JP7147831B2 - Elastic matrix determination method and vibration analysis method for laminated core of transformer - Google Patents

Description

The present invention relates to an elastic matrix determination method and a vibration analysis method in a constitutive equation showing the relationship between stress and strain in elastic deformation of a core applied when performing vibration analysis of a laminated core of a transformer.

Transformers such as distribution transformers are constructed by winding a coil around a laminated core in which electromagnetic steel sheets are laminated. Core loss (no-load loss) characteristics, excitation current characteristics, noise characteristics, etc. are important characteristics of transformers.
Transformers for distribution are installed in various places, and it is strongly required that the noise level of transformers installed in urban areas is low. As described above, these days, noise characteristics are becoming more and more important in consideration of the surrounding environment where transformers are installed.

Grain-oriented electrical steel sheets are often used as core materials for transformers. A grain-oriented electrical steel sheet has material expansion and contraction associated with excitation called magnetostriction, and this excitation magnetostriction vibration is said to be the main cause of transformer noise. For this reason, it is said that the noise performance of transformers strongly depends on the magnetostrictive performance of the magnetic steel sheets used, and when manufacturing low-noise transformers, magnetic steel sheets having low magnetostrictive characteristics are used as iron core materials.

However, there are many cases where a sufficiently low noise characteristic of a transformer cannot be obtained even though an iron core is actually manufactured using an electromagnetic steel sheet with excellent magnetostrictive performance. Investigation of the cause of such occurrence reveals that there are many cases in which it is considered that the resonance phenomenon between the natural frequency of the transformer iron core and the magnetostrictive vibration of the electromagnetic steel sheet. Therefore, it is extremely important to calculate and predict the mechanical vibration characteristics including the natural vibration of the core of the transformer in designing and manufacturing the transformer.
Therefore, each node of the finite element or each finite element according to the magnetic flux density given to the electromagnetic part based on the numerical analysis model that expresses the electromagnetic part containing the magnetic material that causes magnetostriction by combining a plurality of finite elements in the finite element analysis An analysis apparatus and an analysis method for calculating a nodal force equivalent to the strain of the joint have been proposed (see, for example, Patent Document 1).

Japanese Unexamined Patent Application Publication No. 2014-71689

However, in the prior art described in Patent Document 1, using a governing equation for structural analysis composed of a balance equation, a constitutive equation showing the relationship between stress and strain, and a relational equation between displacement and strain, I am trying to do a quasi-static structural analysis.
Among these, the constitutive equation showing the relationship between the stress tensor {σ} and the strain tensor {ε} is
{σ}={D}{ε} ({ } indicates a tensor)
is represented by
Here, {D} is a tensor representing the relationship between strain and stress. When the components are displayed, it becomes like the formula (1).

となり、｛Ｄ｝は８１成分、｛σ｝と｛ε｝は９成分ある。ここで、物理量としてのテンソルは対称テンソルとなるので、｛σ｝と｛ε｝の独立成分はそれぞれ６成分となる。したがって、構成式を
［σ］＝［Ｄ］［ε］ （［ ］は行列であることを示す。［Ｄ］を弾性マトリックスと称する。）
と行列表示して、成分で表示すると、（２）式のようになる。

Thus, {D} has 81 components, and {σ} and {ε} have 9 components. Here, since the tensor as a physical quantity is a symmetric tensor, each of {σ} and {ε} has six independent components. Therefore, the constitutive equation is [σ]=[D][ε] ([ ] indicates a matrix. [D] is called an elastic matrix.)
, and the components are expressed as the formula (2).

The relationship between normal stress σ _i and vertical strain ε _i and the relationship between shear strain τ _ij and shear strain γ _ij are expressed using the elastic matrix [D].
However, in the prior art described above, there is no description about the setting of the elasticity matrix [D], and there is no description about how to determine the elasticity matrix [D]. However, in general, there are many cases where the elastic modulus of the member itself, such as an electromagnetic steel sheet, constituting the electromagnetic component to be structurally analyzed is applied as it is.
In this case, it is known that there is a large discrepancy between the calculated value and the measured value when comparing the mechanical vibration calculation results of the electromagnetic parts subject to structural analysis with the actual mechanical vibration measurement results. It is For this reason, it has been considered difficult to reflect the structural analysis by a structural analysis program in the design of an electromagnetic component, which is a laminated structure formed by laminating steel plates.

Here, since the iron core of the transformer used for transformers such as distribution transformers is also a laminated structure composed of laminated steel plates, it is difficult to predict noise using structural analysis using a structural analysis program. Met. For this reason, the noise of the actually manufactured transformer is high, which may cause problems such as extra costs for soundproofing measures such as soundproof walls. In such a case, if it is possible to reduce the noise of the transformer by changing the design of the core of the transformer, the extra cost increase can be suppressed, but how can the noise be reduced by changing the design? I don't know. Therefore, there is a problem that the design cannot be changed easily. There is a strong demand for noise prediction using structural analysis by a structural analysis program so that this design change can be made.

When comparing the results of mechanical vibration calculations of the transformer core, which is the target of structural analysis, with the results of actual mechanical vibration measurements, the major discrepancy between the calculated values and the measured values is due to the fact that the transformer core is a laminated structure composed of laminated steel plates, and the elastic matrix [D] of the laminated structure is originally different from the elastic matrix [D] of the parts themselves, such as the electromagnetic steel plates that make up the laminated core of the transformer. However, there is no good method for determining the elastic matrix [D] of the laminated structure, so the structural analysis is performed by directly substituting the elastic matrix [D] value of the parts themselves such as electromagnetic steel sheets. It is considered to be due to the fact that
In particular, when performing a vibration analysis of a laminated core in which steel plates are laminated using a constitutive equation expressing the relationship between stress and strain in a matrix representation, the transformer included in the above-mentioned elastic matrix [D] in the constitutive equation There is no established method for determining the transverse elastic modulus in two planes including the lamination direction of the laminated core.

Accordingly, the present invention has been made with a focus on the above-described problems of the prior art, and its object is to provide a laminated core in which steel plates are laminated using a constitutive equation expressing the relationship between stress and strain in a matrix representation. A method for determining the elastic matrix of a laminated core of a transformer that can optimally determine the transverse elastic modulus in two planes including the lamination direction of the laminated core of the transformer included in the elastic matrix in the constitutive equation when performing the vibration analysis of and to provide a vibration analysis method.

In order to solve the above problems, the gist of the present invention is as follows.
[1] When performing a vibration analysis of a laminated core of a transformer in which steel plates are laminated using a constitutive equation expressing the relationship between stress and strain in a matrix representation, the transformer included in the elastic matrix in the constitutive equation The transverse elastic modulus in two planes including the lamination direction of the laminated core is the same in a plurality (n pieces) of parts constituting the laminated core, and determines the transverse elastic modulus in the two planes including the same lamination direction A first step of obtaining a frequency spectrum of noise obtained by measuring excitation noise of the laminated core of the transformer to be subjected to vibration analysis, and lamination of the transformer. A second step of acquiring frequency spectrum data of excitation magnetostriction of the same electromagnetic steel sheet as the electromagnetic steel sheet constituting the iron core, and the transverse elastic modulus in two planes including the lamination direction for the laminated iron core of the transformer to be subjected to vibration analysis. Vibration response analysis is performed with a specific value G selected from a predetermined range, and the frequency spectrum of the vibration response function of the laminated core of the transformer for this specific value G is obtained in the third step, and the second step. The frequency spectrum of the excitation vibration of the laminated core of the transformer is calculated from the frequency spectrum data of the excitation magnetostriction of the electromagnetic steel sheet and the frequency spectrum of the vibration response function of the laminated core of the transformer obtained in the third step. a fifth step of obtaining a degree of agreement between the frequency spectrum of the noise of the laminated core of the transformer obtained in the first step and the frequency spectrum of the excited vibration of the laminated core of the transformer calculated in the fourth step; and a sixth step of changing the specific value G within the predetermined range, repeating the third step to the fifth step, and determining the specific value G that maximizes the degree of matching. A method for determining an elastic matrix of a laminated core of a transformer, comprising:

[2] When performing a vibration analysis of a laminated core of a transformer in which steel plates are laminated using a constitutive equation expressing the relationship between stress and strain in a matrix representation, the transformer included in the elastic matrix in the constitutive equation Lateral modulus of elasticity in two planes including the lamination direction of the laminated core is different for each of the plurality (n pieces) of parts constituting the laminated core. A method for determining an elasticity matrix of a laminated core of a transformer for determining coefficients, comprising: a first step of obtaining a frequency spectrum of noise obtained by measuring excitation noise of the laminated core of the transformer to be subjected to vibration analysis; , a second step of acquiring frequency spectrum data of excitation magnetostriction of the same electromagnetic steel sheet as the electromagnetic steel sheet constituting the laminated core of the transformer; ) are _combined with specific values G ₁ , G ₂ , . ₁ , G ₂ , . . . , a third step of obtaining the frequency spectrum of the vibration response function of the laminated core of the transformer for the combination of G _n , and the frequency spectrum data of the excitation magnetostriction of the electromagnetic steel sheet obtained in the second step. and a fourth step of calculating the frequency spectrum of the excitation vibration of the laminated core of the transformer from the frequency spectrum of the vibration response function of the laminated core of the transformer obtained in the third step; a fifth step for determining the degree of coincidence between the frequency spectrum of the noise of the laminated core of the transformer and the frequency spectrum of the excited vibration of the laminated core of the transformer calculated in the _fourth step; _{, G2 , . _} and a sixth step of repeating the fifth step from and determining a combination of specific values _{G 1} , G ₂ , . A method for determining the elastic matrix of laminated cores.

[3] In the fifth step, the frequency spectrum of the noise of the laminated core of the transformer obtained in the first step, and the frequency spectrum of the excited vibration of the laminated core of the transformer calculated in the fourth step. The method for determining the elasticity matrix of the laminated core of the transformer according to [1] or [2], wherein the method for evaluating the degree of coincidence is the cosine degree of coincidence.

[4] The transverse elastic modulus determined by the elastic matrix determination method according to any one of [1] to [3] is incorporated into the elastic matrix of the constitutive equation expressing the relationship between stress and strain in matrix form. A vibration analysis method for a laminated core of a transformer, characterized in that the vibration analysis is performed for a laminated core of a transformer in which steel plates are laminated in a.

According to the elastic matrix determination method for a laminated core of a transformer according to the present invention, when performing a vibration analysis of a laminated core in which steel plates are laminated using a constitutive equation expressing the relationship between stress and strain in a matrix representation, the configuration It is possible to optimally determine the transverse elastic modulus in two planes including the lamination direction of the laminated core of the transformer included in the elastic matrix in the formula, and to suppress the divergence between the measured value and the calculated value of the vibration characteristics. .
In addition, the vibration analysis method for the laminated core of a transformer according to the present invention incorporates the optimally determined transverse elastic modulus in two planes including the lamination direction of the laminated core of the transformer into the constitutive equation to perform the vibration analysis. , the vibration analysis accuracy can be improved.

FIG. 2 is a configuration diagram showing a vibration analysis device that can be applied to the method for determining the elasticity matrix of the laminated core of the transformer according to the first and second embodiments of the present invention; It is a perspective view which shows a three-phase tripod transformer core. It is a figure explaining normal stress and shear stress. 4 is a flowchart showing procedures of an elasticity matrix determination method according to the first embodiment of the present invention; 4 is a graph showing an example of a frequency spectrum of noise obtained by measuring excitation noise of a laminated core of a transformer to be subjected to vibration analysis in the first embodiment of the present invention; 4 is a graph showing an example of frequency spectrum data of excitation magnetostriction of the same electromagnetic steel sheet as that constituting a laminated core of a transformer to be subjected to vibration analysis in the first embodiment of the present invention. In the first embodiment of the present invention, the laminated core of the transformer for the above-mentioned value G when the vibration response analysis is performed with the transverse elastic modulus in two planes including the lamination direction as a specific value G selected from a predetermined range. is a graph showing an example of the frequency spectrum of the vibration response function of . Graph showing an example of the frequency spectrum of the excitation vibration of the laminated core of the transformer calculated from the frequency spectrum of the magnetostriction of the magnetic steel sheet and the frequency spectrum of the vibration response function of the laminated core of the transformer in the first embodiment of the present invention. is. In the first embodiment of the present invention, the relationship between the cosine coincidence of the frequency spectrum of the noise of the laminated core of the transformer and the frequency spectrum of the excitation vibration of the laminated core of the transformer and the transverse elastic modulus in two planes including the lamination direction It is a graph which shows an example of. FIG. 9 is a flow chart showing procedures of an elasticity matrix determination method according to the second embodiment of the present invention; FIG. 4 is a graph showing the frequency spectrum of the noise obtained by measuring the excitation noise of the laminated core of the transformer to be subjected to vibration analysis in the example. 4 is a graph showing frequency spectrum data of excitation magnetostriction of the same magnetic steel sheet as the magnetic steel sheet forming the laminated core of the transformer to be subjected to vibration analysis in the example. Transverse elastic moduli Gzx, Gyz in two planes including the lamination direction of the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 and lateral elastic moduli Gzx, Gyz in the two planes including the lamination direction of the leg portion 22c in the embodiment are The frequency spectrum of the vibration response function of the laminated core of the transformer for the combination of specific values G ₁ and G ₂ when the vibration response analysis is performed for the combination of specific values G ₁ and G ₂ each selected from a predetermined range. is a graph showing 5 is a graph showing the frequency spectrum of the excitation vibration of the laminated core of the transformer calculated from the frequency spectrum of the magnetostriction of the magnetic steel sheet and the frequency spectrum of the vibration response function of the laminated core of the transformer in the example. 4 is a graph showing calculated values of the frequency spectrum of excitation vibration of the laminated core of the transformer and measured values of the frequency spectrum of the noise obtained by measuring the excitation noise of the laminated core of the transformer in the example.

Hereinafter, embodiments of a laminated core elastic matrix determination method and a laminated core vibration analysis method 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 one. Moreover, the following embodiments are intended to exemplify devices and methods for embodying the technical idea of the present invention, and are not intended to limit the configurations to those described below. That is, the technical idea of the present invention can be modified in various ways within the technical scope described in the claims.

(First embodiment)
FIG. 1 shows a vibration analysis apparatus that can be applied to the elastic matrix determination method for a laminated core of a transformer according to the first and second embodiments of the present invention.
The vibration analysis apparatus 10 is a computer system configured by an arithmetic processing unit 12 having a CPU 11, as shown in FIG. Connected to the CPU 11 via an internal bus 13 are 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 for outputting image data to a display.

The external storage device 15 includes a readable disk drive such as a hard disk drive or a solid state drive, and a drive device such as a CD, DVD, or BD for reading data from a recording medium. A recording medium 18 storing a commercially available vibration analysis program is set in the external storage device 15, and the read vibration analysis program is installed in the disk drive. The installation of the vibration analysis program is not limited to the case where the recording medium 18 is used, and the vibration analysis program may be downloaded via a network.

The CPU 11 performs vibration analysis using the finite element method using analysis input data input according to the installed vibration analysis program, and outputs the analysis results from the output device 17 to the display for display. This analysis result is not limited to being displayed on a display, but can be printed by a printer or transmitted via a network.
The laminated core 21 to be analyzed in the first and second embodiments is, for example, a laminated core for a three-phase tripod transformer used as a distribution transformer. For example, 333 sheets of grain-oriented electromagnetic steel sheets 22 having a thickness of 0.3 mm with three legs 22c connected between 22a and lower yoke 22b are laminated and fixed by winding a glass tape.

As an example, the dimensions of the upper yoke 22a and the lower yoke 22b are set to 100 mm width×500 mm length. The dimensions of the three legs 22c are set to 100 mm in width and 300 mm in length, and are connected between the upper yoke 22a and the lower yoke 22b at intervals of 100 mm.
Note that the laminated core 21 to be analyzed in the first and second embodiments is an example of the laminated core for a three-phase tripod transformer shown in FIG. The number of laminated magnetic steel sheets 22, the dimensions of the upper yoke 22a and the lower yoke 22b, the dimensions of the three legs 22c, and the like are not limited to the examples described above.

When conducting a vibration numerical analysis of the laminated core 21 of such a three-phase three-legged transformer, a constitutive equation representing the relationship between stress and strain, which is a governing equation for elastic structural analysis, is used.
This constitutive equation can be expressed as the following equation (3) by replacing the laminate with an equivalent homogeneous body and expressing the influence of the laminate in terms of matrix physical properties.
[σ]=[C][ε] (3)
Here, [σ] is a stress matrix, [C] is an elasticity matrix (stiffness matrix) as a response function, and [ε] is a strain matrix.

Here, assuming that the lamination direction of the steel sheets 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, the stress matrix [σ] is, as shown in FIG. is expressed by the normal stress σx in the X direction, the normal stress σy in the Y direction, and the normal stress σz in the Z direction, and the shear components are the shear stress τzx in the ZX plane, the shear stress τyz in the YZ plane, and the shear stress τxy in the XY plane. expressed.
Similarly, the strain matrix [ε] is 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. It is represented by a plane shear strain γyz and an XY plane shear strain γxy.
Also, the elastic matrix [C] is represented by 36 elastic coefficients C _ij (i=1 to 6, j=1 to 6).
When these are displayed in a matrix, the following formula (4) is obtained.

Since the laminated core is manufactured by laminating grain-oriented electrical steel sheets, the laminated core has mechanical symmetry, and also has 180-degree symmetry in the longitudinal direction and the perpendicular direction of the laminated steel sheets, so anisotropic As a classification, it has orthogonal anisotropy.
For this reason, for objects having orthotropy, basically, C ₁₁ , C ₁₂ , C ₁₃ , C ₂₂ , C ₂₃ , C ₃₃ , C ₄₄ , C ₅₅ and C ₆₆ can be represented by a total of nine elastic moduli.

Of these, the elastic moduli C ₁₁ , C ₁₂ , C ₁₃ , C ₂₂ , C ₂₃ and C ₃₃ are (6 ) to (12). Further, as shown in equations (13) to (15), the elastic modulus C44 is the lateral elastic modulus _Gyz in the YZ plane, the elastic modulus C55 is the lateral elastic modulus _Gzx in the ZX plane, and the elastic modulus _C66 is the transverse elastic modulus Gxy on the XY plane.

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

Therefore, the Poisson's ratio νyx in the YX plane uses Ex, Ey, and νxy, the Poisson's ratio νzy in the ZY plane uses Ez, Ey, and νyz, and the Poisson's ratio νxz in the XZ plane uses Ez, Ex, and νzx. can be used to represent each.
Thus, a total of nine elastic modulus C ₁₁ , C ₁₂ , C ₁₃ , C ₂₂ , C ₂₃ , C ₃₃ , C ₄₄ , C ₅₅ and C ₆₆ values representing the elastic matrix of an orthotropic body can be expressed using a total of 9 mechanical property values of longitudinal elastic modulus Ex, Ey, Ez, transverse elastic modulus Gyz, Gzx, Gxy and Poisson's ratio νxy, νyz, νzx. Determining the physical property value is equivalent to determining nine elastic moduli representing the elastic matrix. Therefore, the method for determining the modulus of longitudinal elasticity, modulus of transverse elasticity, and Poisson's ratio will be described below.

First, regarding the longitudinal elastic moduli of the laminated core having orthotropic anisotropy, the longitudinal elastic moduli Ex and Ey can be set equal to the longitudinal elastic moduli Ex0 and Ey0 of one steel plate. However, the modulus of longitudinal elasticity Ez cannot be set substantially equal to the modulus of longitudinal elasticity Ez0 of one steel plate. The reason is that there is a slight gap between the laminated steel plates. In the first embodiment and the second 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 sheets. was found, Ez=10 GPa. Since the magnitude of the longitudinal elastic modulus in the lamination direction has little effect on the vibration calculation result, Ez does not have to be limited to this value, and is set equal to the longitudinal elastic modulus Ez0 of one steel plate. is not a large error.

Regarding the Poisson's ratio of the laminated core having orthotropic anisotropy, the Poisson's ratio νxy of the XY plane can be set equal to the Poisson's ratio νxy0 of one steel plate, but the Poisson's ratio νyz of the YZ plane and the Poisson's ratio νyz of the ZX plane The Poisson's ratio νzx cannot be directly set to the Poisson's ratios νyz0 and νzx0 of one steel sheet. The reason for this is that in the case of the laminated core, the mechanical coupling between the strain in the lamination direction and the strain in the direction perpendicular to the lamination direction is considered to be extremely weak. Although it is extremely difficult to actually measure νyz and νzx, they are expected to be extremely small values based on the above considerations. Therefore, in the first and second embodiments, νyz=νzx=0.

Furthermore, regarding the transverse elastic modulus of the laminated core, the transverse elastic modulus Gxy of the XY plane can be set equal to the transverse elastic modulus Gxy0 of one steel plate, but the transverse elastic modulus of two planes including the lamination direction, that is, the transverse elastic modulus of the ZX plane As for the modulus of elasticity Gzx and the modulus of elasticity Gyz of the YZ plane, the modulus of elasticity Gxz0 and Gyz0 of one sheet of steel plate cannot be set as they are. The reason for this is that the laminated steel plates slip in the X and Y directions perpendicular to the lamination direction at the boundary surfaces of the laminated steel plates. Because there is a need.

Therefore, determining the transverse elastic modulus in two planes including the lamination direction of the laminated core of the transformer included in the elastic matrix in the constitutive equation, that is, the transverse elastic modulus Gzx in the ZX plane and the transverse elastic modulus Gyz in the YZ plane, This is an important issue in vibration analysis that uses constitutive equations that express the relationship between stress and strain in a laminated core in matrix form.
However, in order to set the lateral elastic modulus Gzx in the ZX plane and the lateral elastic modulus Gyz in the YZ plane to values that reflect the influence of the slippage between the steel plates, it is necessary to actually manufacture a laminated core for a three-phase tripod transformer and obtain an accurate The transverse elastic moduli Gzx and Gyz must be measured. However, no method has been established for measuring the transverse elastic modulus of a laminated core. In the case of metallic materials, it is possible to measure the mechanical constants, including the modulus of transverse elasticity, by using ultrasonic waves, but in the case of laminated cores, there is slippage between the steel plates, so vibration attenuation is large and measurement is difficult. It seems to be because

One method for obtaining the transverse elastic modulus in two planes including the lamination direction of the laminated core is to measure the natural frequency of the laminated core and estimate the transverse elastic modulus from the measured value. However, it is sometimes difficult to measure the natural frequency of the laminated iron core of a transformer due to the large vibration damping, and it is particularly difficult to measure the natural frequency of a large iron core. be.

Therefore, in the elastic matrix determination method according to the first embodiment, the transverse elastic moduli Gzx and Gyz in two planes including the lamination direction are determined by the procedure shown in FIG. In the elastic matrix determination method according to the first embodiment, the transverse elastic moduli of the plurality (n pieces) of parts that constitute the laminated core 21 are the same, and the laminated core 21 of the transformer included in the elastic matrix in the constitutive formula The lateral elastic moduli Gyz and Gzx on two surfaces including the lamination direction are the same for a plurality (n pieces) of parts that constitute the laminated core 21, and the lateral elastic moduli Gyz and Gzx on the two surfaces including the same lamination direction are determined. I am trying to Specifically, in the first embodiment, the lateral elastic modulus of the upper yoke 22a and the lower yoke 22b and the leg portion 22c, which constitute the laminated core 21, are the same, and two planes including the lamination direction of the laminated core 21 of the transformer are used. are the same for the upper yoke 22a and the lower yoke 22b and the leg portion 22c, which constitute the laminated core 21, and the same lateral elastic coefficients Gyz and Gzx are determined.

First, in step S1 (first step), the vibration analysis apparatus 10 inputs the noise frequency spectrum obtained by measuring the excitation noise of the laminated core 21 of the transformer to be subjected to the vibration analysis shown in FIG. Get at 16. Specifically, the laminated core 21 is subjected to excitation noise measurement at a frequency of 50 Hz, and the excitation noise spectrum is sampled from 100 Hz to 1000 Hz at a pitch of 100 Hz as the noise frequency spectrum. FIG. 5 shows an example of the frequency spectrum of noise sampled in this way. The excitation frequency may be 60 Hz, in which case the spectrum of the excitation noise is sampled at intervals of 120 Hz from 120 Hz to 1200 Hz. Below, the case where the excitation frequency is 50 Hz will be described.
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.

Next, in step S2 (second step), the vibration analysis apparatus 10 sets the excitation magnetostriction frequency Spectral data is acquired with the input device 16 . As the frequency spectrum data of excitation magnetostriction, the spectrum data of excitation magnetostriction amplitude is collected at a pitch of 100 Hz from 100 Hz to 1000 Hz. The frequency spectrum data of the excitation magnetostriction can be obtained by measuring the excitation magnetostriction of the magnetic steel sheet or by obtaining it from the manufacturer of the magnetic steel sheet. FIG. 6 shows an example of frequency spectrum data of magnetostriction collected in this way. In FIG. 6, the magnetostriction amplitude is plotted on the vertical axis. After normalization by dividing by the value at a frequency of 100 Hz, the common logarithm is taken and multiplied by 10 to display in db.

Next, in step S3 (third step), the vibration analysis device 10 uses structural analysis software installed in the vibration analysis device 10 to perform vibration response analysis on the laminated core 21 of the transformer to be subjected to vibration analysis. do.
Here, seven of a total of nine mechanical property values of the longitudinal elastic modulus Ex, Ey, Ez, transverse elastic modulus Gyz, Gzx, Gxy, and Poisson's ratio νxy, νyz, νzx of the laminated core 21 are as described above. set as follows.
Ex=Ex0, Ey=Ey0, Ez=10 GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

Further, since the transverse elastic moduli Gyz and Gzx in the remaining two planes including the lamination directions are the same for the plurality (n pieces) of members constituting the laminated core 21, specifically, the laminated core 21 is composed of Since the lateral elastic modulus of the upper yoke 22a and the lower yoke 22b and the leg portion 22c are the same, Gyz=Gzx=G (a specific value selected from a predetermined range) is set, and the transformer for this specific value G , the frequency spectrum of the vibration response function of the laminated core 21 is determined. An example of the frequency spectrum of the vibration response function of the laminated core 21 of the transformer with respect to the specific value G determined in this way is shown in FIG. The predetermined range in which the specific value G is selected here is actually the range of the transverse elastic modulus expected from the structure of the laminated core 21 of the transformer. Range.

Next, in step S4 (fourth step), the vibration analysis apparatus 10 uses the frequency spectrum data of the excitation magnetostriction of the electromagnetic steel sheet acquired in step S2 (second step) and the transformation obtained in step S3 (third step). The frequency spectrum of the excitation vibration of the laminated core 21 of the transformer is calculated from the frequency spectrum of the vibration response function of the laminated core 21 of the transformer. Specifically, the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer is calculated by multiplying the frequency spectrum data of the excitation magnetostriction of the magnetic steel sheet and the frequency spectrum of the vibration response function of the laminated core 21 of the transformer. (In the case of dB display, it is calculated by addition). An example of the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer calculated in this way is shown in FIG.

Next, in step S5 (fifth step), the vibration analysis apparatus 10 calculates the frequency spectrum of the noise of the laminated core 21 of the transformer acquired in step S1 (first step) and the frequency spectrum calculated in step S4 (fourth step). The degree of matching with the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer is obtained.
Here, the problem is how to evaluate the degree of matching between the frequency spectrum of the 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.

Since there are 10 frequency spectrum data of noise from 100 Hz to 1000 Hz with a pitch of 100 Hz, the frequency spectrum data of the noise is expressed as (S100, S200, S300, ..., S1000), and the frequency spectrum data of the excitation vibration. Since there are 10 frequencies from 100 Hz to 1000 Hz with a pitch of 100 Hz, the frequency spectrum data of the excitation vibration is expressed as (V100, V200, V300, .

As a method of evaluating the degree of matching, the above (S100, S200, S300, . . . , S1000) and (V100, V200, V300, . It is common to take the closeness of the Euclidean distance of both points when considering it as a point in space).
However, it is known that the method of evaluating the degree of matching using the Euclidean distance deteriorates accuracy when there is an offset in the data. Frequency spectrum data of excitation noise and excitation vibration are often expressed in dB values, but in this case, there is a degree of freedom in determining where the reference value should be, and there is concern that this degree of freedom may result in an offset.

Therefore, in this embodiment, the cosine degree of coincidence is adopted as a method of evaluating the degree of coincidence without the above concerns. This cosine coincidence is obtained by taking (S100, S200, S300, ..., S1000) and (V100, V200, V300, ..., V1000) as multidimensional vectors (in this case, ten-dimensional space vectors), and In this method, the cosine value of the angle formed by S and V is used as the matching degree. The cosine matching degree can be represented by the following formula (17).

Here, the cosine coincidence COS θ is expressed by dividing the inner product of vectors S and V by the product of the length of vector S and the length of vector V, and is 1 if vector S and vector V match. , and if they are perpendicular to each other, 0 is taken, and if they are in opposite directions, -1 is taken.

Next, in step S6 (sixth step), the vibration analysis apparatus 10 changes the value of the specific value G of the lateral elastic moduli Gyz and Gzx in two planes including the lamination direction within the above-mentioned predetermined range, and step S3 (third step) to step S5 (fifth step) are repeated until the frequency spectrum of the 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 match each other at a maximum. Determine a particular value G. The determined specific value G becomes the transverse elastic moduli Gyz and Gzx in two planes including the lamination direction of the laminated core 21 . That is, the determined specific value G is the transverse elastic modulus Gyz and Gzx in two planes including the same lamination direction at a plurality of (n) sites constituting the laminated core 21, specifically, the laminated core 21. The upper yoke 22a and lower yoke 22b and the leg portion 22c have the same lateral elastic moduli Gyz and Gzx. Since there is only one parameter (G) in step S6, the search can be performed relatively easily.

In FIG. 9, steps S3 (third step) to step S5 (fifth step) are repeated while changing the value of the transverse elastic modulus Gyz=Gzx=G within the range of 0.02 GPa to 1.0 GPa, and the laminated core An example of calculating the degree of cosine matching between the frequency spectrum of the noise of 21 and the frequency spectrum of the excitation vibration of the laminated core 21 is shown. In FIG. 9, the degree of cosine coincidence between the frequency spectrum of the noise of the laminated core 21 and the frequency spectrum of the excitation vibration of the laminated core 21 is a chevron-shaped function with respect to the transverse elastic modulus G, where the value of G is 0.5. The value of G at the highest point where the degree of cosine coincidence is maximized in the range from 02 GPa to 1.0 GPa is approximately 0.20 GPa.

In the first embodiment, the transverse elastic modulus Gyz and Gzx of the laminated core are assumed to be equal. In general, it is possible that the transverse elastic modulus Gyz and Gzx have different values, but in the case of a laminated core of grain-oriented electrical steel sheets, the transverse elastic modulus Gyz and Gzx may be equal, as shown in FIG. This is confirmed in the case of laminated cores of several transformers with different dimensions. In the first embodiment, the lateral elastic modulus Gyz and Gzx are assumed to be equal.

As described above, according to the method for determining the elasticity matrix of the laminated core of the transformer according to the first embodiment, the laminated core 21 in which the steel plates are laminated using the constitutive equation expressing the relationship between stress and strain in a matrix representation When performing the vibration analysis, the transverse elastic moduli Gyz and Gzx in two planes including the lamination direction of the laminated core 21 of the transformer included in the elastic matrix in the constitutive equation are calculated at a plurality (n pieces) of the laminated core 21. The lateral elastic moduli Gyz and Gzx in two planes including the same lamination direction can be optimally determined, and the deviation between the measured value and the calculated value of vibration characteristics can be suppressed.

Then, the vibration analysis device 10 uses structural analysis software installed in the vibration analysis device 10 to perform vibration analysis of the laminated core 21 of the three-phase tripod transformer having the shape shown in FIG. At this time, among the mechanical elastic moduli of the laminated core 21, the lateral elastic moduli Gyz and Gzx including two planes in the lamination direction are set to the values determined by the above elastic matrix determination method, and the other mechanical elastic moduli of the laminated core 21 are The moduli of longitudinal elasticity Ex, Ey, Ez, the modulus of transverse elasticity Gxy, and the Poisson's ratios νxy, νyz, νzx are set as follows, and incorporated into the above-described equation (5) for calculation.
Ex=Ex0, Ey=Ey0, Ez=10 GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

Thus, according to the vibration analysis method for the laminated core of a transformer according to the first embodiment, the transverse elastic moduli Gyz and Gzx in two planes including the lamination direction of the laminated core 21 of the transformer determined optimally are constructed. Vibration analysis accuracy can be improved by incorporating the equation into the vibration analysis.

(Second embodiment)
Next, a method for determining the elasticity matrix of the laminated core of the transformer according to the second embodiment of the present invention will be described with reference to FIG.
The vibration analysis device applied to the elasticity matrix determination method according to the second embodiment is the vibration analysis device 10 shown in FIG. 1, as described above. The laminated core to be analyzed in the second embodiment is the laminated core 21 for a three-phase tripod transformer shown in FIG. 2 as an example.

In the elastic matrix determination method according to the first embodiment, as described above, the transverse elastic moduli of the plurality (n pieces) of the laminated core 21 are the same, and the transformer included in the elastic matrix in the constitutive equation The transverse elastic moduli Gyz and Gzx on two surfaces including the lamination direction of the laminated core 21 are the same for a plurality (n pieces) of parts constituting the laminated core 21, and the transverse elastic moduli on the two surfaces including the same lamination direction Gyz and Gzx are determined. Specifically, in the first embodiment, the transverse elastic moduli Gyz and Gzx in two planes including the lamination direction of the laminated core 21 of the transformer are the upper yoke 22a, the lower yoke 22b, and the legs 22c that constitute the laminated core 21. are the same, and the same lateral elastic moduli Gyz and Gzx are determined.

On the other hand, in the elastic matrix determination method according to the second embodiment, the transverse elastic moduli of the plurality (n pieces) of the laminated core 21 are different, and the transformer lamination included in the elastic matrix in the constitutive formula The transverse elastic moduli Gyz and Gzx in two planes including the lamination direction of the core 21 are different for each of the plurality (n pieces) of the laminated core 21, and the transverse elastic moduli in the two planes including the different lamination directions. Gyz and Gzx are determined. Specifically, the lateral elastic moduli of the upper yoke 22a and the lower yoke 22b, which constitute the laminated core 21, and the leg portions 22c are different, and the lateral elastic moduli Gyz and Gzx in two planes including the lamination direction of the laminated core 21 of the transformer are different. The upper yoke 22a and the lower yoke 22b and the leg portion 22c, which constitute the laminated core 21, are different. and to decide.

Then, in the elastic matrix determination method according to the second embodiment, the transverse elastic moduli Gzx and Gyz in two planes including a plurality (n pieces) of different lamination directions are calculated by the procedure shown in FIG. Lateral elastic moduli Gyz and Gzx of the lower yoke 22a and the lower yoke 22b and lateral elastic modulus Gyz and Gzx of the leg portion 22c are determined.
First, in step S11 (first step), the vibration analysis apparatus 10 inputs the noise frequency spectrum obtained by measuring the excitation noise of the laminated core 21 of the transformer to be subjected to the vibration analysis shown in FIG. Get at 16. Specifically, the laminated core 21 is subjected to excitation noise measurement at a frequency of 50 Hz, and the excitation noise spectrum is sampled from 100 Hz to 1000 Hz at a pitch of 100 Hz as the noise frequency spectrum.
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.

Next, in step S12 (second step), the vibration analysis apparatus 10 sets the excitation magnetostriction frequency of the same magnetic steel sheet as the grain-oriented magnetic steel sheet 22 constituting the laminated core 21 of the transformer to be subjected to the vibration analysis shown in FIG. Spectral data is acquired with the input device 16 . As the frequency spectrum data of excitation magnetostriction, the spectrum data of excitation magnetostriction amplitude is collected at a pitch of 100 Hz from 100 Hz to 1000 Hz. The frequency spectrum data of the excitation magnetostriction can be obtained by measuring the excitation magnetostriction of the magnetic steel sheet or by obtaining it from the manufacturer of the magnetic steel sheet.

Next, in step S13 (third step), the vibration analysis device 10 uses structural analysis software installed in the vibration analysis device 10 to perform vibration response analysis on the laminated core 21 of the transformer to be subjected to vibration analysis. do.
Here, seven of a total of nine mechanical property values of the longitudinal elastic modulus Ex, Ey, Ez, transverse elastic modulus Gyz, Gzx, Gxy, and Poisson's ratio νxy, νyz, νzx of the laminated core 21 are as described above. set as follows.
Ex=Ex0, Ey=Ey0, Ez=10 GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

Since the transverse elastic moduli Gyz and Gzx in the two planes including the remaining two lamination directions are different for each of the plurality (n pieces) of the laminated core 21, Gyz=Gzx=G ₁ , G ₂ , . . . , G _{n (} G ₁ , _{G 2} , _. , _Gn , the frequency spectrum of the vibration response function of the laminated core 21 of the transformer is obtained. Specifically, the lateral elastic modulus of the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 is set as Gyz=Gzx=G1, and the lateral elastic modulus of the leg portion 22c is set as _Gyz = _Gzx =G2 (G ₁ and G ₂ are specific values 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 the specific values G ₁ and G ₂ is obtained.
Here, the predetermined range in which each of the specific values _{G 1} , G ₂ , . and in the present embodiment, the range is from 0.02 GPa to 1.0 GPa.

Next, in step S14 (fourth step), the vibration analysis apparatus 10 uses the frequency spectrum data of the excitation magnetostriction of the electromagnetic steel sheet acquired in step S12 (second step) and the transformation obtained in step S13 (third step). The frequency spectrum of the excitation vibration of the laminated core 21 of the transformer is calculated from the frequency spectrum of the vibration response function of the laminated core 21 of the transformer. Specifically, the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer is calculated by multiplying the frequency spectrum data of the excitation magnetostriction of the magnetic steel sheet and the frequency spectrum of the vibration response function of the laminated core 21 of the transformer. (In the case of dB display, it is calculated by addition).

Next, in step S15 (fifth step), the vibration analysis apparatus 10 calculates the frequency spectrum of the noise of the laminated core 21 of the transformer acquired in step S1 (first step) and the The degree of matching with the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer is obtained.
Here, the degree of coincidence between the frequency spectrum of the 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 employs the cosine degree of coincidence, as in the first embodiment. .

Next, in step S16 (sixth step), the vibration analysis apparatus 10 changes the _specific values G ₁ , G ₂ , . By changing the combination of the values G ₁ , _{G 2} , . Determine the combination of G ₁ , G ₂ , . . . , G _n . The determined specific values G ₁ , _{G 2} , . becomes. Specifically, the value of the lateral elastic modulus Gyz=Gzx=G1 of the upper yoke 22a and the lower yoke 22b and the value of the lateral elastic modulus _{Gyz =} Gzx=G2 of the leg portion 22c are changed within the aforementioned predetermined ranges. to change the combination of the specific values G ₁ and G _2n , repeat steps S13 (third step) to step S15 (fifth step), and set the specific values G ₁ and G Determine the combination of ₂ . The determined specific values G ₁ and G ₂ are the lateral elastic moduli Gzx and Gyx of the upper yoke 22a and the lower yoke 22b, and the lateral elastic moduli Gzx and Gyx of the leg portion 22c.

In step S16 performed by the vibration analysis apparatus 10, unlike the first embodiment, there are a plurality of (n) parameters (G ₁ , G ₂ , . . . , G _n ). Therefore, the number of search points becomes very large and a great deal of labor is required. Therefore, in the second embodiment, by utilizing AI (artificial intelligence) technology, using an optimization search method using GA (genetic algorithm), the transformer stack obtained in step S1 (first step) A search method was employed in which the degree of matching between the frequency spectrum of the noise of the core 21 and the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer calculated in step S14 (fourth step) was used as an evaluation function. As the GA optimization search tool to be used, commercially available search software may be used, or a uniquely created GA optimization search tool such as that used by the inventors may be employed.
As in the first embodiment, the second embodiment also exemplifies the case where the transverse elastic moduli Gyz and Gzx of the laminated core are equal.

As described above, according to the method for determining the elasticity matrix of the laminated core of the transformer according to the second embodiment, the laminated core 21 in which the steel plates are laminated using the constitutive equation expressing the relationship between stress and strain in a matrix representation When performing vibration analysis, it is possible to optimally determine the transverse elastic moduli Gyz and Gzx in two planes including a plurality (n) of different lamination directions of the laminated core 21 of the transformer included in the elastic matrix in the constitutive equation. , it is possible to suppress the divergence between the measured value and the calculated value of the vibration characteristic.

Then, the vibration analysis device 10 uses structural analysis software installed in the vibration analysis device 10 to perform vibration analysis of the laminated core 21 of the three-phase tripod transformer having the shape shown in FIG. At this time, among the mechanical elastic moduli of the laminated core 21, the transverse elastic moduli Gyz and Gzx in two planes including a plurality (n) of different lamination directions of the laminated core 21 are determined by the above elastic matrix determination method, The longitudinal elastic modulus Ex, Ey, Ez, the transverse elastic modulus Gxy, and the Poisson's ratios νxy, νyz, νzx of the laminated core 21 for other mechanical elastic moduli are set as follows and incorporated into the above-described formula (5). to calculate.
Ex=Ex0, Ey=Ey0, Ez=10 GPa
Gxy=Gxy0
νxy=νxy0, νyz=νzx=0

Thus, according to the vibration analysis method for the laminated core of a transformer according to the second embodiment, the optimally determined multiple (n) different transformer laminated cores 21 in two planes including the lamination direction By incorporating the elastic moduli Gyz and Gzx into the constitutive equation and performing the vibration analysis, it is possible to improve the accuracy of the vibration analysis.

Although the embodiment of the present invention has been described above, the present invention is not limited to this and can be modified and improved in various ways.
For example, the evaluation method of the degree of matching between the frequency spectrum of the 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 is not limited to the degree of cosine matching. Euclidean distance can be used as a standard for display, and other methods of evaluating the degree of agreement essentially indicate the degree of agreement between the frequency spectrum data of excitation noise and excitation vibration quantitatively. It is possible to adopt it.

Further, in the above embodiment, the vibration analysis of the three-phase three-legged transformer has been described, but the present invention is not limited to this, and can also be applied to the vibration analysis of the laminated iron core in the three-phase five-legged transformer and other transformers. can be applied.
In addition, in the elastic matrix determination method according to the first embodiment, the lateral elastic moduli of the plurality (n pieces) of the laminated core 21 are the same. A case in which the lower yoke 22b and the leg 22c have the same lateral elastic modulus is described. The number of a plurality of parts constituting the laminated core 21 is arbitrary, and not only the upper yoke 22a, the lower yoke 22b, and the leg part 22c but also parts other than the upper yoke 22a, the lower yoke 22b, and the leg part 22c are laminated. You may make it comprise the iron core 21. FIG.

In addition, in the elastic matrix determination method according to the second embodiment, the lateral elastic moduli of the plurality (n pieces) of the laminated core 21 are different. A case in which the lateral elastic modulus of the leg portion 22b and the leg portion 22c are different is described. Also in the second embodiment, the number of multiple parts constituting the laminated core 21 is arbitrary, and is not limited to the upper yoke 22a, the lower yoke 22b, and the legs 22c. The laminated core 21 may be configured including the portion of .

(Example)
In order to verify the effects of the present invention, a method for determining the elasticity matrix of the laminated core of the transformer according to the second embodiment was carried out.
First, a grain-oriented electrical steel sheet having a thickness of 0.3 mm was prepared. This grain-oriented electrical steel sheet is the same as the grain-oriented electrical steel sheet 22 constituting the laminated core 21 for the three-phase three-phase transformer shown in FIG. 2, which is the object of the vibration analysis. When the frequency spectrum of magnetostriction was measured for this grain-oriented electrical steel sheet at a magnetic flux density of 1.7 T, the results shown in FIG. 12 were obtained.

Next, the prepared grain-oriented electrical steel sheets were laminated to form a laminated core 21 for a three-phase tripod transformer shown in FIG. 2, which was subjected to vibration analysis. The steel plate lamination thickness of the laminated core 21 was set to 100 mm. The dimensions of the upper yoke 22a and the lower yoke 22b were 100 mm wide×500 mm long. The three legs 22c were set to have a width of 100 mm and a core window length of 300 mm, and were connected between the upper yoke 22a and the lower yoke 22b at intervals of 100 mm.
Then, an IV electric wire is 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 is applied to the coil so that the core magnetic flux density becomes exactly 1.7T. After adjusting the power supply voltage, the excitation noise was measured using a sound level meter. When the noise frequency spectrum was obtained using the function of obtaining the noise frequency spectrum of the sound level meter used, the noise frequency spectrum as shown in FIG. 11 was obtained.

Next, in step S11 (first step) shown in FIG. 10, the vibration analysis apparatus 10 inputs the frequency spectrum of the noise (FIG. 11) obtained by measuring the excitation noise of the laminated core 21 to the input device 16. Acquired.
Next, in step S12 (second step), the vibration analysis apparatus 10 acquires the aforementioned frequency spectrum data ( FIG. 12 ) of magnetostriction using the input device 16 .
Next, in step S13 (third step), the vibration analysis device 10 uses structural analysis software installed in the vibration analysis device 10 to perform vibration response analysis on the laminated core 21 of the transformer to be subjected to vibration analysis. did.

Here, seven of the total nine mechanical property values of the longitudinal elastic modulus Ex, Ey, Ez, transverse elastic modulus Gyz, Gzx, Gxy and Poisson's ratio νxy, νyz, νzx of the laminated core 21 are as follows. set to
Ex = 132 GPa, Ey = 220 GPa, Ez = 10 GPa
Gxy = 116 GPa
vxy=0.37, vyz=vzx=0
Here, x, y, and z refer to the steel sheet rolling direction as x and the steel sheet stacking direction as z.

Further, the lateral elastic moduli Gyz and Gzx in two planes including the remaining two lamination directions are different between the upper yoke 22a and the lower yoke 22b and the leg portion 22c that constitute the laminated core 21. FIG. Therefore, the lateral elastic modulus of the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 is set as Gyz=Gzx=G1, and the lateral elastic modulus of the _leg portion 22c is set as _Gyz = _Gzx =G2 (G1, Each of _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 the specific values _G1 and G2 was obtained. Here, the predetermined range in which each of the specific values G ₁ and G ₂ is selected here is actually the range of the transverse elastic modulus expected from the structure of the laminated core 21 of the transformer. , in the range of 0.02 GPa to 1.0 GPa.
For example, when the lateral elastic modulus Gyz=Gzx=G1 of the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 is 0.2 GPa, and the lateral elastic modulus Gyz=Gzx ₌ G2 of the _leg portion 22c is 0.1 GPa , the frequency spectrum of the vibration response function of the laminated core 21 is shown in FIG.

Next, in step S14 (fourth step), the vibration analysis apparatus 10 uses the frequency spectrum data of the excitation magnetostriction of the electromagnetic steel sheet acquired in step S12 (second step) and the transformation obtained in step S13 (third step). The frequency spectrum of the excitation vibration of the laminated core 21 of the transformer was calculated from the frequency spectrum of the vibration response function of the laminated core 21 of the transformer.
For example, when the lateral elastic modulus Gyz=Gzx=G1 of the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 is 0.2 GPa, and the lateral elastic modulus Gyz=Gzx ₌ G2 of the _leg portion 22c is 0.1 GPa , the frequency spectrum of the excitation vibration of the laminated core 21 is as shown in FIG.

Next, in step S15 (fifth step), the vibration analysis apparatus 10 calculates the frequency spectrum of the noise of the laminated core 21 of the transformer acquired in step S11 (first step) and the frequency spectrum calculated in step S14 (fourth step). The degree of matching with the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer was obtained.
Here, the degree of coincidence between the frequency spectrum of the 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 employs the cosine degree of coincidence, as in the first embodiment. .

Next, in step S16 (sixth step), the vibration analysis apparatus 10 calculates the value of the lateral elastic modulus Gyz=Gzx=G1 of the upper yoke 22a and the lower yoke 22b and the lateral elastic modulus Gyz= _Gzx = of the leg portion 22c. The value of G ₂ is changed within the above-described predetermined range to change the combination of the specific values G ₁ and G ₂ , step S13 (third step) to step S15 (fifth step) are repeated, and the above-described A particular combination of values G ₁ and G ₂ that maximizes the degree of agreement was determined. The determined specific values G ₁ and G ₂ are the lateral elastic moduli Gzx and Gyz of the upper yoke 22a and the lower yoke 22b, and the lateral elastic moduli Gzx and Gyz of the leg portion 22c.

In step S16 performed by the vibration analysis apparatus 10 of the embodiment, there are two parameters (G ₁ , G ₂ ). labor intensive. Therefore, in the embodiment, by utilizing AI (artificial intelligence) technology, using an optimization search method using GA (genetic algorithm), the laminated core 21 of the transformer obtained in step S1 (first step) and the frequency spectrum of the excitation vibration of the laminated core 21 of the transformer calculated in step S14 (fourth step) is used as an evaluation function.

An optimization search using the GA (genetic algorithm) revealed that the lateral elastic modulus G1 of the upper yoke 22a and the _lower yoke 22b was 0.25 GPa, and the lateral elastic modulus G2 of the _leg portion 22c was 0.15 GPa. It was found that when
Finally, the frequency spectrum of the excitation vibration of the laminated core 21 calculated for the combination of G ₁ and G ₂ with G ₁ =0.25 GPa and G ₂ =0.15 GPa is taken as the excitation vibration of the laminated core of the transformer. It was used as the final calculated value of the frequency spectrum.

FIG. 15 shows the calculated values of the frequency spectrum of the excitation vibration of the laminated core of the transformer and the measured values of the frequency spectrum of the noise obtained by measuring the excitation noise of the laminated core of the transformer in the example. show. Both agree very well, and depending on the embodiment, the transverse elastic modulus Gzx and It was confirmed that Gyz and the transverse elastic moduli Gzx and Gyz in two planes including the lamination direction of the legs 22c of the laminated core 21 of the transformer can be obtained with high accuracy.

10 vibration analysis device 11 CPU
12 Arithmetic processing unit 13 Internal bus 14 Internal storage device 15 External storage device 16 Input device 17 Output device 18 Recording medium 21 Laminated iron core 22 Grain-oriented electrical steel sheet (steel sheet)
22a upper yoke 22b lower yoke 22c leg

Claims (4)

When performing a vibration analysis of a laminated core of a transformer in which steel plates are laminated using a constitutive equation expressing the relationship between stress and strain in a matrix representation, the laminated core of the transformer included in the elastic matrix in the constitutive equation Laminated core of a transformer that determines the transverse elastic modulus on two surfaces including the same lamination direction, wherein the transverse elastic modulus on two surfaces including the lamination direction is the same in a plurality (n pieces) of parts constituting the laminated core A method for determining the elasticity matrix of
a first step of obtaining a noise frequency spectrum obtained by measuring excitation noise of a laminated core of the transformer to be subjected to vibration analysis;
a second step of acquiring frequency spectrum data of excitation magnetostriction of the same magnetic steel sheet as the magnetic steel sheet constituting the laminated core of the transformer;
For the laminated core of the transformer to be subjected to vibration analysis, a vibration response analysis is performed with the transverse elastic modulus in two planes including the lamination direction as a specific value G selected from a predetermined range, and the transformation with respect to this specific value G a third step of determining the frequency spectrum of the vibration response function of the laminated core of the vessel;
Excitation vibration of the laminated core of the transformer from the frequency spectrum data of the excitation magnetostriction of the electromagnetic steel sheet acquired in the second step and the frequency spectrum of the vibration response function of the laminated core of the transformer obtained in the third step a fourth step of calculating a frequency spectrum;
A fifth step of obtaining a degree of agreement between the frequency spectrum of the noise of the laminated core of the transformer obtained in the first step and the frequency spectrum of the excitation vibration of the laminated core of the transformer calculated in the fourth step;
a sixth step of changing the specific value G within the predetermined range, repeating the third step to the fifth step, and determining a specific value G that maximizes the degree of matching;
A method for determining an elastic matrix of a laminated core of a transformer, comprising: When performing a vibration analysis of a laminated core of a transformer in which steel plates are laminated using a constitutive equation expressing the relationship between stress and strain in a matrix representation, the laminated core of the transformer included in the elastic matrix in the constitutive equation The transverse elastic modulus in two planes including the lamination direction is different for each of the plurality (n pieces) of parts constituting the laminated core. A method for determining the elastic matrix of a laminated core of a transformer comprising:
a first step of obtaining a noise frequency spectrum obtained by measuring excitation noise of a laminated core of the transformer to be subjected to vibration analysis;
a second step of acquiring frequency spectrum data of excitation magnetostriction of the same magnetic steel sheet as the magnetic steel sheet constituting the laminated core of the transformer;
For the laminated core of the transformer to be subjected to vibration analysis, specific values G ₁ , G ₂ . , _Gn , and obtain the frequency spectrum of the vibration response function of the laminated core of the transformer for the combination of the specific values G ₁ , G ₂ , . . . , _Gn . a step;
Excitation vibration of the laminated core of the transformer from the frequency spectrum data of the excitation magnetostriction of the electromagnetic steel sheet acquired in the second step and the frequency spectrum of the vibration response function of the laminated core of the transformer obtained in the third step a fourth step of calculating a frequency spectrum;
A fifth step of obtaining a degree of agreement between the frequency spectrum of the noise of the laminated core of the transformer obtained in the first step and the frequency spectrum of the excitation vibration of the laminated core of the transformer calculated in the fourth step;
_{The values of the specific values G 1 , G 2 , .} a sixth step of repeating the third step to the fifth step to determine a combination of specific values _{G 1} , G ₂ , .
A method for determining an elastic matrix of a laminated core of a transformer, comprising: The degree of matching between the frequency spectrum of the noise of the laminated core of the transformer obtained in the first step and the frequency spectrum of the excited vibration of the laminated core of the transformer calculated in the fourth step, which is obtained in the fifth step. 3. The method for determining the elasticity matrix of a laminated core for a transformer according to claim 1 or 2, wherein the evaluation method of is a degree of cosine coincidence. Steel plates were laminated by incorporating the transverse elastic modulus determined by the elastic matrix determination method according to any one of claims 1 to 3 into the elastic matrix of the constitutive equation expressing the relationship between stress and strain in matrix form. A vibration analysis method for a laminated core of a transformer, comprising performing a vibration analysis of a laminated core for a transformer.

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