Elastic matrix determination method and vibration analysis method for laminated iron core of transformer, and elastic matrix determination program and vibration analysis program

Abstract

A method for determining an elastic matrix of a laminated core of a transformer includes: calculating a degree of coincidence between a frequency spectrum of noise and a frequency spectrum of excitation vibration for each combination of a first assumed value and a second assumed value of a lateral elastic modulus; and a step in which the first assumed value and the second assumed value when the degree of coincidence becomes the maximum value are used as the lateral elastic modulus. The step of calculating the degree of coincidence includes: a step of calculating the degree of coincidence of test points dispersed within a predetermined range; setting a limited small area; and a step of calculating the degree of coincidence of the search points located between the test points within the defined small region.

Description

Technical Field

[0001] This disclosure relates to methods for determining the elastic matrix and vibration analysis of laminated cores of transformers, as well as procedures for determining the elastic matrix and vibration analysis. Additionally, this disclosure relates to a method for calculating the mechanical vibration characteristics of transformer cores manufactured from laminated electromagnetic steel sheets using a computer. Background Technology

[0002] An analytical apparatus is known to be based on a numerical analysis model of an electromagnetic component comprising a magnetic body that generates magnetostriction, which is represented by a combination of multiple finite elements in the finite element method analysis, and calculates nodal forces equivalent to the strain of each node of the finite element or the strain of each finite element corresponding to the magnetic flux density (see, for example, Patent Document 1).

[0003] Japanese Patent Application Publication No. 2014-71689

[0004] In transformers constructed by winding coils onto a laminated iron core made of laminated electromagnetic steel sheets, noise is generated by the vibration of the iron core due to magnetostriction. Structural analysis aims to improve the design and reduce transformer noise. Summary of the Invention

[0005] Therefore, the purpose of this disclosure is to provide a method for determining the elastic matrix and a vibration analysis method for the laminated core of a transformer, as well as an elastic matrix determination procedure and a vibration analysis procedure, which are helpful for designing transformers to reduce noise.

[0006] (1) An embodiment of this disclosure relates to a method for determining the elastic matrix of a transformer's laminated core, which determines the elastic matrix of the transformer's laminated core. The laminated core is constructed by stacking multiple electromagnetic steel plates and includes at least a first part and a second part. Structural formulas representing the stress-strain relationship of the first part and the second part respectively include mutually different elastic matrices. The elastic matrix includes the transverse elastic modulus of the laminated core in both planes including the stacking direction as elements of the elastic matrix.

[0007] The methods for determining the elastic matrix of the laminated core of the above-mentioned transformer include:

[0008] Step 1: Obtain the spectrum of the excitation noise of the laminated core of the above transformer;

[0009] Step 2: Obtain the excitation magnetostriction spectrum of the above-mentioned electromagnetic steel plate;

[0010] Step 3: For the laminated core of the above-mentioned transformer, determine a first assumed value and a second assumed value to calculate the spectrum of the vibration response function of the laminated core of the above-mentioned transformer when the first assumed value and the second assumed value are applied to the above-mentioned elastic matrix. The first assumed value assumes the value of the transverse elastic modulus in the two sides including the lamination direction in the first part. The second assumed value assumes the value of the transverse elastic modulus in the two sides including the lamination direction in the second part.

[0011] Step 4: Calculate the excitation vibration spectrum of the laminated core of the transformer based on the excitation magnetostriction spectrum data of the electromagnetic steel plate obtained in Step 2 above and the spectrum of the vibration response function of the laminated core of the transformer calculated in Step 3 above.

[0012] Step 5: Calculate the consistency between the spectrum of the excitation noise of the laminated core of the transformer obtained in Step 1 and the spectrum of the excitation vibration of the laminated core of the transformer calculated in Step 4.

[0013] Step 6 involves repeatedly performing steps 3 through 5 by changing the first and second assumptions respectively, and calculating the consistency degree for each combination of the first and second assumptions; and

[0014] Step 7: Detect the maximum value of the consistency calculated in Step 6 for each combination of the first and second assumed values, and use the first assumed value when the consistency becomes the maximum value as the transverse elastic modulus of the laminated core in the first part, including both sides of the stacking direction, and use the second assumed value when the consistency becomes the maximum value as the transverse elastic modulus of the laminated core in the second part, including both sides of the stacking direction.

[0015] Step 6 above includes:

[0016] Step 6-A: When each combination of the first assumed value and the second assumed value corresponding to the above consistency degree is represented as a test point set in a two-dimensional space with the first assumed value as the first axis and the second assumed value as the second axis, points dispersed within a specified range of the above two-dimensional space are selected sequentially as the test points, and the above consistency degree is calculated for the combination of the first assumed value and the second assumed value corresponding to the above test points.

[0017] Step 6-B involves defining a limited small region in the two-dimensional space based on the consistency calculated for the combination of the first and second assumptions corresponding to the aforementioned test points; and

[0018] Step 6-C: Set search points in the aforementioned limited small area with an interval narrower than the interval of the aforementioned test points, and calculate the aforementioned consistency degree for the combination of the aforementioned first assumption value and the aforementioned second assumption value corresponding to the aforementioned search points.

[0019] (2) In the fifth step of the method for determining the elastic matrix of the laminated core of the transformer described in (1) above, the cosine of the angle between the first vector, which takes each frequency component of the noise spectrum of the laminated core of the transformer as an element, and the second vector, which takes each frequency component of the excitation vibration spectrum of the laminated core of the transformer as an element, can be calculated as the consistency degree.

[0020] (3) One embodiment of the vibration analysis method of the present disclosure includes the following steps: performing vibration analysis of the laminated core of the transformer based on a structural formula that embeds the transverse elastic modulus determined by the elastic matrix determination method of the laminated core of the transformer described in (1) or (2) above, representing the stress-strain relationship of each of the first part and the second part above.

[0021] (4) An embodiment of the present disclosure involves a flexible matrix determination program that causes a computer to execute the flexible matrix determination method described in (1) or (2) above.

[0022] (5) In one embodiment of the present disclosure, the vibration analysis program causes a computer to execute the vibration analysis method described in (3) above.

[0023] The method and procedure for determining the elastic matrix of the laminated core of the transformer disclosed herein can reduce the discrepancy between measured and calculated vibration characteristics. Furthermore, the vibration analysis method and procedure for the laminated core of the transformer disclosed herein can improve the accuracy of vibration analysis. Attached Figure Description

[0024] Figure 1 This is a diagram illustrating an example of the structure of a laminated core of a transformer, which is the object of analysis in one embodiment of a vibration analysis method.

[0025] Figure 2A This diagram illustrates the vertical stress acting on the laminated iron core in the lamination direction, i.e., the Z-axis direction.

[0026] Figure 2B This diagram illustrates the vertical stress acting in the direction orthogonal to the stacking direction of the laminated iron core, i.e., the X-axis direction.

[0027] Figure 2C This diagram illustrates the vertical stress acting in the direction orthogonal to the stacking direction of the laminated iron core, namely the Y-axis direction.

[0028] Figure 2D This diagram illustrates the shear stress acting on the ZX plane of the laminated iron core.

[0029] Figure 2E This diagram illustrates the shear stress acting on the XY plane of the laminated iron core.

[0030] Figure 2F This diagram illustrates the shear stress acting on the YZ plane of the laminated iron core.

[0031] Figure 3 This is a flowchart illustrating an example of a method for determining an elastic matrix in one implementation.

[0032] Figure 4 This is a block diagram illustrating an example configuration of a vibration analysis apparatus according to one embodiment.

[0033] Figure 5 This is a graph representing an example of the noise spectrum of a transformer.

[0034] Figure 6 This is a graph representing an example of the spectral data of the excitation magnetostriction of the electromagnetic steel plates that make up the laminated iron core of a transformer.

[0035] Figure 7 This is a graph representing an example of the spectrum of the vibration response function of the laminated core of a transformer.

[0036] Figure 8 This is a graph representing an example of the spectrum of excitation vibration of the laminated iron core of a transformer.

[0037] Figure 9 This is an example of a two-dimensional mapping diagram showing the consistency between the spectrum of excitation vibration and the spectrum of excitation noise of a transformer's laminated core.

[0038] Figure 10 It means in order to obtain Figure 9 A diagram of an example of the trajectory of a search performed using a two-dimensional mapping graph.

[0039] Figure 11 This is a graph representing an example of the noise spectrum of the transformer involved in the embodiment.

[0040] Figure 12 This is a graph representing an example of the spectral data of the excitation magnetostriction of the electromagnetic steel plate constituting the laminated core of the transformer involved in the embodiment.

[0041] Figure 13 This is a graph representing an example of the spectrum of the vibration response function of the laminated core of the transformer involved in the embodiment.

[0042] Figure 14 This is a graph representing an example of the spectrum of excitation vibration of the laminated core of the transformer involved in the embodiment.

[0043] Figure 15 This is a diagram illustrating an example of a two-dimensional mapping of the consistency between the spectrum of excitation vibration and the spectrum of excitation noise of the laminated core of the transformer involved in the embodiment.

[0044] Figure 16 It is a graph comparing the calculated value of the excitation vibration spectrum of the laminated core of the transformer involved in the embodiment with the measured value of the noise spectrum obtained by measuring the excitation noise of the laminated core of the transformer.

[0045] Figure 17 It is a graph representing the trajectory of the search using GA (Genetic Algorithm).

[0046] Figure 18A This is a graph representing an example of test points dispersed at 0.1 GPa intervals on a two-dimensional mapping.

[0047] Figure 18B It means through Figure 18A A chart showing an example of the consistency results calculated from the test points.

[0048] Figure 19A This is a graph representing an example of test points dispersed at 0.075 GPa intervals on a two-dimensional mapping.

[0049] Figure 19B Through Figure 19A A chart showing an example of the consistency results calculated from the test points.

[0050] Figure 20A This is a graph representing an example of test points dispersed at 0.05 GPa intervals on a two-dimensional mapping.

[0051] Figure 20B It means through Figure 20A A chart showing an example of the consistency results calculated from the test points.

[0052] Figure 21A This is a graph representing an example of test points dispersed at 0.025 GPa intervals on a two-dimensional mapping.

[0053] Figure 21B It means through Figure 21A A chart showing an example of the consistency results calculated from the test points. Detailed Implementation

[0054] Transformers, such as those used for power distribution, are constructed by winding coils into a laminated iron core made of stacked electromagnet steel sheets. Important performance characteristics of transformers include, for example, iron loss (no-load loss) characteristics, excitation current characteristics, and noise characteristics.

[0055] Distribution transformers are installed in various locations. Especially for transformers located in urban areas, low noise levels are a strong requirement. Recently, considering the impact of transformer installations on the surrounding environment, noise reduction, particularly the reduction of noise levels, has become increasingly important as a performance requirement for transformers.

[0056] The core material of transformers, typically oriented electromagnetic steel sheets, vibrates due to the material's expansion and contraction associated with excitation. This expansion and contraction is also known as magnetostriction, and the vibration caused by it is called magnetostrictive vibration. Magnetostrictive vibration is one of the main causes of noise in transformers. Therefore, the noise performance of a transformer is highly dependent on the magnetostrictive properties of the electromagnetic steel sheets used as the core material. To reduce transformer noise, electromagnetic steel sheets with low magnetostrictive properties can be used as the core material.

[0057] However, even when using electromagnetic steel plates with excellent magnetostrictive properties as the core material, transformer noise is often not sufficiently reduced. One reason for this insufficient noise reduction is the resonance phenomenon caused by the proximity of the natural vibration frequency of the transformer core to the magnetostrictive vibration frequency of the electromagnetic steel plate. Therefore, in the design and manufacture of transformers, it is extremely important to pre-calculate the mechanical vibration characteristics of the transformer core, such as its natural vibration frequency.

[0058] Here, we consider analyzing the mechanical vibration characteristics of electromagnetic components, such as the core of a transformer, which include magnetic bodies that produce magnetostriction, using the finite element method. For example, based on a numerical analysis model of the electromagnetic component represented by a combination of multiple finite elements in the finite element analysis, the nodal forces equivalent to the strain of each node or individual finite element, corresponding to the magnetic flux density imparted to the electromagnetic component, can be calculated. In this case, a quasi-static structural analysis is performed using the governing equations of structural analysis, consisting of equilibrium equations, structural equations representing the relationship between stress and strain, and equations representing the relationship between displacement and strain.

[0059] In the quasi-static structural analysis described above, the relationship between the stress tensor {σ} and the strain tensor {ε} is expressed by the formula {σ} = {D}{ε}. Here, {·} represents a tensor. {D} is a tensor representing the relationship between strain and stress.

[0060] Here, the components of the above formula are expressed as in formula (1).

[0061] [Formula 1]

[0062]

[0063] In equation (1), {D} is represented by 81 components. {σ} and {ε} are each represented by 9 components. Here, the tensor as a physical quantity is called a symmetric tensor. By considering the symmetric components, the number of independent components of {σ} and {ε} becomes 6 each. The result is that if the tensor relation is represented by a matrix as [σ] = [D][ε] using the notation [·], and further represented by components, it is represented as in equation (2). Here, [D] is also called the elasticity matrix.

[0064] [Formula 2]

[0065]

[0066] Furthermore, the relationship between vertical stress σi and vertical strain εi, as well as the relationship between shear strain τij and shear strain γij, are represented using the elastic matrix [D].

[0067] Here, the elastic modulus of the components themselves, such as the electromagnetic steel plates constituting the electromagnetic components that are the objects of structural analysis, can be directly applied as the elastic matrix [D]. However, it is known that when the elastic modulus of the components themselves is used as the elastic matrix [D], the difference between the calculated results of the mechanical vibration of the electromagnetic components that are the objects of structural analysis and the actual measured results of the mechanical vibration becomes large. Because the difference between the calculated results and the measured results is large, it is difficult to reflect the results of structural analysis based on the structural analysis program in the design of the laminated structure, i.e., the electromagnetic components, which are composed of laminated steel plates.

[0068] Furthermore, the cores used in transformers such as distribution transformers are also laminated structures made of stacked steel plates. Therefore, even when noise is predicted based on the results of structural analysis using structural analysis programs, the prediction accuracy is low. Due to the low accuracy of noise prediction, the actual noise of the manufactured transformers sometimes exceeds expectations. In cases of high transformer noise, additional costs arise due to the need for soundproofing measures such as sound barriers. To reduce transformer noise and suppress additional costs, changes to the transformer core design are considered. However, when there is a large discrepancy between the calculated and measured results of mechanical vibration, it is unclear how to make design changes that will reduce noise. To determine the policy for transformer design changes, it is necessary to improve the prediction accuracy of noise using structural analysis based on structural analysis programs.

[0069] When comparing the calculated mechanical vibration results of the transformer core, which will be the object of structural analysis, with the actual measured mechanical vibration results, consider the following as reasons for the large discrepancy between the calculated and measured values. In the case where the transformer core is a laminated structure composed of laminated steel plates, the elastic matrix [D] of the laminated structure is inherently different from the elastic matrix [D] of the components such as the electromagnetic steel plates constituting the transformer core. Nevertheless, it is still considered that directly substituting the value of the elastic matrix [D] of the components such as the electromagnetic steel plates for structural analysis will result in a large discrepancy between the calculated and measured values.

[0070] Therefore, in order to reduce the difference between the calculated results and the measured results, it is required to determine the elastic matrix [D] of the laminated structure with high precision. In particular, when using a structural formula that represents the relationship between stress and strain in matrix notation to perform vibration analysis of laminated iron cores made of laminated steel plates, it is required to determine the transverse elastic modulus of the transformer's laminated iron core, including the lamination direction, in the elastic matrix [D] of the structural formula with high precision.

[0071] The purpose of this disclosure is to provide a method for determining the elastic matrix of a transformer's laminated core, including the transverse elastic modulus in both sides of the laminated core, within a structural formula representing the relationship between stress and strain using matrix notation. Furthermore, the purpose of this disclosure is to provide a vibration analysis method that improves the accuracy of vibration analysis results by using a structural formula including the determined elastic matrix to analyze the vibration of a laminated core made of laminated steel plates.

[0072] The following describes embodiments of the method for determining the elastic matrix of a laminated iron core and the method for vibration analysis of a laminated iron core according to the present disclosure, based on the accompanying drawings. The drawings are illustrative and may differ from reality. Furthermore, the following embodiments illustrate apparatus or methods for embodying the technical concept of the present invention and do not specify the structure as described below. That is, various modifications can be made to the technical concept of the present disclosure within the scope of the technology claimed in this application.

[0073] (Implementation Method)

[0074] In this embodiment, the laminated iron core 21, which is the object of analysis, is, for example, the laminated iron core used in a three-phase three-limb transformer for distribution transformers. Figure 1As shown, the laminated iron core 21 can be constructed by stacking multiple orientation-oriented electromagnetic steel plates 22, each having a predetermined thickness and connected by three posts 22c between the upper yoke 22a and the lower yoke 22b. As an example, the thickness of the orientation-oriented electromagnetic steel plate 22 is 0.23 mm. As an example, the number of stacked orientation-oriented electromagnetic steel plates 22 is 333. The stacked orientation-oriented electromagnetic steel plates 22 are fixed by winding glass tape. As an example, the dimensions of the upper yoke 22a and the lower yoke 22b are set to a width of 100 mm × a length of 500 mm. As an example, the dimensions of the three posts 22c are set to a width of 100 mm × a length of 300 mm. The three posts 22c are connected between the upper yoke 22a and the lower yoke 22b at 100 mm intervals. The laminated iron core 21 analyzed in this embodiment is not limited to... Figure 1 The illustrated three-phase three-limb transformer uses a laminated iron core. The thickness of the orientation-oriented electromagnetic steel plate 22, the number of laminated sheets of the orientation-oriented electromagnetic steel plate 22, the dimensions of the upper yoke 22a and lower yoke 22b, or the dimensions of the three columns 22c are not limited to the examples described above.

[0075] To perform numerical analysis of the vibration of the laminated core 21 of such a three-phase three-limb transformer, a structural formula representing the relationship between stress and strain is used as the governing equation for elastic structural analysis. The structural formula is expressed as shown in equation (3) below by replacing the laminate with an equivalent homogeneous body and representing the effect of the laminate with matrix properties.

[0076] [σ]=[C][ε]…(3)

[0077] [σ] is the stress matrix. [C] is the elastic matrix (stiffness matrix) that serves as the response function. [C] is the same as [D] mentioned above. [ε] is the strain matrix.

[0078] like Figure 1 As shown, the directions of the laminated iron core 21 are represented by the X-axis, Y-axis, and Z-axis of the XYZ orthogonal coordinate system. The orientation-oriented electromagnetic steel plate 22 extends along the XY plane and is laminated along the Z-axis direction.

[0079] The stress acting on the laminated iron core 21 includes a vertical component acting in the direction perpendicular to the laminated iron core 21 (compression direction or tension direction) and a shear component acting in the shear direction of the laminated iron core 21. Figure 2A , Figure 2B and Figure 2C The vertical stresses acting in the Z-axis, X-axis, and Y-axis directions are illustrated separately. The vertical stresses acting in the Z-axis, X-axis, and Y-axis directions are represented by σz, σx, and σy, respectively. Figure 2D , Figure 2E and Figure 2FShear stresses acting on the ZX, XY, and YZ planes are illustrated. The shear stresses acting on the ZX, XY, and YZ planes are denoted by τzx, τxy, and τyz, respectively. The stress matrix [σ] has components of both perpendicular stress and shear stress.

[0080] The strain of the laminated iron core 21 includes the component of strain in the vertical direction (compression or tension) and the component of strain in the shear direction. The vertical strains in the Z-axis, X-axis, and Y-axis directions are represented by εz, εx, and εy, respectively. The shear strains in the ZX plane, XY plane, and YZ plane are represented by γzx, γxy, and γyz, respectively.

[0081] Furthermore, the elasticity matrix [C] has 6 × 6 = 36 elements that determine the relationship between the 6 components of stress and the 6 components of strain. The 36 elements are represented by the elastic modulus Cij (i = 1 to 6, j = 1 to 6). The relationship between stress and strain is represented by the elasticity matrix as shown in equation (4) below.

[0082] [Formula 3]

[0083]

[0084] The laminated iron core 21 is constructed by laminating oriented electromagnetic steel plates 22, thus possessing the mechanical symmetry of the laminated iron core 21, and also exhibiting 180-degree symmetry in the length direction and orthogonal direction of the laminated oriented electromagnetic steel plates 22. Therefore, it can be said that the laminated iron core 21 has orthogonal anisotropy as a classification of anisotropy. The elastic matrix of an object with orthogonal anisotropy is basically represented by nine elastic moduli: C11, C12, C13, C22, C23, C33, C44, C55, and C66, as shown in Equation (5) below.

[0085] [Formula 4]

[0086]

[0087] The elastic moduli C11, C12, C13, C22, C23 and C33 of the above nine elastic moduli are calculated based on the longitudinal elastic moduli Ex, Ey and Ez and the Poisson's ratios νxy, νyx, νyz, νzy, νzx and νxz, by the following equations (6) to (12).

[0088] [Formula 5]

[0089]

[0090] Furthermore, as shown in equations (13), (14), and (15) below, the elastic modulus C44 corresponds to the transverse elastic modulus Gyz in the YZ plane. The elastic modulus C55 corresponds to the transverse elastic modulus Gzx in the ZX plane. The elastic modulus C66 corresponds to the transverse elastic modulus Gxy in the XY plane.

[0091] [Formula 6]

[0092] C 44 =G yz …(13)

[0093] C 55 =G zx …(14)

[0094] C 66 =G xy …(15)

[0095] Here, Ex, Ey, and Ez represent the longitudinal elastic modulus (Young's modulus) in the X direction, the longitudinal elastic modulus (Young's modulus) in the Y direction, and the longitudinal elastic modulus (Young's modulus) in the Z direction, respectively. νxy, νyx, νyz, νzy, νzx, and νxz represent the Poisson's ratio (the ratio of longitudinal strain in the X direction to transverse strain in the Y direction) in the XY plane, the Poisson's ratio in the YX plane, the Poisson's ratio in the YZ plane, the Poisson's ratio in the ZY plane, the Poisson's ratio in the ZX plane, and the Poisson's ratio in the XZ plane, respectively. The relationship between the longitudinal elastic modulus and the Poisson's ratio, known as the reciprocal theorem, expressed by the following equation (16), holds.

[0096] [Formula 7]

[0097]

[0098] According to the reciprocal theorem, the Poisson's ratio νyx in the YX plane is represented by Ex, Ey, and νxy. The Poisson's ratio νzy in the ZY plane is represented by Ez, Ey, and νyz. The Poisson's ratio νxz in the XZ plane is represented by Ez, Ex, and νzx.

[0099] Thus, the values ​​of the nine elastic moduli C11, C12, C13, C22, C23, C33, C44, C55, and C66 representing the elasticity matrix of an orthogonally anisotropic object are expressed using nine mechanical property values: longitudinal elastic moduli Ex, Ey, and Ez; transverse elastic moduli Gyz, Gzx, and Gxy; and Poisson's ratios νxy, νyz, and νzx. Therefore, determining these nine mechanical property values ​​is equivalent to determining the nine elastic moduli representing the elasticity matrix. The methods for determining the longitudinal elastic modulus, transverse elastic modulus, and Poisson's ratio are explained below.

[0100] First, regarding the longitudinal modulus of elasticity of the orthotropic laminated iron core, the longitudinal modulus of elasticity Ex and Ey can be set to values ​​equal to the longitudinal modulus of elasticity Ex0 and Ey0 of a single steel plate. On the other hand, the longitudinal modulus of elasticity Ez cannot be set to a value equal to the longitudinal modulus of elasticity Ez0 of a single steel plate. This is because there are minute gaps between the laminated steel plates. Therefore, in this embodiment, an experiment is conducted to determine the relationship between load and displacement in the laminated steel plate in the lamination direction, and the longitudinal modulus of elasticity Ez is set based on the experimental results. In this embodiment, Ez is set to 10 GPa based on the experiment. Furthermore, the magnitude of the longitudinal modulus of elasticity in the lamination direction has little impact on the vibration calculation results. Therefore, even if Ez is set to a value equal to the longitudinal modulus of elasticity Ez0 of a single steel plate, the error in the vibration calculation results will not increase.

[0101] Furthermore, regarding the Poisson's ratio of a laminated iron core with orthogonal anisotropy, the Poisson's ratio νxy in the XY plane can be set to a value equal to the Poisson's ratio νxy0 of a single steel plate. On the other hand, the Poisson's ratio νyz in the YZ plane and the Poisson's ratio νzx in the ZX plane cannot be directly set to the Poisson's ratios νyz0 and νzx0 of a single steel plate. This is because it is assumed that the mechanical coupling between strain in the lamination direction and strain perpendicular to the lamination direction in the laminated iron core is extremely weak. Here, it is very difficult to measure νyz and νzx in practice. However, based on the above idea, it is foreseeable that νyz and νzx are extremely small values. Therefore, in this embodiment, both νyz and νzx are assumed to be zero.

[0102] Furthermore, regarding the transverse elastic modulus of the laminated core, the transverse elastic modulus Gxy in the XY plane can be set to a value equal to the transverse elastic modulus Gxy0 of a single steel plate. On the other hand, the transverse elastic moduli of both sides including the lamination direction, namely the transverse elastic modulus Gzx in the ZX plane and the transverse elastic modulus Gyz in the YZ plane, cannot be directly set to the transverse elastic modulus Gxz0 and Gyz0 of a single steel plate. This is because it is necessary to reflect the effect of the sliding between the steel plates caused by the boundary surfaces of the laminated steel plates along the X and Y directions orthogonal to the lamination direction in the transverse elastic moduli Gzx and Gyz. Therefore, in order to improve the analysis accuracy of vibration analysis using structural formulas that represent the stress-strain relationship of the laminated core in matrix notation, it is important to accurately determine the transverse elastic modulus of the transformer's laminated core including both sides including the lamination direction, namely the transverse elastic modulus Gzx in the ZX plane and the transverse elastic modulus Gyz in the YZ plane, as included in the elasticity matrix of the structural formula.

[0103] Here, as a method to determine the transverse elastic modulus Gzx in the ZX plane and Gyz in the YZ plane as values ​​reflecting the effect of slippage between steel plates, we consider measuring the accurate transverse elastic moduli Gzx and Gyz using laminated iron cores actually manufactured for three-phase three-limb transformers. However, a method for measuring the transverse elastic modulus of laminated iron cores has not yet been established. This is because: in the case of metallic materials, it is believed that mechanical constants including the transverse elastic modulus can be measured using ultrasonic measurements, but in the case of laminated iron cores, the slippage between the steel plates significantly attenuates the vibration, making accurate measurement difficult.

[0104] Furthermore, as one method for determining the transverse modulus of elasticity in both sides of a laminated core, including the lamination direction, one approach is to measure the natural vibration frequency of the laminated core and infer the transverse modulus of elasticity based on its value. However, there are cases where it remains difficult to measure the natural vibration frequency of a transformer's laminated core due to significant vibration attenuation. This is especially true when the core is large, making it particularly challenging to measure the natural vibration frequency.

[0105] Therefore, in the elastic matrix determination method according to this embodiment, by executing Figure 3 The process shown determines the transverse elastic moduli Gzx and Gyz in both sides, including the lamination direction. In this embodiment, Figure 1 The laminated core 21 of a three-phase three-limb transformer, shown as an example, is the subject of analysis. In this embodiment, the lateral elastic modulus of the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 are the same. Moreover, the lateral elastic modulus of the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 is different from that of the column portion 22c. That is, the lateral elastic moduli Gyz and Gzx of the laminated core 21 of the transformer, including both sides in the lamination direction, included in the elasticity matrix in the structural formula are different in the upper yoke 22a and the lower yoke 22b constituting the laminated core 21 and the column portion 22c. Therefore, in the elasticity matrix determination method according to this embodiment, the lateral elastic moduli Gyz and Gzx including multiple different lamination directions are determined. The transverse elastic moduli Gyz and Gzx of the upper yoke 22a and lower yoke 22b and the transverse elastic moduli Gyz and Gzx of the column 22c are determined by executing the elastic matrix determination method involved in this embodiment.

[0106] The upper yoke 22a and lower yoke 22b are also collectively referred to as the first part. The column portion 22c is also referred to as the second part. That is, the laminated iron core 21 has the first part and the second part. The transverse elastic moduli Gyz and Gzx of the first part are different from those of the second part. The transverse elastic moduli Gyz and Gzx of the first part and the second part are determined by performing the elasticity matrix determination method according to this embodiment.

[0107] The various processes of the elasticity matrix determination method involved in this embodiment can be derived from... Figure 4 The illustrated vibration analysis device 40 is used. The vibration analysis device 40 includes a control unit 42, a storage unit 44, and an interface 46.

[0108] The control unit 42 controls and manages the various functional units constituting the vibration analysis device 40 and the vibration analysis device 40 as a whole. To control and manage the various functions, the control unit 42 may be configured to include at least one processor, such as a CPU (Central Processing Unit). The control unit 42 may consist of one processor or multiple processors. The processor constituting the control unit 42 can implement the functions of the vibration analysis device 40 by reading and executing programs stored in the storage unit 44.

[0109] The storage unit 44 can function as a memory for storing various types of information. For example, the storage unit 44 can store programs executed in the control unit 42, or data or results of processing performed in the control unit 42. Furthermore, the storage unit 44 can function as working memory for the control unit 42. The storage unit 44 can be constructed from, for example, semiconductor memory, but is not limited to this, and can be configured to include any storage device. For example, the storage unit 44 can be configured as internal memory used as the processor of the control unit 42, or it can be configured as a hard disk drive (HDD) accessible by the control unit 42.

[0110] Interface 46 can be configured to include a communication interface for communicating with other devices via wired or wireless means. Interface 46 can be configured to include input / output ports for inputting and outputting data with other devices. Interface 46 transmits and receives necessary data and signals to a process computer or host system. Interface 46 can communicate based on wired communication standards or wireless communication standards. For example, wireless communication standards may include cellular phone communication standards such as 3G, 4G, or 5G. Other wireless communication standards may include, for example, IEEE 802.11 or Bluetooth (registered trademark). Interface 46 can support one or more of these communication standards. Interface 46 is not limited to these examples and can communicate with other devices or input / output data based on various standards.

[0111] Hereinafter, it will be described assuming that each process of the elastic matrix determination method according to this embodiment is executed by the control unit 42 of the vibration analysis device 40. Each process of the elastic matrix determination method may also be executed by other devices or by humans.

[0112] First of all, Figure 3 In step S1 (step 1), the control unit 42 acquires the information regarding... Figure 1 The results shown are the measurement results of the noise spectrum obtained by measuring the excitation noise of the laminated iron core 21 of the transformer, which is the object of vibration analysis. Specifically, the excitation noise was measured with the excitation frequency set to 50Hz in the laminated iron core 21. The spectrum of the transformer's excitation noise consists of frequency components that are integer multiples of twice the excitation frequency, i.e., even multiples of the excitation frequency. Therefore, the spectrum of the excitation noise at each frequency in 100Hz intervals within the range of 100Hz to 1000Hz is obtained as the noise spectrum. In the transformer manufacturing site, the excitation noise characteristics of the transformer are widely measured as a quality management item for finished products. Therefore, its measurement is not particularly difficult. The excitation frequency can be set to 60Hz. With the excitation frequency set to 60Hz, the spectrum of the excitation noise at 120Hz intervals from 120Hz to 1200Hz is obtained.

[0113] The following explanation assumes the excitation frequency is set to 50Hz. An example of the noise spectrum obtained when the excitation frequency is set to 50Hz is shown below. Figure 5 This is shown as a chart. Figure 5 In the chart, the horizontal axis represents frequency, and the vertical axis represents the magnitude of excitation noise.

[0114] Next, in Figure 3 In step S2 (the second step), the control unit 42 acquires and configures... Figure 1 The image shows the excitation magnetostriction spectrum data of the same electromagnetic steel sheet 22 as the orientation electromagnetic steel sheet of the laminated iron core 21 of the transformer, which is the object of vibration analysis. The excitation magnetostriction spectrum data is obtained by acquiring the spectrum data of the excitation magnetostriction amplitude at 100Hz intervals within the range of 100Hz to 1000Hz. The excitation magnetostriction spectrum data 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, etc. An example of the acquired excitation magnetostriction spectrum data is shown in... Figure 6 This is shown as a chart. Figure 6In the graph, the horizontal axis represents frequency. The vertical axis represents the magnitude of the magnetostrictive amplitude. The magnitude of the magnetostrictive amplitude at each frequency is expressed in dB as a normalized value obtained by dividing by the magnetostrictive amplitude at a frequency of 100 Hz. The dB value corresponds to the value obtained by multiplying the common logarithm of the displayed value by 10.

[0115] Next, in step S3 (step 3), the control unit 42 assumes the transverse elastic moduli Gyz and Gzx, and calculates the spectrum of the vibration response function for the assumed transverse elastic moduli. Specifically, the control unit 42 uses structural analysis software to perform vibration response analysis on the laminated core 21 of the transformer, which is the object of vibration analysis. Of the nine mechanical property values ​​of the laminated core 21—the longitudinal elastic moduli Ex, Ey, and Ez, the transverse elastic moduli Gyz, Gzx, and Gxy, and the Poisson's ratios νxy, νyz, and νzx—the seven excluding the transverse elastic moduli Gyz and Gzx are set as described above.

[0116] Ex=Ex0, Ey=Ey0, Ez=10GPa

[0117] Gxy=Gxy0

[0118] νxy=νxy0, νyz=νzx=0

[0119] The two transverse moduli of elasticity, Gyz and Gzx, which are located on both sides of the stacking direction, are different for each of the multiple (2) portions constituting the stacked core 21. Specifically, the transverse moduli of elasticity, Gyz and Gzx, of the upper yoke 22a and lower yoke 22b are different from those of the column portion 22c. Here, the transverse moduli of elasticity of the upper yoke 22a and lower yoke 22b are assumed to be set as Gyz = Gzx = G1. The transverse moduli of elasticity of the column portion 22c is assumed to be set as Gyz = Gzx = G2. G1 and G2 are values ​​temporarily selected from a specified range and set as transverse moduli of elasticity, and are also referred to as assumed values ​​of transverse moduli of elasticity. G1 corresponds to the transverse moduli of elasticity, Gyz and Gzx, of the first portion, and is also referred to as the first assumed value. G2 corresponds to the transverse moduli of elasticity, Gyz and Gzx, of the second portion, and is also referred to as the second assumed value. The control unit 42 changes the combination of assumed values ​​(G1, G2) and calculates the spectrum of the vibration response function of the laminated iron core 21 of the transformer for each combination.

[0120] An example of the spectrum of the vibration response function of the laminated core 21 of the transformer calculated for a specific combination of values ​​(G1, G2) is shown in Figure 7 This is shown as a chart. Figure 7In the graph, the horizontal axis represents frequency, and the vertical axis represents the magnitude of the response function. The magnitude of the response function is indicated by normalization, with the vibration response value at a frequency of 100 Hz being 0 dB. Here, it is assumed that each of the values ​​(G1, G2) is actually selected from the range of transverse modulus of elasticity contemplated according to the construction of the laminated core 21 of the transformer. In this embodiment, each of G1 and G2 is selected from the range of 0.05 GPa to 0.5 GPa.

[0121] Next, in step S4 (step 4), the control unit 42 calculates the spectrum of the excitation vibration of the transformer's laminated core 21 based on the spectrum data of the excitation magnetostriction of the electromagnetic steel plate obtained in step S2 (step 2) and the spectrum of the vibration response function of the transformer's laminated core 21 calculated in step S3 (step 3). Specifically, the control unit 42 calculates the spectrum of the excitation vibration of the transformer's laminated core 21 as the product of the spectrum data of the excitation magnetostriction of the electromagnetic steel plate and the spectrum of the vibration response function of the transformer's laminated core 21. When the spectrum is indicated in dB, the control unit 42 calculates the spectrum of the excitation vibration of the transformer's laminated core 21 as a sum.

[0122] An example of the excitation vibration spectrum of the transformer's laminated core 21 calculated in this way is... Figure 8 This is shown as a chart. Figure 8 In the graph, the horizontal axis represents frequency. The vertical axis represents the calculated magnitude of the excitation vibration. The magnitude of the excitation vibration is expressed in dB.

[0123] Next, in step S5 (step 5), the control unit 42 calculates the consistency between the measurement result of the noise spectrum of the transformer's laminated core 21 obtained in step S1 (step 1) and the calculation result of the excitation vibration spectrum of the transformer's laminated core 21 calculated in step S4 (step 4).

[0124] The spectral data of noise were measured for each frequency in 100Hz intervals from 100Hz to 1000Hz. Therefore, the number of noise spectral data points is 10. Thus, each frequency component of the noise spectral data is labeled (S100, S200, S300, ..., S1000). Additionally, the spectral data of excitation vibration were calculated for each frequency in 100Hz intervals from 100Hz to 1000Hz. Therefore, the number of excitation vibration spectral data points is 10. Thus, each frequency component of the excitation vibration spectral data is labeled (V100, V200, V300, ..., V1000). The method for calculating the consistency will be explained below based on these labels.

[0125] The frequency components (S100, S200, S300, ..., S1000) representing the noise spectrum data and the frequency components (V100, V200, V300, ..., V1000) representing the excitation vibration spectrum data are respectively regarded as data points in multi-dimensional space. In this case, these data points are regarded as data points in 10-dimensional space.

[0126] Here, the control unit 42 can typically calculate the consistency between the noise spectrum data and the excitation vibration spectrum data as the Euclidean distance between data points in a multidimensional space. However, it is known that when the consistency is calculated as Euclidean distance, the accuracy of the consistency calculation decreases due to data offsets. When the spectrum data of excitation noise and excitation vibration are expressed in dB values, there is a concern that the degree of freedom in determining where to take the reference value may cause data offsets and degrade the accuracy of the consistency calculation.

[0127] Therefore, in order to avoid concerns about the deterioration of calculation accuracy due to data offset, in this embodiment, the control unit 42 calculates the cosine uniformity as the uniformity. When considered as multidimensional vectors S and V (in this case, 10-dimensional spatial vectors) having elements (S100, S200, S300, ..., S1000) and (V100, V200, V300, ..., V1000) respectively, the cosine uniformity is calculated as the cosine value of the angle between the two vectors. The multidimensional vector S is also referred to as the first vector. The multidimensional vector V is also referred to as the second vector. The cosine uniformity is calculated using the following equation (17). In equation (17), COSθ represents the cosine uniformity. Symbols marked with "→" above the symbols "S" and "V" represent the multidimensional vectors S and V.

[0128] [Formula 8]

[0129]

[0130] The cosine uniformity is calculated by dividing the inner product of multidimensional vectors S and V by the product of the lengths of S and V. If multidimensional vectors S and V are aligned, the cosine uniformity is calculated as 1. If multidimensional vectors S and V are orthogonal, the cosine uniformity is calculated as 0. If multidimensional vectors S and V are oriented in opposite directions, the cosine uniformity is calculated as -1.

[0131] Next, in step S6 (step 6), the control unit 42 determines whether the mapping of the consistency within the specified range has ended by changing the assumed values ​​according to the process of steps S3 to S5. Specifically, the control unit 42 repeatedly executes the process of steps S3 to S5 while changing the combination of assumed values ​​(G1, G2), and calculates the consistency in each combination of assumed values ​​(G1, G2). The control unit 42 maps the consistency calculated for each combination of assumed values ​​onto a two-dimensional mapping diagram. Specifically, an example of the calculation result of the consistency between the spectrum of excitation vibration and the spectrum of excitation noise of the laminated core 21 of the transformer is shown in... Figure 9 It is shown as a two-dimensional mapping diagram. Figure 9 In the two-dimensional mapping diagram, the vertical axis and the horizontal axis represent G1 and G2, respectively. Figure 9 The text describes contour lines representing equal uniformity. Figure 9 In the contour lines that form closed curves, the smaller-diameter closed curves correspond to contour lines with high uniformity. The combination of G1 and G2, where the uniformity becomes a maximum, corresponds to the vicinity of the center of the closed curve. The control unit 42 can map the uniformity of each combination of assumed values ​​to a two-dimensional mapping graph, and determine that the mapping is complete when a specified range is filled. Alternatively, the control unit 42 can also determine that the mapping is complete when a maximum value can be detected in the two-dimensional mapping graph with mapped uniformity.

[0132] If the mapping is not determined to be complete (step S6: No), the control unit 42 returns to the process of step S3, and repeats the process of steps S3 to S6 until the mapping is determined to be complete. If the mapping is determined to be complete (step S6: Yes), the control unit 42 proceeds to the process of step S7.

[0133] In step S7 (step 7), the control unit 42 detects points where the uniformity reaches a maximum value from the two-dimensional mapping diagram. Then, the control unit 42 uses a combination of assumed values ​​(G1, G2) when the uniformity reaches a maximum value as the transverse elastic modulus Gzx and Gyz in both sides including the stacking direction for each of the multiple (2) parts constituting the laminated core 21. Specifically, the control unit 42 uses G1 as the transverse elastic modulus Gzx and Gyz for the upper yoke 22a and lower yoke 22b. That is, the control unit 42 sets Gzx = Gyz = G1 for the upper yoke 22a and lower yoke 22b. In addition, the control unit 42 uses G2 as the transverse elastic modulus Gzx and Gyz for the column portion 22c. That is, the control unit 42 sets Gzx = Gyz = G2 for the column portion 22c. After executing step S7, the control unit 42 ends the process. Figure 3 The execution of the flowchart process.

[0134] In this embodiment, during the repeated execution of steps S3 to S6, the control unit 42 terminates the mapping of the consistency degree and changes the two parameters G1 and G2 to detect the maximum value of the consistency degree. That is, the control unit 42 needs to perform a two-dimensional numerical search. Due to the two-dimensional search, the number of search points becomes very large. In addition, the two-dimensional search requires a huge computational load. Therefore, in this embodiment, artificial intelligence (AI) technology is effectively utilized, and an optimization search method using a genetic algorithm (GA) is used. Specifically, the consistency degree between the noise spectrum of the transformer's laminated core 21 obtained in step S1 and the excitation vibration spectrum of the transformer's laminated core 21 calculated in step S4 is used as the evaluation function in the optimization search method. As the GA optimization search tool used, commercially available search software can be used. Alternatively, a custom-made GA optimization search tool can be used, as has been done by the inventors.

[0135] Furthermore, in this embodiment, the case where the transverse modulus of elasticity, Gyz, is considered to be equal to Gzx for a laminated iron core is illustrated. The values ​​of Gyz and Gzx may also differ. However, the inventors have not only considered... Figure 1 The illustrated laminated core further confirms that the values ​​of Gyz and Gzx can be considered equal in laminated cores with various sizes of oriented electromagnetic steel sheets. Therefore, in this embodiment, the values ​​of the transverse modulus of elasticity Gyz and Gzx are considered to be equal.

[0136] This is an example of the consistency between the spectrum of the excitation vibration and the spectrum of the excitation noise of the transformer's laminated core 21, calculated in step 6 of the method for determining the elasticity matrix of the transformer's laminated core 21 described above. Figure 9 In the two-dimensional mapping diagram, the values ​​of (G1, G2) representing the maximum values ​​can be used as the transverse elastic moduli Gyz and Gzx of the transformer in both planes including the stacking direction. The accuracy of the vibration analysis was confirmed to be based on... Figure 9 The vibration analysis in step 7 is improved by embedding Gyz and Gzx into the structural formula using a two-dimensional mapping diagram. Therefore, the accuracy of the transformer vibration analysis is improved by performing the above-described steps 1 to 7 to determine the elastic matrix of the transformer's laminated core 21.

[0137] Here, in order to obtain the consistency between the spectrum representing excitation vibration and the spectrum representing excitation noise... Figure 9 The search performed using the GA optimization search tool based on the two-dimensional mapping graph. Figure 10 The trajectory shown in the chart is executed. Figure 10 The vertical and horizontal axes correspond to G1 and G2, respectively. Figure 10 In the chart, each circle corresponds to a search point. Figure 10The number of search points drawn in the diagram is approximately 800.

[0138] In step 6, the consistency of each search point is calculated repeatedly. The consistency of each search point is calculated by performing steps 3 through 5. The vibration response analysis performed as part of step 3 during the consistency calculation process is performed, for example, using structural analysis software. The time required to perform the vibration response analysis using structural analysis software depends on the performance of the computer used, but even using a high-performance computer typically used in numerical computation, each search point generally requires approximately 2 hours. Figure 9 As shown in the two-dimensional mapping, to obtain a two-dimensional mapping with a data density sufficient to determine the maximum points of consistency between the spectrum of excitation vibration and the spectrum of excitation noise, at least approximately 800 search points are required. Therefore, in order to obtain... Figure 9 The required vibration response analysis time is 2 hours × 800 (points) = 1600 hours = approximately 67 days. That is, in the case of performing only a search using the GA optimization search tool, in order to obtain... Figure 9 The result will take more than two months.

[0139] Therefore, the inventors investigated a method to shorten the time required to calculate the two-dimensional mapping of consistency in step 6 above. As a result, it was found that step 6 of the elasticity matrix determination method according to this disclosure, comprising the following process, can shorten the time required to calculate the two-dimensional mapping of consistency.

[0140] Specifically, the control unit 42 of the vibration analysis device 40 performs step 6-A as step 6, that is, when each combination of the first assumed value G1 and the second assumed value G2, which are the objects of the consistency calculation, is represented as test points for trial search, points scattered in a two-dimensional space with the first assumed value G1 as the first axis and the second assumed value G2 as the second axis are selected as test points in sequence, and the consistency calculation is repeatedly performed on the selected test points by processing steps 3 to 5.

[0141] The control unit 42 performs step 6-B, which is to set a limited small area within the region where test points are scattered in two-dimensional space as the object to be searched more meticulously, based on the consistency calculated in step 6-A.

[0142] The control unit 42 executes step 6-C, which is to set search points between test points in the limited small area set in step 6-B and perform a search. Steps 3 to 5 are processed at each search point and the consistency is calculated repeatedly. The consistency is calculated in the limited small area to become a combination of maximum values ​​(G1, G2).

[0143] As a method for performing the search by setting search points in a limited small area in step 6-C, AI (artificial intelligence) technology can be effectively utilized. An optimization search method using GA (genetic algorithm) is employed, which uses the consistency between the noise spectrum of the transformer's laminated core 21 obtained in step 1 and the excitation vibration spectrum of the transformer's laminated core 21 calculated in step 4 as the evaluation function.

[0144] As described above, by setting search points within a limited small region, the total number of test points and search points required to calculate the combination where the consistency reaches a maximum (G1, G2) is significantly reduced. The result is a substantial reduction in the time required to calculate the two-dimensional map of consistency and the combination where the consistency reaches a maximum (G1, G2).

[0145] Finally, the values ​​of (G1, G2) when the consistency reaches its maximum are embedded in the structural formula as the transverse elastic moduli Gyz and Gzx of the transformer in both sides including the stacking direction to perform the vibration analysis in step 7. This not only improves the accuracy of the vibration analysis, but also significantly reduces the required time and speeds up the process.

[0146] As described above, according to the elasticity matrix determination method for the laminated core 21 of the transformer according to this embodiment, when performing vibration analysis on the laminated core 21 with laminated steel plates using a structural formula representing the relationship between stress and strain in matrix notation, the multiple (two) different transverse elastic moduli Gyz and Gzx of the laminated core 21 of the transformer, including the lamination direction, included in the elasticity matrix of the structural formula, are determined to be optimal. As a result, the deviation between the measured and calculated values ​​of the vibration characteristics is suppressed.

[0147] (Example)

[0148] The following is an example illustrating the verification of the effectiveness of the elastic matrix determination method and vibration analysis method for the laminated core of the transformer involved in this embodiment.

[0149] First, a 0.23mm thick oriented electromagnetic steel sheet was prepared. Next, the prepared oriented electromagnetic steel sheet was stacked, thus... Figure 1As illustrated, a laminated core 21 for a three-phase, three-limb transformer, which is the subject of vibration analysis, was manufactured. The thickness of the steel plates laminated in the laminated core 21 is 100 mm. Furthermore, the upper yoke 22a and lower yoke 22b are 100 mm wide and 500 mm long. Additionally, the three columns 22c are 100 mm wide and have a core window length of 300 mm. The columns 22c are connected between the upper yoke 22a and lower yoke 22b at 100 mm intervals. Moreover, excitation coils are formed by winding IV (Indoor PVC) wires around the three columns 22c of the manufactured laminated core 21.

[0150] A 50Hz three-phase current was applied to the coil, and the power supply voltage was adjusted so that the core magnetic flux density was exactly 1.7T. Under these conditions, [the following conditions apply]. Figure 3 Similarly, in step S1, the excitation noise is measured using a noise meter, thereby obtaining the noise spectrum. Figure 11 The image shows an example of the measurement results of the noise spectrum. Figure 11 Explanation of the vertical and horizontal axes of the chart. Figure 5 The charts are the same.

[0151] Next, the magnetostriction of the prepared oriented electromagnetic steel plate was measured using a magnetostriction measuring device under conditions of excitation frequency of 50 Hz and magnetic flux density of 1.5 T, 1.6 T and 1.7 T, respectively, thereby obtaining the magnetostriction spectrum. Figure 12 The image shows an example of the measurement results of the magnetostriction spectrum. Figure 12 In the graph, the horizontal axis represents frequency, and the vertical axis represents the magnitude of magnetostriction.

[0152] Next, vibration response analysis was performed on the laminated core 21 of the transformer, which became the object of vibration analysis, using structural analysis software. Here, seven out of the nine mechanical properties of the laminated core 21, namely the longitudinal elastic modulus Ex, Ey and Ez, the transverse elastic modulus Gyz, Gzx and Gxy, and the Poisson's ratios νxy, νyz and νzx, were set as follows.

[0153] Ex=132GPa, Ey=220GPa, Ez=10GPa

[0154] Gxy = 116 GPa

[0155] νxy=0.37, νyz=νzx=0

[0156] Here, x corresponds to the rolling direction of the steel plate. y corresponds to the direction orthogonal to x. z corresponds to the stacking direction of the steel plate.

[0157] Furthermore, regarding the remaining two transverse elastic moduli Gyz and Gzx, which are located on both sides of the stacking direction, the transverse elastic moduli Gyz and Gzx of the upper yoke 22a and lower yoke 22b constituting the laminated core 21 are different from those of the column portion 22c. In this case, the transverse elastic moduli of the upper yoke 22a and lower yoke 22b constituting the laminated core 21 are set as Gyz = Gzx = G1. The transverse elastic moduli of the column portion 22c are set as Gyz = Gzx = G2. Here, G1 and G2 are assumed values ​​selected from a specified range. Moreover, the spectrum of the vibration response function of the laminated core 21 of the transformer for the combination of these assumed values ​​(G1, G2) is calculated. The specified range for each of the assumed values ​​(G1, G2) is actually the range of transverse elastic moduli expected based on the construction of the laminated core 21 of the transformer, which in this embodiment is the range of 0.05 GPa to 0.4 GPa.

[0158] For example, the calculated spectrum of the vibration response function of the laminated iron core 21 under the condition that the transverse elastic modulus of the upper yoke 22a and lower yoke 22b constituting the laminated iron core 21 is Gyz = Gzx = G1 = 0.2 GPa, and the transverse elastic modulus of the column portion 22c is Gyz = Gzx = G2 = 0.2 GPa, is... Figure 13 As shown in the image. Figure 13 Explanation of the vertical and horizontal axes of the chart. Figure 7 The charts are the same.

[0159] Next, with Figure 3 The process of step S4 is the same, based on... Figure 3 The excitation magnetostriction spectrum data of the electromagnetic steel plate obtained in step S2 and in Figure 3 In step S3, the spectrum of the vibration response function of the laminated core 21 of the transformer was calculated, and the spectrum of the excitation vibration of the laminated core 21 of the transformer was calculated. For example, the calculation result of the spectrum of the excitation vibration of the laminated core 21 when the transverse elastic modulus of the upper yoke 22a and lower yoke 22b constituting the laminated core 21 is Gyz = Gzx = G1 = 0.2 GPa, and the transverse elastic modulus of the column 22c is Gyz = Gzx = G2 = 0.2 GPa, is as follows: Figure 14 As shown in the image. Figure 14 Explanation of the vertical and horizontal axes of the chart. Figure 8 The charts are the same.

[0160] Next, with Figure 3 The process of step S5 is the same, calculating in Figure 3 The noise spectrum of the laminated core 21 of the transformer obtained in step S1 is compared with that in... Figure 3The consistency of the excitation vibration spectrum of the laminated core 21 of the transformer, calculated in step S4, is used here. The cosine consistency is calculated as the consistency between the noise spectrum of the laminated core 21 and the excitation vibration spectrum of the transformer's laminated core 21. The cosine consistency is also known as the Cosine similarity.

[0161] Next, with Figure 3 The process of step S6 is similar, in which the values ​​of the transverse elastic modulus Gyz=Gzx=G1 of the upper yoke 22a and the lower yoke 22b, and the values ​​of the transverse elastic modulus Gyz=Gzx=G2 of the column 22c are changed within the above-mentioned specified ranges to change the combination of assumed values ​​(G1, G2), and this process is repeated. Figure 3 The processes of steps S3 to S5 are used to create a two-dimensional mapping diagram representing the consistency between the spectrum of excitation vibration and the spectrum of excitation noise. Figure 15 An example of a two-dimensional mapping diagram produced through this embodiment is shown. Figure 15 The vertical and horizontal axes of the chart correspond to G1 and G2, respectively.

[0162] In addition, Figure 3 In step S6, there are two parameters (G1, G2), thus requiring a two-dimensional numerical search. Therefore, the number of search points becomes very large, necessitating significant labor. Therefore, in this embodiment, artificial intelligence (AI) technology is effectively utilized, employing an optimization search method based on a genetic algorithm (GA), which... Figure 3 The noise spectrum of the laminated core 21 of the transformer obtained in step S1 is compared with that in... Figure 3 The search method uses the consistency of the excitation vibration spectrum of the transformer's laminated core 21 calculated in step S4 as the evaluation function.

[0163] for Figure 15 In the two-dimensional mapping diagram, for points representing the maximum value of uniformity, the transverse elastic modulus Gyz = Gzx = G1 of the upper yoke 22a and lower yoke 22b constituting the laminated iron core 21 is 0.25 GPa, and the transverse elastic modulus Gyz = Gzx = G2 of the column portion 22c is 0.15 GPa. Thus, the combination of (G1, G2) that determines when the uniformity becomes a maximum is determined. The combination of the determined specific values ​​(G1, G2) is used as the transverse elastic modulus Gzx and Gyz of the upper yoke 22a and lower yoke 22b, and the transverse elastic modulus Gzx and Gyz of the column portion 22c, respectively.

[0164] The excitation vibration spectrum of the laminated core 21 calculated using the combination of (G1, G2) with the transverse elastic modulus Gyz = Gzx = G1 = 0.25 GPa for the upper yoke 22a and lower yoke 22b constituting the laminated core 21 and the transverse elastic modulus Gyz = Gzx = G2 = 0.15 GPa for the column portion 22c is the final calculated value of the excitation vibration spectrum of the laminated core 21 of the transformer.

[0165] The chart in the embodiment comparing the calculated value of the excitation vibration spectrum of the transformer's laminated core with the measured value of the noise spectrum obtained by measuring the excitation noise of the transformer's laminated core is shown in [the figure]. Figure 16 As shown in the figure, the trend of the calculated values ​​of the spectrum is very consistent with the trend of the measured values. Therefore, through the embodiment, it can be confirmed that the transverse elastic moduli Gzx and Gyz of the upper yoke 22a and lower yoke 22b of the laminated core 21 of the transformer, including the two sides in the lamination direction, and the transverse elastic moduli Gzx and Gyz of the column portion 22c of the laminated core 21 of the transformer, including the two sides in the lamination direction, can be calculated with high accuracy.

[0166] In order to obtain Figure 15 The two-dimensional map of consistency shown is the trajectory of the search points searched using the optimized search method of GA (Genetic Algorithm). Figure 17 As shown in the image. Figure 17 The total number of search points shown is 832. In this case, it would take two months (8 weeks) to complete the search.

[0167] Therefore, a method to improve speed was studied by reducing the total number of search points. First, as... Figure 18A As shown, points at equal intervals of 0.1 GPa for G1 and G2 were selected as test points on the two-dimensional mapping map. As step 6-A, the selected test points were repeatedly processed using steps 3 to 5 to calculate the consistency. Through... Figure 18A The two-dimensional mapping of consistency obtained by performing step 6-A on the test points shown is in Figure 18B As shown in [the image]. Figure 18B In the two-dimensional mapping diagram, positive solution points with G1 of 0.25 GPa and G2 of 0.15 GPa are not included in the regions with a consistency of 0.9 or higher. Therefore, it can be seen that even if 0.1 GPa is set as the interval for the test points, the interval is too wide.

[0168] Next, as Figure 19AAs shown, points evenly spaced at intervals of 0.075 GPa for G1 and G2 were selected as test points on the two-dimensional mapping map. As step 6-A, the selected test points were repeatedly processed using steps 3 to 5 to calculate the consistency. Through... Figure 19A The two-dimensional mapping of consistency obtained by performing step 6-A on the test points shown is in Figure 19B As shown in [the image]. Figure 19B In the two-dimensional mapping diagram, positive solution points with G1 of 0.25 GPa and G2 of 0.15 GPa are not included in the regions with a consistency of 0.9 or higher. Therefore, it can be seen that even if 0.075 GPa is set as the interval for the test points, the interval is too wide.

[0169] Next, as Figure 20A As shown, points evenly spaced at intervals of 0.05 GPa for G1 and G2 were selected as test points on the two-dimensional mapping map. As step 6-A, the selected test points were repeatedly processed using steps 3 to 5 to calculate the consistency. Through... Figure 20A The two-dimensional mapping of consistency obtained by performing step 6-A on the test points shown is in Figure 20B As shown in [the image]. Figure 20B In the two-dimensional mapping diagram, the regions with a consistency of 0.9 or higher include positive solution points with G1 of 0.25 GPa and G2 of 0.15 GPa.

[0170] When positive solution points are included in regions with a consistency of 0.9 or higher, proceed as step 6-B. Figure 20B Regions with a consistency score of 0.9 or higher are designated as limited small regions for search using an optimization search method employing GA (Genetic Algorithm). As a step 6-C, within these limited small regions, an optimization search method utilizing GA (Genetic Algorithm) is employed. This method uses the consistency score between the noise spectrum of the transformer's laminated core obtained in step 1 and the excitation vibration spectrum of the transformer's laminated core calculated in step 4 as an evaluation function, and calculates the maximum point of consistency score. The results up to step 6-C confirm that the values ​​of (G1, G2) when the consistency score reaches its maximum are (0.25 GPa, 0.15 GPa).

[0171] The number of test points, evenly spaced at 0.05 GPa intervals and used to calculate consistency in step 6-A, is 8 × 8 = 64 points. Additionally, the number of search points used in step 6-C for the optimized search using GA (Genetic Algorithm) over a limited small region is 100 points. Therefore, the total number of test and search points is 164. As a result, the time required to perform the search is reduced to... Figure 17The search points shown represent approximately one-quarter of the total search points over approximately two weeks.

[0172] And, as Figure 21A As shown, test points were set on the two-dimensional mapping map, with equal intervals of 0.025 GPa for G1 and G2, and were selected sequentially. As step 6-A, the selected test points were repeatedly processed using steps 3 to 5 to calculate the consistency. Through... Figure 21A The two-dimensional mapping of consistency obtained by performing step 6-A on the test points shown is in Figure 21B As shown in [the image]. Figure 21B In the two-dimensional mapping diagram, the regions with a consistency of 0.9 or higher include positive solution points with G1 of 0.25 GPa and G2 of 0.15 GPa.

[0173] When positive solution points are included in regions with a consistency of 0.9 or higher, proceed as step 6-B. Figure 21B Regions with a consistency score of 0.9 or higher are designated as limited small regions for search using an optimization search method employing GA (Genetic Algorithm). As a step 6-C, within these limited small regions, an optimization search method utilizing GA (Genetic Algorithm) is employed. This method uses the consistency score between the noise spectrum of the transformer's laminated core obtained in step 1 and the excitation vibration spectrum of the transformer's laminated core calculated in step 4 as an evaluation function, and calculates the maximum point of consistency score. The results up to step 6-C confirm that the values ​​of (G1, G2) when the consistency score reaches its maximum are (0.25 GPa, 0.15 GPa).

[0174] The number of test points, evenly distributed at 0.025 GPa intervals and used to calculate consistency in step 6-A, is 15 × 15 = 225 points. Additionally, the number of search points used in step 6-C for the optimized search using GA (Genetic Algorithm) over a limited small region is 50. Therefore, the total number of test and search points is 275. As a result, the time required to perform the search is reduced to... Figure 17 The search points shown represent approximately one-third of the search results over approximately three weeks.

[0175] Based on the above results, it is evident that in order to significantly shorten the time required to calculate the consistency of each search point and the two-dimensional mapping of consistency in step 6, changing the process of step 6 to include steps 6-A, 6-B, and 6-C is extremely effective.

[0176] However, in step 6-A, when the values ​​of G1 and G2 corresponding to the test points are set to points that are evenly distributed within the range of the transverse elastic modulus expected based on the construction of the transformer's laminated core 21, i.e., within a specified range, for example, the test points are set at a wide interval such as 0.075 GPa or more, thus... Figure 18B and Figure 19B As shown, in regions with a consistency of 0.9 or higher, positive solution points with G1 of 0.25 GPa and G2 of 0.15 GPa are not included, resulting in incorrect results. Therefore, it is necessary to set test points at finer intervals, such as below 0.05 GPa.

[0177] On the other hand, even with finer intervals for setting test points, such as 0.025 GPa, the calculation accuracy of (G1, G2) values ​​when the consistency reaches its maximum does not improve. Instead, the time required for step 6-A increases, thus failing to shorten the overall time required for step 6. The reason why excessive fineness cannot improve calculation accuracy is that setting many test points for deviations from the correct solutions of G1 and G2 within the specified ranges selected for G1 and G2 becomes futile. Therefore, in this embodiment, setting the segmentation interval to 0.05 GPa is most suitable for achieving both improved calculation accuracy of G1 and G2 and faster overall time required for step 6.

[0178] While embodiments of this disclosure have been described with reference to the accompanying drawings and examples, it should be noted that those skilled in the art can make various modifications or alterations based on this disclosure. Therefore, it should be understood that such modifications or alterations are included within the scope of this disclosure. For example, the functions included in each component or step can be reconfigured in a logically consistent manner, and multiple components or steps can be combined into one or divided. Embodiments of this disclosure can also be implemented as a program executed by a processor of a device or a storage medium containing a program. It should be understood that these are also included within the scope of this disclosure.

[0179] For example, the evaluation method for the consistency between the noise spectrum of the laminated core 21 of the transformer and the excitation vibration spectrum of the laminated core 21 of the transformer is not limited to the calculation of cosine consistency. Euclidean distance can also be used as the consistency evaluation method by taking a reference value in dB that does not include offset. Furthermore, other consistency evaluation methods can also be used as long as they essentially quantitatively represent the consistency between the spectral data of excitation noise and excitation vibration.

[0180] Furthermore, while the vibration analysis of a three-phase three-limb transformer has been described in the above embodiments, it is not limited thereto. The present invention can also be applied to the vibration analysis of laminated cores in three-phase five-limb transformers or other transformers.

[0181] Furthermore, this embodiment assumes that the elasticity matrix determination method is applied to multiple (two) portions constituting the laminated core 21 where the lateral elastic moduli are different. Specifically, it is illustrated in the case where the lateral elastic moduli of the first portion, including the upper yoke 22a and lower yoke 22b, constituting the laminated core 21, are different from the lateral elastic moduli of the second portion, including the column portion 22c. The elasticity matrix determination method of this embodiment can also be applied to the case where the lateral elastic moduli of the first portion, including the upper yoke 22a and lower yoke 22b, constituting the laminated core 21, are the same as the lateral elastic moduli of the second portion, including the column portion 22c.

[0182] Furthermore, in this embodiment, the structure of the laminated iron core 21 having the first part and the second part as the object of analysis is described. The laminated iron core 21 may also have three or more parts. That is, it can be said that the laminated iron core 21 has at least the first part and the second part. When the laminated iron core 21 has three or more parts, the assumed value of the transverse elastic modulus is not only the first assumed value and the second assumed value, but also three or more assumed values, such as the third assumed value. Moreover, the maximum value of consistency is detected in a mapping diagram of three dimensions or more.

[0183] In the above embodiments, the test points are evenly spaced within a specified range, but they can also be spaced at indefinite intervals. Furthermore, in the above embodiments, the test points are spaced such that the interval between the first assumed value G1 and the interval between the second assumed value G2 are the same, but they can also be spaced such that the interval between the first assumed value G1 and the interval between the second assumed value G2 are different.

[0184] The location of the test points can be determined based on the results of analyzing other transformers using the elastic matrix determination method or vibration analysis method described in this embodiment. For example, the location of the test points can be determined based on the trend of the consistency distribution obtained by statistically processing the analysis results of other transformers in advance. In this way, test points can be set in a way that finds the positive solution point where the consistency reaches its maximum value with fewer test points. Furthermore, since the analysis results of other transformers are processed in advance, the time required to set test points based on the analysis results of other transformers will not increase.

[0185] Search points are set between test points. Search points can also be set at intervals narrower than the test point intervals. Search points can be set at locations offset from the test point grid. Search points can also be set at locations unrelated to the test point grid.

[0186] The method for determining the elasticity matrix of the laminated iron core 21 of the transformer can also be implemented as an elasticity matrix determination program executed by the computer or processor constituting the control unit 42 of the vibration analysis device 40. The vibration analysis method for the laminated iron core 21 of the transformer can also be implemented as a vibration analysis program executed by the computer or processor constituting the control unit 42 of the vibration analysis device 40. The elasticity matrix determination program or the vibration analysis program can be stored in a non-transitory computer-readable medium.

[0187] Explanation of reference numerals in the attached figures

[0188] 21…Laminated iron core; 22…Oriented electromagnetic steel plate (22a: upper yoke, 22b: lower yoke, 22c: column); 40…Vibration analysis device (42: control unit, 44: storage unit, 46: interface).

Claims

1. A method for determining the elastic matrix of a laminated iron core of a transformer, characterized in that, The laminated iron core is constructed by stacking multiple electromagnetic steel plates, and includes at least a first part and a second part. The structural formulas representing the stress-strain relationship of the first part and the second part include mutually different elasticity matrices. The elasticity matrix includes the transverse elastic modulus of the laminated iron core in both sides including the lamination direction as elements of the elasticity matrix. The method for determining the elastic matrix of the laminated iron core of the transformer includes: Step 1: Obtain the spectrum of the excitation noise of the laminated iron core of the transformer; Step 2: Obtain the excitation magnetostriction spectrum of the electromagnetic steel plate; Step 3: For the laminated core of the transformer, determine a first assumed value and a second assumed value to calculate the spectrum of the vibration response function of the laminated core of the transformer when the first assumed value and the second assumed value are applied to the elastic matrix. The first assumed value assumes the value of the transverse elastic modulus in the two sides of the first part including the lamination direction, and the second assumed value assumes the value of the transverse elastic modulus in the two sides of the second part including the lamination direction. Step 4: Calculate the excitation vibration spectrum of the laminated core of the transformer based on the excitation magnetostriction spectrum data of the electromagnetic steel plate obtained in Step 2 and the spectrum of the vibration response function of the laminated core of the transformer calculated in Step 3. Step 5: Calculate the consistency between the spectrum of the excitation noise of the laminated core of the transformer obtained in Step 1 and the spectrum of the excitation vibration of the laminated core of the transformer calculated in Step 4. Step 6 involves repeatedly executing steps 3 through 5 by changing the first and second assumed values ​​respectively to calculate the consistency degree for each combination of the first and second assumed values; and Step 7: Detect the maximum value of the consistency calculated in step 6 for each combination of the first and second assumed values. Use the first assumed value, where the consistency becomes a maximum, as the transverse modulus of elasticity in both sides of the laminated core at the first portion, including the stacking direction. And use the second assumed value, where the consistency becomes a maximum, as the transverse modulus of elasticity in both sides of the laminated core at the second portion, including the stacking direction. The sixth step includes: Step 6-A: When each combination of the first assumed value and the second assumed value corresponding to the consistency degree is represented as a test point set in a two-dimensional space with the first assumed value as the first axis and the second assumed value as the second axis, points dispersed within a specified range in the two-dimensional space are selected sequentially as the test points, and the consistency degree is calculated for the combination of the first assumed value and the second assumed value corresponding to the test point. Step 6-B involves defining a limited small region in the two-dimensional space based on the consistency calculated for the combination of the first and second assumptions corresponding to the test point; and Step 6-C: Set search points located between the test points within the defined small area and calculate the consistency degree for the combination of the first assumption value and the second assumption value corresponding to the search points.

2. The method for determining the elastic matrix of the laminated iron core of a transformer according to claim 1, characterized in that, In the fifth step, the cosine of the angle between the first vector, which takes each frequency component of the noise spectrum of the laminated core of the transformer as an element, and the second vector, which takes each frequency component of the excitation vibration spectrum of the laminated core of the transformer as an element, is calculated as the consistency degree.

3. A vibration analysis method, characterized in that, Includes the following steps: Vibration analysis of the laminated core of the transformer is performed based on a structural formula representing the stress-strain relationship of the first part and the second part, which is embedded with the elastic matrix determination method of the laminated core of the transformer as described in claim 1 or 2.

4. A flexible matrix determination procedure, characterized in that, The computer is made to execute the elastic matrix determination method as described in claim 1 or 2.

5. A vibration analysis program, characterized in that, The computer is made to execute the vibration analysis method as described in claim 3.

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