Analysis device, analysis method, and program

Abstract

To improve analysis speed by improving convergence of nonlinear convergence calculation in electromagnetic field analysis.SOLUTION: An analysis equipment 300 obtains a vector potential of an analysis target area for each of a plurality of elements, as a physical quantity indicating a relation between magnetic flux density and magnetic field strength in the analysis target area, based on physical quantities including a first physical quantity that defines a relation between a quantity of change in magnitude of a magnetic flux density vector and a quantity of change in magnitude of a magnetic field intensity vector as a scalar quantity.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to an analysis device, an analysis method, and a program, and is particularly suitable for use in analyzing electromagnetic fields. [Background technology]

[0002] Electromagnetic field analysis is a method of determining the magnetic properties of an analysis target area, such as an iron core of an electric device such as a motor or a transformer, by numerical analysis based on the governing equations (basic equations) of the electromagnetic field based on Maxwell's equations. The magnetic properties are magnetic properties exhibited by a magnetized magnetic body (magnetic material), such as magnetic flux density, magnetic field strength, magnetic permeability, differential magnetic permeability, coercive force, and residual magnetic flux density. In the electromagnetic field analysis, for example, the magnetic flux density is determined by providing an initial value of magnetic permeability to the discretized governing equation. After that, the magnetic properties of the analysis target area are determined (calculated) by performing a convergence calculation that repeats the process of determining the magnetic permeability again (by changing it linearly) using the determined magnetic flux density and magnetization properties. The magnetization properties indicate the relationship between magnetic flux density and magnetic field strength, and are also called BH properties (BH curves), etc.

[0003] The magnetic permeability is expressed by a straight line passing through the origin in the magnetization characteristic (BH characteristic). Therefore, if the magnetic characteristics that are the solution of the numerical analysis for the analysis target area are obtained by applying the magnetic permeability to the discretized governing equation, there is a risk that the magnetic characteristics that are the solution of the numerical analysis are searched for in an area far removed from the magnetization characteristics of the actual analysis target area, and the accuracy of the numerical analysis solution may decrease. When the magnetization characteristic has nonlinearity, this tendency becomes prominent in the magnetic saturation area where the magnetic flux density is high.

[0004] Therefore, in the electromagnetic field analysis, if the magnetic flux density and magnetic permeability are calculated by the numerical analysis as described above and the convergence conditions are not satisfied, the magnetic flux density and magnetic permeability are calculated again by updating the magnetic permeability given to the governing equation to the calculated magnetic permeability, and the convergence calculation is repeated until the convergence conditions are satisfied. The calculation time of the electromagnetic field analysis depends greatly on the time required to solve the discretized governing equation. For example, when the magnetization characteristics are nonlinear, the nonlinearity of the magnetization characteristics is expressed by changing the magnetic permeability linearly. Therefore, the convergence of the convergence calculation decreases and the number of convergence calculations increases. Accordingly, the number of times the discretized governing equations are solved also increases, and the calculation time of the electromagnetic field analysis becomes longer.

[0005] Therefore, non-patent document 1 discloses that differential permeability defined as a tensor quantity (the ratio of the amount of change in magnetic flux density vector to the amount of change in magnetic field strength vector) is used to construct a governing equation of the electromagnetic field in the T-Ω method, and a numerical analysis based on the governing equation of the electromagnetic field is performed using the T-Ω method.

[0006] Patent Document 1 also discloses that a governing equation (diffusion equation) for determining one-dimensional magnetic properties (distribution of the x and y components of magnetic flux density in the z-axis direction) is constructed as the governing equation of the electromagnetic field in the A-φ method using the in-plane components (x and y components) of differential permeability, and a numerical analysis based on the governing equation of the electromagnetic field is performed using the A-φ method.

[0007] In the techniques described in Non-Patent Document 1 and Patent Document 1, differential permeability rather than permeability is used to search for magnetic properties, which are solutions of numerical analysis, and the differential permeability is updated when performing convergence calculation. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] JP 2019-125097 A [Non-patent literature]

[0009] [Non-Patent Document 1] IEEE TRANSACTIONS ON MAGNETICS, VOL46, NO.8, AUGUST 2010, A New Formulation Using Differential Permeability Based on the Source-Field Method, JPA Bastos and N. Sadowski [Non-Patent Document 2] Takayoshi Nakata and Norio Takahashi, "Finite Element Method in Electrical Engineering", 2nd Edition, Morikita Publishing Co., Ltd., April 1986 Summary of the Invention [Problem to be solved by the invention]

[0010] However, in the technology described in Non-Patent Document 1 and Patent Document 1, the differential permeability is determined for each axis component (directional component). Therefore, for example, even if the magnitude of the magnetic flux density is the same, the differential permeability obtained is different between when the x-axis component is large and the y-axis component is small and when the x-axis component is small and the y-axis component is large. When the magnitude of the magnetic flux density increases regardless of the direction of the magnetic flux density, the magnetic material becomes magnetically saturated and it becomes difficult to increase the magnetic field strength. Therefore, in the technology described in Non-Patent Document 1 and Patent Document 1, there is a risk that the obtained differential permeability (i.e., the relationship between the magnetic flux density and the magnetic field strength) does not accurately match the change (slope) of the actual magnetization characteristics. Therefore, when performing a convergence calculation, there is a risk that the differential permeability does not accurately follow the change in the actual magnetization characteristics, and the number of convergence calculations cannot be reduced. For this reason, there is a risk that the calculation time of the electromagnetic field analysis cannot be reduced.

[0011] The present invention has been made in consideration of the above problems, and has an object to improve the speed of analysis by improving the convergence of nonlinear convergence calculation in electromagnetic field analysis. [Means for solving the problem]

[0012] The analysis device of the present invention is an analysis device that performs electromagnetic field analysis, and includes a physical quantity that indicates the relationship between magnetic flux density and magnetic field strength in an analysis target area. Muden The system is equipped with a numerical analysis unit that calculates a magnetic vector potential for each of a plurality of elements that constitute the analysis target region based on a governing equation of a magnetic field, and the physical quantities include a first physical quantity that defines the relationship between the amount of change in magnitude of a magnetic flux density vector and the amount of change in magnitude of a magnetic field strength vector as a scalar quantity.

[0013] The analysis method of the present invention is a method for performing an electromagnetic field analysis, comprising the steps of: The analysis device It includes physical quantities that show the relationship between the magnetic flux density and magnetic field strength in the analysis area. Muden The method includes a numerical analysis process for determining a magnetic vector potential for each of a plurality of elements constituting the analysis target region based on a governing equation of a magnetic field, and the physical quantities include a first physical quantity that defines, as a scalar quantity, the relationship between the amount of change in magnitude of a magnetic flux density vector and the amount of change in magnitude of a magnetic field strength vector.

[0014] The program of the present invention causes a computer to function as each part of the analysis device. Effect of the Invention

[0015] According to the present invention, when the magnetic properties of an analysis target area are obtained by numerical analysis, a physical quantity that indicates the relationship between the amount of change in the magnitude of a magnetic flux density vector and the amount of change in the magnitude of a magnetic field strength vector, such as differential permeability, is defined as a scalar quantity. This makes it possible to obtain the relationship between the magnetic flux density and the magnetic field strength so as to accurately match the change (gradient) in the magnetization properties of the magnetic material included in the analysis target area. Therefore, it is possible to improve the convergence of the nonlinear convergence calculation in the electromagnetic field analysis, and to increase the analysis speed. [Brief description of the drawings]

[0016] [Figure 1] FIG. 4 is a diagram showing an example of magnetization characteristics. [Diagram 2]11 is a diagram showing an example of a time change in a magnetic field intensity vector relative to a time change in the x-component of a magnetic flux density vector. FIG. [Diagram 3] FIG. 2 illustrates an example of a functional configuration of an analysis device. [Figure 4] 11 is a flowchart illustrating an example of an analysis method. [Diagram 5] FIG. 11 is a diagram showing a first example of initial values ​​of the magnitudes of magnetic flux density vectors in a plurality of elements in an analysis target area. [Figure 6] FIG. 11 is a diagram showing a first example of values ​​of the magnitude of a magnetic flux density vector in a plurality of elements in an analysis target area after convergence calculation. [Figure 7] FIG. 11 is a diagram showing a first example of the relationship between the maximum magnetic flux density difference and the number of convergence calculations. [Figure 8] FIG. 11 is a diagram showing a second example of initial values ​​of the magnitudes of magnetic flux density vectors in a plurality of elements in an analysis target area. [Figure 9] FIG. 11 is a diagram showing a second example of values ​​of the magnitude of magnetic flux density vectors in a plurality of elements in an analysis target area after convergence calculation. [Figure 10] FIG. 11 is a diagram showing a second example of the relationship between the maximum magnetic flux density difference and the number of convergence calculations. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In addition, the term "the same objects in terms of length, position, size, spacing, etc." includes not only those that are strictly the same, but also those that are different within the scope of the invention (for example, those that differ within the tolerance range determined at the time of design).

[0018] (background) First, the background to the present embodiment will be described. In electromagnetic field analysis, the governing equations of the electromagnetic field (hereinafter simply referred to as governing equations) are discretized for each of the multiple elements of an analytical model, such as a finite element model, and the discretized equations created for each of the multiple elements are solved simultaneously under the boundary conditions to obtain a magnetic vector potential (hereinafter simply referred to as vector potential) that satisfies the boundary conditions. Most of the calculation time in numerical analysis is spent on solving the simultaneous equations. For this reason, if it is possible to search for magnetic properties that accurately match the change (gradient) in the magnetization properties, it is expected that the convergence of the iterative calculations can be improved and the calculation time can be significantly shortened.

[0019] FIG. 1 is a diagram showing an example of magnetization characteristics (magnetization curve) 100. As described in the Background section, in nonlinear electromagnetic field analysis, a convergence calculation is performed in which an analysis is repeated with the magnetic permeability assumed to be linear, and the magnetic permeability is corrected each time the convergence calculation is repeated, thereby expressing the nonlinear characteristics of the magnetization characteristics 100. However, since the magnetic permeability is corrected assuming that the magnetic permeability changes linearly, as shown in FIG. 1, the relationship between the magnitude B of the magnetic flux density and the magnitude H of the magnetic field strength is restricted to a straight line 110 passing through the origin 0. In particular, in a magnetic saturation region where the magnitude B of the magnetic flux density is large, a solution (e.g., magnetic flux density) is searched for on the straight line 110 that is far removed from the magnetization characteristics 100. For example, a point 130 on the magnetization characteristics (magnetization curve) 100 belongs to a magnetic saturation region in which the change in the magnitude B of the magnetic flux density relative to the change in the magnitude H of the magnetic field strength is small, but at the point 130, the change (slope) of the magnetization characteristics 100 is significantly different from the slope (=linear magnetic permeability) of the straight line 110 passing through the origin 0 and the point 130. Therefore, there is a risk that the convergence of the convergence calculation will deteriorate.

[0020] On the other hand, the differential permeability is defined as the magnetic flux density differentiated by the magnetic field strength, and is represented, for example, by the tangent 120 of the magnetization characteristic 100 shown in FIG. 1. Therefore, when performing the convergence calculation, correcting the differential permeability rather than correcting the permeability searches for a solution in a range close to the tangent 120 (straight line) of the magnetization characteristic 100, and is closer to the magnetization characteristic 100, so that it is considered that the convergence of the convergence calculation is improved. However, as described in the section on problems to be solved by the invention, if the differential permeability is determined for each component of each axis as described in Non-Patent Document 1 and Patent Document 1, magnetic saturation occurs not for each component of the magnetic flux density but according to the absolute value of the magnetic flux density, so there is a risk that the differential permeability cannot be obtained so as to accurately match the change (gradient) of the magnetization characteristic 100. Therefore, if the differential permeability is expressed as a vector, there is a risk that the differential permeability cannot be corrected so as to accurately follow the change (gradient) of the actual magnetization characteristic 100 when performing the convergence calculation.

[0021] Therefore, the inventors of the present invention have focused on the fact that magnetic materials become magnetically saturated when the magnitude of magnetic flux density becomes large regardless of the direction of magnetic flux density, and have considered that if a governing equation can be derived by expressing the relationship between magnetic flux density and magnetic field strength using differential permeability (scalar quantity) defined as the ratio of the magnitude of the magnetic flux density vector to the magnitude of the magnetic field strength vector, it will be possible to search for a solution in a range closer to the tangent 120 of the magnetization characteristic 100, including the magnetic saturation region. The inventors have found that by doing so, it is possible to improve the convergence of the convergence calculation and significantly shorten the calculation time.

[0022] (Governing equation) The governing equations derived by the present inventors are explained below. Here, an example is taken of solving magnetic properties using the A method. A general governing equation in the A method is composed of the following Ampere's law (1), Faraday's law (2), and the definition of vector potential (3).

[0023]

number

[0024] Here, H→ is the magnetic field strength vector (A / m). Note that H→ corresponds to the symbol H with → above it in each formula, and indicates that it is a vector (this method of notation is the same for symbols other than H→). E→ is the electric field strength vector (V / m). B→ is the magnetic flux density vector (T). A→ is the vector potential (Wb / m). σ is the electrical conductivity (S / m). By solving equations (1) to (3) simultaneously, we obtain the following equation (4).

[0025]

number

[0026] where J0 is the forced current density vector (A / m 2 ) In order to eliminate the magnetic field strength vector H→ from equation (4) and turn it into an equation for vector potential A→, an equation for the relationship between the magnetic flux density vector B→ and the magnetic field strength vector H→ is required, and usually the constitutive equation (5) below is used.

[0027]

number

[0028] Here, μ is the magnetic permeability (H / m). From equations (3) to (5), the following equation (6) is obtained as the governing equation.

[0029]

number

[0030] When differential permeability is not used instead of permeability μ, the vector potential A → (A x , A y , A z ) is required. On the other hand, when differential permeability is used, if the differential permeability is expressed as a vector, the x-component μ' of the differential permeability is x , y component μ' y , z component μ' z are defined as the following equations (7), (8), and (9), respectively. In Non-Patent Document 1 and Patent Document 1, the differential permeability is defined as the following equations (7) to (9).

[0031]

number

[0032] Using equations (7) to (9), the x, y, and z components on the left side of equation (4) are transformed into the following equations (10), (11), and (12), respectively.

[0033]

number

[0034] In equation (3), the x-component B of the magnetic flux density vector B→ x ,y component B y , z component B z The x-component A of the vector potential A x , y component A y ,z component A z And the x component of the vector potential A is A x , y component A y ,z component A z The x-component of the magnetic flux density vector B → B x ,y component B y , z component B z By applying this to the right-hand side of equations (10) to (12), the right-hand side of equations (10) to (12) can be expressed as the x-component A of vector potential A. x , y component A y ,z component A z And the x component of the vector potential A is A x , y component A y ,z component A zThe right-hand sides of equations (10) to (12) expressed as follows are taken as the x, y, and z components of the left-hand side of equation (4). Then, equation (4) can be expressed as the following equations (13) to (15).

[0035]

number

[0036] Here, the dimensions of the electromagnetic field analysis need only be two or more, but for simplicity, the dimensions of the electromagnetic field analysis are limited to two dimensions defined by the x-axis and y-axis, and the coordinate system in which the electromagnetic field analysis is performed is a two-dimensional Cartesian coordinate system. In this case, the x-component A of the vector potential A→ x , y component A y ,z component A z Of these, the z component A z Since only θ is required, equation (13) becomes equation (16) below.

[0037]

number

[0038] Differential permeability μ' in Eq. (16) x , μ′ y are defined as equations (7) and (8), respectively. Therefore, when the differential permeability is expressed for each axis component, the governing equation becomes equation (16). However, as already explained, the differential permeability μ' in equation (16) x , μ′ y is to be defined in terms of the relationship between the magnitude of the magnetic flux density and the magnitude of the magnetic field strength. Therefore, in this embodiment, the differential permeability μ′ is defined as a scalar quantity as shown in the following equation (17).

[0039]

number

[0040] Here, ||B→|| is the magnitude (norm) of the magnetic flux density vector, and ||H→|| is the magnitude (norm) of the magnetic field strength vector. In this embodiment, the differential permeability μ' defined as in equation (17) is used. Therefore, in order to construct the governing equation of the electromagnetic field using the differential permeability μ', 1 / μ' in equation (16) is used. x , 1 / μ' y , that is, ∂H x / ∂B x , ∂H y / ∂B y must be expressed using the magnitude of the magnetic flux density vector ||B→|| and the magnitude of the magnetic field strength vector ||H→||.

[0041] In the following, we use the magnitude of the magnetic flux density vector ||B→|| and the magnitude of the magnetic field strength vector ||H→|| to define ∂H x / ∂B x This section explains how to express the above. 2 is a diagram showing an example of the time change of the magnetic field strength vector H→ with respect to the time change of the x-component of the magnetic flux density vector B→. As described above, the magnetic flux density vector B→ and the magnetic field strength vector H→ are assumed to be two-dimensional vectors consisting of an x ​​component and a y component. In addition, for the sake of simplicity, it is assumed that there is no phase difference due to magnetization rotation between the magnetic flux density vector B→ and the magnetic field strength vector H→.

[0042] In FIG. 2, the magnetic flux density vector B→ and the magnetic field strength vector H→ at the analysis time t are respectively t →, H t The magnetic flux density vector B→ and the magnetic field strength vector H→ at the analysis time t+Δt, which is a time step Δt after the analysis time t, are denoted as B t+Δt →, H t+Δt It is written as →.

[0043] When the magnetization characteristics are linear, when the x-component of the magnetic field strength vector B→ changes with time, only the x-component of the magnetic field strength vector H→ also changes with time, just like the magnetic flux density vector B→. In contrast, when the magnetization characteristics are nonlinear, as shown in Figure 2, when the x-component of the magnetic flux density vector B→ changes with time, only the x-component of the magnetic field strength vector H→ changes with time.x The magnetic flux density vector B→ changes with time by t → to B t+Δt →, the magnetic field strength vector H→ changes in time not only the x component but also the y component, H t →From H t+Δt →Time changes.

[0044] Here, the differential magnetic reluctance v' is defined as the reciprocal of the differential permeability μ' defined by equation (17) as shown in the following equation (18).

[0045]

number

[0046] The differential magnetic resistivity ν' at the analysis time t is ν t ', the following equation (19) holds from equation (18).

[0047]

number

[0048] As shown in Fig. 2, the magnetic flux density vector B t The angle (°) between → and the x-axis is θ x Then, Δ||B in Eq. (19) t →|| is geometrically expressed as the following equation (20). Note that the magnetic flux density vector B t → angle θ with the x-axis x is the magnetic flux density vector B at analysis time t t →The smaller of the angles it makes with the x-axis (acute angle) or 90°.

[0049]

number

[0050] From equation (20), the magnitude of the magnetic flux density vector at analysis time t+Δt is ||B t+Δt→|| is expressed as the following equation (21). Also, from equations (19) and (20), the magnitude of the magnetic field strength vector ||H t+Δt →|| is expressed as the following equation (22).

[0051]

number

[0052] Here, the x-component of the magnetic flux density vector B→ is assumed to change over time. Therefore, the magnitude of the magnetic flux density vector ||B t+Δt →|| and the magnitude of the magnetic field strength vector ||H t+Δt →The ratio of || is the x-component B of the magnetic flux density vector at the analysis time t+Δt. x +ΔB x and the x-component of the magnetic field strength vector H x +ΔH x Therefore, the following equation (23) holds.

[0053]

number

[0054] From equations (22) to (23), the following equation (24) is established.

[0055]

number

[0056] By rearranging equation (24) and approximating the second-order infinitesimal terms to 0 (zero), we obtain the following equation (25).

[0057]

number

[0058] (25) Both sides of equation (25) are ||B t →|| ||H tDividing by →|| gives the following equation (26).

[0059]

number

[0060] Here, the x-component of the magnetic flux density vector B→ is assumed to change with time. Therefore, the following equation (27) holds. Substituting equation (27) into equation (26), the following equation (28) is obtained.

[0061]

number

[0062] ΔH x / ΔB x In order to make them independent, we add ||H t →|| / ΔB x Multiplying by this gives us the following equation (29).

[0063]

number

[0064] Here, if the ratio of the magnitude of the magnetic flux density vector ||B→|| to the magnitude of the magnetic field strength vector ||H→|| is defined as a scalar quantity, the magnetic permeability μ, and its reciprocal, the magnetic reluctance rate ν, are defined as shown in the following equation (31).

[0065]

number

[0066] Using the magnetic resistivity ν shown in equation (31), ∂B x / ∂H x can be expressed as the following equation (32) from equation (29).

[0067]

number

[0068] As shown in equation (32), ∂H x / ∂B x is expressed using the magnitude of the magnetic flux density vector ||B→|| and the magnitude of the magnetic field strength vector ||H→||. ∂H y / ∂B y If we consider in the same way, it can be expressed as the following equation (33).

[0069]

number

[0070] Equations (32) and (33) are the 1 / μ' in equation (16), respectively. x , 1 / μ' y Therefore, equation (16) can be expressed as the following equation (34).

[0071]

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[0072] In this embodiment, the governing equation for two-dimensional electromagnetic field analysis is defined as in equation (34). As described above, the inventors have conceived of a governing equation that can be obtained using a magnetic reluctance v and a differential magnetic reluctance v' that are defined by the magnitude ||B→|| of the magnetic flux density vector and the magnitude ||H→|| of the magnetic flux density vector. The governing equation for two-dimensional electromagnetic field analysis defined in equation (34) expresses the z-component A of the vector potential A→(A→(A)) using the magnetic reluctance v and the differential magnetic reluctance v'. z ) is the equation to find

[0073] By applying the magnetic resistivity ν and the differential magnetic resistivity ν' as constants to equation (34), the z component A of the vector potential A→( z ) is obtained. Then, the z component A of the vector potential A→( z) based on the following equations (35) and (36), the magnetic flux density vector B → components of each axis B x , B y is required.

[0074]

number

[0075] In other words, the governing equation for two-dimensional electromagnetic field analysis defined by equation (34) is the component B of each axis of the magnetic flux density vector B x , B y and the magnetic field strength vector H → components H of each axis x , H y In the technology described in Non-Patent Document 1 and Patent Document 1, even if the (magnitude of) the differential permeability defined by equation (17) is the same, when the (components of each axis) of the differential permeability defined by equations (7) and (8) is different, the z-component A of the vector potential A→(obtained by equation (16), which is the governing equation when the differential permeability is determined for each component of each axis, is expressed as z In contrast, in the governing equation for two-dimensional electromagnetic field analysis defined by equation (34), if the (magnitude of) the differential permeability defined by equation (17) is the same, even if the (components of each axis of) the differential permeability defined by equations (7) to (8) are different, the z-component A of the vector potential A→(obtained by the governing equation) z ) will be the same. In other words, if differential permeability is defined as a vector quantity, the differential permeability may change depending on the direction of the magnetic flux density vector B→ even if the magnitude of the magnetic flux density vector ||B→|| is the same, but by defining differential permeability μ' as a scalar quantity using the magnitude of the magnetic flux density vector ||B→|| and the magnitude of the magnetic flux density vector ||H→||, as long as the magnitude of the magnetic flux density vector ||B→|| is the same, differential permeability μ' will not change depending on the direction of the magnetic flux density vector B→, and it will accurately match the changes (gradient) in the magnetization characteristics of the magnetic materials included in the analysis target area.

[0076] Magnetic flux density vector B at analysis time t t The angles (°) between the x-axis, y-axis, and z-axis are θ x , θ y , θ z Then, the governing equation for three-dimensional electromagnetic field analysis can be obtained by expanding the two-dimensional orthogonal coordinate system described above in the derivation of the governing equation for two-dimensional electromagnetic field analysis to a three-dimensional orthogonal coordinate system, and is defined by the following equation (37). Note that the magnetic flux density vector B t The angles (°) between the x-axis, y-axis, and z-axis are θ x , θ y , θ z are the magnetic flux density vectors B at analysis time t, respectively. t →The smaller of the angles it makes with the x-axis, y-axis, or z-axis (acute angle) or 90°.

[0077]

number

[0078] Here, K in Eq. (37) x , K y , K z are defined by the following equations (38), (39), and (40), respectively.

[0079]

number

[0080] Vector potential A → (A x , A y , A z ) and the magnetic flux density vector B → components B of each axis are calculated as follows (41) to (43). x , B y , B z is required.

[0081]

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[0082] Incidentally, a person skilled in the art who can understand the above explanation with reference to equations (16) to (34) can derive the governing equations in three-dimensional electromagnetic source analysis by extending the above explanation with reference to equations (16) to (34) to a three-dimensional orthogonal coordinate system, and therefore a detailed explanation of the derivation process of equation (37) will be omitted here.

[0083] As described above, when performing a two-dimensional electromagnetic field analysis, the governing equation shown in equation (34) is discretized for each of the multiple elements instead of equation (6) (expressing the differential equation as a simultaneous equation), and the vector potential A → (z component A of z When performing a three-dimensional electromagnetic field analysis, the governing equation shown in equation (37) is discretized for each of the multiple elements instead of equation (6), and the vector potential A → (x component A of x , y component A y ,z component A z ) is required.

[0084] Furthermore, equations (34) and (37) may be expressed using differential permeability μ' defined in equation (17) and permeability μ defined in equation (30) instead of the differential magnetic reluctance v' defined in equation (18) and the magnetic reluctance v defined in equation (31).

[0085] In addition, here, the coordinate system of the governing equation is an orthogonal coordinate system. However, the coordinate system of the governing equation is not limited to the orthogonal coordinate system. For example, the coordinates (x, y, z) of the orthogonal coordinate system shown in the formula (34) and the formula (37) may be converted into the coordinates of other coordinate systems such as a polar coordinate system or a cylindrical coordinate system to construct the governing equation in each coordinate system.

[0086] Also, here, the case where the governing equation in the A method is expressed using the differential magnetic reluctance v' defined by the formula (18) and the magnetic reluctance v defined by the formula (31) is exemplified. However, the governing equation is not limited to the governing equation in the A method. For example, the governing equation in a solution method other than the A method, such as the A-φ method in which the Maxwell equation is rewritten using the vector potential A and the electric scalar potential φ to solve the vector potential A and the electric scalar potential φ, or the T-Ω method in which the Maxwell equation is rewritten using the current vector potential T and the magnetic scalar potential Ω to solve the current vector potential T and the magnetic scalar potential Ω, may be expressed using the differential magnetic reluctance v' defined by the formula (18) and the magnetic reluctance v defined by the formula (31).

[0087] As explained with reference to equations (1) to (43), the governing equations in the solution methods other than Method A are the x-component μ' of the differential permeability defined by equations (7) to (9). x , y component μ' y , z component μ' z Rewrite using The governing equations can be derived by rewriting them using the differential magnetic reluctance v' defined by the formula (18) and the magnetic reluctance v defined by the formula (31). That is, a person skilled in the art who has knowledge of general governing equations in solutions other than the A method can derive governing equations expressed using the differential magnetic reluctance v' defined by the formula (18) and the magnetic reluctance v defined by the formula (31) as governing equations in solutions other than the A method by referring to the above explanation with reference to the formulas (1) to (43). Therefore, a detailed explanation of the derivation process of these governing equations will be omitted here. Note that these governing equations may also be expressed using the differential permeability μ' defined by the formula (17) and the magnetic permeability μ defined by the formula (30) instead of the differential magnetic reluctance v' defined by the formula (18) and the magnetic reluctance v defined by the formula (31).

[0088] (Analysis device) Next, analysis device 300 will be described with reference to Fig. 3. Fig. 3 is a diagram showing an example of a functional configuration of analysis device 300. The hardware of analysis device 300 is realized by using, for example, a processor, a storage device such as a main storage device or an external storage device, and an information processing device (computer) equipped with various interfaces, or dedicated hardware. Analysis device 300 is a device for determining the vector potential of an analysis target region that includes a magnetic body by numerical analysis based on governing equations of an electromagnetic field.

[0089] The magnetic body is, for example, a soft magnetic body such as an electromagnetic steel sheet. The analysis target area may be, for example, a part or all of an electric device having an iron core, such as a motor, a generator, and a transformer (voltage transformer or current transformer). The part of an electric device may be, for example, a component part of the electric device, such as a stator of a motor. The analysis target area is not limited to a part or all of an electric device. For example, the analysis target area may be a part or all of a magnetically shielded room. The analysis target area may be a part or all of a molded magnetic body (for example, a steel plate, a steel bar, a steel pipe, etc.). The analysis target area does not have to be an area of ​​an actual object. For example, the analysis target area may be a part or all of a newly designed non-existent object. In addition, when an object to be analyzed has symmetry, one of a plurality of symmetrical areas of the object may be the analysis target area.

[0090] The governing equation when performing a two-dimensional electromagnetic field analysis is, for example, the governing equation shown in equation (34). The governing equation when performing a three-dimensional electromagnetic field analysis is, for example, the governing equation shown in equation (37). When equation (34) or equation (37) is used as the governing equation, the vector potential obtained by analysis device 300 is vector potential A→.

[0091] 3, analysis device 300 includes an acquisition unit 310 and a numerical analysis unit 320, and is configured to be able to determine the vector potential of an area to be analyzed by numerical analysis based on a governing equation of an electromagnetic field. In this embodiment, analysis device 300 further includes an output unit 330. Each of these functional units will be described below.

[0092] <Acquisition part 310> The acquiring unit 310 acquires various information necessary for a numerical analysis in the numerical analysis unit 320 described later. In this embodiment, the acquiring unit 310 includes an analysis model acquiring unit 311, a magnetization characteristic acquiring unit 312, an equation acquiring unit 313, and an initial value acquiring unit 314.

[0093] The analytical model acquisition unit 311 acquires an analytical model, such as a finite element model, of the analysis target area. The analytical model is an approximation of the shape of the analysis target area using multiple elements so that numerical analysis can be performed by a computer, and includes information that identifies the multiple elements. The elements are also called meshes or minute areas. The information that identifies the multiple elements includes, for example, the coordinate values ​​of each element.

[0094] The analytical model acquisition unit 311 may acquire information on the analytical model in response to, for example, an input operation of the analytical model using a user interface of the analysis device 300. The analytical model acquisition unit 311 may also receive and acquire information on the analytical model transmitted from an external device. The analytical model acquisition unit 311 may also read and acquire information on the analytical model stored in a portable storage medium.

[0095] The magnetization characteristic acquisition unit 312 acquires information indicating the magnetization characteristics of the magnetic material included in the analysis target region. The magnetization characteristics indicate the relationship between the magnitude ||B→|| of the magnetic flux density vector and the magnitude ||H→|| of the magnetic field intensity vector. Like the magnetization characteristic 100 shown in Fig. 1, the magnetization characteristics identified by the information acquired by the magnetization characteristic acquisition unit 312 are nonlinear, and a nonlinear electromagnetic field analysis is performed by the numerical analysis unit 320 described later. However, the magnetization characteristics identified by the information acquired by the magnetization characteristic acquisition unit 312 may be linear.

[0096] The information indicating the magnetization characteristics may be, for example, a relational expression between the magnitude ||B→|| of the magnetic flux density vector and the magnitude ||H→|| of the magnetic field intensity vector. However, the information indicating the magnetization characteristics is not limited to the relational expression between the magnitude ||B→|| of the magnetic flux density vector and the magnitude ||H→|| of the magnetic field intensity vector. For example, the information indicating the magnetization characteristics may be a table that stores the magnitude ||B→|| of the magnetic flux density vector and the magnitude ||H→|| of the magnetic field intensity vector in a mutually associated manner. In this case, information not stored in the table can be found by performing interpolation and extrapolation using information stored in the table.

[0097] For example, the magnetization characteristic acquisition unit 312 may acquire information indicating the magnetization characteristics in response to an input operation of information indicating the magnetization characteristics using a user interface of the analysis device 300. The magnetization characteristic acquisition unit 312 may also receive and acquire information indicating the magnetization characteristics transmitted from an external device. The magnetization characteristic acquisition unit 312 may also read and acquire information indicating the magnetization characteristics stored in a portable storage medium.

[0098] The equation acquisition unit 313 acquires simultaneous equations including equations discretized based on a plurality of elements specified by the analytical model acquired by the analytical model acquisition unit 311. In this embodiment, when a two-dimensional electromagnetic field analysis is performed, the governing equation is the governing equation defined by equation (34). On the other hand, when a three-dimensional electromagnetic field analysis is performed, the governing equation is the governing equation defined by equation (37).

[0099] As a method of numerical analysis, for example, a known method such as the finite element method (FEM) and the finite difference method (FDM) is used. Therefore, in the numerical analysis, the governing equation defined by the formula (34) or (37) itself is not used, but a simultaneous equation is used in which the governing equation defined by the formula (34) or (37) is discretized for each of a plurality of elements so that the numerical analysis can be performed by these methods. In addition, in this embodiment, a case where a vector potential is calculated at each analysis time t for each time step Δt is illustrated. Therefore, the governing equation defined by the formula (34) or (37) needs to be further discretized for each time step Δt. When calculating a vector potential at one analysis time t, discretization for each time step Δt is not necessary.

[0100] The equation acquisition unit 313 acquires information indicating the governing equation defined by equation (34) or equation (37). The equation acquiring unit 313 may acquire information indicating the governing equations in response to, for example, an input operation of information indicating the governing equations using a user interface of the analysis device 300. The equation acquiring unit 313 may also acquire information indicating the governing equations by receiving the information transmitted from an external device. The equation acquiring unit 313 may also acquire information indicating the governing equations by reading the information stored in a portable storage medium.

[0101] Then, the equation acquisition unit 313 discretizes the governing equation defined by equation (34) or equation (37) based on the multiple elements and the time step Δt, and formulates (creates) multiple equations (discretized governing equations) for each of the multiple elements. At this time, the equation acquisition unit 313 identifies the multiple elements based on information identifying the multiple elements included in the analysis model acquired by the analysis model acquisition unit 311. In addition, the equation acquisition unit 313 identifies the time step Δt based on, for example, an input operation of information indicating the time step Δt using a user interface of the analysis device 300. Then, the equation acquisition unit 313 formulates (creates) simultaneous equations by simultaneous equations of the multiple equations formulated (created) as described above.

[0102] Incidentally, the equation acquiring unit 313 does not necessarily have to acquire the simultaneous equations used in the numerical analysis in the above manner. For example, the equation acquiring unit 313 may acquire information indicating the simultaneous equations used in the numerical analysis (as they are), rather than the governing equations themselves defined by equation (34) or equation (37), by performing an input operation using a user interface of the analysis device 300, receiving the information from an external device, or reading the information from a portable storage medium.

[0103] The initial value acquisition unit 314 acquires an initial value of a physical quantity indicating the relationship between magnetic flux density and magnetic field strength. The physical quantity indicating the relationship between magnetic flux density and magnetic field strength is a physical quantity indicating how the magnetic field strength changes with respect to the change in magnetic flux density. In this embodiment, a case is illustrated in which the physical quantity indicating the relationship between the magnetic flux density and magnetic field strength of the analysis target area includes differential permeability μ', which is an example of a first physical quantity that defines the relationship between the magnitude ||B→|| of the magnetic flux density vector, Δ||B→||, and the magnitude ||H→|| of the magnetic field strength vector, Δ||H→||, as a scalar quantity. Furthermore, in this embodiment, a case is illustrated in which the physical quantity indicating the relationship between the magnetic flux density and magnetic field strength of the analysis target area includes permeability μ, which is an example of a second physical quantity that defines the relationship between the magnitude ||B→|| of the magnetic flux density vector, and the magnitude ||H→||, as a scalar quantity. Therefore, the initial value acquisition unit 314 acquires the initial value of differential permeability μ' for each of the multiple elements, and the initial value of permeability μ in the multiple elements. In this embodiment, the differential permeability μ′ and the permeability μ are defined by equations (17) and (30), respectively.

[0104] The first physical quantity, which defines the relationship between the change amount Δ||B→|| of the magnetic flux density vector magnitude ||B→|| and the change amount Δ||H→|| of the magnetic field intensity vector magnitude ||H→|| as a scalar quantity, is not limited to the differential permeability μ', and may be, for example, the differential magnetic reluctance v' defined by the formula (18), or may be a value obtained by performing a predetermined operation on the differential permeability μ', such as squaring the differential permeability μ'. The second physical quantity, which defines the relationship between the magnetic flux density vector magnitude ||B→|| and the magnetic field intensity vector magnitude ||H→|| as a scalar quantity, is not limited to the permeability μ, and may be, for example, the magnetic reluctance v defined by the formula (31), or may be a value obtained by performing a predetermined operation on the magnetic reluctance v, such as squaring the magnetic reluctance v. In this case, the initial value acquisition unit 314 acquires the differential magnetic reluctance ν' defined by equation (18) and the magnetic reluctance ν defined by equation (31) instead of the differential permeability μ' defined by equation (17) and the magnetic permeability μ defined by equation (30).

[0105] In this embodiment, the initial value acquisition unit 314 acquires initial values ​​of the vector potential A→ in the multiple elements, and determines initial values ​​of the magnetic flux density vector B→ in the multiple elements based on the initial values ​​of the vector potential A→ in the multiple elements (see the above formulas (35) and (36), or formulas (41) to (43)). Then, the initial value acquisition unit 314 determines initial values ​​of the differential permeability μ' in the multiple elements and initial values ​​of the magnetic permeability μ in the multiple elements, based on the initial values ​​of the magnetic flux density vector B→ in the multiple elements and the magnetization characteristics specified by the information acquired by the magnetization characteristic acquisition unit 312.

[0106] The numerical analysis in the numerical analysis unit 320 described later begins at analysis start time t s From analysis completion time t e The initial value acquisition unit 314 is executed at each analysis time t discretized for each time step Δt up to the analysis start time t s The initial value of the vector potential A→ when performing the numerical analysis at the analysis time t s The initial value of the vector potential A→ when performing the numerical analysis at does not necessarily have to be obtained using a random number. The initial value acquisition unit 314 may, for example, set a preset value (e.g., 0 (zero)) at the analysis time t s It may be obtained as the initial value of the vector potential A→ when performing a numerical analysis in

[0107] In addition, the initial value acquisition unit 314 acquires the analysis start time t s As the initial value of the vector potential A→ when performing a numerical analysis at an analysis time t later than the analysis start time t, a value obtained by a numerical analysis at an analysis time t-Δt immediately preceding the analysis time t may be obtained. sThe initial value of the vector potential A→ when performing a numerical analysis at an analysis time t later than this analysis time t is not limited to the value found by numerical analysis at the analysis time t-Δt immediately preceding the analysis time t. The initial value acquisition unit 314 may acquire, for example, the value one cycle before the analysis time t, as the initial value of the vector potential A→ when performing the numerical analysis at the analysis time t.

[0108] The initial value acquisition unit 314 acquires initial values ​​of the magnetic flux density vector B→ in the plurality of elements at the analysis time t based on the initial value of the vector potential A→ in the plurality of elements at the analysis time t, and acquires initial values ​​of the differential permeability μ' in the plurality of elements at the analysis time t and the initial value of the magnetic permeability μ in the plurality of elements at the analysis time t based on the initial value of the magnetic flux density vector B→ in the plurality of elements at the analysis time t and the magnetization characteristics specified by the information acquired by the magnetization characteristic acquisition unit 312, at an analysis start time t s From analysis completion time t e This is performed for each analysis time t for each time step Δt up to

[0109] It is not necessary for the initial value acquisition unit 314 to acquire the initial values ​​of the differential permeability μ' and the initial values ​​of the magnetic permeability μ in the multiple elements at each analysis time t in the above manner. For example, the initial value acquisition unit 314 may acquire the initial values ​​of the magnetic flux density vector B→ in the multiple elements without acquiring the initial values ​​of the vector potential A→ in the multiple elements, or may acquire the initial values ​​of the differential permeability μ' in the multiple elements and the initial values ​​of the magnetic permeability μ in the multiple elements without acquiring the initial values ​​of the vector potential A→ in the multiple elements and the initial values ​​of the magnetic flux density vector B→ in the multiple elements.

[0110] The information acquired by the acquisition unit 310 is various information necessary for the numerical analysis in the numerical analysis unit 320 described later, and is not limited to the information described above. For example, the acquisition unit 310 may acquire general information necessary for the numerical analysis in addition to the information described above. For example, the acquisition unit 310 may acquire information indicating the physical property values ​​(conductivity σ, etc.) of the region to be analyzed, information indicating the boundary conditions, information indicating the analysis time (the analysis start time t s From analysis completion time t e It is also possible to obtain information indicating the period until the expiration date.

[0111] <Numerical Analysis Department 320> The numerical analysis unit 320 is started after the acquisition unit 310 acquires information necessary for the numerical analysis in the numerical analysis unit 320. The numerical analysis unit 320 obtains the vector potential of the analysis target area for each of the multiple elements by numerical analysis based on the governing equation, based on a physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength of the analysis target area. As described above, in this embodiment, the governing equation defined by the formula (34) or (37) is solved as a simultaneous equation obtained by discretizing the equation based on the multiple elements and the time step Δt, thereby obtaining the vector potential A→ for each of the multiple elements at each analysis time t for each time step Δt. In this embodiment, a case will be illustrated in which the simultaneous equation obtained by discretizing the equation based on the multiple elements and the time step Δt is the simultaneous equation obtained by the equation acquisition unit 313.

[0112] The process in the numerical analysis unit 320 is, for example, the following processes (a) to (h) starting from the analysis start time t s From analysis completion time t e This is realized by executing the analysis at each analysis time t for each time step Δt up to

[0113] (a) First, the numerical analysis unit 320 finds the vector potential A→ in each of the multiple elements by solving the above-mentioned simultaneous equations so as to satisfy the boundary conditions, based on the initial values ​​of the physical quantities indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements.

[0114] As described above, in this embodiment, the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength includes the differential permeability μ' and the magnetic permeability μ. Therefore, the initial values ​​of the differential permeability μ' in the multiple elements and the initial values ​​of the magnetic permeability μ in the multiple elements acquired by the initial value acquisition unit 314 are used as the initial values ​​of the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements. In addition, the boundary conditions are specified from the information indicating the boundary conditions acquired by the acquisition unit 310.

[0115] (b) Next, the numerical analysis unit 320 calculates at least one physical quantity that determines the value of the magnetization characteristic of the multiple elements based on the vector potential of the multiple elements calculated in (a), and calculates a physical quantity that indicates the relationship between the magnetic flux density and the magnetic field strength of the multiple elements based on the physical quantity that determines the value of the magnetization characteristic of the multiple elements.

[0116] The magnetization characteristic indicates the relationship between magnetic flux density and magnetic field strength. Therefore, the physical quantities that determine the value of the magnetization characteristic are magnetic flux density and magnetic field strength. In this embodiment, the physical quantity that determines the value of the magnetization characteristic is magnetic flux density. As described above, in this embodiment, the physical quantities that indicate the relationship between magnetic flux density and magnetic field strength are differential permeability μ' and magnetic permeability μ.

[0117] Therefore, in this embodiment, the numerical analysis unit 320 obtains the magnetic flux density vector B→ in the multiple elements based on the vector potential A→ in the multiple elements. Then, the numerical analysis unit 320 obtains the differential permeability μ' in the multiple elements and the magnetic permeability μ in the multiple elements based on the magnetic flux density vector B→ in the multiple elements and the magnetization characteristics specified by the information acquired by the magnetization characteristic acquisition unit 312. For example, a point 130 on the magnetization characteristic (magnetization curve) 100 corresponding to the magnitude of the magnetic flux density vector B→ shown in FIG. 1 is obtained, and the gradient of the tangent 120 of the magnetization characteristic (magnetization curve) 100 at the obtained point 130 is obtained as the differential permeability μ'. In addition, the gradient of the straight line 110 passing through the origin 0 and the obtained point 130 is obtained as the magnetic permeability μ. The numerical analysis unit 320 may obtain the differential magnetic reluctance v' and the magnetic reluctance v instead of or in addition to the differential permeability μ' and the magnetic permeability μ.

[0118] (c) Next, the numerical analysis unit 320 judges whether or not the convergence condition is satisfied. The convergence condition may be, for example, a condition that the difference between the previous value and the current value of at least one of the physical quantities that determine the value of the magnetization characteristic in the plurality of elements is equal to or less than a threshold value. For example, the magnetic flux density may be used as at least one of the physical quantities that determine the value of the magnetization characteristic. In this case, the convergence condition may be, for example, a condition that the difference between the previous value and the current value of the representative value of the magnetic flux density vector B→ in the plurality of elements is equal to or less than a threshold value. The representative value may be, for example, any one of the average value, median value, mode value, and maximum value of the magnitude of the magnetic flux density vector B→. In addition, the convergence condition is not limited to such a condition, and may be, for example, a condition that the number of times of judgment as to whether or not the convergence condition is satisfied reaches a predetermined number.

[0119] (d) If the result of the judgment in (c) indicates that the convergence condition is not satisfied, the numerical analysis unit 320 updates the physical quantities indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements to those obtained in the process in (b). In this embodiment, the numerical analysis unit 320 updates the differential permeability μ′ and the permeability μ in the multiple elements to those obtained in the process in (b). (e) Next, the numerical analysis unit 320 performs the processes (a) to (c) again, regarding the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements in the process (a) as having been updated in the process (d). Then, if it is determined that the convergence condition is not satisfied in the process (c), the numerical analysis unit 320 performs the process (d) again. (f) The numerical analysis unit 320 executes, as an example of a first iterative calculation, a convergence calculation in which the processes of (d) and (e) are repeated until it is determined that the convergence condition is satisfied in the process of (c).

[0120] The convergence calculation is realized by a known method such as the Newton-Raphson method. Therefore, when the convergence calculation is executed, the equation acquisition unit 313 acquires simultaneous equations formulated (created) so as to realize the convergence calculation by the Newton-Raphson method or the like. Note that the method of numerical analysis itself is a general method as described in Non-Patent Document 2 and the like, and therefore a detailed description thereof will be omitted.

[0121] (g) The numerical analysis unit 320 performs the above-mentioned processes (a) to (f) from the analysis start time t s From analysis completion time t e The process executed at each analysis time t for each time step Δt up to is executed as an example of the second iterative calculation. The physical quantity (magnetic flux density (more specifically, magnetic flux density vector B→) in this embodiment) that determines the value of the magnetization characteristic in the multiple elements at each analysis time t is the physical quantity that determines the value of the magnetization characteristic in the multiple elements, obtained by the process (b) described above at each analysis time t. Similarly, the physical quantity (differential permeability μ' and permeability μ in this embodiment) that indicates the relationship between the magnetic flux density and the magnetic field strength in the multiple elements at each analysis time t is the physical quantity that indicates the relationship between the magnetic flux density and the magnetic field strength in the multiple elements, obtained by the process (b) described above at each analysis time t.

[0122] (h) The numerical analysis unit 320 judges whether or not the analysis end condition is satisfied. The analysis end condition is, for example, the analysis end time t eThe condition for terminating the analysis may be that a physical quantity (in this embodiment, magnetic flux density (more specifically, magnetic flux density vector B→)) that determines the values ​​of the magnetization characteristics of multiple elements has been obtained. However, the condition for terminating the analysis is not limited to such a condition. For example, the condition for terminating the analysis may be that a physical quantity that determines the values ​​of the magnetization characteristics of multiple elements satisfies a predetermined condition. In this case, the predetermined condition may be, for example, that the difference between the magnetic flux density vector B→ in each element and the target value is equal to or less than a threshold value.

[0123] <Output unit 330> The output unit 330 outputs information representing a physical quantity (magnetic flux density in this embodiment) that determines the value of the magnetization characteristic in the plurality of elements at each analysis time t, and a physical quantity (differential permeability μ' and permeability μ in this embodiment) that indicates the relationship between the magnetic flux density and the magnetic field strength in the plurality of elements, which are obtained by the numerical analysis unit 320. The destination of the information output by the output unit 330 is not particularly limited. In this embodiment, it is a computer display 340, but in addition to or instead of this, at least one of the following forms may be adopted: transmission to an external device, and storage in a storage medium inside or outside the analysis device 300.

[0124] (Analysis method) Next, an example of the analysis method according to this embodiment, which is executed by analysis device 300, will be described with reference to the flowchart of FIG. First, in step S401, the analytical model acquisition unit 311 acquires an analytical model for the analysis target region.

[0125] Next, in step S402, the magnetic property acquisition unit 312 acquires information indicating the magnetic property of the magnetic material included in the analysis target region. Next, in step S403, the equation acquisition unit 313 acquires simultaneous equations by discretizing the governing equation shown in formula (34) or formula (37) based on a plurality of elements and a time step Δt. The simultaneous equations are obtained, for example, by discretizing the governing equation shown in formula (34) or formula (37) into equations for each of a plurality of elements so that a numerical analysis can be performed using the finite element method, the finite difference method, or the like, and transforming these equations for each of the plurality of elements so that a convergence calculation can be performed using the Newton-Raphson method, or the like. Next, in step S404, the analysis device 300 sets the current analysis time t to the analysis start time t s Set to.

[0126] Next, in step S405, the initial value acquisition unit 314 acquires initial values ​​of physical quantities indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements when performing the numerical analysis at the current analysis time t. In this embodiment, the initial value acquisition unit 314 acquires initial values ​​of the vector potential A→ in the multiple elements when performing the numerical analysis at the current analysis time t. Then, based on the initial values ​​of the vector potential A→ in the multiple elements, the initial value acquisition unit 314 determines initial values ​​of the magnetic flux density vector B→ in the multiple elements when performing the numerical analysis at the current analysis time t. Then, based on the initial values ​​of the magnetic flux density vector B→ in the multiple elements and the magnetization characteristics specified by the information acquired in step S402, the initial value acquisition unit 314 determines initial values ​​of the differential permeability μ' in the multiple elements and the initial values ​​of the magnetic permeability μ in the multiple elements when performing the numerical analysis at the current analysis time t.

[0127] Next, in step S406, the numerical analysis unit 320 obtains the vector potential of the analysis target region for each of the elements by numerical analysis based on the governing equation, based on the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength in the elements. Then, based on the vector potential in the elements, the numerical analysis unit 320 obtains the physical quantity that determines the value of the magnetization property in the elements and the physical quantity that indicates the relationship between the magnetic flux density and the magnetic field strength in the elements.

[0128] In the first process of step S406 at each analysis time t, the initial value acquired in step S405 is used as the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements. In the second and subsequent processes of step S406 at each analysis time t, the value updated in step 408 described later is used as the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements.

[0129] In this embodiment, an example is shown in which the physical quantity that determines the value of the magnetization characteristics in multiple elements is magnetic flux density, and the physical quantities that indicate the relationship between the magnetic flux density and magnetic field strength in multiple elements are differential permeability μ' and magnetic permeability μ. Therefore, the numerical analysis unit 320 finds the vector potential A→ in the multiple elements at the current analysis time t by solving the simultaneous equations acquired in step S403. Then, the numerical analysis unit 320 finds the magnetic flux density vector B→ in the multiple elements at the current analysis time t, based on the vector potential A→ in the multiple elements at the current analysis time t. Then, the numerical analysis unit 320 finds the differential permeability μ' in the multiple elements at the current analysis time t and the magnetic permeability μ in the multiple elements at the current analysis time t, based on the magnetic flux density vector B→ in the multiple elements at the current analysis time t and the magnetization characteristics identified by the information acquired in step S402.

[0130] Next, in step S407, the numerical analysis unit 320 judges whether the convergence condition is satisfied. If the result of this judgment is that the convergence condition is not satisfied (NO in step S407), the process of step S408 is executed. In step S408, the numerical analysis unit 320 updates the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements to that obtained in step S406. In this embodiment, the numerical analysis unit 320 updates the differential permeability μ′ and the magnetic permeability μ to that obtained in step S406, which is immediately before this step S408.

[0131] Then, the process of step S406 described above is executed again. As described above, in the second and subsequent processes of step S406 at each analysis time t, the values ​​updated in step 408 are used as the values ​​of the physical quantities (in this embodiment, the differential permeability μ' and the permeability μ) indicating the relationship between the magnetic flux density and the magnetic field strength in the multiple elements. Then, the processes of steps S406 to S408 are repeatedly executed until it is determined in step S407 that the convergence condition is satisfied. In the flowchart shown in FIG. 4, the processes of steps S406 to S408 are an example of a first iterative calculation.

[0132] If it is determined in step S407 that the convergence condition is satisfied (YES in step S407), the process of step S409 is executed. In step S409, the numerical analysis unit 320 stores the information indicating the physical quantity (magnetic flux density in this embodiment) that determines the value of the magnetization characteristic in the multiple elements and the physical quantity (differential permeability μ' and permeability μ in this embodiment) that indicates the relationship between the magnetic flux density and the magnetic field strength in the multiple elements, which were obtained in step S406 immediately before this step S409, as the physical quantity that determines the value of the magnetization characteristic in the multiple elements at the current analysis time t and the physical quantity that indicates the relationship between the magnetic flux density and the magnetic field strength in the multiple elements at the current analysis time t. Note that since the magnetic flux density is a vector quantity, the information indicating the magnetic flux density is information that can identify the magnetic flux density vector B→.

[0133] Next, in step S410, the numerical analysis unit 320 judges whether or not the analysis end condition is satisfied. If the result of this judgment is that the analysis end condition is not satisfied (NO in step S410), the process of step S411 is executed. In step S411, the analysis device 300 updates the analysis time t. In this embodiment, in step S411, the analysis device 300 adds the time step Δt to the current analysis time t to set the new analysis time t. Then, the process of step S405 is executed again, and the processes of steps S405 to S409 are executed for the updated analysis time t. In the flowchart shown in FIG. 4, the processes of steps S405 to S411 are an example of the second iterative calculation.

[0134] As a result of the determination in step S410, if the analysis end condition is satisfied (YES in step S410), the process of step S412 is executed. In step S412, the output unit 330 outputs information indicating the physical quantity (magnetic flux density in this embodiment) that determines the value of the magnetization characteristic in the multiple elements and the physical quantity (differential permeability μ′ and magnetic permeability μ in this embodiment) that indicates the relationship between the magnetic flux density and the magnetic field intensity in the multiple elements, which were stored in step S409 at each analysis time t. When the process of step S412 ends, the process according to the flowchart in FIG. 4 ends.

[0135] (Calculation example) Next, a calculation example will be described. In this calculation example, a convergence calculation was performed to obtain the magnetic flux density vector B→ at one analysis time in each of a method using equation (34) as the governing equation (hereinafter referred to as an example of the invention) and a method using equation (6) expressed in a two-dimensional orthogonal coordinate system of x-axis and y-axis as the governing equation (hereinafter referred to as a comparative example). Table 1 shows the conditions of the numerical analysis.

[0136] [Table 1]

[0137] <First calculation example> First, a first calculation example will be described. FIG. 5 is a diagram showing a first example of the initial value of the magnitude ||B→|| of the magnetic flux density vector in a plurality of elements in the analysis target area. The rectangular two-dimensional area shown in FIG. 5 is the analysis target area 500, and the analysis target area 500 is divided into 20×20 lattice-like areas as shown in Table 1, and each of the areas obtained by dividing the analysis target area 500 is the plurality of elements. The initial value of the vector potential A→ in each of the plurality of elements in the analysis target area 500 is set using a random number, and the initial value of the magnetic flux density vector B→ in each of the plurality of elements in the analysis target area 500 is obtained based on the initial value of the vector potential A→. Area 510 shows the correspondence relationship between the magnitude ||B→|| of the magnetic flux density vector and the concentration. The magnitude ||B→|| of the initial value of the magnetic flux density vector in each of the plurality of elements is converted into a concentration according to the correspondence relationship shown in area 510, and is shown in the analysis target area 500 in FIG. 5 as the initial distribution of magnetic flux density.

[0138] For the analysis target area 500 in which the initial distribution of magnetic flux density was set as described above, a vector potential A→ was set as a boundary condition such that the magnetic flux density in the analysis target area would be a uniform magnetic flux density of 1.25 T, and a magnetic flux density vector B→ that satisfies the boundary condition was found by nonlinear convergence calculation using the Newton-Raphson method as shown in Table 1, using each of the methods of the invention example and the comparative example. In the nonlinear convergence calculation, the absolute value ΔB of the difference between the previous value and the current value of the maximum value of the magnetic flux density vector magnitude ||B→|| in multiple elements was calculated. max 10 -5 The convergence condition is that the magnitude of the magnetic flux density vector ||B→|| in the multiple elements is equal to or smaller than T. In the following explanation, the absolute value ΔB max The maximum magnetic flux density difference ΔB max It is also called.

[0139] In the comparative example, in order to prevent the magnetic flux density vector B→ from diverging without converging, the vector potential A→ was multiplied by a relaxation coefficient, thereby changing the obtained vector potential A→ so that the amount of change with respect to the vector potential A→ obtained in the previous convergence calculation was reduced, and the magnetic flux density vector B→ was obtained based on the vector potential A→ after the change, and the magnetic permeability was obtained based on the obtained magnetic flux density vector B→.

[0140] 6A and 6B are diagrams showing a first example of values ​​of the magnitude ||B→|| of the magnetic flux density vector in a plurality of elements in an analysis target area after convergence calculation, where Fig. 6(a) is a diagram of an example of the invention, and Fig. 6(b) is a diagram of a comparative example. As shown in Fig. 6(a), in the example of the invention, the magnetic flux density in the analysis target region 500 was uniformly distributed at about 1.25 T, similar to the comparative example shown in Fig. 6(b). Thus, it can be seen that in the example of the invention, the magnetic flux density vector ||B→|| can be obtained with the same level of accuracy as the already established method.

[0141] Figure 7 shows the maximum magnetic flux density difference ΔB max FIG. 13 is a diagram illustrating a first example of the relationship between the number of convergence calculations and As shown in FIG. 7, the maximum magnetic flux density difference ΔB max It can be seen that the maximum magnetic flux density difference ΔB drops sharply from the third convergence calculation. max 10 -5 It can be seen that the convergence condition is satisfied as a result of the calculation being performed 12 times. In contrast, in the comparative example, although a relaxation coefficient was used to make it easier to satisfy the convergence condition, the convergence condition is not satisfied even after 12 convergence calculations.

[0142] As described above, from the results of the first calculation example, when the soft magnetic material included in the analysis region is not magnetically saturated, it is possible to reduce the number of convergence calculations while maintaining the accuracy of the magnetic flux density distribution, and therefore it is possible to reduce the time required for numerical analysis.

[0143] <Second calculation example> Next, a second calculation example will be described. In the second calculation example, the initial value of the magnitude ||B→|| of the magnetic flux density vector in a plurality of elements in the analysis target area and the boundary conditions are changed from those in the first calculation example.

[0144] FIG. 8 is a diagram showing a second example of the initial values ​​of the magnitude ||B→|| of the magnetic flux density vector in a plurality of elements in the analysis target area. The analysis target area 800 shown in FIG. 8 and the plurality of elements in the analysis target area 800 are the same as the analysis target area 500 and the plurality of elements in the analysis target area 500 shown in FIG. 6. The difference from FIG. 5 and FIG. 8 is only the initial value (concentration) of the magnitude ||B→|| of the magnetic flux density vector in each element. Area 810 shows the correspondence relationship between the magnitude ||B→|| of the magnetic flux density vector and the concentration. The magnitude ||B→|| of the initial value of the magnetic flux density vector in each of the plurality of elements is converted into concentration according to the correspondence relationship shown in area 810, and is shown in the analysis target area 800 of FIG. 8 as the initial distribution of magnetic flux density.

[0145] For the analysis target area 800 in which the initial distribution of magnetic flux density was set as described above, a vector potential A→ was set as a boundary condition such that the magnetic flux density in the analysis target area would be a uniform magnetic flux density of 1.8 T. In each of the methods of the invention example and the comparative example, a magnetic flux density vector B→ that satisfies the boundary condition was found by nonlinear convergence calculation using the Newton-Raphson method as shown in Table 1. The convergence conditions were the same as in the first calculation example (ΔB max <= 10 -5 T). As in the first calculation example, in the second calculation example, the convergence calculation was performed without using a relaxation coefficient in the inventive example, whereas the convergence calculation was performed using a relaxation coefficient in the comparative example.

[0146] 9A and 9B are diagrams showing a second example of values ​​of the magnitude ||B→|| of the magnetic flux density vector in a plurality of elements in the analysis target area after convergence calculation, where Fig. 9(a) is a diagram of an example of the invention, and Fig. 9(b) is a diagram of a comparative example. As shown in Fig. 9(a), in the example of the invention, the magnetic flux density in the analysis target area 800 was uniformly distributed at about 1.8 T, similar to the comparative example shown in Fig. 9(b). Thus, it can be seen that in the example of the invention, even when the soft magnetic material included in the analysis target area is magnetically saturated, the magnetic flux density vector ||B→|| can be obtained with the same level of accuracy as the already established method.

[0147] Figure 10 shows the maximum magnetic flux density difference ΔB max FIG. 13 is a diagram illustrating a second example of the relationship between the number of convergence calculations and As shown in FIG. 10, the maximum magnetic flux density difference ΔB max It can be seen that the maximum magnetic flux density difference ΔB drops sharply from the third convergence calculation onwards. max 10 -5 It can be seen that the convergence condition is satisfied as a result of the convergence calculation being performed 13 times, even though the comparative example uses a relaxation coefficient to make it easier to satisfy the convergence condition.

[0148] As described above, the results of the second calculation example show that even when the soft magnetic material included in the analysis region is magnetically saturated, it is possible to reduce the number of convergence calculations while maintaining the accuracy of the magnetic flux density distribution, thereby reducing the time required for numerical analysis.

[0149] (summary) As described above, in this embodiment, the analysis device 300 obtains the vector potential of the analysis target area for each of a plurality of elements based on physical quantities including a first physical quantity that defines the relationship between the amount of change in the magnitude of the magnetic flux density vector and the amount of change in the magnitude of the magnetic field intensity vector as a scalar quantity, as a physical quantity that indicates the relationship between the magnetic flux density and the magnetic field intensity of the analysis target area. This makes it possible to obtain the relationship between the magnetic flux density and the magnetic field intensity so as to more accurately match the change (gradient) in the magnetization characteristics of the magnetic material included in the analysis target area than when the physical quantity that indicates the relationship between the magnetic flux density and the magnetic field intensity is determined for each component (when defined as a vector quantity). Therefore, it is possible to improve the convergence of the nonlinear convergence calculation in the electromagnetic field analysis, and to increase the analysis speed.

[0150] In this embodiment, the differential permeability (see formula (17)) defined as the value obtained by partially differentiating the magnitude of the magnetic flux density vector with respect to the magnitude of the magnetic field intensity vector, or the differential magnetic reluctance (see formula (18)) defined as the reciprocal of the differential permeability, is used as the first physical quantity that defines the relationship between the amount of change in the magnitude of the magnetic flux density vector and the amount of change in the magnitude of the magnetic field intensity vector as a scalar quantity. Therefore, the gradient of the tangent to the magnetization characteristic of the magnetic body included in the analysis target area can be obtained as the first physical quantity.

[0151] In this embodiment, when analyzing the electromagnetic field in a two-dimensional orthogonal coordinate system consisting of the x-axis and the y-axis, v and v' are expressed as equations (31) and (18), respectively, and the governing equation is expressed as equation (34). Therefore, the relationship between the magnetic flux density and the magnetic field strength in the two-dimensional orthogonal coordinate system can be obtained so as to accurately match the change (gradient) of the magnetization characteristics of the magnetic body included in the analysis target area.

[0152] In this embodiment, when analyzing an electromagnetic field in a three-dimensional orthogonal coordinate system consisting of the x-axis, y-axis, and z-axis, K x , K y , K z The governing equation is expressed by equation (34) where v, v' are equations (38), (39), (40), (31), and (18), respectively. Therefore, the relationship between the magnetic flux density and the magnetic field strength in the three-dimensional orthogonal coordinate system can be obtained so as to accurately match the change (gradient) in the magnetization characteristics of the magnetic material included in the analysis target area.

[0153] In this embodiment, the analysis device 300 acquires an initial value of a physical quantity indicating the relationship between magnetic flux density and magnetic field strength. The analysis device 300 executes a first iterative calculation in which the vector potential of the analysis target area is calculated for each of a plurality of elements based on the acquired initial value of the physical quantity indicating the relationship between magnetic flux density and magnetic field strength, the physical quantity indicating the relationship between magnetic flux density and magnetic field strength is updated based on the calculated vector potential of the analysis target area, and the vector potential of the analysis target area is calculated for each of a plurality of elements based on the updated physical quantity indicating the relationship between magnetic flux density and magnetic field strength, and the first iterative calculation is repeated until a convergence condition is satisfied. Therefore, for example, in the first iterative calculation executed when the accuracy of the vector potential is low in one calculation, the physical quantity indicating the relationship between magnetic flux density and magnetic field strength can be corrected so as to accurately follow the change in the actual magnetization characteristics, and the number of first iterative calculations can be reduced. Therefore, the calculation time of the numerical analysis can be reduced.

[0154] Furthermore, in this embodiment, when the convergence condition is satisfied in the first iterative calculation, the analysis device 300 executes a second iterative calculation in which the time step is updated and the first iterative calculation is executed at the next time, and this is repeated until the analysis end condition is satisfied. Since the number of times of the first iterative calculation can be reduced as described above, the time of the second iterative calculation can also be reduced. Therefore, the time change of the vector potential in multiple elements in the analysis target area can be obtained in a short time.

[0155] In the present embodiment, the analysis device 300 acquires information indicating the relationship between the magnitude of the magnetic flux density vector and the magnitude of the magnetic field strength vector as information indicating the magnetization characteristics of the magnetic body included in the analysis target area, and obtains a physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength based on the magnitude of the magnetic flux density vector or the magnitude of the magnetic field strength vector determined based on the vector potential and the magnetization characteristics. Therefore, the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength can be obtained according to the magnetization characteristics of the magnetic body included in the analysis target area. Therefore, the physical quantity indicating the relationship between the magnetic flux density and the magnetic field strength can be obtained with higher accuracy.

[0156] In this embodiment, the analysis device 300 further uses the magnetic permeability (see formula (30)) defined as the ratio of the magnitude of the magnetic flux density vector to the magnitude of the magnetic field intensity vector, or the magnetic reluctance (see formula (31)) defined as the reciprocal of the magnetic permeability, as a second physical quantity that defines the relationship between the magnitude of the magnetic flux density vector and the magnitude of the magnetic field intensity vector as a scalar quantity, as a physical quantity indicating the relationship between the magnetic flux density and the magnetic field intensity. Therefore, the slope of the line connecting the origin and a point on the magnetization characteristic of the magnetic body included in the analysis target area can be obtained as the second physical quantity, and the second physical quantity can be used in addition to the first physical quantity as a physical quantity indicating the relationship between the magnetic flux density and the magnetic field intensity. Therefore, the vector potential of the analysis target area can be obtained with higher accuracy.

[0157] In the present embodiment, the analysis device 300 obtains an analysis model including information for identifying the plurality of elements as an analysis model of the analysis target region. Therefore, for example, the shape of the analysis target region can be approximated to the plurality of elements according to the intention of the analyst.

[0158] Furthermore, in this embodiment, the analysis device 300 obtains a system of simultaneous equations obtained by discretizing the governing equation for each of a plurality of elements, and calculates the vector potential by solving the obtained system of simultaneous equations. Therefore, for example, a system of simultaneous equations according to the number of dimensions of the electromagnetic field to be analyzed, the coordinate system, the solution method, etc. can be obtained to obtain the vector potential.

[0159] In this embodiment, the analysis device 300 obtains at least one of a magnetic flux density vector and a magnetic field strength vector based on the vector potential, and therefore can quantify the magnetic flux density and magnetic field strength of the analysis target region for each of a plurality of elements.

[0160] Moreover, in this embodiment, the analysis device 300 determines the vector potential A→. Therefore, the vector potential A→ can be determined based on the A method or the A-φ method, which are considered to have superior convergence of nonlinear iteration compared to the T-Ω method.

[0161] In this embodiment, the analysis device 300 analyzes electromagnetic fields in two or more dimensions. Therefore, the analysis target area is a plane or space, and the vector potential in the plane or space can be obtained for each of a plurality of elements. Therefore, the magnetic properties of the analysis target area can be obtained in more detail.

[0162] (Modification) In this embodiment, the magnetic flux density vector B→ is calculated as a physical quantity that determines the value of the magnetization characteristic. However, this is not necessarily required. For example, the magnetic field strength vector H→ may be calculated in addition to or instead of the magnetic flux density vector B→ as a physical quantity that determines the value of the magnetization characteristic. In this case, the physical quantity (differential permeability μ' and permeability μ in this embodiment) that indicates the relationship between the magnetic flux density and the magnetic field strength may be calculated based on the magnetic field strength vector H→ and the magnetization characteristic. In addition, the abnormal eddy current loss of the soft magnetic material included in the analysis target area may be calculated based on the magnetic flux density vector B→. In addition, the hysteresis loss of the soft magnetic material included in the analysis target area may be calculated based on the magnetic field strength vector H→.

[0163] In addition, in the present embodiment, the case where two-dimensional and three-dimensional electromagnetic fields are analyzed has been exemplified, but this is not necessarily required. For example, a one-dimensional electromagnetic field may be analyzed.

[0164] Furthermore, performing the first iterative calculation (convergence calculation) as in this embodiment is preferable because it allows the vector potential (and the magnetic properties calculated based on the vector potential) to be calculated with higher accuracy. However, it is not always necessary to perform the first iterative calculation. For example, when the magnetic flux density in the analysis target region is low, it may be possible to calculate the vector potential with a certain degree of accuracy without performing the first iterative calculation, so it is not always necessary to perform the first iterative calculation. Furthermore, when calculating the vector potential at one analysis time t, it is not necessary to perform the second iterative calculation for calculating the vector potential at each analysis time t for each time step Δt.

[0165] The above-described embodiment of the present invention can be realized by a computer executing a program. A computer-readable recording medium having the program recorded thereon and a computer program product such as the program can also be applied as an embodiment of the present invention. Examples of the recording medium that can be used include a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, and a ROM. The embodiment of the present invention can be realized by a PLC (Programmable Logic Controller) or dedicated hardware such as an ASIC (Application Specific Integrated Circuit). Furthermore, the above-described embodiments of the present invention are merely examples of the implementation of the present invention, and the technical scope of the present invention should not be interpreted as being limited by these. In other words, the present invention can be implemented in various forms without departing from its technical concept or main features. [Explanation of symbols]

[0166] 100 Magnetization properties 110 Straight line passing through the origin of the magnetic properties 120 Tangent of magnetic properties 130 Points on the magnetization characteristic corresponding to magnetic flux density 300 Analysis equipment 310 Acquisition Department 311 Analysis Model Acquisition Section 312 Magnetization characteristic acquisition section 313 Equation acquisition part 314 Initial value acquisition section 320 Numerical Analysis Department 330 Output section 340 Computer Display 500 Analysis area in the first calculation example 510 Region showing the correspondence between magnetic flux density and concentration 800 Analysis area in the second calculation example 810 Region showing the correspondence between magnetic flux density and concentration B magnetic flux density H Magnetic field strength ||B→|| Magnitude of magnetic flux density vector B t → Magnetic flux density vector at analysis time t B t+Δt → Magnetic flux density vector at analysis time t+Δt H t → Magnetic field strength vector at analysis time t H t+Δt → Magnetic field strength vector at analysis time t+Δt ΔB x Time change in the x-component of the magnetic flux density vector ΔH x Time change of the x-component of the magnetic field strength vector θ x Angle between the magnetic flux density vector and the x-axis ΔB max Maximum magnetic flux density difference

Claims

1. An analysis device for performing electromagnetic field analysis, a numerical analysis unit that calculates a magnetic vector potential for each of a plurality of elements constituting an analysis target region based on a governing equation of an electromagnetic field including a physical quantity that indicates a relationship between a magnetic flux density and a magnetic field strength in the analysis target region, The physical quantities include a first physical quantity that defines, as a scalar quantity, a relationship between an amount of change in magnitude of a magnetic flux density vector and an amount of change in magnitude of a magnetic field strength vector.

2. 2. The analysis device according to claim 1, wherein the first physical quantity is a differential permeability defined as a value obtained by partially differentiating a magnitude of the magnetic flux density vector with respect to a magnitude of the magnetic field strength vector, or a differential magnetic reluctance defined as the inverse of the differential permeability.

3. the electromagnetic field being an electromagnetic field in a two-dimensional orthogonal coordinate system consisting of an x-axis and a y-axis; 3. The analysis device according to claim 1, wherein the governing equation is expressed by the following equation (A) where v and v' are the following equations (B) and (C), respectively. [0010]

4. the electromagnetic field is an electromagnetic field in a three-dimensional orthogonal coordinate system having an x-axis, a y-axis, and a z-axis; The governing equation is K x , K y , K z 3. The analysis device according to claim 1, wherein v, v' are expressed by the following formula (E), (F), (G), (H), and (I), respectively, and the analysis device is expressed by the following formula (D). [0025]

5. An initial value acquisition unit that acquires an initial value of the physical quantity, The analysis device according to any one of claims 1 to 4, wherein the numerical analysis unit executes a first iterative calculation in which a magnetic vector potential of the analysis target area is calculated for each of the plurality of elements based on an initial value of the physical quantity acquired by the initial value acquisition unit, the physical quantity is updated based on the calculated magnetic vector potential of the analysis target area, and the magnetic vector potential of the analysis target area is calculated for each of the plurality of elements based on the updated physical quantity, and the first iterative calculation is repeated until a convergence condition is satisfied.

6. 6. The analysis device according to claim 5, wherein when the convergence condition is satisfied, the numerical analysis unit updates a time step and executes the first iterative calculation at a next analysis time, repeating this process until an analysis end condition is satisfied, thereby executing a second iterative calculation to determine a magnetic vector potential of the analysis target region at each analysis time for each time step for each of the multiple elements.

7. a magnetic property acquisition unit for acquiring information indicating magnetic properties of a magnetic body included in the analysis target area, The magnetization characteristic is a relationship between the magnitude of a magnetic flux density vector and the magnitude of a magnetic field strength vector, The analysis device according to any one of claims 1 to 6, wherein the numerical analysis unit determines the physical quantity based on a magnitude of a magnetic flux density vector or a magnitude of a magnetic field strength vector determined based on the magnetic vector potential and the magnetization characteristics.

8. The analysis device according to any one of claims 1 to 7, wherein the physical quantity further includes a second physical quantity that defines the relationship between the magnitude of the magnetic flux density vector and the magnitude of the magnetic field strength vector as a scalar quantity, the second physical quantity being a permeability defined as the ratio of the magnitude of the magnetic flux density vector to the magnitude of the magnetic field strength vector, or a magnetic reluctance defined as the reciprocal of the permeability.

9. An analysis method for performing an electromagnetic field analysis, comprising the steps of: The analysis device includes a numerical analysis step of determining a magnetic vector potential for each of a plurality of elements constituting an analysis target region based on a governing equation of an electromagnetic field including a physical quantity indicating a relationship between a magnetic flux density and a magnetic field intensity in the analysis target region, The analysis method, wherein the physical quantity includes a first physical quantity that defines, as a scalar quantity, a relationship between an amount of change in magnitude of a magnetic flux density vector and an amount of change in magnitude of a magnetic field strength vector.

10. A program for causing a computer to function as each part of the analysis device according to any one of claims 1 to 8.

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