Dielectric gradient insulator preparation method based on electric field topology optimization and 3D printing

Abstract

The application discloses a dielectric gradient insulator preparation method based on electric field topology optimization and 3D printing. A geometric and electrostatic field model of the insulator is established, the minimum electric field strength is taken as an optimization objective function, the insulator is preset as n layers along a radial direction or an axial direction, a global search is performed on dielectric constant numerical values of each layer through parameterized scanning, a numerical combination that most stabilizes electric field distribution at a junction of a high-voltage electrode, the insulator and insulating gas is searched, and optimal dielectric constants of the layers are obtained. A slurry is prepared according to the optimal dielectric constants of the layers. The prepared slurry is subjected to 3D printing to obtain the dielectric gradient insulator. Through construction of a spatial gradient distribution of the dielectric constant inside the insulator, which gradually decreases from the high-voltage electrode to the ground electrode, charges in a field strength concentration area can be accurately guided to a low field strength area, and field strength distortion at a junction of the high-voltage electrode, the insulator and the insulating gas is effectively relieved.

Description

Technical Field

[0001] This invention belongs to the field of high-voltage power equipment manufacturing technology. The invention relates to a method for preparing intermediate-gradient insulators based on electric field topology optimization and 3D printing. Background Technology

[0002] Gas-insulated metal-enclosed transmission lines (GILs) are key equipment for high-capacity power transmission, and their operational reliability largely depends on the performance of pot-type insulators. These insulators not only provide mechanical support and gas sealing, but their surface electric field distribution characteristics are also a core factor determining the insulation strength and long-term operational stability of the equipment. However, traditional homogeneous insulators, limited by the uniform dielectric properties of their materials, are prone to electric field concentration at the interface between the high-voltage electrode and the insulator, leading to partial discharge and even surface flashover, becoming a major bottleneck restricting the improvement of GIL insulation performance.

[0003] The core problem of insulation failure stems primarily from the extreme non-uniformity of the electric field distribution. First, at the interface between the solid dielectric, the high-voltage conductor, and the insulating gas, the significant difference in dielectric constant between the solid material and the gaseous medium causes severe refraction and distortion of the electric field lines. If the contact angle is improperly designed, the electric field strength in this region theoretically tends towards infinity, easily inducing partial discharge or even surface flashover. Second, the electric field distribution on the surface of traditional homogeneous insulators typically exhibits a U-shaped characteristic, meaning the electric field strength surges dramatically on both sides of the electrode while the utilization rate of the electric field strength in the middle region is insufficient. This uneven distribution not only causes redundancy in material properties but also limits further reduction in equipment size.

[0004] To address these challenges, traditional industries primarily employ methods such as geometric optimization (e.g., adding skirts, changing thickness), pre-embedded metal shielding rings, or coating with nonlinear resistive coatings. However, geometric optimization often leads to a dramatic increase in insulator volume and extremely complex manufacturing molds; while metal shielding rings can reshape the potential distribution, the internal interfaces they introduce are prone to generating air gaps, which may evolve into new discharge points under high voltage; and coating technology faces stability challenges such as peeling, aging, and adhesion failure during long-term operation.

[0005] In recent years, the rise of Functionally Graded Materials (FGMs) has provided a new physical paradigm for overcoming the aforementioned predicament. By constructing a gradient distribution of dielectric constant or conductivity in a spatial dimension, the electric field can be modulated using the distribution of material properties. By introducing high dielectric constant components into key regions where the field strength is concentrated, the electric field can be guided to shift inward or to regions with lower field strength using the principle of capacitive voltage division, effectively suppressing the maximum field strength. However, the engineering application of FGMs has long been constrained by the lack of manufacturing technology: traditional casting technology can only produce homogeneous structures; centrifugal casting is limited to radial one-dimensional gradients; and the step interfaces formed by multi-stage casting have become weak links in mechanics and electricity.

[0006] 3D printing technology, especially photopolymerization, theoretically grants materials pixel-level spatial control. However, in the field of high-voltage insulator manufacturing, this technology still faces three major challenges: First, the optimization of dielectric properties heavily relies on the introduction of a high proportion of inorganic fillers, but this leads to extreme deterioration of the slurry's rheological properties and a strong ultraviolet light scattering effect, making it difficult to simultaneously achieve both molding accuracy and curing depth. Second, the dielectric anisotropy and microscopic interface defects caused by the interlayer stacking process easily induce space charge accumulation under extremely high electric fields, becoming electrical weak points caused by partial discharge and electrical treeing. Simultaneously, existing multi-material printing technologies mostly involve step-by-step component switching, making it difficult to construct an ideal smooth and continuous gradient distribution. Summary of the Invention

[0007] The purpose of this invention is to provide a method for preparing a dielectric gradient insulator based on electric field topology optimization and 3D printing, aiming to overcome the continuous manufacturing challenges of complex spatial gradient distributions and achieve in-depth optimization of the electric field distribution and performance breakthroughs in insulation equipment.

[0008] The technical solution to achieve the purpose of this invention is as follows: A method for fabricating dielectric gradient insulators based on electric field topology optimization and 3D printing includes the following steps: A geometric and electrostatic field model of the insulator is established. The objective function is to minimize the maximum electric field strength. The insulator is preset to n layers along the radial or axial direction. The dielectric constant of the insulator shows a decreasing gradient distribution from the high-voltage electrode side to the ground electrode side along the radial or axial direction. The dielectric constant values ​​of each layer are globally searched through parameterized scanning to find the combination of values ​​that makes the electric field distribution at the junction of the high-voltage electrode, the insulator and the insulating gas most moderate, and the optimal dielectric constant of each layer is obtained. Prepare the slurry according to the obtained optimal dielectric constant of each layer; The prepared slurry is used to 3D print insulators with dielectric gradation.

[0009] In the preferred technical solution, the method for smoothing the electric field distribution at the junction of the high-voltage electrode, the insulator, and the insulating gas is as follows: According to the electromagnetic field interface conditions, the tangential component of the electric field intensity is continuous while the normal component is inversely proportional to the dielectric constant. By arranging high dielectric constant materials in the region near the electrode, electrons are attracted into the solid insulating medium, thereby reducing the tangential electric field component on the gas side and smoothing the electric field distribution at the junction of the high voltage electrode, the insulator, and the insulating gas.

[0010] In the preferred technical solution, after performing a global search for the dielectric constant values ​​of each layer through parametric scanning, the solution further includes: By increasing the layer density and using a restricted Boltzmann machine to smooth the spatial dielectric constant ε difference between layers, a material spatial distribution topology with optimized electric field utilization is obtained.

[0011] In the preferred technical solution, the method of smoothing the spatial dielectric constant ε difference between layers using a restricted Boltzmann machine includes: The discrete layered dielectric constant values ​​and their corresponding spatial coordinates obtained through global search are encoded into the input vector v of the visible layer unit, and the hidden layer unit h is used to extract higher-order features of the discrete data. For a given state (v, h), the energy of the system is defined as:

[0012] in, These are the weights connecting the visible layer units and the hidden layer units. a i and b j These are the bias terms for the two layers, where n is the number of visible layer units and m is the number of hidden layer units. It is the i-th input feature. It is the j-th hidden feature; The joint probability distribution of the observed data is obtained through this energy function:

[0013] Where Z is the partition function; During training, the goal is to maximize the log-likelihood function of the training samples. For a given visible layer, the activation states of each unit in the hidden layer are conditionally independent, and their activation probabilities follow the sigmoid function.

[0014] in, For the Sigmoid function; By using Gibbs sampling, the restricted Boltzmann machine model iterates repeatedly between the visible and hidden layers, continuously refining its design. w ij Once the model converges, the Restricted Boltzmann Machine (RBM) model learns the probability distribution of the optimal dielectric constant in space. By increasing the layer density and inputting the refined spatial coordinates into the model, the RBM model can generate predicted dielectric constant values ​​at the new coordinates based on the learned features through a reconstruction process.

[0015] In the preferred technical solution, nano-barium titanate is used as filler, photosensitive epoxy resin is used as matrix, and the required slurry formulation is calculated using the Lichtenecker logarithmic mixture prediction model.

[0016] In the preferred technical solution, the required slurry formulation is calculated using the Lichtenecker logarithmic mixture prediction model, including: For a two-phase system composed of photosensitive epoxy resin and barium titanate, its basic expression is:

[0017] Where, ε eff ε is the effective relative permittivity of the composite material. f ε is the relative permittivity of the filler. m The relative permittivity of the matrix is ​​. v % represents the volume fraction of filler in the composite material; The basic expression is restructured by introducing a correction parameter k:

[0018] By performing nonlinear regression analysis on the experimental data, the k value that best fits the current process system was determined. The required nanofiller loading for each layer was calculated.

[0019] In the preferred technical solution, the preparation of the slurry further includes: The prepared slurry was magnetically stirred at 500 rpm for a certain period of time, and temperature control measures were taken to prevent the resin from thermally polymerizing by intermittently stirring at certain intervals. By adding 10wt% of dispersant BYK-9076 by the filler mass, the viscosity of the slurry was controlled below 850 mPa·s, and deep vacuum defoaming was performed before molding.

[0020] In the preferred technical solution, the insulator with dielectric constant obtained by 3D printing the prepared slurry includes: Based on the height characteristics of the simulation model, the printing task is divided into multiple process segments with different ε values. When the printing platform reaches the preset layer interface height, the equipment automatically pauses. After raising the printing platform, the surface of the formed part and the platform are sprayed with isopropanol for cleaning, and then dried with compressed air. The Z-axis zero point is then recalibrated. Different exposure strategies are implemented for layers with different dielectric loads: for pure resin layers, the exposure time is set to 5-6s; for high-load layers with 50wt%, the exposure time is extended to 33s, and a high lift distance is used.

[0021] This invention also discloses a dielectric gradient insulator fabrication system based on electric field topology optimization and 3D printing, used to implement the aforementioned dielectric gradient insulator fabrication method based on electric field topology optimization and 3D printing, comprising: The model building and optimization module establishes the geometric and electrostatic field models of the insulator. The optimization objective function is to minimize the maximum electric field strength. The insulator is preset to n layers along the radial or axial direction. The dielectric constant of the insulator shows a decreasing gradient distribution from the high-voltage electrode side to the ground electrode side along the radial or axial direction. The dielectric constant values ​​of each layer are globally searched through parametric scanning to find the combination of values ​​that makes the electric field distribution at the junction of the high-voltage electrode, the insulator and the insulating gas most moderate, and the optimal dielectric constant of each layer is obtained. The slurry preparation module prepares the slurry based on the obtained optimal dielectric constants of each layer. The 3D printing module uses 3D printing to obtain insulators with dielectric gradation from the prepared slurry.

[0022] Compared with the prior art, the significant advantages of this invention are: 1. From physical modeling to multi-dimensional optimization to determine the optimal number of layers and the dielectric constant of each layer, a particle swarm optimization algorithm and COMSOL are used in real time to perform a global search, and finally the dielectric constant step value that makes the charge distribution inside the insulator most balanced is obtained.

[0023] 2. By adjusting the dielectric constant gradient to change the refraction angle of the electric field lines, the potential gradient at the junction point is smoothed out, making the electric field distribution change from steep to gentle. This fundamentally suppresses the inducing factors of surface flashover and increases the initiation discharge voltage of the insulation system.

[0024] 3. A restricted Boltzmann machine (RBM) is used to smooth the spatial evolution of the dielectric constant of the insulating material and the dielectric constant at the interlayer boundaries, further eliminating the secondary distortion of the local electric field caused by the step change in interlayer dielectric constant due to discrete delamination. This smoothed spatial topology effectively eliminates the electric field concentration effect caused by the abrupt change in interlayer dielectric constant, making the utilization rate of electric field intensity inside and on the surface of the insulator approach the theoretical ideal state. This digital description of material distribution also provides precise formulation guidance for the subsequent preparation of graded functional materials through variable concentration doping.

[0025] 4. This invention significantly enhances the electrical insulation strength of the parts through precise layering of material components and high-precision photopolymerization molding. It not only endows the material with pixel-level (voxel-level) spatial control capabilities, ensuring a high degree of consistency between the dielectric distribution and the simulation model at the sub-millimeter level, but also significantly reduces the risk of local charge injection and electric field distortion induced by manufacturing errors or microscopic "staircase effects" due to its excellent molding accuracy and surface roughness control. Attached Figure Description

[0026] Figure 1 This is a flowchart of the method for preparing a dielectric gradient insulator based on electric field topology optimization and 3D printing in this embodiment; Figure 2(a)-2(d) are the layered mesh diagrams of the electric field topology optimization in this embodiment; Figure 3 This is a layered sample diagram of this embodiment; Figures 4(a)-4(d) show the surface electric field distribution and optimization effect of insulators with different layering density in this embodiment; Figure 5 This represents the maximum electric field strength at the gas-solid interface of insulators with different layering density in this embodiment. Figure 6 This embodiment optimizes the gas-solid interface efficiency of insulators with different layering density levels. Figures 7(a)-7(d) show the test results of surface flashover voltage of insulators with different layering density in this embodiment. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0028] Example: like Figure 1 As shown, a method for fabricating a dielectric gradient insulator based on electric field topology optimization and 3D printing includes the following steps: A geometric and electrostatic field model of the insulator is established. The objective function is to minimize the maximum electric field strength. The insulator is preset to n layers along the radial or axial direction. The dielectric constant of the insulator shows a decreasing gradient distribution from the high-voltage electrode side to the ground electrode side along the radial or axial direction. The dielectric constant values ​​of each layer are globally searched through parameterized scanning to find the combination of values ​​that makes the electric field distribution at the junction of the high-voltage electrode, the insulator and the insulating gas most moderate, and the optimal dielectric constant of each layer is obtained. Prepare the slurry according to the obtained optimal dielectric constant of each layer; The prepared slurry is used to 3D print insulators with dielectric gradation.

[0029] The core of this invention lies in actively controlling the electric field distribution around an insulator by utilizing dielectric functionally graded materials (d-FGM). By constructing a non-uniform spatial dielectric constant ε arrangement inside the insulator, the electric field is controlled by making full use of the material property distribution.

[0030] In the optimization design phase, determining the optimal number of layers and the dielectric constant of each layer is a process that progresses from physical modeling to multidimensional optimization and then to refined reconstruction. First, using the COMSOL Multiphysics finite element simulation platform, based on Maxwell's equations and Gauss's law... Establish a two-dimensional axisymmetric or three-dimensional full model of the insulator. It is a divergence operator, It is the dielectric constant, It is electric field strength, This refers to the volume free charge density. To avoid local optima, a particle swarm optimization algorithm is used in real-time in conjunction with COMSOL when determining the optimization algorithm. After pre-setting the insulator to have n layers radially or axially, the algorithm will operate within a pre-defined dielectric constant range (e.g., ε). r The parameters of each layer are randomly initialized (between 2 and 10). Through continuous iteration, the algorithm automatically calls the finite element kernel to calculate the electric field distribution under each combination of dielectric constants, and uses the maximum electric field intensity E as the criterion. max Minimizing the fitness function is used for a global search, and finally a set of dielectric constant step values ​​that can make the charge distribution inside the insulator most balanced is locked.

[0031] For the region of most severe electric field distortion—the triple junction of the high-voltage electrode, insulator, and insulating gas—the detailed optimization logic lies in altering the refraction angle of the electric field lines by controlling the dielectric constant gradient. According to the electromagnetic field interface conditions, the tangential component of the electric field intensity is continuous, while the normal component is inversely proportional to the dielectric constant. By placing a high-dielectric-constant material near the electrode, electrons can be effectively attracted into the solid insulating medium, thereby reducing the tangential electric field component on the gas side. This design significantly smooths the potential gradient at the triple junction, transforming its electric field distribution from steep to gentle, fundamentally suppressing the inducing factors of surface flashover and increasing the initiation discharge voltage of the insulation system.

[0032] To further eliminate the secondary distortion of the local electric field caused by the step change in dielectric constant between layers due to discrete layering, a transition layer design concept and an advanced data smoothing algorithm were introduced. When the layer density increases from 3 layers to 8 layers or even more, the property differences between layers become minimal, exhibiting characteristics of a continuous gradient material (FGM). At this point, using a restricted Boltzmann machine (RBM) deep learning model, the discrete optimal data obtained from previous optimization can be used as the input training set. Through its powerful nonlinear feature extraction capabilities, the optimal probability distribution of the dielectric constant in space can be learned and reconstructed.

[0033] When using Restricted Boltzmann Machines (RBMs) for the spatial evolution and smoothing of the dielectric constant of insulating materials, the core lies in constructing a generative probabilistic model capable of describing the complex nonlinear mapping between "material properties, spatial location, and electric field distribution." An RBM is a two-layer undirected graphical model containing a visible layer and a hidden layer. In the specific implementation, the discrete layered dielectric constant values ​​and their corresponding spatial coordinates obtained through global search are encoded as input vectors v for the visible layer units. The hidden layer units h are responsible for extracting the higher-order features behind these discrete data, such as the gradient trend of electric field stress or the inherent logic of dielectric polarization.

[0034] The mathematical logic of RBMs is based on the energy function. For a given state (v, h), the energy of the system is defined as:

[0035] in, These are the weights connecting the visible layer units and the hidden layer units. a i and b j These are the bias terms for the two layers, where n is the number of visible layer units and m is the number of hidden layer units. It is the i-th input feature. This is the j-th hidden feature. Using this energy function, the joint probability distribution of the observed data can be derived:

[0036] Where Z is the partition function. During training, our goal is to maximize the log-likelihood function of the training samples. Due to the unconnected nature of RBM layers, given the visible layer, the activation states of each unit in the hidden layer are conditionally independent, and their activation probabilities follow the Sigmoid function:

[0037] To achieve the evolution from discrete layers to continuous gradients, we typically use a contrastive divergence algorithm for weight updates. Through Gibbs sampling, the model iterates repeatedly between visible and hidden layers, continuously refining its approach. w ij Once the model converges, the RBM has essentially learned the probability distribution of the optimal dielectric constant in space. At this point, we increase the layer density from n=3 to n=8 or even higher, and input the refined spatial coordinates into the model. Based on the learned features, the RBM can generate predicted dielectric constant values ​​at these new coordinates through a reconstruction process.

[0038] This RBM-based generative evolution method, compared to traditional linear interpolation, has the advantage that it does not mechanically connect two points, but rather fills in the gaps based on the statistical properties of global electric field optimization. It generates... The spatial distribution curve is mathematically smoother and physically more consistent with the natural continuity of the potential line. Ultimately, this smoothed spatial topology effectively eliminates the electric field concentration effect caused by abrupt changes in interlayer dielectric constant, making the utilization rate of electric field intensity inside and on the surface of the insulator approach the theoretical ideal state. This digitized description of material distribution also provides precise formulation guidance for the subsequent preparation of graded functional materials through variable concentration doping.

[0039] While maintaining monotonicity, the dielectric constant at the interlayer interface is smoothly transitioned. This method elevates the originally discrete topology to a quasi-continuous material spatial distribution topology, not only eliminating stress concentration at the interface but also achieving ultimate optimization of electric field utilization across the entire domain.

[0040] In engineering applications, this optimization method also needs to consider the feasibility of material preparation processes. By increasing the layer density, we can obtain an ideal dielectric constant distribution curve, but in actual production, a specific dielectric constant value is often achieved by adjusting the volume fraction of the doped nanofiller. By converting the topological results obtained from the above algorithm into specific filler concentration gradient instructions, it is possible to guide 3D printing or centrifugal casting processes to produce high-performance insulators with truly gradient functional characteristics.

[0041] In terms of manufacturing processes and engineering applications, the photopolymerization 3D printing technology employed in this invention solves the technical bottlenecks of traditional centrifugal and lamination methods, such as poor controllability, weak interlayer interfaces, and the inability to form a single piece. This technology not only endows materials with pixel-level (voxel-level) spatial control capabilities, ensuring a high degree of consistency between the medium distribution and the simulation model at the sub-millimeter level, but also significantly reduces the risk of local charge injection and electric field distortion induced by manufacturing errors or microscopic "staircase effects" due to its excellent forming accuracy and surface roughness control.

[0042] Meanwhile, this invention introduces a dielectric constant prediction model based on Lichtenecker's mixing law. For a two-phase system composed of photosensitive resin (matrix) and barium titanate (filler), its basic expression is:

[0043] Where, ε eff ε is the effective relative permittivity of the composite material (i.e., the target value for simulation design). f ε is the relative permittivity of the filler. m The relative permittivity of the matrix is ​​.v % represents the volume fraction of filler in the composite material.

[0044] In practical engineering applications, due to the size effect of nanoparticles, interfacial polarization, and micropores during the printing process, a simple logarithmic model may be biased. By experimentally preparing a small number of standard samples with different gradients and measuring their actual dielectric constants, a correction parameter k (shape factor) can be introduced to reconstruct the formula:

[0045] By performing nonlinear regression analysis on the experimental data, the k-value that best fits the current process system was determined. This step ensures that the prediction model not only has theoretical support but also possesses empirical accuracy consistent with DLP photopolymerization. Through experimental calibration of the model parameters, this invention can accurately calculate the required nanofiller loading for each functional layer based on the ideal dielectric distribution obtained from simulation, thereby achieving seamless alignment between the material formulation and design objectives, and strictly controlling the dielectric constant adjustment error within the engineering-permissible range.

[0046] Furthermore, because this scheme can maximize the insulation potential of materials by actively controlling the electric field distribution, the physical size of insulators can be further reduced without sacrificing (or even improving) insulation performance. This breakthrough not only effectively solves the problem of weak insulation in key parts of GIS / GIL, but also provides key technical support and theoretical reference for the miniaturization and compact design of high-voltage and ultra-high-voltage power transmission and transformation equipment.

[0047] The specific process includes the following steps: 1. Digital electric field topology optimization design stage First, a geometric model of the insulator is established in finite element simulation software based on Maxwell's equations, and boundary conditions for the high-voltage electrode and the grounding terminal are set. The core innovation of this process lies in the pre-setting of the insulator as an initial structure of $n$ layers along the radial or axial direction, and the introduction of a restricted Boltzmann machine (RBM) algorithm to perform in-depth evolution of the spatial distribution of the dielectric constant ε. Discrete coordinates and initial electric field data are input through the visible layer, and higher-order features of the charge distribution are extracted using the hidden layer, combined with the minimization criterion of the energy function E(v,h) for iterative training.

[0048] This process aims to find the numerical combination that minimizes the potential gradient at the three junctions. By leveraging the generative properties of RBMs, the originally discrete 3-4 layer dielectric distribution is transformed into a quasi-continuous gradient topology with 8 or more layers. This design utilizes the high dielectric component (ε=26-30) on the high-voltage side to guide the electric field distribution, and combines it with the low dielectric component (ε=4-6) on the ground electrode side to reduce the field strength along the surface, thereby mathematically eliminating the electric field distortion caused by the step change in interlayer dielectric constant.

[0049] 2. Formulation of functional photosensitive composite materials

[0050] Based on the target dielectric constants of each layer obtained through RBM optimization, the photosensitive resin and barium titanate (BaTiO3) nanoparticles were precisely weighed. To ensure the electrical stability and molding accuracy of the slurry, magnetic stirring at 500 rpm for 4 hours was performed, with temperature control measures including 10-minute intervals every hour to prevent resin thermal polymerization. By adding a fixed amount of dispersant BYK-9076 (10 wt% of filler mass), the slurry viscosity was controlled below 850 mPa·s, and deep vacuum defoaming was performed before molding to ensure the absence of air gaps and defects within the material.

[0051] 3. Segmented slurry replacement photocuring integrated manufacturing

[0052] This process employs a segmented slurry replacement strategy to map the ideal topology to physical entities. The specific operations are as follows: (1) Multi-stage molding control: Based on the height characteristics of the simulation model, the printing task is divided into 3-4 process segments with different ε values. When the printing platform reaches the preset layer interface height, the equipment automatically pauses.

[0053] (2) Interface cleaning and zero-point compensation: After raising the printing platform, isopropyl alcohol (IPA) is used to spray and clean the surface of the molded part and the platform, and compressed air is used to dry it to completely eliminate the dielectric contamination of the residual high dielectric paste on the next low dielectric area. Then the Z-axis zero point is recalibrated to compensate for the micron-level displacement caused by the interlayer shrinkage of the heterogeneous material.

[0054] (3) Dynamic optical parameter control: Different exposure strategies are implemented for layers with different dielectric loads. For pure resin layers, the exposure time is set to 5-6s; for high-load layers with 50wt%, due to the strong scattering effect of fillers on ultraviolet light, the exposure time needs to be extended to 33s, and a high lifting distance of 10mm is used to ensure sufficient backflow and smoothing of high-viscosity slurry at the interface.

[0055] 4. Post-processing and performance enhancement

[0056] After printing, the green body needs to undergo secondary curing in a UV curing chamber for more than 2 hours. This process utilizes photochemical crosslinking to promote chemical bonding at the interface of heterogeneous materials, enhancing interlayer adhesion. Finally, a mechanical polishing process is used to optimize the surface roughness to Ra < 1.6 µm, eliminating the inherent staircase effect of 3D printing.

[0057] Another embodiment provides a dielectric gradient insulator fabrication system based on electric field topology optimization and 3D printing, used to implement the aforementioned dielectric gradient insulator fabrication method based on electric field topology optimization and 3D printing, comprising: The model building and optimization module establishes the geometric and electrostatic field models of the insulator. The optimization objective function is to minimize the maximum electric field strength. The insulator is preset to n layers along the radial or axial direction. The dielectric constant of the insulator shows a decreasing gradient distribution from the high-voltage electrode side to the ground electrode side along the radial or axial direction. The dielectric constant values ​​of each layer are globally searched through parametric scanning to find the combination of values ​​that makes the electric field distribution at the junction of the high-voltage electrode, the insulator and the insulating gas most moderate, and the optimal dielectric constant of each layer is obtained. The slurry preparation module prepares the slurry based on the obtained optimal dielectric constants of each layer. The 3D printing module uses 3D printing to obtain insulators with dielectric gradation from the prepared slurry.

[0058] The following example illustrates the method for fabricating dielectric-elliptic insulators based on electric field topology optimization and 3D printing: Example 1: Gradient ladder insulator based on three-level differential optimization This embodiment aims to suppress field strength distortion at the "three-junction point" through layered dielectric distribution, and is applicable to key parts of the basin insulator in compact GIS equipment.

[0059] (1) Model reconstruction based on electric field topology optimization

[0060] An electrostatic field model of the ladder insulator was established using COMSOL Multiphysics software to reduce the maximum electric field E at the junction of the high-voltage electrode, insulator, and insulating gas. max To achieve this, the model is divided into four functional regions along the axial direction. The optimal dielectric constant sequence for each layer is determined by parametric scanning: from the high-voltage side to the ground side, the values ​​are ε1=26, ε2=10, and ε3=4.

[0061] (2) Precise slurry preparation based on Lichtenecker's mixing law

[0062] To achieve the aforementioned dielectric constant target, this embodiment uses nano-barium titanate as a filler and photosensitive epoxy resin as the matrix. The required slurry formulation is calculated using the Lichtenecker logarithmic mixture prediction model. High-pressure layer (ε1=26): BaTiO3 mass fraction is 51wt%; Transition layer (ε2=10): BaTiO3 mass fraction is 30wt%; Low-pressure layer (ε3=4): Made of pure photosensitive resin.

[0063] The slurry preparation requires magnetic stirring at 500 rpm for 4 hours and vacuum defoaming to ensure that the filler is uniformly distributed at the submicron scale.

[0064] (3) Photopolymerization molding process with dynamic switching of multiple materials

[0065] The DLP photopolymerization 3D printing equipment was used, and its forming accuracy was set to 0.01 mm.

[0066] Segmented printing: First, pour in 51wt% slurry to print the high-pressure layer. When the preset height is reached, the equipment will automatically pause. Interface cleaning and decontamination: Elevate the platform, use industrial alcohol spray to clean the solidified parts of the surface, and blow dry with compressed air to prevent uncontrolled mixing of slurries of different concentrations at the interface; Switch to the next concentration of resin tank, recalibrate the Z-axis reference point, and complete the stacking of subsequent layers.

[0067] (4) Verification of technical effects

[0068] Tests showed that the gradient insulator, under an SF6 gas environment of 0.4 MPa, had an AC flashover voltage that was 19.48% higher than that of the traditional homogeneous insulator, effectively reducing the electric field stress at the electrode edge.

[0069] Example 2: Continuous gradient evolution scheme with interlayer transition layers

[0070] This embodiment aims to eliminate local charge accumulation caused by material step interfaces by increasing micro-layering.

[0071] (1) Refined hierarchical design

[0072] Based on the three-level differential in Example 1, this scheme introduces a transitional layering, refining the physical structure into 8 layers (e.g., 26-20-14-10-8-6-4-4).

[0073] (2) Working principle

[0074] By increasing the layer density, the difference in relative permittivity between the layers is reduced. According to Maxwell's stress tensor analysis, the smaller dielectric jump energy significantly reduces the space charge generated by interface polarization. Experiments show that its maximum electric field strength can be further reduced by about 7.5% compared to the ordinary three-layer gradient structure.

[0075] (3) Printing strategy

[0076] At each stage of slurry switching, a specific exposure control algorithm is used to compensate for light scattering. Since the ultraviolet light transmission depth of the high-load layer (51wt%) is reduced, its exposure time is extended to 33s, while that of the low-load layer is kept at 5-8s to ensure consistent overall crosslinking.

[0077] Electric field topology optimization layered mesh diagram, such as Figure 2As shown, (a) is an unlayered image, (b) is a two-layered image, (c) is a three-layered image, and (d) is a four-layered image. Layered samples are shown below. Figure 3 As shown.

[0078] Figure 4 shows the surface electric field distribution and optimization effect of insulators with different layering density, where 4(a) is unlayered, 4(b) is two-layered, 4(c) is three-layered, and 4(d) is four-layered.

[0079] Maximum electric field strength at the gas-solid interface of insulators with different layer numbers and dielectric strengths, such as Figure 5 As shown. The optimization rate of the gas-solid interface of insulators with different layering density levels, such as... Figure 6 As shown.

[0080] Simulation data show that the layered gradient structure can effectively homogenize the surface electric field distribution. Specifically, the maximum electric field intensity at the gas-solid interface of the three-layer structure decreases from 2.75 kV / mm to 0.89 kV / mm, a reduction of 68.6%, significantly better than the unlayered and other layered schemes. This deep electric field homogenization effect fundamentally suppresses the causes of partial discharge and surface flashover.

[0081] In terms of improving insulation performance, this invention significantly enhances the electrical insulation strength of the parts through precise layering of material components and high-precision photocuring molding.

[0082] The test results of surface flashover voltage of insulators with different layering dielectric gradations are shown in Figure 7. 7(a) is without layering, 7(b) is with two layers, 7(c) is with three layers, and 7(d) is with four layers.

[0083] Experimental results show that the optimized three-layer gradient structure improves the surface flashover voltage by 19.96%, 22.05%, and 19.48% in air, CO2, and SF6 environments, respectively, compared to homogeneous insulators, confirming the significant enhancement effect of the dielectric gradient design on insulation performance.

[0084] The gradient insulators fabricated using the above process achieve a scientific gradient distribution of dielectric constant from the high-voltage end to the ground electrode in their physical structure. Experimental data show that the AC flashover voltage of the devices fabricated using this process is increased by about 20% compared to similar homogeneous components, and the maximum electric field strength at the internal interface is reduced by about 70%, achieving ultimate optimization of electric field utilization.

[0085] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for fabricating a dielectric gradient insulator based on electric field topology optimization and 3D printing, characterized in that, Includes the following steps: A geometric and electrostatic field model of the insulator is established. The objective function is to minimize the maximum electric field strength. The insulator is preset to n layers along the radial or axial direction. The dielectric constant of the insulator shows a decreasing gradient distribution from the high-voltage electrode side to the ground electrode side along the radial or axial direction. The dielectric constant values ​​of each layer are globally searched through parameterized scanning to find the combination of values ​​that makes the electric field distribution at the junction of the high-voltage electrode, the insulator and the insulating gas most moderate, and the optimal dielectric constant of each layer is obtained. Prepare the slurry according to the obtained optimal dielectric constant of each layer; The prepared slurry is used to 3D print insulators with dielectric gradation.

2. The method for fabricating a dielectric gradient insulator based on electric field topology optimization and 3D printing according to claim 1, characterized in that, The method to smooth the electric field distribution at the junction of the high-voltage electrode, insulator, and insulating gas is as follows: According to the electromagnetic field interface conditions, the tangential component of the electric field intensity is continuous while the normal component is inversely proportional to the dielectric constant. By arranging high dielectric constant materials in the region near the electrode, electrons are attracted into the solid insulating medium, thereby reducing the tangential electric field component on the gas side and smoothing the electric field distribution at the junction of the high voltage electrode, the insulator, and the insulating gas.

3. The method for fabricating a dielectric gradient insulator based on electric field topology optimization and 3D printing according to claim 1, characterized in that, After performing a global search for the dielectric constant values ​​of each layer using parametric scanning, the following steps are also included: By increasing the layer density and using a restricted Boltzmann machine to smooth the spatial dielectric constant ε difference between layers, a material spatial distribution topology with optimized electric field utilization is obtained.

4. The method for preparing a dielectric gradient insulator based on electric field topology optimization and 3D printing according to claim 3, characterized in that, Methods for smoothing the spatial dielectric constant ε differences between layers using a restricted Boltzmann machine include: The discrete layered dielectric constant values ​​and their corresponding spatial coordinates obtained through global search are encoded into the input vector v of the visible layer unit, and the hidden layer unit h is used to extract higher-order features of the discrete data. For a given state (v, h), the energy of the system is defined as: in, These are the weights connecting the visible layer units and the hidden layer units. a i and b j These are the bias terms for the two layers, where n is the number of visible layer units and m is the number of hidden layer units. It is the i-th input feature. It is the j-th hidden feature; The joint probability distribution of the observed data is obtained through this energy function: Where Z is the partition function; During training, the goal is to maximize the log-likelihood function of the training samples. For a given visible layer, the activation states of each unit in the hidden layer are conditionally independent, and their activation probabilities follow the sigmoid function. in, For the Sigmoid function; By using Gibbs sampling, the restricted Boltzmann machine model iterates repeatedly between the visible and hidden layers, continuously refining its design. w ij Once the model converges, the Restricted Boltzmann Machine (RBM) model learns the probability distribution of the optimal dielectric constant in space. By increasing the layer density and inputting the refined spatial coordinates into the model, the RBM model can generate predicted dielectric constant values ​​at the new coordinates based on the learned features through a reconstruction process.

5. The method for fabricating a dielectric gradient insulator based on electric field topology optimization and 3D printing according to claim 1, characterized in that, The required slurry formulation was calculated using nano-barium titanate as filler and photosensitive epoxy resin as matrix, and the Lichtenecker logarithmic mixture prediction model was used.

6. The method for preparing a dielectric gradient insulator based on electric field topology optimization and 3D printing according to claim 5, characterized in that, The required slurry formulation was calculated using the Lichtenecker logarithmic mixture prediction model, including: For a two-phase system composed of photosensitive epoxy resin and barium titanate, its basic expression is: Where, ε eff ε is the effective relative permittivity of the composite material. f ε is the relative permittivity of the filler. m The relative permittivity of the matrix is ​​. v % represents the volume fraction of filler in the composite material; The basic expression is restructured by introducing a correction parameter k: By performing nonlinear regression analysis on the experimental data, the k value that best fits the current process system was determined. The required nanofiller loading for each layer was calculated.

7. The method for preparing a dielectric gradient insulator based on electric field topology optimization and 3D printing according to claim 1, characterized in that, The preparation of the slurry also includes: The prepared slurry was magnetically stirred at 500 rpm for a certain period of time, and temperature control measures were taken to prevent the resin from thermally polymerizing by intermittently stirring at certain intervals. By adding 10wt% of dispersant BYK-9076 by the filler mass, the viscosity of the slurry was controlled below 850 mPa·s, and deep vacuum defoaming was performed before molding.

8. The method for preparing a dielectric gradient insulator based on electric field topology optimization and 3D printing according to claim 1, characterized in that, The prepared slurry is used to 3D print insulators with dielectric constants, including: Based on the height characteristics of the simulation model, the printing task is divided into multiple process segments with different ε values. When the printing platform reaches the preset layer interface height, the equipment automatically pauses. After raising the printing platform, the surface of the formed part and the platform are sprayed with isopropanol for cleaning, and then dried with compressed air. The Z-axis zero point is then recalibrated. Different exposure strategies are implemented for layers with different dielectric loads: for pure resin layers, the exposure time is set to 5-6s; for high-load layers with 50wt%, the exposure time is extended to 33s, and a high lift distance is used.

9. A system for fabricating dielectric gradient insulators based on electric field topology optimization and 3D printing, characterized in that, A method for fabricating a dielectric gradient insulator based on electric field topology optimization and 3D printing as described in any one of claims 1-8 includes: The model building and optimization module establishes the geometric and electrostatic field models of the insulator. The optimization objective function is to minimize the maximum electric field strength. The insulator is preset to n layers along the radial or axial direction. The dielectric constant of the insulator shows a decreasing gradient distribution from the high-voltage electrode side to the ground electrode side along the radial or axial direction. The dielectric constant values ​​of each layer are globally searched through parametric scanning to find the combination of values ​​that makes the electric field distribution at the junction of the high-voltage electrode, the insulator and the insulating gas most moderate, and the optimal dielectric constant of each layer is obtained. The slurry preparation module prepares the slurry based on the obtained optimal dielectric constants of each layer. The 3D printing module uses 3D printing to obtain insulators with dielectric gradation from the prepared slurry.

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