A method and system for optimizing the anti-vibration effect of a surge absorber based on finite element analysis

Abstract

This invention relates to the field of vibration damper design optimization technology, and in particular to a method and system for optimizing the vibration damping effect of vibration dampers based on finite element analysis. The method includes acquiring vibration frequency data of conductors at high-voltage transmission lines and material dimensional parameters of the vibration damper; creating a three-dimensional vibration damping model based on the material dimensional parameters of the vibration damper; performing finite element analysis on the three-dimensional vibration damping model using the vibration frequency data of the conductors at the high-voltage transmission line site, including vibration damper cell partitioning, modal analysis based on transmission line constraints, and parameter sensitivity analysis based on variance; and outputting key adjustment parameters of the vibration damper based on the analysis results. This scheme, through finite element analysis combined with field vibration data, optimizes the vibration damper to form multiple fixed resonant frequencies, covering key vibration frequency bands. Compared with traditional vibration dampers, it achieves precise resonant frequency matching and a wider coverage range.

Description

Technical Field

[0001] This invention relates to the field of vibration damper design optimization technology, and in particular to a method and system for optimizing the vibration damping effect of vibration dampers based on finite element analysis. Background Technology

[0002] With the rapid development of the power industry and the large-scale construction of overhead transmission lines, the operational safety of transmission lines has become increasingly important. In overhead transmission lines, conductors and ground wires often experience strong vibrations, leading to conductor strand breakage, hardware damage, and line tripping, seriously threatening the safe operation of the lines. Under normal circumstances, under light wind vibration, the self-damping of transmission lines alone cannot guarantee their safety; therefore, vibration dampers need to be installed. Commonly used vibration dampers include vibration dampers, damping wires, and damping spacers. Based on transmission line operation experience, vibration dampers can eliminate most light wind vibrations under normal conditions, achieving relatively good experimental and application results. However, some problems also exist, such as low matching degree between the vibration damper's resonant frequency and the conductor's self-damping frequency, the need to improve its own energy consumption level, and conductor strand breakage and wear at the clamps.

[0003] Currently, vibration dampers both domestically and internationally are selected based on conductor diameter; that is, the larger the conductor diameter, the greater the mass of the selected damper and the lower the resonant frequency range. Since the resonant frequency is obtained from a single excitation frequency test, it can only characterize the damper's vibration damping performance at a specific vibration velocity. For actual power lines, the wind speeds causing light vibrations are typically between 0.5 m / s and 5 m / s. Due to the variety of conductor types, the actual vibration range of conductors with the same diameter varies considerably. The amplitude at which conductors experience fatigue failure also differs. Therefore, matching the damper's diameter directly to the conductor's vibration damping frequency is unreasonable. How to improve the match between the damper's resonant frequency and the conductor's self-damping frequency, while simultaneously significantly improving the damper's energy consumption level, has become a major research direction in the design and manufacturing of vibration dampers.

[0004] In summary, in order to enable the vibration damper to meet the wind vibration prevention requirements of transmission line conductors in a specific frequency band, data and modal analysis were conducted on it. With a specific number and value of resonant frequencies as the target, the resonant frequency of the tuning fork vibration damper was redesigned to meet more scientific vibration prevention requirements. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method and system for optimizing the vibration damping effect of vibration dampers based on finite element analysis.

[0006] In a first aspect, the present invention provides a method for optimizing the vibration damping effect of a vibration damper based on finite element analysis, which adopts the following technical solution: A method for optimizing the vibration damping effect of a vibration damper based on finite element analysis includes: Obtain data on the vibration frequency of conductors and the material dimensions of vibration dampers at high-voltage transmission sites; Three-dimensional vibration damping model of components based on material size parameters of vibration damping hammer; Finite element analysis was performed on a three-dimensional vibration isolation model using high-voltage transmission line conductor vibration frequency data, including vibration damper cell division, modal analysis based on transmission line constraints, and parameter sensitivity analysis based on variance. Based on the analysis results, the key adjustment parameters of the vibration damper are output.

[0007] Furthermore, the three-dimensional vibration damping model based on the material size parameters of the vibration damping hammer includes modeling using SolidWorks software according to the component modeling logic. Specifically, the wire clamp model is designed with a double-bolt structure, and the bolts and wire clamps are fixedly connected to simulate actual assembly strength. The steel strand model simulates the single-wire twisting state through multi-body part functionality, with the twist pitch set according to actual parameters to ensure the flexibility and stiffness characteristics of the steel strand are consistent with the actual object. The hammer head model is drawn as a solid according to the design weight and dimensions, and the model mass is ensured to be consistent with the design value by adjusting the solid density. The assembly constraint logic includes binding constraints between the two ends of the steel strand and the hammer head; and fitting constraints and bolt pre-tightening constraints between the wire clamp and the steel strand. Finally, the physical properties of the model are verified and corrected. The core verification parameters include: total mass, center of gravity coordinates (x, y, z), and moment of inertia (Ix, Iy, Iz). The total mass is calculated as follows: ,in Let the density of the i-th component be... Let n be the volume of the i-th component, and n be the total number of components; Calculation of barycentric coordinates: , , ,in Let the mass of the i-th component be... Let the coordinates of the center of gravity of the i-th component be given; calculation of moment of inertia: ,in Let be the moment of inertia of the i-th component about its own x-axis. This is a correction term for the parallel axis theorem.

[0008] Furthermore, the cell division of the vibration damper includes considering the impact of mesh division on the accuracy of finite element analysis results and the problem of increased computation time as the number of meshes increases. The vibration damper head is divided into cells using a tetrahedral method, while the wire clamps and steel strands are divided into cells using a hexahedral method. This ensures both the accuracy of the natural frequency calculation and computational efficiency. The cell size is set to 5mm. After the mesh division is completed, there are a total of 17,944 cells and 41,366 nodes.

[0009] Furthermore, the vibration damper cell division also includes grid size calculation and determination, and grid quality verification and optimization. The grid size calculation and determination includes the principle of matching the minimum structural feature size to ensure that the cells accurately reproduce structural details. The calculation formula is as follows: ,in: This refers to the grid size; This is the proportionality coefficient. The minimum characteristic dimension of the component is the diameter of the steel strand. During the calculation, the minimum characteristic dimension of the vibration damper is the diameter of the steel strand. The hammer head is an irregular structure, while the clamp and steel strand are regular structures. The finite element analysis requirements are met if the distortion rate of all elements is less than the predetermined value, as checked by the mesh quality analysis tool. The mesh quality verification and optimization includes evaluation based on the mesh aspect ratio and twist, and local densification of the stress concentration area of ​​the structure based on the evaluation results, while maintaining the predetermined size in the smooth area of ​​the structure.

[0010] Furthermore, the modal analysis based on transmission line constraints includes applying fixed constraints at the connection aperture between the vibration damper clamp and the transmission line according to the actual transmission line requirements, thereby performing modal analysis. The vibration modal effect of the vibration damper is obtained through modal analysis calculation, including a first-order mode and a second-order mode. The first-order mode is the translation of the vibration damper, and the second-order mode is the rotation of the vibration damper. The frequencies of the two stages are 9Hz and 29Hz, which are close to the theoretical calculation and the actual situation.

[0011] Furthermore, the modal analysis based on transmission line constraints also includes solving for the eigenvalues ​​of the structure based on modal analysis, wherein the finite element governing equations are: ,in: The structural stiffness matrix is ​​obtained by superimposing the material elastic modulus E, Poisson's ratio μ, and the stiffness of the mesh elements. The structural mass matrix is ​​obtained by superimposing the material density ρ and the mass of the mesh elements. Let f be the natural angular frequency, and its relationship with the natural frequency f is: ; The mode shape vector is used; then the Lanczos algorithm is used to solve for the material parameters, obtaining the first two modes: First mode: The mode shape is the overall translation of the vibration damper along the direction perpendicular to the conductor, with a natural angular frequency. And the natural frequency f1; second-order mode: the mode shape is the rotational motion of the anti-vibration hammer winding clamp, and the natural angular frequency f1. And the natural frequency f2; finally, the first-order translational frequency is calculated using a simplified theoretical formula, the formula is as follows: ,in: The equivalent stiffness of the steel strand is given by the formula. Calculate where A is the cross-sectional area of ​​the steel strand and L is the effective length of the steel strand; This represents the total mass of the hammerhead.

[0012] Furthermore, the variance-based parameter sensitivity analysis includes qualitatively and quantitatively allocating the uncertainty in the model output to input variables from different sources in the model. Using variance sensitivity analysis, the continuous optimization variables are represented by a uniform distribution of interactions without variables. The proportion of output variance caused by random input variables is quantified. Finite element analysis is used to simulate changes in various parameters of the vibration damper and to verify the sensitivity of the vibration damper design parameters. The influence of each parameter on the power characteristics of the vibration damper is verified. Among them, the steel strand diameter is more sensitive to the influence of the natural frequency, followed by the steel strand length, and the hammer head weight is the least sensitive.

[0013] Furthermore, the variance-based parameter sensitivity analysis also includes parameter selection based on the structural characteristics and manufacturing process feasibility of the vibration damper, selecting three adjustable core input parameters, the resonant frequency f, and the energy consumption P as output evaluation indicators; then, based on variance decomposition logic, the total variance V(Y) of the output indicator Y is decomposed into the variance caused by each individual parameter. Variance caused by parameter interaction (i≠j), that is: Finally, based on the definition of the Sobel index, the first-order Sobel index and the total Sobel index are calculated, where the first-order Sobel index is expressed as: , representing the proportion of the total variance caused by the i-th parameter alone; Total Sobel index: ,in To eliminate the variance of the output after the i-th parameter, the influence of each parameter on the fluctuation of resonant frequency and power consumption is finally determined based on the interaction effect of the parameters.

[0014] Furthermore, the key adjustment parameters of the vibration damper based on the analysis results are output, including obtaining the influence values ​​of sensitive parameters affecting the resonant frequency and energy consumption level of the vibration damper through finite element analysis of the vibration damper, and obtaining the key adjustment parameters of the three fixed-frequency vibration damper design, which are, in order, the diameter of the single wire of the steel strand, the length of the steel strand and the mass of the hammer head.

[0015] Secondly, a vibration damping effect optimization system based on finite element analysis for vibration damping hammers includes: The data acquisition module is configured to acquire the vibration frequency data of the conductors at the high-voltage transmission site and the material size parameters of the vibration damper. The model building module is configured to create a three-dimensional vibration damping model of the component based on the material size parameters of the vibration damper. The finite element analysis module is configured to perform finite element analysis on the three-dimensional vibration isolation model using the vibration frequency data of the conductors at the high-voltage transmission site, including vibration isolation hammer cell division, modal analysis based on transmission line constraints, and parameter sensitivity analysis based on variance. The adjustment module is configured to output key adjustment parameters of the vibration damper based on the analysis results.

[0016] Thirdly, the present invention provides a computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis.

[0017] Fourthly, the present invention provides a terminal device, including a processor and a computer-readable storage medium, wherein the processor is used to implement various instructions; the computer-readable storage medium is used to store multiple instructions, the instructions being adapted to be loaded and executed by the processor to provide the method for optimizing the vibration damping effect of a vibration damper based on finite element analysis.

[0018] In summary, the present invention has the following beneficial technical effects: This solution utilizes finite element analysis combined with on-site vibration data to optimize the vibration damper, resulting in multiple fixed resonant frequencies that cover key vibration frequency bands, offering a wider frequency coverage compared to traditional vibration dampers. Its resonant frequencies can precisely match the actual frequency band of transmission line vibrations caused by light winds, resolving the mismatch issues resulting from traditional conductor diameter-based selection. It can adapt to the vibration requirements of different types of conductors, reducing safety hazards such as conductor strand breakage and hardware damage from the source.

[0019] This invention, based on parameter sensitivity analysis to pinpoint core adjustment parameters, combined with targeted structural design and material selection, significantly enhances the vibration damper's ability to absorb vibration energy. Compared to conventional vibration dampers, the optimized solution exhibits a marked improvement in energy consumption, more efficiently dissipating the vibration energy of transmission lines and significantly reducing the impact of light wind vibrations on the lines, with vibration damping effects far exceeding traditional solutions.

[0020] This invention achieves precise iterative design of vibration dampers by employing component-based modeling and precise physical property verification, combined with techniques such as mesh generation optimization, modal analysis, and parameter sensitivity analysis. The entire optimization process avoids blind trial and error, clearly defines key adjustment parameters and optimization directions, and considers both production process feasibility and on-site installation requirements. It can directly guide engineering production and application, shorten the R&D cycle, reduce application costs, and simultaneously ensure the reliability and stability of the vibration damper after installation. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the method for optimizing the vibration damping effect of the vibration damping hammer according to Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the vibration damper grid division in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the first-order mode of the vibration damper in Embodiment 1 of the present invention; Figure 4This is a schematic diagram of the second-order mode of the vibration damper in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of a three-dimensional model of the vibration damper in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram of the vibration damper structure of Embodiment 1 of the present invention; Figure 7 This is the power characteristic diagram of the conventional vibration damper in Embodiment 1 of the present invention; Figure 8 This is a power characteristic diagram of the vibration damper of the unequal-sided scheme in Embodiment 1 of the present invention; Figure 9 This is the power characteristic diagram of the vibration damper of the unequal coarseness scheme in Embodiment 1 of the present invention. Figure 10 This is a power characteristic diagram of another unequal coarseness scheme vibration damper in Embodiment 1 of the present invention. Figure 11 This is a comparison diagram of the modal analysis of the vibration damper mesh in Embodiment 1 of the present invention; Among them, 1. wire clamp; 2. steel strand; 3. hammer head; 4. sledgehammer; 5. small hammer. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to the accompanying drawings.

[0023] Example 1 Reference Figure 1 This embodiment of a method for optimizing the vibration damping effect of a vibration damper based on finite element analysis includes: Obtain data on the vibration frequency of conductors and the material dimensions of vibration dampers at high-voltage transmission sites; Three-dimensional vibration damping model of components based on material size parameters of vibration damping hammer; Finite element analysis was performed on a three-dimensional vibration isolation model using high-voltage transmission line conductor vibration frequency data, including vibration damper cell division, modal analysis based on transmission line constraints, and parameter sensitivity analysis based on variance. Based on the analysis results, the key adjustment parameters of the vibration damper are output.

[0024] Specifically, it includes the following steps: S1. Obtain the vibration frequency data of the conductors at the high-voltage transmission site and the material size parameters of the vibration damper. Test the frequency distribution of the ultra-high voltage transmission conductors when the vibration exceeds the standard under micro-wind conditions. Determine that the main frequency ranges of the hazards of excessive micro-wind vibration under long-term operation of the transmission conductors are 10-15Hz, 20-25Hz, and 30-35Hz. The three arbitrary frequency values ​​in the three frequency bands are the resonant frequencies of the three fixed-frequency vibration dampers designed. S2. Three-dimensional vibration damping model of components based on material size parameters of vibration damping hammer; For composite structures such as steel strands, the cross-sectional area formula is required. (n is the number of single wires, d is the diameter of the single wire) Calculate the actual load-bearing cross-sectional area to ensure the accuracy of its mechanical properties calculation; the structural dimension error must be controlled within ±0.5%, and the error of key dimensions (such as clamp hole diameter, steel strand length) ≤ ±0.3%.

[0025] Choose professional CAE software such as SolidWorks or ANSYS DesignModeler. These software programs support complex structural modeling and parametric adjustment, and can meet the needs of multi-component assembly of vibration dampers.

[0026] Component modeling logic: (1) Modeling of wire clamp: Based on the actual structure of double bolts, the bolts and clamp body adopt a "fixed connection" to simulate the actual assembly strength; (2) Steel strand modeling: The single-wire twisting state is simulated by the "multi-body parts" function. The twist pitch is set according to the actual parameters to ensure that the flexibility and stiffness characteristics of the steel strand are consistent with the actual object, and to avoid simplification into a rigid rod that leads to vibration response distortion. (3) Hammer head modeling: Draw the solid according to the design weight and external dimensions. Adjust the solid density (if the shape and weight do not match) to ensure that the model quality is consistent with the design value. The center of gravity coordinates are verified by the software’s built-in “center of gravity calculation” function.

[0027] Assembly constraint logic: The two ends of the steel strand and the hammer head are "bonded" to simulate the actual fixed connection; the wire clamp and the steel strand are "contact" + "bolt pre-tightening" to restore the tightness effect of the wire clamp on the steel strand and avoid vibration analysis errors caused by assembly loosening.

[0028] Ignore minor structures that do not affect vibration characteristics, such as threads on the chuck surface, non-load-bearing chamfers on the hammer head, and minor scratches on the surface of the steel strand. These structures do not change the overall stiffness and mass distribution, but can reduce the number of model elements and improve the efficiency of subsequent analysis. The core structure must be preserved, including the diameter and length of the steel strand, the position and mass of the hammer's center of gravity, and the diameter of the connecting hole of the clamp. These parameters directly determine the natural frequency and vibration mode of the vibration damper.

[0029] Model physical property verification and correction Core verification parameters: total mass, center of gravity coordinates (x, y, z), and moment of inertia (Ix, Iy, Iz). These parameters are key indicators for measuring the consistency between the model and the actual object.

[0030] Total mass calculation: ,in Let the density of the i-th component be... Let n be the volume of the i-th component, and n be the total number of components (clamp, steel strand, sledgehammer, hammer, rubber pad). This formula calculates the total mass of the model by summing the products of the density and volume of each component. The result should be compared with the actual weighing result, with an error ≤ ±3%.

[0031] Calculation of centroid coordinates: , , ,in Let the mass of the i-th component be... Let be the coordinates of the center of gravity of the i-th component. The position of the center of gravity directly affects the rotational mode of the vibration damper. If the calculated value and the actual measured value (measured by a center of gravity tester) have an error exceeding ±5%, the component size or density distribution needs to be adjusted.

[0032] Calculation of moment of inertia: ,in Let be the moment of inertia of the i-th component about its own x-axis. This is a correction term for the parallel axis theorem (because the center of gravity of the component does not coincide with the center of gravity of the model as a whole). The moment of inertia determines the rotational response speed of the vibration damper, which needs to be compared with the theoretical calculation value, with an error ≤ ±8%.

[0033] Correction process: If a physical parameter does not meet the standard, first check whether the part size is accurate, then check whether the material parameters are entered incorrectly, and finally adjust the model structure (such as the shape of the hammer head) to ensure that the physical properties match.

[0034] S3. Finite element analysis of the three-dimensional vibration isolation model is performed using vibration frequency data from high-voltage transmission sites, including vibration damper cell division, modal analysis based on transmission line constraints, and parameter sensitivity analysis based on variance. 1. This study imports the model into the finite element modal analysis and sets the material of the vibration damper model. In the finite element analysis process, mesh generation has a significant impact on the accuracy of the results. As the number of meshes increases, the computation time also increases, but the accuracy decreases accordingly. To address these issues, the vibration damper head is meshed using a tetrahedral method, while the clamps and steel strands are meshed using a hexahedral method. This approach ensures both accuracy and computational efficiency in calculating the natural frequency. The cell size is set to 5mm. After mesh generation, a total of 17944 elements and 41366 nodes are generated, as shown in Table 1. Figure 2 As shown.

[0035] Table 1 Main Parameters of FDY-6 Vibration Damper Material Specifically, mesh generation is the foundation of finite element analysis. Essentially, it discretizes a continuous vibration damper structure into a finite number of non-overlapping elements. By solving the mechanical equations of each element and superimposing them, the overall structural response is obtained. Mesh quality (size, shape, density) directly affects computational accuracy and efficiency: an overly coarse mesh leads to excessive computational errors, while an overly fine mesh causes an exponential increase in computation time. Therefore, a balance must be found between accuracy and efficiency.

[0036] Grid type selection and adaptation logic Hammerhead: The structure has an irregular shape (usually cylindrical or irregular), with many curved surfaces, and uses a tetrahedral mesh. The advantage of this type of mesh is its ability to flexibly adapt to complex geometries; by combining tetrahedral elements to fit irregular curved surfaces, it avoids mesh distortion. Wire clamps and steel strands: The wire clamps have a regular block structure, while the steel strands have a slender columnar structure, using a hexahedral mesh. This type of mesh uses regular cubic elements, resulting in high computational accuracy, fast convergence speed, and more accurate transmission of stress and vibration energy. Furthermore, it requires fewer elements, leading to higher computational efficiency.

[0037] Mesh size calculation and determination Dimension calculation principle: The mesh size must match the minimum feature size of the structure, generally taking 1 / 5 to 1 / 3 of the minimum feature size. This ensures that the element can reproduce the structural details while avoiding redundant calculations caused by the element being too small.

[0038] Calculation formula and parameter explanation: ,in: This refers to the grid size; This is a proportionality coefficient, adjusted according to the structure type; a value of 0.2 is used for regular structures. 0.3，不规则结构取0.3 0.4; This refers to the minimum feature size of the component (i.e., the shortest critical dimension in the structure, such as the diameter of the steel strand or the minimum thickness of the hammerhead).

[0039] Actual calculation process: The minimum characteristic dimension of the vibration damper is the diameter of the steel strand (φ13mm). The hammer head has an irregular structure (k=0.38), while the clamp and steel strand have a regular structure (k=0.38, consistent with the hammer head to simplify calculation). Substituting into the formula, we get... .

[0040] Mesh generation verification: After meshing to a 5mm size, the model generated a total of 17,944 elements and 41,366 nodes, including 12,860 hammerhead tetrahedral elements and 5,084 wire clamp and steel strand hexahedral elements. Mesh quality analysis showed that the distortion rate of all elements was ≤5% (distortion rate is a key indicator of mesh shape; ≤5% indicates a high-quality mesh), meeting the requirements of finite element analysis.

[0041] Mesh quality verification and optimization Core evaluation metrics: Aspect Ratio: The ideal aspect ratio for a hexahedral mesh is 1 (cubic element), and the actual aspect ratio is controlled to be ≤3; the aspect ratio for a tetrahedral mesh is controlled to be ≤5; Warpage: measures the degree to which an element deviates from its ideal shape, with a warpage of ≤10° for a hexahedral mesh and ≤15° for a tetrahedral mesh.

[0042] Optimization process: If there are unqualified meshes (such as excessive distortion or aspect ratio exceeding the standard), adopt the strategy of "local densification" or "re-division": locally densify the mesh in areas of structural stress concentration (such as the connection between the steel strand and the hammer head, and around the bolt holes of the clamp), and reduce the mesh size to 3mm; maintain a size of 5mm in areas of gentle structure (such as the middle of the hammer head and the side of the clamp) to ensure that the accuracy in key areas meets the standard, while controlling the overall number of units.

[0043] 2. Modal analysis Based on the actual requirements of the transmission line, a fixed constraint is applied at the connection hole between the vibration damper clamp and the transmission conductor. Modal analysis is then performed, and the vibration modes of the vibration damper are calculated as follows: Figures 7-10 As shown, the first mode is the translation of the vibration damper, and the second mode is the rotation of the vibration damper. The frequencies of the two stages are 9Hz and 29Hz, which are close to the theoretical calculations and actual values.

[0044] Specifically, modal analysis essentially solves for the inherent vibration characteristics of a structure, namely its natural frequencies and mode shapes. The natural frequencies of a vibration damper are inherent properties, independent of external excitation, and determined solely by the structure's mass and stiffness; mode shapes are the vibration patterns of the structure at the corresponding natural frequencies. Through modal analysis, the possible vibration modes of the vibration damper during actual operation can be identified, and it can be determined whether its resonant frequencies match the vibration frequencies of the transmission lines, thus preventing structural damage caused by resonance.

[0045] Constraint application and actual working condition restoration Constraint logic: During actual installation of the vibration damper, the clamp is fixed to the power transmission line by bolts. There is no relative movement between the clamp and the power transmission line. Therefore, corresponding fixed constraints need to be applied in the model.

[0046] Specific operation: At the hole where the line clamp is fixedly connected to the transmission line, a fixed constraint is applied to restrict all degrees of freedom in this area: translational degrees of freedom in the X, Y, and Z directions (Ux=Uy=Uz=0) and rotational degrees of freedom about the X, Y, and Z axes (Rx=Ry=Rz=0); the other components (hammer head and steel strand) have no additional constraints and remain in a free state to simulate the vibration space of the hammer head and steel strand in actual operation.

[0047] Modal solution formulas and calculation process Core governing equations: Modal analysis is essentially about solving the eigenvalue problem of a structure. The finite element governing equations are: ,in: The structural stiffness matrix is ​​obtained by superimposing the material's elastic modulus E, Poisson's ratio μ, and the stiffness of the mesh elements, and reflects the structure's ability to resist deformation. The structural mass matrix is ​​obtained by superimposing the material density ρ and the mass of the mesh elements, reflecting the inertial characteristics of the structure. Let f be the natural angular frequency, and its relationship with the natural frequency f is: ; The mode vector describes the vibration pattern of the structure at the corresponding natural frequency.

[0048] Algorithm Selection: The Lanczos algorithm was adopted. This algorithm is suitable for modal analysis of large structures, with fast convergence speed and high calculation accuracy, especially suitable for solving the first few core modes (the first two modes play a dominant role in vibration damping). Calculation Process and Results: Substituting the material parameters in Table 1 (steel strand E=200GPa, ρ=7850kg / m³; hammer head E=200GPa, ρ=7850kg / m³; clamp E=69GPa, ρ=2700kg / m³), the first two modes were obtained: First mode: The vibration mode is the overall translation of the vibration damper along the direction perpendicular to the conductor, with a natural angular frequency of... The natural frequency f1 = 9Hz; the second-order mode is the rotational motion (rotation) of the vibration damper winding clamp, with a natural angular frequency of f1 = 9Hz. The natural frequency is f2 = 29 Hz.

[0049] Results verification and validity assessment Theoretical verification: The first-order translational frequency was calculated using a simplified theoretical formula, the formula is as follows: ,in: The equivalent stiffness of the steel strand is given by the formula. Calculate (A is the cross-sectional area of ​​the steel strand, L is the effective length of the steel strand); The total mass of the hammerhead is the sum of the masses of the large hammer and the small hammer.

[0050] Substitute parameters to calculate: cross-sectional area of ​​steel strand (Assuming the number of monofilaments n=7), effective length L=170mm=0.17m, elastic modulus E=200GPa=2×10¹¹Pa, therefore the equivalent stiffness of the steel strand is... The total mass of the hammerhead, M = 3.0 + 3.0 = 6.0 kg, can be obtained by substituting into the frequency formula. .

[0051] Validity judgment: The error between the finite element calculation result (9Hz) and the theoretical calculation result (8.7Hz) is ≤3.4%, and it is consistent with the field measured value (approximately 8.8~9.2Hz), indicating that the constraint setting is reasonable, the model is effective, and the modal analysis results are reliable.

[0052] 3. Sensitivity analysis studies how to qualitatively or quantitatively allocate the uncertainty in the model output to the input variables from different sources. Variance-based sensitivity analysis, by representing continuous optimization variables with a uniform distribution of interactions without variables, directly quantifies the proportion of output variance caused by random input variables, making it suitable for optimization preprocessing. Finite element analysis was used to simulate and change various parameters of the vibration damper to verify the sensitivity of the damper's design parameters, verifying the influence of each parameter on the damper's power characteristics. The sensitivity analysis of the design parameters is shown in Table 2. The table shows that the steel strand diameter has the largest impact on the natural frequency, accounting for approximately 83%, followed by the steel strand length, accounting for approximately 13%. The hammer head weight has a relatively small impact, less than 5%, and the wire clamp is fixed, so its influence is negligible.

[0053] The purpose of parameter sensitivity analysis is to quantify the influence of each design parameter on the performance of the vibration damper (resonant frequency, power consumption). Variance-based sensitivity analysis (Sobel index method) quantitatively describes the importance of a parameter by calculating the proportion of the output variance caused by each parameter to the total variance: the larger the proportion, the more significant the impact of that parameter on performance, and the more crucial it is for optimization design.

[0054] Among them, the analysis parameters and evaluation indicators are defined. Input parameter selection: Considering the structural characteristics of the vibration damper and the feasibility of the production process, three adjustable core parameters are selected. The wire clamp parameter is a fixed structure with no adjustment space, so it is not included in the analysis: Steel strand single wire diameter d: variable range ±10% (the diameter adjustment accuracy in actual production is ±0.1mm); Steel strand length L: variable range ±15% (length adjustment is limited by installation space and must be within the feasible range); Hammer head mass m: variable range ±10% (mass adjustment is achieved by changing the hammer head material or thickness).

[0055] Output evaluation indicators: Resonant frequency f: Directly affects the matching degree between the vibration damper and the transmission line vibration frequency, and is a core performance indicator; Energy consumption power P: Positively correlated with the vibration damper's ability to absorb vibration energy; the larger P is, the better the vibration damping effect. The calculation formula is as follows: (α is a coefficient related to the stiffness of the steel strand, which is calibrated to 0.0012 through experiments).

[0056] Principles and formulas for calculating variance sensitivity Variance decomposition logic: Decompose the total variance V(Y) of the output index Y (f or P) into the variance caused by each individual parameter. Variance caused by parameter interaction (i≠j) etc., that is: .

[0057] Sobel index definition: First-order Sobel exponent (individual effect): , which represents the proportion of the variance caused by the i-th parameter alone to the total variance, reflecting the main effect of the parameter; Total Sobel index (including interaction effects): ,in To exclude the variance of the output after the i-th parameter, it reflects the sum of the main effect and interaction effect of the parameter.

[0058] Simplified processing: Experimental verification shows that the interaction effect of the three parameters is ≤2%, which has a minimal impact on the results. Therefore, the first-order Sobel index is used to approximate the total effect and simplify the calculation process.

[0059] Calculation process and result analysis Sample point design: A uniform design method is adopted to generate 30 non-overlapping parameter combinations (sample points) within the range of parameter variables, ensuring that the samples cover the entire parameter space and avoiding analytical bias caused by uneven sample distribution.

[0060] Simulation test: For each set of sample points, the corresponding output indices f and P are calculated using finite element analysis software, and 30 sets of "parameter-performance" data pairs are recorded.

[0061] Variance calculation and Sobel index solution: Total variance calculation: For 30 sets of output index data, calculate the variance using the variance formula. (n=30, For the k-th data set, Calculate the total variance V(Y) for the data (mean). Single-parameter variance calculation: Fix the other two parameters as the mean, change only the i-th parameter, and calculate the output variance caused by that parameter. ; Sobel exponent calculation: Substituting into the first-order Sobel exponent formula, we obtain the sensitivity percentage of each parameter: Steel strand single wire diameter d: (Affecting 98%) Length L of steel strand: (Influence accounts for 13%) Hammer mass m: (5% impact).

[0062] Interpretation of results: The diameter of the steel strand is the most critical parameter affecting the performance of the vibration damper. Even a small change in the diameter can lead to significant fluctuations in the resonant frequency and power consumption. The length of the steel strand is the second most important parameter. The mass of the hammer head has the least impact. Therefore, the optimization design should prioritize adjusting the diameter of the steel strand, followed by the length of the steel strand, and finally fine-tuning the mass of the hammer head.

[0063] Table 2 Sensitivity Analysis of Vibration Damper Parameters The reliability of the theoretical model and finite element analysis was verified through the above theoretical simulation and finite element analysis. By defining the input parameters of the vibration damper, a parametric model was constructed, and then modal analysis of the vibration damper was performed to analyze its vibration modes and natural frequencies. By calibrating the range of input parameters, sample points were selected to construct a sample space, and then response surface analysis was performed to complete the target optimization. Finally, the optimization results were analyzed to determine whether the optimization results met the target and to decide whether to continue optimization.

[0064] S4. Output key adjustment parameters of the vibration damper based on the analysis results. Through finite element analysis of the vibration damper, the influence values ​​of sensitive parameters affecting the resonant frequency and energy consumption level of the vibration damper are obtained, and the key adjustment parameters for the design of the three fixed-frequency vibration dampers are obtained, in order: diameter of single wire of steel strand, length of steel strand, and mass of hammer head; Specifically, With the vibration frequency requirements (10-15Hz, 20-25Hz, 30-35Hz) of high-voltage transmission sites as the target, and combined with the results of parameter sensitivity analysis, the key parameters are iteratively optimized and adjusted to ensure that the resonant frequency of the vibration damper accurately covers the target frequency band, while maximizing energy consumption, and finally outputting the optimal parameter combination that meets the vibration damping requirements.

[0065] Among them, the optimization objectives and constraints are set. The core objectives include: Frequency coverage target: The three-frequency vibration damper must have three resonant frequencies, respectively covering the three out-of-standard frequency bands of 10-15Hz, 20-25Hz, and 30-35Hz, that is... , , Energy consumption maximization objective: Within the target frequency band, maximize the energy consumption power P, i.e. ( (where α is the average mass of the hammerhead, α = 0.0012).

[0066] Constraints (Production Process and Installation Limitations): Steel Strand Single Wire Diameter: ( The initial diameter is 13mm, i.e., d∈[11.7,14.3]mm; the length of the steel strand is: ( The initial length is 170mm, i.e., L∈[144.5,195.5]mm; hammer mass: ( (where m is the initial mass, 3.0 kg), i.e., m ∈ [2.7, 3.3] kg.

[0067] Parameter optimization iterative calculation Iterative optimization logic: Based on parameter sensitivity priority (steel strand diameter d > steel strand length L > hammer mass m), a strategy of "primary and secondary adjustment + fine-tuning optimization" is adopted to gradually approach the target frequency, specifically divided into three rounds of iteration: the first round of iteration (core parameter adjustment: steel strand diameter d): Optimization logic: The diameter of the single wire of the steel strand has the greatest impact on the resonant frequency. By changing the diameter, the first-order resonant frequency f1 can be adjusted to cover the 10-15Hz frequency band.

[0068] Calculation Formula and Application: The resonant frequency is positively correlated with the stiffness of the steel strand, and the stiffness is positively correlated with the square of the diameter. Therefore, the relationship between frequency and diameter can be simplified to: ,Right now (When other parameters are fixed).

[0069] Calculation process: With L=170mm and m=3.0kg fixed, and the initial diameter d=13mm, f1=11.25Hz (calculated by substituting into the modal analysis formula). This frequency is in the target frequency band of 10-15Hz, so d is temporarily set to 13mm and no further adjustment is needed.

[0070] Second iteration (minor parameter adjustment: strand length L): Optimization logic: The length of the steel strand affects the second resonant frequency f2. By adjusting the length, f2 can cover the 20-25Hz frequency band.

[0071] Calculation formula and application: The relationship between frequency and strand length is as follows (When other parameters are fixed), that is, the longer the length, the lower the frequency; the shorter the length, the higher the frequency.

[0072] Calculation process: With d=13mm and m=3.0kg fixed, when L=160mm, substitute into the formula. Since the frequency is in the target frequency band of 20-25Hz, L is tentatively set to 160mm (small hammer distance) and 170mm (large hammer distance, taking into account the first-order frequency stability).

[0073] Third iteration (fine-tuning parameters: hammer mass m): Optimization logic: The hammerhead mass affects the third-order resonant frequency f3. By fine-tuning the mass, f3 can cover the 30-35Hz frequency band, while maximizing power consumption.

[0074] Calculation formula and application: The relationship between frequency and hammer mass is as follows: (With other parameters fixed), power consumption .

[0075] Calculation process: With d=13mm and L=170mm (large hammer) / 160mm (small hammer) fixed, when m=3.0kg, f3=31Hz (substitute into the formula for calculation), which is in the target frequency band of 30-35Hz; at this time, the energy consumption power P=0.0012×(11.25²+24²+31²)×3.0≈0.0012×(126.56+576+961)×3.0≈0.0012×1663.56×3.0≈5.99W, reaching the maximum energy consumption level. If m is adjusted to 3.3kg, f3=29.5Hz (exceeding the target frequency band); if m is adjusted to 2.7kg, f3=32.8Hz (within the target frequency band), but the power consumption P=0.0012×(11.25²+24²+32.8²)×2.7≈0.0012×(126.56+576+1075.84)×2.7≈0.0012×1778.4×2.7≈5.87W, which is lower than the power consumption when m=3.0kg. Therefore, the hammer mass is determined to be 3.0kg.

[0076] Experimental verification and final parameter determination Simulation screening: Based on the optimized parameter combination, 40 different fine adjustment schemes were designed (such as hammer distance ±10mm, hammer mass ±0.1kg). The resonant frequency and energy consumption of each scheme were calculated by finite element simulation, and 10 schemes with complete frequency coverage and high energy consumption were selected.

[0077] Physical experiment: Prepare 10 sets of physical samples for the screening schemes, simulate the micro-wind vibration environment of power transmission lines on a laboratory vibration table (wind speed 0.5-5m / s, vibration frequency 10-35Hz), and test the actual resonant frequency and energy consumption of the samples.

[0078] The key parameters affecting the resonant frequency and energy consumption level of the vibration damper, such as the diameter of the single wire of the steel strand, the length of the steel strand, and the mass of the hammer head, were adjusted. Through simulation and experimental verification of the power characteristics of the vibration damper, the parameters of the diameter of the single wire of the steel strand, the length of the steel strand, the mass of the hammer head, and the three fixed-frequency resonant frequencies of the vibration damper were determined, as shown in Table 3.

[0079] Table 3 Power characteristic data of three fixed-frequency hammers (φ13 custom steel strand) Experimental verification The vibration damper was modeled and analyzed in three dimensions. Parameters such as the center of gravity, mass, and moment of inertia of the hammer head were obtained using SolidWorks 3D software. Modal analysis was performed using the software, and combined with previous research results, the parameters were changed to obtain the relevant resonant frequencies.

[0080] Multiple simulations were conducted on the vibration damper schemes. Based on the simulation results, 40 sets of data were selected for testing, including conventional, unequal-sided, and unequal-coarse vibration damper schemes, with 4 large hammers and 5 small hammers. The test results are shown in Table 4. The power characteristics of each vibration damper scheme are as follows: Figures 7-10 As shown, where Figure 7 The power characteristics of a conventional vibration damper. Figure 8 The power characteristics of the vibration damper for the unequal-sided scheme are as follows: Figure 9 For the power characteristics of the vibration damper with unequal coarse scheme, Figure 10 The power characteristics of the vibration damper with unequal coarse scheme.

[0081] Table 4 Power characteristic data of three fixed-frequency vibration dampers (φ13 steel strand) The above data shows that the three-frequency vibration damper can cover three frequencies, specifically: The asymmetric vibration damper has an asymmetrical structure and theoretically has four resonant frequencies: frequencies one and three correspond to the translational vibration mode relative to the clamp and the rotational vibration mode relative to the center of mass on one side; frequencies two and four correspond to the translational vibration mode relative to the clamp and the rotational vibration mode relative to the center of mass on one side. From the above data, it can be seen that the improved vibration damper can basically cover the required three frequencies. Comparing the conventional FDY-6 vibration damper scheme with several different schemes including three-frequency unequal-sided and unequal-thickness designs, the vibration damping effect was simulated and analyzed. Based on the optimal vibration damping effect, the three-frequency vibration damper uses high-performance steel strand, as shown in Table 5.

[0082] Table 5 Power characteristic data of three fixed-frequency hammers (φ13 custom steel strand) To analyze the vibration damping effect of the new type of vibration damper, a simulation analysis was conducted to compare its vibration damping effect with that of various other schemes. The comparison results are shown below. Figure 11 .

[0083] The parameters of the vibration dampers for each scheme are compared in Table 7.

[0084] Table 7 Comparison of vibration damper parameters for each scheme The above data chart analysis concludes that: ① Compared to the existing conventional vibration damper which has 2 resonant frequencies, the optimized unequal-sided, unequal-thickness steel strand and high-performance steel strand solutions all have 3-4 resonant frequencies, with the three frequencies ranging from 5-45Hz. The frequency range can cover the 3 resonant frequencies required by this design, providing a wider coverage.

[0085] ② Compared with the conventional scheme, the energy consumption of the three optimized schemes is higher than that of the conventional scheme, and the energy consumption effect is better. Among them, the unequal side scheme, the unequal thickness steel strand scheme, and the high strength steel strand scheme have increased energy consumption by 1.5, 2, and 4 times respectively compared with the conventional scheme. Under the same conditions, they can absorb more wind vibration energy.

[0086] ③ The three optimized schemes have basically the same resonance frequency. In terms of energy consumption, the high-performance steel strand consumes the most energy. The unequal side scheme and the unequal thickness scheme consume basically the same energy. The high-performance steel strand has a better vibration damping effect. Compared with the original scheme, the vibration damping performance is improved by 1.5-2 times at 13, 17 and 23 Hz, and by 6 times at 33 Hz. It is recommended that the high-performance steel strand scheme be adopted for subsequent lines.

[0087] This embodiment of a double-bolt fixed-frequency vibration damper includes a clamp 1, a steel strand 2, and a hammer head 3. The clamp of the vibration damper in this embodiment adopts a double-bolt structure, which improves the energy consumption level of the vibration damper while ensuring its own reliability after installation on the conductor. Its unique structural dimensions, hammer head weight, and steel strand diameter ensure that the vibration damper has three fixed resonant frequencies of 11.25±20%, 24±20%, and 31±20% within the frequency coverage range of 5-45Hz. From the perspective of power characteristics, the vibration damper's vibration damping performance is improved by 6 times at the 31±20% frequency and by 1.5-2 times at other frequencies, which can absorb more vibration energy and has a better vibration damping effect. See Table 8 for detailed parameters.

[0088] Table 8 Power characteristic data of three fixed-frequency hammers (φ13 custom steel strand) The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis, characterized in that, include: Obtain data on the vibration frequency of conductors and the material dimensions of vibration dampers at high-voltage transmission sites; Three-dimensional vibration damping model of components based on material size parameters of vibration damping hammer; Finite element analysis was performed on a three-dimensional vibration isolation model using vibration frequency data from high-voltage power transmission sites, including vibration damper cell division, modal analysis based on transmission line constraints, and parameter sensitivity analysis based on variance. Based on the analysis results, the key adjustment parameters of the vibration damper are output.

2. The method for optimizing the vibration damping effect of a vibration damper based on finite element analysis according to claim 1, characterized in that, The three-dimensional vibration damping model based on the material size parameters of the vibration damping hammer is constructed using SolidWorks software according to the component modeling logic. Specifically, the wire clamp is modeled as a double-bolt structure, with the bolts and clamps fixedly connected to simulate actual assembly strength. The steel strand is modeled using multi-body parts to simulate the twisting state of single wires, with the twist pitch set according to actual parameters to ensure the flexibility and stiffness characteristics of the steel strand are consistent with the physical object. The hammer head is modeled as a solid entity based on the design weight and dimensions, and the model mass is adjusted to ensure consistency with the design value. The assembly constraint logic includes binding constraints between the two ends of the steel strand and the hammer head; and fitting constraints and bolt pre-tightening constraints between the wire clamp and the steel strand. Finally, the physical properties of the model are verified and corrected. The core verification parameters include: total mass, center of gravity coordinates (x, y, z), and moment of inertia (Ix, Iy, Iz). The total mass is calculated as follows: ,in Let the density of the i-th component be... Let n be the volume of the i-th component, and n be the total number of components; Calculation of barycentric coordinates: , , ,in Let the mass of the i-th component be... Let the coordinates of the center of gravity of the i-th component be given; calculation of moment of inertia: ,in Let be the moment of inertia of the i-th component about its own x-axis. This is a correction term for the parallel axis theorem.

3. The method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis according to claim 2, characterized in that, The vibration damper cell division includes addressing the impact of mesh division on the accuracy of finite element analysis results and the issue of increased computation time due to the increased number of meshes. Therefore, a tetrahedral method is used for cell division of the vibration damper head, while a hexahedral method is used for cell division of the wire clamps and steel strands. This ensures both accuracy in natural frequency calculation and computational efficiency. The cell size is set to 5mm, resulting in a total of 17,944 elements and 41,366 nodes after mesh division.

4. The method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis according to claim 3, characterized in that, The vibration damper cell division also includes grid size calculation and determination, and grid quality verification and optimization. The grid size calculation and determination includes the principle of matching the minimum structural feature size to ensure that the cells accurately reproduce structural details. The calculation formula is as follows: ,in: This refers to the grid size; This is the proportionality coefficient. The minimum characteristic dimension of the component is the diameter of the steel strand. During the calculation, the minimum characteristic dimension of the vibration damper is the diameter of the steel strand. The hammer head is an irregular structure, while the clamp and steel strand are regular structures. The finite element analysis requirements are met if the distortion rate of all elements is less than the predetermined value, as checked by the mesh quality analysis tool. The mesh quality verification and optimization includes evaluation based on the mesh aspect ratio and twist, and local densification of the stress concentration area of ​​the structure based on the evaluation results, while maintaining the predetermined size in the smooth area of ​​the structure.

5. The method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis according to claim 4, characterized in that, The modal analysis based on transmission line constraints includes applying fixed constraints at the connection aperture between the vibration damper clamp and the transmission line according to the actual transmission line requirements, thereby performing modal analysis. The vibration modal effect of the vibration damper is obtained through modal analysis calculation, including first-order mode and second-order mode. The first-order mode is the translation of the vibration damper, and the second-order mode is the rotation of the vibration damper. The frequencies of the two stages are 9Hz and 29Hz, which are close to the theoretical calculation and the actual situation.

6. The method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis according to claim 5, characterized in that, The modal analysis based on transmission line constraints also includes solving for the eigenvalues ​​of the structure based on modal analysis, wherein the finite element governing equations are: ,in: The structural stiffness matrix is ​​obtained by superimposing the material elastic modulus E, Poisson's ratio μ, and the stiffness of the mesh elements. The structural mass matrix is ​​obtained by superimposing the material density ρ and the mass of the mesh elements. Let f be the natural angular frequency, and its relationship with the natural frequency f is: ; The mode shape vector is used; then the Lanczos algorithm is used to solve for the material parameters, obtaining the first two modes: First mode: The mode shape is the overall translation of the vibration damper along the direction perpendicular to the conductor, with a natural angular frequency. And the natural frequency f1; second-order mode: the mode shape is the rotational motion of the anti-vibration hammer winding clamp, and the natural angular frequency f1. And the natural frequency f2; finally, the first-order translational frequency is calculated using a simplified theoretical formula, the formula is as follows: ,in: The equivalent stiffness of the steel strand is given by the formula. Calculate where A is the cross-sectional area of ​​the steel strand and L is the effective length of the steel strand; This represents the total mass of the hammerhead.

7. The method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis according to claim 6, characterized in that, The variance-based parameter sensitivity analysis includes qualitatively and quantitatively allocating the uncertainty in the model output to input variables from different sources in the model. Using variance sensitivity analysis, the continuous optimization variables are represented by a uniform distribution of interactions without variables. The proportion of output variance caused by random input variables is quantified. Finite element analysis is used to simulate changes in various parameters of the vibration damper and to verify the sensitivity of the vibration damper design parameters. The influence of each parameter on the power characteristics of the vibration damper is verified. Among them, the steel strand diameter is more sensitive to the influence of the natural frequency, followed by the steel strand length, and the hammer head weight is the least sensitive.

8. The method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis according to claim 7, characterized in that, The variance-based parameter sensitivity analysis also includes parameter selection based on the structural characteristics and manufacturing process feasibility of the vibration damper. Three adjustable core input parameters, along with the resonant frequency f and energy consumption P, are selected as output evaluation indicators. Then, based on variance decomposition logic, the total variance V(Y) of the output indicator Y is decomposed into the variance caused by each individual parameter. Variance caused by parameter interaction (i≠j), that is: Finally, based on the definition of the Sobel index, the first-order Sobel index and the total Sobel index are calculated, where the first-order Sobel index is expressed as: , representing the proportion of the total variance caused by the i-th parameter alone; Total Sobel index: ,in To eliminate the variance of the output after the i-th parameter, the influence of each parameter on the fluctuation of resonant frequency and power consumption is finally determined based on the interaction effect of the parameters.

9. The method for optimizing the vibration damping effect of a vibration damping hammer based on finite element analysis according to claim 8, characterized in that, The key adjustment parameters of the vibration damper are output based on the analysis results. This includes obtaining the influence values ​​of sensitive parameters affecting the resonant frequency and energy consumption level of the vibration damper through finite element analysis of the vibration damper, and obtaining the key adjustment parameters for the design of the three fixed-frequency vibration dampers, which are, in order, the diameter of the single wire of the steel strand, the length of the steel strand, and the mass of the hammer head.

10. A vibration damping effect optimization system based on finite element analysis for vibration damping hammers, characterized in that, include: The data acquisition module is configured to acquire the vibration frequency data of the conductors at the high-voltage transmission site and the material size parameters of the vibration damper. The model building module is configured to create a three-dimensional vibration damping model of the component based on the material size parameters of the vibration damper. The finite element analysis module is configured to perform finite element analysis on the three-dimensional vibration isolation model using vibration frequency data from high-voltage transmission sites, including vibration damper cell division, modal analysis based on transmission line constraints, and variance-based parameter sensitivity analysis. The adjustment module is configured to output key adjustment parameters of the vibration damper based on the analysis results.

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