JP2007304688A - Polycrystalline substance magnetic field analyzing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a magnetic field analyzing method capable of providing a magnetic characteristic of a polycrystalline magnetic substance, by analyzing a magnetic field, by taking into consideration a crystal grain and crystal orientation. <P>SOLUTION: Data on a shape D10 of the crystal grain, the crystal orientation D20, the magnetic characteristic D30 of a monocrystal and an excitation condition D40 is input, and polycrystalline substance is first divided into spatial meshes along a shape of the crystal grain (S100). Next, coordinates are converted on the basis of the crystal orientation of the crystal grain, and the magnetic characteristic of the monocrystal can be input to the individual crystal grain, and a magnetic field analyzing calculation is executed with every crystal grain (S200). When finishing the calculation with all the crystal grains, the magnetic flux density distribution (S300) and the iron loss distribution (S400) are provided. Afterwards, magnetic flux density and the iron loss distribution as a crystal are provided by executing leveling processing. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a magnetic field analysis method for analyzing and evaluating magnetic characteristics of a polycrystalline body.

  Conventionally, the magnetic properties of polycrystalline materials such as steel plates have been evaluated based on measurement data obtained by applying a magnetic field to the material and measuring the iron loss and magnetization properties. For example, in the Epstein method and the single plate test method, magnetic properties in one direction such as the rolling direction are measured, and the magnetic properties are evaluated based on the measurement results. However, the Epstein method and the single plate test method cannot obtain magnetic properties such as magnetic properties when a rotating magnetic field is applied or distributed magnetic properties in a steel plate. It is difficult to evaluate in consideration of the above.

  In recent years, a 2D-MAG measurement method (two-dimensional vector magnetic property measurement method) capable of obtaining magnetic characteristics such as a rotating magnetic field and anisotropy has been proposed (see Non-Patent Documents 1 and 2 and Patent Document 1). . However, the measurement is limited to the average value in a certain region in the steel sheet, and a magnetic characteristic distribution in consideration of the crystal grain size cannot be obtained. In addition, according to the proposed DMM (distributed magnetic measurement method), it is possible to obtain magnetic characteristics in consideration of crystal grains and crystal orientation in a steel sheet (see Non-Patent Document 2 and Patent Document 2). However, this measurement method also obtains magnetic properties by measuring actual materials, and can only obtain magnetic properties for materials that can be manufactured or obtained. Further, the value for exciting the material is also limited by the excitation device that can be used, and a portion with a high or low magnetic flux density cannot be fully evaluated.

M. Enokizono, “Two-dimensional Magnetic Property”, JIEE-A, Vol.115, No.1, pp.1-8, 1998. K. Fujisaki, Y. Nemoto, S. Sato, M. Enokizono and H. Shimoji, ”2-D vector magnetic method in comparison with conventional method”, 7th International Workshop on 1 & 2-Dimensional Magnetic Measurement and Testing. Proceeding, edited by J. Sievert (PTB-E-81). Pp.159-166., 2002 Gion, Tanabe "Local two-dimensional magnetic properties of oriented silicon steel sheets" Journal of Japan Society of Applied Magnetics, vol.22, pp.901-904,1998 Japanese Patent Application No. 2005-073336 Japanese Patent Application No. 2005-073337

  In view of the above problems, the present invention performs magnetic field analysis in consideration of crystal grains and crystal orientations based on magnetic properties of single crystals and physical properties close to them (hereinafter referred to as magnetic properties of single crystals). An object of the present invention is to provide a magnetic field analysis method capable of obtaining the magnetic characteristics of the magnetic field.

  To achieve the above object, a polycrystalline magnetic field analysis method of the present invention includes a step of dividing a polycrystalline body into a plurality of elements along at least the shape of each crystal grain, a step of applying an external magnetic field, and a single crystal Are converted to a coordinate system determined by the crystal orientation of the crystal grains and applied to the crystal grains, and a magnetic field analysis is performed on each crystal grain.

  Furthermore, a step of obtaining a magnetic property distribution of the polycrystalline body may be included.

Furthermore, it may have a step of obtaining the magnetic characteristics of the whole polycrystalline body by averaging the magnetic characteristic distribution of the polycrystalline body.
The magnetic property may be a magnetic flux density, a magnetic field, or iron loss.
The magnetic properties of the single crystal can be calculated using micromagnetism, or can be obtained by measuring a single crystal material.

  The crystal orientation of the crystal grain can be obtained based on a diffraction image obtained by irradiating the crystal grain with radiation or a particle beam. The crystal orientation can be <100>, <001>, <111>. Furthermore, the magnetic characteristics of the polycrystal can be those of <100>, <001>, and <111>.

A boundary cell may be disposed at the boundary between the crystal bodies, and the boundary cell may have a magnetic property lower than that of the polycrystalline material.
The external magnetic field may be given as a rotating magnetic field.

  According to the present invention, in the magnetic field analysis of a polycrystalline body, the coordinate system is converted for each crystal grain based on the given crystal grain shape and crystal orientation, so that the magnetic characteristics considering the crystal grain are calculated. It is possible to obtain magnetic characteristics that could not be obtained by analysis by conventional measurement. Furthermore, a polycrystalline body having desired magnetic properties can be formed by adjusting the shape and crystal orientation of crystal grains.

  Hereinafter, an embodiment of a magnetic field analysis of a polycrystalline body according to the present invention will be described with reference to the drawings. The analysis object of this embodiment is a grain-oriented electrical steel sheet, and FIG. 1 shows an analysis region 100 to be analyzed. The analysis region 100 is approximately 80 mm × 80 mm and consists of crystal grains 1-10. The rolling direction r of the grain-oriented electrical steel sheet is the horizontal direction of FIG. 1, and the rolling direction r is the average direction of the easy axis of magnetization for the entire polycrystalline body to be analyzed. However, when viewed finely, the direction of the easy magnetization axis is different for each crystal grain. For example, the easy axis of region 3 is deviated by an angle α3 within the surface of the steel plate from the rolling direction r, which is the entire easy axis as shown.

  FIG. 2 shows deviations of the easy magnetization axes of the crystal grains 1 to 10 in FIG. 1 from the whole easy magnetization axis r by angles α, β, and γ. That is, the direction of the crystal orientation of each crystal grain with respect to the rolling direction (that is, the direction of, for example, cubic (X, Y, Z)) is expressed by angles α, β, γ. Here, the angle α is an angle in a direction horizontal to the steel plate surface, the angle β is an angle in a direction perpendicular to the steel plate surface, and the angle γ is a rotation angle around the easy magnetization axis. In this embodiment, since the rolling direction, that is, the whole easy axis r is determined, the deviation angle can be defined by α, β, γ, but in the case of a general polycrystal such as a non-oriented electrical steel sheet A crystal orientation shift determined by <100>, <110>, and <111>, which is expressed by a three-dimensional Euler angle or a Miller index in crystallography, is used. In this case, since iron is assumed, bcc (body-centered cubic lattice) is assumed, but other orientations such as cobalt (hexagonal crystal) are used.

  The crystal orientation for each crystal grain size can be measured by irradiation with radiation such as X-rays, electron beams, neutrons, or particle beams, and the resulting diffraction. For example, a crystal orientation of each crystal grain constituting the steel plate can be obtained from a backscattered electron diffraction image generated when a steel plate is set as an electron microscope sample and irradiated with an electron beam.

  3 and 4 show the single crystal magnetic characteristics of the grain-oriented electrical steel sheet used in the present embodiment, and FIG. 3 shows the BH characteristics that are the relationship between the magnetic flux density B and the magnetic field H. FIG. 4 shows a BW characteristic which is a relationship between the magnetic flux density B and the iron loss W. Here, the angle φ is an angle from the easy axis of magnetization of the single crystal in the plane of the grain-oriented electrical steel sheet, and indicates the inclination angle of the applied external magnetic field. 3 and 4 can be measured by the Epstein method or the SST (Single-Sheet Test) method using a sample rotated by a predetermined angle φ from the easy axis of the steel plate. The details are described in International Electrical Commission, 404-3, Second edition, 1992, and Japan Industrial Standard, C2556, 1996. The magnetic flux density B is the time integration of the output voltage of the search coil wound around the sample. Can be obtained. 3 and 4, the data of the 2D-MAG measurement method described in Non-Patent Document 1 may be used.

  In the case of a non-oriented electrical steel sheet in which the easy magnetization axis is not always clear and the direction of the easy magnetization axis is not as aligned as that of the directional electrical steel sheet, the magnetic properties of the single crystal are <100> as shown in FIG. Magnetic characteristics of <110> and <111> orientations are used. As shown in FIG. 5, <100> has the best magnetization characteristics, <110> is the middle, and <111> is the worst.

  The magnetic properties of a single crystal can be acquired by actually applying a magnetic field to the single crystal and measuring it, but it can also be acquired by a technique called micromagnetism. Micromagnetism is based on the theory of magnetic domain structure (micrometer size level) in magnetic material theory. This is a method to calculate the magnetization vector that minimizes the magnetic energy such as exchange energy, anisotropic energy, and magnetostatic energy. The Landau-Lifschitz-Gilbert (LLG) equation is calculated numerically by the finite element method or the like. Thus, the magnetization process is theoretically calculated.

FIG. 6 shows an outline of the flow of magnetic field analysis of the present embodiment.
As data, the shape data D10 of the crystal grains constituting the electromagnetic steel plate to be analyzed shown in FIG. 1, the orientation data D20 of the crystal grains shown in FIG. 2, the magnetic property data D30 of the single crystal shown in FIG. Excitation condition data D40, for example, a coil current value, for exciting an electromagnetic steel sheet, that is, providing an external magnetic field for the electromagnetic steel sheet is given. As a method of applying an external magnetic field, there is a method of applying a coil current to the electromagnetic steel sheet shown here considering an exciter, but there is also a method of applying it with boundary conditions.

  In the present embodiment, not only directional electrical steel sheets with uniform crystal orientation but also non-oriented electrical steel sheets with high crystal orientation randomness are analyzed. Each is a polycrystal, and each crystal has a single crystal orientation, and a model is constructed.

  In the present embodiment, the calculation is performed by numerical analysis such as a finite element method, a difference method, or a boundary element method. Here, the finite element method is described as an example, but the same applies to other numerical analysis methods. As in the normal finite element method, the object to be analyzed is analyzed by breaking it down into a fine mesh. First, in step S100, as shown in FIG. Then, the mesh M which becomes an element of the finite element method is started in the entire material internal space. The mesh M may be divided along the crystal grain shape, but the mesh shape may be fixed. In that case, the crystal grain shape is uneven along the fixed mesh shape. When this becomes a problem, the mesh on the crystal grain boundary may be considered to apportion the physical property values (crystal orientation, etc.) of each crystal by volume. Further, in this embodiment, it is considered that single crystal grains have the same crystal orientation, but often referred to as sub-grain boundaries, crystal orientations with single-grain boundaries as boundary conditions in single crystal grains. May be different. In this case, the mesh may be divided along the subgrain boundaries to give different crystal orientations. The mesh is usually a three-dimensional mesh, but may be a two-dimensional mesh depending on the analysis target. Further, in the present embodiment, the external excitation condition is input to the external excitation unit by cutting the mesh (not shown). A boundary cell such as a void cell, which is part of the mesh, is placed at each crystal grain boundary (grain boundary), and the magnetic characteristics of the boundary cell are lower than the magnetic characteristics to be analyzed. May be input to indicate that it is a boundary.

  When the creation of the spatial mesh is completed, in step S200, analysis calculation of the electromagnetic field by the finite element method is performed. The flow of this calculation will be described later with reference to FIG. 8, but in this embodiment, the material to be analyzed is considered as an aggregate of crystal grains, each crystal has a single crystal orientation, and the crystal orientation is For example, it is executed as what can be expressed by rotation of each axis from the entire coordinate system of the material which is a polycrystal. For this purpose, a coordinate transformation that transforms the coordinate system based on the crystal orientation of each crystal and the coordinate system of the entire material is considered. Since the coordinate transformation is expressed as a matrix and is performed on each crystal grain, a transformation matrix of the whole material which is a polycrystal is also defined. The conversion matrix is a matrix in which small matrices for each crystal grain are arranged diagonally, and is converted from the overall coordinate system of the material to local coordinates for each crystal grain. The BH characteristics (FIG. 3) and BW characteristics (FIG. 4) of the single crystal input as data are the angle φ from the easy axis in the plane of the grain-oriented electrical steel sheet (in-plane angle). In other words, the individual crystal grains whose easy magnetization axes are shifted cannot be used as data as they are. In order to input data to individual crystal grains, correction is required corresponding to the deviation of the easy axis of magnetization of each crystal grain, and the correction is performed by coordinate transformation.

  When the analysis result of the electromagnetic field for each crystal grain is obtained by converting the deviation of the easy magnetization axis of each crystal grain, the distribution of electromagnetic characteristics such as magnetic flux density is obtained in step S300, and then the loss such as iron loss is obtained in step S400. Get the distribution. The iron loss distribution may be calculated based on the BW characteristics (FIG. 4), or the vector inner product of the magnetic flux density vector and the magnetic field vector in each mesh is integrated for one period to obtain the magnetic energy. The iron loss may be obtained by calculation. Thereafter, in step S500, an averaging process is performed to obtain the magnetic flux density, the magnetic field strength, the iron loss, and the like as the entire material to be analyzed. Further, in step S600, BH characteristics and BW characteristics as a magnetic material that is a polycrystalline body are obtained from the obtained magnetic flux density, magnetic field strength, and iron loss.

  In this embodiment, the mesh is created in consideration of the shape of the crystal grains, the coordinate conversion is performed in consideration of the crystal orientation, and the magnetic field analysis is executed. Therefore, the crystal grain shape and the crystal orientation in units of crystal grains are determined. It is possible to analyze in consideration, and a detailed analysis of the magnetic property distribution in the polycrystalline material is possible. Furthermore, by adjusting the shape and orientation of crystal grains, it is possible to present crystal orientation characteristics and crystal grain shapes so that a polycrystalline material having desired electromagnetic characteristics can be obtained.

  Hereinafter, the steps of FIG. 6 will be described in more detail. FIG. 8 shows a flow of electromagnetic field analysis calculation by the finite element method corresponding to step S200. The calculation is performed for the entire material based on coordinate conversion for each crystal grain. First, in step S101, along with the input of the shape and orientation of the crystal grain to be calculated, single crystal magnetic characteristics and external magnetic field excitation conditions, which are data common to all crystal grains, are input.

  In step S102, a conversion matrix is calculated for conversion from the coordinates common to the entire polycrystal (the entire coordinate system of the material) to the coordinate system unique to each crystal grain to be calculated. As described above, this conversion matrix is a matrix in which small matrices for each crystal grain are arranged diagonally, and is expressed by a matrix that converts from the overall coordinate system of the material to local coordinates for each crystal grain. . This is because magnetic characteristics (BH characteristics, BW characteristics) of a single crystal can be input as appropriate data to the crystal grains.

  Here, an example of coordinate rotation as coordinate transformation will be described. When the crystal orientation is obtained as a three-dimensional Euler angle, the following coordinate rotation can be performed.

  FIGS. 9A and 9B are diagrams for explaining Euler angles and coordinate rotation. As shown in FIG. 9A, in the three-dimensional space, consider rotation of the rotation angle γ around the x axis, rotation of the rotation angle β around the y axis, and rotation of the rotation angle α around the z axis. In this case, the rotation matrix around the x axis is R (x, γ), the rotation matrix around the y axis is R (y, β), and the rotation matrix of the rotation angle α around the z axis is R (z, α). As shown in FIG. 9B, each rotation can be expressed by a rotation matrix. The Euler angle is expressed by combining these three rotation matrices R (x, γ), R (y, β), and R (z, α).

For example, the position vector P = (x, y, z) T on the coordinate axes of the entire grain-oriented electrical steel sheet of the present embodiment, and the position vector P3 on the coordinate axes of crystal grains rotated by Euler angles α, β, γ therefrom. = (X1, y2, z3) T through the position vectors P1 and P2, the following relationship P = R (z, α) P1
P1 = R (y, β) P2
P2 = R (x, γ) P3
If
P = R (z, α) R (y, β) R (x, γ) P3
It becomes. This relationship is reversible, and vice versa
P3 = R-1 (x, [gamma]) R-1 (y, [beta]) R-1 (z, [alpha]) P
It becomes. here,
T = R-1 (x, γ) R-1 (y, β) R-1 (z, α)
After all,
P3 = TP
Thus, the conversion from the coordinate axes of the entire grain-oriented electrical steel sheet to the coordinate axes of crystal grains rotated by Euler angles by α, β, and γ has been performed.

  In this way, by rotating the coordinate axis according to the crystal orientation, the magnetic characteristics of the single crystal can be input with the coordinate axis compensated for the deviation of the crystal orientation of the crystal grains. It becomes possible.

高周波での磁気特性のごとく渦電流および異常渦電流を考慮した電磁場解析の場合は、以下の式をベースに展開する。 In this embodiment, as a solution for elucidating the electromagnetic phenomenon, a case where analysis is performed based on the A-φ method (A: vector potential [Wb / m], φ: scalar potential [V / m]) is shown. As long as the analysis method is based on an equation, for example, a method of directly obtaining the magnetic flux density may be used. Therefore, in the case of a static magnetic field, it develops based on the following formula.

In the case of electromagnetic field analysis considering eddy currents and abnormal eddy currents like magnetic characteristics at high frequencies, the following formula is developed.

いずれの場合に対しても以下の展開は同じなので、静磁場について述べる。
有限要素法では、メッシュ分割された各要素内の任意の場所のベクトルポテンシャルは、その要素の節点でのベクトルポテンシャルの線形結合で表現されるものとしている。線形結合の係数は、その節点の位置座標の値より算出されるものである。これを元に、解析対象全体の磁気エネルギーは、汎関数χとして定義され数値解析で算出される。汎関数が最小となる条件が実在の物理量であると考えると、任意の節点でのベクトルポテンシャルによる汎関数χの偏微分がゼロになるので、以下の行列が導出される。

Since the following development is the same for both cases, the static magnetic field will be described.
In the finite element method, the vector potential at an arbitrary place in each element divided into meshes is expressed by a linear combination of vector potentials at the nodes of the element. The linear combination coefficient is calculated from the position coordinate value of the node. Based on this, the magnetic energy of the entire analysis target is defined as a functional χ and calculated by numerical analysis. If the condition that minimizes the functional is an actual physical quantity, the partial differentiation of the functional χ by the vector potential at an arbitrary node becomes zero, so the following matrix is derived.

  Here, [H] is that each element of the overall coefficient matrix is calculated by the position coordinates and magnetic permeability of each node, and the matrix is a sparse matrix. {A} is the vector potential of each orientation (absolute coordinate system) of each node, and nu is the total number of unknown nodes multiplied by the number of coordinates (3 in the case of three-dimensional analysis). {G} is calculated from a known vector potential and excitation current density given by boundary conditions and the like, and is known.

が導出される。式（５）で表示されている各ベクトル、行列は、各結晶粒の局所座標系からみたものである。今回の多結晶材料の解析では、磁気特性は各結晶粒の局所座標系からみたものであるので、各結晶粒の局所座標系からみた式（５）の全体係数行列およびベクトルポテンシャルの全体ベクトルが算出される。しかしながら、境界条件および励磁条件は、絶対座標に対して与えられるものであり、求めたいものは絶対座標系におけるベクトルポテンシャルである。 Here, each vector and matrix displayed in Expression (3) is viewed from the absolute coordinate system. Considering the local coordinate system for each crystal grain,

Is derived. Each vector and matrix displayed in Expression (5) is viewed from the local coordinate system of each crystal grain. In the analysis of the polycrystalline material this time, the magnetic characteristics are as seen from the local coordinate system of each crystal grain. Therefore, the overall coefficient matrix of equation (5) and the overall vector of the vector potential as seen from the local coordinate system of each crystal grain are Calculated. However, the boundary condition and the excitation condition are given with respect to absolute coordinates, and what is to be obtained is a vector potential in the absolute coordinate system.

が導出される。つまり、局所座標系で算出される全体係数行列は、座標変換を施すことで絶対座標系での式に変換することができる。 Therefore, if the transformation matrix calculated in S102 is [T],

Is derived. That is, the entire coefficient matrix calculated in the local coordinate system can be converted into an expression in the absolute coordinate system by performing coordinate conversion.

  If the permeability is fixed as in linear analysis, the overall coefficient matrix is known, so the inverse matrix can be transformed directly into a Gaussian elimination method, modified Koresky method, sequential over-relaxation (SOR = Successive Overrelaxation) By calculating with an iterative method such as the conjugate gradient method (CG = Conjugate Gradient), the unknown vector potential of each node can be calculated.

  Since normal magnetic characteristics have a magnetic saturation phenomenon, non-linear calculation of permeability is necessary, and for this purpose, the generally used Newton-Raphson method is used. According to the Newton-Raphson method, an approximate solution of the vector potential of the node i obtained by the (k + 1) th iteration is given as the following equation (8).

Here, the potential Ai and the functional χ are k-th values, and nu is the total number of unknown nodes. Equation (8) is derived by applying the minimum magnetic energy condition and ignoring higher-order terms in Taylor expansion even for the minute fluctuation of the functional χ with respect to the minute fluctuation δA _i ^(k) of the vector potential. Is done.

  As can be seen from equation (8), since the kth potential A is known, if the kth variation δA is known, the k + 1th potential is known. In this way, iterative calculation is performed until the potential A converges.

In step S104, the potential A, the magnetoresistance ratio [nu (inverse of permeability) required to compute the vectors of the matrix and the right side of the left-hand side of equation (9), the initial value of the ∂ν / ∂B ^2. Here, the magnetic characteristics (BH characteristics) of the material are expressed by a relational expression ν = g (B ² ) between the magnetic resistivity ν and the magnetic flux density B. This is applicable to an isotropic material, but as shown in FIG. 3, φ anisotropy (BH characteristics are presented as a function of the angle difference φ between the easy axis and the magnetic flux density vector B). It can also be applied to the case. Similarly, in the case of the three-dimensional case, when the magnetic characteristic (BH curve) can be defined by the angle difference between the easy axis and the magnetic flux density vector B (in this case, it may be defined by α angle and β angle). Applicable. That is, even an anisotropic model is applied when the magnetic resistivity ν can be uniquely defined according to the magnetic flux density vector.

On the other hand, as a model of the anisotropic material, there is a method of calculating the magnetic resistance at each axis by decomposing the magnetic flux density vector into each axis (in this case, it is not necessarily perpendicular). For example, in the orthogonal coordinate system of the two-dimensional analysis, the magnetoresistance ratio [nu _x magnetization easy axis of the magnetic flux density B _x, by a magnetic flux density B _y of hard magnetization axis direction perpendicular magnetic low efficiency [nu _y axis of easy magnetization It is expressed as follows.

νx = g (Bx ²⁾
νy = g (By ² )
Here, the axes for decomposing the magnetic flux density vector do not necessarily have to be at right angles, and may be decomposed into orientations such as <100>, <110>, and <111>, for example. If there is a significant difference in magnetic properties between <100>, <110>, and <111> as in iron (see FIG. 5), it is better to disassemble it into <100>, <110>, and <111>. .
The above discussion of the Newton-Raphson method is also considered in the local coordinate system of each crystal grain.

を用いる。ここで逆行列計算が必要であるがその解法については前述した。 In step S105, the coefficient matrix [K ^L ] of the Newton-Raphson method of Equation (9) at each crystal grain is calculated. The coefficient matrix [K ^L ] is a matrix based on the magnetic characteristics calculated in the local coordinate system for each crystal grain. Therefore, it is necessary to replace the coordinate system with an absolute coordinate system by performing coordinate transformation, as in the discussion in Expressions (3) to (7). That is, in the calculation of the ^kth variation δA ^(k) in step S106,

Is used. Here, inverse matrix calculation is necessary, but the solution method has been described above.

In step S107, the ^{(k + 1)} th potential A ^{(k + 1)} is ^obtained according to equation (8). Then, by performing a convergence determination in step S108, if not converged, in step S109, in the local coordinate system of each crystal grain, the B ² calculates, by further calculating the ν and ∂ν / ∂B ² The process returns to step S105. Steps S105 to S108 are repeated until the potential A converges in step S108.
When the potential A converges in step S108, the flow of FIG.

  In the next steps S400 and S600 (FIG. 6), an electromagnetic characteristic distribution such as magnetic flux density and a loss distribution such as iron loss are obtained from the obtained magnetic vector potential. Further, in step S500, an averaging process is performed for analysis. The electromagnetic characteristics of the target grain-oriented electrical steel sheet are obtained. The averaging process is executed according to the following formula, for example.

  Here, <B>, <H>, and <W> are a volume averaged magnetic flux density, an averaged magnetic field strength, and an averaged iron loss in a predetermined region, respectively. Inside the steel material, it is distributed by such crystal orientation and crystal grain shape, but when used as a motor and a transformer, the average value is discussed. The magnetic properties of electrical steel sheets used in the design of motors and transformers are average values that allow the crystal grain shape to be ignored.

  When the averaged magnetic flux density, magnetic field strength, and iron loss are obtained, in step S600, the <B>-<H> curve and the <B>-<W> curve, which are the relationships between them, are obtained. Can do.

  In FIG. 10, the result of having compared the calculated value of the iron loss by this embodiment with the measured value of an actual iron loss is shown. A graph indicated by a solid line shows a value obtained by averaging the iron loss distribution calculated by applying an external magnetic field with a tilt angle of 0 ° to 45 ° to the steel sheet in the region L (FIG. 7). A broken line shows the value actually measured on the same conditions. As can be seen from FIG. 10, it can be seen that the calculation results and the measured values agree very well up to an inclination angle of 15 ° to 45 °.

  As described above, the magnetic properties of a polycrystalline magnetic material such as a steel plate can be obtained only by actually measuring the polycrystalline magnetic material that has been manufactured or available in the past. In contrast, in the present embodiment, since the simulation can be executed with high accuracy by considering the crystal grains, for example, the magnetic characteristics can be evaluated prior to the manufacture. Furthermore, a polycrystalline magnetic body having desired magnetic properties can be formed by changing the shape or crystal orientation of the crystal grains of the simulated polycrystalline body.

  In the present embodiment, a grain-oriented electrical steel sheet is taken as an example, but the present invention can be applied even to a non-oriented electrical steel sheet. Further, the present invention can be applied to any magnetic material as well as a steel plate. Further, the external magnetic field can be applied to the polycrystalline magnetic body at an arbitrary angle. Therefore, analysis can also be performed by applying a rotating magnetic field to the polycrystalline magnetic material. The rotating magnetic field is as shown in FIG. 11 and is generated inside the motor and the transformer. The rotating magnetic field shows a planar trajectory of the magnetic flux density in one cycle. The maximum value Bmax of the magnitude of magnetic flux density in one cycle and the ratio of the minimum value Bmin and Bmax of the magnitude of magnetic flux density in one cycle ( (Axis ratio) α = Bmin / Bmax, and an angle Inc from an axis (an easy axis of the steel plate) of the magnetic flux density vector at Bmax. The magnetic characteristics require a highly accurate measuring device using 2D-MAG, but if this analysis is used, it can be evaluated by numerical analysis. When analysis is performed by applying a rotating magnetic field to a polycrystalline magnetic material, the excitation current of the electromagnetic steel sheet that is a polycrystalline material is changed every moment so that a predetermined region of the polycrystalline magnetic material is as shown in FIG. Can be calculated.

It is a figure explaining the grain oriented electrical steel sheet which is the object of magnetic field analysis by one embodiment of the present invention. It is a figure which shows the shift | offset | difference angle from the rolling direction (the whole easy magnetization axis) of the crystal grain contained in the grain-oriented electrical steel sheet of FIG. It is a figure which shows the BH characteristic of the single crystal of the grain-oriented electrical steel sheet of FIG. It is a figure which shows the BW characteristic of the single crystal of the grain-oriented electrical steel sheet of FIG. It is a figure which shows the BH characteristic of <100> <110> <111> orientation of a common single crystal magnetic body. It is a figure which shows the general | schematic flow of the magnetic field analysis by one Embodiment of this invention. FIG. 2 is a diagram illustrating a mesh of the polycrystalline magnetic body of FIG. 1 according to an embodiment of the present invention. It is a figure which shows the flow of the magnetic field analysis calculation of step S200 of FIG. It is a figure explaining Euler angle and coordinate rotation. It is a figure which compares the iron loss calculated by one Embodiment of this invention with the iron loss actually measured. It is explanatory drawing of a rotating magnetic field.

Explanation of symbols

100 Analysis target of grain-oriented electrical steel sheet 1-10 Grain γ Rolling direction

Claims (11)

A magnetic field analysis method for evaluating magnetic characteristics of a polycrystal composed of a plurality of crystal grains under an external magnetic field,
Dividing the polycrystalline body into a plurality of elements along at least the shape of each crystal grain;
Giving each crystal grain a unique crystal orientation;
Applying an external magnetic field;
Giving the magnetic properties of the single crystal;
A step of performing an electromagnetic field analysis calculation using a coordinate transformation between a coordinate system determined by a crystal orientation of each crystal grain and a coordinate system of the entire polycrystalline body;
A polycrystalline magnetic field analysis method having   The polycrystalline magnetic field analysis method according to claim 1, further comprising a step of obtaining a magnetic characteristic distribution of the polycrystalline body.   The polycrystalline magnetic field analysis method according to claim 2, further comprising the step of obtaining the characteristics of the whole polycrystalline body by averaging the magnetic characteristic distribution of the polycrystalline body.   The polycrystalline magnetic field analysis method according to claim 1, wherein the magnetic property is a magnetic flux density, a magnetic field, or an iron loss.   The polycrystalline magnetic field analysis method according to claim 1, wherein the magnetic characteristics of the single crystal are calculated using micromagnetism.   The polycrystalline magnetic field analysis method according to claim 1, wherein the magnetic characteristics of the single crystal are obtained by measuring a single crystal material.   The polycrystalline magnetic field analysis method according to claim 1, wherein the crystal orientation of the crystal grain is obtained based on a diffraction image obtained by irradiating the crystal grain with radiation or a particle beam.   The single crystal is a cubic crystal, and the magnetic properties of the single crystal are the magnetic properties of the crystal orientations <100>, <001>, and <111>, respectively. Of polycrystalline magnetic field analysis.   9. The electromagnetic field analysis calculation according to claim 8, wherein the magnetic flux density vector in the electromagnetic field analysis is decomposed into the crystal orientations <100>, <001>, and <111>, and the convergence calculation is performed so that the respective magnetic characteristics are obtained. Polycrystalline magnetic field analysis method.   10. The polycrystalline magnetic field analysis method according to claim 1, wherein a boundary cell is disposed at a boundary between the crystal bodies, and the boundary cell has a magnetic property lower than that of the polycrystalline material.   The polycrystalline magnetic field analysis method according to claim 1, wherein the external magnetic field is provided as a rotating magnetic field.

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