JP2003240831A - Electromagnetic field analyzing system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To evaluate iron loss by solving a Maxwell equation in consideration of anisotropy of magnetic permeability and reluctivity of a steel plate. <P>SOLUTION: This electromagnetic field analyzing system is characterized by having a database for storing therein H-B curves with an angle θ between a predetermined direction of the steel plate in a minute area and the direction of magnetic flux density and/or stress σ used as parameters of anisotropy, a database for storing therein W-B curves, a magnetic flux density vector determining means for determining the angle θ and the size B of magnetic flux density based on the Maxwell equation in the minute area, an iron loss calculating means for calculating iron loss in the minute area, and an iron loss summing means for finding the sum of iron loss in the minute area. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electromagnetic field analysis system in which anisotropy and stress of a magnetic material such as a steel plate are taken into consideration. Concerning the law.

[0002]

2. Description of the Related Art Conventionally, an electromagnetic field analysis method based on the Maxwell equation has been used for evaluating iron loss of a ferromagnetic material such as a steel plate. Hereafter, a steel sheet that is practically used as a ferromagnetic material will be representatively described.
Computer is used for electromagnetic field analysis,
The size of the minute region divided for the calculation, the magnetic flux density B with respect to the magnetic field H, the stress σ applied to the steel sheet, the frequency, etc. are adopted as the physical property parameter conditions for obtaining the calculation solution by the computer. That is, a computer solution of the Maxwell equation can be obtained taking these conditions into consideration.

The iron loss is calculated in consideration of the data (B-W curve) of the iron loss W measured corresponding to the magnetic flux density B in the computer solution of the Maxwell equation. Figure 1
FIG. 5 is a block diagram showing a flow of an iron loss numerical calculation routine executed based on the conventional technique. First, H-B with parameters such as the shape of the steel sheet, minute region division, and frequency
Given a condition such as a curve for obtaining a solution, obtain a numerical solution of Maxwell's equation by calculation. Data of the iron loss W of the steel material in a minute region (BW curve) measured corresponding to the magnetic flux density B is given to the above numerical solution, and the loss W of the entire steel sheet is calculated. Here, it is assumed that the effect of the stress acting on the steel sheet is ignored and that the magnetic characteristics do not change even when the stress is applied to the steel sheet.

Here, a method of solving the Maxwell equation will be briefly described. As is apparent from many known documents, the Maxwell equation is given by the following equation.

[Formula 1] Here, B, H, D, E, and J are magnetic flux density, magnetic field, electric flux density, electric field, and current density, respectively. Further, ρ is the charge density. The following relationships exist among B, H, D, E, and J.

[Formula 2] Here, μ, ε, and σ are magnetic permeability, permittivity, and conductivity, respectively.

On the other hand, according to "Finite element method of electrical engineering" by Takayoshi Nakata and Norio Takahashi (Morikita Publishing, 1982), analysis on electromagnetic field is described in detail. According to the document, dD / dt is ignored. Since the divergence of the magnetic flux is always zero, it is continuous, and the magnetic vector potential A is given by the following equation.

[Formula 3] From these formulas,

[Formula 4] Has been obtained. Therefore,

[Formula 5] Is obtained. Here, -grad φ = E, J ₀ is a forced current density from the outside, Je is an eddy current density, and the magnetic resistivity [ν] given by the amount of tensor is [ν] = 1 / [μ]. (5)
The equation is solved two-dimensionally and three-dimensionally by the Galerkin method. In practice, magnetic permeability is generally affected by stress. However, in the conventional iron loss evaluation method, numerical analysis was performed and a solution was sought, assuming that the magnetic permeability was not considered to be affected by stress.

A numerical solution of the magnetic flux density B with respect to the magnetic field H can be obtained by applying HB curve data in each minute region of the steel sheet to the Maxwell equation.
Here, the H-B curve is assumed to have isotropic permeability,
The data is obtained by measuring in advance using the stress σ _i (i = 1, 2, ... N) applied to the steel sheet as a parameter.
The H-B curve data is prepared for each stress value set at appropriate intervals and stored in the database. Here, the numerical solution of the magnetic flux density B with respect to the magnetic field H, which corresponds to the stress σ that is an intermediate value between the stress σ _j and the stress σ _{j + 1} , can be obtained by interpolation approximation or series approximation. In this way, from the magnetic flux density B with the stress σ _j (i = 1, 2, 3 ... N) as a parameter, which is obtained for each minute region for the given magnetic field strength H, the magnetic flux density in each minute region is obtained. Distribution is required. On the other hand, the relationship between the magnetic flux density B and the iron loss W is measured in advance using the stress σ as a parameter and stored in the database in the form of a WB curve.

Further, it is assumed that the H-B curve has no influence on stress and is constant. In this way, for each minute region for a given magnetic field strength H,
From the H-B curve, the distribution of magnetic flux density in each minute region can be obtained. On the other hand, the relationship between the magnetic flux density B and the iron loss W is
Is stored in the database in the form of a WB curve. Therefore, if the magnetic flux density distribution obtained by the numerical calculation is applied to the WB curve stored in the database, the iron loss of the entire steel sheet for the given magnetic field strength H can be obtained by the numerical calculation. In the above conventional technique, in the electromagnetic field analysis for obtaining the iron loss,
Since the magnetic permeability is assumed to be isotropic and the magnetic permeability is calculated by ignoring the influence of stress, the anisotropy of magnetic permeability and the influence of stress existing in actual steel materials are ignored. However, the difference between the measured value and the calculated value cannot be ignored, and there is a drawback that the iron loss cannot be sufficiently evaluated.

[0008]

Therefore, the present invention solves the problems of the prior art as described above, and, while following the conventional analysis method, the influence of anisotropy and stress on the physical property parameters of the steel material. It is an object to provide an electromagnetic field analysis system that takes into consideration the above and realize an accurate iron loss evaluation.

[0009]

Means for Solving the Problems The inventors have found a means for evaluating iron loss in consideration of the influences of the anisotropy and stress of the material by rolling on the H-B curve and the WB curve, and have established an electromagnetic field analysis system. The gist is the following contents as described in the claims. (1) A region dividing unit that divides the electromagnetic field analysis target region into a plurality of minute regions, and an angle θ between a predetermined direction of the magnetic body and the direction of the magnetic flux density in the minute regions is used as an anisotropy parameter. , A database storing an H-B curve based on an analytical expression or data relating the magnetic flux density and the magnetic field, and based on the H-B curve stored in the database, based on the Maxwell equation in the minute region , The angle θ, and a magnetic flux density vector determination unit that determines the magnitude B of the magnetic flux density. (2) A region dividing unit that divides the electromagnetic field analysis target region into a plurality of minute regions, and an angle θ between a predetermined direction of the magnetic body and the direction of the magnetic flux density in the minute regions is used as an anisotropy parameter. , A database storing a WB curve based on an analytical expression or data relating the magnetic flux density and the iron loss, and calculating the iron loss of the minute region based on the WB curve stored in the database An electromagnetic field analysis system, comprising: an iron loss calculating means for: and an iron loss summing means for calculating a sum of iron losses of the minute areas.

(3) A region dividing means for dividing the electromagnetic field analysis target region into a plurality of minute regions, and the angle θ between a predetermined direction of the magnetic body and the direction of the magnetic flux density in the minute regions is anisotropic. And a database storing an H-B curve based on an analytical expression and data relating the magnetic flux density and the magnetic field, and an analytical expression relating the magnetic flux density and iron loss and a W-B curve based on the data. A magnetic flux density vector determining means for determining the angle θ and the magnitude B of the magnetic flux density in the minute region based on the Maxwell equation based on the H-B curve stored in the database; An iron loss calculating means for calculating the iron loss of the minute area based on the WB curve stored in the, and an iron loss summing means for calculating the sum of the iron loss of the minute area. An electromagnetic field analysis system having: (4) Anisotropy of the angle θ and the stress σ between a predetermined direction of the magnetic body and the direction of the magnetic flux density in the minute area, the area dividing means dividing the electromagnetic field analysis object area into a plurality of minute areas. A database that stores an H-B curve based on an analytical expression and data relating the magnetic flux density and the magnetic field as a parameter of, and a WB curve based on the analytical expression relating the magnetic flux density and iron loss and the data. Magnetic flux density vector determining means for determining the angle θ and the magnitude B of the magnetic flux density based on the Maxwell equation and the stress σ in the minute region based on the H-B curve stored in the database. , An iron loss calculating means for calculating the iron loss of the micro region and a total of the iron loss of the micro region are obtained based on the WB curve stored in the database. Electromagnetic analysis system characterized by having a loss summation means.

(5) The electromagnetic field analysis system according to any one of (1) to (4), wherein the magnetic flux density and the magnetic field are vectors that take into consideration the phase difference Θ _BH between the magnetic flux density and the magnetic field. (6) The electromagnetic field analysis system according to any one of (1) to (5), wherein the magnetic flux density is a vector considering time harmonics. (7) The magnetic flux density and the magnetic field are defined as an angle θ between a predetermined direction of the magnetic body in the minute region and the stress σ.
The electromagnetic field analysis system according to any one of (1) to (6), characterized in that the vector takes σ into consideration.

(8) The magnetic flux density vector determining means determines the residual stress generated in the processing of the magnetic body as the stress σ based on the structural analysis.
The electromagnetic field analysis system according to claim 4, further comprising a stress calculation unit that is obtained by the calculation of. (9) In the magnetic flux density vector determining means for determining the angle θ and the magnitude B of the magnetic flux density based on the Maxwell equation in the minute region based on the HB curve stored in the database, The magnetic flux density vector in the minute region is decomposed into an angle θ formed by the magnitude Bmax and a predetermined direction of the steel sheet, and the angle θ is calculated from the H-B curve using the anisotropy as a parameter. And a means for performing a convergence calculation so that the magnetic flux density in the minute region and the angle θ and the magnetic field thereof are present on the curve (1) or The electromagnetic field analysis system according to (3) to (8).

(10) H stored in the database
In the determining means for determining the magnetic flux density vector based on the Maxwell equation and the stress σ in the micro area based on the −B curve, the magnetic flux density vector in the micro area is calculated based on the magnitude Bmax and Decompose into an angle θ formed by a predetermined direction of the magnetic body,
An H-B curve at the angle θ is derived from the H-B curve with the anisotropy as a parameter so that the magnetic flux density in the minute region and the angle θ and the magnetic field exist on the curve. , The electromagnetic field analysis system according to (7) or (8), wherein the convergence calculation is performed. (11) A region dividing unit that divides the electromagnetic field analysis target region into a plurality of minute regions, and an H-B curve based on an analytical expression or data relating the magnetic flux density and the magnetic field with the stress σ in the minute regions as a parameter is stored. And a magnetic flux density vector determining means for determining the magnetic flux density based on the Maxwell equation in the minute divided area based on the H-B curve stored in the database. Electromagnetic field analysis system.

(12) Area dividing means for dividing the electromagnetic field analysis target area into a plurality of minute areas, and WB based on an analytical expression or data relating the magnetic flux density and the iron loss with the stress σ in the minute areas as a parameter. A database for storing a curve, an iron loss calculating means for calculating an iron loss in the micro region based on a WB curve stored in the database, and an iron loss for calculating a sum of iron losses in the micro region. An electromagnetic field analysis system having a summing means. (13) Area dividing means for dividing an electromagnetic field analysis target area into a plurality of minute areas, an H-B curve based on an analytical expression and data relating the magnetic flux density and the magnetic field with the stress σ as a parameter in the minute areas, and , A database that stores an WB curve based on analytical data and data relating magnetic flux density and iron loss with stress σ as a parameter, and the minute curve based on the HB curve stored in the database. Magnetic flux density vector determining means for determining the magnetic flux density based on the Maxwell equation in the area, and iron loss calculating means for calculating the iron loss in the minute area based on the WB curve stored in the database. And an iron loss summing means for calculating the sum of iron losses in the minute region.

(14) The magnetic flux density vector determining means is provided with a stress calculating means for calculating the residual stress generated during the processing of the magnetic body by calculating the stress σ based on the structural analysis (11) or (13). ) Electromagnetic field analysis system described in. (15) The H-B curve or the W-B curve stored in the database uses the angle θ between the predetermined direction of the magnetic material and the direction of the magnetic flux density in the minute region as an anisotropic parameter. (11) to (1)
The electromagnetic field analysis system according to 4).

(16) From the relationship between the magnetic flux density and the magnetic field with the stress as a parameter, the magnetic field increment coefficient α (= Hσ / Hσ _{= 0} ),
From the relationship between magnetic flux density and iron loss value, the iron loss increment coefficient β (= Wσ / W
[sigma] _{= 0} ), and a means for obtaining a BH, BW curve considering stress by multiplying the base H-B, BW curve by the magnetic field increment coefficient [alpha] and iron loss increment coefficient [beta]. The electromagnetic field analysis system according to (11) to (15). (17) The electromagnetic field analysis system according to (16), wherein the magnetic field increment coefficient α and the iron loss increment coefficient β are regression equations. (18) The regression equation of the magnetic field increment coefficient α is such that α = 1 near the magnetic flux density B = 0 and the magnetic flux density B = 2T.
The regression equation of the iron loss increment coefficient β is a linear equation, and the electromagnetic field analysis system according to (17) is characterized. In addition, although the above-mentioned solving means is expressed as a combination of means for realizing the electromagnetic field analysis system, it can also be realized as a method invention using each of the means.

[0017]

DETAILED DESCRIPTION OF THE INVENTION The present invention will be described in detail below with reference to the drawings. In the steel material, the magnetic permeability is anisotropic in a predetermined direction of the steel material, for example, in the rolling direction and the direction perpendicular thereto. If the anisotropy of magnetic permeability of such a steel material is taken into consideration, it becomes possible to accurately evaluate the iron loss. In this case, assuming that the entire area to be subjected to the electromagnetic field analysis is divided into a plurality of minute areas, the magnetic permeability satisfies the isotropic property inside each minute area, and the value of the angle θ is constant, There is no problem in calculation even if there is a difference in the magnetic permeability μ and the magnetic resistivity ν between the minute regions and the angle θ between the predetermined direction, for example, the rolling direction and the direction of the magnetic flux density B. Given the permeability and the angle θ in this way, a computer can be used to find the solution of the Maxwell equation.

In many cases, stress caused by mechanical processing such as caulking and welding is applied to steel materials, and the magnetic characteristics such as magnetic permeability greatly change due to the stress. If the influence of stress on the magnetic permeability of such a steel material is taken into consideration, the iron loss can be accurately evaluated. In this case, if the entire area to be subjected to the electromagnetic field analysis is divided into a plurality of minute areas and the stress is constant inside each minute area, the same magnetic characteristics and magnetic permeability are used in the minute areas. It doesn't matter. Given the relationship between permeability and stress in this way, a computer can be used to find the solution of the Maxwell equation.
FIG. 1 is an explanatory view showing a pattern in which the entire target area of a steel material is divided into a plurality of grid-like minute areas. In FIG. 1, steel materials are 1, 2, 3 ..., i, i + 1, i +
2, ..., J, j + 1, j + 2, .. For example, the magnetic flux density of the i-th minute area is Δ
B _i and the iron loss is Δw _i .

In each of the minute regions divided in FIG. 1, the magnetic permeability μ and the magnetic resistivity ν are constant values. In this way, in the finite element method, it can be considered that even if the boundary between the minute regions is discontinuous, it has a uniform parameter in the region. Therefore, even in the calculation of iron loss of steel materials having anisotropy / stress and non-linearity, it is possible to easily calculate the total loss by obtaining the sum of the iron loss of each minute region calculated in advance. it can. In Fig. 1, the overall iron loss W (watts)
Is

[Formula 6] Given in. Here, Δw _i is the iron loss in the minute region. Also, △ direction θ and magnitude .DELTA.B _i of B _i takes each different value by each micro area. The iron loss W has a larger value as the magnetic flux density B is larger, but is not necessarily in a linear relationship. The above-mentioned area division is carried out on the assumption that the finite element method is applied, but it goes without saying that it can be applied to the difference method or other similar calculation methods.

FIG. 2 is an explanatory diagram showing the anisotropy of the magnetic flux density. Below, let us consider the case where not only the stress but also the anisotropy of the magnetic flux density is taken into consideration. RD is the rolled direction of the steel sheet, and TD is the direction perpendicular to it.
sversal direction). If the angle between the direction of the magnetic flux density B and the rolling direction RD of the steel sheet is θ, the θ dependency of the H-B curve and the WB curve is, for example, as shown in FIG.
It is given in a shape as shown in (b). Here, instead of the rolling direction of the steel sheet, any predetermined direction can be adopted. 3 (a) and 3 (b) both show the angle θ.
The data for multiple leaves also show the dependence on the stress σ. Stress σ is compressive stress (σ _c ), tensile stress (σ _t ), and shear stress (σ _s ).
Caused by. These stresses are vector quantities, but typical ones are used.

In FIG. 3, the data of θ = 0 °, 15 °, 30 ° ... Are given as the HB function and the WB function, but the data is not given as the function at other angles θ. . In this case, the relationship between the magnetic flux density and the magnetic field that needs to be obtained at θ = 20 ° is θ = 15 ° and θ = 3.
About the approximate function obtained from the data at 0 °,
It can be obtained by interpolation interpolation described in detail below, or iteratively calculated by coupling with the Maxwell equation from Taylor expansion by the Newton-Raphson method. On the other hand, the iron loss when the magnetic flux density is given is θ = 15 degrees and θ =
It is obtained by interpolation interpolation from the data at 30 degrees. Here, when the change of the stress σ is small enough to be ignored, the stress σ may be assumed to be constant. if,
When the stress σ changes sufficiently large, the H-B curve and the WB curve corresponding to the respective stress σ are selected and the repeated calculation is executed. Where H-B curve and B-
Although the method for obtaining the W curve based on the data is described, an analytical expression such as an analytical expression theoretically obtained and a regression expression obtained from the data may be used.

Next, the dependence on the stress σ included in FIGS. 3A and 3B will be described in some detail. As for the stress σ, a positive value indicates tension and a negative value indicates compression. For example, in FIGS. 3A and 3B, +20 MPa>σ> −50
Data in the range of MPa (MPa: megapascal) is dealt with and shown as data for the sampled stress σ values. Therefore, the magnetic flux density and iron loss for stress values not given in the data table can be obtained by interpolation from Taylor expansion by the Newton-Raphson method as in the case of the angle θ. That is, the iron loss w _i in the minute region _i is obtained by (B _i , θ _I , σ).

For example, σ = + 20MP shown in FIG.
In the data of a, the curve of θ = 15 ° and 30 °, and B = 2.0wb / m ² and 3.0wb / m ² were cut, and the point AB
Assuming a region surrounded by CD, point P (θ = 20
The iron loss at B, 2.5 wb / m ² ) shall be obtained.
First, a series expansion is performed from the curves of θ = 15 ° and 30 ° by interpolation approximation to obtain a WB curve of θ = 20 °.
Next, the WB curve of θ = 20 ° is cut by a straight line (curve may be used) of B = 2.0 wb / m ² and 3.0 wb / m ² , and B
Determine the point P at B = 2.5 wb / m ² by on-axis interpolation. The iron loss W can be read from the y coordinate axis of the determined point P. In the actual process, the graph of FIG. 3B is stored in the database, and therefore the iron loss can be calculated by performing the interpolation calculation by the software process of the computer.

As described with reference to FIG. 3, the HB curve changes due to the influence of the stress σ. For example, a concave iron core is shaped by shearing a steel plate, and is used for a rotating machine or the like. At this time, residual stress exists in the iron core due to shearing, mechanical compression, and extension. FIG. 4 is an explanatory diagram showing an example of the influence of stress in the iron core on the magnetic flux density.
In FIG. 4, x is a rolling direction as a certain direction of the steel plate,
B indicates the tangential direction of the magnetic flux, and θ indicates the angle between the x-axis and the magnetic flux density B. When the designated position on the space is determined, the magnetic flux density vector B is given and the value of the stress σ is determined.
That is, at the designated spatial position (H-B)
(θ, σ) is obtained, and by this (WB) (θ, σ)
Is determined. The stress corresponding to the spatial position can be obtained by CAD according to the theory of material mechanics.

FIG. 5 is a diagram showing the phase difference between the magnetic flux density and the magnetic field vector. In FIG. 5, magnetic field H and magnetic flux density B
Is a vector and there is a phase difference Θ _BH between them. At this time,
The magnetic resistance ν can be simply modeled as the following equation.

[Formula 7] At this time, the magnetic density vector and the magnetic field vector are expressed by the following equations.

[Formula 8]

[Formula 9] Therefore, the magnetoresistance ν is a function of B and θ.

[Formula 10] It can be obtained from the BH curve as shown in FIG. Also, the phase difference Θ _BH between the magnetic flux density B and the magnetic field H is
And as a function of θ

[Formula 11] The magnetic flux density vector considering Θ _BH can be determined by using the B-Θ _BH curve as shown in FIG. 7 as a database.

FIG. 8 is a diagram showing the change over time in the magnetic flux density B. In FIG. 8, the horizontal axis represents time and the vertical axis represents magnetic flux density. For example, even if the magnetic field H is a sine wave, the magnetic flux density B does not become a sine wave and includes a time harmonic component, so that distortion as shown in FIG. 8 occurs. Therefore, in order to perform accurate electromagnetic field analysis, It is necessary to consider this time harmonic. Therefore, the magnetic flux density B including the time harmonic component is subjected to Fourier series expansion, and the BH curve as shown in FIG.
By using the BW curve as shown in FIG. 10 as a database, it is possible to perform an electromagnetic field analysis in consideration of time harmonic components. From this BH curve and BW curve,
The magnetic resistance ν and the iron loss W are given by the following equations as a function of B, θ and the frequency f.

[Formula 12]

[Formula 13] Further, when the magnetic flux density B including the time harmonic component is expanded by Fourier series, the x component and the y component of B are respectively expressed by the following equations.

[Formula 14]

[Formula 15] Thus, the i-th magnetic flux density vector in the harmonic and its phase difference can be defined by the following equation.

[Formula 16]

[Formula 17] Thereby, the iron loss in the harmonic component can be calculated by the following equation.

[Formula 18] In this way, the iron loss W _Fe based on the magnetic flux density vector including the harmonic component can be obtained, and the iron loss value becomes about 30% larger than that in the case where the harmonic component is not taken into consideration, and more accurate electromagnetic field analysis can be performed. Can be realized.

FIG. 11 is a diagram showing the directions of stress σ, magnetic flux density B, and magnetic field H. In FIG. 11, the stress σ deviates from the rolling direction (RD) by θσ. As shown in FIG. 12, a B-H curve and a B-W curve are created for each value of the stress σ and the direction θ σ, and a database of the magnetic flux density B and the iron loss W is constructed, so that the rolling direction (RD) is obtained. Electromagnetic field analysis can be performed in consideration of the stress direction θσ. From this BH curve and BW curve, the magnetic resistance ν
And iron loss W _Fe are given by the following equations as a function of B, θ, σ and θσ.

[Formula 19]

[Formula 20]

FIG. 13 shows a routine of the above calculation processing.
In FIG. 13, 1 is a region dividing means, 2 is a magnetic flux density vector determining means, 3 is a database of magnetic flux density and iron loss,
4 is an interpolation interpolation calculation means, 5 is an iron loss calculation means in a minute area,
6 is a total iron loss means. The database 3 is composed of a database showing an H-B curve and a database showing a WB curve. The H-B curve is frequency dependent and the magnetoresistivity ν increases with increasing frequency. Therefore,
In the Maxwell equation, the frequency characteristic of the steel sheet is included by ν. The area dividing means 1 divides the entire target area of the steel material into a plurality of minute areas (i = 1 to n). If the steel material is a flat plate material having a uniform thickness, the shape of the minute region can be made triangular, and in this case, the calculation by the finite element method can be easily applied. The magnetic flux density vector determination means 2 receives the stress distribution data based on the stress analysis, while the area division result from the area division means 1 and the (H-B curve) data from the database 3 are input. In the magnetic flux density vector determination means 2, the Newton-Raphson method is used for each divided region, and the convergence calculation of the magnetic flux density vector is performed from the Taylor expansion by coupling with the Maxwell equation.

That is, based on the input data from the area dividing means 1, the magnetic flux density vector determining means 2 determines the minute area a _i.
Then, the angle θ between the rolling direction RD of the steel sheet and the direction of the magnetic flux density and the magnitude B of the magnetic flux density are determined and given to the interpolation / interpolation calculation means 4. Here, the rolling direction may be replaced by any predetermined direction. The database 3 of the magnetic field (H-B curve) and iron loss (W-B curve) with respect to the magnetic flux density stores a table of data divided into a plurality of leaves according to data in which the value of the stress σ is used as a parameter, and each data is stored. The table stores the H-B curve and the WB curve for the angle θ. H stored in database 3
The −B curve and the WB curve give the relationship between the magnetic flux density and the magnetic field, and the relationship between the magnetic flux density and the iron loss, corresponding to the angle θ and the stress σ given by sampling. These data hold pre-measured data in the form of a function of sampled angle θ and stress σ.

Therefore, the relation between the magnetic flux density B and the loss W with respect to an arbitrary angle θ and stress σ is calculated by repeating the interpolation using the Newton-Raphson method by adopting the interpolation interpolation method by the interpolation calculation means 4. Ask. Iron loss data for steel materials (W
-B curve) is provided to the interpolation means 4 from the database. Next, using the data of the WB curve from the database 3, the magnetic flux density B and the angle θ in the minute area a _i obtained by the interpolation / interpolation calculating means 4 are used, and the iron loss in the minute area calculating means 5 is used. Calculate iron loss w _i . Therefore,
The iron loss summation means 6 obtains the total sum W of the iron loss w _i in the minute area a _i . In this way, the iron loss of the steel material having anisotropy is specifically obtained by numerical calculation.

In FIG. 14, H- based on the actual measurement is performed.
Regarding the B curve data, the iron loss calculation routine of the steel material considering the anisotropy was shown. The solution of Maxwell's equations executed by this routine is accurately obtained by the theoretical model as follows. That is, when the current density J ₀ is expressed using the magnetic vector potential A,
The following equation is given.

[Formula 21] If ν is expressed as a tensor and expressed as a two-dimensional field equation, the following equation is obtained.

[Formula 22] The corresponding function χ is given by the following equation.

[Formula 23] If this is represented by the value in the element e, and partial differentiation is performed with the potential of the node ie that constitutes the element e,

[Formula 24] Is obtained. Therefore,

[Formula 25] Is an equation to be solved by the finite element method.

Here, nu is the total number of unknown nodes. Then, rewriting to apply the Newton-Raphson method gives the following equation.

[Formula 26] K-th δA obtained by solving this matrix
_{If j} is obtained, the node i obtained in the k + 1th iteration
Approximate solution of the potential at

[Formula 27] Is obtained. However,

[Formula 28] Further analysis gives the following equation.

[Formula 29] According to the above analysis, the magnetic resistivity represented by a tensor can be obtained by numerical calculation using an analytical model. FIG. 14 shows an example of a specific calculation routine. As shown in FIG. 14, the time is set to 0 in the first step S61.

Next, in S62,

[Formula 30] Set the initial value of. Here, when t = 0:

[Formula 31] When t> 0,

[Formula 32] And the previous time value is used. Next, in S63, Expression 26
Based on, the stiffness matrix [K] and load vector [F] are calculated. From this, in S64, based on Equation 29, δA
Calculate ^{(k, t)} . From this, in S65, the vector potential at k + 1

[Formula 33] To calculate.

In S66, the magnetic flux density vector B is obtained from the equation 3 based on the vector potential. Therefore,
Convergence judgment in S67

[Formula 34] If the predetermined convergence is satisfied, the process proceeds to S71. If the convergence is insufficient, the process proceeds to S68. S
At 68, the magnetic flux density vector is

[Formula 35] Then, it is decomposed into the angle between the maximum value and a certain direction. So S
69, H- in consideration of anisotropy in the database in advance
From the B curve, the relationship between the magnetic flux density and the magnetic field at that angle θ ^{(k, t)} is known, and the magnetic resistivity can be obtained from it. The H-B curve here is an H-B curve in the stress in the minute region, and by using the H-B curve considering the influence of this stress, the magnetic flux density considering the anisotropy and the stress is obtained. be able to.

From this,

[Formula 36] Can be calculated. These values are used to obtain the stiffness matrix and load vector used in S63. In step S71, advance k by one. And S63
Go to and continue the calculation. The calculation from S63 to S70 is
Calculate for all areas. By performing this convergence calculation, it is possible to calculate the magnetic flux density vector on the H-B curve in consideration of stress in each minute region, and it is possible to calculate in consideration of stress. If it converges in S67,
In S71, the time is advanced by one, and the process proceeds to S62. In this calculation, a plurality of cycles are calculated, and the calculation is continued until one cycle is converged. When it converges, it advances to S72 and calculates iron loss.
As shown in FIG. 14, since the magnetoresistivity ν considering the stress is accurately given as the tensor amount from the numerical solution of the Maxwell equation, the H-B curve can be analyzed accurately.

Next, a method for obtaining the H-B curve and the B-W curve by using the magnetic field increment coefficient α and the iron loss increment coefficient β will be described. In the first place, it is usually difficult to obtain the H-B curve and the B-W curve in consideration of all steel materials and anisotropy, and some kind of simple calculation is required.
Here, the basic H-B curve and B-W curve are obtained, and on the other hand, when there is an H-B curve and B-W curve corresponding to stress, other steel materials and anisotropy are determined. The method of obtaining the considered characteristics is described.

FIG. 16 is an example of a relationship diagram between the stress and the magnetic field with the magnetic flux density obtained from the experiment as a parameter.
The magnetic field characteristics when the stress is applied from compression to tension are shown for the magnetic flux densities B1 to B4. At this time, using the magnetic flux density B as a parameter, the magnetic field increment coefficient α (= Hσ / H
σ _{= 0)} (where, Hσ _{= 0:} magnetic field at the time of no stress, H
σ: magnetic field at stress σ) can be obtained for each point on FIG. FIG. 17 shows the relationship between the magnetic flux density and the magnetic field increment coefficient α using the stress as a parameter. A regression curve is also shown together so that the characteristics may be smooth for each stress. The regression equation is preferable in consideration of variations in experimental measurement. In the case of the magnetic field increment coefficient α, due to the characteristics, α = 1 near B = 0, and α increases as the magnetic flux density B increases, but α = 1 again near 2T where the magnetic flux density B is saturated. I understand. Therefore, the regression equation here is

[Formula 37] Was used. a is a parameter to be obtained from experimental data. B _sat is the saturation magnetic flux density of the steel plate, which is about 2-2.1 T for ordinary iron.

FIG. 18 is an example of a relation diagram between stress and iron loss with the magnetic flux density obtained as a parameter being a parameter.
The iron loss characteristics when stress is applied from compression to tension are shown for magnetic flux densities B1 to B4. At this time, using the magnetic flux density B as a parameter, the iron loss increment coefficient β (= Wσ / W
σ _{= 0)} (where, Wσ _{= 0:} iron loss when there is no stress, W
σ: iron loss at stress σ) can be obtained for each point on FIG. FIG. 19 shows the relationship between the magnetic flux density and the iron loss increment coefficient β using the stress as a parameter. The regression curve is also shown together so that the characteristics may be smooth for each stress. . The regression equation is preferable in consideration of variations in experimental measurement. In the case of the iron loss increment coefficient β, it can be seen that the relationship between the magnetic flux density and the iron loss increment coefficient β is almost a linear line. Therefore, the regression equation here is

[Formula 38] Was used. b and c are parameters to be obtained from experimental data.

At this time, when a BH curve without stress is given as shown by the dotted line in FIG. 20, when a stress σ is applied by the following formula for a certain magnetic flux density on the dotted line. The magnetic field Hσ can be obtained.

[Formula 39] If this is calculated for all the magnetic flux densities of the B-H curve without stress, the B-H curve with stress can be obtained. This is shown by the solid line in FIG.

On the other hand, when a BW curve without stress is given as shown by the dotted line in FIG. 21, the magnetic field when the stress σ is applied by the following formula for a certain magnetic flux density on the dotted line. Wσ can be obtained.

[Formula 40] If this is calculated for all the magnetic flux densities of the BW curve without stress, the BW curve with stress can be obtained. This is shown by the solid line in FIG.

Although the scale of the database could not be easily increased in the past, in recent years, 1 GB to 50 G has been increased.
It has become easy to realize even a size such as B. With such advances in computer peripheral technology, it has become extremely easy to consider the stress σ. Therefore,
The evaluation system shown in FIG. 4 has been evaluated by taking into consideration the mechanical stress generated inside during the caulking and welding of steel materials. Furthermore, it has become possible to make a detailed analysis and create a database relating to stress and the like in consideration of the grain size of the crystal structure of a steel material or the like. Therefore,
It is also within the scope of the evaluation system of the present invention to include the grain size as a factor of the stress σ in the database as an anisotropic parameter.

FIG. 22 is a diagram showing an example of the hardware configuration of the present invention. The hardware for realizing the electromagnetic field analysis system according to the present invention may be a stand-alone computer and a hard disk having a sufficient storage capacity, but in order to prepare an environment that many users can use, a network as shown in FIG. 22 is used. It is preferable to install a computer and a dedicated server. Thereby, each user accesses the electromagnetic field analysis system of the present invention stored in the network computer from his / her terminal and inputs the analysis conditions necessary for the electromagnetic field analysis, so that the electromagnetic field analysis system of the present invention performs the analysis through the network. It is possible to receive iron loss evaluation information as a result of electromagnetic field analysis. Detailed technical information and sales information regarding electromagnetic field analysis are provided to each user via the sales department.

[0043]

As described above, the present invention divides the entire area of the steel material into minute areas, and an angle formed by a predetermined direction and the magnetic flux density direction with respect to each of the divided minute areas, Calculate the iron loss data that takes into account the stress caused by processing as a parameter from the database,
Furthermore, by taking the sum of the iron loss data obtained in each minute region, even if the material has a large influence of anisotropy or stress, the anisotropy of the magnetic flux density or the influence of the stress or the nonlinearity of the magnetic flux density with respect to the magnetic field It is possible to evaluate and calculate iron loss without paying attention to sex. In addition, it is possible to perform an electromagnetic field analysis in consideration of the phase difference Θ _BH between the magnetic flux density B and the magnetic field H, the time harmonic, and the stress direction θ σ, which is industrially useful and has a remarkable effect.

[Brief description of drawings]

FIG. 1 is an explanatory view showing a pattern in which a steel material is divided into lattice-shaped minute regions.

FIG. 2 is an explanatory diagram used for explaining anisotropy of magnetic flux density.

FIG. 3 is a graph showing an angle θ dependency and a stress σ dependency of an HB curve and a WB curve by giving a dependency on stress in a graph of a plurality of leaves.

FIG. 4 is an explanatory diagram showing an example of the influence of stress in the iron core on the magnetic flux density.

FIG. 5 is a diagram showing a phase difference between a magnetic flux density and a magnetic field vector.

FIG. 6 is a diagram showing a BH curve used in the present invention.

FIG. 7 is a diagram showing a B-Θ _BH curve used in the present invention.

FIG. 8 is a diagram showing a temporal change in magnetic flux density B.

FIG. 9 is a diagram showing a BH curve used in the present invention.

FIG. 10 is a diagram showing a BW curve used in the present invention.

FIG. 11 is a diagram showing directions of stress σ, magnetic flux density B, and magnetic field H.

FIG. 12 is a diagram showing a BH curve and a BW curve used in the present invention.

FIG. 13 is a block diagram showing an iron loss calculation routine of a steel material in consideration of anisotropy.

FIG. 14 is an explanatory diagram showing a routine for accurately obtaining a magnetoresistivity ν using a Maxwell equation as a tensor.

FIG. 15 is an explanatory diagram showing a routine for obtaining an iron loss of a steel material by using the Maxwell equation according to a conventional technique.

FIG. 16 is an example of a relationship diagram between a stress and a magnetic field with a magnetic flux density obtained from an experiment as a parameter.

FIG. 17 is an example of a relationship diagram between the magnetic flux density and the magnetic field increase coefficient with the stress obtained from FIG. 8 as a parameter.

FIG. 18 is an example of a relationship diagram between stress and iron loss using a magnetic flux density obtained as a parameter.

FIG. 19 is an example of a relationship diagram between the magnetic flux density and the magnetic flux density increment coefficient with the stress obtained from FIG. 18 as a parameter.

FIG. 20 is a graph of B when there is stress obtained from FIG.
It is a figure which shows an example of a -H curve.

FIG. 21 is a graph in which the stress obtained from FIG. 19 is used as a parameter B
It is a figure which shows an example of a -W curve.

FIG. 22 is a diagram illustrating a hardware configuration of the present invention.

[Explanation of symbols]

1: area dividing means, 2: magnetic flux density vector determination means, 3: Database of magnetic flux density and iron loss, 4: interpolation interpolation calculation means, 5: means for calculating iron loss in a minute area, 6: Iron loss summation means

Claims (18)

[Claims] 1. An area dividing means for dividing an electromagnetic field analysis target area into a plurality of minute areas, and an angle θ between a predetermined direction of a magnetic body and a magnetic flux density direction in the minute areas is anisotropy. As a parameter, a database that stores an H-B curve based on an analytical expression or data that relates the magnetic flux density to the magnetic field, and the Max-Well equation in the minute area based on the H-B curve stored in the database The magnetic field density vector determining means for determining the angle θ and the magnitude B of the magnetic flux density based on the above. 2. An area dividing means for dividing an electromagnetic field analysis target area into a plurality of minute areas, and an angle θ between a predetermined direction of a magnetic body and a magnetic flux density direction in the minute areas is anisotropy. As a parameter, a database storing a WB curve based on an analytical expression or data relating the magnetic flux density and the iron loss, and an iron loss of the minute region based on the WB curve stored in the database. An electromagnetic field analysis system, comprising: an iron loss calculating means for calculating a total of the iron loss in the minute area; 3. An area dividing means for dividing an electromagnetic field analysis target area into a plurality of minute areas, and an angle θ between a predetermined direction of a magnetic body and a magnetic flux density direction in the minute areas is anisotropy. A database that stores, as parameters, an H-B curve based on an analytical expression and data relating the magnetic flux density and the magnetic field, and a WB curve based on the analytical expression and data relating the magnetic flux density to the iron loss. Magnetic flux density vector determining means for determining the angle θ and the magnitude B of the magnetic flux density based on the Maxwell equation in the minute region based on the H-B curve stored in the database; An iron loss calculating means for calculating the iron loss of the minute area and an iron loss summing means for calculating the sum of the iron loss of the minute area based on the stored WB curve. Electromagnetic analysis system, characterized by. 4. An area dividing means for dividing an electromagnetic field analysis target area into a plurality of minute areas, and an angle θ and a stress σ between a predetermined direction of a magnetic body and a magnetic flux density direction in the minute areas are different. A database for storing an H-B curve based on an analytical expression and data relating the magnetic flux density and the magnetic field as a parameter of the directionality, and an analytical expression relating the magnetic flux density and iron loss and a W-B curve based on the data. And based on the H-B curve stored in the database, the magnetic flux density vector determination for determining the angle θ and the magnetic flux density magnitude B based on the Maxwell equation and the stress σ in the minute region. Means, an iron loss calculating means for calculating the iron loss of the micro region based on the WB curve stored in the database, and a total of the iron loss of the micro region. Electromagnetic field analysis system and having a core loss sum means for obtaining. 5. The magnetic flux density and the magnetic field are set to the magnetic flux density.
Difference between magnetic field and magnetic field Θ _BHTo consider the vector as
The electromagnetic field analysis system according to any one of claims 1 to 4, characterized in that
Stem. 6. The method according to claim 1, wherein the magnetic flux density is a vector considering time harmonics.
Electromagnetic field analysis system described in. 7. The magnetic flux density and the magnetic field are vectors that take into consideration an angle θσ between a predetermined direction of the magnetic body and the stress σ in the minute region. 6. The electromagnetic field analysis system according to 6. 8. The electromagnetic field according to claim 4, wherein the magnetic flux density vector determining means includes a stress calculating means for obtaining a residual stress generated in processing the magnetic body by calculating a stress σ based on structural analysis. Analysis system. 9. A magnetic flux density vector determining means for determining the angle θ and the magnitude B of the magnetic flux density based on the Maxwell equation in the minute region based on the HB curve stored in the database. , The magnetic flux density vector in the micro area in the previous period, and its magnitude Bmax,
It is decomposed into an angle θ formed by a predetermined direction of the magnetic body, and an H-B curve at the angle θ is derived from the H-B curve using the anisotropy as a parameter, and the 9. The electromagnetic field analysis system according to claim 1, further comprising means for performing a convergence calculation so that the magnetic flux density, the angle θ thereof, and the magnetic field exist on the curve. . 10. The H-B stored in the database
In the determining means for determining the magnetic flux density vector based on the Maxwell equation and the stress σ in the micro region based on the curve, the magnetic flux density vector in the micro region is calculated based on the magnitude Bmax and the magnetic substance. To an angle θ formed with a predetermined direction, and from the H-B curve using the anisotropy as a parameter, the angle θ
8. The H-B curve in is derived, and the convergence calculation is performed so that the magnetic flux density in the first minute region and the angle θ and the magnetic field thereof exist on the curve. The electromagnetic field analysis system according to claim 8. 11. An area dividing means for dividing an electromagnetic field analysis object area into a plurality of minute areas, and an H based on an analytical expression or data relating a magnetic flux density and a magnetic field with a stress σ in the minute areas as a parameter.
A database storing a -B curve, and a magnetic flux density vector determining means for determining the magnetic flux density based on the Maxwell equation in the minute divided region based on the HB curve stored in the database. An electromagnetic field analysis system characterized in that 12. An area dividing means for dividing an electromagnetic field analysis target area into a plurality of minute areas, and a stress σ in the minute areas.
Is used as a parameter, a database storing a WB curve based on an analytical expression or data relating the magnetic flux density and the iron loss, and the iron loss of the minute region based on the WB curve stored in the database. An electromagnetic field analysis system, comprising: an iron loss calculating means for calculating a total of the iron loss in the minute area; 13. A region dividing means for dividing an electromagnetic field analysis target region into a plurality of minute regions, and an H-B based on an analytical formula and data relating the magnetic flux density and the magnetic field with the stress σ as a parameter in the minute regions.
Based on a curve and a database that stores a WB curve based on analytical data and data relating the magnetic flux density and the iron loss with the stress σ as a parameter, and based on the HB curve stored in the database. , A magnetic flux density vector determining means for determining the magnetic flux density based on the Maxwell equation in the micro region, and an iron for calculating the iron loss in the micro region based on the WB curve stored in the database. An electromagnetic field analysis system comprising: a loss calculating means and an iron loss summing means for calculating a sum of iron losses in the minute areas. 14. The magnetic flux density vector determination means comprises a stress calculation means for calculating a residual stress generated during processing of a magnetic body by calculating a stress σ based on structural analysis. Electromagnetic field analysis system described in. 15. The H-B stored in the database
The curve or the WB curve uses the angle θ between a predetermined direction of the magnetic material and the direction of the magnetic flux density in the minute region as an anisotropy parameter.
15. The electromagnetic field analysis system according to claim 14. 16. A magnetic field increment coefficient α (= Hσ / Hσ _{= 0} ) based on the relationship between the magnetic flux density and the magnetic field, and an iron loss increment coefficient β (= Wσ / W) based on the relationship between the magnetic flux density and the iron loss value, using stress as a parameter.
σ _{= 0} ), and a means for obtaining a BH, BW curve considering stress by multiplying the base H-B, B-W curve by the magnetic field increment coefficient α and the iron loss increment coefficient β. The electromagnetic field analysis system according to any one of claims 11 to 15. 17. The electromagnetic field analysis system according to claim 16, wherein the magnetic field increment coefficient α and the iron loss increment coefficient β are regression equations. 18. The regression formula for the magnetic field increment coefficient α is such that α = 1 near the magnetic flux density B = 0 and the magnetic flux density B = 2T, and the regression formula for the iron loss increment coefficient β is a linear equation. The electromagnetic field analysis system according to claim 17, wherein: