Methods and Systems for Establishing Dynamic Response and Damage Models of Dry Casings under Earthquake Influence

Abstract

This invention belongs to the field of electrical equipment technology and discloses a method for calculating the dynamic response of dry bushings under seismic loading and establishing a core crack damage model. After simulating the vibration response of transformer bushings under seismic conditions, this invention can obtain various important data, including acceleration response, displacement response, actual stress, deformation degree, and stress concentration. This allows for the adjustment and optimization of various structural and material parameters. Through this simulation, the various physical effects in 110kV resin-impregnated paper dry bushings can be predicted, and the service life of the material in actual scenarios can be accurately determined. This invention establishes two fracture phase-field models to simulate crack propagation in thin plates under different loading conditions. By establishing a phase-field model for isotropic plate fracture problems, numerical calculations are performed using finite element analysis software to study the crack propagation process of thin plates with initial cracks under tensile and shear loads, and the influence of various parameters on crack propagation is calculated.

Description

Technical Field

[0001] This invention belongs to the field of electrical equipment technology, and in particular relates to a method and system for calculating the dynamic response of dry bushings and establishing a core crack damage model under seismic loading. Background Technology

[0002] Dry bushings are characterized by stable electrical performance, oil-free flame retardancy, small size, and light weight. Compared to oil-impregnated paper bushings, they offer superior fire and explosion protection. With increasingly stringent safety and performance requirements for power grids and electrical equipment, the application of dry bushings is growing. However, their manufacturing process is complex and challenging, especially for large-size bushings. Improper process control during production can lead to defects such as bubbles, cracks, and foreign objects. These defects often have a minor impact on the overall insulation performance of the bushing initially, but under extreme conditions such as earthquakes, these minute internal defects are easily affected by strong loads and can rapidly develop, causing severe damage to the core. This poses a significant threat to the safety of the power system, ultimately leading to reduced insulation performance or breakdown, thus affecting the safe and stable operation of the power grid.

[0003] Transformer bushings are critical substation equipment for the normal operation of power transmission and transformation systems. They mainly consist of two parts: the transformer tank and the insulating bushing. The tank structure is complex, while the bushing structure is slender. Statistics from major earthquakes both domestically and internationally show that, because the natural frequency of transformers is close to the frequency of seismic waves, they suffer severe damage in high-intensity earthquake zones, causing not only direct economic losses but also serious secondary disasters. Currently, there is limited research on the dynamics of dry-type bushings under special operating conditions, and the electrical characteristics of dry-type bushings under seismic conditions still require in-depth study.

[0004] The transformer-bushing system is one of the most important pieces of equipment in a power system, and it suffers significant damage in earthquakes. Existing numerical models have simplified the original structure considerably, especially the simulation of the connection between the bushing flange and the riser, which greatly affects the bushing response results. Furthermore, due to the large size of high-voltage transformers, it is difficult to conduct shaking table tests on prototype transformer structures under current conditions. Therefore, in order to establish a reasonable method for analyzing the seismic performance of high-voltage transformer-bushing systems and optimize their seismic design, it is essential to establish a finite element model of the high-voltage transformer-bushing system and calculate and analyze its dynamic response under seismic loading.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] The transformer-bushing system is one of the most important pieces of equipment in a power system, and it is often severely damaged in earthquakes. Existing numerical models have simplified the original structure considerably, especially the simulation of the connection between the bushing flange and the riser, which greatly affects the bushing response results. Furthermore, due to the large size of high-voltage transformers, it is difficult to conduct shaking table tests on a prototype transformer structure under current conditions. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a method for calculating the dynamic response of dry casing under seismic loading and establishing a core crack damage model.

[0008] This invention is implemented as follows: A method for calculating the dynamic response of dry casing and establishing a core crack damage model under seismic loading includes:

[0009] Step 1: Establish a simulation model for the transformer-bushing system;

[0010] Transformer-lifting seat-bushing model: The insulating bushing is connected to the oil tank via the lifting seat. The transformer side plate and bottom plate are 15mm thick, the top plate is 20mm thick, the lifting seat is 1600mm long, the wall thickness is 20mm, the tilt angle is 20°, and the structure is made of Q235 steel. The overall height of the bushing is 2840mm, the maximum outer diameter at the flange is 200mm, and the air side height is 1450mm.

[0011] Step 2, Seismic wave selection and loading method;

[0012] A finite element model was established based on the actual dry sleeve impregnated with paper to conduct simulation analysis. The time history analysis method was used to analyze the overall force distribution characteristics of the sleeve under the simulated base vibration load, and the influence of mechanical vibration load on the force distribution was studied.

[0013] Step 3, Transformer-Bushing Vibration Response Analysis under Seismic Conditions;

[0014] Step 4: Crack propagation model established.

[0015] Furthermore, the selection and loading method of the seismic waves:

[0016] (1) For electrical equipment with an axisymmetric structure and vertical arrangement, a single horizontal seismic test shall be conducted; for electrical equipment with an asymmetrical structure, two horizontal seismic tests shall be considered; for electrical equipment with long cantilever or large span, a vertical seismic test shall also be considered.

[0017] (2) The test response spectrum (TRS) generated by the vibration table should be enveloped to meet the requirements of the required response spectrum (RRS). If a small number of individual points in the TRS are outside the tolerance band and are offset from the resonant frequency of the test equipment, it is also acceptable. Considering that the maximum displacement of some vibration tables is limited and the lower frequency part has little impact on the equipment, the tolerance of the spectrum value below 0.7 times the natural frequency of the equipment can be left uncontrolled.

[0018] Furthermore, the transformer-bushing vibration response under the aforementioned seismic conditions is analyzed as follows:

[0019] 1) Modal analysis;

[0020] First, modal analysis was performed on the overall model to obtain the natural frequencies and mode shapes of the first 20 modes. Mode shapes 1-6 were mainly concentrated on the side wall of the tank, showing an alternating pattern of absorption and expansion. At the same time, small local buckling also occurred at the upper end of the casing. Mode shape 7 showed an upward bending of the casing, and mode shape 12 showed a rightward bending of the casing. Modes 16-20 all showed significant deformation of the casing. The mode shapes of each order were mainly concentrated on the slender structure at the top of the casing and the side plate of the tank.

[0021] 2) Acceleration response analysis at different positions of the dry bushing;

[0022] Since the bushing has a slender structure and is connected to the transformer box through a riser, in order to study the bushing acceleration response under different earthquake levels, the response to different earthquake ground motions was studied separately; the acceleration response values ​​at the top, flange and bottom of the bushing were extracted and analyzed separately.

[0023] 3) Displacement response analysis at different positions of the dry bushing;

[0024] 4) Stress response analysis at different locations of dry bushing.

[0025] Furthermore, the displacement response of the dry bushing at different positions is analyzed:

[0026] As the height of the casing increases, its displacement shows a significant upward trend, that is, the displacement at the top is greater than that at the middle and greater than that at the bottom. Among them, the maximum horizontal displacement at the top of the casing is most affected by ground motion, while the maximum vertical displacement at the middle and bottom is most affected by ground motion.

[0027] Furthermore, stress response analysis was performed at different locations of the dry bushing:

[0028] The maximum acceleration, maximum displacement, and maximum stress of the bushing vibration response under different earthquake magnitudes were extracted. As the earthquake magnitude increased, the peak values ​​of each response showed an upward trend. When the earthquake magnitude reached level 8, the peak value of the maximum acceleration on the bushing was 163.83 m / s², the peak value of the displacement was 25.35 mm, and the peak value of the stress was 4.55 MPa. Under this earthquake magnitude, the acceleration at the top was 4.3 times greater than that at the bottom, posing a great safety hazard to the mechanical performance of the transformer bushing. Since the epoxy core is a brittle material, its tensile and compressive strength is much lower than that of other components.

[0029] Furthermore, the crack propagation model is established:

[0030] Two fracture phase-field models were established to simulate crack propagation in thin plates under different loading conditions. By establishing a phase-field model for the fracture problem of isotropic plates and performing numerical calculations using finite element analysis software, the crack propagation process of thin plates with initial cracks under tensile and shear loads was studied, and the influence of various parameters on crack propagation was calculated.

[0031] Another objective of this invention is to provide a system for calculating the dynamic response of dry casing and establishing a core crack damage model under seismic loading, comprising:

[0032] The simulation model building module is used to build simulation models of transformer-bushing systems.

[0033] The loading module is used for selecting and loading seismic waves.

[0034] The response analysis module is used for transformer-bushing vibration response analysis under seismic conditions.

[0035] The extended model building module is used for building crack propagation models.

[0036] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, the computer program being executed by the processor causing the processor to perform the steps of the method for calculating the dynamic response of dry casing under seismic loading and establishing a core crack damage model.

[0037] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method for calculating the dynamic response of dry casing under seismic loading and establishing a core crack damage model.

[0038] Another objective of this invention is to provide an information data processing terminal, which is used to implement the method system for calculating the dynamic response of dry casing and establishing a core crack damage model under seismic loading.

[0039] Another objective of this invention is to provide a system for calculating the dynamic response of dry casing under seismic loading and establishing a core crack damage model, comprising:

[0040] A simulation model module for transformer-lifting seat-dry bushing was established, in which the transformer is connected to the oil tank through the lifting seat. The structural parameters of the bushing are: overall bushing height 2840mm, maximum outer diameter at the flange 200mm, air side height 1450mm, lifting seat length 1600mm, wall thickness 20mm, and tilt angle 20°. The model is made of Q235 steel.

[0041] The seismic wave loading module, based on the time history analysis method, simulates the vibration of the foundation by loading actual seismic waves and analyzes the influence of mechanical vibration load on the stress distribution of the casing.

[0042] The dynamic response analysis module is used to calculate the dynamic response of the transformer-bushing system under seismic loads, including displacement, velocity, acceleration, and stress distribution.

[0043] The crack propagation model module is used to predict the generation and propagation path of cracks in dry casing under seismic loading through simulation analysis of stress concentration areas.

[0044] Furthermore, the system also includes an acceleration response analysis module, which is used to analyze the acceleration response at three locations—the top, flange, and bottom of the dry casing—under different earthquake levels, and output the acceleration distribution characteristics at each location of the casing under different earthquake conditions.

[0045] Furthermore, the system also includes a displacement response analysis module, which is used to analyze the displacement response of the dry casing under different seismic loads and output the displacement change trends of the top, middle and bottom ends, especially the displacement response of the top end in the horizontal direction and the middle and bottom ends in the vertical direction.

[0046] Furthermore, the system also includes a crack propagation analysis module, which simulates the crack propagation path through finite element calculation, outputs the generation and propagation process of casing cracks under different seismic conditions, and evaluates the impact of crack propagation on the casing structure.

[0047] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0048] First, after completing the simulation of the transformer bushing vibration response under seismic conditions, this invention can obtain various important data, such as acceleration response, displacement response, actual force, deformation degree, stress concentration, and other relevant data. This allows for the adjustment and optimization of various structural and material parameters. Through this simulation, the various physical effects in 110kV resin-impregnated paper dry bushings can be predicted, and the service life of the material in actual scenarios can be accurately determined.

[0049] This invention establishes two fracture phase field models to simulate crack propagation in thin plates under different loading conditions. By establishing a phase field model for the fracture problem of isotropic plates and using finite element analysis software for numerical calculation, the crack propagation process of thin plates with initial cracks under tensile and shear loads is studied, and the influence of various parameters on crack propagation is calculated.

[0050] Secondly, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0051] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0052] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0053] Currently, there is limited research both domestically and internationally on the vibration response characteristics of 110kV dry bushings, and the potential defects caused by seismic loading have not yet been studied. This paper investigates the dynamic response of the bushing under seismic conditions, extracts the core stress distribution, and applies it as an external load to a crack propagation model of an epoxy core thin plate to study the accelerated evolution of crack defects under seismic loading.

[0054] (3) Whether the technical solution of the present invention solves the technical problem that people have long wanted to solve but have never been able to solve successfully:

[0055] Dry bushings are large in volume, and field tests are difficult and the operating conditions are complex, making it difficult to reflect the internal stress and defect distribution of the dry bushing core under different operating conditions. By simulating extreme operating conditions, this study investigates the dynamic response and crack damage development of the bushing under different earthquake levels, reveals the stress-weak areas and damage mechanisms of the dry bushing, provides a research basis for the structural optimization of dry bushings, and provides a research basis for improving the operation and maintenance risk prevention and control of dry bushings.

[0056] (4) Does the technical solution of the present invention overcome technical bias? Attached Figure Description

[0057] Figure 1 This is a flowchart of the method for calculating the dynamic response of dry casing and establishing a core crack damage model under seismic loading, provided in an embodiment of the present invention.

[0058] Figure 2 This is a system structure diagram of the method for calculating the dynamic response of dry casing and establishing a core crack damage model under seismic loading, provided in an embodiment of the present invention.

[0059] Figure 3 This is a transformer-bushing model diagram provided in an embodiment of the present invention.

[0060] Figure 4 This is a standard reaction spectrum curve provided in the embodiments of the present invention.

[0061] Figure 5 This is an artificial reaction spectrum curve provided in an embodiment of the present invention.

[0062] Figure 6 These are time history curves of different seismic wave accelerations provided in embodiments of the present invention.

[0063] Figure 7 The modal shape diagrams provided in the embodiments of the present invention are (a) 1st order and (b) 16th order.

[0064] Figure 8 This is a model mode-frequency correspondence diagram provided in an embodiment of the present invention.

[0065] Figure 9 This is an acceleration response diagram of the sleeve at different positions provided in an embodiment of the present invention.

[0066] Figure 10 This is a maximum acceleration distribution diagram at different positions of the sleeve provided in an embodiment of the present invention.

[0067] Figure 11 This is a displacement diagram in the x-direction provided in an embodiment of the present invention.

[0068] Figure 12 This is a displacement diagram in the y-direction provided in an embodiment of the present invention.

[0069] Figure 13 This is a displacement diagram in the z-direction provided in an embodiment of the present invention.

[0070] Figure 14 This is a distribution diagram of the displacement response at different positions of the bushing provided in an embodiment of the present invention.

[0071] Figure 15 This is a maximum displacement distribution diagram of the sleeve at different positions provided in an embodiment of the present invention.

[0072] Figure 16 This is a sleeve stress distribution diagram provided in an embodiment of the present invention.

[0073] Figure 17 This is a stress distribution diagram of the core flange provided in an embodiment of the present invention.

[0074] Figure 18 This is a core stress distribution diagram provided in an embodiment of the present invention.

[0075] Figure 19 This is a stress distribution diagram of a transformer bushing provided in an embodiment of the present invention.

[0076] Figure 20 This is a distribution diagram of vibration response parameters under different earthquake levels provided in the embodiments of the present invention.

[0077] Figure 21 These are crack propagation model diagrams provided in embodiments of the present invention. (a) Tensile load model (b) Shear load model.

[0078] Figure 22 This is a crack propagation path diagram under tensile stress provided in an embodiment of the present invention. (a) Initiation (b) Propagation (c) Fracture.

[0079] Figure 23 This is a stress distribution diagram of crack propagation under different earthquake levels provided in the embodiments of the present invention.

[0080] Figure 24 This is a diagram showing the crack propagation initiation time and maximum stress distribution provided in an embodiment of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0082] like Figure 1 As shown in the figure, the method for calculating the dynamic response of dry casing and establishing a core crack damage model under seismic loading provided by this embodiment of the invention includes the following steps:

[0083] S101, Establishment of simulation model for transformer-bushing system;

[0084] Transformer-lifting seat-bushing model: The insulating bushing is connected to the oil tank via the lifting seat. The transformer side plate and bottom plate are 15mm thick, the top plate is 20mm thick, the lifting seat is 1600mm long, the wall thickness is 20mm, the tilt angle is 20°, and the structure is made of Q235 steel. The overall height of the bushing is 2840mm, the maximum outer diameter at the flange is 200mm, and the air side height is 1450mm.

[0085] S102, Seismic wave selection and loading method;

[0086] A finite element model was established based on the actual dry sleeve impregnated with paper to conduct simulation analysis. The time history analysis method was used to analyze the overall force distribution characteristics of the sleeve under the simulated base vibration load, and the influence of mechanical vibration load on the force distribution was studied.

[0087] S103, Analysis of Transformer-Bushing Vibration Response under Seismic Conditions;

[0088] S104, Crack propagation model established.

[0089] The seismic wave selection and loading method provided in this embodiment of the invention:

[0090] (1) For electrical equipment with an axisymmetric structure and vertical arrangement, a single horizontal seismic test shall be conducted; for electrical equipment with an asymmetrical structure, two horizontal seismic tests shall be considered; for electrical equipment with long cantilever or large span, a vertical seismic test shall also be considered.

[0091] (2) The test response spectrum (TRS) generated by the vibration table should be enveloped to meet the requirements of the required response spectrum (RRS). If a small number of individual points in the TRS are outside the tolerance band and are offset from the resonant frequency of the test equipment, it is also acceptable. Considering that the maximum displacement of some vibration tables is limited and the lower frequency part has little impact on the equipment, the tolerance of the spectrum value below 0.7 times the natural frequency of the equipment can be left uncontrolled.

[0092] The transformer-bushing vibration response analysis under seismic conditions provided in this embodiment of the invention:

[0093] 1) Modal analysis;

[0094] First, modal analysis was performed on the overall model to obtain the natural frequencies and mode shapes of the first 20 modes. Mode shapes 1-6 were mainly concentrated on the side wall of the tank, showing an alternating pattern of absorption and expansion. At the same time, small local buckling also occurred at the upper end of the casing. Mode shape 7 showed an upward bending of the casing, and mode shape 12 showed a rightward bending of the casing. Modes 16-20 all showed significant deformation of the casing. The mode shapes of each order were mainly concentrated on the slender structure at the top of the casing and the side plate of the tank.

[0095] 2) Acceleration response analysis at different positions of the dry bushing;

[0096] Since the bushing has a slender structure and is connected to the transformer box through a riser, in order to study the bushing acceleration response under different earthquake levels, the response to different earthquake ground motions was studied separately; the acceleration response values ​​at the top, flange and bottom of the bushing were extracted and analyzed separately.

[0097] 3) Displacement response analysis at different positions of the dry bushing;

[0098] 4) Stress response analysis at different locations of dry bushing.

[0099] The displacement response analysis of the dry bushing at different positions provided in the embodiments of the present invention:

[0100] As the height of the casing increases, its displacement shows a significant upward trend, that is, the displacement at the top is greater than that at the middle and greater than that at the bottom. Among them, the maximum horizontal displacement at the top of the casing is most affected by ground motion, while the maximum vertical displacement at the middle and bottom is most affected by ground motion.

[0101] Stress response analysis of dry bushing at different locations provided in this embodiment of the invention:

[0102] The maximum acceleration, maximum displacement, and maximum stress of the casing vibration response under different earthquake magnitudes were extracted. As the earthquake magnitude increased, the peak values ​​of all responses showed an upward trend; when the earthquake magnitude reached 8, the maximum peak acceleration experienced by the casing was 163.83 m / s². 2The peak displacement was 25.35 mm and the peak stress was 4.55 MPa. Under this earthquake level, the acceleration at the top was 4.3 times greater than that at the bottom, posing a great safety hazard to the mechanical performance of the transformer bushing. Because the epoxy core is a brittle material, its tensile and compressive strength is much lower than that of other components.

[0103] The crack propagation model established according to the embodiments of the present invention:

[0104] Two fracture phase-field models were established to simulate crack propagation in thin plates under different loading conditions. By establishing a phase-field model for the fracture problem of isotropic plates and performing numerical calculations using finite element analysis software, the crack propagation process of thin plates with initial cracks under tensile and shear loads was studied, and the influence of various parameters on crack propagation was calculated.

[0105] like Figure 2 As shown, this embodiment of the invention provides a system for calculating the dynamic response and establishing a crack damage model of dry bushings under seismic loading. The system includes four main modules: a simulation model establishment module for creating a simulation model of the transformer-bushing system; a loading module for selecting and loading seismic waves; a response analysis module for analyzing the vibration response of the transformer-bushing system under seismic conditions; and a crack propagation model establishment module for simulating crack propagation behavior, thereby enabling more accurate damage analysis.

[0106] Another object of the present invention is to provide a computer device comprising a memory and a processor. The memory stores a corresponding computer program, and when the processor executes the program, it can implement all the steps of the method for calculating the dynamic response of dry casing and establishing a crack damage model provided by the present invention. This computer device can effectively simulate the stress and damage conditions of casing under seismic conditions, providing a scientific basis for analysis.

[0107] Furthermore, this invention proposes a computer-readable storage medium in which a computer program, when executed by a processor, causes the processor to perform steps related to the calculation of the dynamic response of the dry bushing and crack propagation. This storage medium allows for the convenient portability of simulation methods to different computing environments, improving the system's application flexibility.

[0108] This invention also proposes an information data processing terminal specifically designed for calculating the dynamic response of dry casing under seismic conditions and establishing a crack propagation model. Through the collaborative operation of the aforementioned modules, this terminal can complete the entire process from data input, seismic wave loading, response analysis to crack propagation simulation, providing a scientific basis for engineering design.

[0109] In practical implementation, the simulation model is established starting with the physical model of the transformer-bushing system. The insulating bushing is connected to the oil tank via a riser. The transformer side plate and bottom plate are 15mm thick, the top plate is 20mm thick, the riser is 1600mm long, 20mm thick, and tilted at a 20° angle. The structural material is Q235 steel. The overall height of the bushing is 2840mm, the maximum outer diameter at the flange is 200mm, and the air-side height is 1450mm. This model ignores the influence of the radiator and aluminum foil, and treats the core as an equivalent epoxy-impregnated paper core.

[0110] During modeling, the insulating oil inside the tank was uniformly distributed as an additional mass on the sidewalls of the tank, and the damping ratio of the model was determined to be 2% according to the "Code for Seismic Design of Power Facilities". The material parameters required for the simulation were set through standardized mechanical properties to ensure the accuracy and reliability of the simulation results.

[0111] Table 1 Main Material Properties

[0112] Material <![CDATA[Density [kg / m 3 > <![CDATA[Young's modulus GPa > Poisson's ratio steel frame 7850 210 0.3 flange 2700 70 0.33 outer sheath 870 20 0.47 Core 1200 4.5 0.38 copper guide rod 8940 126 0.34

[0113] To study the operating conditions of dry bushings subjected to complex environmental dynamics such as mechanical vibration and reduce the probability of transformer dry bushing accidents, a finite element model was established based on actual resin-impregnated paper bushings for simulation analysis. The time history analysis method was used to analyze the overall stress distribution characteristics of the bushing under simulated base vibration load, and the influence of mechanical vibration load on the stress distribution was studied.

[0114] The calculations were performed in accordance with the requirements for seismic input specified in the "Code for Seismic Design of Power Facilities" (GB50260-2013), the "Technical Specification for Seismic Design and Installation and Maintenance of Vibration Reduction Devices for UHV Porcelain Insulated Electrical Equipment" (Q / GDW11132-2013), and the "Technical Specification for Seismic Testing of High Voltage Support-Type Electrical Equipment" (Q / GDW11391-2015). Specific requirements are as follows:

[0115] (1) Electrical equipment with an axisymmetric structure and vertical arrangement can be subjected to single-horizontal seismic tests; for electrical equipment with an asymmetrical structure, seismic tests in two horizontal directions should be considered; for electrical equipment with long cantilever or large span, vertical seismic tests should also be considered. According to the requirements of the "Technical Specification for Seismic Design and Installation and Maintenance of Vibration Reduction Devices for UHV Porcelain Insulated Electrical Equipment", when considering vertical seismic action, the vertical seismic load combination factor is taken as 0.8, and the seismic motion in both directions must meet the correlation requirements specified in the current specifications.

[0116] (2) The test response spectrum (TRS) generated by the vibration table should enclose the required response spectrum (RRS). It is acceptable if a small number of individual points of the TRS are outside the tolerance band and are offset from the resonant frequency of the test equipment. In addition, considering that the maximum displacement of some vibration tables is limited and the lower frequency part has little impact on the equipment, the tolerance of the spectrum value below 0.7 times the natural frequency of the equipment can be left uncontrolled.

[0117] Based on the above requirements and considering that current engineering sites are all within Class III sites, this invention selects artificially synthesized ground motions and two measured ground motions—El-centro wave and Taft wave—for seismic vibration simulation calculations. The artificially synthesized ground motion is generated by fitting the response spectrum (hereinafter referred to as the "standard response spectrum") specified in the "Technical Specification for Seismic Design and Installation and Maintenance of Vibration Reduction Devices for Ultra-High Voltage Porcelain Insulated Electrical Equipment" (QIGDW 11132-2013). The characteristic period of the standard response spectrum is 0.9s, which can almost encompass Class I to III sites in my country. El-centro wave and Taft wave are typical representative ground motions of Class II or III soil sites. The damping ratio of electrical equipment should be determined based on the measured damping ratio during seismic calculations. When measured data is lacking, the damping ratio can be taken as 2%. The artificial ground motion response spectrum has a high degree of fit with the standard response spectrum, and its spectral envelope is wider than that of El-centro wave and Taft wave. The influence of the characteristics of the ground motion response spectrum on the seismic response of transformer bushings is analyzed.

[0118] This study investigates the vibration response and crack propagation of casing under seismic conditions. The earthquake-affected area is Guangdong Province. By consulting earthquake magnitude and intensity data for different regions across the country, the seismic fortification intensity in Guangzhou can be broadly categorized into three levels: seismic fortification intensity 6 degrees (design basic seismic acceleration value 0.05g), seismic fortification intensity 7 degrees (design basic seismic acceleration value 0.10g), and seismic fortification intensity 8 degrees (design basic seismic acceleration value 0.20g). Based on the regional conditions, this study sets the earthquake magnitude as a rare earthquake of 6-8 degrees, with the design earthquake group being Group 1 and the site category being Class II. According to the "Code for Seismic Design of Buildings" GB50011-2010 and the seismic fortification intensity data for various regions in Guangdong Province, four artificial wave response spectrum curves corresponding to these four different earthquake magnitudes were generated based on the standard response spectrum, as shown in the figure. Two actual seismic waves were used as a control group. This invention selects synthetic ground motion and two measured ground motions—El-centro wave and Taft wave—for earthquake simulation. Artificially synthesized ground motions are generated by fitting the response spectrum, or "standard response spectrum," specified in the Technical Specifications for Seismic Design of Electrical Equipment and Installation and Maintenance of Vibration Reduction Devices. The figure below shows a high degree of consistency between the artificial wave and the standard response spectrum, verifying the validity of the artificial wave data. El-centro and Taft waves are typical representative ground motions for Class II or Class I sites. According to relevant standards such as GB 50260-2013 and O / GDW11132-2013, the damping ratio of electrical equipment in seismic calculations should be determined based on the measured damping ratio. When measured data is lacking, the damping ratio can be taken as 2%.

[0119] In the simulation, accelerations with a scaling factor of 1:1:0.8 in the x, y, and z directions were simultaneously applied to the bottom of the transformer to simulate the vibration response of the transformer structure under actual seismic loading. The x-direction acceleration curves for different earthquake magnitudes are shown in the figure below. The acceleration load was applied at a ratio of 1:1:0.8. The scaling factors in the x and y directions are equal, reflecting the seismic impact on the horizontal plane, while the scaling factor in the z direction is slightly lower, considering that vertical seismic acceleration is typically smaller. The figure shows the acceleration time history curve converted from the above response spectrum. Figure 6 Time history curves of acceleration for different seismic waves.

[0120] After completing the simulation of the transformer bushing vibration response under seismic conditions, various important data can be obtained, such as acceleration response, displacement response, actual stress, deformation degree, stress concentration, etc., which allows for the adjustment and optimization of various parameters of the structure and materials. Through this simulation, the various physical effects in 110kV resin-impregnated paper dry bushings can be predicted, and the service life of the material in actual scenarios can be accurately determined.

[0121] Analysis of transformer-bushing vibration response under seismic conditions.

[0122] First, modal analysis was performed on the overall model to obtain the natural frequencies and mode shapes of the first 20 modes. Mode shapes 1-6 are mainly concentrated on the sidewall of the tank, exhibiting alternating absorption and expansion patterns, while the upper end of the casing also shows minor local buckling. Mode shape 7 shows an upward bending of the casing, mode shape 12 shows a rightward bending of the casing, and modes 16-20 all show significant deformation of the casing. The mode shapes are mainly concentrated on the slender upper structure of the casing and the side plate of the tank.

[0123] Figure 7 Modal shape diagram

[0124] Figure 8 Model mode-frequency correspondence diagram

[0125] The figure shows the modal and frequency correspondence of a transformer bushing system model. The fundamental frequency of the model is 3.8057Hz, and the first nine frequencies are almost all between 1 and 10Hz, which is close to the earthquake frequency. Under seismic loading, resonance is highly likely to occur. Resonance refers to the phenomenon where the natural frequency of a structure matches the external excitation frequency, resulting in a significant increase in vibration amplitude, which may lead to structural damage. Therefore, it is essential to study the vibration response characteristics of a transformer bushing system under earthquake influence.

[0126] 3.2 Acceleration Response Analysis at Different Positions of Dry Bushing

[0127] Because the bushing has a slender structure and is connected to the transformer tank via a riser, this invention studies the bushing's acceleration response under different earthquake magnitudes. Acceleration response values ​​are extracted and analyzed from three locations: the top of the bushing, the flange, and the bottom. The following analysis uses a magnitude 7 earthquake as an example.

[0128] Figure 9 Acceleration response at different positions of the bushing

[0129] The figure shows the vibration response distribution of the casing under a magnitude 7 earthquake. The peak acceleration response in the y-direction is largest at the top of the casing. As time increases, the acceleration in the x, y, and z directions shows an oscillating decreasing trend, consistent with the ground motion distribution trend. The amplitude of the casing's acceleration response in the y-direction is the largest, followed by the x-direction, while the amplitude in the z-direction is relatively smaller, indicating that the casing is significantly affected by horizontal ground motion. In the y-direction, the maximum acceleration at the top of the casing is 43.4 m / s², occurring at 15.76 s, corresponding to the rapid acceleration rise phase in the seismic wave response spectrum. At the flange, i.e., the middle of the casing, the acceleration distribution curve shows the largest acceleration in the y-direction, followed by the x-direction, indicating that the middle of the casing is still significantly affected by horizontal ground motion. Another figure shows the acceleration distribution curve at the bottom of the casing, i.e., at the bottom of the casing's equalization shield. Similar to the distribution trends at the top and middle, the acceleration in the y-direction is the largest, followed by the x-direction, indicating that the casing is still significantly affected by horizontal y-direction ground motion.

[0130] Figure 10 Maximum acceleration distribution at different locations of the casing

[0131] The figure shows the maximum response acceleration distribution curves in the x, y, and z directions at different positions at the top, middle, and bottom of the casing. Due to the slender structure of the casing, the acceleration at the top is greater than that at the middle and bottom. Because the casing is significantly affected by horizontal ground motion, the acceleration response is greatest in the y direction, greater than that in the z direction, and greater than that in the x direction.

[0132] In the displacement response analysis of different locations on the dry casing, with the rapid changes in ground motion, the displacement at the top of the casing reaches its maximum value in the y-direction, followed by the z-direction, indicating that horizontal ground motion has a significant impact on the top displacement. In contrast, the displacement at the middle end decreases significantly compared to the top, with the maximum displacement being about half that of the top, showing significant differences in the impact of ground motion on the casing at different locations. The displacement at the bottom of the casing decreases further, with the largest total displacement in the z-direction, followed by the y-direction, and the smallest displacement in the x-direction.

[0133] As the casing height increases, the displacement shows a significant upward trend, with the largest displacement at the top, followed by the middle, and the smallest at the bottom. Horizontally, the maximum displacement at the top of the casing is most significantly affected by seismic activity, while the maximum displacement at the middle and bottom is more significantly affected by seismic activity in the vertical direction. This indicates that the stress conditions on the casing differ at different heights, especially under seismic conditions, where the displacement response varies significantly at different locations.

[0134] In the stress response analysis, the maximum stress value of the bushing reached 17 MPa, occurring at the connection between the flange and the silicone rubber sheath. Because the epoxy core is a brittle material, it experiences greater stress, with its stress intensity significantly higher than other parts. Analysis shows that the stress is concentrated in the connection area between the core and the flange. Under seismic motion, the stress in the core is 1.6 MPa, a significant increase compared to the stress under gravity-only conditions, thus becoming a stress concentration zone.

[0135] Vibration response parameters under different earthquake magnitudes show that the displacement, acceleration, and stress response of the casing all show a significant increasing trend with increasing earthquake magnitude. These responses are concentrated at the flange and core connection, and the stress situation of the casing presents a higher safety hazard, especially under high-magnitude earthquake conditions.

[0136] The maximum acceleration, maximum displacement, and maximum stress of the bushing vibration response under different earthquake magnitudes were extracted. As the earthquake magnitude increased, the peak values ​​of each response showed an upward trend. When the earthquake magnitude reached level 8, the peak value of the maximum acceleration on the bushing was 163.83 m / s², the peak value of the displacement was 25.35 mm, and the peak value of the stress was 4.55 MPa. Under this earthquake magnitude, the acceleration at the top was 4.3 times greater than that at the bottom, posing a significant safety hazard to the mechanical performance of the transformer bushing. Since the epoxy core is a brittle material with tensile and compressive strengths far lower than other components, the crack propagation model of the epoxy core will be studied below.

[0137] To address the brittle fracture problem of epoxy resin thin sheets, this invention establishes two fracture phase-field models to simulate crack propagation in thin sheets under different loading conditions. By establishing a phase-field model for the fracture problem of isotropic plates and performing numerical calculations using finite element analysis software, the crack propagation process of thin sheets with initial cracks under tensile and shear loads is studied, and the influence of various parameters on crack propagation is calculated.

[0138] like Figure 19 The diagram shows the establishment of a casing core crack model dominated by tensile stress. A time-varying displacement u is applied to the upper end of the model. Under the initial conditions, the displacement increment u = 10⁻⁵ mm at each time step, Young's modulus E = 15 GPa, and Poisson's ratio is 0.38. Three main modules—a solid mechanics module, a history variable module, and a phase field module—were established through a solid mechanics and mathematical interface to conduct transient studies of crack propagation. Figure 21 This is a crack propagation model.

[0139] The crack propagation states at different stages are shown in the figure below. During the crack initiation stage, a phase field change is observed at the tip of the pre-existing crack in the phase field distribution, but its value is less than 1, and strain concentration occurs at the crack tip. Before crack initiation, high strain concentration first appears at the tip of the pre-existing crack, and micro-damage forms in the high-strain region. As the load increases, the values ​​of the phase field and principal strain in the crack fracture zone gradually increase. When the phase field value reaches 1, the principal strain also reaches the critical value, at which point the specimen reaches the critical state for crack initiation. Subsequent loading leads to crack initiation, and a clear phase field crack is observed at the tip of the pre-existing crack in the phase field distribution. New micro-damage appears at the crack tip. Crack propagation is the result of stress concentration leading to the continuous accumulation of micro-damage, eventually causing the crack to evolve until it penetrates the specimen. Initially, the crack width changes slowly. When the internal stress of the specimen accumulates to a certain stage, the appearance of a macroscopic crack causes a rapid increase in crack width. Subsequently, the crack width increases at a relatively rapid rate until the crack penetrates the thin plate model.

[0140] As shown in the figure below, the core crack propagation direction under tensile stress is forward along the original crack direction. By looking at the curve of loading displacement and equivalent stress at the loading point, it can be found that as the crack propagates, the crack tip moves forward continuously, and the location of the stress concentration area also moves forward.

[0141] Figure 22 Crack propagation path under tensile stress

[0142] When the deformation energy released by crack propagation is equal to or greater than the energy required for crack propagation, the crack will become unstable and fracture. The energy released per unit thickness of the plate when the crack propagates one unit length from one end is the critical energy release rate. The crack propagation pattern is summarized by the curves of the loaded displacement and von Mises equivalent stress at the loading point. Under tensile and shear loads, the stress-displacement curves show a trend of first increasing and then decreasing. The region of rapid stress increase is the crack initiation stage. Subsequently, the crack propagates rapidly, and the stress value begins to decrease until crack propagation ends.

[0143] Based on the aforementioned research, the maximum stress on the surface of the epoxy core under seismic conditions was extracted as the condition for applying the crack boundary load, and the crack propagation law under different seismic levels was studied.

[0144] Figure 23 Crack propagation stress distribution under different earthquake magnitudes

[0145] When the deformation energy released by crack propagation is equal to or greater than the energy required for crack propagation, the crack will become unstable and fracture. The energy released per unit thickness of the plate when the crack propagates one unit length from one end is the critical energy release rate. The crack propagation pattern is summarized by the curve of the loading displacement at the loading point versus the von Mises equivalent stress. Under tensile load, the stress-displacement curve shows a trend of first increasing and then decreasing. The region of rapid stress increase is the crack initiation stage. Subsequently, the crack propagates rapidly, and the stress value begins to decrease until crack propagation ends.

[0146] Figure 24 Crack propagation initiation time and maximum stress distribution

[0147] As earthquake magnitude increases, crack boundary loads increase, leading to a decrease in the critical energy release rate for crack propagation, a decrease in the maximum stress that the material can withstand, a decrease in the energy required for fracture, a reduction in the stress accumulation time during crack initiation, a reduction in the time to reach the rapid propagation stage, a significant increase in the propagation rate, and the crack will propagate at an earlier time.

[0148] I. Specific application areas or related products of this invention.

[0149] It can be applied to the structural optimization research of power equipment.

[0150] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0151] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the dynamic response of dry casing under seismic loading and establishing a core crack damage model, characterized in that, Includes the following steps: Step 1: Establish a simulation model of transformer-lifting seat-dry bushing, wherein the transformer is connected to the oil tank through the lifting seat; Step 2: Select actual seismic waves and apply load. Analyze the stress distribution of the casing under mechanical vibration load using a finite element model, and simulate the impact of base vibration on the stress of the casing using time history analysis. Step 3: Analyze the vibration response of the transformer-bushing system under seismic conditions, and calculate the dynamic response characteristics of the system under seismic load, including displacement, velocity, acceleration and stress distribution; Step 4: Establish a crack propagation model based on simulation analysis. Through stress analysis of local stress concentration areas, predict the generation and propagation path of cracks in dry casing under seismic loading. Analysis of transformer-bushing vibration response under seismic conditions: 1) Modal analysis; First, modal analysis was performed on the overall model to obtain the natural frequencies and mode shapes of the first 20 modes. Mode shapes 1-6 were mainly concentrated on the side wall of the tank, showing an alternating pattern of absorption and expansion. At the same time, small local buckling also occurred at the upper end of the casing. Mode shape 7 showed an upward bending of the casing, and mode shape 12 showed a rightward bending of the casing. Modes 16-20 all showed significant deformation of the casing. The mode shapes of each order were mainly concentrated on the slender structure at the top of the casing and the side plate of the tank. 2) Acceleration response analysis at different positions of the dry bushing; Since the bushing has a slender structure and is connected to the transformer box through a riser, in order to study the bushing acceleration response under different earthquake levels, the response to different earthquake ground motions was studied separately; the acceleration response values ​​at the top, flange and bottom of the bushing were extracted and analyzed separately. 3) Displacement response analysis at different positions of the dry bushing; 4) Stress response analysis at different locations of the dry bushing; Displacement response analysis of the dry bushing at different locations: As the height of the casing increases, its displacement shows a significant upward trend, that is, the displacement at the top is greater than that at the middle and greater than that at the bottom. Among them, the maximum horizontal displacement at the top of the casing is most affected by ground motion, while the maximum vertical displacement at the middle and bottom is most affected by ground motion.

2. The method for calculating the dynamic response of dry casing under seismic loading and establishing a core crack damage model as described in claim 1, characterized in that, The crack propagation model is established as follows: Two fracture phase-field models were established to simulate crack propagation in thin plates under different loading conditions. By establishing a phase-field model for the fracture problem of isotropic plates and performing numerical calculations using finite element analysis software, the crack propagation process of thin plates with initial cracks under tensile and shear loads was studied, and the influence of various parameters on crack propagation was calculated.

3. A system for calculating the dynamic response of dry casing under seismic loading and establishing a core crack damage model according to the method described in any one of claims 1-2, characterized in that, include: A simulation model module for transformer-lifting seat-dry bushing was established, in which the transformer is connected to the oil tank through the lifting seat. The structural parameters of the bushing are: overall bushing height 2840mm, maximum outer diameter at the flange 200mm, air side height 1450mm, lifting seat length 1600mm, wall thickness 20mm, and tilt angle 20°. The model is made of Q235 steel. The seismic wave loading module, based on the time history analysis method, simulates the vibration of the foundation by loading actual seismic waves and analyzes the influence of mechanical vibration load on the stress distribution of the casing. The dynamic response analysis module is used to calculate the dynamic response of the transformer-bushing system under seismic loads, including displacement, velocity, acceleration, and stress distribution. The crack propagation model module is used to predict the generation and propagation path of cracks in dry casing under seismic loading through simulation analysis of stress concentration areas.

4. The system as described in claim 3, characterized in that, The system also includes an acceleration response analysis module, which is used to analyze the acceleration response at the top, flange and bottom of the dry casing under different earthquake levels and output the acceleration distribution characteristics of each location of the casing under different earthquake conditions.

5. The system as described in claim 4, characterized in that, The system also includes a displacement response analysis module, which is used to analyze the displacement response of the dry casing under different seismic loads, output the displacement change trends of the top, middle and bottom ends, and output the displacement response of the top end in the horizontal direction and the middle and bottom ends in the vertical direction.

6. The system as described in claim 5, characterized in that, The system also includes a crack propagation analysis module, which simulates the crack propagation path through finite element calculation, outputs the generation and propagation process of casing cracks under different seismic conditions, and evaluates the impact of crack propagation on the casing structure.

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