetic field is analyzed has been described. In the present embodiment, a case where a three-dimensional electromagnetic field is analyzed will be described. Thus, the present embodiment and the first embodiment described above differ only in the dimension of the electromagnetic field to be analyzed. Therefore, the same parts as those of the first embodiment described above are shown in FIG. Detailed description will be omitted by attaching the same reference numerals as those shown in FIG.

  FIG. 18 is a diagram showing an example of the configuration of a magnetic shield device that performs analysis by the electromagnetic field analysis device of the present embodiment. In the present embodiment, an electromagnetic field analyzer for evaluating the shielding performance of the magnetic shield device 180 will be described.

  In FIG. 18, the magnetic shield device 180 is configured by combining 32 steel plates having a length of 300 mm, a width of 25 mm, and a thickness of 1 mm. More specifically, the magnetic shield device 180 is configured by stacking four sets of four steel plates arranged in a “mouth” shape at intervals of 30 mm. In this case, an equivalent element 182 and an equivalent element 183 can be considered as equivalent elements composed of a magnetic body and a non-magnetic body. In the present embodiment, an equivalent magnetic characteristic in the case of the equivalent element 182 will be described first. FIG. 18 corresponds to FIG. 2 in the first embodiment described above.

  FIG. 19 is a diagram showing an example of an analysis model for obtaining the magnetic characteristics of the equivalent element 182 shown in FIG. 18, and corresponds to FIG. 3 or FIG. 17 in the first embodiment described above. As shown in FIG. 19, an equivalent element 182 exists in the analysis region 190, and the central part 181 a of the magnetic body 181 is in the equivalent element 182.

  In the present embodiment, the magnetic body (central part) 181a in the equivalent element 182 has a width (vertical axis (Z axis) direction perpendicular to the easy magnetization axis (X axis) and the hard magnetization axis (Y axis). ) Is 25 mm, the thickness (length in the hard axis (Y axis) direction) is 1 mm, and the length (length in the easy axis (X axis) direction) is 25 mm.

In addition, the analysis region 190 in the present embodiment is a three-dimensional region (space) including the equivalent element 182 at the center.
Thus, in the present embodiment, an electromagnetic field generated in a three-dimensional region (space) defined by the easy magnetization axis X, the hard magnetization axis Y, and the vertical axis Z of the steel plate 20 is analyzed.

  In the present embodiment, as shown in FIG. 20A, the analysis region 190 is divided into a plurality of divided regions made of a cube or a rectangular parallelepiped. Each of the plurality of divided regions has an appropriate size that can be calculated by a finite element method (FEM).

When the external magnetic field H _ext is applied to the boundary region of the analysis region 190, the average magnetic field calculation unit 4a obtains the magnetic flux density B and the magnetic field H generated in each of the plurality of divided regions by electromagnetic field analysis using the finite element method. . The external magnetic field H _ext is expressed as in the following (Expression 17).
H _ext = {H _extX , H _extY , H _extz } (Expression 17)

Thus, the external magnetic field H _ext is a three-dimensional vector having a direction of easy magnetization value H _EXTx, the values of H _ExtY the hard axis direction, and a value of the vertical axis value H _Extz .

When such an external magnetic field H _{ext is applied} to the equivalent element 190, the magnetic flux density B (i, j, k) generated in the divided area indicated by the oblique lines in FIG. 20A and the magnetic field H (i, j , K) are expressed by the following (Equation 18) and (Equation 19), respectively.

B (i, j, k) = {B _X (i, j, k), B _Y (i, j, k), B _z (i, j, k)} (18)
H (i, j, k) = {H _X (i, j, k), H _Y (i, j, k), B _z (i, j, k)} (Equation 19)

In the above, i, j, and k are natural numbers for specifying the location of the divided region.
Thus, the magnetic flux density B (i, j, k) and magnetic field H (i, j, k) generated in each divided region are also values B _X (i, j, k), H _X ( i, j, k), values B _Y (i, j, k), H _Y (i, j, k) in the hard axis direction, and values B _z (i, j, k) in the vertical axis direction, A three-dimensional vector having H _z (i, j, k).

The average magnetic field calculation unit 4a uses the magnetic flux density B (i, j, k) and the magnetic field H (i, j, k) in each divided region obtained as described above to generate the magnetic flux density in the equivalent element 181. B (i, j, k) and magnetic field H (i, j, k) are extracted. From the extracted magnetic flux density B (i, j, k) and magnetic field H (i, j, k), the equivalent element 182 The average magnetic flux density B _ave and the average magnetic field H _ave are obtained.

As shown in FIG. 20, in this embodiment, the average magnetic flux density B _ave is _obtained by dividing it into a component B _{aveX-Y in the} easy axis-hard magnetization axis direction and a component B _{aveZ in} the vertical axis direction. In the following description, the component B _{aveX-Y in the} easy axis-hard magnetization axis direction and the component B _{aveZ in} the vertical axis direction of the average magnetic flux density B _ave are respectively _expressed as the second and third average magnetic flux densities B _{aveX. -Y} and _BaveZ .

The average magnetic field H _ave is also _obtained by dividing into a component H _{aveX-Y in the} easy axis-hard magnetization axis direction and a component H _{aveZ in} the vertical axis direction. In the following description, the component H _{aveX-Y in the} easy axis-hard magnetization axis direction and the component H _{aveZ in} the vertical axis direction of the average magnetic field H _ave are respectively _expressed as the second and third average magnetic fields H _{aveX-Y. And HaveZ} .

As for the easy magnetization axis-hard magnetization axis direction, as in the first embodiment described above, the magnitude and direction of the external magnetic field H _ext1 are changed, and the second average magnetic flux density B _aveX-Y , the average magnetic field H _avex-Y 2, and angle theta _BHX-Y of the second average flux density B _avex-Y and a second average magnetic field H _avex-Y seek (see Figure 20).
In the above, the external magnetic field H _ext1 represents a component of the external magnetic field H _{ext in} the direction of the easy axis to the hard axis.

On the other hand, in the vertical axis direction, the magnitude of the external magnetic field H _ext2 is changed to change the third average magnetic flux density B _aveZ , the third average magnetic field H _aveZ , the third average magnetic flux density B _aveZ, and the third average magnetic flux density B _aveZ . An angle θ _BHZ formed with the average magnetic field H _aveZ is obtained.
In the above, the external magnetic field H _ext2 represents the vertical axis direction component of H _ext .

The magnetic characteristic curve creation unit 4b performs the second and third average magnetic flux densities B _aveX-Y and B _aveZ obtained by the average magnetic field calculation unit 4a as described above, and the second and third average magnetic fields H _{aveX. Based on -Y} and _HaveZ , BH curves 2001 and 2002 as shown in FIG. 21 are created. Further, the second and third average magnetic flux density B _avex-Y, based on the angle theta _BHX-Y, to create a B-theta curve 2101 as shown in FIG. 22.

That is, the BH curves 2001a to 2001n obtained from the second average magnetic flux density _BaveX-Y and the second average magnetic field _HaveX-Y are created in the same manner as in the first embodiment described above. Further, a BH curve 2002 obtained from the third average magnetic flux density B _aveZ and the third average magnetic field H _aveZ is created.
Further, a second average flux density B _avex-Y, the second average flux density B _avex-Y and B-theta curve 2101a determined from the angle theta _BHX-Y of the second average magnetic field H _avex-Y To 2101n are created in the same manner as in the first embodiment described above.

As described above, in the present embodiment, the average magnetic flux density B _ave and the average magnetic field H _ave having three-dimensional values are obtained separately for the easy magnetization axis-hard magnetization axis direction component and the vertical direction component. As for the easy axis to hard axis direction component, a BH curve 2001 and a B-θ curve 2101 are created in the same manner as in the first embodiment described above, and the vertical axis direction is separately B. Since the −H curve 2002 is created, the BH curve and the B−θ curve in the three-dimensional equivalent element 182 can be created without performing complicated calculations.

In the present embodiment, the third average magnetic flux density B _avez and the third average magnetic field H _avez are calculated, but they may be prepared in advance without calculating them. That is, a BH curve prepared in advance may be used for the component in the vertical axis direction. In this case, the magnetic permeability (relative magnetic permeability) may be constant. For example, the value of relative permeability may be set to 1000.

Further, when _obtaining the average magnetic flux density B _ave and the average magnetic field H _ave as described above, the three axes (easy magnetization axis X, difficult magnetization axis Y, vertical axis Z) in the equivalent element 181 and the analysis region 180 are orthogonal to each other. If the three axes (vertical, horizontal and height axes) to be matched do not coincide with each other, the equivalent element 182 is subjected to coordinate transformation or rotational transformation, and the three axes in the equivalent element 182 and the three axes in the analysis region 190 Are preferably matched with each other.

  Furthermore, in the present embodiment, the analysis region 190 and the equivalent element 182 are three-dimensional regions (spaces) determined from the easy magnetization axis X, the hard magnetization axis Y, and the vertical axis Z. Similarly to the embodiment, the analysis region and the equivalent element may be a two-dimensional region (plane) determined from the easy magnetization axis X and the hard magnetization axis Y.

  Further, the equivalent element 183 shown in FIG. 18 may be processed similarly to the case of obtaining the magnetic characteristics of the equivalent element 182. In this case, a three-dimensionally expanded model shown in FIG. 17 may be used as an analysis model for obtaining the magnetic characteristics of the equivalent element, and the corner portion of the analysis model may be used as the equivalent element.

(Fourth embodiment)
Next, a fourth embodiment of the present invention will be described. Note that the present embodiment and the third embodiment described above differ only in the calculation method of the average magnetic flux density B _ave and the average magnetic field H _ave , and therefore the first to third embodiments described above. About the same part, detailed description is abbreviate | omitted by attaching | subjecting the code | symbol same as the code | symbol attached | subjected to FIGS.

  As shown in FIG. 23, the analysis region 190 and the equivalent element 182 in the present embodiment are the same as those in the third embodiment. The analysis area 190 is divided into a plurality of divided areas as shown in FIG.

When the external magnetic field H _ext is applied to the boundary region of the analysis region 190, the average magnetic field calculation unit 4a obtains the magnetic flux density B and the magnetic field H generated in each of the plurality of divided regions by electromagnetic field analysis using the finite element method. . The external magnetic field H _ext is a three-dimensional vector as in the second embodiment described above (see (Equation 17)).

Further, when the external magnetic field H _{ext is applied} to the equivalent element 182, the magnetic flux density B (i, j, k) and magnetic field H (i, j, k) generated in the divided area indicated by the oblique lines in FIG. Is also a three-dimensional vector (see (Equation 18) and (Equation 19)), as in the third embodiment described above.

The average magnetic field calculation unit 4a uses the magnetic flux density B (i, j, k) generated in the equivalent element 182 from the magnetic flux density B (i, j, k) generated in each divided region and the magnetic field H (i, j, k). ) And the magnetic field H (i, j, k), and the average magnetic flux density B _ave in the equivalent element 182 is calculated from the extracted magnetic flux density B (i, j, k) and the magnetic field H (i, j, k). An average magnetic field H _ave is obtained. Specifically, it is obtained by the following (Expression 20) to (Expression 27).

In the above, B _X (i, j, k) is a value in the easy axis direction of the magnetic flux density B (i, j, k). B _Y (i, j, k) is a value of the magnetic flux density B (i, j, k) in the hard axis direction. B _Z (i, j, k) is a value in the vertical axis direction of the magnetic flux density B (i, j, k).

H _X (i, j, k) is a value in the easy axis direction of the magnetic field H (i, j, k). H _Y (i, j, k) is a value in the hard axis direction of the magnetic field H (i, j, k). H _Z (i, j, k) is a value in the vertical axis direction of the magnetic field H (i, j, k).
ΔV (i, j, k) is the size (volume) of the divided area.

And as shown to Fig.24 (a), in this Embodiment, the direction of average magnetic flux density _Bave is specified by angle (alpha) _B , (beta) _B. Specifically, the angle α _B is an angle formed between the reference line OP and the hard magnetization axis Y. Here, the reference line OP is a vector determined from the value B _{aveX in the} easy axis direction of the average magnetic flux density B _ave and the value B _aveY in the hard axis direction. The angle β _B is an angle formed by the reference line OP and the average magnetic flux density B _ave .

Here, the angle α _B is expressed by the following (Equation 28).
α _B = 90−θ _B (Expression 28)
In the above, θ _B is an angle formed by the reference line OP and the easy axis X, and corresponds to the angle θ _B described in the first to third embodiments.

Further, as shown in FIG. 24B, in the present embodiment, the direction of the average magnetic field H _ave is specified by the angles α _H and β _H. Specifically, the angle α _H is an angle formed by the reference line OQ and the hard magnetization axis Y. Here, the reference line OQ is a vector determined from the value H _aveX of the average magnetic field H _{ave in} the easy axis direction and the value H _aveY in the hard axis direction. The angle β _H is an angle formed by the reference line OQ and the average magnetic flux density H _ave .

Here, the angle α _H is expressed by the following (formula 29).
α _H = 90−θ _H (Expression 29)
In the above, θ _H is an angle formed by the reference line OQ and the easy axis X, and corresponds to the angle θ _H described in the first to third embodiments.

Then, the average magnetic field calculation unit 4a changes the magnitude and direction of the external magnetic field H _ext and performs calculations according to the above (20 formula) to (27 formula) to obtain the average magnetic flux density B _ave and the average magnetic field H _ave .

In the present embodiment, the direction of the external magnetic field H _ext is specified by the angles φ ₁ and φ ₂ as shown in FIG. Here, the angle φ ₁ is an angle between the easy axis X and the reference line OR determined from the value H _{extx in the} easy axis direction of the external magnetic field H _ext and the value H _extY in the hard axis direction. Further, the angle φ ₂ is an angle formed by the reference line OR and the external magnetic field H _ext . In the following description, the case where the direction of the external magnetic field H _ext is specified by using the angles φ ₁ and φ ₂ will be described as an example. However, if the direction of the external magnetic field H _ext can be specified, the angle φ ₁ , The direction of the external magnetic field H _ext need not be specified using φ ₂ .

Further, the average magnetic field calculation unit 4a obtains an angle α _BH formed by the reference line OP and the reference line OQ, as shown in FIG. The angle α _BH corresponds to the angle θ _BH described in the first to third embodiments.

As described above, the average magnetic field calculation unit 4a of the present embodiment obtains the following six relationships using the magnitude of the external magnetic field H _ext and the angles φ ₁ and φ ₂ as parameters, respectively.
1. External magnetic field H _{ext −average} magnetic flux density B _ave
2. External magnetic field H _{ext -average} magnetic field H _ave
3. External magnetic field H _{ext -angle} α _B
4). External magnetic field H _{ext -angle} β _B
5. External magnetic field H _{ext -angle} β _H
6). External magnetic field H _{ext -angle} α _H
In the above, the relationship between the external magnetic field H _ext and the angle β _H (external magnetic field H _{ext −angle} β _H ) or the relationship between the external magnetic field H _ext and the angle α _H (external magnetic field H _{ext −angle} α _H ). Instead, the relationship between the external magnetic field H _ext and the angle α _BH (external magnetic field H _{ext −angle} α _BH ) may be obtained.

Then, as shown in FIG. 25, the magnetic characteristic curve creating unit 4b uses the angles α _B and β _B as parameters, and the BH curves 2401a to 2401n in the equivalent element 182, that is, the average magnetic flux density B _ave and the average magnetic field H. Create a curve representing the relationship with _ave .

As shown in FIG. 26, the magnetic characteristic curve creating unit 4b uses the angles α _B and β _B as parameters, and the first B-θ curves 2501a to 2501n in the equivalent element 182, that is, the average magnetic flux density B _ave Then, a curve representing the relationship between the angle α _BH formed by the reference line OP and the reference line OQ is created.
Further, as shown in FIG. 27, the magnetic characteristic curve creating unit 4b uses the angles α _B and β _B as parameters, and the second B-θ curves 2601a to 2601n in the equivalent element 182, that is, the average magnetic flux density B _ave Then, a curve representing the relationship between the reference line OQ and the angle β _H formed by the average magnetic field H _ave is created.

As described above, in the present embodiment, the relationship between the average magnetic flux density B _ave having a three-dimensional value and the average magnetic field H _ave , the relationship between the average magnetic flux density B _ave and the angle α _BH , and the average magnetic flux density B _ave And the angle β _H are obtained using the angles α _B and β _B as parameters, the average magnetic flux density B _ave and average magnetic field H _ave having three-dimensional values can be obtained more accurately.

  In the present embodiment, the magnetic characteristic curve creation unit 4b creates the BH curves 2401a to 2401n and the first and second B-θ curves 2501a to 2501n and 2601a to 2601n. Needless to say, if the magnetic field distribution calculation unit 4c can determine the lines of magnetic force generated in the magnetic shield device, the curve created by the magnetic characteristic curve creation unit 4b is not limited to these.

(Fifth embodiment)
Next, a fifth embodiment of the present invention will be described. In the following description, the same portions as those in the first to fourth embodiments described above are denoted by the same reference numerals as those in FIGS. 1 to 27, and detailed description thereof is omitted.
In this embodiment, the three-dimensional analysis in the third and fourth embodiments described above is simplified.

The average magnetic field calculation unit 4a first calculates the average magnetic flux density _BaveX in the equivalent element 182 when the external magnetic field _HextX is applied only in the easy axis (X axis) direction in the analysis model shown in FIG. The magnetic field _HaveX is determined using the above (Expression 22) and (Expression 25).

Next, the average magnetic field calculation unit 4a includes the average magnetic flux density B _aveY in the equivalent element 182 when the external magnetic field H _extY is applied only in the hard axis (Y axis) direction in the analysis model shown in FIG. The average magnetic field _HaveY is obtained using the above (Expression 23) and (Expression 26).

Further, the average magnetic field calculation unit 4a includes the average magnetic flux density _BaveZ in the equivalent element 182 and the average magnetic field when the external magnetic field _HextZ is applied only in the vertical axis (Z-axis) direction in the analysis model shown in FIG. _HaveZ is obtained using the above (Equation 24) and (Equation 27).

The magnetic characteristic curve creation unit 4b creates a BH curve in the easy axis (X axis) direction from the average magnetic flux density B _aveX obtained by the average magnetic field calculation unit 4a and the average magnetic field H _aveX .
Further, the magnetic characteristic curve creation unit 4b creates a BH curve in the hard axis (Y axis) direction from the average magnetic flux density B _aveY obtained by the average magnetic field calculation unit 4a and the average magnetic field H _aveY .
Further, the magnetic characteristic curve creation unit 4b creates a BH curve in the vertical axis (Z-axis) direction from the average magnetic flux density B _aveZ obtained by the average magnetic field calculation unit 4a and the average magnetic field H _aveZ .

  The magnetic field distribution calculation unit 4c includes (three) B− for each of the easy magnetization axis (X axis), the hard magnetization axis (Y axis), and the vertical axis (Z axis) created by the magnetic characteristic curve creation unit 4b. Analysis of the electromagnetic field in the magnetic shield device 180 shown in FIG. 18 is executed using the H curve.

  As described above, in the present embodiment, the average magnetic flux density and the average magnetic field in the equivalent element 182 are obtained for each of the easy magnetization axis (X axis), the hard magnetization axis (Y axis), and the vertical axis (Z axis). As a result, the electromagnetic field can be analyzed at higher speed. The method described in this embodiment is effective when it is required to execute analysis at a higher speed than the analysis accuracy.

(Sixth embodiment)
Next, a sixth embodiment of the present invention will be described. In the following description, the same portions as those in the first to fifth embodiments described above are denoted by the same reference numerals as those in FIGS. 1 to 27, and detailed description thereof is omitted. In the present embodiment, the three-dimensional analysis in the third to fifth embodiments is further simplified.

  First, the electromagnetic field analysis apparatus according to the present embodiment includes a magnetic characteristic calculation unit instead of the average magnetic field calculation unit 4a and the magnetic characteristic curve creation unit 4b. This magnetic characteristic calculation part calculates | requires the magnetic permeability in the magnetic shield apparatus 290 shown in FIG. 29 as follows. Note that the magnetic shield device 290 shown in FIG. 29 is a device that shields a magnetic field from the outside. In this embodiment, the case where the shielding performance of the magnetic shield device 290 is evaluated will be described as an example.

  In FIG. 29, the magnetic shield device 290 is configured by combining 32 steel plates having a length of 300 mm, a width of 25 mm, and a thickness of 1 mm. More specifically, the magnetic shield device is configured by stacking four sets of four steel plates arranged in a “mouth” shape at intervals of 30 mm. FIG. 29 corresponds to FIG. 2 in the first embodiment described above.

  In this case, as an equivalent element composed of a magnetic body and a non-magnetic body, there are a case where a combination of an equivalent element 291 and an equivalent element 292 is considered, and a case where a combination of an equivalent element 293 and an equivalent element 294 is considered. The equivalent element 291 and the equivalent element 293 correspond to the parallel part of the steel plate, and the thickness of the steel plate is 1 mm. The equivalent element 292 and the equivalent element 294 correspond to the corner portion of the steel plate, and the thickness of the steel plate is 2 mm.

First, consider a set of equivalent elements 293 and equivalent elements 294. As will be described later, although the details are different, both the equivalent element 293 and the equivalent element 294 are as shown in FIG. In FIG. 28, the magnetic body (steel plate) 280 is occupied in the X-axis direction and the Z-axis direction, but is only partially occupied in the Y-axis direction. In FIG. 28, L _X , L _Y , and L _Z are the length of the equivalent element 293 in the X-axis direction is L _X , the length in the Y-axis direction is L _Y , and the length in the Z-axis direction. Is L _Z.

In the present embodiment, in FIG. 28, the outer shape of the equivalent element 293 can be L _X = 25 mm, L _Y = 30 mm, and L _Z = 25 mm. Here, the length L _Y in the Y-axis direction of the equivalent element 293 is set to 30 mm because four steel plates combined in a “mouth” shape in the side view of the magnetic shield device 290 shown in FIG. 29 are used. This corresponds to stacking at intervals of 30 mm.

  Then, the difference between the equivalent element 293 and the equivalent element 294 results in a difference in whether the thickness d of the steel plate 280 in FIG. 28 is 1 mm or 2 mm. However, the equivalent element 294 is slightly different from the equivalent element 293 in terms of the easy axis and the hard axis of the steel plate 280.

  Further, the three-dimensional orientation (X axis, Y axis, Z axis) of the magnetic shield device 290 shown in FIG. 29 and the three-dimensional orientation (X axis, Y axis, Z axis) of the equivalent element 290 shown in FIG. ) Must be considered as appropriate conversion in consideration of the easy axis and the hard axis of the steel plate 280 present in the equivalent element. Here, it is assumed that the X axis shown in FIG. 28 is the easy axis of magnetization of the steel sheet, and the Y axis is the hard axis of magnetization of the steel sheet.

  Based on such an assumption, FIG. 28 and FIG. 29 are compared, so that the X axis of FIG. 29 (the easy axis of the equivalent element 293, the steel plate continues continuously) is changed to the X axis of FIG. (The easy axis of the equivalent element model 293 is filled and occupied by the steel plate in this direction), and the Y axis of FIG. 29 (the hard axis of magnetization of the equivalent element 293) is the Y axis of FIG. It can be considered that the hard axis of the equivalent element model is not occupied by filling the steel plate in this direction, and the Z axis in FIG. 29 (the vertical axis of the equivalent element 293, the steel plate continues repeatedly) However, it can be considered as the Z axis in FIG. 28 (the vertical axis of the equivalent element model, in which the steel plate is filled and occupied).

  In this case, in FIG. 28, there are regions that are filled and occupied by the steel plate 280 in the X-axis direction and the Z-axis direction, and the steel plate 280 is filled and not occupied in the Y-axis direction.

  Thereby, the magnetic permeability of each axis (X axis, Y axis, Z axis) in the equivalent element 293 of FIG. 28 is as shown in the following (30 formula) to (33 formula).

In the above, k is a constant that takes into account the influence of the demagnetizing field. In the present embodiment, the thickness d of the magnetic body 280 in the equivalent element 293 in the Y-axis direction is sufficiently thinner than the length of the equivalent element 293 in the Y-axis direction. Therefore, as shown in the above (Expression 16), the magnetic permeability μ _Y in the Y-axis direction of the equivalent element 293 can be approximated to the magnetic permeability μ ₀ of air (nonmagnetic material).

Further, μ _XFe is the permeability in the easy axis (X axis) direction of the steel plate 280 in the equivalent element 293, and even if it is a non-linear property such as a BH curve, the property can be considered. The BH curve of 280 in the easy axis direction is reduced to d / L _X.

μ _ZFe is the magnetic permeability in the vertical axis (Z-axis) direction of the steel plate 280 in the equivalent element 293, and even if it is non-linear like the BH curve, its characteristics can be taken into consideration, and the hard magnetization axis of the steel plate 280 The BH curve is reduced to d / L _Z.

  The above (Expression 30) to (Expression 33) are derived from the following concept. For simplicity, only the X-axis direction is considered. The average magnetic flux density and the average magnetic field in the X-axis direction of the equivalent element 293 shown in FIG. 28 are as shown in the following (Expression 33) and (Expression 34), respectively.

In the above, B _i is the magnetic flux density in the X-axis direction of a region (divided region) i obtained by dividing the equivalent element 293 (see FIG. 20). ΔV _i is the volume of a region (divided region) i obtained by dividing the equivalent element 293 model (see FIG. 20). B _Fe is the magnetic flux density in the X-axis direction of the steel plate 280 in the equivalent element 293 (provided that the magnetic flux density in the steel plate 280 is uniform). B _air is the magnetic flux density in the X-axis direction of air in the equivalent element 293 (provided that the magnetic flux density in the air is uniform).

N is the number of areas into which the equivalent element 293 is divided. H _i is a magnetic field in the X-axis direction of a region (divided region) i obtained by dividing the equivalent element 293 (see FIG. 20). H _Fe is a magnetic field in the X-axis direction of the steel plate 280 in the equivalent element 293 (provided that the magnetic field in the steel plate 280 is uniform). H _air is a magnetic field in the X-axis direction of air in the equivalent element 293 (it is assumed that the magnetic field in the air is uniform).
Then, from the above (Expression 33) and (Expression 34), the permeability μ _aveX that relates the average magnetic flux density and the average magnetic field is _expressed by the following (Expression 35).

Here, considering that the magnetic field is continuous with respect to the parallel component of the steel plate 280, it can be assumed that the magnetic field of the steel plate 280 and the air magnetic field are the same as in the following (Equation 36). Therefore, the magnetic permeability μ _aveX relating the average magnetic flux density and the average magnetic field is as _shown in the following (Expression 37).

This is based on the permeability μ _XFe , μ _YFe , μ _ZFe and air (non-magnetic) obtained by using the magnetic flux density and magnetic field of the steel plate (magnetic material) 280 in each of the X-axis, Y-axis, and Z-axis directions. a magnetic permeability mu ₀ of the body), the equivalent element 293 and the magnetic body 280, and is obtained by apportioning the ratio of cross sectional area perpendicular to that direction.

That is, in the equivalent element 293, the average magnetic flux densities B _aveX , B _aveZ and the average magnetic field H in the direction (X-axis direction, Z-axis direction) where the region occupied by the steel plate (magnetic body) 280 is filled. _avex, H _avez and the relate permeability mu _avex, mu _avez is in the equivalent element 293 steel plate (magnetic body) 280, the direction (X-axis direction, Z-axis direction) of the magnetic permeability mu _XFE, mu _ZFE And the magnetic permeability μ _{0 in} that direction of the air (non-magnetic material) in the equivalent element 293 is the steel plate (magnetic material) 280 in the equivalent element 293 in that direction (X-axis direction, Z-axis direction). And the cross-sectional area of the air (non-magnetic material) in the equivalent element 293 are apportioned.

Further, in the equivalent element 293, the magnetic permeability μ that relates the average magnetic flux density B _aveY and the average magnetic field H _{aveY in} a direction (Y-axis direction) in which there is a region not filled with the steel plate (magnetic material) 280. _aveY is the permeability μ ₀ of air (nonmagnetic material) in that direction (Y-axis direction) in the equivalent element 293.

On the other hand, for the equivalent element 294, the easy magnetization axes of the two steel plates that overlap in the equivalent element 294 exist in the X-axis direction and the Z-axis direction in FIG. That is, the easy axis of magnetization of the lower steel plate in the equivalent element 294 of FIG. 29 coincides with the X axis of FIG. 29, whereas the easy magnetization axis of the upper steel plate in the equivalent element 294 of FIG. It coincides with 29 Z-axis. In this case, for example, the above-described calculation is performed using the average value of the BH curve in the easy axis direction and the BH curve in the hard axis direction as the permeability of the steel plate (magnetic material), and the equivalent element 294 The magnetic permeability μ _aveX , μ _aveY , and μ _aveZ are obtained.

  Next, the case of a set of an equivalent element 291 and an equivalent element 292 will be described. The equivalent element 291 is as shown in FIG. In the equivalent element 291, the steel plate (magnetic material) is occupied in the X-axis direction, but is only partially occupied in the Y-axis direction and the Z-axis direction. Therefore, in this case, there is a region filled and occupied by the steel plate in the X-axis direction, and the steel plate is not filled and occupied in the Y-axis direction and the Z-axis direction. For this reason, the magnetic permeability of each axis (X axis, Y axis, Z axis) in the equivalent element is as in the following (formula 38) to (formula 40).

In the above, “k _z , k _Y ” on the Z axis and the Y axis are constants that take into account the influence of the demagnetizing field. As shown in FIG. 30, when the thickness d in the Y-axis direction of the magnetic body 280 in the equivalent element 293 and the length W in the Z-axis direction are thin (small), the magnetic permeability μ in the Y-axis direction in the equivalent element _aveY and the permeability μ _aveZ in the Z-axis direction of the equivalent element are substantially the same as the permeability μ _{0 of} air.

Then, in the magnetic field distribution calculation unit 4c, the magnetic permeability μ _aveX , μ _aveY , and μ _aveZ of the X axis, the Y axis, and the Z axis obtained by the magnetic characteristic calculation unit as described above are used in FIG. The electromagnetic field analysis of the magnetic shield apparatus 290 shown is performed.

As described above, in the present embodiment, the permeability μ _aveX , μ _aveY , and μ _aveZ of the X-axis, Y-axis, and Z-axis in the equivalent element are _expressed by (Expression 30) to (Expression 32) and (Expression 38). Since the electromagnetic field in the magnetic shield device 290 is analyzed using the obtained magnetic permeability μ _aveX , μ _aveY , and μ _aveZ , the electromagnetic field can be analyzed at higher speed. . The method described in this embodiment is effective when it is required to execute analysis at a higher speed than the analysis accuracy.
In this embodiment, the magnetic permeability is obtained, but a magnetic resistivity that is the reciprocal of the magnetic permeability may be obtained.

(Seventh embodiment)
Next, a seventh embodiment of the present invention will be described. In addition, in the following description, about the part same as the 1st-6th embodiment mentioned above, the code | symbol same as the code | symbol attached | subjected to FIGS. 1-30 is attached | subjected, and detailed description is abbreviate | omitted.

  In the above-described first to sixth embodiments, the description has mainly been given of the case where one or two equivalent elements are required when analyzing an electromagnetic field. On the other hand, in the present embodiment, when there are a plurality of equivalent elements, the magnetic flux lines can be obtained more efficiently.

FIG. 31 is a block diagram showing an example of the configuration of the electromagnetic field analysis system of this embodiment.
In FIG. 31, in the electromagnetic field analysis system, n (n is a natural number of 2 or more) electromagnetic field analysis devices 2701a to 2701n and an overall model analysis device 2702 are connected via a network 2703 so that they can communicate with each other. The network 2703 may be any wired or wireless telecommunication line. For example, examples of the network 2703 include a LAN and the Internet.

  FIG. 32 is a block diagram showing an example of the configuration of the electromagnetic field analyzer 2701a of the present embodiment. FIG. 32 shows the configuration of the electromagnetic field analysis device 2701a, but other electromagnetic field analysis devices (for example, 2701n) also have the same configuration, so description of these other electromagnetic field analysis devices will be omitted.

In FIG. 32, the electromagnetic field analysis device 2701a includes an operation unit 2801, a display unit 2802, a processing unit 2803, and an input / output unit 2804.
The operation unit 2801 corresponds to the operation unit 2 shown in FIG. 1 and includes a keyboard and a mouse.
The display unit 2802 corresponds to the display unit 3 illustrated in FIG. 1 and includes a display or the like.

The processing unit 2803 corresponds to the processing unit 4 illustrated in FIG. 1 and includes a CPU, a ROM, a RAM, and the like.
Specifically, the processing unit 2803 includes the above-described average magnetic field calculation unit 4a and the magnetic characteristic curve creation unit 4b.

  The input / output unit 2804 is a device configured by a communication interface or the like, and is a device for communicating with the overall model analysis device 2702. The processing unit 2803 receives information from the overall model analysis device 2702 and transmits information to the overall model analysis device 2702 via the input / output unit 2804.

FIG. 33 is a block diagram showing an example of the configuration of the overall model analysis apparatus 2702 of the present embodiment.
In FIG. 33, the overall model analysis device 2702 includes an operation unit 2901, a display unit 2902, a processing unit 2903, and an input / output unit 2904. The operation unit 2901, display unit 2902, processing unit 2903, and input / output unit 2904 are respectively the operation unit 2801, display unit 2802, processing unit 2803, and input / output unit 2804 shown in FIG. Have the same hardware configuration.

  The processing unit 2903 has a model determination unit 2903a, an electromagnetic field analysis device allocation unit 2903b, an equivalent element calculation unit 2903c, and a magnetic field distribution calculation unit 2903d as specific functions.

  For example, the model determination unit 2903a activates predetermined application software for electromagnetic field analysis in accordance with the operation of the user operation unit 2901, and causes the display unit 2902 to display a predetermined graphic user interface. Then, based on the contents inputted by the user using this graphic user interface, the overall model of the magnetic shield device to be analyzed for the electromagnetic field and the equivalent element model in the magnetic shield device are determined.

  In the above, the overall model of the magnetic shield device is, for example, a model that represents the entire magnetic shield device, in which the size of the magnetic shield device, the size, shape, and shape of the steel plate constituting the magnetic shield device, and It is determined by the material. Moreover, an equivalent element model is an element which comprises a magnetic shield apparatus, for example, is a steel plate part of the magnetic shield apparatus repeated, or a corner part comprised of several steel plates. In other words, the magnetic shield device as an overall model is composed of several equivalent elements as its constituent elements. In this method, several equivalent elements exist repeatedly in the magnetic shield device. Therefore, the equivalent elements are obtained by numerical analysis of the magnetic characteristics (BH curve, etc.), and are analyzed in the overall model. The purpose is to reduce the number of cells.

  The electromagnetic field analysis device allocation unit 2903b allocates each equivalent element model determined by the model determination unit 2903a to the electromagnetic field analysis device 2701. That is, it is determined which equivalent element model is applied in which electromagnetic field analysis device 2701. For example, one equivalent element model is assigned to one electromagnetic field analyzer 2701.

  Here, when the number of equivalent element models determined by the model determination unit 2903a is larger than the number of electromagnetic field analysis devices 2701 managed by the overall model analysis device 2702, the electromagnetic field analysis device allocation unit 2903b manages them. In the electromagnetic field analysis device 2701, all the equivalent element models are processed so that calculations can be performed. That is, in such a case, a plurality of equivalent element models are assigned to one electromagnetic field analysis device 2701. In this way, the electromagnetic field analysis device 2701 to which a plurality of equivalent element models are assigned, for example, sequentially performs calculations for other equivalent element models after finishing the calculation for one equivalent element model.

  The equivalent element calculation unit 2903c derives parameters (parameters for specifying each equivalent element model) necessary for performing an electromagnetic field analysis using each equivalent element model determined by the model determination unit 2903a. That is, the derivation of parameters for calculating the average magnetic flux density and the average magnetic field by the average magnetic field calculation unit 4a of the electromagnetic field analyzer 2701, and the magnetic characteristic curve (for example, the BH curve 90 in FIG. ˜93 and B-θ curves 100 to 103 in FIG. 10 are derived. More specifically, the equivalent element calculation unit 2903c includes, for example, the position and size of the analysis region, the number and size of the divided regions, and the magnetic property curve created by the magnetic property curve creation unit 4b of the electromagnetic field analyzer 2701. The number, type, and discrete interval are derived.

Then, the equivalent element calculation unit 2903c outputs the derived parameter to the electromagnetic field analysis device 2701 assigned by the electromagnetic field analysis device assignment unit 2903b via the input / output unit 2904.
Specifically, for example, when the electromagnetic field analysis device allocation unit 2903b determines that the first equivalent element model determined by the model determination unit 2903a is calculated by the electromagnetic field analysis device 2701a, the equivalent element calculation unit 2903c Outputs the parameters derived for the first equivalent element model to the electromagnetic field analyzer 2701a. Similarly, when the electromagnetic field analysis device assignment unit 2903b determines that the n-th equivalent element model determined by the model determination unit 2903a is calculated by the electromagnetic field analysis device 2701n, the equivalent element calculation unit 2903c The parameters derived for the equivalent element model are output to the electromagnetic field analyzer 2701n.

  The magnetic field distribution calculation unit 2903d is based on the parameters output by the equivalent element calculation unit 2903c, and the magnetic characteristic curves created by the electromagnetic field analysis devices 2701a to 2701n (for example, the BH curves 90 to 93 in FIG. The B-θ curves 100 to 103 in FIG. 10 are input via the input / output unit 2904. And the magnetic flux line which arises in the whole model of the magnetic shielding apparatus determined by the model determination part 2903a is calculated | required based on each input magnetic characteristic curve. And the magnetic flux density in the desired position in the whole model of a magnetic shield apparatus is calculated | required from the calculated | required magnetic flux line. Note that the magnetic flux lines generated in the overall model of the magnetic shield device are obtained by using a finite element method (FEM).

Next, an example of the processing operation in the overall model analysis apparatus 2702 of this embodiment will be described with reference to the flowchart of FIG.
First, in the first step S41, the model determination unit 2903a activates predetermined application software for electromagnetic field analysis in accordance with the operation of the user operation unit 2901 and causes the display unit 2902 to display a predetermined graphic user interface.

  Next, in step S42, the model determination unit 2903a stands by until a predetermined instruction is input by the user using the graphic user interface displayed in step S41. When a predetermined instruction is input, the process proceeds to step S43, and the model determination unit 2903a determines an overall model of the magnetic shield device and an equivalent element model of the magnetic shield device based on the result of the instruction input. .

Next, in step S44, the electromagnetic field analysis device allocation unit 2903b allocates each equivalent element model determined in step S43 to any one of the electromagnetic field analysis devices 2701.
Next, in step S45, the electromagnetic field analysis device assignment unit 2903b determines whether or not all the equivalent element models determined in step S43 have been assigned to any one of the electromagnetic field analysis devices 2701. The processes in steps S44 and S45 are repeated until all the equivalent element models are assigned to any one of the electromagnetic field analysis devices 2701.
In step S44, it is preferable to assign the equivalent element model so that the number of equivalent element models assigned to each electromagnetic field analysis device 2701 is as small as possible. This is because the calculation time in each electromagnetic field analysis device 2701 can be shortened as much as possible, and the actual benefit of processing a plurality of electromagnetic field analysis devices 2701 in parallel is improved.

When all the equivalent element models are assigned to any one of the electromagnetic field analysis devices 2701 in this way, in step S46, the equivalent element calculation unit 2903c performs an electromagnetic field analysis using each equivalent element model determined in step S43. Deriving the parameters necessary for doing this.
Next, in step S47, the equivalent element calculation unit 2903c outputs the parameters derived in step S46 to the electromagnetic field analysis device 2701 assigned in step S44 via the input / output unit 2904.

  Next, in step S48, the magnetic field distribution calculation unit 2903d stands by until the magnetic characteristic curves created by the electromagnetic field analyzers 2701a to 2701n are input based on the parameters output in step S47. In step S48, the process waits until the magnetic characteristic curves in all the equivalent element models determined in step S43 are input.

  Each of the electromagnetic field analysis devices 2701a to 2701n obtains an equivalent element, an analysis region, and the like based on the parameters output in step S47, calculates an average magnetic flux density and an average magnetic field in the obtained equivalent element, and calculates an average magnetic flux density. And the average magnetic field are calculated. These calculation methods are as described in the first to third embodiments. And a magnetic characteristic curve (For example, BH curve 90-93, B-theta curve 100-103) is calculated | required from a calculation result.

When the magnetic characteristic curve is input in this way, the magnetic field distribution calculation unit 2903d obtains the magnetic flux lines generated in the overall model of the magnetic shield device determined in step S43 based on each input magnetic characteristic curve.
Finally, in step S49, the magnetic field distribution calculation unit 2903d causes the display unit 2902 to display the distribution of magnetic flux lines obtained in step S48.

  As described above, in the present embodiment, since the analysis of the electromagnetic field performed using a plurality of equivalent elements is performed in parallel using a plurality of CPUs, a plurality of equivalent elements are applied to the overall model. Even in this case, the electromagnetic field can be analyzed as fast as possible.

(Other embodiments of the present invention)
Control operations by the electromagnetic field analysis apparatus and the overall model analysis apparatus in each of the above-described embodiments can be realized by using a computer system as shown in FIG.
FIG. 35 is a block diagram showing an example of the configuration of a computer system disposed in the electromagnetic field analysis devices 1 and 2701 and the overall model analysis device 2702.
35, a computer system 3100 includes a CPU 3101, a ROM 3102, a RAM 3103, a keyboard controller (KBC) 3105 of a keyboard (KB) 3104, a CRT controller (CRTC) 3107 of a CRT display (CRT) 3106 as a display unit, The disk controller (DKC) 3110 of the hard disk (HD) 3108 and flexible disk (FD) 3109 and the network interface controller (NIC) 3112 for connection to the network 3111 can communicate with each other via the system bus 3113. Connected configuration.

The CPU 3101 comprehensively controls each component connected to the system bus 3103 by executing software stored in the ROM 3102 or the HD 3108 or software supplied from the FD 3109.
That is, the CPU 3101 performs a control for realizing an operation to be described later by reading a processing program according to a predetermined processing sequence from the ROM 3102, the HD 3108, or the FD 3109 and executing it.

The RAM 3103 functions as a main memory or work area for the CPU 3101.
The KBC 3105 controls an instruction input from the KB 3104 or a pointing device (not shown).

A CRTC 3107 controls the display of the CRT 3106.
The DKC 3110 controls access to the HD 3108 and the FD 3109 that store a boot program, various applications, edit files, user files, a network management program, a predetermined processing program in the present embodiment, and the like.
The NIC 3112 exchanges data bidirectionally with devices or systems on the network 3111.

  In order to operate various devices so as to realize the functions of the above-described embodiments, the functions of the above-described embodiments can be realized for an apparatus connected to the various devices or a computer in the system. Implementations by supplying software program codes and operating the various devices in accordance with programs stored in a computer (CPU or MPU) of the system or apparatus are also included in the scope of the present invention.

  In this case, the program code itself of the software realizes the functions of the above-described embodiments, and the program code itself and means for supplying the program code to the computer, for example, the program code are stored. The recorded medium constitutes the present invention. As a recording medium for storing the program code, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.

  Further, by executing the program code supplied by the computer, not only the functions of the above-described embodiments are realized, but also the OS (operating system) or other application software in which the program code is running on the computer. Such program code is also included in the embodiment of the present invention when the functions of the above-described embodiment are realized in cooperation with the above.

  Further, after the supplied program code is stored in the memory provided in the function expansion board of the computer or the function expansion unit connected to the computer, the CPU provided in the function expansion board or function expansion unit based on the instruction of the program code The present invention also includes a case where the functions of the above-described embodiment are realized by performing part or all of the actual processing.

It is the block diagram which showed the 1st Embodiment of this invention and showed an example of the structure of the electromagnetic field analyzer. It is the figure which showed the 1st Embodiment of this invention and showed an example of the model of the magnetic shield apparatus analyzed with an electromagnetic field analyzer. It is the figure which showed the 1st Embodiment of this invention and showed an example of the analysis area | region and the equivalent element. It is the figure which showed the 1st Embodiment of this invention and showed an example of the division area obtained by dividing | segmenting an analysis area. It is the figure which showed the 1st Embodiment of this invention and showed an example of the BH curve of a steel plate. It is the figure which showed the 1st Embodiment of this invention and showed an example of the curve showing the relationship between the angle which an average magnetic flux density and an easy magnetization axis make, and an external magnetic field. It is the figure which showed the 1st Embodiment of this invention and expanded and showed the curve showing the relationship between the angle which an average magnetic flux density and an easy magnetization axis make, and an external magnetic field. It is the figure which showed the 1st Embodiment of this invention and showed an example of the BH curve in an equivalent element. It is the figure which showed the 1st Embodiment of this invention and showed an example of the BH curve in the equivalent element which performed the leveling process. It is the figure which showed an example of the B-theta curve in an equivalent element. It is a flowchart which shows the 1st Embodiment of this invention and demonstrates an example of the processing operation in an electromagnetic field analyzer. It is a flowchart which shows the 1st Embodiment of this invention and demonstrates an example of the specific process operation at the time of creating the BH curve in an electromagnetic field analyzer. It is a flowchart which shows the 1st Embodiment of this invention and demonstrates an example of the specific process operation at the time of creating the B-theta curve in an electromagnetic field analyzer. It is the figure which showed the 1st Embodiment of this invention and showed collectively the method of calculating | requiring the electromagnetic field which arises in a magnetic shielding apparatus. It is a figure which shows the 1st Embodiment of this invention and compared the result analyzed by the method of this Embodiment, and the result analyzed by the conventional method. It is the figure which showed the 1st Embodiment of this invention and showed an example of the number of elements required when analyzing by the method of this Embodiment, and an example of the number of elements required when analyzing by the conventional method. It is the figure which showed the 1st Embodiment of this invention and showed the other example of the equivalent element. It is the figure which showed the 2nd Embodiment of this invention and showed an example of the structure of the magnetic shielding apparatus. It is the figure which showed the 2nd Embodiment of this invention and showed an example of the analysis model. It is the figure which showed the 2nd Embodiment of this invention and showed an example of the division area obtained by dividing | segmenting an analysis area. It is the figure which showed the 2nd Embodiment of this invention and showed an example of the BH curve in an equivalent element. It is the figure which showed the 2nd Embodiment of this invention and showed an example of the B-theta curve in an equivalent element. It is the figure which showed the 3rd Embodiment of this invention and showed an example of the analysis model. It is a figure which shows the 3rd Embodiment of this invention and demonstrates an example of the method of specifying the direction of an average magnetic flux density and the direction of an average magnetic field. It is the figure which showed the 3rd Embodiment of this invention and showed an example of the BH curve in an equivalent element. It is the figure which showed the 3rd Embodiment of this invention and showed an example of the 1st B-theta curve in an equivalent element. It is the figure which showed the 3rd Embodiment of this invention and showed an example of the 2nd B-theta curve in an equivalent element. It is the figure which showed the 6th Embodiment of this invention and showed an example of the equivalent element. It is the figure which showed the 6th Embodiment of this invention and showed an example of the structure of the magnetic shielding apparatus. It is the figure which showed the 6th Embodiment of this invention and showed the other example of the equivalent element. It is the block diagram which showed the 7th Embodiment of this invention and showed an example of the structure of an electromagnetic field analysis system. It is the block diagram which showed the 7th Embodiment of this invention and showed an example of the structure of an electromagnetic field analyzer. It is the block diagram which showed the 7th Embodiment of this invention and showed an example of the structure of the whole model analyzer. It is a flowchart which shows the 7th Embodiment of this invention and demonstrates an example of the processing operation in a whole model analyzer. It is the block diagram which showed other embodiment of this invention and showed an example of the structure of the computer system arrange | positioned by the electromagnetic field analyzer and the whole model analyzer.

Explanation of symbols

1, 2701 Electromagnetic field analyzer 2, 2801, 2901 Operation unit 3, 2802, 2902 Display unit 4, 2803, 2903 Processing unit 4a Average magnetic field calculation unit 4b Magnetic characteristic curve creation unit 4c Magnetic field distribution calculation unit 20, 170, 181, 280 Magnetic material (steel plate)
21, 171 Analysis target regions 30, 172, 190 Analysis regions 31, 182, 291-294 Equivalent elements 90-93, 2001, 2002, 2401 BH curves 100-103, 2101 B-θ curve 2501 First B- θ curve 2601 Second B-θ curve 2702 Overall model analysis device 2903a Model determination unit 2903b Electromagnetic field analysis device allocation unit 2903c Equivalent element calculation unit 2903d Magnetic field distribution calculation unit

Claims (71)

An average magnetic field calculating means for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic material;
An electromagnetic field analysis apparatus comprising: an electromagnetic field analysis means for analyzing an electromagnetic field generated in a region wider than the equivalent element using the average magnetic flux density and the average magnetic field. An average magnetic field density calculating means for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic body, and calculating an angle formed by the average magnetic flux density and the average magnetic field;
Using electromagnetic field analysis means for analyzing an electromagnetic field generated in a region wider than the equivalent element, using the average magnetic flux density, the average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field. Electromagnetic field analyzer. The BH curve representing the relationship between the average magnetic flux density calculated by the average magnetic field calculation means and the average magnetic field, the relationship between the average magnetic flux density, and the angle between the average magnetic flux density and the average magnetic field. A magnetic characteristic curve creating means for creating a B-θ curve;
The electromagnetic field analysis means analyzes an electromagnetic field generated in a region wider than the equivalent element based on the BH curve and the B-θ curve created by the magnetic characteristic curve creation means. Item 3. The electromagnetic field analysis apparatus according to Item 1 or 2. The plurality of substances are a magnetic material and a non-magnetic material,
The average magnetic field calculation means calculates an average magnetic flux density and an average magnetic field in an equivalent element occupied by a part of the magnetic material and a surrounding nonmagnetic material. 4. The electromagnetic field analysis device according to any one of 3 above.   5. The electromagnetic field analysis apparatus according to claim 1, wherein the electromagnetic field analysis unit analyzes an electromagnetic field generated in a region where a plurality of substances including the magnetic body are repeatedly present.   The average magnetic field calculating means calculates an average magnetic flux density and an average magnetic field in a two-dimensional equivalent element determined from an easy magnetization axis of the magnetic material and a hard magnetization axis of the magnetic material, and the average magnetic flux. The electromagnetic field analysis apparatus according to claim 1, wherein an angle formed by a density and the average magnetic field is calculated.   7. The electromagnetic field analysis according to claim 6, wherein the average magnetic flux density and the average magnetic field are two-dimensional vectors determined from a value in the easy magnetization axis direction and a value in the hard magnetization axis direction. apparatus.   8. The magnetic characteristic curve creating means creates the BH curve and the B-θ curve by using an angle formed by the average magnetic flux density and the easy magnetization axis as a parameter. The electromagnetic field analyzer described.   The magnetic characteristic curve creating means forms a curve representing a relationship between an external magnetic field applied to the equivalent element and an angle formed between the average magnetic flux density and the easy axis of magnetization with the external magnetic field and the easy axis of magnetization. Create an angle as a parameter, and use the created curve to determine the average magnetic flux density and average magnetic field when the angle between the average magnetic flux density and the easy axis of magnetization is a predetermined value. The electromagnetic field analysis apparatus according to claim 8, wherein a BH curve representing a relationship between a magnetic field and an average magnetic field is created.   The magnetic characteristic curve creating means includes a relationship between an external magnetic field applied to the equivalent element and an angle formed by the average magnetic flux density and the easy axis of magnetization, an external magnetic field applied to the equivalent element, and the average magnetic flux density. And a curve representing a relationship between an external magnetic field applied to the equivalent element and the average magnetic field, and an external magnetic field applied to the equivalent element and an angle formed by the average magnetic flux density and the average magnetic field. 10. The electromagnetic field according to claim 9, wherein the direction of the external magnetic field is created as a parameter, and the BH curve and the B-θ curve are created using the created curve. Analysis device.   The average magnetic field calculation means includes an average magnetic flux density in a three-dimensional equivalent element defined by an easy magnetization axis of the magnetic material, a hard magnetization axis of the magnetic material, and a vertical axis perpendicular to these axes, and an average 6. The electromagnetic field analysis apparatus according to claim 1, wherein a magnetic field is calculated and an angle formed by the average magnetic flux density and the average magnetic field is calculated.   The average magnetic flux density and the average magnetic field are three-dimensional vectors determined from a value in the easy axis direction, a value in the hard axis direction, and a value in the vertical axis direction. The electromagnetic field analysis apparatus according to claim 11. The average magnetic field calculation means includes a second average magnetic flux density determined from a value of the average magnetic flux density in the easy axis direction and a value in the hard axis direction, a value of the average magnetic field in the easy axis direction, and a hard magnetization. A second average magnetic field determined from an axial value, and an angle formed by the second average magnetic flux density and the second average magnetic field,
The magnetic characteristic curve creating means includes a BH curve representing a relationship between the second average magnetic flux density and the second average magnetic field, the second average magnetic flux density, and the second average density. 13. The B-θ curve representing the relationship with the second average magnetization is created by using an angle between the second average magnetic flux density and the easy magnetization axis as a parameter. Electromagnetic field analyzer.   14. The electromagnetic field analysis according to claim 13, further comprising recording means for previously recording a BH curve representing a relationship between the average magnetic flux density in the vertical axis direction and the average magnetic field in the vertical axis direction on a recording medium. apparatus.   15. The electromagnetic field analysis apparatus according to claim 14, wherein a slope of a BH curve representing a relationship between the average magnetic flux density in the vertical axis direction and the average magnetic field in the vertical axis direction is constant. The average magnetic field calculation means includes a first reference line defined by a value of the average magnetic flux density in the easy magnetization axis direction and a value of the hard magnetization axis direction, a value of the average magnetic field in the easy magnetization axis direction, and a hard magnetization axis. A second reference line determined from the direction value,
The magnetic characteristic curve creating means includes a BH curve representing a relationship between the average magnetic flux density and the average magnetic field, an angle formed by the first reference line and the second reference line, and the average magnetic flux. A first B-θ curve representing the relationship with density, a second B-θ curve representing the relationship between the average magnetic flux density, and the angle between the second reference line and the average magnetic field, The electromagnetic field according to claim 12, wherein an angle formed by the first reference line and the hard axis of magnetization and an angle formed by the first reference line and the average magnetic flux density are created as parameters. Analysis device.   The magnetic characteristic curve creating means includes a relationship between the external magnetic field applied to the equivalent element and the average magnetic flux density, a relationship between the external magnetic field applied to the equivalent element and the average magnetic field, and an external applied to the equivalent element. The relationship between the magnetic field and the angle formed by the first reference line and the hard axis, the external magnetic field applied to the equivalent element, and the angle formed by the first reference line and the average magnetic flux density The relationship between the external magnetic field applied to the equivalent element and the angle formed by the first reference line and the second reference line, and the external magnetic field applied to the equivalent element, and the second reference line Curves representing the relationship with the angle formed with the second average magnetic field are created using the direction of the external magnetic field as a parameter, and the BH curve and the first B are created using the created curves. -Θ curve and the second B Electromagnetic field analysis apparatus according to claim 16, characterized in that to create a θ curve.   The magnetic characteristic curve creating means generates a BH curve representing the relationship between the average magnetic flux density and the average magnetic field, and includes an easy magnetization axis of the magnetic material, a hard magnetization axis of the magnetic material, and an easy magnetization axis and a hard magnetization. The electromagnetic field analysis apparatus according to claim 3, wherein the electromagnetic field analysis apparatus is created for each axis of a vertical axis perpendicular to the axis.   The average magnetic field calculating means calculates a mean magnetic flux density and an average magnetic field in the equivalent element by using a representative area in the area as an equivalent element. The electromagnetic field analyzer according to item 1.   The electromagnetic field analysis apparatus according to any one of claims 1 to 19, wherein the electromagnetic field analysis means analyzes an electromagnetic field generated in a region wider than the equivalent element by applying a side element finite element method. . A magnetic property calculating means for calculating the magnetic permeability or the magnetic resistivity in an equivalent element occupied by a plurality of substances including a magnetic material;
Electromagnetic field analysis means for analyzing the electromagnetic field generated in the analysis target area wider than the equivalent element using the magnetic permeability or magnetic resistivity,
The magnetic permeability or magnetic resistivity is a physical quantity that correlates an average magnetic flux density and an average magnetic field in the equivalent element. An electromagnetic field analyzer for analyzing an electromagnetic field generated in an analysis target region where a plurality of magnetic bodies and non-magnetic bodies are repeatedly present,
Magnetic characteristic calculation means for calculating the magnetic permeability or the magnetic resistivity in an equivalent element occupied by a plurality of substances including the magnetic body and the non-magnetic body,
Electromagnetic field analysis means for analyzing the electromagnetic field generated in the analysis target region using the magnetic permeability or magnetic resistivity,
The magnetic permeability or magnetic resistivity is a physical quantity that associates the average magnetic flux density and the average magnetic field in the equivalent element,
The magnetic property calculating means determines the magnetic permeability or magnetic resistance of the magnetic material in the equivalent element when determining the magnetic permeability or magnetic resistivity in a direction in which a region occupied by the plurality of magnetic materials is filled and occupied. Depending on the cross-sectional area of the magnetic body in the equivalent element and the cross-sectional area of the non-magnetic body in the equivalent element. Electromagnetic field analyzer characterized by apportioning.   The magnetic property calculating means uses the permeability or magnetic resistivity of the non-magnetic material in the equivalent element as the magnetic permeability or magnetic resistivity in a direction in which there is a region not filled and occupied by the plurality of magnetic materials. The electromagnetic field analyzer according to claim 22, wherein the electromagnetic field analyzer is used. The plurality of substances are a magnetic material and a non-magnetic material,
24. The magnetic characteristic calculation means calculates a magnetic permeability or a magnetic resistivity in an equivalent element occupied by a part of the magnetic body and a non-magnetic body around the magnetic body. The electromagnetic field analysis apparatus according to any one of the above.   25. The magnetic characteristic calculation means according to claim 21, wherein a representative region in the region is used as an equivalent element, and a magnetic permeability or a magnetic resistivity in the equivalent element is calculated. Electromagnetic field analyzer described in 1.   The electromagnetic field analysis apparatus according to any one of claims 21 to 25, wherein the electromagnetic field analysis means analyzes an electromagnetic field generated in a region wider than the equivalent element by applying a side element finite element method. . A plurality of electromagnetic field analyzers having an average magnetic field calculating means for calculating an average magnetic flux density in an equivalent element occupied by a plurality of substances including a magnetic body and an average magnetic field;
Using an average magnetic flux density calculated by the plurality of electromagnetic field analysis devices and an average magnetic field, and an overall model analysis device having an electromagnetic field analysis means for analyzing an electromagnetic field generated in a region wider than the equivalent element,
Each of the average magnetic field calculation means included in the plurality of electromagnetic field analysis devices calculates an average magnetic flux density and an average magnetic field in different equivalent elements. Mean magnetic field calculating means for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic body and calculating an angle formed by the average magnetic flux density and the average magnetic field A plurality of electromagnetic field analyzers;
Electromagnetic field analysis means for analyzing an electromagnetic field generated in a region wider than the equivalent element using an average magnetic flux density calculated by the plurality of electromagnetic field analyzers, an average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field And an overall model analysis device having
Each of the average magnetic field calculation means included in the plurality of electromagnetic field analysis devices calculates an average magnetic flux density and an average magnetic field in different equivalent elements. The plurality of electromagnetic field analyzers include an average magnetic flux density calculated by the average magnetic field calculating means and a BH curve representing a relationship between the average magnetic field, the average magnetic flux density, the average magnetic flux density, and the average magnetic field. Magnetic characteristic curve creating means for creating a B-θ curve representing the relationship with the angle formed by
The electromagnetic field analysis means possessed by the overall model analysis apparatus uses the BH curve created by the magnetic characteristic curve creation means and the B-θ curve to generate an electromagnetic field generated in a wider area than the equivalent element. The electromagnetic field analysis system according to claim 27 or 28, wherein The overall model analysis apparatus includes a model determination unit that determines an overall model in a region wider than the equivalent element and a plurality of equivalent element models in a region wider than the equivalent element;
An electromagnetic field analyzer assigning means for assigning a plurality of equivalent element models determined by the model determining means to the plurality of electromagnetic field analyzers;
Each of the average magnetic field calculation means possessed by the plurality of electromagnetic field analysis devices has an average magnetic flux density and an average magnetic field in an equivalent element specified by the equivalent element model assigned by the electromagnetic field analysis device assignment means. The electromagnetic field analysis system according to any one of claims 27 to 29, wherein the electromagnetic field analysis system performs calculation. The overall model analysis device has equivalent element calculation means for deriving parameters for identifying a model of a plurality of equivalent elements assigned by the electromagnetic field analysis device assignment means,
Each of the average magnetic field calculation means possessed by the plurality of electromagnetic field analysis devices is specified by the equivalent element model assigned by the electromagnetic field analysis device assignment means, using the parameters derived by the equivalent element calculation means. The electromagnetic field analysis system according to claim 30, wherein an equivalent element is obtained.   32. The electromagnetic field analysis device allocating unit allocates a plurality of equivalent element models determined by the model determining unit to the plurality of electromagnetic field analysis devices as equally as possible. Electromagnetic field analysis system. An average magnetic field calculation step for calculating an average magnetic flux density in an equivalent element occupied by a plurality of substances including a magnetic material and an average magnetic field;
An electromagnetic field analysis method comprising: an electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element using the average magnetic flux density and the average magnetic field. Calculating an average magnetic flux density in an equivalent element occupied by a plurality of substances including a magnetic material and an average magnetic field, and calculating an average magnetic field calculating step for calculating an angle formed by the average magnetic flux density and the average magnetic field;
An electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element by using the average magnetic flux density, the average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field. Electromagnetic field analysis method. The BH curve representing the relationship between the average magnetic flux density calculated in the average magnetic field calculation step and the average magnetic field, the relationship between the average magnetic flux density, and the angle between the average magnetic flux density and the average magnetic field. A magnetic characteristic curve creating step for creating a B-θ curve,
The electromagnetic field analysis step analyzes an electromagnetic field generated in a region wider than the equivalent element based on the BH curve and the B-θ curve created by the magnetic characteristic curve creation step. Item 35. The electromagnetic field analysis method according to Item 33 or 34. The plurality of substances are a magnetic material and a non-magnetic material,
The average magnetic field calculating step calculates an average magnetic flux density and an average magnetic field in an equivalent element occupied by a part of the magnetic material and a nonmagnetic material around the magnetic material. 36. The electromagnetic field analysis method according to any one of 35.   37. The electromagnetic field analysis method according to any one of claims 33 to 36, wherein the electromagnetic field analysis step analyzes an electromagnetic field generated in a region where a plurality of substances including the magnetic substance are repeatedly present.   The average magnetic field calculating step calculates an average magnetic flux density and an average magnetic field in a two-dimensional equivalent element determined from an easy magnetization axis of the magnetic material and a hard magnetization axis of the magnetic material, and the average magnetic flux. The electromagnetic field analysis method according to any one of claims 33 to 37, wherein an angle formed by a density and the average magnetic field is calculated.   The electromagnetic field analysis according to claim 38, wherein the average magnetic flux density and the average magnetic field are two-dimensional vectors determined from a value in the easy axis direction and a value in the hard axis direction. Method.   40. The magnetic characteristic curve creating step creates the BH curve and the B-θ curve with the angle formed between the average magnetic flux density and the easy magnetization axis as a parameter. The electromagnetic field analysis method described.   In the magnetic characteristic curve creation step, a curve representing a relationship between an external magnetic field applied to the equivalent element and an angle formed between the average magnetic flux density and the easy axis is formed between the external magnetic field and the easy axis. Create an angle as a parameter, and use the created curve to determine the average magnetic flux density and average magnetic field when the angle between the average magnetic flux density and the easy axis of magnetization is a predetermined value. 41. The electromagnetic field analysis method according to claim 40, wherein a BH curve representing a relationship between the magnetic field and the average magnetic field is created.   The magnetic characteristic curve creating step includes a relationship between an external magnetic field applied to the equivalent element and an angle formed by the average magnetic flux density and the easy magnetization axis, an external magnetic field applied to the equivalent element, and the average magnetic flux density. And a curve representing a relationship between an external magnetic field applied to the equivalent element and the average magnetic field, and an external magnetic field applied to the equivalent element and an angle formed by the average magnetic flux density and the average magnetic field. 42. The electromagnetic field according to claim 41, wherein the direction of the external magnetic field is created as a parameter, and the BH curve and the B-θ curve are created using the created curve. analysis method.   The average magnetic field calculation step includes an average magnetic flux density in a three-dimensional equivalent element defined by an easy magnetization axis of the magnetic material, a hard magnetization axis of the magnetic material, and a vertical axis perpendicular to these axes, and an average The electromagnetic field analysis method according to any one of claims 33 to 37, wherein a magnetic field is calculated, and an angle formed by the average magnetic flux density and the average magnetic field is calculated.   The average magnetic flux density and the average magnetic field are three-dimensional vectors determined from a value in the easy axis direction, a value in the hard axis direction, and a value in the vertical axis direction. The electromagnetic field analysis method according to claim 43. The average magnetic field calculating step includes a second average magnetic flux density determined from a value of the average magnetic flux density in the easy axis direction and a value of the hard axis direction, a value of the average magnetic field in the easy axis direction, and a hard magnetization. A second average magnetic field determined from an axial value, and an angle formed by the second average magnetic flux density and the second average magnetic field,
The magnetic characteristic curve creating step includes a BH curve representing a relationship between the second average magnetic flux density and the second average magnetic field, the second average magnetic flux density, and the second average density. 45. The B-θ curve representing the relationship with the second average magnetization is created by using an angle between the second average magnetic flux density and the easy axis as a parameter. Electromagnetic field analysis method.   46. The electromagnetic field analysis according to claim 45, further comprising a recording step of previously recording a BH curve representing a relationship between the average magnetic flux density in the vertical axis direction and the average magnetic field in the vertical axis direction on a recording medium. Method.   47. The electromagnetic field analysis method according to claim 46, wherein a slope of a BH curve representing a relationship between the average magnetic flux density in the vertical axis direction and the average magnetic field in the vertical axis direction is constant. The average magnetic field calculating step includes a first reference line determined from a value of the average magnetic flux density in the easy axis direction and a value in the hard axis direction, a value of the average magnetic field in the easy axis direction and the hard axis of magnetization. A second reference line determined from the direction value,
The magnetic characteristic curve creating step includes a BH curve representing a relationship between the average magnetic flux density and the average magnetic field, an angle formed by the first reference line and the second reference line, and the average magnetic flux. A first B-θ curve representing the relationship with density, a second B-θ curve representing the relationship between the average magnetic flux density, and the angle between the second reference line and the average magnetic field, 45. The electromagnetic field according to claim 44, wherein the electromagnetic field is created by using an angle formed by the first reference line and the hard axis and an angle formed by the first reference line and the average magnetic flux density as parameters. analysis method.   The magnetic characteristic curve creating step includes a relationship between the external magnetic field applied to the equivalent element and the average magnetic flux density, a relationship between the external magnetic field applied to the equivalent element and the average magnetic field, and an external applied to the equivalent element. The relationship between the magnetic field and the angle formed by the first reference line and the hard axis, the external magnetic field applied to the equivalent element, and the angle formed by the first reference line and the average magnetic flux density The relationship between the external magnetic field applied to the equivalent element and the angle formed by the first reference line and the second reference line, and the external magnetic field applied to the equivalent element, and the second reference line Curves representing the relationship with the angle formed with the second average magnetic field are created using the direction of the external magnetic field as a parameter, and the BH curve and the first B are created using the created curves. -Θ curve and the second Electromagnetic field analysis method according to claim 48, characterized in that to create a B-theta curve.   In the magnetic characteristic curve creation step, a BH curve representing the relationship between the average magnetic flux density and the average magnetic field is expressed by using the easy magnetization axis of the magnetic material, the hard magnetization axis of the magnetic material, and the easy magnetization axis and the hard magnetization. The electromagnetic field analysis method according to any one of claims 35 to 37, wherein each of the axes is created with respect to a vertical axis perpendicular to the axis.   51. The average magnetic field calculating step calculates a mean magnetic flux density and an average magnetic field in an equivalent element of a representative area in the area, and calculating an average magnetic field in the equivalent element. 2. The electromagnetic field analysis method according to item 1.   52. The electromagnetic field analysis method according to claim 33, wherein the electromagnetic field analysis step analyzes an electromagnetic field generated in a region wider than the equivalent element by applying a side element finite element method. . A magnetic property calculating step for calculating the magnetic permeability or the magnetic resistivity in an equivalent element occupied by a plurality of substances including a magnetic material;
An electromagnetic field analysis step for analyzing an electromagnetic field generated in an analysis target area wider than the equivalent element using the magnetic permeability or the magnetic resistivity;
The electromagnetic permeability analysis method, wherein the magnetic permeability or magnetic resistivity is a physical quantity that associates an average magnetic flux density and an average magnetic field in the equivalent element. An electromagnetic field analysis method for analyzing an electromagnetic field generated in an analysis target region where a plurality of magnetic bodies and non-magnetic bodies are present repeatedly,
A magnetic property calculation step for calculating a magnetic permeability or a magnetic resistivity in an equivalent element occupied by a plurality of substances including the magnetic material and the non-magnetic material;
An electromagnetic field analysis step for analyzing an electromagnetic field generated in the analysis target region using the magnetic permeability or the magnetic resistivity;
The magnetic permeability or magnetic resistivity is a physical quantity that associates the average magnetic flux density and the average magnetic field in the equivalent element,
In the magnetic characteristic calculation step, the magnetic permeability or magnetic resistance of the magnetic body in the equivalent element is determined when the magnetic permeability or magnetic resistivity in a direction in which the region filled and occupied by the plurality of magnetic bodies is determined. Depending on the cross-sectional area of the magnetic body in the equivalent element and the cross-sectional area of the non-magnetic body in the equivalent element. Electromagnetic field analysis method characterized by apportioning.   In the magnetic characteristic calculation step, the magnetic permeability or magnetic resistivity of the non-magnetic material in the equivalent element is used as the magnetic permeability or magnetic resistivity in a direction in which there is a region not filled and occupied by the plurality of magnetic materials. The electromagnetic field analysis method according to claim 54, wherein the electromagnetic field analysis method is used. The plurality of substances are a magnetic material and a non-magnetic material,
The magnetic characteristic calculation step calculates a magnetic permeability or a magnetic resistivity in an equivalent element occupied by a part of the magnetic body and a non-magnetic body surrounding the part. The electromagnetic field analysis method according to any one of claims.   57. The magnetic characteristic calculation step according to claim 53, wherein a representative region in the region is used as an equivalent element, and a magnetic permeability or a magnetic resistivity in the equivalent element is calculated. Electromagnetic field analysis method described in 1.   The electromagnetic field analysis method according to any one of claims 53 to 57, wherein the electromagnetic field analysis means analyzes an electromagnetic field generated in a wider area than the equivalent element by applying a side element finite element method. . A plurality of electromagnetic field analyzers perform an average magnetic field calculation step for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic body,
Using the average magnetic flux density calculated by the plurality of electromagnetic field analysis devices and the average magnetic field, the overall model analysis device performs an electromagnetic field analysis step for analyzing an electromagnetic field generated in a region wider than the equivalent element,
Each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analysis devices calculates an average magnetic flux density and an average magnetic field in different equivalent elements. A plurality of average magnetic field calculation steps for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic body and calculating an angle formed by the average magnetic flux density and the average magnetic field The electromagnetic field analyzer of
An electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element using an average magnetic flux density calculated by the plurality of electromagnetic field analyzers, an average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field The overall model analyzer performs
Each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analysis devices calculates an average magnetic flux density and an average magnetic field in different equivalent elements. The BH curve representing the relationship between the average magnetic flux density calculated in the average magnetic field calculation step and the average magnetic field, the relationship between the average magnetic flux density, and the angle between the average magnetic flux density and the average magnetic field. A plurality of electromagnetic field analyzers perform a magnetic characteristic curve creation step for creating a B-θ curve,
In the electromagnetic field analysis step performed by the overall model analysis apparatus, an electromagnetic field generated in a region wider than the equivalent element is analyzed using the BH curve and the B-θ curve created by the magnetic characteristic curve creation step. The electromagnetic field analysis method according to claim 45 or 46, wherein: A model determining step for determining an overall model of a region wider than the equivalent element and a model of a plurality of equivalent elements in a region wider than the equivalent element;
The overall model analysis device performs an electromagnetic field analysis device assignment step of assigning a plurality of equivalent element models determined by the model determination step to the plurality of electromagnetic field analysis devices,
Each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analysis devices calculates an average magnetic flux density and an average magnetic field within the equivalent element specified by the equivalent element model assigned by the electromagnetic field analysis device assignment step. The electromagnetic field analysis method according to any one of claims 45 to 47, wherein: The overall model analysis device performs an equivalent element calculation step for deriving a parameter for specifying a model of a plurality of equivalent elements assigned by the electromagnetic field analysis device assignment means,
Each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analyzers is equivalent to the equivalent element specified by the equivalent element model assigned by the electromagnetic field analyzer assignment step, using the parameters derived by the equivalent element calculation step. 49. The electromagnetic field analysis method according to claim 48, wherein an element is obtained.   50. The electromagnetic field analysis device assignment step assigns the plurality of equivalent element models determined by the model determination step to the plurality of electromagnetic field analysis devices as equally as possible. Electromagnetic field analysis method. An average magnetic field calculation step for calculating an average magnetic flux density in an equivalent element occupied by a plurality of substances including a magnetic material and an average magnetic field;
A computer program for causing a computer to execute an electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element using the average magnetic flux density, the average magnetic field, and the average magnetic flux density. Calculating an average magnetic flux density in an equivalent element occupied by a plurality of substances including a magnetic material and an average magnetic field, and calculating an average magnetic field calculating step for calculating an angle formed by the average magnetic flux density and the average magnetic field;
Electromagnetic field analysis for analyzing an electromagnetic field generated in a region wider than the equivalent element using the average magnetic flux density calculated by the average magnetic field calculation step, the average magnetic field, and the angle formed by the average magnetic flux density and the average magnetic field A computer program for causing a computer to execute the steps. A magnetic property calculating step for calculating the magnetic permeability or the magnetic resistivity in an equivalent element occupied by a plurality of substances including a magnetic material;
Using the magnetic permeability or magnetic resistivity, let the computer execute an electromagnetic field analysis step for analyzing the electromagnetic field generated in the analysis target area wider than the equivalent element,
The computer program according to claim 1, wherein the magnetic permeability or magnetic resistivity is a physical quantity that associates an average magnetic flux density and an average magnetic field in the equivalent element. A computer program for causing a computer to analyze an electromagnetic field generated in an analysis target area where a plurality of magnetic bodies and non-magnetic bodies are repeatedly present,
A magnetic property calculation step for calculating a magnetic permeability or a magnetic resistivity in an equivalent element occupied by a plurality of substances including the magnetic material and the non-magnetic material;
Using the magnetic permeability or magnetic resistivity, let the computer execute an electromagnetic field analysis step for analyzing the electromagnetic field generated in the analysis target region,
The magnetic permeability or magnetic resistivity is a physical quantity that associates the average magnetic flux density and the average magnetic field in the equivalent element,
In the magnetic characteristic calculation step, the magnetic permeability or magnetic resistance of the magnetic body in the equivalent element is determined when the magnetic permeability or magnetic resistivity in a direction in which the region filled and occupied by the plurality of magnetic bodies is determined. Depending on the cross-sectional area of the magnetic body in the equivalent element and the cross-sectional area of the non-magnetic body in the equivalent element. A computer program characterized by apportioning. A plurality of electromagnetic field analyzers perform an average magnetic field calculation step for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic body,
Using the average magnetic flux density calculated by the plurality of electromagnetic field analysis devices and the average magnetic field, the overall model analysis device performs an electromagnetic field analysis step for analyzing an electromagnetic field generated in a region wider than the equivalent element,
A computer program for causing a computer to calculate an average magnetic flux density and an average magnetic field in different equivalent elements in each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analysis devices. A plurality of average magnetic field calculation steps for calculating an average magnetic flux density and an average magnetic field in an equivalent element occupied by a plurality of substances including a magnetic body and calculating an angle formed by the average magnetic flux density and the average magnetic field The electromagnetic field analyzer of
An electromagnetic field analysis step of analyzing an electromagnetic field generated in a region wider than the equivalent element using an average magnetic flux density calculated by the plurality of electromagnetic field analyzers, an average magnetic field, and an angle formed by the average magnetic flux density and the average magnetic field The overall model analyzer performs
A computer program for causing a computer to calculate an average magnetic flux density and an average magnetic field in different equivalent elements in each of the average magnetic field calculation steps performed by the plurality of electromagnetic field analysis devices.   A computer-readable recording medium on which the computer program according to any one of claims 65 to 70 is recorded.

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