JP7563411B2 - Apparatus for determining elasticity matrix of laminated iron core, method for determining elasticity matrix of laminated iron core, and computer program - Google Patents

Description

The present invention relates to an elasticity matrix determination device for a laminated iron core, an elasticity matrix determination method for a laminated iron core, and a computer program that determine the elasticity matrix in a constitutive equation that indicates the relationship between stress and strain in the elastic deformation of the iron core to be applied when performing vibration analysis of a laminated iron core.

Transformers such as power distribution transformers are constructed by winding a coil around a laminated core made of laminated electromagnetic steel sheets. Important performance characteristics of a transformer include iron loss (no-load loss), excitation current characteristics, and noise characteristics.
Distribution transformers are installed in various locations, but there is a strong demand for low noise levels, especially for transformers installed in urban areas. In recent years, noise characteristics have become increasingly important, due to considerations of the surrounding environment in which the transformers are installed.

Grain-oriented electromagnetic steel sheets are often used as the iron core material for transformers. Grain-oriented electromagnetic steel sheets undergo material expansion and contraction due to excitation, a phenomenon known as magnetostriction, and this magnetostrictive vibration due to excitation is said to be the main cause of transformer noise. For this reason, it is said that the noise performance of a transformer is highly dependent on the magnetostrictive performance of the electromagnetic steel sheets used, and when manufacturing low-noise transformers, electromagnetic steel sheets with low magnetostrictive properties are used as the iron core material.

However, even when magnetic steel sheets with excellent magnetostrictive performance are actually used to manufacture the core, there are often cases where the transformer does not achieve sufficient low-noise characteristics. When investigating the cause of this, it is often found to be due to a resonance phenomenon between the natural frequency of the transformer core and the magnetostrictive vibration of the magnetic steel sheet. For this reason, it is extremely important in designing and manufacturing transformers to calculate and predict mechanical vibration characteristics, including the natural frequency of the transformer core.

Therefore, an analysis device and analysis method have been proposed that calculates each node of a finite element according to the magnetic flux density applied to an electromagnetic component, or a nodal force equivalent to the distortion of each finite element, based on a numerical analysis model that represents an electromagnetic component containing a magnetic body that generates magnetostriction as a combination of multiple finite elements in finite element analysis (see, for example, Patent Document 1).

Japanese Patent Application Publication No. 2014-71689

However, in the prior art described in the above Patent Document 1, quasi-static structural analysis is performed using a governing equation for structural analysis that is composed of an equation of balance, a constitutive equation showing the relationship between stress and strain, and an equation for the relationship between displacement and strain.
Among these, the constitutive equation showing the relationship between the stress tensor {σ} and the strain tensor {ε} is
{σ} = {D}{ε} (where { } denotes a tensor)
It is represented as:
Here, {D} is a tensor that expresses the relationship between strain and stress. When expressed as components, it becomes equation (1).

Generally, {D} has 81 components, while {σ} and {ε} each have 9 components. Here, the tensor as a physical quantity is a symmetric tensor, so {σ} and {ε} each have 6 independent components. Therefore, the constitutive formula is [σ] = [D][ε] ([ ] indicates that it is a matrix. [D] is called the elastic matrix.)
When expressed as a matrix and expressed in components, it becomes equation (2).

The relationship between the normal stress σ _i and the normal strain ε _i and the relationship between the shear stress τ _ij and the shear strain γ _ij are expressed using the elasticity matrix [D].
However, the above-mentioned prior art does not disclose any description of how to set the elasticity matrix [D], nor does it disclose how to determine the elasticity matrix [D]. However, in general, the elasticity coefficient of the member itself, such as an electromagnetic steel sheet, constituting the electromagnetic component to be subjected to the structural analysis is often applied as it is.

In such cases, it is known that when the mechanical vibration calculation results of the electromagnetic component that is the subject of structural analysis are compared with the results of actually measuring the mechanical vibration, there is a large discrepancy between the calculated values and the actual measured values. For this reason, it has generally been considered difficult to use structural analysis using a structural analysis program for the design of electromagnetic components, which are laminated structures made by stacking steel plates.

Here, since the cores of transformers used in transformers such as power distribution transformers are also laminated structures made up of stacked steel plates, it has been difficult to predict noise using structural analysis with a structural analysis program. As a result, problems such as the loud noise of the actually manufactured transformers can arise, resulting in extra costs for soundproofing measures such as soundproofing walls. In such cases, if the noise of the transformer could be reduced by changing the design of the transformer core, the extra cost increase could be suppressed, but it is not clear how to make design changes to reduce noise. For this reason, there is a problem that design changes cannot be made easily. There is a strong demand for the ability to predict noise using structural analysis with a structural analysis program so that design changes can be made.

When comparing the results of mechanical vibration calculations of a transformer core that is the subject of structural analysis with the results of actual measurement of mechanical vibration, a large discrepancy occurs between the calculated values and the actual measured values. This is thought to be because the transformer core is a laminated structure formed by stacking steel plates, and although the elastic matrix [D] of the laminated structure is inherently different from the elastic matrix [D] of the components themselves, such as the electromagnetic steel plates, that make up the laminated core of the transformer, there is no good method for determining the elastic matrix [D] of the laminated structure, and therefore the structural analysis is carried out by directly using the value of the elastic matrix [D] of the components themselves, such as the electromagnetic steel plates.
In particular, when performing vibration analysis of a laminated core made of laminated steel plates using a constitutive equation that expresses the relationship between stress and strain in a matrix, a method for determining the transverse elastic modulus in two planes including the lamination direction of a laminated core of a transformer, which is included in the above-mentioned elastic matrix [D] in the constitutive equation, has not been established.

The present invention has been made with a focus on the problems of the prior art described above, and its purpose is to provide an elasticity matrix determination device, elasticity matrix determination method, and computer program for a laminated core that can optimally determine the transverse elastic modulus in two planes, including the lamination direction, of the first and second parts of the laminated core, contained in the elasticity matrix in the constitutive equation, when performing vibration analysis of a laminated core made of stacked steel plates using a constitutive equation that expresses the relationship between stress and strain in a matrix format.

In order to solve the above problems, an elasticity matrix determination device for a laminated core according to one aspect of the present invention is a laminated core elasticity matrix determination device that, when performing vibration analysis of a laminated core using a constitutive equation that expresses the relationship between stress and strain in a matrix representation, determines transverse elasticity coefficients in two planes including the lamination direction of the first and second parts of the laminated core, which are included in the elasticity matrix in the constitutive equation, and includes an excitation noise spectrum acquisition unit that acquires a frequency spectrum of the excitation noise of the laminated core obtained by measuring the excitation noise of the laminated core to be subjected to vibration analysis for each of a plurality of excitation magnetic flux densities, an excitation magnetostriction spectrum acquisition unit that acquires a frequency spectrum of the excitation magnetostriction of the steel plate obtained by measuring the excitation magnetostriction of the same steel plate as the steel plate constituting the laminated core for each of a plurality of excitation magnetic flux densities having the same excitation magnetic flux densities as the plurality of excitation magnetic flux densities, the frequency spectrum of the excitation noise for each of the plurality of excitation magnetic flux densities acquired by the excitation noise spectrum acquisition unit, a differential spectrum calculation unit which calculates a differential spectrum with respect to the frequency spectrum of excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired by the excitation magnetostriction spectrum acquisition unit; an average spectrum calculation unit which calculates an average spectrum of the differential spectrum for each of the plurality of excitation magnetic flux densities calculated by the differential spectrum calculation unit; a selection unit which selects, according to a degree of agreement between the differential spectrum for each of the plurality of excitation magnetic flux densities calculated by the differential spectrum calculation unit and the average spectrum calculated by the average spectrum calculation unit, a frequency spectrum of excitation noise at a specific excitation magnetic flux density to be adopted for analysis from among the frequency spectra of the excitation noise for each of the plurality of excitation magnetic flux densities acquired by the excitation noise spectrum acquisition unit, and a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density to be adopted for analysis from among the frequency spectra of the excitation noise for each of the plurality of excitation magnetic flux densities acquired by the excitation magnetostriction spectrum acquisition unit; and a selection unit which selects, according to a degree of agreement between the differential spectrum for each of the plurality of excitation magnetic flux densities calculated by the differential spectrum calculation unit and the average spectrum calculated by the average spectrum calculation unit, a specific value (G a vibration response function spectrum calculation unit that applies a specific value (G ₁ , G ₂ ) to the elastic matrix to perform a vibration response analysis and obtains a frequency spectrum of a vibration response function of the laminated iron core for the combination of specific values (G ₁ , G ₂ ); an excitation vibration spectrum calculation unit that calculates a frequency spectrum of an excitation vibration of the laminated iron core from the frequency spectrum of excitation magnetostriction of the steel sheet at the specific excitation magnetic flux density selected by the selection unit and the frequency spectrum of the vibration response function of the laminated iron core calculated by the vibration response function spectrum calculation unit; a coincidence calculation unit that calculates a coincidence between the _frequency spectrum of excitation noise of the laminated iron core at the specific excitation magnetic flux density selected by the _selection unit and the _frequency spectrum of the excitation vibration of the laminated iron core calculated by the excitation vibration spectrum calculation unit _; a degree of agreement determination unit that changes the combination of the values of each of the specific values ( _{G1, G2) and repeats the processes of the vibration response function spectrum calculation unit, the excitation vibration spectrum calculation unit, and the degree of agreement calculation unit, for each combination of specific values (G1} , _G2 ) that exist the same number of times as the number of repetitions, and determines a degree of agreement between the frequency spectrum of the excitation noise of the laminated iron core at the specific excitation magnetic flux density selected by the selection unit and the _frequency spectrum of the excitation vibration of the laminated iron core calculated by the excitation vibration spectrum calculation unit; and a transverse elasticity coefficient determination unit that detects the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined by the degree of agreement determination unit, and adopts the combination of specific values (G1, _G2 ) with which the degree of agreement is maximum as the value of the transverse elasticity coefficient in two planes including the lamination direction of the laminated iron core of the first portion and the second portion.

A method for determining an elastic matrix of a laminated core according to another aspect of the present invention is a method for determining an elastic matrix of a laminated core, the method comprising the steps of: performing vibration analysis of a laminated core using a constitutive equation that expresses the relationship between stress and strain in a matrix; the laminated core is formed by stacking a plurality of steel plates and has at least a first portion and a second portion; and determining transverse elastic moduli in two planes including the lamination direction of the first portion and the second portion of the laminated core, which are included in the elastic matrix of the constitutive equation; the method includes an excitation noise spectrum acquisition step of acquiring a frequency spectrum of the excitation noise of the laminated core obtained by measuring the excitation noise of the laminated core to be subjected to vibration analysis for each of a plurality of excitation magnetic flux densities; an excitation magnetostriction spectrum acquisition step of acquiring a frequency spectrum of the excitation magnetostriction of the steel plate obtained by measuring the excitation magnetostriction of the same steel plate as the steel plate constituting the laminated core for each of a plurality of excitation magnetic flux densities having the same excitation magnetic flux densities as the plurality of excitation magnetic flux densities; and a difference spectrum calculation step of calculating a difference spectrum with the frequency spectrum of excitation magnetostriction for each of the plurality of excitation magnetic flux densities obtained in the difference spectrum calculation step; an average spectrum calculation step of calculating an average spectrum of the difference spectrum for each of the plurality of excitation magnetic flux densities calculated in the difference spectrum calculation step; a selection step of selecting a frequency spectrum of excitation noise at a specific excitation magnetic flux density to be used in the analysis from among the frequency spectra of excitation noise for each of the plurality of excitation magnetic flux densities obtained in the excitation noise spectrum acquisition step, and a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density to be used in the analysis from among the frequency spectra of excitation magnetostriction for each of the plurality of excitation magnetic flux densities obtained in the excitation magnetostriction spectrum acquisition step, depending on a degree of agreement between the difference spectrum for each of the plurality of excitation magnetic flux densities calculated in the difference spectrum calculation step and the average spectrum calculated in the average spectrum calculation step; and a selection step of selecting a specific value (G a vibration response function spectrum calculation step of calculating a frequency spectrum of the vibration response function of the laminated iron core for a combination of specific values (G ₁ , G ₂ ) and determining a frequency spectrum of the vibration response function of the laminated iron core for the combination of specific values (G ₁ , G ₂ ); an excitation vibration spectrum calculation step of calculating a frequency spectrum of the excitation vibration of the laminated iron core from the frequency spectrum of the excitation magnetostriction of the steel sheet at the specific excitation magnetic flux density selected in the selection step and the frequency spectrum of the vibration response function of the laminated iron core calculated in the vibration response function spectrum calculation step; a coincidence calculation step of determining a coincidence between the _{frequency spectrum} of the excitation noise of the laminated iron core at the specific excitation magnetic flux density selected in the selection _step and the frequency spectrum of the excitation vibration of the laminated iron core calculated in the excitation vibration spectrum calculation step _; the vibration response function spectrum calculation step, the excitation vibration spectrum calculation step, and the degree of agreement calculation step are repeated, and for each combination of specific values ( _G1 , _G2 ) that exist the same number of times as the number of repetitions, a degree of agreement is determined between the frequency spectrum of the excitation noise of the laminated iron core at the specific excitation magnetic flux density selected in the selection step and the frequency spectrum of the excitation vibration of the laminated iron core calculated in the excitation vibration spectrum calculation step; and a transverse elasticity determination step of detecting the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined in the degree of agreement determination step, and adopting the combination of specific values ( _G1 , _G2 ) that provides the maximum degree of agreement as the value of the transverse elasticity coefficient in two planes including the lamination direction of the laminated iron core of the first portion and the second portion.

Further, a computer program according to another aspect of the present invention is a computer program for performing vibration analysis of a laminated core using a constitutive equation that expresses the relationship between stress and strain in a matrix representation, the laminated core being formed by stacking a plurality of steel plates and having at least a first portion and a second portion, and causing a computer to calculate transverse elastic moduli in two planes including the lamination directions of the first portion and the second portion of the laminated core, which are included in an elastic matrix in the constitutive equation, the computer including: an excitation noise spectrum acquisition step of acquiring a frequency spectrum of the excitation noise of the laminated core obtained by measuring the excitation noise of the laminated core to be subjected to vibration analysis for each of a plurality of excitation magnetic flux densities; an excitation magnetostriction spectrum acquisition step of acquiring a frequency spectrum of the excitation magnetostriction of the steel plate obtained by measuring the excitation magnetostriction of the same steel plate as the steel plate constituting the laminated core for each of a plurality of excitation magnetic flux densities having the same excitation magnetic flux densities as the plurality of excitation magnetic flux densities; and a frequency spectrum of the excitation noise for each of the plurality of excitation magnetic flux densities acquired in the excitation noise spectrum acquisition step. a difference spectrum calculation step of calculating a difference spectrum between the frequency spectrum of excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired in the difference spectrum calculation step and the frequency spectrum of excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired in the difference spectrum calculation step; an average spectrum calculation step of calculating an average spectrum of the difference spectrum for each of the plurality of excitation magnetic flux densities calculated in the difference spectrum calculation step; a selection step of selecting a frequency spectrum of excitation noise at a specific excitation magnetic flux density to be used in analysis from among the frequency spectrum of excitation noise for each of the plurality of excitation magnetic flux densities acquired in the excitation noise spectrum acquisition step, and a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density to be used in analysis from among the frequency spectrum of excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired in the excitation magnetostriction spectrum acquisition step; and a selection step of selecting specific values (G a vibration response function spectrum calculation step of calculating a frequency spectrum of the vibration response function of the laminated iron core for a combination of specific values (G ₁ , G ₂ ) and determining a frequency spectrum of the vibration response function of the laminated iron core for the combination of specific values (G ₁ , G ₂ ); an excitation vibration spectrum calculation step of calculating a frequency spectrum of the excitation vibration of the laminated iron core from the frequency spectrum of the excitation magnetostriction of the steel sheet at the specific excitation magnetic flux density selected in the selection step and the frequency spectrum of the vibration response function of the laminated iron core calculated in the vibration response function spectrum calculation step; a coincidence calculation step of determining a coincidence between the _{frequency spectrum} of the excitation noise of the laminated iron core at the specific excitation magnetic flux density selected in the selection _step and the frequency spectrum of the excitation vibration of the laminated iron core calculated in the excitation vibration spectrum calculation step _; the combination of the values of _G1 , G2 is changed, and the processes of the vibration response function spectrum calculation step, the excitation vibration spectrum calculation step, and the degree of agreement calculation step are repeated, and for each combination of specific values (G1, _G2 ) that exist the same number of times as the number of repetitions, a degree of agreement is determined between the frequency spectrum of the excitation noise of the laminated iron core at the specific excitation magnetic flux density selected in the selection step and the frequency spectrum of the excitation vibration of the laminated iron core calculated in the excitation vibration spectrum calculation step; and a transverse elasticity coefficient determination step of detecting the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined in the degree of agreement determination step, and adopting the combination of specific values ( _G1 , _G2 ) with which the degree of agreement is maximum as the value of the transverse elasticity coefficient in two planes including the lamination direction of the laminated iron core of the first portion and the second portion.

The elasticity matrix determination device, elasticity matrix determination method, and computer program of the present invention for a laminated iron core can provide an elasticity matrix determination device, elasticity matrix determination method, and computer program for a laminated iron core that can optimally determine the transverse elastic modulus in two planes including the lamination direction of the first and second parts of the laminated iron core contained in the elastic matrix in the constitutive equation when performing vibration analysis of a laminated iron core made of laminated steel plates using a constitutive equation that expresses the relationship between stress and strain in a matrix representation.

1 is a configuration diagram showing an elasticity matrix determination device for a laminated core according to an embodiment of the present invention; FIG. 2 is a perspective view showing a three-phase, three-limbed transformer core. FIG. 1 is a diagram illustrating normal stress and shear stress. FIG. 2 is a functional block diagram of an elasticity matrix determination device for a laminated core shown in FIG. 1 . 5 is a flowchart for explaining a process flow in the elasticity matrix determination device for a laminated core shown in FIG. 4 . Graph (a) shows a frequency spectrum of the excitation noise of a laminated core obtained by measuring the excitation noise of the laminated core that is the subject of vibration analysis for each of a plurality of excitation magnetic flux densities (1.5T to 1.9T) in an embodiment; graph (b) shows a frequency spectrum of the excitation magnetostriction (acceleration) of an electromagnetic steel sheet obtained by measuring the excitation magnetostriction of the same electromagnetic steel sheet as the electromagnetic steel sheet that constitutes the laminated core for each of a plurality of excitation magnetic flux densities (1.5T to 1.9T); and graph (c) shows a differential spectrum between the frequency spectrum of the excitation noise for each of a plurality of excitation magnetic flux densities (1.5T to 1.9T) and the frequency spectrum of the excitation magnetostriction for each of the plurality of excitation magnetic flux densities (1.5T to 1.9T). 1 is a graph showing an example of a frequency spectrum of excitation noise at a specific excitation magnetic flux density (1.6 T) used in the analysis in the examples. 1 is a graph showing an example of a frequency spectrum of magnetostriction at a specific excitation magnetic flux density (1.6 T) used in the analysis in the examples. 13 is a graph showing a frequency spectrum of a vibration response function of a laminated core when a vibration response analysis is performed by applying to an elastic matrix a transverse elastic modulus Gyz=Gzx= _G1 of 0.2 GPa in two planes including the stacking direction of a first portion consisting of an upper yoke and a lower yoke, and a transverse elastic modulus Gyz=Gzx= _G2 of 0.1 GPa in two planes including the stacking direction of a second portion consisting of legs in an embodiment. 13 is a graph showing a frequency spectrum of excitation vibration of a laminated core calculated by an excitation vibration spectrum calculation unit in an embodiment when the transverse elastic modulus Gyz=Gzx= _G1 in two planes including the stacking direction of a first portion consisting of an upper yoke and a lower yoke is 0.2 GPa, and the transverse elastic modulus Gyz=Gzx= _G2 in two planes including the stacking direction of a second portion consisting of legs is 0.1 GPa. FIG. ₁ is a two-dimensional map showing the degree of agreement between the frequency spectrum of the excitation noise of a laminated core at a specific excitation magnetic flux density (1.6 T) _and the frequency spectrum of the excitation vibration of the laminated core, determined for each combination of specific values (G1, G2) that exist the same number of times as the number of repetitions in an embodiment. 11 is a graph showing calculated values of the frequency spectrum of excitation vibration of a laminated iron core and actual measured values of the frequency spectrum of excitation noise obtained by measuring the excitation noise of a laminated iron core in an example. 10 is a flowchart for explaining a process flow in an elasticity matrix determination device for a laminated core according to a reference example. 10 is a graph showing an example of a frequency spectrum of excitation noise obtained by measuring excitation noise of a laminated core that is a target of vibration analysis in a reference example. 11 is a graph showing an example of a frequency spectrum of excitation magnetostriction of an electromagnetic steel sheet that is the same as the electromagnetic steel sheet that constitutes the laminated core that is the subject of vibration analysis in a reference example. This is a graph showing an example of a frequency spectrum of the vibration response function of a laminated core for a combination of specific values ( _G1 , _G2) when a vibration response analysis is performed by applying the transverse elastic moduli Gzx, Gyz in two planes including the stacking direction of the upper yoke 22a and the lower yoke 22b that constitute the laminated core 21 in a reference example and the transverse elastic moduli Gzx, Gyz in two planes including the stacking direction of the leg portion 22c as combinations of specific values _G1 , _G2 selected from a predetermined range to an elastic matrix. 11 is a graph showing an example of a frequency spectrum of excitation vibration of a laminated core calculated from a frequency spectrum of excitation magnetostriction of an electromagnetic steel sheet and a frequency spectrum of a vibration response function of the laminated core in a reference example. FIG _{. 1} is an example of a two- _dimensional map showing the degree of correspondence between the frequency spectrum of excitation noise of a laminated iron core and the frequency spectrum of excitation vibration of the laminated iron core, determined for each combination of specific values (G1, G2) that exist the same number of times as the number of repetitions in a reference example.

Below, an embodiment of the method for determining the elastic matrix of a laminated iron core and the method for analyzing vibration of a laminated iron core according to the present invention will be described with reference to the drawings. Note that each drawing is schematic and may differ from the actual product. Furthermore, the following embodiment illustrates an apparatus and method for embodying the technical idea of the present invention, and does not specify the configuration as described below. In other words, the technical idea of the present invention can be modified in various ways within the technical scope described in the claims.

FIG. 1 shows an elastic matrix determination device for a laminated core according to an embodiment of the present invention.
1 is a computer configured with an arithmetic processing device 12 having a CPU 11. To the CPU 11, an internal storage device 14 such as a RAM and a ROM, an external storage device 15, an input device 16 such as a keyboard and a mouse, and an output device 17 that outputs image data to a display are connected via an internal bus 13.

The external storage device 15 is configured to include a disk drive capable of reading data from a hard disk drive, solid state drive, etc., and a drive device for reading data from a recording medium, such as a CD, DVD, or BD. A recording medium 18 storing a computer program is set in the external storage device 15, and the read computer program is installed in the disk drive. Note that the installation of the computer program is not limited to using the recording medium 18, and the computer program may also be downloaded via a network.

The CPU 11 performs vibration analysis (including determination of elasticity matrix) using the finite element method with the analysis input data input in accordance with the instructions of the installed computer program, and outputs and displays the analysis results on a display from the output device 17. The analysis results can be printed out by a printer or transmitted via a network, without being limited to being displayed on a display.
The laminated core 21 to be analyzed in this embodiment is a laminated core for a three-phase, three-limbed transformer used, for example, as a distribution transformer, and as shown in Figure 2, is made up of, for example, 333 layers of 0.3 mm-thick directional electromagnetic steel sheets 22, each having three legs 22c connected between an upper yoke 22a and a lower yoke 22b, and fixed in place by wrapping glass tape around them.

For example, the upper yoke 22a and the lower yoke 22b are each set to a width of 100 mm and a length of 500 mm. The three legs 22c are each set to a width of 100 mm and a length of 300 mm, and are connected to the upper yoke 22a and the lower yoke 22b at intervals of 100 mm.
The laminated core 21 to be analyzed in this embodiment is an example of a laminated core for a three-phase three-limbed transformer shown in Figure 2, and the thickness of the directional electromagnetic steel sheet 22, the number of laminated sheets of the directional electromagnetic steel sheet 22, the dimensions of the upper yoke 22a and the lower yoke 22b, the dimensions of the three legs 22c, etc. are not limited to the example described above.

When performing a vibration numerical analysis of the laminated core 21 of such a three-phase three-limbed transformer, a constitutive equation that shows the relationship between stress and strain, which is the governing equation for elastic structural analysis, is used.
This constitutive formula is expressed as the following formula (3) when the laminated material is replaced with an equivalent homogeneous material and the influence of the laminated material is expressed in terms of the matrix properties.
[σ] = [C] [ε] ... (3)
Here, [σ] is the stress matrix, [C] is the elasticity matrix (stiffness matrix) corresponding to the response function indicating the ratio of input to output when considering strain as the input and stress as the output, and [ε] is the strain matrix.

Here, if the lamination direction of the steel plates is the Z direction, one of the two-dimensional planes perpendicular to the Z direction is the X direction, and the other is the Y direction, then the stress matrix [σ], as shown in FIG. 3, has vertical components represented by a vertical stress σx in the X direction, a vertical stress σy in the Y direction, and a vertical stress σz in the Z direction, and has shear components represented by a shear stress τzx in the ZX plane, a shear stress τyz in the YZ plane, and a shear stress τxy in the XY plane.
Similarly, the strain matrix [ε] has vertical components represented by the vertical strain εx in the X direction, the vertical strain εy in the Y direction, and the vertical strain εz in the Z direction, and has shear components represented by the shear strain γzx in the ZX plane, the shear strain γyz in the YZ plane, and the shear strain γxy in the XY plane.
The elasticity matrix [C] is expressed by 36 elastic coefficients C _ij (i=1 to 6, j=1 to 6).
When these are expressed in a matrix, the following formula (4) is obtained.

Since laminated cores are manufactured by stacking grain-oriented electromagnetic steel sheets, they have 180-degree symmetry around the stacking direction as an axis, as well as 180-degree symmetry in the longitudinal direction of the laminated steel sheets and in the direction perpendicular to that direction. As a result, they are classified as orthogonal anisotropic.
For this reason, an object having orthogonal anisotropy can basically be expressed by a total of nine elastic coefficients, C ₁₁ , C ₁₂ , C ₁₃ , C ₂₂ , C ₂₃ , C ₃₃ , C ₄₄ , C ₅₅ and C _{66, as shown in the following formula (5)} .

Of these, the elastic moduli _C11 , _C12 , _C13 , _C22 , _C23 , and _C33 can be calculated from the longitudinal elastic moduli Ex, Ey, and Ez and the Poisson's ratios vxy, vyx, vyz, vzy, vzx, and vxz using equations (6) to (12). As shown in equations (13) to (15), the elastic modulus _C44 is the transverse elastic modulus Gyz in the YZ plane, the elastic modulus _C55 is the transverse elastic modulus Gzx in the ZX plane, and the elastic modulus _C66 is the transverse elastic modulus Gxy in the XY plane.

Here, Ex is the X-direction elastic modulus (Young's modulus), Ey is the Y-direction elastic modulus (Young's modulus), Ez is the Z-direction elastic modulus (Young's modulus), νxy is the Poisson's ratio of the XY plane (the ratio of the longitudinal strain in the X direction to the lateral strain in the Y direction), νyx is the Poisson's ratio of the YX plane, νyz is the Poisson's ratio of the YZ plane, νzy is the Poisson's ratio of the ZY plane, νzx is the Poisson's ratio of the ZX plane, and νxz is the Poisson's ratio of the XZ plane.
Here, the relationship between the Young's modulus and the Poisson's ratio is expressed by the following equation (16), which is called the reciprocity theorem.

For this reason, the Poisson's ratio vyx in the YX plane can be expressed using Ex, Ey, and vxy, the Poisson's ratio vzy in the ZY plane can be expressed using Ez, Ey, and vyz, and the Poisson's ratio vxz in the XZ plane can be expressed using Ez, Ex, and vzx.
In this way, _the values of the nine elastic coefficients _C11 , _C12 , _C13 , C22, _C23 , _C33 , _C44 , _C55 and _C66 that represent the elastic matrix of an object having orthogonal anisotropy can be expressed using a total of nine mechanical property values, namely, the longitudinal elastic modulus Ex, Ey, Ez, the transverse elastic modulus Gyz, Gzx, Gxy and the Poisson's ratios νxy, νyz, νzx, so that determining these nine mechanical property values is equivalent to determining the nine elastic coefficients that represent the elastic matrix. Therefore, the following describes how to determine the longitudinal elastic modulus, the transverse elastic modulus and the Poisson's ratio.

First, for the longitudinal elastic modulus of the laminated core having orthogonal anisotropy, the longitudinal elastic modulus Ex and Ey can be set equal to the longitudinal elastic modulus Ex0 and Ey0 of one steel plate. However, the longitudinal elastic modulus Ez cannot be set approximately equal to the longitudinal elastic modulus Ez0 of one steel plate. This is because there is a small gap between the laminated steel plates. In this embodiment, an experiment was conducted to determine the longitudinal elastic modulus Ez from the relationship between the load and displacement in the lamination direction of the laminated steel plates, and it was found that the longitudinal elastic modulus Ez had a value of approximately 10 GPa, so Ez = 10 GPa. Note that the effect of the magnitude of the longitudinal elastic modulus in the lamination direction on the vibration calculation result is small, so Ez does not need to be limited to this value, and there is no large error even if it is set equal to the longitudinal elastic modulus Ez0 of one steel plate.

In addition, for the Poisson's ratio of a laminated core having orthogonal anisotropy, the Poisson's ratio νxy in the XY plane can be set equal to the Poisson's ratio νxy0 of a single steel plate, but the Poisson's ratio νyz in the YZ plane and the Poisson's ratio νzx in the ZX plane cannot be set directly to the Poisson's ratios νyz0 and νzx0 of a single steel plate. This is because, in the case of a laminated core, the mechanical bond between the strain in the lamination direction and the strain in the lamination direction and perpendicular directions is considered to be extremely weak. Although it is extremely difficult to actually measure νyz and νzx, it is expected that they will be extremely small based on the above considerations, so in the first and second embodiments, νyz = νzx = 0.

Furthermore, regarding the transverse elastic modulus of a laminated core, the transverse elastic modulus Gxy in the XY plane can be set equal to the transverse elastic modulus Gxy0 of a single steel plate, but the transverse elastic modulus of two planes including the lamination direction, i.e., the transverse elastic modulus Gzx in the ZX plane and the transverse elastic modulus Gyz in the YZ plane, cannot be set directly to the transverse elastic modulus Gxz0 and Gyz0 of a single steel plate. This is because, in laminated steel plates, slip occurs in the X and Y directions perpendicular to the lamination direction at the interface between each stacked steel plate, so the effect of slippage between the steel plates needs to be reflected in the transverse elastic modulus Gzx and Gyz.

Therefore, determining the transverse elastic modulus in two planes including the lamination direction of the laminated core of the transformer, which is included in the elastic matrix in the constitutive equation, i.e., the transverse elastic modulus Gzx in the ZX plane and the transverse elastic modulus Gyz in the YZ plane, is an important issue in vibration analysis that uses a constitutive equation that expresses the relationship between stress and strain in a laminated core in matrix form.
However, in order to make the transverse elastic modulus Gzx in the ZX plane and the transverse elastic modulus Gyz in the YZ plane reflect the influence of slippage between the steel sheets, it is necessary to actually manufacture a laminated core for a three-phase three-leg transformer and measure the transverse elastic modulus Gzx and Gyz accurately. However, a method for measuring the transverse elastic modulus of a laminated core has not been established. In the case of metal materials, mechanical constants including the transverse elastic modulus can be measured by ultrasonic measurement, but in the case of a laminated core, there is slippage between the steel sheets, so vibration damping is large and measurement is difficult.

One method for determining the modulus of transverse elasticity in two planes including the lamination direction of a laminated core is to measure the natural frequency of the laminated core and estimate the modulus of transverse elasticity from the measured value. However, measuring the natural frequency of a laminated core of a transformer can be difficult due to the large vibration damping, and it is particularly difficult to measure the natural frequency when the core is large.
On the other hand, there are cases where the laminated core of the transformer includes at least a first portion and a second portion, and the transverse elastic moduli Gzx and Gyz in two planes including the lamination direction of the laminated core included in the elastic matrix in the constitutive formula differ between the first portion and the second portion. Even in this case, it is desirable to obtain appropriate transverse elastic moduli in two planes including the lamination direction of the first portion and the second portion.

For this reason, in the previous reference example, the transverse elastic moduli Gyz and Gzx in two planes including the lamination direction of the first and second parts constituting the laminated core were determined according to the procedure shown in Fig. 13. Fig. 13 shows the flow of processing in the elasticity matrix determination device for a laminated core according to the reference example.
In this reference example, the laminated core 21 to be analyzed comprises a first portion composed of an upper yoke 22a and a lower yoke 22b, and a second portion composed of legs 22c. The transverse elastic moduli Gzx and Gyz in two planes including the lamination direction of the laminated core 21, which are included in the elasticity matrix in the constitutive formula, are different between the first portion and the second portion, and the elasticity matrix determination device determines the transverse elastic moduli Gyz, Gzx of the first portion and the transverse elastic moduli Gyz, Gzx of the second portion.

First, as shown in FIG. 13, in step S11, the elastic matrix determination device (not shown) according to the reference example measures the excitation noise of the laminated core 21 of the transformer to be subjected to vibration analysis shown in FIG. 2 to obtain the frequency spectrum of the excitation noise of the laminated core 21. Specifically, the excitation noise of the laminated core 21 is measured at an excitation frequency of 50 Hz, and the excitation noise spectrum is collected at 100 Hz pitch from 100 Hz to 1000 Hz as the frequency spectrum of the excitation noise. An example of the frequency spectrum of the excitation noise collected in this manner is shown in FIG. 14. Here, the excitation frequency may be 60 Hz, in which case the excitation noise spectrum is collected at 120 Hz pitch from 120 Hz to 1200 Hz. The following describes the case where the excitation frequency is 50 Hz.

Next, in step S12, the elastic matrix determination device obtains the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet obtained by measuring the excitation magnetostriction of the same electromagnetic steel sheet as the directional electromagnetic steel sheet 22 constituting the laminated core 21 of the transformer. Specifically, the excitation magnetostriction of the same electromagnetic steel sheet as the directional electromagnetic steel sheet 22 constituting the laminated core 21 of the transformer to be subjected to the vibration analysis shown in FIG. 2 is measured at an excitation frequency of 50 Hz, and spectrum data of the excitation magnetostriction amplitude at 100 Hz pitch from 100 Hz to 1000 Hz is collected as the frequency spectrum of the excitation magnetostriction. The frequency spectrum of the excitation magnetostriction can be obtained by measuring the excitation magnetostriction of the electromagnetic steel sheet or by obtaining it from the manufacturer of the electromagnetic steel sheet. An example of the frequency spectrum of the excitation magnetostriction collected in this way is shown in FIG. 15. In FIG. 15, the vertical axis shows the magnetostriction amplitude, which is divided by the value at a frequency of 100 Hz for standardization, then the common logarithm is taken and multiplied by 10 to display in dB.

Next, in step S13, the elasticity matrix determination device performs a vibration response analysis on the laminated core 21 of the transformer that is the target of the vibration analysis.
Here, seven of the nine mechanical property values of the laminated core 21, namely, the longitudinal elastic moduli Ex, Ey, Ez, the transverse elastic moduli Gyz, Gzx, Gxy, and the Poisson's ratios vxy, vyz, vzx, are set as described above as follows.
Ex=Ex0, Ey=Ey0, Ez=10GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

As for the transverse elastic moduli Gyz and Gzx in the two planes including the remaining two lamination directions, they may be equal or different between the first portion formed by the upper yoke 22a and the lower yoke 22b and the second portion formed by the leg 22c, but the cases where they are different include the case where they are equal (in the following explanation, it is sufficient to set _G1 = _G2 ), so the case where they are different will be explained below. The elasticity matrix determination device sets Gyz = Gzx = _G1 , _G2 (each of _G1 and _G2 is a specific value selected from a predetermined range), and obtains the frequency spectrum of the vibration response function of the laminated core 21 of the transformer for the combination of these specific values ( _G1 , _G2 ). Specifically, the transverse elastic modulus of the first portion consisting of the upper yoke 22a and the lower yoke 22b is set as Gyz = Gzx = _G1 , and the transverse elastic modulus of the second portion consisting of the leg portion 22c is set as Gyz = Gzx = _G2 (each of _G1 and _G2 is a specific value selected from a predetermined range), and the frequency spectrum of the vibration response function of the laminated core 21 of the transformer for the combination of these specific values ( _G1 , _G2 ) is obtained.

Here, the predetermined range for which each of the specific values ( _G1 , _G2 ) is selected is actually the range of transverse elastic modulus expected from the structure of the laminated iron core 21 of the transformer, and in the reference example, it is set to the range of 0.05 GPa to 0.5 GPa.
An example of the frequency spectrum of the vibration response function of laminated core 21 of a transformer for a combination of specific values (G ₁ , G ₂ ) thus determined is shown in FIG. 16 (where the vibration response value at a frequency of 100 Hz is shown as 0 dB).

Next, in step S14, the elasticity matrix determination device calculates the frequency spectrum of the excitation vibration of the transformer laminated core 21 from the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheets acquired in step S12 and the frequency spectrum of the vibration response function of the transformer laminated core 21 obtained in step S13. Specifically, the frequency spectrum of the excitation vibration of the transformer laminated core 21 is calculated as the product of the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheets and the frequency spectrum of the vibration response function of the transformer laminated core 21 (calculated by addition in the case of dB display).
FIG. 17 shows an example of the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer calculated in this manner.

Next, in step S15, the elasticity matrix determination device determines the degree of agreement between the frequency spectrum of the excitation noise of the transformer laminated core 21 acquired in step S11 and the frequency spectrum of the excitation vibration of the transformer laminated core 21 calculated in step S14.
Here, the question arises as to how to evaluate the degree of agreement between the frequency spectrum of the excitation noise of the laminated iron core 21 of the transformer and the frequency spectrum of the excitation vibration of the laminated iron core 21 of the transformer.

There are 10 frequency spectrum data for excitation noise with a 100 Hz pitch from 100 Hz to 1000 Hz, so the frequency spectrum data for that noise is expressed as (S100, S200, S300, ..., S1000), and there are 10 frequency spectrum data for excitation vibration with a 100 Hz pitch from 100 Hz to 1000 Hz, so the frequency spectrum data for that excitation vibration is expressed as (V100, V200, V300, ..., V1000) to explain the degree of agreement.

The common method for evaluating the degree of similarity is to take the Euclidean distance between the above points (S100, S200, S300, ..., S1000) and (V100, V200, V300, ..., V1000) when considering them as data points in a multidimensional space (in this case, points in a 10-dimensional space).
However, it is known that the accuracy of the method of evaluating the degree of coincidence using Euclidean distance decreases if there is an offset in the data. Frequency spectrum data of excitation noise and excitation vibration is often expressed in dB values, but in this case, there is a degree of freedom in where the reference value is taken, and there is a concern that this degree of freedom may result in an offset.

Therefore, in the reference example, cosine similarity is adopted as a method of evaluating similarity that does not involve the above concerns. This cosine similarity is a method in which (S100, S200, S300, ..., S1000) and (V100, V200, V300, ..., V1000) are multidimensional vectors (in this case, 10-dimensional spatial vectors), and the cosine value of the angle between the two vectors S and V is used as the similarity. Cosine similarity can be expressed mathematically as in the following formula (17).

Here, the cosine coincidence COSθ is expressed as the inner product of vectors S and V divided by the product of the length of vector S and the length of vector V, and takes a value of 1 if vector S and vector V are the same, 0 if they are perpendicular, and −1 if they are in opposite directions.
Next, in step S16, the elasticity matrix determination device changes the values of the specific values ( _G1 , _G2 ) within the aforementioned specified ranges to change the combination of the specific values ( _G1 , _G2 ), repeats steps S13 to S15, and determines the degree of correspondence between the frequency spectrum of the excitation noise of the laminated core ₂₁ of the transformer and the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer in step S15 for each combination of the specific values (G1, _G2 ) that exists for the number of repetitions.

FIG _{. 18} shows an example of a two- _dimensional map indicating the degree of agreement between the frequency spectrum of the excitation noise of the laminated core and the frequency spectrum of the excitation vibration of the laminated core, determined in this way for each combination of specific values (G1, G2) that exist for the number of repetitions.
Finally, in step S17, the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined in step S16 is detected, and the combination of the specific values ( _G1 , _G2 ) with the maximum degree of agreement is adopted as the values of the transverse elastic moduli Gyz and Gzx in two planes including the lamination direction of the laminated core 21 in the first portion composed of the upper yoke 22a and the lower yoke 22b and the second portion composed of the legs 22c. In other words, the adopted specific values _G1 and _G2 respectively become the transverse elastic moduli Gzx and Gyx of the first portion composed of the upper yoke 22a and the lower yoke 22b, and the transverse elastic moduli Gzx and Gyx of the second portion composed of the legs 22c.

The specific values G ₁ and G ₂ are assumed to be the transverse elastic moduli Gzx and Gyx in two planes including the lamination direction of the transformer, and are incorporated into the constitutive equation to perform vibration analysis, thereby improving the accuracy of the vibration analysis.
As described in this reference example, if the elastic matrix of the laminated core 21 of the transformer can be determined according to the procedure from step S11 to step S17, it is basically possible to improve the accuracy of vibration analysis of the transformer.

However, in the procedure from step S11 to step S17, particularly in the measurement of the excitation noise of the laminated core 21 of the transformer in step S11 and the measurement of the excitation magnetostriction of the electromagnetic steel sheets in step S12, the actual measurement data contains disturbance noise and errors. Therefore, when detecting the maximum value of the degree of agreement for each combination of specific values ( _G1 , _G2 ) in step S17, two or more maximum values may be found, and the transverse elastic moduli Gzx and Gyx in two planes including the lamination direction of the transformer may not be calculated appropriately.

For this reason, in this embodiment, the conditions for measuring the excitation noise of the laminated iron core 21 in the excitation noise spectrum acquisition unit 31 (step S1) described later and the excitation magnetostriction of the electromagnetic steel sheet in the excitation magnetostriction spectrum acquisition unit 32 (step S2) of the elastic matrix determination device 10 are appropriately selected, and the frequency spectrum of the excitation noise of the laminated iron core 21 acquired in the excitation noise spectrum acquisition unit 31 (step S1) and the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet acquired in the excitation magnetostriction spectrum acquisition unit 32 (step S2) are appropriately selected.

As shown in FIG. 4, the elasticity matrix determination device 10 according to this embodiment includes an excitation noise spectrum acquisition unit 31, an excitation magnetostriction spectrum acquisition unit 32, a difference spectrum calculation unit 33, an average spectrum calculation unit 34, a selection unit 35, a vibration response function spectrum calculation unit 36, an excitation vibration spectrum calculation unit 37, a coincidence calculation unit 38, a coincidence determination unit 39, and a transverse elasticity coefficient determination unit 40, and determines the transverse elasticity coefficients Gzx and Gyz in two planes including the lamination direction of the first and second parts constituting the laminated core in the procedure shown in FIG. 5. FIG. 4 is a functional block diagram of the elasticity matrix determination device 10 for the laminated core shown in FIG. 1. FIG. 5 is a flowchart for explaining the flow of processing in the elasticity matrix determination device 10 for the laminated core shown in FIG. 4.

The elasticity matrix determination device 10 executes the functions of the excitation noise spectrum acquisition unit 31 (step S1: excitation noise spectrum acquisition step), excitation magnetostriction spectrum acquisition unit 32 (step S2: excitation magnetostriction spectrum acquisition step), difference spectrum calculation unit 33 (step S3: difference spectrum calculation step), average spectrum calculation unit 34 (step S4: average spectrum calculation step), selection unit 35 (step S5: selection step), vibration response function spectrum calculation unit 36 (step S6: vibration response function spectrum calculation step), excitation vibration spectrum calculation unit 37 (step S7: excitation vibration spectrum calculation step), agreement calculation unit 38 (step S8: agreement calculation step), agreement determination unit 39 (step S9: agreement determination step), and transverse elasticity coefficient determination unit 40 (step S10: transverse elasticity coefficient determination step) in accordance with the instructions of the computer program installed in the external storage device 15.

In this embodiment, the laminated core 21 of the transformer to be analyzed is formed by stacking multiple directional electromagnetic steel sheets 22, and has a first portion formed by an upper yoke 22a and a lower yoke 22b, and a second portion formed by legs 22c. The transverse elastic moduli Gzx and Gyz in two planes including the lamination direction of the laminated core 21 included in the elastic matrix in the constitutive formula are different between the first portion and the second portion, and the elastic matrix determination device determines the transverse elastic moduli Gyz, Gzx of the first portion and the transverse elastic moduli Gyz, Gzx of the second portion.

The excitation noise spectrum acquisition unit 31 of the elasticity matrix determination device 10 acquires the frequency spectrum of the excitation noise of the laminated core 21, which is the subject of vibration analysis shown in Fig. 2, measured for each of a plurality of excitation magnetic flux densities. Specifically, the excitation noise of the laminated core 21 is measured for each of a plurality of excitation magnetic flux densities (1.5T, 1.6T, 1.7T, 1.8T, and 1.9T in the example shown in Fig. 6(a)) at an excitation frequency of 50 Hz, and the excitation noise spectrum is collected at 100 Hz intervals from 100 Hz to 1000 Hz as the frequency spectrum of the excitation noise. Fig. 6(a) shows the frequency spectrum of the excitation noise of the laminated core, which is the subject of vibration analysis in the embodiment described later, measured for each of a plurality of excitation magnetic flux densities (1.5T to 1.9T). Here, the excitation frequency may be 60 Hz, in which case the spectrum of excitation noise is collected at 120 Hz intervals from 120 Hz to 1200 Hz. The following description will be given for a case where the excitation frequency is 50 Hz.
Furthermore, at transformer manufacturing sites, the excitation noise characteristics of transformers are widely measured as a quality control item for shipped products, and there is no particular difficulty in measuring them.

The excitation magnetostriction spectrum acquisition unit 32 of the elastic matrix determination device 10 acquires the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet obtained by measuring the excitation magnetostriction of the same electromagnetic steel sheet as the directional electromagnetic steel sheet 22 constituting the laminated core 21 for each of the multiple excitation magnetic flux densities that are the same as the multiple excitation magnetic flux densities described above. Specifically, the excitation magnetostriction of the same electromagnetic steel sheet as the directional electromagnetic steel sheet 22 constituting the laminated core 21 of the transformer to be subjected to the vibration analysis shown in FIG. 2 is measured for each of multiple excitation magnetic flux densities (1.5T to 1.9T), and spectrum data of the excitation magnetostriction amplitude at 100 Hz pitch from 100 Hz to 1000 Hz is collected as the frequency spectrum of the excitation magnetostriction. The frequency spectrum of the excitation magnetostriction can be obtained by measuring the excitation magnetostriction of the electromagnetic steel sheet or by obtaining it from the manufacturer of the electromagnetic steel sheet. FIG. 6(b) shows the frequency spectrum of the excitation magnetostriction (acceleration) of an electromagnetic steel sheet obtained by measuring the excitation magnetostriction of the same electromagnetic steel sheet as that constituting the laminated core 21 at multiple excitation magnetic flux densities (1.5 T to 1.9 T).

The difference spectrum calculation unit 33 of the elastic matrix determination device 10 calculates the difference spectrum between the frequency spectrum of the excitation noise for each of the multiple excitation magnetic flux densities acquired by the excitation noise spectrum acquisition unit 31 and the frequency spectrum of the excitation magnetostriction for each of the multiple excitation magnetic flux densities acquired by the excitation magnetostriction spectrum acquisition unit 32. Figure 6 (c) shows the difference spectrum between the frequency spectrum of the excitation noise for each of the multiple excitation magnetic flux densities (1.5T to 1.9T) and the frequency spectrum of the excitation magnetostriction for each of the multiple excitation magnetic flux densities (1.5T to 1.9T) in an embodiment described later.

In the example shown in FIG. 6(c), among multiple excitation magnetic flux densities (1.5T to 1.9T), the differential spectrum at excitation magnetic flux densities of 1.8T and 1.9T behaves significantly differently from the differential spectrum at other excitation magnetic flux densities, so the data of the differential spectrum at excitation magnetic flux densities of 1.8T and 1.9T was excluded. In the example shown in FIG. 6(c), in the subsequent processing by the elastic matrix determination device 10, data of the differential spectrum at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T, the frequency spectrum of excitation noise at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T, and the frequency spectrum of excitation magnetostriction at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T were used.

The average spectrum calculation unit 34 of the elastic matrix determination device 10 calculates the average spectrum of the difference spectrum for each of the multiple excitation magnetic flux densities calculated by the difference spectrum calculation unit 33. In the example shown in FIG. 6(c), the difference spectrum data at excitation magnetic flux densities of 1.8 T and 1.9 T is excluded, so the average spectrum calculation unit 34 calculates the average spectrum of the difference spectrum at excitation magnetic flux densities of 1.5 T, 1.6 T, and 1.7 T.

The selection unit 35 of the elastic matrix determination device 10 selects the frequency spectrum of the excitation noise at a specific excitation magnetic flux density to be used in the analysis from the frequency spectrum of the excitation noise at each of the multiple excitation magnetic flux densities acquired by the excitation noise spectrum acquisition unit 31, and the frequency spectrum of the excitation magnetostriction at a specific excitation magnetic flux density to be used in the analysis from the frequency spectrum of the excitation magnetostriction at each of the multiple excitation magnetic flux densities acquired by the excitation magnetostriction spectrum acquisition unit 32, depending on the degree of agreement between the difference spectrum for each of the multiple excitation magnetic flux densities calculated by the difference spectrum calculation unit 33 and the average spectrum calculated by the average spectrum calculation unit 34.

Specifically, the selection unit 35 calculates the cosine coincidence between the difference spectrum for each of the multiple excitation magnetic flux densities calculated by the difference spectrum calculation unit 33 and the average spectrum calculated by the average spectrum calculation unit 34, and selects the frequency spectrum of the excitation noise at a specific excitation magnetic flux density that constitutes the difference spectrum with the largest calculated cosine coincidence, and the frequency spectrum of the excitation magnetostriction at a specific excitation magnetic flux density that constitutes the difference spectrum with the largest cosine coincidence, as the spectrum to be used in the analysis. The cosine coincidence here is calculated by the above-mentioned formula (17).

In the example shown in FIG. 6(c), the cosine coincidence between the difference spectrum at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T calculated by the difference spectrum calculation unit 33 and the average spectrum of the difference spectrum at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T calculated by the average spectrum calculation unit 34 is calculated. In this case, the cosine coincidence between the difference spectrum at excitation magnetic flux density 1.6T and the average spectrum of the difference spectrum at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T is the largest. Therefore, the frequency spectrum of the excitation noise at a specific excitation magnetic flux density of 1.6T constituting the difference spectrum with the largest calculated cosine coincidence, and the frequency spectrum of the excitation magnetostriction at a specific excitation magnetic flux density of 1.6T constituting the difference spectrum with the largest cosine coincidence are selected to be used in the analysis.

FIG. 7 shows an example of a frequency spectrum of excitation noise at a specific excitation magnetic flux density (1.6 T) used in the analysis in the examples, and FIG. 8 shows an example of a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density (1.6 T) used in the analysis in the examples.
In addition, the vibration response function spectrum calculation unit 36 of the elasticity matrix determination device 10 performs vibration response analysis by applying the values of the transverse elastic moduli Gyz, Gzx in two planes including the stacking direction of the first and second parts to the elasticity matrix as combinations of specific values ( _G1 , _G2 ) selected from a predetermined range for the laminated core 21 that is the subject of vibration analysis, and obtains the frequency spectrum of the vibration response function of the laminated core 21 for the combination of specific values ( _G1 , _G2 ).

Here, seven of the nine mechanical property values of the laminated core 21, namely, the longitudinal elastic moduli Ex, Ey, Ez, the transverse elastic moduli Gyz, Gzx, Gxy, and the Poisson's ratios vxy, vyz, vzx, are set as described above as follows.
Ex=Ex0, Ey=Ey0, Ez=10GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

As for the transverse elastic coefficients Gyz and Gzx in the two planes including the remaining two stacking directions, they are different between the first portion consisting of the upper yoke 22a and the lower yoke 22b and the second portion consisting of the leg portion 22c, so the vibration response function spectrum calculation unit 36 sets Gyz = Gzx = _G1 , _G2 (where _G1 and _G2 are each specific values selected from a predetermined range) and applies this to the elasticity matrix to perform vibration response analysis, thereby obtaining the frequency spectrum of the vibration response function of the transformer laminated core 21 for the combination of these specific values ( _G1 , _G2 ). Specifically, the vibration response function spectrum calculation unit 36 sets the transverse elastic coefficient Gyz = Gzx = _G1 of the first portion consisting of the upper yoke 22a and the lower yoke 22b, and sets the transverse elastic coefficient Gyz = Gzx = _G2 of the second portion consisting of the leg portion 22c (each of _G1 and _G2 is a specific value selected from a predetermined range), applies this combination of specific values ( _G1 , _G2 ) to an elasticity matrix to perform vibration response analysis, and obtains the frequency spectrum of the vibration response function of the laminated core 21 of the transformer for this combination of specific values ( _G1 , _G2 ).
Here, the predetermined range for selecting each of the specific values ( _G1 , _G2 ) is actually the range of transverse elastic modulus expected from the structure of the laminated iron core 21 of the transformer, which is set to the range of 0.05 GPa to 0.5 GPa in this embodiment.

9 shows a frequency spectrum of the vibration response function of the laminated core 21 when a vibration response analysis is performed by applying to an elastic matrix a transverse elastic modulus Gyz=Gzx= _G1 of 0.2 GPa in two planes including the lamination direction of the first portion composed of the upper yoke 22a and the lower yoke 22b, and a transverse elastic modulus Gyz=Gzx= _G2 of 0.1 GPa in two planes including the lamination direction of the second portion composed of the legs 22c in an embodiment described later. In FIG. 9, the vibration response value at a frequency of 100 Hz is displayed as 0 dB.

The excitation vibration spectrum calculation unit 37 of the elastic matrix determination device 10 calculates the frequency spectrum of the excitation vibration of the laminated core 21 from the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet at the specific excitation magnetic flux density selected by the selection unit 35 and the frequency spectrum of the vibration response function of the laminated core 21 calculated by the vibration response function spectrum calculation unit 36. Specifically, the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer is calculated as the product of the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet at the specific excitation magnetic flux density selected by the selection unit 35 and the frequency spectrum of the vibration response function of the laminated core 21 of the transformer (calculated by addition when expressed in dB).

FIG. 10 shows a frequency spectrum of the excitation vibration of the laminated core 21 calculated by the excitation vibration spectrum calculation unit 37 when the transverse elastic modulus Gyz=Gzx= _G1 in two planes including the stacking direction of the first portion formed by the upper yoke 22a and the lower yoke 22b is 0.2 GPa, and the transverse elastic modulus Gyz=Gzx= _G2 in two planes including the stacking direction of the second portion formed by the leg portions 22c is 0.1 GPa in an embodiment described later.
In addition, the coincidence calculation unit 38 of the elastic matrix determination device 10 determines the coincidence between the frequency spectrum of the excitation noise of the laminated iron core 21 at the specific excitation magnetic flux density selected by the selection unit 35 and the frequency spectrum of the excitation vibration of the laminated iron core 21 calculated by the excitation vibration spectrum calculation unit 37.

Here, the degree of agreement between the frequency spectrum of the excitation noise of the transformer laminated core 21 and the frequency spectrum of the excitation vibration of the laminated core 21 is the cosine agreement calculated by equation (17), as in the above-mentioned reference example.
In addition, the consistency determination unit 39 of the elastic matrix determination device 10 changes each of the aforementioned specific values ( _G1 , _G2 ) within the aforementioned specified range to change the combination of each of the specific values ( _G1 , _G2 ), and repeats the processing of the vibration response function spectrum calculation unit 36, the excitation vibration spectrum calculation unit 37, and the consistency calculation unit 38, and determines the consistency between the frequency spectrum of the excitation noise of the laminated core ₂₁ at the specific excitation magnetic flux density selected by the selection unit 35 and the frequency spectrum of the excitation vibration of the laminated core 21 calculated by the excitation vibration spectrum calculation unit 37 for each combination of the specific values ( _{G1, G2} ) that exist for the number of repetitions.

FIG. 11 shows the degree of agreement between the frequency spectrum of the excitation noise of the laminated core at a specific excitation magnetic flux density (1.6 T) and the frequency spectrum of the excitation vibration of the laminated core 21, determined for _each combination of specific values (G1, _G2 ) that exist the same number of times as the number of repetitions in an embodiment described later.
In the processing by the coincidence determination unit 39, since there are a plurality of (two) parameters _G1 and _G2 , it becomes necessary to perform a two-dimensional numerical search, and the number of search points becomes very large, requiring a great deal of effort. Therefore, in this embodiment, a search method is adopted in which an optimization search method using a GA (genetic algorithm) by utilizing AI (artificial intelligence) technology is used, and the coincidence between the frequency spectrum of the excitation noise of the laminated core 21 at the specific excitation magnetic flux density selected by the selection unit 35 and the frequency spectrum of the excitation vibration of the laminated core 21 calculated by the excitation vibration spectrum calculation unit 37 is used as an evaluation function. The GA optimization search tool used may be a commercially available search software, or may be a GA optimization search tool created independently as done by the inventors.

In addition, the transverse elastic modulus determination unit 40 of the elastic matrix determination device 10 detects the maximum degree of agreement for each combination of specific values ( _G1 , _G2 ) determined by the degree of agreement determination unit 39, and adopts the combination of specific values ( _G1 , _G2 ) that gives the maximum degree of agreement as the values of the transverse elastic modulus Gzx and Gyz in two planes including the stacking direction between the first part consisting of the upper yoke 22a and the lower yoke 22b and the second part consisting of the leg 22c.
Here, the maximum degree of match means a value at which the degree of match is maximum within the above-mentioned predetermined range that the specific values G ₁ and G ₂ can take.

The specific values _G1 , _G2 adopted by the transverse elasticity coefficient determining unit 40 respectively become the transverse elasticity coefficients Gzx and Gyx of the first portion formed by the upper yoke 22a and the lower yoke 22b, and the transverse elasticity coefficients Gzx and Gyx of the second portion formed by the leg portions 22c.
The specific values G ₁ and G ₂ are assumed to be the transverse elastic moduli Gzx and Gyx in two planes including the lamination direction of the laminated core 21, and are incorporated into the constitutive equation to perform vibration analysis, thereby improving the accuracy of the vibration analysis.

In this embodiment, the transverse elastic modulus Gzx and Gyx are set equal on two surfaces including the lamination direction of the laminated core 21 (Gyz=Gzx= _G1 is set in the first portion, and the transverse elastic modulus Gyz=Gzx= _G2 is set in the second portion). Although it is generally possible for the values of the transverse elastic modulus Gzx and Gyx to be different on two surfaces including the lamination direction of the laminated core 21, it has been confirmed in the case of laminated cores of several transformers having different dimensions from the laminated core 21 illustrated in FIG. 2 that it is acceptable to set the values of the transverse elastic modulus Gzx and Gyx equal in the case of a laminated core made of grain-oriented electromagnetic steel sheets.

In this way, according to the laminated core elasticity matrix determination device 10 of this embodiment, when performing vibration analysis of a laminated core 21 made of laminated steel plates using a constitutive equation that expresses the relationship between stress and strain in a matrix, if the transverse elastic moduli Gzx and Gyz in two planes including the stacking direction of the laminated core 21 included in the elasticity matrix in the constitutive equation are different between the first and second parts, the transverse elastic moduli Gyz, Gzx of the first part and the transverse elastic moduli Gyz, Gzx of the second part can be optimally determined, and the deviation between the measured and calculated values of the vibration characteristics can be suppressed.

Next, the elasticity matrix determination method for a laminated core according to this embodiment will be described with reference to a flowchart for explaining the flow of processing in the elasticity matrix determination device 10 shown in FIG.
First, in step S1, the excitation noise spectrum acquisition unit 31 of the elastic matrix determination device 10 acquires the frequency spectrum of the excitation noise of the laminated core 21 that is the subject of vibration analysis shown in FIG. 2 by measuring the excitation noise of the laminated core 21 for each of a plurality of excitation magnetic flux densities (excitation noise spectrum acquisition step).

Next, in step S2, the excitation magnetostriction spectrum acquisition unit 32 of the elastic matrix determination device 10 acquires a frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet obtained by measuring the excitation magnetostriction of the same electromagnetic steel sheet as the directional electromagnetic steel sheet 22 constituting the laminated iron core 21 for each of a plurality of excitation magnetic flux densities identical to the aforementioned plurality of excitation magnetic flux densities (excitation magnetostriction spectrum acquisition step).
Next, in step S3, the differential spectrum calculation unit 33 calculates a differential spectrum between the frequency spectrum of the excitation noise for each of the multiple excitation magnetic flux densities acquired in step S1 and the frequency spectrum of the excitation magnetostriction for each of the multiple excitation magnetic flux densities acquired in step S2 (difference spectrum calculation step).

Next, in step S4, the average spectrum calculation unit 34 calculates an average spectrum of the difference spectra for each of the multiple excitation magnetic flux densities calculated in step S3 (average spectrum calculation step).
Next, in step S5, the selection unit 35 selects, depending on the degree of agreement between the difference spectrum for each of the multiple excitation magnetic flux densities calculated in step S3 and the average spectrum calculated in step S4, a frequency spectrum of excitation noise at a specific excitation magnetic flux density to be used in the analysis from among the frequency spectra of excitation noise for each of the multiple excitation magnetic flux densities acquired in step S1, and a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density to be used in the analysis from among the frequency spectra of excitation magnetostriction for each of the multiple excitation magnetic flux densities acquired in step S2 (selection step).

Specifically, in step S5, the selection unit 35 calculates the cosine coincidence between the difference spectrum for each of the multiple excitation magnetic flux densities calculated in step S3 and the average spectrum calculated in step S4, and selects the frequency spectrum of the excitation noise at a specific excitation magnetic flux density constituting the difference spectrum with the largest calculated cosine coincidence, and the frequency spectrum of the excitation magnetostriction at a specific excitation magnetic flux density constituting the difference spectrum with the largest cosine coincidence, as the spectrum to be used in the analysis.

Next, in step S6, the vibration response function spectrum calculation unit 36 performs vibration response analysis on the laminated core 21 that is the subject of vibration analysis by applying the values of the transverse elastic moduli Gyz, Gzx in two planes including the stacking direction of the first and second parts to an elastic matrix as combinations of specific values ( _G1 , _G2 ) selected from a predetermined range, and obtains the frequency spectrum of the vibration response function of the laminated core 21 for the combination of specific values ( _G1 , _G2 ) (vibration response function spectrum calculation step).

Here, seven of the nine mechanical property values of the laminated core 21, namely, the longitudinal elastic moduli Ex, Ey, Ez, the transverse elastic moduli Gyz, Gzx, Gxy, and the Poisson's ratios vxy, vyz, vzx, are set as described above as follows.
Ex=Ex0, Ey=Ey0, Ez=10GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

As for the transverse elastic coefficients Gyz and Gzx in the two planes including the remaining two stacking directions, they are different between the first portion consisting of the upper yoke 22a and the lower yoke 22b and the second portion consisting of the leg portion 22c, so the vibration response function spectrum calculation unit 36 sets Gyz = Gzx = _G1 , _G2 (where _G1 and _G2 are each specific values selected from a predetermined range) and applies this to the elasticity matrix to perform vibration response analysis, thereby obtaining the frequency spectrum of the vibration response function of the transformer laminated core 21 for the combination of these specific values ( _G1 , _G2 ). Specifically, the vibration response function spectrum calculation unit 36 sets the transverse elastic coefficient Gyz = Gzx = _G1 of the first portion consisting of the upper yoke 22a and the lower yoke 22b, and sets the transverse elastic coefficient Gyz = Gzx = _G2 of the second portion consisting of the leg portion 22c (each of _G1 and _G2 is a specific value selected from a predetermined range), applies this combination of specific values ( _G1 , _G2 ) to an elasticity matrix to perform vibration response analysis, and obtains the frequency spectrum of the vibration response function of the laminated core 21 of the transformer for this combination of specific values ( _G1 , _G2 ).

Here, the predetermined range for selecting each of the specific values ( _G1 , _G2 ) is actually the range of transverse elastic modulus expected from the structure of the laminated iron core 21 of the transformer, which is set to the range of 0.05 GPa to 0.5 GPa in this embodiment.
Next, in step S7, the excitation vibration spectrum calculation unit 37 of the elastic matrix determination device 10 calculates the frequency spectrum of the excitation vibration of the laminated core 21 from the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet at the specific excitation magnetic flux density selected in step S5 and the frequency spectrum of the vibration response function of the laminated core 21 calculated in step S6 (excitation vibration spectrum calculation step).

Next, in step S8, the coincidence calculation unit 38 of the elastic matrix determination device 10 determines the coincidence between the frequency spectrum of the excitation noise of the laminated core 21 at the specific excitation magnetic flux density selected in step S5 and the frequency spectrum of the excitation vibration of the laminated core 21 calculated in step S7 (consistency calculation step).
Here, the degree of agreement between the frequency spectrum of the excitation noise of the laminated core 21 of the transformer and the frequency spectrum of the excitation vibration of the laminated core 21 is the cosine agreement calculated by equation (17), as described above.

Next, in step S9, the consistency determination unit 39 of the elasticity matrix determination device 10 changes each of the specific values ( _G1 , _G2 ) described above within the specified range to change the combination of the specific values ( _G1 , _G2 ), and repeats the processes of steps S6, S7, and S8 to _determine the consistency between the frequency spectrum of the excitation _noise of the laminated core 21 at the specific excitation magnetic flux density selected in step S5 and the frequency spectrum of the excitation vibration of the laminated core 21 calculated in step S7 for each combination of specific values (G1, G2) that exists for the number of repetitions (consistency determination step).

Finally, in step S10, the transverse elastic modulus determination unit 40 of the elastic matrix determination device 10 detects the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined in step S9, and adopts the combination of specific values ( _G1 , _G2 ) with the maximum degree of agreement as the values of the transverse elastic modulus Gzx and Gyz in two planes including the stacking direction between the first portion consisting of the upper yoke 22a and the lower yoke 22b and the second portion consisting of the leg portion 22c (transverse elastic modulus determination step).

Here, the maximum degree of match means a value at which the degree of match is maximum within the above-mentioned predetermined range that the specific values G ₁ and G ₂ can take.
The specific values G ₁ and G ₂ adopted in step S10 respectively become the transverse elastic moduli Gzx and Gyx of the first portion formed by the upper yoke 22a and the lower yoke 22b, and the transverse elastic moduli Gzx and Gyx of the second portion formed by the leg portion 22c.
This completes the processing in the elasticity matrix determination device 10.

The specific values _G1 and _G2 adopted in step S10 are incorporated into the constitutive equation as the transverse elastic moduli Gzx and Gyx in two planes including the lamination direction of the laminated core 21, and vibration analysis is performed, thereby improving the accuracy of the vibration analysis.
In this way, according to the method for determining the elastic matrix of a laminated core of this embodiment, when performing vibration analysis of a laminated core 21 made of stacked steel plates using a constitutive equation that expresses the relationship between stress and strain in matrix form, if the transverse elastic moduli Gzx and Gyz in two planes including the stacking direction of the laminated core 21 included in the elastic matrix in the constitutive equation are different between the first and second parts, it is possible to optimally determine the transverse elastic moduli Gyz, Gzx of the first part and the transverse elastic moduli Gyz, Gzx of the second part, and to suppress the deviation between the measured and calculated values of the vibration characteristics.

In addition, the computer program according to this embodiment causes the computer (elasticity matrix determination device 10) to calculate the transverse elastic modulus Gyz, Gzx in two planes including the lamination direction of the laminated iron core 21 included in the elasticity matrix in the constitutive formula when the transverse elastic modulus Gyz, Gzx in two planes including the lamination direction of the first part and the second part are different between the first part and the second part. Then, this computer program causes the computer to execute the above-mentioned step S1 (excitation noise spectrum acquisition step), step S2 (excitation magnetostriction spectrum acquisition step), step S3 (difference spectrum calculation step), step S4 (average spectrum calculation step), step S5 (selection step), step S6 (vibration response function spectrum calculation step), step S7 (excitation vibration spectrum calculation step), step S8 (degree of agreement calculation step), step S9 (degree of agreement determination step), and step S10 (transverse elastic modulus determination step).

As a result, when performing vibration analysis of a laminated core 21 made of laminated steel plates using a constitutive equation that expresses the relationship between stress and strain in a matrix, if the transverse elastic moduli Gzx and Gyz in two planes including the lamination direction of the laminated core 21 contained in the elastic matrix in the constitutive equation are different between the first and second parts, the transverse elastic moduli Gyz, Gzx of the first part and the transverse elastic moduli Gyz, Gzx of the second part can be optimally determined, and the deviation between the measured and calculated vibration characteristics can be suppressed.

Although the embodiment of the present invention has been described above, the present invention is not limited to this and various modifications and improvements can be made.
For example, the method of evaluating the degree of match between the frequency spectrum of the excitation noise of the transformer laminated core 21 and the frequency spectrum of the excitation vibration of the transformer laminated core 21 is not limited to cosine match, and it is also possible to adopt Euclidean distance by taking a dB standard so as not to include offset, and other methods of evaluating the degree of match can also be adopted as long as they essentially quantitatively indicate the degree of match between the frequency spectrum data of the excitation noise and the excitation vibration.

In the above embodiment, the vibration analysis of a three-phase three-limbed transformer has been described, but the present invention is not limited to this and can be applied to vibration analysis of laminated cores in three-phase five-limbed transformers and other transformers. Furthermore, the present invention can be applied to vibration analysis of laminated cores of reactors and other transformers other than transformers, so long as they use laminated cores.
Furthermore, in the above embodiment, the laminated core 21 is formed by stacking a plurality of directional electromagnetic steel sheets 22, and vibration analysis is performed on the laminated core 21; however, the laminated core 21 may be formed by stacking steel sheets other than the directional electromagnetic steel sheets 22, for example carbon steel sheets, and vibration analysis may be performed on the laminated core 21.

In addition, in the above embodiment, a case has been described in which the transverse elastic moduli Gyz, Gzx in two planes including the stacking direction of the laminated iron core 21 included in the elastic matrix in the constitutive formula are different between the first part and the second part, but the transverse elastic moduli Gyz, Gzx in two planes including the stacking direction of the laminated iron core 21 included in the elastic matrix in the constitutive formula may be the same between the first part and the second part.
In addition, in the example shown in FIG. 6C, among the multiple excitation magnetic flux densities (1.5 T to 1.9 T), the differential spectrum data at excitation magnetic flux densities of 1.8 T and 1.9 T are excluded, but this process of excluding the differential spectrum is not necessarily required.
Furthermore, it is sufficient that the laminated core 21 includes at least the first portion and the second portion, and it may include portions other than the first portion and the second portion.

(Example)
In order to verify the effects of the present invention, a method for determining the elasticity matrix of a laminated core of a transformer according to the second embodiment was carried out.
First, a grain-oriented electrical steel sheet having a thickness of 0.23 mm was prepared.
Next, the prepared grain-oriented electromagnetic steel sheets were laminated to create a laminated core 21 for a three-phase three-legged transformer shown in Fig. 2, which was the subject of vibration analysis. The steel sheet lamination thickness of the laminated core 21 was 100 mm. The dimensions of the upper yoke 22a and the lower yoke 22b were 100 mm wide x 500 mm long. The dimensions of the three legs 22c were set to a width of 100 mm and a core window length of 300 mm, and the upper yoke 22a and the lower yoke 22b were connected at intervals of 100 mm.

Then, IV wire was wound around each of the three legs 22c of the laminated core 21 to form an excitation coil, and a three-phase current of 50 Hz was passed through the coil to adjust the power supply voltage so that the excitation magnetic flux density was 1.5 T, 1.6 T, 1.7 T, 1.8 T, and 1.9 T. The excitation noise was then measured using a sound level meter. The noise frequency spectrum was calculated using the sound level meter's function for calculating the noise frequency spectrum, and the frequency spectrum of the excitation noise shown in Figure 6(a) was obtained.

Then, in step S1, the excitation noise spectrum acquisition unit 31 of the elastic matrix determination device 10 measured the excitation noise of the laminated core 21 that was the subject of vibration analysis for multiple excitation magnetic flux densities of 1.5T, 1.6T, 1.7T, 1.8T, and 1.9T to acquire the frequency spectrum of the excitation noise of the laminated core 21 (the frequency spectrum of the excitation noise shown in FIG. 6(a)).

Next, in step S2, the excitation magnetostriction spectrum acquisition unit 32 of the elastic matrix determination device 10 measured the excitation magnetostriction of the same electromagnetic steel sheet as the grain-oriented electromagnetic steel sheet constituting the laminated iron core 21 for multiple excitation magnetic flux densities of 1.5T, 1.6T, 1.7T, 1.8T, and 1.9T to obtain the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet. In other words, when the excitation magnetostriction of the prepared grain-oriented electromagnetic steel sheet constituting the laminated iron core 21 at an excitation frequency of 50 Hz and multiple excitation magnetic flux densities of 1.5T, 1.6T, 1.7T, 1.8T, and 1.9T was measured using a magnetostriction measurement device, the frequency spectrum of the excitation magnetostriction was obtained as shown in FIG. 6(b), and the excitation magnetostriction spectrum acquisition unit 32 obtained the frequency spectrum of the excitation magnetostriction for each of the multiple excitation magnetic flux densities of 1.5T, 1.6T, 1.7T, 1.8T, and 1.9T.

Next, in step S3, the difference spectrum calculation unit 33 of the elastic matrix determination device 10 calculated the difference spectrum between the frequency spectrum of the excitation noise for each of the multiple excitation magnetic flux densities 1.5T, 1.6T, 1.7T, 1.8T, and 1.9T obtained in step S1 and the frequency spectrum of the excitation magnetostriction for each of the multiple excitation magnetic flux densities 1.5T, 1.6T, 1.7T, 1.8T, and 1.9T obtained in step S2. This difference spectrum is shown in FIG. 6(c).

In Figure 6(c), among multiple excitation magnetic flux densities (1.5T to 1.9T), the differential spectrum at excitation magnetic flux densities of 1.8T and 1.9T behaves significantly differently from the differential spectrum at other excitation magnetic flux densities, so the data for the differential spectrum at excitation magnetic flux densities of 1.8T and 1.9T was excluded. Specifically, an average differential spectrum was calculated by averaging the differential spectra at excitation magnetic flux densities of 1.5T to 1.9T shown in Figure 6(c), and the difference between the differential spectrum at each magnetic flux density and the average differential spectrum was evaluated at 10 points from 100Hz to 1000Hz. Then, the differential spectrum of magnetic flux densities with two or more points where the difference was 5dB or more was determined to behave significantly differently from the others. When we investigated the reason why the difference spectrum at excitation magnetic flux densities of 1.8T and 1.9T behaved significantly differently from the difference spectrum at other excitation magnetic flux densities, we found that the distortion of the magnetic flux waveform during excitation magnetostriction measurement was large at excitation magnetic flux densities of 1.8T and 1.9T, making the magnetostriction data inaccurate. For this reason, we excluded the data of the difference spectrum at magnetic flux densities of 1.8T and 1.9T. In subsequent processing by the elastic matrix determination device 10, data of the difference spectrum at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T, the frequency spectrum of excitation noise at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T, and the frequency spectrum of excitation magnetostriction at excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T were used.

Then, in step S4, the average spectrum calculation unit 34 of the elastic matrix determination device 10 calculated the average spectrum of the difference spectrum for each of the multiple excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T calculated in step S3. In FIG. 6(c), since the difference spectrum data for excitation magnetic flux densities of 1.8T and 1.9T was excluded in the process in step S3, the average spectrum of the difference spectrum for excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T was calculated in step S4.

Next, in step S5, the selection unit 35 of the elastic matrix determination device 10 selected the frequency spectrum of the excitation noise at a specific excitation magnetic flux density to be used in the analysis from among the frequency spectra of the excitation noise at the multiple excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T obtained in step S1, and the frequency spectrum of the excitation magnetostriction at a specific excitation magnetic flux density to be used in the analysis from among the frequency spectra of the excitation magnetostriction at the multiple excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T obtained in step S2, depending on the degree of agreement between the difference spectrum for the multiple excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T calculated in step S3 and the average spectrum calculated in step S4.

Specifically, in step S5, the selection unit 35 calculated the cosine coincidence between the difference spectrum for each of the excitation magnetic flux densities of 1.5T, 1.6T, and 1.7T calculated in step S3 and the average spectrum calculated in step S4. As a result, the selection unit 35 determined that the cosine coincidence between the difference spectrum and the average spectrum at the excitation magnetic flux density of 1.6T was the largest, and therefore selected the frequency spectrum of the excitation noise at the specific excitation magnetic flux density of 1.6T constituting the difference spectrum with the largest calculated cosine coincidence, and the frequency spectrum of the excitation magnetostriction at the specific excitation magnetic flux density of 1.6T constituting the difference spectrum with the largest cosine coincidence, as the spectrum to be adopted for analysis. The frequency spectrum of the excitation noise at the specific excitation magnetic flux density of 1.6T selected for analysis is shown in FIG. 7, and the frequency spectrum of the excitation magnetostriction at the specific excitation magnetic flux density of 1.6T selected for analysis is shown in FIG. 8.

Next, in step S6, the vibration response function spectrum calculation unit 36 of the elasticity matrix determination device 10 performs vibration response analysis by applying the values of the transverse elastic moduli Gyz, Gzx in two planes including the stacking direction of the first part consisting of the upper yoke 22a and the lower yoke 22b and the second part consisting of the leg 22c to the elasticity matrix as combinations of specific values ( _G1 , _G2 ) selected from a predetermined range for the laminated core 21 that is the subject of vibration analysis, and obtains the frequency spectrum of the vibration response function of the laminated core 21 for the combination of specific values ( _G1 , _G2 ).

Here, seven of the nine mechanical property values of the laminated core 21, namely, the longitudinal elastic moduli Ex, Ey, Ez, the transverse elastic moduli Gyz, Gzx, Gxy, and the Poisson's ratios vxy, vyz, vzx, are set as described above as follows.
Ex=Ex0, Ey=Ey0, Ez=10GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

As for the transverse elastic coefficients Gyz and Gzx in the two planes including the remaining two stacking directions, they are different between the first portion consisting of the upper yoke 22a and the lower yoke 22b and the second portion consisting of the leg portion 22c, so the vibration response function spectrum calculation unit 36 sets Gyz = Gzx = _G1 , _G2 (where _G1 and _G2 are each specific values selected from a predetermined range) and applies this to the elasticity matrix to perform vibration response analysis, thereby obtaining the frequency spectrum of the vibration response function of the transformer laminated core 21 for the combination of these specific values ( _G1 , _G2 ). Specifically, the vibration response function spectrum calculation unit 36 sets the transverse elastic coefficient Gyz = Gzx = _G1 of the first portion consisting of the upper yoke 22a and the lower yoke 22b, and sets the transverse elastic coefficient Gyz = Gzx = _G2 of the second portion consisting of the leg portion 22c (each of _G1 and _G2 is a specific value selected from a predetermined range), applies this combination of specific values ( _G1 , _G2 ) to an elasticity matrix to perform vibration response analysis, and obtains the frequency spectrum of the vibration response function of the laminated core 21 of the transformer for this combination of specific values ( _G1 , _G2 ).
Here, the predetermined range for selecting each of the specific values ( _G1 , _G2 ) is actually the range of transverse elastic modulus expected from the structure of the laminated iron core 21 of the transformer, which is set to the range of 0.05 GPa to 0.5 GPa in this embodiment.

9 shows a frequency spectrum of the vibration response function of the laminated core 21 when a vibration response analysis is performed by applying to an elastic matrix a transverse elastic modulus Gyz=Gzx= _G1 of 0.2 GPa in two planes including the lamination direction of the first portion formed by the upper yoke 22a and the lower yoke 22b, and a transverse elastic modulus Gyz=Gzx= _G2 of 0.1 GPa in two planes including the lamination direction of the second portion formed by the legs 22c. In FIG. 9, the vibration response value at a frequency of 100 Hz is displayed as 0 dB.
Next, in step S7, the excitation vibration spectrum calculation unit 37 of the elastic matrix determination device 10 calculated the frequency spectrum of the excitation vibration of the laminated core 21 from the frequency spectrum of the excitation magnetostriction of the electromagnetic steel sheet at the specific excitation magnetic flux density of 1.6 T selected in step S5 and the frequency spectrum of the vibration response function of the laminated core 21 calculated in step S6.

FIG. 10 shows the frequency spectrum of the excitation vibration of the laminated core 21 calculated by the excitation vibration spectrum calculation unit 37 when the transverse elastic modulus Gyz=Gzx= _G1 in two planes including the stacking direction of the first portion formed by the upper yoke 22a and the lower yoke 22b is 0.2 GPa, and the transverse elastic modulus Gyz=Gzx= _G2 in two planes including the stacking direction of the second portion formed by the leg portions 22c is 0.1 GPa.

Next, in step S8, the coincidence calculation unit 38 of the elasticity matrix determination device 10 determined the coincidence between the frequency spectrum of the excitation noise of the laminated core 21 at the specific excitation magnetic flux density of 1.6 T selected in step S5 and the frequency spectrum of the excitation vibration of the laminated core 21 calculated in step S7.
Here, the degree of agreement between the frequency spectrum of the excitation noise of the laminated core 21 of the transformer and the frequency spectrum of the excitation vibration of the laminated core 21 was determined by using the cosine agreement calculated by equation (17).

Next, in step S9, the consistency determination unit 39 of the elasticity matrix determination device 10 changes each of the specific values ( _G1 , _G2 ) within the aforementioned specified range to change the combination of each of the specific values ( _G1 , _G2 ), and repeats the processes of steps S6, S7 _{, and} S8, and determines the consistency between the frequency spectrum of the excitation noise of the laminated core 21 at the specific excitation magnetic flux density of 1.6 T selected in step S5 and the frequency spectrum of the excitation vibration of the laminated core 21 calculated in step S7 for each combination of specific values (G1, G2) that exists for the number of repetitions (consistency determination step).

FIG. 11 shows the degree of agreement between the frequency _spectrum of the excitation noise of the laminated core at a specific excitation magnetic flux density of 1.6 T _and the frequency spectrum of the excitation vibration of the laminated core 21, determined for each combination of specific values (G1, G2) that exist for the number of repetitions.
Finally, in step S10, the transverse elastic modulus determination unit 40 of the elastic matrix determination device 10 detects the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined in step S9, and adopts the combination of specific values ( _G1 , _G2 ) with the maximum degree of agreement as the values of the transverse elastic modulus Gzx and Gyz in two planes including the stacking direction between the first part consisting of the upper yoke 22a and the lower yoke 22b and the second part consisting of the leg portion 22c.

In FIG. 11, the degree of agreement was maximized when the modulus of transverse elasticity Gzx=Gyz= _G1 of the first portion formed by the upper yoke 22a and the lower yoke 22b was 0.15 GPa, and the modulus of transverse elasticity Gzx=Gyz= _G2 of the second portion formed by the leg portion 22c was 0.25 GPa.
The specific values G ₁ and G ₂ adopted in step S10 respectively become the transverse elastic moduli Gzx and Gyx of the first portion formed by the upper yoke 22a and the lower yoke 22b, and the transverse elastic moduli Gzx and Gyx of the second portion formed by the leg portion 22c.

Finally, the frequency spectrum of the excitation vibration of the laminated core 21 calculated for the combination of G1 and _G2 in which the transverse elastic modulus Gzx = Gyz = _G1 of the first portion formed by the upper yoke 22a and the lower yoke 22b is 0.15 _GPa and the transverse elastic modulus Gzx = Gyz = _G2 of the second portion formed by the leg 22c is 0.25 GPa was determined as the final calculated value of the frequency spectrum of the excitation vibration of the laminated core of the transformer.

Figure 12 shows the calculated value of the frequency spectrum of the excitation vibration of the laminated iron core of the transformer in the embodiment, and the actual value of the frequency spectrum of the excitation noise obtained by measuring the excitation noise of the laminated iron core of the transformer. In Figure 12, the two values match very well, and it was confirmed that the embodiment can accurately determine the transverse elastic modulus Gzx and Gyz in two planes including the lamination direction of the first part composed of the upper yoke 22a and lower yoke 22b of the laminated iron core 21 of the transformer, which are included in the elastic matrix in the constitutive formula, and the transverse elastic modulus Gzx and Gyz in two planes including the lamination direction of the second part composed of the legs 22c of the laminated iron core 21 of the transformer.

10 Elasticity matrix determination device 11 CPU
12 Processing unit 13 Internal bus 14 Internal storage device 15 External storage device 16 Input device 17 Output device 18 Recording medium 21 Laminated core 22 Grain-oriented electromagnetic steel sheet (steel sheet)
22a Upper yoke (first part)
22b Lower yoke (first part)
22c Leg (second part)
31 Excitation noise spectrum acquisition unit 32 Excitation magnetostriction spectrum acquisition unit 33 Difference spectrum calculation unit 34 Average spectrum calculation unit 35 Selection unit 36 Vibration response function spectrum calculation unit 37 Excitation vibration spectrum calculation unit 38 Matching degree calculation unit 39 Matching degree determination unit 40 Transverse elasticity coefficient determination unit

Claims (6)

A laminated core elasticity matrix determination device for performing vibration analysis of a laminated core using a constitutive equation that expresses the relationship between stress and strain in a matrix, the laminated core being formed by stacking a plurality of steel plates and having at least a first portion and a second portion, the device determining transverse elastic moduli in two planes including a lamination direction of the first portion and the second portion of the laminated core, the transverse elastic moduli being included in the elasticity matrix in the constitutive equation,
an excitation noise spectrum acquisition unit that acquires a frequency spectrum of the excitation noise of the laminated core that is the subject of vibration analysis, the frequency spectrum being determined by measuring the excitation noise of the laminated core for each of a plurality of excitation magnetic flux densities;
an excitation magnetostriction spectrum acquisition unit that acquires a frequency spectrum of the excitation magnetostriction of the steel plate obtained by measuring the excitation magnetostriction of the same steel plate as the steel plate constituting the laminated core for each of a plurality of excitation magnetic flux densities that are the same as the plurality of excitation magnetic flux densities;
a differential spectrum calculation unit that calculates a differential spectrum between a frequency spectrum of the excitation noise for each of the plurality of excitation magnetic flux densities acquired by the excitation noise spectrum acquisition unit and a frequency spectrum of the excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired by the excitation magnetostriction spectrum acquisition unit;
an average spectrum calculation unit that calculates an average spectrum of the difference spectra for each of the plurality of excitation magnetic flux densities calculated by the difference spectrum calculation unit;
a selection unit which selects, according to a degree of coincidence between the difference spectrum for each of the plurality of excitation magnetic flux densities calculated by the difference spectrum calculation unit and the average spectrum calculated by the average spectrum calculation unit, a frequency spectrum of excitation noise at a specific excitation magnetic flux density to be used for analysis from among the frequency spectra of the excitation noise for each of the plurality of excitation magnetic flux densities acquired by the excitation noise spectrum acquisition unit, and a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density to be used for analysis from among the frequency spectra of excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired by the excitation magnetostriction spectrum acquisition unit;
a vibration response function spectrum calculation unit that performs vibration response analysis by applying to the elastic matrix values of transverse elastic modulus in two planes including the lamination direction of the laminated core of the first portion and the second portion as combinations of specific values ( _G1 , _G2 ) selected from a predetermined range for the laminated core as a target of vibration analysis, and obtains a frequency spectrum of the vibration response function of the laminated core for the combination of the specific values ( _G1 , _G2 );
an excitation vibration spectrum calculation unit that calculates a frequency spectrum of excitation vibration of the laminated core from a frequency spectrum of excitation magnetostriction of the steel sheet at the specific excitation magnetic flux density selected by the selection unit and a frequency spectrum of a vibration response function of the laminated core calculated by the vibration response function spectrum calculation unit;
a coincidence calculation unit that calculates a degree of coincidence between a frequency spectrum of excitation noise of the laminated core at a specific excitation magnetic flux density selected by the selection unit and a frequency spectrum of excitation vibration of the laminated core calculated by the excitation vibration spectrum calculation unit;
a coincidence determination unit which changes each of the specific values ( _G1 , _G2 ) within the predetermined range to change the combination of the specific values ( _G1 , _G2 ), repeats the processes of the vibration response function spectrum calculation unit, the excitation vibration spectrum calculation unit, and the coincidence calculation unit, _and determines the coincidence between the frequency _spectrum of the excitation noise of the laminated core at the specific excitation magnetic flux density selected by the selection unit and the frequency spectrum of the excitation vibration of the laminated core calculated by the excitation vibration spectrum calculation unit for each combination of the specific values (G1, G2) that exists for the number of repetitions;
a transverse elastic modulus determination unit that detects the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined by the degree of agreement determination unit, and adopts the combination of specific values ( _G1 , _G2 ) that gives the maximum degree of agreement as the value of the transverse elastic modulus in two planes including the lamination direction of the laminated core of the first part and the second part. The elasticity matrix determination device for a laminated core according to claim 1, characterized in that the selection unit calculates the cosine coincidence between the difference spectrum for each of the multiple excitation magnetic flux densities calculated by the difference spectrum calculation unit and the average spectrum calculated by the average spectrum calculation unit, and selects the frequency spectrum of the excitation noise at a specific excitation magnetic flux density constituting the difference spectrum with the largest calculated cosine coincidence and the frequency spectrum of the excitation magnetostriction at a specific excitation magnetic flux density constituting the difference spectrum with the largest cosine coincidence as the spectrum to be adopted for analysis. A method for determining an elastic matrix of a laminated core, in which a vibration analysis of the laminated core is performed using a constitutive equation that expresses the relationship between stress and strain in a matrix, the laminated core being formed by stacking a plurality of steel plates and having at least a first portion and a second portion, the method determining transverse elastic moduli in two planes including a lamination direction of the first portion and the second portion of the laminated core, the transverse elastic moduli being included in the elastic matrix of the constitutive equation,
an excitation noise spectrum acquisition step of acquiring a frequency spectrum of the excitation noise of the laminated core, which is the subject of vibration analysis, obtained by measuring the excitation noise of the laminated core for each of a plurality of excitation magnetic flux densities;
an excitation magnetostriction spectrum acquisition step of acquiring a frequency spectrum of the excitation magnetostriction of the steel plate obtained by measuring the excitation magnetostriction of the same steel plate as the steel plate constituting the laminated core for each of a plurality of excitation magnetic flux densities having the same excitation magnetic flux densities as the plurality of excitation magnetic flux densities;
a differential spectrum calculation step of calculating a differential spectrum between a frequency spectrum of the excitation noise for each of the plurality of excitation magnetic flux densities acquired in the excitation noise spectrum acquisition step and a frequency spectrum of the excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired in the excitation magnetostriction spectrum acquisition step;
an average spectrum calculation step of calculating an average spectrum of the difference spectra for each of the plurality of excitation magnetic flux densities calculated in the difference spectrum calculation step;
a selection step of selecting a frequency spectrum of excitation noise at a specific excitation magnetic flux density to be used for analysis from among the frequency spectra of the excitation noise for each of the multiple excitation magnetic flux densities acquired in the excitation noise spectrum acquisition step, and a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density to be used for analysis from among the frequency spectra of excitation magnetostriction for each of the multiple excitation magnetic flux densities acquired in the excitation magnetostriction spectrum acquisition step, according to a degree of coincidence between the difference spectrum for each of the multiple excitation magnetic flux densities calculated in the difference spectrum calculation step and the average spectrum calculated in the average spectrum calculation step;
a vibration response function spectrum calculation step of performing a vibration response analysis by applying to the elastic matrix the values of the transverse elastic modulus in two planes including the lamination direction of the laminated core of the first portion and the second portion as a combination of specific values ( _G1 , _G2 ) selected from a predetermined range for the laminated core to obtain a frequency spectrum of the vibration response function of the laminated core for the combination of the specific values ( _G1 , _G2 );
an excitation vibration spectrum calculation step of calculating a frequency spectrum of excitation vibration of the laminated core from a frequency spectrum of excitation magnetostriction of the steel sheet at the specific excitation magnetic flux density selected in the selection step and a frequency spectrum of the vibration response function of the laminated core calculated in the vibration response function spectrum calculation step;
a coincidence calculation step of determining a degree of coincidence between a frequency spectrum of excitation noise of the laminated core at the specific excitation magnetic flux density selected in the selection step and a frequency spectrum of excitation vibration of the laminated core calculated in the excitation vibration spectrum calculation step;
a degree of agreement determination step of changing each of the specific values ( _G1 , _G2 ) within the predetermined range to change the combination of the specific values ( _G1 , _G2 ), and repeating the processes of the vibration response function spectrum calculation step, the excitation vibration spectrum calculation step, _and the _degree of agreement calculation step to determine a degree of agreement between the frequency spectrum of the excitation noise of the laminated core at the specific excitation magnetic flux density selected in the selection step and the frequency spectrum of the excitation vibration of the laminated core calculated in the excitation vibration spectrum calculation step for each combination of the specific values (G1, G2) that exists for the number of repetitions;
a transverse elastic modulus determination step of detecting the maximum degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined in the degree of agreement determination step, and adopting the combination of the specific values ( _G1 , _G2 ) with which the degree of agreement is maximum as the value of the transverse elastic modulus in two planes including the lamination direction of the laminated core of the first part and the second part. The elastic matrix determination method for a laminated core according to claim 3, characterized in that in the selection step, the cosine coincidence between the difference spectrum for each of the multiple excitation magnetic flux densities calculated in the difference spectrum calculation step and the average spectrum calculated in the average spectrum calculation step is calculated, and the frequency spectrum of the excitation noise at a specific excitation magnetic flux density constituting the difference spectrum with the largest calculated cosine coincidence and the frequency spectrum of the excitation magnetostriction at the specific excitation magnetic flux density with the largest cosine coincidence are selected as those to be adopted for analysis. A computer program for causing a computer to calculate, when performing vibration analysis of a laminated core using a constitutive equation that expresses the relationship between stress and strain in a matrix, the laminated core being formed by stacking a plurality of steel plates and having at least a first portion and a second portion, transverse elastic moduli in two planes including a lamination direction of the first portion and the second portion of the laminated core, the transverse elastic modulus being included in an elastic matrix in the constitutive equation,
The computer includes:
an excitation noise spectrum acquisition step of acquiring a frequency spectrum of the excitation noise of the laminated core, which is the subject of vibration analysis, obtained by measuring the excitation noise of the laminated core for each of a plurality of excitation magnetic flux densities;
an excitation magnetostriction spectrum acquisition step of acquiring a frequency spectrum of the excitation magnetostriction of the steel plate obtained by measuring the excitation magnetostriction of the same steel plate as the steel plate constituting the laminated core for each of a plurality of excitation magnetic flux densities having the same excitation magnetic flux densities as the plurality of excitation magnetic flux densities;
a differential spectrum calculation step of calculating a differential spectrum between a frequency spectrum of the excitation noise for each of the plurality of excitation magnetic flux densities acquired in the excitation noise spectrum acquisition step and a frequency spectrum of the excitation magnetostriction for each of the plurality of excitation magnetic flux densities acquired in the excitation magnetostriction spectrum acquisition step;
an average spectrum calculation step of calculating an average spectrum of the difference spectra for each of the plurality of excitation magnetic flux densities calculated in the difference spectrum calculation step;
a selection step of selecting a frequency spectrum of excitation noise at a specific excitation magnetic flux density to be used for analysis from among the frequency spectra of the excitation noise for each of the multiple excitation magnetic flux densities acquired in the excitation noise spectrum acquisition step, and a frequency spectrum of excitation magnetostriction at a specific excitation magnetic flux density to be used for analysis from among the frequency spectra of excitation magnetostriction for each of the multiple excitation magnetic flux densities acquired in the excitation magnetostriction spectrum acquisition step, according to a degree of coincidence between the difference spectrum for each of the multiple excitation magnetic flux densities calculated in the difference spectrum calculation step and the average spectrum calculated in the average spectrum calculation step;
a vibration response function spectrum calculation step of performing a vibration response analysis by applying to the elastic matrix the values of the transverse elastic modulus in two planes including the lamination direction of the laminated core of the first portion and the second portion as a combination of specific values ( _G1 , _G2 ) selected from a predetermined range for the laminated core to obtain a frequency spectrum of the vibration response function of the laminated core for the combination of the specific values ( _G1 , _G2 );
an excitation vibration spectrum calculation step of calculating a frequency spectrum of excitation vibration of the laminated core from a frequency spectrum of excitation magnetostriction of the steel sheet at the specific excitation magnetic flux density selected in the selection step and a frequency spectrum of the vibration response function of the laminated core calculated in the vibration response function spectrum calculation step;
a coincidence calculation step of determining a degree of coincidence between a frequency spectrum of excitation noise of the laminated core at the specific excitation magnetic flux density selected in the selection step and a frequency spectrum of excitation vibration of the laminated core calculated in the excitation vibration spectrum calculation step;
a degree of agreement determination step of changing each of the specific values ( _G1 , _G2 ) within the predetermined range to change the combination of each of the specific values ( _G1 , _G2 ), and repeating the processes of the vibration response function spectrum calculation step, the excitation vibration spectrum calculation step, _and the _degree of agreement calculation step to determine a degree of agreement between the frequency spectrum of the excitation noise of the laminated core at the specific excitation magnetic flux density selected in the selection step and the frequency spectrum of the excitation vibration of the laminated core calculated in the excitation vibration spectrum calculation step for each combination of the specific values (G1, G2) that exists for the number of repetitions;
a transverse elastic modulus determination step of detecting a maximum value of the degree of agreement for each combination of the specific values ( _G1 , _G2 ) determined in the degree of agreement determination step, and adopting the combination of the specific values ( _G1 , _G2 ) with which the degree of agreement is maximum as the value of the transverse elastic modulus in two planes including the lamination direction of the laminated core of the first portion and the second portion;
A computer program characterized by: The computer program according to claim 5, characterized in that in the selection step, the cosine coincidence between the difference spectrum for each of the multiple excitation magnetic flux densities calculated in the difference spectrum calculation step and the average spectrum calculated in the average spectrum calculation step is calculated, and the frequency spectrum of the excitation noise at a specific excitation magnetic flux density constituting the difference spectrum with the largest calculated cosine coincidence and the frequency spectrum of the excitation magnetostriction at a specific excitation magnetic flux density constituting the difference spectrum with the largest cosine coincidence are selected as those to be adopted for analysis.

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