JP4493389B2 - Electromagnetic field analysis device, electromagnetic field analysis method, computer program, and computer-readable recording medium - Google Patents

Description

  The present invention relates to an electromagnetic field analysis device, an electromagnetic field analysis method, a computer program, and a computer-readable recording medium, and in particular, used for analyzing an electromagnetic field generated in a region where a plurality of substances including a magnetic material exist. Is preferred.

  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 device of the present invention is an electromagnetic field analysis device that analyzes an electromagnetic field generated in an analysis target region, and from a magnetic flux density and a magnetic field at each position inside an equivalent element occupied by a plurality of substances including a magnetic material, Using the equivalent element calculation means for calculating the average magnetic flux density and the average magnetic field in the equivalent element, the average magnetic flux density and the average magnetic field in the equivalent element, the equivalent element has the same shape and size. There is a magnetic characteristic , that is, an element in which an average magnetic flux density and an average magnetic field are considered to be the same , but an intermediate for calculating an average magnetic flux density and an average magnetic field in an intermediate element including a plurality of elements equivalent to the equivalent element. Using an element calculation means, an average magnetic flux density in the intermediate element calculated by the intermediate element calculation means, and an average magnetic field, it is generated in an analysis target area wider than the intermediate element. And having a electromagnetic field analysis means for analyzing the electromagnetic field.
Another feature of the present invention is that the average magnetic flux density in the equivalent element and the average magnetic flux density are calculated from the magnetic flux density and magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic substance. and calculates the magnetic field, and the average magnetic flux density, equivalent elements computing means for creating a B-H curve of the equivalent elements in which represents the relationship between the average magnetic field, the B-H curve in the above equivalent elements used In the intermediate element comprising a plurality of elements equivalent to the equivalent element, the shape and size being the same as those of the equivalent element, and the magnetic characteristics , that is, the average magnetic flux density and the average magnetic field can be regarded as the same. BH curve in the intermediate element representing the relationship between the average magnetic flux density and the average magnetic field, the average magnetic flux density, the reference line OP, and the reference line The angle formed with OQ A first B-theta curve representing the relationship, and the intermediate element calculating means for creating the said mean magnetic flux density, and a second B-theta curve representing the relationship between the angle between the reference line OQ and the average magnetic field The average magnetic flux density in the intermediate element calculated by the intermediate element calculating means, the average magnetic field, the angle formed by the reference line OP and the hard axis of magnetization of the magnetic material, and the reference line OP and the average magnetic flux density An angle formed by the reference line OP and the reference line OQ, an angle formed by the reference line OQ and the average magnetic field, a BH curve in the intermediate element, and the first B-θ curve. And an electromagnetic field analyzing means for analyzing an electromagnetic field generated in an analysis target region wider than the intermediate element using the second B-θ curve, and the reference line OP is a magnetization of the average magnetic flux density. Determined from the value in the easy axis direction and the value in the hard axis direction The reference line OQ is a vector determined from the value of the average magnetic field in the easy axis direction and the value in the hard axis direction.

The electromagnetic field analysis method of the present invention is an electromagnetic field analysis method for analyzing an electromagnetic field generated in a region to be analyzed, from a magnetic flux density and a magnetic field at each position inside an equivalent element occupied by a plurality of substances including a magnetic substance, The equivalent element calculation step for calculating the average magnetic flux density and the average magnetic field in the equivalent element, and the equivalent magnetic flux density and the average magnetic field from the magnetic flux density and the magnetic field at each position inside the equivalent element. The average magnetic flux density in an intermediate element comprising a plurality of elements equivalent to the equivalent element, where the element, shape and size are the same and the magnetic characteristics , that is, the average magnetic flux density and the average magnetic field can be regarded as the same. An intermediate element calculation step for calculating the average magnetic field, an average magnetic flux density in the intermediate element calculated by the intermediate element calculation step, and an average magnetic field And having a electromagnetic field analysis step of analyzing the electromagnetic field generated in the broad analysis target area than the intermediate element.
Another feature of the present invention is that the average magnetic flux density in the equivalent element and the average magnetic flux density are calculated from the magnetic flux density and magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic substance. and calculates the magnetic field, and the average magnetic flux density, equivalent elements calculation step of creating a B-H curve of the equivalent elements in representing the relation between the average magnetic field, the B-H curve in the above equivalent elements used In the intermediate element comprising a plurality of elements equivalent to the equivalent element, the shape and size being the same as those of the equivalent element, and the magnetic characteristics , that is, the average magnetic flux density and the average magnetic field can be regarded as the same. BH curve in the intermediate element representing the relationship between the average magnetic flux density and the average magnetic field, the average magnetic flux density, the reference line OP, and the reference line Angle with OQ A first B-theta curve representing the relationship between the intermediate element calculation to create the said mean magnetic flux density, and a second B-theta curve representing the relationship between the angle between the reference line OQ and the average magnetic field Step, an average magnetic flux density in the intermediate element calculated by the intermediate element calculating step, an average magnetic field, an angle formed by the reference line OP and the hard axis of magnetization of the magnetic material, the reference line OP and the average magnetic flux density , The angle formed between the reference line OP and the reference line OQ, the angle formed between the reference line OQ and the average magnetic field, the BH curve in the intermediate element, and the first B-θ. An electromagnetic field analysis step of analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element using a curve and the second B-θ curve, and the reference line OP is the average magnetic flux density Value of the easy axis of magnetization and the direction of hard axis The reference line OQ is a vector determined from the value of the average magnetic field in the easy axis direction and the value in the hard axis direction.

A computer program according to the present invention is a computer program for causing a computer to execute a step of analyzing an electromagnetic field generated in an analysis target region, wherein the magnetic flux density at each position inside an equivalent element occupied by a plurality of substances including a magnetic material is obtained. An equivalent element calculation step for calculating an average magnetic flux density in the equivalent element and an average magnetic field from the magnetic field, an average magnetic flux density in the equivalent element, and an average magnetic field, and using the equivalent element, shape, and magnitude. And the magnetic characteristics , that is, the average magnetic flux density and the average magnetic field are elements that can be regarded as the same, the average magnetic flux density in the intermediate element including a plurality of elements equivalent to the equivalent element, and the average magnetic field An intermediate element calculation step for calculating the average magnetic flux density in the intermediate element calculated by the intermediate element calculation step. By using the average magnetic field, characterized in that to execute the electromagnetic field analysis step of analyzing the electromagnetic field generated in the broad analysis target area than the intermediate element to the computer.
Another feature of the present invention is that the average magnetic flux density in the equivalent element and the average magnetic flux density are calculated from the magnetic flux density and magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic substance. and calculates the magnetic field, and the average magnetic flux density, equivalent elements calculation step of creating a B-H curve of the equivalent elements in representing the relation between the average magnetic field, the B-H curve in the above equivalent elements used In the intermediate element comprising a plurality of elements equivalent to the equivalent element, the shape and size being the same as those of the equivalent element, and the magnetic characteristics , that is, the average magnetic flux density and the average magnetic field can be regarded as the same. BH curve in the intermediate element representing the relationship between the average magnetic flux density and the average magnetic field, the average magnetic flux density, the reference line OP, and the reference line Angle with OQ A first B-theta curve representing the relationship between the intermediate element calculation to create the said mean magnetic flux density, and a second B-theta curve representing the relationship between the angle between the reference line OQ and the average magnetic field Step, an average magnetic flux density in the intermediate element calculated by the intermediate element calculating step, an average magnetic field, an angle formed by the reference line OP and the hard axis of magnetization of the magnetic material, the reference line OP and the average magnetic flux density , The angle formed between the reference line OP and the reference line OQ, the angle formed between the reference line OQ and the average magnetic field, the BH curve in the intermediate element, and the first B-θ. Using the curve and the second B-θ curve , the computer executes an electromagnetic field analysis step of analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element, and the reference line OP Average magnetic flux density value in the easy axis direction And the reference line OQ is a vector determined from the value of the average magnetic field in the easy axis direction and the value in the hard axis direction. .

  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 substance are calculated, and the calculated average magnetic flux density and average magnetic field in the equivalent element are used. Calculating the average magnetic flux density and the average magnetic field in the intermediate element including a plurality of elements equivalent to the equivalent element, and using the calculated average magnetic flux density and average magnetic field in the intermediate element, Since the electromagnetic field generated in the analysis target area wider than the element is analyzed, the electromagnetic field generated in the analysis target area can be analyzed without dividing the analysis target area into a large 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 this embodiment, when analyzing an electromagnetic field generated in the analysis target region 21 including a magnetic shield device configured by combining a plurality of steel plates having the same width and thickness as shown in FIGS. Will be described as an example. FIG. 2 is a plan view of an analysis target region to be analyzed by the electromagnetic field analyzer as viewed from above. FIG. 3A is a side view of the analysis target region viewed from the direction A in FIG. FIG. 3B is a front view of the analysis target region viewed from the B direction in FIG.

  Moreover, in FIG.2 and FIG.3, the steel plate is filled and shown. The analysis target region 21 is a rectangular parallelepiped region having a size of 640 [mm] in the vertical direction, 860 [mm] in the horizontal direction and 400 [mm] in the height. Furthermore, in FIG. 2 and FIG. 3, in order to show the analysis target region 21 in an easy-to-understand manner, the ratio between the dimensions of the steel plate and the analysis target region 21 is different from the actual one.

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.

As shown in FIG. 1, the processing unit 4 specifically includes an equivalent element calculation unit 5, an intermediate element calculation unit 6, and a magnetic field distribution calculation unit 7.
The equivalent element calculation unit 5 regards a predetermined area 22 in the analysis target area 21 shown in FIG. 2 as an equivalent element 22 and calculates a magnetic characteristic in the equivalent element 22. In the present invention, the equivalent element 22 is referred to as an equivalent element 22.

Specifically, the equivalent element calculation unit 5 includes an average magnetic field calculation unit 5a and a magnetic characteristic curve creation unit 5b.
The average magnetic field calculator 5a calculates the average magnetic flux density B _ave and the average magnetic field H _ave in the equivalent element 22. In the above, bold indicates a vector.
As shown in FIG. 2, in the analysis target region 21, an equivalent element 22 composed of a magnetic body (steel plate) and a non-magnetic body (air) is repeatedly present. Therefore, in the present embodiment, the magnetic body in the analysis target region 21 in FIG. 2 is replaced with the equivalent element 22, and the electromagnetic field in the analysis target region 21 is calculated using the magnetic characteristics of the equivalent element 22. 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 22 are the average magnetic field calculation sections 5a and 6a and the magnetic characteristic curve creation sections 5b and 6b of the processing section 4 in FIG. The magnetic field distribution calculation unit 7 of the processing unit 4 is a part that analyzes the electromagnetic field in the analysis target region 21 by using the magnetic characteristics of the element 22 so that the number of divisions in the analysis target region 21 is significantly smaller than the conventional one.
Here, the analysis region and equivalent elements in the present embodiment will be described in detail with reference to FIGS. 4 and 5.

  As shown in FIG. 4, the equivalent element 22 is a three-dimensional region (space) formed by a part of the steel plate shown in FIGS. 2 and 3 and air on the side thereof, and one side is 25 [ mm] in the shape of a cube.

The analysis region 40 is a three-dimensional region (space) including the equivalent element 22 in the center, and is, for example, a cubic region having a side of 200 [mm].
Thus, in this embodiment, an electromagnetic field generated in a space defined by the easy axis X, the hard axis Y, the easy axis X, and the vertical axis Z perpendicular to the hard axis Y of the steel sheet is analyzed. I am doing so.

  In the present embodiment, as shown in FIG. 5, the analysis region 40 is divided into a plurality of regions made of a rectangular parallelepiped or a cube. 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.

When the external magnetic field H _ext is applied to the boundary region of the analysis region 40, the average magnetic field calculation unit 5a obtains the magnetic flux density B and the magnetic field H generated in each of the plurality of divided regions by the electromagnetic field analysis by the finite element method. . The external magnetic field H _ext is expressed as (Formula 1) below.
H _ext = {H _extX , H _extY , H _extz } (1 set)

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 .
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 FIGS. 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 .

When such an external magnetic field H _{ext is applied} to the equivalent element 22, the magnetic flux density B (i, j, k) and magnetic field H (i, j, k) generated in the divided area shown by the oblique lines in FIG. Are respectively represented by the following (formula 2) and (formula 3).

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

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 magnetic flux density B (i, j, k) and magnetic field H (i, j, k) 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, k) and the magnetic field H (i, j, k) are obtained therefrom. 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 5a uses the magnetic flux density B (i, j, k) generated in the equivalent element 22 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) are extracted, and the average magnetic flux density B _ave in the equivalent element 22 is extracted from the extracted magnetic flux density B (i, j, k) and the magnetic field H (i, j, k). And the average magnetic field H _ave . Specifically, it is obtained by the following (formula 6) to (formula 13).

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.

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 22. Further, the average magnetic field H _ave is regarded as a magnetic field generated in the equivalent element 22.

In this embodiment, as shown in FIG. 6A, in this embodiment, the direction of the average magnetic flux density _Bave is specified by the angles α _B and β _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 (14).
α _B = 90−θ _B (Expression 14)
In the above, θ _B is an angle formed by the reference line OP and the easy axis X.

As shown in FIG. 6B, in this 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 βH is an angle formed by the reference line OQ and the average magnetic field _Have .

Here, the angle α _H is expressed by the following (Expression 15).
α _H = 90−θ _H (Expression 15)
In the above, θ _H is an angle formed by the reference line OQ and the easy magnetization axis X.
Furthermore, as shown in FIG. 6C, the average magnetic field calculation unit 5a obtains an angle α _BH formed by the reference line OP and the reference line OQ.

  When obtaining the magnetic flux density B (i, j) and magnetic field H (i, j) generated in each divided region as described above, the B- of the steel plate measured in advance as shown in FIG. Use H curve. In FIG. 7, a BH curve 71 plotted with black circles is a BH curve in the easy axis direction of the steel plate. Moreover, the BH curve 72 plotted by the white square is a BH curve in the hard axis direction of a steel plate.

Then, repeated (and the magnitude of the external magnetic field H _ext, the angle phi _1, phi ₂₎ the external magnetic field H _ext magnitude and direction by changing the, the calculation by the (expression 2) to (15 type).
More specifically, for example, the angles φ ₁ and φ ₂ are set to 0, 15, 30, 45, 60, 75, and 90 [°], respectively, and the external magnetic field H _ext is changed at each angle φ ₁ and φ ₂ . From the magnitude of the average magnetic flux density B _{ave and} the magnitude of the average magnetic field H _{ave when} the magnitude is 0, 100, 500, 1000, 2000, 5000, and 10000 [Gauss], the average magnetic flux density B _ave and the average magnetic field H are calculated. _{Ask for ave} .

As described above, the average magnetic field calculation unit 5a according to 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.

The magnetic characteristic curve creation unit 5b creates a BH curve in the equivalent element 22 based on the average magnetic flux density B _ave and the average magnetic field H _ave calculated by the average magnetic field calculation unit 5a. 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 22 will be described with reference to FIGS.

First, as shown in FIG. 8, curves 80 to 86 representing the relationship between the angles α _B and β _B and the external magnetic field H _ext are created using the angles φ ₁ and φ ₂ as parameters.

Then, from these curves, the average magnetic flux density B _ave and the average magnetic field H _ave when the angles α _B and β _B are 0, 15, 30, 90 [°] are obtained. Needless to say, the angles α _B and β _B used at this time are not limited to 0, 15, 30, 90 [°].

More specifically, for example, as shown in FIG. 9, an intersection 91 between a line 90 having an angle α _B of 30 [°] and a curve (for example, a curve 84) shown in FIG. 8 is obtained. Then, the average magnetic flux density B _ave (easy magnetization axis component−hard magnetization axis component) and average magnetic field H _ave (easy magnetization axis component−hard magnetization axis component) at the obtained intersection 91 are obtained.

At this time, it performs linear interpolation using the average magnetic flux density B _ave before and after the point 92 and 93 of the intersection 91 and the average magnetic field H _ave, computing the the average magnetic flux density B _ave at the intersection 91 and the average magnetic field H _ave Can do.

Similarly, for example, the intersection of a line with an angle β _B of 30 [°] and, for example, the curve 84 is obtained, and the average magnetic flux density B _ave (vertical axis component) and average magnetic field H _ave (vertical axis component) at the obtained intersection. And ask.

The magnetic characteristic curve generator unit 5b, to create a B-H curve 100 to 103 representing the relationship between the average magnetic flux density B _ave and the average magnetic field H _ave obtained as described above (see Figure 10). Further, a leveling process is performed on the BH curves 100 to 103. In the present embodiment, the BH curves 110 to 113 that have been subjected to the leveling process are defined as BH curves in the equivalent element 22 (see FIG. 11).

As described above, the magnetic characteristic curve creating unit 5b creates the BH curve in the equivalent element 22 using the angles α _B and β _B as parameters. FIG. 12 shows an example of the concept of the BH curves 1201a to 1201n created by the magnetic characteristic curve creation unit 4b.

  The intermediate element calculation unit 6 regards a region in which the BH curve can be regarded as equivalent to the equivalent element 22 shown in FIGS. 2 to 4 as an intermediate element 23, and determines the magnetic characteristics in the intermediate element 23. Calculate and create a magnetic characteristic curve representing the calculated magnetic characteristics. In the present invention, the intermediate element 23 is referred to as an intermediate element 23. As shown in FIG. 2, in the present embodiment, a cubic region having a side of 150 [mm] including the equivalent element 22 is used as the intermediate element 23.

As shown in FIG. 1, the intermediate element calculation unit 6 specifically includes an average magnetic field calculation unit 6a and a magnetic characteristic curve creation unit 6b.
First, the average magnetic field calculation unit 6a sets a rectangular parallelepiped or cubic analysis region including the intermediate element 23 as a center. This analysis region plays the same role as the analysis region 40 shown in FIG. 4 and is divided into a plurality of divided regions made of a rectangular parallelepiped or a cube. Each of the divided areas has an appropriate size that can be calculated by a finite element method (FEM).

The average magnetic field calculation unit 6a 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 (see (Expression 1) to (Expression 3)). ).
At this time, the average magnetic field calculation unit 6a obtains the magnetic flux density B and the magnetic field H generated in each of the plurality of divided regions using the BH curve 1201 created by the magnetic characteristic curve creation unit 5a described above.

The average magnetic field calculation unit 6a then calculates the magnetic flux density B (i, j) generated in the equivalent element 22 from the magnetic flux density B (i, j, k) generated in each divided region and the magnetic field H (i, j, k). , K) and the magnetic field H (i, j, k) are extracted, and the average magnetic flux density B in the intermediate element 23 is extracted from the extracted magnetic flux density B (i, j, k) and the magnetic field H (i, j, k). _ave and average magnetic field H _ave are obtained, and angles α _BH and β _H are obtained (see (Equation 6) to (15)). The method for obtaining the average magnetic flux density B _ave , the average magnetic field H _ave , and the angle α _{BH is} the same as the method in the average magnetic field calculation unit 5a, and the description thereof is omitted.

As described above, the average magnetic field calculation unit 5a obtains the following six relationships in the intermediate element 23 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 directly as in the average magnetic field calculation unit 5a.

The magnetic characteristic curve creation unit 6b creates a BH curve in the intermediate element 23 based on the average magnetic flux density B _ave and the average magnetic field H _ave calculated by the average magnetic field calculation unit 6a. Since the method for creating the BH curve in the intermediate element 23 is the same as the method for creating the BH curve in the magnetic characteristic curve creation unit 5b described above, the description thereof is omitted.

As shown in FIG. 13, the magnetic characteristic curve creating unit 6b uses the angles α _B and β _B as parameters, and the first B-θ curves 1301a to 1301n in the intermediate element 23, that is, the average magnetic flux density B _ave and A curve representing the relationship with the angle α _BH is created and recorded on the recording medium.
Further, as shown in FIG. 14, the magnetic characteristic curve creating unit 6b uses the angles α _B and β _B as parameters, and the second B-θ curves 1401a to 1401n in the intermediate element 23, that is, the average magnetic flux density B _ave and A curve representing the relationship with the angle β _H is created.

  The magnetic field distribution calculation unit 7 performs analysis based on the BH curve created by the magnetic characteristic curve creation unit 6b of the intermediate element calculation unit 6 and the first and second B-θ curves as described above. An electromagnetic field (magnetic flux line) generated in the target region 21 is obtained. Then, the magnetic flux density and magnetic field at a desired position in the analysis target region 21 are obtained from the obtained magnetic flux lines. Note that the electromagnetic field (magnetic flux lines) generated in the analysis target region 21 is obtained using a finite element method (FEM). The electromagnetic field analysis method by the finite element method is as described above.

  Thus, when obtaining an electromagnetic field using the finite element method, it is preferable to apply the side element finite element method. 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, a number (this embodiment) obtained by multiplying the number of vertices (nodes) in the element (8 in this embodiment) by the number of dimensions (3 in this embodiment). Then, data based on 24) 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 (12 in the present embodiment).

  In addition, there is an advantage that the electromagnetic field (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, only a pair of opposed surfaces are at the boundary of different substances (in this embodiment, steel plate and air), and the other surfaces are in a single substance (in this embodiment, steel plate or air). When the nodal element finite element method is applied to a cuboid (or cube) region (element) that is in contact, 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 the sides belonging to the pair of opposed faces is a mixture of physical quantities of the different substances, but the sides belonging to the other faces are mixed. The physical quantity obtained from is the physical quantity of one substance. Therefore, in the region (element) as described above, the electromagnetic field (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.

Note that when an external magnetic field H _ext is applied to the equivalent element 22 in order to obtain the magnetic characteristics of the equivalent element 22, the magnetic body in the equivalent element 22 is magnetized, but depending on the shape and number of magnetic bodies, the demagnetizing field In some cases, the predetermined magnetic characteristics cannot be obtained due to the influence. For this reason, in the present embodiment, as shown in FIG. 2, a wide area in which attention is paid to the number and size of magnetic materials so as not to generate a demagnetizing field is considered as an area for analyzing an electromagnetic field. preferable.

Next, an example of the processing operation in the electromagnetic field analysis device 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 5a sets the magnitude of the external magnetic field _Hext applied to the analysis region 40 to an initial value (0 [Gauss]).

Next, in step S2, the average magnetic field calculation unit 5a sets the angles φ ₁ and φ ₂ to initial values (0 [°]).
Thus, the direction of the external magnetic field H _ext is set by setting the angles φ ₁ and φ ₂ .

Next, in step S3, the average magnetic field calculation unit 5a sets the boundary condition of the analysis region 40 with respect to the equivalent element 22 according to the external magnetic field _Hext . More 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 40 of FIG. Try to set.

Next, in step S4, the average magnetic field calculation unit 5a calculates the magnetic flux density B (i, j, k) and magnetic field H (i, j, k) generated in the analysis region 40 in accordance with the setting contents of the external magnetic field _Hext. To do.
More specifically, the above-described finite element method electromagnetic field analysis is performed on the analysis region 40 with the external magnetic field H _ext as a boundary condition.

  Next, in step S5, the average magnetic field calculator 5a calculates the equivalent element 22 from the magnetic flux density B (i, j, k) and magnetic field H (i, j, k) obtained by the processing in step S4. The magnetic flux density B (i, j, k) and the magnetic field H (i, j, k) generated in the above are extracted.

Next, in step S6, the average magnetic field calculation unit 5a uses the magnetic flux density B (i, j, k) and the magnetic field H (i, j, k) extracted in step S5 to determine the magnetic characteristics ( The average magnetic flux density B _ave (i, j, k) and the average magnetic field H _ave (i, j, k) in the equivalent element 22 are obtained and stored in the recording medium. Further, the angles α _BH and β _{H are} obtained and stored in the recording medium.

Next, in step S7, the average magnetic field calculation unit 5a determines whether or not the magnitude of the external magnetic field H _ext is the 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.

If the result of determination in step S7 is that the magnitude of the external magnetic field H _ext is not a specified value, the process proceeds to step S6 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.

Next, in step S10, the average magnetic field calculation unit 5a determines whether or not the set value of the direction of the external magnetic field H _ext (angles φ ₁ and φ ₂ ) is a specified value.
In the present embodiment, the angle φ ₁ is increased in the order of 0, 15, 30, 45, 60, 75, 90 [°], and the angle φ ₂ is increased to 0, 15, 30, 45, 60, 75, The angle is increased in the order of 90 [°]. Accordingly, when both the values of the angles φ ₁ and φ ₂ are 90 [°], it is determined to be the specified value.

As a result of the determination in step S10, if the set value in the direction of the external magnetic field H _ext is not a specified value, the process proceeds to step S11 and the set value is changed. For example, when the setting value of the angle φ ₁ is 0 [°] and the setting value of the angle φ ₁ is 0 [°], the setting value of the angle φ ₁ is changed to 15 [°]. The set value of the angle φ ₂ remains 0 [°]. Then, the process returns to step S3.

On the other hand, if the set value in the direction of the external magnetic field H _ext is a specified value, the process proceeds to step S12 and the set value is reset to the initial value.

Next, in step S13, the magnetic characteristic curve creating unit 5b calculates an equivalent element from the average magnetic flux density B _ave (i, j, k) obtained in step S6 and the average magnetic field H _ave (i, j, k). A BH curve 1301 at 22 is created.
Through the processes in steps S1 to S13 described above, the process by the equivalent element calculation unit 5 ends, and the process by the intermediate element calculation unit 6 starts. In the following description, detailed description of the same processing as that of the equivalent element calculation unit 5 is omitted.

Next, in step S14, the average magnetic field calculation unit 6a sets the boundary condition of the analysis region with respect to the intermediate element 23 according to the external magnetic field _Hext .

Next, in step S15, the average magnetic field calculation unit 6a calculates the magnetic flux density B (i, j, k) and magnetic field H (i, j, k) generated in the divided region according to the setting contents of the external magnetic field _Hext. The calculation is performed using the BH curve 1201 created in step S13.

  Next, in step S16, the average magnetic field calculation unit 6a applies the intermediate element 23 from the magnetic flux density B (i, j, k) and magnetic field H (i, j, k) obtained by the processing in step S15. The resulting magnetic flux density B (i, j, k) and magnetic field H (i, j, k) are extracted.

Next, in step S17, the average magnetic field calculation unit 6a uses the magnetic flux density B (i, j, k) and the magnetic field H (i, j, k) extracted in step S16 to determine the magnetic characteristics ( An average magnetic flux density B _ave (i, j, k) and an average magnetic field H _ave (i, j, k)) in the intermediate element 23 are obtained and stored in the recording medium. Further, the angles α _BH and β _{H are} obtained and stored in the recording medium.

Next, in step S18, the average magnetic field calculation unit 6a determines whether the magnitude of the external magnetic field H _ext is the specified value.
As a result of the determination in step S18, if the magnitude of the external magnetic field H _ext is not a specified value, the process proceeds to step S19 to change the set value.
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 S20 and the set value is reset to the initial value.

Next, in step S21, the average magnetic field calculating section 6a, the direction of the set values of the external magnetic field H _ext is equal to or a predetermined value.
As a result of the determination, if the set value in the direction of the external magnetic field H _ext is not the specified value, the process proceeds to step S22 and the set value is changed.
On the other hand, when the set value in the direction of the external magnetic field H _ext is a specified value, the process proceeds to step S23 and the set value is reset to the initial value.

Next, in step S24, the magnetic characteristic curve creating unit 6b determines an intermediate element from the average magnetic flux density B _ave (i, j, k) and average magnetic field H _ave (i, j, k) obtained in step S17. A BH curve at 23 is created.

Next, in step S25, the magnetic characteristic curve creation unit 6b determines the first B− in the intermediate element 23 from the average magnetic flux density B _ave (i, j, k) obtained in step S17 and the angle α _BH. A θ curve 1301 is created. Further, the magnetic characteristic curve creation unit 6b creates a second B-θ curve 1401 in the intermediate element 23 from the average magnetic flux density B _ave (i, j, k) obtained in step S17 and the angle β _H. To do.
Through the processes in steps S14 to S25 described above, the process by the intermediate element calculation unit 6 ends, and the process by the magnetic field distribution calculation unit 7 starts.

  Finally, in step S36, the magnetic field distribution calculation unit 7 uses the BH curve in the intermediate element 23 created in steps S24 and S25, and the first and second B-θ curves 1301 and 1401. An electromagnetic field generated in the analysis target region 21 is obtained.

  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.

As described above, in the present embodiment, a predetermined region occupied by the steel plate and the surrounding air is defined as one equivalent element 22, and the average magnetic flux density B _ave generated in the equivalent element 22 and the average magnetic field H _ave A BH curve 1201 representing the relationship is created, and the average magnetic flux density B _ave and the average magnetic field H _ave in the intermediate element 23 including a plurality of elements that can be regarded as equivalent to the equivalent element 22 are represented by the BH curve 1201 created above. The BH curve and the first and second B-θ curves 1301 and 1401 in the intermediate element 23 are created, and the created BH curve and the first and second B-θ curves 1301 are obtained. 1401 is used to obtain the electromagnetic field (magnetic flux lines) in the analysis target region 21, so that even if the analysis target region 21 is large, the analysis target region 21 is not divided into a large number of elements. Analysis vs. It can be analyzed an electromagnetic field generated in the region 21. 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.

  For example, the BH curve and the first and second B-θ curves in the equivalent element 22 were used without using the BH curve and the first and second B-θ curves in the intermediate element 23. In this case, the finite element method cannot be applied unless the analysis target region 21 is divided into 300,000 or more cells. Therefore, even if it has a memory of 4 [GB], it cannot be analyzed by one computer, and it takes an analysis time. On the other hand, when the BH curve and the first and second B-θ curves in the intermediate element 23 are used as in the present embodiment, the analysis target area 21 is about 210,000 cells. The finite element method can be applied. Therefore, if the memory of 4 [GB] is provided, the analysis can be performed quickly and reliably by one computer.

In the present embodiment, the equivalent element calculation unit 5, has been to seek only the BH curve 1201, the average magnetic flux density B _ave and the angle alpha _BH in the first B-theta curve (equivalent elements 21 the relationship) and the second B-theta curve (relationship between the average magnetic flux density B _ave and the angle beta _H in the equivalent element 21), may create an equivalent element calculation unit 5. In this case, the intermediate element calculation unit 6 calculates the average magnetic flux density B _ave and the average magnetic field H _ave in the intermediate element 23 using the first and second B-θ curves created by the equivalent element calculation unit 5. You may do it.

Further, in the present embodiment, the case where there is one intermediate element is illustrated, but a plurality of intermediate elements may be set.
For example, as shown in FIG. 18, an equivalent element 180 (corresponding to the equivalent element 22 shown in FIGS. 2 to 4), a first intermediate element 181 including a plurality of elements equivalent to the equivalent element 180, A second intermediate element 181 including a plurality of elements equivalent to the intermediate element 181, and an n-th (n is a natural number of 3 or more) intermediate element 183 including a plurality of elements equivalent to the (n-1) th intermediate element; May be set for the analysis target region 21.

In the case of FIG. 18, the intermediate element calculation unit 6 shown in FIG. 1 is as shown in FIG. That is, the intermediate element calculation unit 190 includes first to nth intermediate element calculation units 191 to 193.
The first intermediate element calculation unit 191 uses the BH curve created by the equivalent element calculation unit 5 to calculate the average magnetic flux density B _ave , average magnetic field H _ave , and angle α _BH in the first equivalent element 181. Using the average magnetic field calculation unit 191a for determining β _H , the average magnetic flux density B _ave , the average magnetic field H _ave , and the angles α _BH and β _H calculated by the average magnetic field calculation unit 191a, B in the first intermediate element 181 A magnetic characteristic curve creating unit 191b for creating a −H curve.

The second intermediate element calculation unit 192 uses the BH curve created by the first intermediate element calculation unit 191 to calculate the average magnetic flux density B _ave , average magnetic field H _ave , and angle in the second equivalent element 182. Using the average magnetic field calculation unit 192a for obtaining α _BH and β _H , the average magnetic flux density B _ave , the average magnetic field H _ave , and the angles α _BH and β _H obtained by the average magnetic field calculation unit 192a, the second intermediate element And a magnetic characteristic curve creating unit 192b for creating a BH curve at 182.

The n-th intermediate element calculation unit 193 uses the BH curve created by the (n−1) -th intermediate element calculation unit to calculate the average magnetic flux density B _ave and the average magnetic field H _ave in the n-th equivalent element 183. , and the angle alpha _BH, with an average magnetic field calculating unit 193a to determine the beta _H, the average magnetic flux density B _ave obtained by the average magnetic field calculating unit 193a, the average magnetic field H _ave, and the angle alpha _BH, the beta _H, the n The intermediate element 183 includes a BH curve and a magnetic characteristic curve creation unit 193b that creates first and second B-θ curves.

Then, the magnetic field distribution calculation unit 7 obtains an electromagnetic field in the analysis target region using the BH curve created by the nth intermediate element calculation unit 193 and the first and second B-θ curves.
In the above, the average magnetic flux density B _ave , the average magnetic field H _ave , and the angles α _BH and β _H can be obtained by performing the same processing as the processing performed by the above-described average magnetic field calculation units 5a and 6a. In addition, the BH curve and the first and second B-θ curves can be created by performing the same process as the process performed by the magnetic characteristic curve creating units 5b and 6b described above.

  For example, when analyzing an electromagnetic field in a magnetic shield device having a structure in which steel plates and air are repeatedly arranged, a plurality of intermediate elements can be set as shown in FIG. The number of cells required for the operation can be further reduced.

  Further, the intermediate element is not limited to the elements as shown in FIGS. For example, as shown in FIG. 20, intermediate elements may be applied to the ridge lines 200 to 202 and the corners 203 and 204 of the magnetic shield device. Moreover, as shown in FIG. 21, the joint part 210 of the steel strip which comprises a magnetic shielding apparatus, the junction part 211 of a flat steel plate and a steel strip, the separation part 212 of a steel strip, the flat steel plate part 213, and between flat steel plates An intermediate element may be applied to the joint portion 214. Furthermore, as shown in FIG. 22, intermediate elements may be applied to the side portions 220 of the windows, the corner portions 221 of the windows, and the lower end portions 222 of the windows provided in the magnetic shield device. An intermediate element may be applied to the side portion 223 of the door, the lower end portion 224 of the door, and the corner portion 225 of the door provided in the shield device.

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 the present embodiment, the BH curve is created using the angles α _B and β _B as parameters, but these may be created using the angles α _H and β _H as parameters.

Moreover, you may make it obtain | require the iron loss which arises when the external magnetic field _Hext is given. More specifically, for example, the iron loss is obtained based on the BH curve created by the magnetic characteristic curve creating unit 6b. Also, a curve representing the relationship between the calculated iron loss and the average magnetic flux density B _ave is created using the angles α _B and β _B formed by the average magnetic flux density B _ave and the easy magnetization axis X as parameters, and the created curve is You may make it record on a recording medium.

  Furthermore, the equivalent element is not limited to that shown in FIG. 3 as long as it is a region occupied by a plurality of substances including a magnetic substance. That is, if it is a typical area | region in the analysis area | region 40, the position and magnitude | size of an equivalent element are not limited to what was shown in FIGS. 2-4, The range from which the electromagnetic field in the analysis object area | region 21 is obtained appropriately Can be determined as appropriate.

  In addition, the analysis region described above may be composed of a plurality of types of equivalent elements, in which 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 intermediate elements and a plurality of types of equivalent BH curves corresponding thereto.

  Moreover, in this Embodiment, although the area | region formed with a part of steel plate and the air of the side was made into the equivalent element 22, the substance contained in an 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.

Further, when _obtaining the average magnetic flux density B _ave and the average magnetic field H _ave as described above, the three axes (the easy axis X, the hard axis Y, the vertical axis Z) in the intermediate element 23 (or the equivalent element 22), If the three orthogonal axes (vertical, horizontal, and height axes) of the analysis region do not coincide with each other, the intermediate element 23 (or equivalent element 22) is subjected to coordinate transformation or rotational transformation, etc. It is preferable that the three axes in (or equivalent element 22) coincide with the three axes in the analysis region.

Furthermore, in the present embodiment, the case where an electromagnetic field generated in a three-dimensional space is analyzed is exemplified, but an electromagnetic field generated in a two-dimensional plane may be analyzed. For example, when analyzing an electromagnetic field generated on a plane defined by the easy magnetization axis X and the hard magnetization axis Y, the above-described processing may be performed with the angles β _B and φ _{2 set} to 0 [°].

(Second Embodiment)
Next, a second embodiment of the present invention will be described. This embodiment is different from the first embodiment described above only in how to obtain the magnetic characteristics of the equivalent elements, and the other parts are the same as those of the first embodiment described above. Therefore, in the following description, the same parts as those in the first embodiment described above are denoted by the same reference numerals as those in FIGS. 1 to 22, and detailed description thereof is omitted.

  The electromagnetic field analysis apparatus according to the present embodiment has a magnetic characteristic calculation unit instead of the average magnetic field calculation unit 5a and the magnetic characteristic curve creation unit 5b in the equivalent element calculation unit 5 shown in FIG. This magnetic characteristic calculation part calculates | requires the magnetic permeability in the magnetic shield apparatus 290 shown in FIG. 23 as follows. Note that the magnetic shield device 290 shown in FIG. 23 is a device that shields a magnetic field from the outside. In this embodiment, a case where the shielding performance of the magnetic shield device 290 is evaluated will be described as an example.

  In FIG. 23, 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, a magnetic shield device is configured by stacking eight sets of four steel plates arranged in a “mouth” shape at intervals of 30 mm. FIG. 23 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. 24, 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. 24, 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. 24, 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. 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. 24 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. 23 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. 24 is the easy axis of magnetization of the steel sheet and the Y axis is the hard axis of magnetization of the steel sheet.

  23 and 24 are compared based on such an assumption, the X axis of FIG. 23 (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. 23 (the hard axis of magnetization of the equivalent element 293) is the Y axis of FIG. (The hard axis of the equivalent element model, which is not filled and occupied by the steel plate in this direction), and the Z axis in FIG. 23 (the vertical axis of the equivalent element 293, the steel plate continues repeatedly) However, it can be considered as the Z axis in FIG. 24 (the vertical axis of the equivalent element model, which is filled and occupied by the steel plate in this direction).

  Then, in FIG. 23, 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 (16 formulas) to (18 formulas).

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, 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 16) to (Expression 18) 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. 24 are expressed by the following (Equation 19) and (Equation 20), 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. 5). ΔV _i is the volume of a region (divided region) i obtained by dividing the equivalent element 293 model (see FIG. 5). 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 (divided 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. 5). 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 (Equation 19) and (Equation 20), the permeability μ _aveX that relates the average magnetic flux density and the average magnetic field is as _shown in the following (Equation 21).

Here, considering that the magnetic field is continuous for the parallel component of the steel plate 280, it can be assumed that the magnetic field of the steel plate 280 and the magnetic field of air are the same as in the following (Equation 22). Therefore, the permeability μ _aveX that relates the average magnetic flux density to the average magnetic field is as _shown in the following (Equation 23).

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 and occupied by the steel plate (magnetic body) 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, with respect to the equivalent element 294, the easy magnetization axes of the two steel plates overlapping 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. 23 coincides with the X axis of FIG. 23, whereas the easy magnetization axis of the upper steel plate in the equivalent element 294 of FIG. It coincides with the Z axis of 23. 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. Therefore, the magnetic permeability of each axis (X axis, Y axis, Z axis) in the equivalent element is as shown in the following (24 formula) to (26 formula).

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. 25, 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 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, as in the first embodiment described above, the intermediate element calculation unit 6 regards the equivalent elements 291 to 294 and the region where the BH curve can be regarded as equivalent as an intermediate element (intermediate element). The magnetic characteristics in the intermediate element are calculated by the finite element method (FEM) using the magnetic permeability μ _aveX , μ _aveY , and μ _aveZ obtained by the magnetic characteristic calculation unit as described above, and the calculated magnetic characteristics Is created.

  The magnetic field distribution calculation unit 7 uses the magnetic characteristic curve created by the intermediate element calculation unit 6 to perform an electromagnetic field analysis of the magnetic shield device 290 shown in FIG.

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 16) to (Expression 18) and (Expression 24). ~ determined using a (26-type), obtained permeability mu _avex, mu _AveY, with mu _avez, calculates the magnetic properties of the intermediate element, using the calculated magnetic properties in the intermediate elements, magnetic shield Since the electromagnetic field in the apparatus 290 is analyzed, the electromagnetic field can be analyzed at higher speed. The method described in this embodiment is particularly effective when it is required to perform analysis at a higher speed than the analysis accuracy.
In this embodiment, the magnetic permeability μ _aveX , μ _aveY , and μ _aveZ are _obtained , but a magnetic resistivity that is the reciprocal of the magnetic permeability may be obtained.

(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. 26 is a block diagram showing an example of the configuration of a computer system arranged in the electromagnetic field analysis apparatus 1.
26, a computer system 2300 includes a CPU 2301, a ROM 2302, a RAM 2303, a keyboard controller (KBC) 2305 of a keyboard (KB) 2304, a CRT controller (CRTC) 2307 of a CRT display (CRT) 2306 as a display unit, The disk controller (DKC) 2310 of the hard disk (HD) 2308 and flexible disk (FD) 2309 and the network interface controller (NIC) 2312 for connection to the network 2311 can communicate with each other via the system bus 2313. Connected configuration.

The CPU 2301 performs overall control of each component connected to the system bus 2303 by executing software stored in the ROM 2302 or the HD 2308 or software supplied from the FD 2309.
That is, the CPU 2301 reads out a processing program according to a predetermined processing sequence from the ROM 2302, the HD 2308, or the FD 2309 and executes it, thereby performing control for realizing an operation described later.

A RAM 2303 functions as a main memory or a work area for the CPU 2301.
The KBC 2305 controls instruction input from the KB 2304, a pointing device (not shown), or the like.

The CRTC 2307 controls display on the CRT 2306.
The DKC 2310 controls access to the HD 2308 and the FD 2309 that store a boot program, various applications, an edit file, a user file, a network management program, a predetermined processing program in the present embodiment, and the like.
The NIC 2312 exchanges data bidirectionally with devices or systems on the network 2311.

  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 looked at the analysis object area | region analyzed with an electromagnetic field analyzer from the upper direction. It is the figure which showed the 1st Embodiment of this invention and looked at the analysis object area | region analyzed with an electromagnetic field analyzer from the side and the front. 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 a figure which shows the 1st 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 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 direction of an average magnetic flux density, 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 direction of an average magnetic flux density, 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 the 1st Embodiment of this invention and showed an example of the concept 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 1st B-theta curve in an equivalent element. It is the figure which showed the 1st Embodiment of this invention and showed an example of the 2nd 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. FIG. 16 is a flowchart illustrating an example of a processing operation in the electromagnetic field analysis device according to the first embodiment of this invention and continued from FIG. 15. 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 an analysis object area | region. It is the figure which showed the 1st Embodiment of this invention and showed the other example of the equivalent element and the intermediate element. It is the figure which showed the 1st Embodiment of this invention and showed the other example of the intermediate element calculating part. It is the figure which showed the 1st Embodiment of this invention and showed the other example of the application object of an intermediate element. It is the figure which showed the 1st Embodiment of this invention and showed the other example of the application object of an intermediate element. It is the figure which showed the 1st Embodiment of this invention and showed the other example of the application object of an intermediate element. It is the figure which showed the 2nd Embodiment of this invention and showed an example of the structure of the analysis object area | region analyzed with an electromagnetic field analyzer. It is the figure which showed the 2nd Embodiment of this invention and showed an example of the equivalent element. It is the figure which showed the 2nd Embodiment of this invention and showed the other example of the equivalent element. 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 at the electromagnetic field analyzer.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Electromagnetic field analyzer 2 Operation part 3 Display part 4 Processing part 5a, 6a, 191a-193a Average magnetic field calculating part 5b, 6b, 191b-193b Magnetic characteristic curve preparation part 7 Magnetic field distribution calculating part 21,290 Analysis object area | region 22,180 , 291 to 294 Equivalent element 23, 181 to 183 Intermediate element 40 Analysis region 110 to 113, 1201 BH curve 1301 First B-θ curve 1401 Second B-θ curve

Claims (17)

An electromagnetic field analyzer for analyzing an electromagnetic field generated in an analysis target area,
An equivalent element calculating means for calculating an average magnetic flux density in the equivalent element and an average magnetic field from the magnetic flux density and the magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic substance;
Using the average magnetic flux density and the average magnetic field in the equivalent element, the shape and size of the equivalent element are the same, and the magnetic characteristics , that is, the elements that can be considered to have the same average magnetic flux density and average magnetic field , Intermediate element calculation means for calculating an average magnetic flux density and an average magnetic field in an intermediate element comprising a plurality of elements equivalent to the equivalent element;
An electromagnetic field analyzing means for analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element using an average magnetic flux density in the intermediate element calculated by the intermediate element calculating means and an average magnetic field. Electromagnetic field analyzer. An electromagnetic field analyzer for analyzing an electromagnetic field generated in an analysis target area,
From the magnetic flux density and magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic material, the average magnetic flux density in the equivalent element and the average magnetic field are calculated , and the average magnetic flux density, Equivalent element calculation means for creating a BH curve in the equivalent element representing the relationship with the average magnetic field ;
Using the BH curve in the equivalent element, the equivalent element is the element having the same shape and size as the equivalent element and having the same magnetic characteristics , that is, the average magnetic flux density and the average magnetic field. A BH curve in the intermediate element representing a relationship between the average magnetic flux density and the average magnetic field by calculating an average magnetic flux density and an average magnetic field in the intermediate element including a plurality of equivalent elements ; The first B-θ curve representing the relationship between the average magnetic flux density and the angle formed by the reference line OP and the reference line OQ, and the relationship between the average magnetic flux density and the angle formed by the reference line OQ and the average magnetic field. Intermediate element computing means for creating a second B-θ curve representing
The average magnetic flux density in the intermediate element calculated by the intermediate element calculating means, the average magnetic field, the angle between the reference line OP and the hard axis of magnetization of the magnetic material, and the reference line OP and the average magnetic flux density An angle, an angle formed by the reference line OP and the reference line OQ, an angle formed by the reference line OQ and the average magnetic field, a BH curve in the intermediate element, and the first B-θ curve, An electromagnetic field analyzing means for analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element using the second B-θ curve ;
The reference line OP is a vector determined from a value in the easy axis direction of the average magnetic flux density and a value in the hard axis direction,
The reference line OQ is a vector determined from a value of the average magnetic field in the easy magnetization axis direction and a value in the hard magnetization axis direction. The intermediate element is an element in which the relationship between the average magnetic flux density in the element and the average magnetic field is equivalent to that of the equivalent element, that is, the equivalent element has the same shape and size, and BH in the element curve, electromagnetic field analysis apparatus according to claim 1 or 2, characterized in that it comprises a plurality of elements which can be regarded as identical to the B-H curve of the equivalent elements. The plurality of substances are a magnetic material and a non-magnetic material,
The equivalent element calculating means calculates an average magnetic flux density and an average magnetic field in an equivalent element occupied by a part of the magnetic body and a nonmagnetic body around the part. electromagnetic field analysis apparatus according to any one of 3. The electromagnetic field analysis means is a region where a plurality of substances containing the magnetic substance are present repeatedly, that is, a plurality of substances containing the magnetic substance are present in the same shape, the same size and at a constant interval. The electromagnetic field analysis apparatus according to any one of claims 1 to 4 , wherein an electromagnetic field generated in the electromagnetic field is analyzed. The intermediate element calculation means uses a mean magnetic flux density and an average magnetic field in the equivalent element calculated by the equivalent element calculation means, and includes a plurality of elements equivalent to the equivalent element in the first intermediate element. First intermediate element calculating means for calculating an average magnetic flux density and an average magnetic field in
Using the average magnetic flux density and the average magnetic field in the first intermediate element calculated by the first intermediate element calculation means, an element equivalent to the first intermediate element, that is, the intermediate element, shape and size Second intermediate element calculation for calculating the average magnetic flux density and the average magnetic field in the second intermediate element including a plurality of elements having the same magnetic characteristics , that is, the average magnetic flux density and the average magnetic field can be regarded as the same Means,
The electromagnetic field analysis means uses the average magnetic flux density and the average magnetic field in the intermediate element calculated by the second intermediate element calculation means to generate an electromagnetic field generated in an analysis target area wider than the second intermediate element. The electromagnetic field analysis device according to claim 1, wherein the electromagnetic field analysis device is analyzed. The intermediate element calculation means uses a mean magnetic flux density and an average magnetic field in the equivalent element calculated by the equivalent element calculation means, and includes a plurality of elements equivalent to the equivalent element in the first intermediate element. First intermediate element calculating means for calculating an average magnetic flux density and an average magnetic field in
A second intermediate element comprising a plurality of elements equivalent to the first intermediate element using an average magnetic flux density and an average magnetic field in the first intermediate element calculated by the first intermediate element calculating means The second intermediate element calculation means for calculating the average magnetic flux density and the average magnetic field in the first to (n-1) th (n-1) intermediate element calculation means (n is a natural number of 3 or more). The average magnetic flux density and the average magnetic field in the nth intermediate element including a plurality of elements equivalent to the (n-1) th intermediate element using the average magnetic flux density and the average magnetic field in the intermediate element N-th intermediate element calculating means for calculating
The electromagnetic field analysis means uses the average magnetic flux density and the average magnetic field in the intermediate element calculated by the nth intermediate element calculation means to generate an electromagnetic field generated in an analysis target area wider than the nth intermediate element. The electromagnetic field analysis device according to claim 1, wherein the electromagnetic field analysis device is analyzed. An electromagnetic field analysis method for analyzing an electromagnetic field generated in an analysis target area,
An equivalent element calculation step of calculating an average magnetic flux density in the equivalent element and an average magnetic field from the magnetic flux density and the magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic body;
From the magnetic flux density and magnetic field at each position inside the equivalent element, using the average magnetic flux density and the average magnetic field, the equivalent element has the same shape and size, and the magnetic characteristics , that is, the average magnetic flux density and the average magnetic field are An intermediate element calculation step for calculating an average magnetic flux density and an average magnetic field in an intermediate element including a plurality of elements equivalent to the equivalent element, which are elements that can be regarded as the same;
Using an average magnetic flux density in the intermediate element calculated by the intermediate element calculation step and an average magnetic field, and an electromagnetic field analysis step for analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element, Electromagnetic field analysis method. An electromagnetic field analysis method for analyzing an electromagnetic field generated in an analysis target area,
From the magnetic flux density and magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic material, the average magnetic flux density in the equivalent element and the average magnetic field are calculated , and the average magnetic flux density, An equivalent element calculation step of creating a BH curve in the equivalent element representing the relationship with the average magnetic field ;
Using the BH curve in the equivalent element, the equivalent element is the element having the same shape and size as the equivalent element and having the same magnetic characteristics , that is, the average magnetic flux density and the average magnetic field. A BH curve in the intermediate element representing a relationship between the average magnetic flux density and the average magnetic field by calculating an average magnetic flux density and an average magnetic field in the intermediate element including a plurality of equivalent elements ; The first B-θ curve representing the relationship between the average magnetic flux density and the angle formed by the reference line OP and the reference line OQ, and the relationship between the average magnetic flux density and the angle formed by the reference line OQ and the average magnetic field. An intermediate element calculation step of creating a second B-θ curve representing
The average magnetic flux density in the intermediate element calculated by the intermediate element calculation step, the average magnetic field, the angle formed by the reference line OP and the magnetization difficult axis of the magnetic material, and the reference line OP and the average magnetic flux density are formed. An angle, an angle formed by the reference line OP and the reference line OQ, an angle formed by the reference line OQ and the average magnetic field, a BH curve in the intermediate element, and the first B-θ curve, An electromagnetic field analysis step for analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element using the second B-θ curve ,
The reference line OP is a vector determined from a value in the easy axis direction of the average magnetic flux density and a value in the hard axis direction,
The electromagnetic field analysis method, wherein the reference line OQ is a vector determined from a value in the easy axis direction of the average magnetic field and a value in the hard axis direction. The intermediate element is an element in which the relationship between the average magnetic flux density in the element and the average magnetic field is equivalent to that of the equivalent element, that is, the equivalent element has the same shape and size, and BH in the element 10. The electromagnetic field analysis method according to claim 8, wherein the curve includes a plurality of elements that can be regarded as the same as the BH curve of the equivalent element. The plurality of substances are a magnetic material and a non-magnetic material,
The equivalent element calculation step, the magnetic and some of the body, and the average magnetic flux density in the equivalent element occupied by a non-magnetic material around, claim 8, characterized in that for calculating the average magnetic field - The electromagnetic field analysis method according to any one of 10 above. In the electromagnetic field analysis step, a region where a plurality of substances containing the magnetic material are present repeatedly, that is, a region where a plurality of materials containing the magnetic material are present at the same shape, the same size and at regular intervals. The electromagnetic field analysis method according to any one of claims 8 to 11 , wherein an electromagnetic field generated in said step is analyzed. The intermediate element calculating step uses a mean magnetic flux density and an average magnetic field in the equivalent element calculated in the equivalent element calculating step, and includes a plurality of elements equivalent to the equivalent element. A first intermediate element calculation step of calculating an average magnetic flux density and an average magnetic field in
Using the average magnetic flux density and the average magnetic field in the first intermediate element calculated by the first intermediate element calculation step, an element equivalent to the first intermediate element, that is, the intermediate element, shape and size Second intermediate element calculation for calculating the average magnetic flux density and the average magnetic field in the second intermediate element including a plurality of elements having the same magnetic characteristics , that is, the average magnetic flux density and the average magnetic field can be regarded as the same And having steps
The electromagnetic field analysis step uses an average magnetic flux density and an average magnetic field in the intermediate element calculated by the second intermediate element calculation step to generate an electromagnetic field generated in an analysis target area wider than the second intermediate element. 9. The electromagnetic field analysis method according to claim 8 , wherein analysis is performed. The intermediate element calculating step uses a mean magnetic flux density and an average magnetic field in the equivalent element calculated in the equivalent element calculating step, and includes a plurality of elements equivalent to the equivalent element. A first intermediate element calculation step of calculating an average magnetic flux density and an average magnetic field in
A second intermediate element comprising a plurality of elements equivalent to the first intermediate element by using the average magnetic flux density in the first intermediate element calculated by the first intermediate element calculation step and the average magnetic field. Calculated from the second intermediate element calculation step to the (n-1) th intermediate element calculation step (n-1 is a natural number of 3 or more). The average magnetic flux density and the average magnetic field in the nth intermediate element including a plurality of elements equivalent to the (n-1) th intermediate element using the average magnetic flux density and the average magnetic field in the intermediate element And an nth intermediate element calculation step for calculating
The electromagnetic field analysis step uses an average magnetic flux density and an average magnetic field in the intermediate element calculated by the nth intermediate element calculation step to generate an electromagnetic field generated in an analysis target area wider than the nth intermediate element. 9. The electromagnetic field analysis method according to claim 8 , wherein analysis is performed. A computer program for causing a computer to execute a step of analyzing an electromagnetic field generated in an analysis target region,
An equivalent element calculation step of calculating an average magnetic flux density in the equivalent element and an average magnetic field from the magnetic flux density and the magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic body;
Using the average magnetic flux density and the average magnetic field in the equivalent element, the shape and size of the equivalent element are the same, and the magnetic characteristics , that is, the elements that can be considered to have the same average magnetic flux density and average magnetic field , An intermediate element calculation step of calculating an average magnetic flux density and an average magnetic field in the intermediate element including a plurality of elements equivalent to the equivalent element;
Causing the computer to execute an electromagnetic field analysis step of analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element using the average magnetic flux density in the intermediate element calculated by the intermediate element calculation step and the average magnetic field. A computer program characterized by the above. A computer program for causing a computer to execute a step of analyzing an electromagnetic field generated in an analysis target region,
From the magnetic flux density and magnetic field at each position inside the equivalent element occupied by a plurality of substances including a magnetic material, the average magnetic flux density in the equivalent element and the average magnetic field are calculated , and the average magnetic flux density, An equivalent element calculation step of creating a BH curve in the equivalent element representing the relationship with the average magnetic field ;
Using the BH curve in the equivalent element, the equivalent element is the element having the same shape and size as the equivalent element and having the same magnetic characteristics , that is, the average magnetic flux density and the average magnetic field. A BH curve in the intermediate element representing a relationship between the average magnetic flux density and the average magnetic field by calculating an average magnetic flux density and an average magnetic field in the intermediate element including a plurality of equivalent elements ; The first B-θ curve representing the relationship between the average magnetic flux density and the angle formed by the reference line OP and the reference line OQ, and the relationship between the average magnetic flux density and the angle formed by the reference line OQ and the average magnetic field. An intermediate element calculation step of creating a second B-θ curve representing
The average magnetic flux density in the intermediate element calculated by the intermediate element calculation step, the average magnetic field, the angle formed by the reference line OP and the magnetization difficult axis of the magnetic material, and the reference line OP and the average magnetic flux density are formed. An angle, an angle formed by the reference line OP and the reference line OQ, an angle formed by the reference line OQ and the average magnetic field, a BH curve in the intermediate element, and the first B-θ curve, Using the second B-θ curve, and causing the computer to execute an electromagnetic field analysis step of analyzing an electromagnetic field generated in an analysis target area wider than the intermediate element,
The reference line OP is a vector determined from a value in the easy axis direction of the average magnetic flux density and a value in the hard axis direction,
The computer program, wherein the reference line OQ is a vector determined from a value of the average magnetic field in the easy axis direction and a value in the hard axis direction. A computer-readable recording medium on which the computer program according to claim 15 or 16 is recorded.

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