Rapid simulation method for vibration noise of oil-immersed transformer based on multi-path coupling and dynamic stiffness correction

Abstract

The invention discloses an oil-immersed transformer vibration noise rapid simulation method based on multipath coupling and dynamic stiffness correction. The method comprises the following steps: step 1, shell unit FEM modeling and winding vibration calculation; 2, oil tank vibration calculation considering fluid and structure coupling; step 3, noise calculation; according to the method, by optimizing an electromagnetic force loading strategy, a modal screening mechanism and dynamic stiffness modeling, the calculation efficiency and prediction precision are remarkably improved, and efficient and reliable technical support is provided for transformer noise control and structure optimization design in scenes such as a hydropower station and a transformer substation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power equipment vibration and noise control, and particularly relates to a transformer vibration and noise rapid simulation method based on multi-path coupling and dynamic stiffness correction. BACKGROUND

[0002] The current power transformer vibration and noise analysis technology generally has the contradiction between the calculation efficiency and the prediction accuracy. By using the traditional three-dimensional finite element model, the transformer winding needs to be finely meshed, so that the number of model elements is huge (more than one million, and large transformers reach ten million), and the time consumption of a single modal analysis is more than 20 hours, which is difficult to meet the rapid iterative design requirement. In addition, the high-order vibration mode is prone to resonance misjudgment due to the grid discretization error, which seriously affects the reliability of noise prediction. Although the existing research attempts to use shell element, boundary element method and other methods to calculate the vibration and noise, there are still some defects. One is that the shell element model ignores the magnetic leakage effect at the winding end, resulting in high error of electromagnetic force distribution; two is that the redundant modal calculation is large, and there is no modal selection mechanism for the target frequency band; three is that the high-frequency dynamic stiffness characteristics of the bolt connection are not modeled, and the structure transmission path noise has prediction deviation. These problems make it difficult for the traditional method to accurately quantify the vibration contribution of the fluid path (oil-tank coupling) and the structure path (bolt transmission), so that the design optimization direction is ambiguous, and in actual engineering, it is often necessary to try repeatedly, which is costly and inefficient. SUMMARY

[0003] The present application aims to overcome the above-mentioned deficiencies, and provides a transformer vibration and noise rapid simulation method based on multi-path coupling and dynamic stiffness correction, which aims to solve the problems of the traditional method that the shell element simplified modeling has high calculation efficiency but the end electromagnetic force distribution is distorted, the three-dimensional solid model has low calculation efficiency, the bolt connection static stiffness model ignores the high-frequency attenuation characteristics, and the structure transmission noise prediction deviation is large.

[0004] To solve the above technical problems, the technical scheme adopted by the present application is as follows: a transformer vibration and noise rapid simulation method based on multi-path coupling and dynamic stiffness correction, which comprises the following steps:

[0005] Step 1. Shell element FEM modeling and winding vibration calculation;

[0006] Step 2: oil tank vibration calculation considering fluid and structure coupling;

[0007] Step 3: noise calculation.

[0008] Preferably, the step 1 comprises the following process:

[0009] Step 1.1. Shell unit FEM modeling according to transformer structure: high-voltage winding is built into N-layer laminated disc shell unit, low-voltage winding is built into cylindrical shell unit, copper wire parameters of high and low voltage coils are set; the gasket between each layer of high-voltage winding is modeled according to the actual size and the parameters are set;

[0010] Step 1.2. Electromagnetic force calculation and loading;

[0011] Step 1.3. Modal analysis and frequency response calculation.

[0012] Preferably, the step 1.2 includes the following process:

[0013] Step 1.2.1. Calculate the electromagnetic force distribution of each coil layer:

[0014]

[0015] wherein, is an edge effect correction term to compensate for the end force error caused by the simplification of the shell unit; electromagnetic force, unit: Newton; current, unit: ampere; magnetic induction intensity, unit: Tesla;

[0016] Step 1.2.2. According to the electromagnetic force calculation result, load the axial and radial force distribution to the shell unit node.

[0017] Preferably, the step 1.3 includes the following process:

[0018] Step 1.3.1. Modal extraction: modal analysis is performed using finite element software to extract the first 300 natural frequencies f r and mode shapes {φ r} of the coil;

[0019] Step 1.3.2. Calculate the winding acceleration response:

[0020]

[0021] wherein, the modal density weight factor f target takes the electromagnetic force frequency 100Hz, which is used to preferentially select the modes within a certain range of target frequency; a coil (f): acceleration response of the coil, unit: meter per second square; m r : mass of the rth mode, unit: kilogram, indicating the mass contribution of the mode; {φ r} displacement shape of the rth mode, unit: meter, indicating the vibration mode of the mode; F(f): electromagnetic force, unit: Newton, indicating the external load generated by the current density and magnetic field; f r: natural frequency of the rth mode, unit: Hz; f: working frequency, unit: Hz, representing the frequency of electromagnetic force action; η r : rth order modal loss factor;

[0022] This formula gives the total vibration acceleration by superimposing the vibration responses of different modes.

[0023] Preferably, the step 2 comprises the following process:

[0024] Step 2.1, considering the boundary element BEM modeling of insulating oil and oil tank vibration calculation;

[0025] Step 2.2, considering solid connection, oil tank vibration calculation;

[0026] Step 2.3, total vibration synthesis.

[0027] Preferably, the step 2.1 comprises the following process:

[0028] Step 2.1.1, calculate the sound pressure gradient according to the coil acceleration obtained in step 1:

[0029]

[0030] wherein, : sound pressure normal gradient at source boundary element m, unit: Pa / m; p oil : transformer insulating oil density; a coil,m (f): coil vibration acceleration at source boundary element m;

[0031] Step 2.1.2, BEM equation discretization to solve sound pressure;

[0032] 1) Establish Green's function: describe the attenuation law of sound wave from source m to target l:

[0033]

[0034] wherein, r km : distance from the center of source boundary element m to the center of target boundary element l; : wave number, unit: rad / m; c is the sound speed in oil;

[0035] 2) Discretization equation: calculate the sound pressure p l :

[0036]

[0037] wherein, p l : sound pressure at target boundary element l; S m : area of source boundary element m;

[0038] 3) Matrix solution: solve the linear equations by ANSYS Workbench software to get the sound pressure {p} of all target boundary elements;

[0039] Step 2.1.3, oil tank vibration response calculation;

[0040] 1) Oil tank modal parameter calculation;

[0041] Geometric modeling of the oil tank, meshing the oil tank with shell elements to ensure the accuracy and computational efficiency of modal analysis; boundary conditions are set at the bottom of the oil tank; modal analysis is performed to extract the first 300 modal parameters, including:

[0042] Natural frequency: f r,tank , the rth order vibration frequency of the oil tank;

[0043] Mode shape: {φ r,tank}, the rth order mode shape displacement vector of the oil tank;

[0044] Modal mass: m r,tank , the rth order modal mass of the oil tank;

[0045] Loss factor: η r,tank = 0.01, representing the damping characteristics of the oil tank material;

[0046] 2) Sound pressure loading and vibration response calculation

[0047] The sound pressure distribution p l on the inner wall of the oil tank calculated by the boundary element method BEM l is loaded to the oil tank shell element nodes as external excitation, and the modal superposition method is used to calculate the oil tank acceleration:

[0048]

[0049] Where A l : the area of the oil tank shell element corresponding to the target boundary element l; f: electromagnetic force frequency.

[0050] Preferably, the step 2.2 comprises the following processes:

[0051] Step 2.2.1, bolt dynamic stiffness calculation;

[0052] 1) Static stiffness:

[0053]

[0054] Where E steel is the elastic modulus of the bolt material; A bolt = π(d / 2) 2 is the cross-sectional area of the bolt; L bolt is the length of the bolt;

[0055] 2) Dynamic stiffness correction, bolt stiffness attenuation at high frequencies:

[0056]

[0057] where f c The frequency point at which the bolt stiffness starts to significantly attenuate is calibrated by experiment;

[0058] Step 2.2.2, structure transfer force and vibration response calculation;

[0059] 1) Convert coil acceleration to equivalent displacement excitation, then calculate transfer force through dynamic stiffness, i.e. coil vibration acceleration a coil (f) Force transmitted to the tank through the bolt:

[0060]

[0061] 2) Calculate tank acceleration by modal superposition method:

[0062]

[0063] where f r,tank : the rth natural frequency of the tank; {φ r,tank} : the rth mode shape displacement vector of the tank; η r,tank : modal loss factor of the tank.

[0064] Preferably, the step 3 includes the following process:

[0065] Based on the total vibration acceleration of the tank a tank,total (f), calculate the noise sound pressure level SPL at a distance of 30 cm from the tank; according to the previous steps, the tank vibration acceleration is known:

[0066] a tank,total (f) = a tank,fluid (f) + a tank,struct (f)

[0067] where a tank,fluid (f): fluid path acceleration; a tank,struct (f): structure path acceleration;

[0068] 3.1 Acoustic parameter setting: air density p air , sound speed c, reference sound pressure p0;

[0069] 3.2 Sound pressure calculation.

[0070] Preferably, the step 3.2 includes the following process:

[0071] Step 3.2.1, conversion of vibration acceleration to sound pressure;

[0072] Sound pressure gradient relationship:

[0073]

[0074] wherein, Normal sound pressure gradient of source unit j, unit: Pa / m) ; a tank,total (f) : oil tank surface vibration acceleration, unit: m / s 2 ;

[0075] Step 3.2.2, sound pressure calculation:

[0076]

[0077] wherein, p i : sound pressure at target unit i; Green function from source unit j to target unit i; r ij : distance from the center of source unit j to the center of target unit i; Wave number, unit: rad / m, c is the sound speed in air; S j : area of source unit j; N: total number of source units;

[0078] Step 3.3.3, sound pressure level SPL and A-weighting correction.

[0079] Preferably, in the step 3.3.3:

[0080] Sound pressure level SPL calculation:

[0081]

[0082] wherein, Sound pressure effective value, frequency domain directly taking amplitude |p i |;

[0083] A-weighting correction:

[0084] SPL A (f) = SPL(f) + A(f)

[0085] wherein, A(f) : A-weighting correction value.

[0086] Advantages of the present application:

[0087] 1. The method of the present application significantly improves the calculation efficiency and prediction accuracy by optimizing the electromagnetic force loading strategy, modal selection mechanism and dynamic stiffness modeling, and provides efficient and reliable technical support for transformer noise control and structural optimization design in scenarios such as hydropower stations and transformer substations.

[0088] 2. This invention solves the problem that while simplified shell element modeling has high computational efficiency in traditional methods, it cannot solve the problem of distortion in the distribution of electromagnetic forces at the ends. Specifically, the leakage magnetic effect at the winding ends is not compensated, the axial force calculation error is large, and thus the acceleration calculation error becomes larger. It also solves the problem of low computational efficiency of three-dimensional solid models, reducing the number of model elements to 1 / 50 of that of traditional solid models and shortening the calculation time to 5% of the original time. Furthermore, it solves the problem that the static stiffness model of bolted connections ignores high-frequency attenuation characteristics, resulting in large deviations in the prediction of structural noise transmission. Attached Figure Description

[0089] Figure 1 This is a schematic diagram of a rapid simulation method for vibration and noise of an oil-immersed transformer based on multi-path coupling and dynamic stiffness correction.

[0090] Figure 2 A comparative diagram showing experimental data on the axial acceleration of a portion of the high-voltage winding, data calculated using the method proposed in this invention, and data calculated using the traditional method without considering edge effects and modal density weighting.

[0091] Figure 3 This is a schematic diagram comparing the calculated values ​​obtained by the calculation method proposed in this invention with the experimental measured values. Detailed Implementation

[0092] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0093] Example 1: As Figure 1 As shown, a rapid simulation method for vibration and noise of oil-immersed transformers based on multi-path coupling and dynamic stiffness correction is presented. The specific steps are as follows:

[0094] Step 1. Shell element FEM modeling and winding vibration calculation

[0095] 1.1 Shell element FEM modeling is performed based on the transformer structure. The high-voltage winding is constructed as an N-layer laminated disc shell element, and the low-voltage winding is constructed as a cylindrical shell element. The copper conductor parameters of the high- and low-voltage coils are set. The spacers between each layer of the high-voltage winding are modeled according to actual dimensions and their parameters are set.

[0096] 1.2 Electromagnetic Force Calculation and Loading

[0097] 1.2.1 Calculate the electromagnetic force distribution of each coil layer:

[0098]

[0099] in, This is an edge effect correction term to compensate for end force errors caused by shell element simplification;

[0100] Electromagnetic force, unit: Newton (N);

[0101] Current, unit: Ampere;

[0102] Magnetic induction, unit: Tesla (T)

[0103] 1.2.2 Load axial and radial force distribution to shell element nodes according to electromagnetic force calculation results.

[0104] 1.3 Modal analysis and frequency response calculation

[0105] 1.3.1 Modal extraction: Perform modal analysis using finite element software to extract the first 300 natural frequencies f r and mode shapes {φ r} of the coil.

[0106] 1.3.2 Calculate winding acceleration response:

[0107]

[0108] where modal density weighting factor f target is taken as 100 Hz of electromagnetic force frequency, which is used to prioritize the selection of modes within a certain range of target frequencies.

[0109] a coil (f): Acceleration response of the coil, unit: meter per second square (m / s 2 ).

[0110] m r : Mass of the rth mode, unit: kilogram (kg), representing the mass contribution of the mode.

[0111] {φ r}: Displacement shape of the rth mode, unit: meter (m), representing the vibration mode of the mode.

[0112] F(f): Electromagnetic force, unit: Newton (N), representing the external load generated by current density and magnetic field.

[0113] f r : Natural frequency of the rth mode, unit: Hertz (Hz).

[0114] f: Operating frequency, unit: Hertz (Hz), representing the frequency of electromagnetic force action.

[0115] η r : Loss factor of the rth mode.

[0116] This formula obtains the total vibration acceleration by superimposing the vibration responses of different modes.

[0117] Step 2: Tank vibration calculation considering fluid-structure coupling

[0118] 2.1 Fluid path: Boundary Element Method (BEM) modeling of insulating oil and tank vibration calculation

[0119] 2.1.1 Calculate the sound pressure gradient from the coil acceleration obtained in Step 1:

[0120]

[0121] Symbol explanation:

[0122] Normal gradient of sound pressure at source boundary element m (unit: Pa / m)

[0123] p oil : Density of transformer insulating oil

[0124] a coil,m : Coil vibration acceleration at source boundary element m (unit: m / s 2 )

[0125] 2.1.2 Discretize and solve the BEM equation for sound pressure

[0126] 1) Establish the Green's function: describe the attenuation law of sound wave propagation from source m to target l.

[0127]

[0128] r lm : Distance from the center of source boundary element m to the center of target boundary element l (unit: m)

[0129] Wave number (unit: rad / m), c is the sound speed in oil

[0130] 2) Discretize the equation: calculate the sound pressure p at target boundary element l l .

[0131]

[0132] p l : Sound pressure at target boundary element l (unit: Pa)

[0133] S m : Area of source boundary element m (unit: m 2 )

[0134] 3) Matrix solution: solve the linear equation system by ANSYS Workbench software to get the sound pressure of all target boundary elements {p}.

[0135] 2.1.3 Oil tank vibration response calculation

[0136] 1) Oil tank modal parameter calculation

[0137] The oil tank is geometrically modeled and meshed with shell elements, thickness 9mm, local stiffened area 8mm, mesh size 40mm, to ensure the accuracy and computational efficiency of modal analysis. The boundary condition is set as oil tank bottom fixed (simulate the actual installation constraint). Modal analysis is performed and the first 300 modal parameters are extracted, including:

[0138] Natural frequency: f r,tank (unit: Hz), the rth order vibration frequency of the oil tank.

[0139] Mode shape: {φ r,tank} (dimensionless), the rth order mode shape displacement vector of the oil tank.

[0140] Modal mass: m r,tank (unit: kg), the rth order modal mass of the oil tank.

[0141] Loss factor: η r,tank = 0.01, representing the damping characteristics of the oil tank material.

[0142] 2) Sound pressure loading and vibration response calculation

[0143] The sound pressure distribution p l on the inner wall of the oil tank is calculated by the boundary element method (BEM), and the sound pressure p l is loaded to the oil tank shell element nodes as external excitation, and the modal superposition method is used to calculate the oil tank acceleration:

[0144]

[0145] A l : the oil tank shell element area corresponding to the target boundary element l (unit: m 2 )

[0146] f: electromagnetic force frequency (100Hz).

[0147] 2.2 Solid path: oil tank vibration calculation considering solid connection

[0148] 2.2.1 Bolt dynamic stiffness calculation

[0149] 1) Static stiffness:

[0150]

[0151] Bolt material (steel) elastic modulus E steel

[0152] Bolt cross-sectional area A bolt= π(d / 2) 2

[0153] Bolt length L bolt .

[0154] 2) Dynamic stiffness correction (bolt stiffness attenuation at high frequency)

[0155]

[0156] f c The frequency point at which the bolt stiffness starts to attenuate significantly is indicated by experimental calibration.

[0157] 2.2.2 Structural transfer force and vibration response calculation

[0158] 1) Convert coil acceleration to equivalent displacement excitation, then calculate the transfer force via dynamic stiffness, i.e. coil vibration acceleration a coil (f) Force transferred to the tank via the bolts:

[0159]

[0160] 2) Calculate tank acceleration via modal superposition method:

[0161]

[0162] f r,tank : rth natural frequency of the tank

[0163] {φ r,tank} : rth mode shape displacement vector of the tank

[0164] η r,tank : modal loss factor of the tank

[0165] 2.3 Total vibration synthesis

[0166] Superimpose the vibration contributions from the fluid path and the structural path to obtain the total vibration acceleration on the tank surface:

[0167] a tank,total (f) = a tank,fluid (f) + a tank,struct (f)

[0168] a tank,fluid (f): vibration acceleration of the fluid transfer path (unit: m / s 2 ), which is the vibration generated on the inner wall of the tank excited by the coil vibration via the oil acoustic pressure.

[0169] a tank,struct (f): vibration acceleration of the solid structure transfer path (unit: m / s 2 ), which is the vibration transferred to the tank mechanically via the bolts and the frame from the coil vibration.

[0170] Step 3: Noise calculation

[0171] Based on the total tank vibration acceleration a tank,total (f), the noise sound pressure level (SPL) at 30 cm from the tank is calculated. The tank vibration acceleration is known from the previous steps:

[0172] a tank,total (f) = a tank,fluid (f) + a tank,struct (f)

[0173] a tank,fluid (f): fluid path acceleration

[0174] a tank,struct (f): structure path acceleration

[0175] 3.1 Acoustic parameter setup: air density p, sound speed (at normal temperature and pressure) c, reference sound pressure p0 air

[0176] 3.2 Sound pressure calculation

[0177] 3.2.1 Conversion of vibration acceleration to sound pressure

[0178] Sound pressure gradient relation:

[0179]

[0180] Normal sound pressure gradient of source element j (unit: Pa / m),

[0181] a tank,total (f): tank surface vibration acceleration (unit: m / s 2 ).

[0182] 3.2.2 Sound pressure calculation (BEM discrete equation):

[0183]

[0184] p i : sound pressure at target element i (unit: Pa)

[0185] Green function of source element j to target element i

[0186] r ij : distance from center of source element j to center of target element i (unit: m)

[0187] Wave number (unit: rad / m), c is sound speed in air

[0188] ​S j : Area of source element j (unit: m 2 )

[0189] N: Total number of source elements.

[0190] 3.3.3 Sound Pressure Level (SPL) and A-Weighting Correction

[0191] Sound Pressure Level (SPL) calculation:

[0192]

[0193] Sound Pressure Effective Value (frequency domain direct amplitude |p i |).

[0194] A-Weighting Correction:

[0195] SPL A (f) = SPL(f) + A(f)

[0196] A(f): A-Weighting Correction Value.

[0197] Example 2: A 66kV oil-immersed transformer is taken as the object to carry out vibration and noise simulation calculation, and the experimental data is combined to prove the advancement and effectiveness of the method, the specific steps are as follows:

[0198] Step 1. Shell element FEM modeling and winding vibration calculation

[0199] 1.1 Shell element FEM modeling according to transformer structure. The high-voltage winding is made into a 68-layer laminated disc-shaped shell element (wherein the thickness of each layer of high-voltage winding is 8.6mm, and the outer diameter is 591mm). The low-voltage winding is made into a cylindrical shell element, including 4 layers (the outer diameters are 352.3mm, 357.7mm, 388.2mm, and 400.8mm, and the thickness of each layer is 8.9mm). The copper wire parameters of high and low voltage coils are set as follows: Young's modulus 117GPa, Poisson's ratio 0.34, density 8900kg / m 3 . The gasket between each layer of high-voltage winding is modeled according to the actual size, 20 gaskets per layer, thickness 4-12mm, width 40mm, length 100mm, and Young's modulus 520MPa.

[0200] 1.2 Electromagnetic force calculation and loading

[0201] 1.2.1 Calculation of electromagnetic force distribution of each coil layer:

[0202]

[0203] wherein, is an edge effect correction term to compensate for the end force error caused by the simplification of the shell element;

[0204] Electromagnetic force, unit: Newton (N);

[0205] Current, unit: Ampere;

[0206] Magnetic induction, unit: Tesla (T)

[0207] 1.2.2 According to the calculation results of electromagnetic force, axial and radial force distribution is loaded to the shell element node.

[0208] 1.3 Modal analysis and frequency response calculation

[0209] 1.3.1 Modal extraction: modal analysis is performed using finite element software to extract the first 300 natural frequencies f r and mode shapes {φ r}.

[0210] 1.3.2 Calculation of winding acceleration response:

[0211]

[0212] Where the modal density weight factor f target Take the electromagnetic force frequency 100Hz, used to prioritize screening the modal within a certain range of target frequency.

[0213] a coil (f): acceleration response of the coil, unit: meter per second square (m / s 2 ).

[0214] m r : the mass of the rth mode, unit: kilogram (kg), representing the mass contribution of the mode.

[0215] {φ r}: displacement shape of the rth mode, unit: meter (m), representing the vibration mode of the mode.

[0216] F(f): electromagnetic force, unit: Newton (N), representing the external load generated by current density and magnetic field.

[0217] f r : the natural frequency of the rth mode, unit: Hertz (Hz).

[0218] f: working frequency, unit: Hertz (Hz), representing the frequency of electromagnetic force action.

[0219] η r : the rth order modal loss factor.

[0220] This formula gives the total vibration acceleration by superimposing the vibration responses of different modes, and the results are shown in Figure 2 Figure 2 The partial line pie axial acceleration experimental data of high-voltage winding, the data calculated by the method proposed in the patent, and the data calculated by the traditional method (without considering edge effect and modal density weight) are shown, and the errors of the calculation results at the end (No. 1 measuring point) and the overall calculation results are reduced, which proves the beneficial effect of the new method.

[0221] Step 2: Oil tank vibration calculation considering fluid-structure coupling

[0222] 2.1 Fluid path: Boundary element (BEM) modeling of insulating oil and oil tank vibration calculation

[0223] 2.1.1 Calculate the sound pressure gradient according to the coil acceleration obtained in step 1:

[0224]

[0225] Symbol explanation:

[0226] Normal gradient of sound pressure at source boundary element m (unit: Pa / m)

[0227] p oil = 900 kg / m 3 : Density of transformer insulating oil

[0228] a coil,m (f): Coil vibration acceleration at source boundary element m (unit: m / s 2 )

[0229] 2.1.3 Discretization of BEM equation to solve sound pressure

[0230] 1) Establish Green's function: describe the attenuation law of sound wave propagation from source m to target l.

[0231]

[0232] r lm : Distance from the center of source boundary element m to the center of target boundary element l (unit: m)

[0233] Wave number (unit: rad / m), c=1400 m / s is the sound speed in oil

[0234] 2) Discretization equation: calculate the sound pressure p l at target boundary element l.

[0235]

[0236] p l ​: Sound pressure at target boundary element l (unit: Pa)

[0237] S m : Area of source boundary element m (unit: m 2 )

[0238] 3) Matrix solution: Solve the linear equations by ANSYS Workbench software, get the sound pressure {p} of all target boundary elements.

[0239] 2.1.4 Oil tank vibration response calculation

[0240] 1) Oil tank modal parameter calculation

[0241] Geometric modeling of the oil tank, meshing the oil tank with shell elements, thickness 9mm, local reinforcement area 8mm, mesh size 40mm, to ensure the accuracy and computational efficiency of modal analysis. The boundary conditions are set as the oil tank bottom fixed (simulating the actual installation constraints). Perform modal analysis and extract the first 300 modal parameters, including:

[0242] Natural frequency: f r,tank (unit: Hz), the rth order vibration frequency of the oil tank.

[0243] Mode shape: {φ r,tank} (dimensionless), the rth order mode shape displacement vector of the oil tank.

[0244] Modal mass: m r,tank (unit: kg), the rth order modal mass of the oil tank.

[0245] Loss factor: η r,tank = 0.01, representing the damping characteristics of the oil tank material.

[0246] 2) Sound pressure loading and vibration response calculation

[0247] The sound pressure distribution p l on the inner wall of the oil tank calculated by the boundary element method (BEM) l is loaded to the oil tank shell element nodes as external excitation, and the modal superposition method is used to calculate the oil tank acceleration:

[0248]

[0249] A l : Area of the oil tank shell element corresponding to the target boundary element l (unit: m 2 )

[0250] f: Electromagnetic force frequency (100Hz).

[0251] 2.2 Solid path: oil tank vibration calculation considering solid connection

[0252] 2.2.1 Bolt dynamic stiffness calculation

[0253] 1) Static stiffness:

[0254]

[0255] Bolt material (steel) elastic modulus E steel = 210 GPa

[0256] Bolt cross-sectional area A bolt = π(d / 2) 2 (d = 12 mm)

[0257] Bolt length L bolt = 50 mm.

[0258] 2) Dynamic stiffness correction (bolt stiffness attenuation at high frequency)

[0259]

[0260] f c Through experimental calibration, the frequency point at which the bolt stiffness begins to significantly attenuate is set to 500 Hz.

[0261] 2.2.2 Structure transfer force and vibration response calculation

[0262] 1) Convert coil acceleration to equivalent displacement excitation, then calculate transfer force through dynamic stiffness, i.e. coil vibration acceleration a coil (f) Force transmitted to the tank through the bolt:

[0263]

[0264] 2) Calculate tank acceleration using modal superposition method:

[0265]

[0266] f r,tank : rth order natural frequency of the tank

[0267] {φ r,tank} : rth order mode shape displacement vector of the tank

[0268] η r,tank = 0.01: modal loss factor of the tank

[0269] 2.3 Total vibration synthesis

[0270] Superimpose the vibration contributions of the fluid path and the structure path to obtain the total vibration acceleration on the tank surface:

[0271] a tank,total (f) = a tank,fluid (f) + atank,struct (f)

[0272] a tank,fluid (f) : Vibration acceleration of oil liquid transfer path (unit: m / s 2 ), which is the vibration generated by the coil vibration exciting the inner wall of the tank through the sound pressure of the oil liquid.

[0273] a tank,struct (f) : Vibration acceleration of solid structure transfer path (unit: m / s 2 ), which is the vibration transmitted to the tank by the coil vibration through the bolt and the frame.

[0274] Step 3: Noise calculation

[0275] Based on the total vibration acceleration a tank,total (f) of the tank, the noise sound pressure level (SPL) at a distance of 30 cm from the tank is calculated. The tank vibration acceleration is known according to the previous steps:

[0276] a tank,total (f) = a tank,fluid (f) + a tank,struct (f)

[0277] a tank,fluid (f) : Fluid path acceleration

[0278] a tank,struct (f) : Structure path acceleration

[0279] 3.1 Acoustic parameter setting

[0280] Air density: p air = 1.225 kg / m 3

[0281] Sound speed (normal temperature and pressure): c = 343 m / s

[0282] Reference sound pressure: p0 = 20 μPa

[0283] 3.2 Sound pressure calculation process

[0284] 3.2.1 Conversion of vibration acceleration to sound pressure

[0285] Sound pressure gradient relationship:

[0286]

[0287] Normal sound pressure gradient of source unit j (unit: Pa / m),

[0288] a tank,total (f) : Tank surface vibration acceleration (unit: m / s 2 ).

[0289] 3.2.2 Sound pressure calculation (BEM discrete equation):

[0290]

[0291] p i : sound pressure at target unit i (unit: Pa)

[0292] Green function from source unit j to target unit i

[0293] r ij : distance from center of source unit j to center of target unit i (unit: m)

[0294] Wave number (unit: rad / m), c = 343 m / s for sound speed in air

[0295] S j : area of source unit j (unit: m 2 )

[0296] N: total number of source units.

[0297] 3.3.3 Sound pressure level (SPL) and A-weighting correction

[0298] Sound pressure level (SPL) calculation:

[0299]

[0300] Sound pressure effective value (frequency domain direct amplitude |p i |).

[0301] A-weighting correction:

[0302] SPL A (f) = SPL(f) + A(f)

[0303] A(f): A-weighting correction value.

[0304] Figure 3 The comparison of the calculated values obtained by the calculation method and the experimental measurement values of the present application shows that the error is small.

[0305] The above embodiments are only preferred technical solutions of the present application, and should not be regarded as a limitation of the present application. The protection scope of the present application should be based on the technical solutions recited in the claims, including equivalent replacement solutions of the technical features recited in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present application.

Claims

1. A method for fast simulation of vibration and noise of oil-immersed transformer based on multipath coupling and dynamic stiffness correction, characterized in that: It comprises the following steps: Step 1. Shell unit FEM modeling and winding vibration calculation; Step 2: Tank vibration calculation considering fluid-structure coupling; Step 3: Noise calculation.

2. The method of claim 1, wherein the method is characterized by: The step 1 comprises the following processes: Step 1.1, Shell unit FEM modeling according to transformer structure: high-voltage winding is built into N-layer laminated disc shell unit, low-voltage winding is built into cylindrical shell unit, copper wire parameters of high and low voltage coils are set; The gasket between each layer of high-voltage winding is modeled according to the actual size and the parameters are set; Step 1.2, Electromagnetic force calculation and loading; Step 1.3, Modal analysis and frequency response calculation.

3. The method of claim 2, wherein the method is characterized by: The step 1.2 comprises the following processes: Step 1.2.1, Calculation of electromagnetic force distribution of each coil layer: wherein, is an edge effect correction term that compensates for end force errors resulting from shell element simplification; electromagnetic force in Newton; current in Ampere; magnetic induction in Tesla; Step 1.2.2, According to the calculation results of electromagnetic force, the axial and radial force distribution is loaded to the shell unit node.

4. The method of claim 2, wherein the method is characterized by: The step 1.3 comprises the following processes: Step 1.3.1, modal extraction: modal analysis is performed using finite element software to extract the first 300 natural frequencies f r and mode shapes {φ r} of the coil Step 1.3.2, Calculation of winding acceleration response: wherein the modal density weight factor f target Taking the electromagnetic force frequency 100 Hz, the modal within a certain range of target frequency is preferentially screened;a coil (f): acceleration response of the coil, unit: meter per second square; m r : the mass of the rth mode, unit: kilogram, indicating the mass contribution of the mode;{φ r}the displacement shape of the rth mode, unit: meter, indicating the vibration mode of the mode; F(f): electromagnetic force, unit: Newton, indicating the external load generated by the current density and magnetic field; f r : the natural frequency of the rth mode, unit: hertz; f: working frequency, unit: hertz, indicating the frequency of electromagnetic force action; η r : the rth order modal loss factor; This formula obtains the total vibration acceleration by superimposing the vibration responses of different modes.

5. The method of claim 4, wherein the method is characterized by: The step 2 comprises the following processes: Step 2.1, Boundary element BEM modeling of insulating oil and tank vibration calculation; Step 2.2, Tank vibration calculation considering solid connection; Step 2.3, Total vibration synthesis.

6. The method of claim 5, wherein: The step 2.1 comprises the following processes: Step 2.1.1, Sound pressure gradient calculation according to the coil acceleration obtained in step 1: wherein, sound pressure normal gradient at the source boundary element m, unit: Pa / m; p oil : transformer insulating oil density; a coil,m (f): coil vibration acceleration at the source boundary element m; Step 2.1.2, Discretization of BEM equation to solve sound pressure; 1) Establishment of Green function: describe the attenuation law of sound wave from source m to target l: wherein r lm : distance from the center of the source boundary element m to the center of the target boundary element l; wave number, unit: rad / m; c is the sound speed in oil; 2) Discretized equation: Calculate the sound pressure p at the target boundary element I l : where p l : sound pressure at target boundary element I; S m : area of source boundary element m; 3) Matrix solution: solve the linear equation set by ANSYS Workbench software to obtain the sound pressure {p} of all target boundary elements; Step 2.1.3, Tank vibration response calculation; 1) Tank modal parameter calculation; Geometric modeling is performed on the tank, shell elements are used for meshing to ensure the accuracy and calculation efficiency of modal analysis; The boundary condition is set as the tank bottom fixed; Modal analysis is performed to extract the first 300 modal parameters, including: Natural frequency: f r,tank , the rth order vibration frequency of the oil tank Mode: {φ r,tank}, the rth mode displacement vector of the oil tank Modal mass: m r,tank , the rth modal mass of the tank Loss factor: η r,tank = 0.01, representing the damping properties of the tank material; 2) Sound pressure loading and vibration response calculation The sound pressure distribution p on the inner wall of the tank calculated by the boundary element method BEM l The sound pressure p l is loaded to the tank shell element nodes as external excitation, and the tank acceleration is calculated using the modal superposition method: where A l : target boundary element l corresponding to the tank shell element area; f: electromagnetic force frequency.

7. The method of claim 6, wherein the method is characterized by: The step 2.2 comprises the following processes: Step 2.2.1, Bolt dynamic stiffness calculation; 1) Static stiffness: where the bolt material modulus of elasticity E steel ; bolt cross-sectional area A bolt = π(d / 2) 2 ; bolt length L bolt ; 2) Dynamic stiffness correction, bolt stiffness attenuation at high frequency: where f c The frequency point at which the bolt stiffness begins to significantly attenuate is indicated by experimental calibration. Step 2.2.2, Structure transfer force and vibration response calculation; 1) Coil acceleration is converted to equivalent displacement excitation, and the force is transferred through dynamic stiffness calculation, i.e. coil vibration acceleration a coil (f) Force transferred to the tank by the bolts: 2) Modal superposition method to calculate tank acceleration: where f r,tank : the rth natural frequency of the tank;{φ r,tank} : the rth mode shape displacement vector of the tank;η r,tank : the modal loss factor of the tank.

8. The method of claim 7, wherein: The step 3 Comprises the following processes: Based on the total tank vibration acceleration a tank,total (f) the noise sound pressure level SPL at 30 cm from the tank is calculated; the tank vibration acceleration is known from the previous steps: a tank,total (f) = a tank,fluid (f) + a tank,struct (f) wherein a tank,fluid (f) : fluid path acceleration; a tank,struct (f) : structural path acceleration; 3.1 Acoustic parameter settings: air density p air , sound speed c, reference sound pressure p0; 3.2 Sound pressure calculation.

9. The method of claim 8, wherein the method is characterized by: The step 3.2 comprises the following processes: Step 3.2.1, Conversion of vibration acceleration to sound pressure; Sound pressure gradient relationship: wherein, Normalised sound pressure gradient of source unit j, units: Pa / m); a tank,total (f): Tank surface vibration acceleration, units: m / s 2 ; Step 3.2.2, Sound pressure calculation: where p i : sound pressure at target unit i; Green function from source unit j to target unit i; r ij : distance from center of source unit j to center of target unit i; wave number, unit: rad / m, c is sound speed in air; S j : area of source unit j; N: total number of source units; Step 3.3.3, Sound pressure level SPL and A-weighting correction.

10. The method of claim 8, wherein the method is characterized by: In the step 3.3.3: Sound pressure level SPL calculation: wherein Sound pressure effective value, frequency domain direct taking amplitude |p i |; A-weighting correction: SPL A (f) = SPL(f) + A(f) Wherein, A(f): A-weighting correction value.

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