A GIS conductive arm silver plating layer thickness control method based on dynamic electric field simulation

Abstract

The present application belongs to the technical field of electroplating control, and particularly relates to a GIS conductive arm silver plating layer thickness control method based on dynamic electric field simulation, to solve the technical problem that the existing model lacks a mechanism capable of adjusting an anode current according to simulation results and generating a specific executable time-division and section control strategy. The control method comprises: S1, establishing an electrochemical simulation environment; S2, calculating a local conductivity attenuation matrix to correct an electric field model; updating a three-dimensional geometric model of the GIS conductive arm according to a corrected surface growth rate distribution, and adjusting a next time step according to a maximum plating layer increment of a current time step; S3, forming an anode current time-division and section control sequence for guiding an actual electroplating process. The present application improves the uniformity and thickness controllability of the GIS conductive arm silver plating layer, reduces the waste of precious metal materials, and provides a technical path for realizing the electroplating of workpieces.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electroplating control, and particularly relates to a GIS conductive arm silver plating layer thickness control method based on dynamic electric field simulation. BACKGROUND

[0002] The conductive arm inside a gas insulated metal enclosed switchgear (GIS) is an important component for carrying and conducting large current. In order to reduce the contact resistance of the conductive arm connection, improve the conductive efficiency, and enhance the oxidation resistance and corrosion resistance, the surface of the conductive arm needs to be plated with silver. If the plating layer is too thin, the protective performance and conductive performance will decrease, and the service life will be shortened. If the plating layer is too thick, not only the precious metal material is wasted, and the production cost is increased, but also the assembly of the component may be affected due to local overthickness.

[0003] However, in the electroplating process, the current density is unevenly distributed on the surface of the workpiece, resulting in that the convex part has a too thick plating layer, and the concave and inner surface regions have a too thin plating layer, which is difficult to meet the requirement of thickness uniformity.

[0004] Although the computer simulation technology can predict the current density distribution by establishing an electric field model, thereby guiding the setting of process parameters, with the growth of the plating layer, the geometric shape of the conductive arm is constantly changing, and the silver ion concentration in the electrolyte produces local gradient due to consumption and diffusion, which will in turn affect the electric field distribution. In addition, the existing electric field model does not consider the influence of the randomness of the micro-level lattice growth on the macro-morphology, and lacks a mechanism capable of adjusting the anode current according to the simulation results and generating a specific executable time-division and segmented control strategy, resulting in a deviation between the simulation prediction and the actual electroplating result, and failing to solve the control problem of the plating layer thickness. SUMMARY

[0005] The application provides a GIS conductive arm silver plating layer thickness control method based on dynamic electric field simulation, to solve the technical problem that the existing model lacks a mechanism capable of adjusting the anode current according to the simulation results and generating a specific executable time-division and segmented control strategy.

[0006] A GIS conductive arm silver plating layer thickness control method based on dynamic electric field simulation, comprising the following steps:

[0007] S1, an electrochemical simulation environment containing an initial three-dimensional geometric model of a GIS conductive arm, a segmented anode and an electrolyte is established;

[0008] S2, in the multi-time-step iterative simulation, the following operations are performed in each time step: Based on the local curvature and silver ion concentration gradient of the GIS conductive arm surface in the previous time step, calculate the local conductivity decay matrix to correct the electric field model; based on the deviation between the target thickness distribution and the current simulated thickness distribution, calculate the piecewise anode current adjustment vector, and solve the corresponding surface current density distribution under the corrected electric field model; update the Markov chain model according to the surface current density distribution, and use this model to generate a spatially correlated random perturbation field; superimpose the spatially correlated random perturbation field onto the basic growth rate determined by the surface current density distribution to obtain a corrected surface growth rate distribution containing the randomness of micro-lattice growth; update the three-dimensional geometric model of the GIS conductive arm according to the corrected surface growth rate distribution, and adjust the next time step size according to the maximum coating increment of the current time step;

[0009] S3, repeat the multi-time-step iterative simulation until the total electroplating time is reached, and integrate the segmented anode current adjustment vectors generated by all time steps to form a time-segmented anode current control sequence to guide the actual electroplating process.

[0010] Furthermore, an electrochemical simulation environment was established, including an initial three-dimensional geometric model of the GIS conductive arm, segmented anodes, and electrolyte, comprising:

[0011] A 3D laser scanner was used to scan the GIS conductive arm to generate point cloud data, which was then processed by reverse engineering software to construct an initial 3D geometric model.

[0012] N columnar soluble silver anodes are arranged in a ring array around the GIS conductive arm as segmented anodes;

[0013] The electrolyte is set to be an aqueous solution of silver nitrate.

[0014] Furthermore, the surface mesh element size of the initial three-dimensional geometric model is 0.5 mm.

[0015] Furthermore, there are eight columnar soluble silver anodes, each with a diameter of 20 mm.

[0016] Furthermore, the concentration of silver ions in the silver nitrate aqueous solution is 50 g / L, and the concentration of the additive sodium dodecyl sulfate is 100 mg / L.

[0017] Furthermore, based on the local curvature and silver ion concentration gradient of the GIS conductive arm surface in the previous time step, the local conductivity decay matrix is ​​calculated to correct the electric field model, including:

[0018] For each surface mesh node of the 3D geometric model, the Gaussian curvature is calculated using information from adjacent nodes;

[0019] The silver ion concentration at each node was obtained by solving the problem using the finite element method, and the normal gradient was calculated.

[0020] The local conductivity of each node satisfies the following relationship: ;

[0021] in, Local conductivity; The bulk conductivity of the electrolyte; The curvature is Gaussian, and its unit is . ; The normal gradient is expressed in units of . ; The curvature influence coefficient; The concentration gradient influence coefficient is used; the local conductivity of all nodes is combined to form the local conductivity attenuation matrix.

[0022] Furthermore, based on the deviation between the target thickness distribution and the current simulated thickness distribution, the segmented anode current adjustment vector is calculated, including: dividing the GIS conductive arm surface into N regions corresponding to N segmented anodes, and calculating the average deviation between the simulated thickness and the target thickness of all grid nodes in each region;

[0023] The proportional-integral control algorithm is used to calculate the current adjustment of each anode, and the current adjustment satisfies the following relationship: ;

[0024] in, Let be the current adjustment amount of the j-th segment anode at time t, j=1,…,N; This is the proportionality coefficient. The integral coefficient; The average deviation of the j-th region at time t;

[0025] Add the current adjustment amount to the anode current of the previous time step to obtain the total anode current of each segment used for electric field solution in the current time step.

[0026] Furthermore, the Markov chain model is updated based on the surface current density distribution, and the model is used to generate a spatially correlated random perturbation field, including:

[0027] Each grid node on the surface of the GIS conductive arm is defined as a state unit, and the state of the state unit is either lattice growth or lattice vacancy.

[0028] At each time step, the probability of each grid node being classified as a lattice growth state is determined to be related to the current density at the grid node, and satisfies the following relationship: ;

[0029] in, The probability of determining it as a lattice growth state; Current density, in units of ; This represents the current time step, in seconds (s). These are probability conversion coefficients;

[0030] All grid nodes on the surface of the GIS conductive arm are randomly determined according to this probability, and a two-dimensional random field consisting of +1 corresponding to lattice growth and -1 corresponding to lattice vacancies is generated as a spatially correlated random perturbation field.

[0031] Furthermore, the spatially correlated random perturbation field is superimposed on the basic growth rate determined by the surface current density distribution to obtain a modified surface growth rate distribution that incorporates the randomness of microcrystalline lattice growth, including:

[0032] According to Faraday's law of electrolysis, the basic growth rate is calculated from the surface current density.

[0033] The modified surface growth rate satisfies the following relationship: ,in, To correct the surface growth rate; Basic growth rate; Let p be a spatially correlated random perturbation field, and p be any grid node on the surface of the GIS conductive arm. A is the dimensionless amplitude coefficient.

[0034] Furthermore, the next time step size is adjusted based on the maximum coating increment at the current time step, including:

[0035] After the simulation at the current time step is completed, traverse all grid nodes on the surface of the GIS conductive arm to find the actual maximum coating increment.

[0036] Calculate the next time step, which satisfies the following relationship: ;in, Set the next time step and set the value range to between 0.5 seconds and 10 seconds; This is the current time step; The maximum permissible increment of the coating at any location within each time step; This represents the actual maximum coating increment.

[0037] The beneficial effects are as follows: This invention improves the accuracy of electroplating process prediction by constructing a high-fidelity simulation model that can represent the evolution of workpiece geometry, changes in electrolyte ion concentration, and the randomness of microcrystalline lattice growth during the electroplating process. The simulation iteration utilizes feedback control, which calculates and plans the adjustment amount of the anode current for each segment based on the deviation between the target thickness and the current simulated thickness. This forms a detailed time-sharing and segmented anode current control scheme that can be directly applied to actual production, improving the uniformity and thickness controllability of the silver plating layer on the GIS conductive arm, reducing the waste of precious metal materials, and providing a technical path for realizing workpiece electroplating. Attached Figure Description

[0038] Figure 1 The flowchart shows a method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation.

[0039] Figure 2 A schematic diagram of the spatial layout of the GIS conductive arm and segmented anodes;

[0040] Figure 3 The current adjustment distribution of each segment anode at a certain time step is shown in the diagram.

[0041] Figure 4 This is a comparison diagram of the macroscopic trend and microscopic perturbation of the surface normal growth rate of a GIS conductive arm. Detailed Implementation

[0042] An embodiment of the method for controlling the silver plating thickness of a GIS conductive arm based on dynamic electric field simulation provided by this invention:

[0043] like Figure 1 As shown, a method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation includes the following steps:

[0044] S1. Establish an electrochemical simulation environment that includes the initial three-dimensional geometric model of the GIS conductive arm, segmented anodes, and electrolyte.

[0045] Specifically, a digital model of the GIS conductive arm was constructed using 3D modeling software and imported into a multiphysics simulation platform. Within the simulation platform, multiple geometrically independent anode models were created based on the actual layout of the electroplating tank, and these were defined as segmented anodes. For example... Figure 2 As shown, the space between the GIS conductive arm and the segmented anode is defined as the electrolyte domain, and initial physicochemical parameters are set for the electrolyte domain, including initial silver sulfate concentration, additive concentration, conductivity, and diffusion coefficient. The entire simulation domain is meshed, especially the surface region of the GIS conductive arm, which uses a boundary layer mesh.

[0046] In an optional embodiment, an electrochemical simulation environment is established, including an initial three-dimensional geometric model of the GIS conductive arm, segmented anodes, and electrolyte, comprising:

[0047] A 3D laser scanner was used to scan the GIS conductive arm to generate point cloud data, which was then processed by reverse engineering software to construct an initial 3D geometric model.

[0048] N columnar soluble silver anodes are arranged in a ring array around the GIS conductive arm as segmented anodes;

[0049] The electrolyte is set to be an aqueous solution of silver nitrate.

[0050] For example, the surface mesh unit size of the initial three-dimensional geometric model is 0.5 mm; the number of columnar soluble silver anodes is 8, and their diameter is 20 mm; the silver ion concentration of the silver nitrate aqueous solution is 50 g / L, and the concentration of the additive sodium dodecyl sulfate is 100 mg / L.

[0051] Specifically, operators use a 3D laser scanner, such as the FaroFocus S150, to perform a 3D scan of the actual GIS conductive arm workpiece. The scanning process generates point cloud data containing millions of coordinate points, detecting the surface contour of the GIS conductive arm. The point cloud data is imported into the reverse engineering software Geomagic DesignX, which generates a continuous polygonal mesh model through a series of processes such as point cloud registration, denoising, and encapsulation. The target cell size is set to 0.5mm in the meshing settings, and a high-fidelity 3D geometric model in STL or STEP format is exported.

[0052] Import the 3D model of the GIS conductive arm generated in the previous step and set this model as the cathode. Create a large cylindrical geometric domain around the model to represent the electrolyte in the electroplating tank. Within this electrolyte domain, create eight independent cylindrical geometries in a ring array around the GIS conductive arm. Each cylinder has a diameter of 20 mm and the same height as the GIS conductive arm. Define these cylindrical geometries as soluble silver anodes. Set the physicochemical properties for the electrolyte domain, selecting silver nitrate aqueous solution as the electrolyte, and input key parameters, including a silver ion concentration of 50 g / L and sodium dodecyl sulfate (100 mg / L) as an additive to improve the smoothness of the plating layer. After these steps, the complete simulation environment, including the cathode, segmented anode, and electrolyte, is built.

[0053] S2, in the multi-time-step iterative simulation, the following operations are performed in each time step: Based on the local curvature and silver ion concentration gradient of the GIS conductive arm surface in the previous time step, calculate the local conductivity decay matrix to correct the electric field model; Based on the deviation between the target thickness distribution and the current simulated thickness distribution, calculate the piecewise anode current adjustment vector, and solve the corresponding surface current density distribution under the corrected electric field model; Update the Markov chain model according to the surface current density distribution, and use the model to generate a spatially correlated random perturbation field; Superimpose the spatially correlated random perturbation field onto the basic growth rate determined by the surface current density distribution to obtain a corrected surface growth rate distribution containing the randomness of micro-lattice growth; Update the three-dimensional geometric model of the GIS conductive arm according to the corrected surface growth rate distribution, and adjust the next time step size according to the maximum coating increment of the current time step.

[0054] Specifically, at the end of the previous time step, the local curvature values ​​of each grid node on the surface of the GIS conductive arm are calculated using the geometric analysis module. Simultaneously, the silver ion concentration within the electrolyte thin layer adjacent to the GIS conductive arm surface is extracted from the mass transfer simulation results, and its normal gradient is calculated. Using the local curvature values ​​and the normal gradient of the anion concentration as inputs, a conductivity attenuation coefficient between 0 and 1 is calculated for each grid node using a preset empirical function or lookup table. The conductivity attenuation coefficients of all surface grid nodes together form a diagonal matrix, i.e., the local conductivity attenuation matrix. When solving the Laplace equation for the potential field at the current time step, the basic conductivity of the electrolyte is multiplied by the local conductivity attenuation matrix to obtain a non-uniform conductivity field, thereby simulating the combined effects of tip effects and concentration polarization on the electric field distribution.

[0055] Set the preset uniform target thickness value, for example, 15. The thickness deviation distribution map is obtained by comparing the accumulated simulated thickness on each grid node of the GIS conductive arm surface. Using a proportional-integral-derivative (PID) control algorithm, the average thickness deviation of the GIS conductive arm region mainly affected by each segmented anode is used as input to calculate the current adjustment amount required for that segmented anode at the current time step. The current adjustments of all segmented anodes together constitute a multi-dimensional current adjustment vector, such as... Figure 3 As shown, the multidimensional current adjustment vector is superimposed on the anode current setpoint of the previous time step as a new anode current boundary condition. Based on the modified electric field model, the electrochemical module is solved to obtain a new current density distribution on the surface of the GIS conductive arm.

[0056] A Markov chain model representing the evolution of the coating's microstructure is established, with three states defined: smooth growth, dendritic growth, and passivation. The key parameter of this model, the state transition probability matrix, is set as a function of the surface current density. Based on the obtained current density distribution, the corresponding state transition probability matrix is ​​updated for each grid node on the GIS conductive arm surface. A Markov chain Monte Carlo simulation is performed on the entire GIS conductive arm surface, generating a random state for each grid node. These discrete state values ​​are converted into continuous perturbation coefficient values ​​through a mapping function and smoothed using a Gaussian spatial filter. This simulates the mutual influence between adjacent grain growth, resulting in a continuous and spatially correlated spatially associated random perturbation field.

[0057] According to Faraday's law of electrolysis, the obtained surface current density distribution map is used to... The basic coating normal growth rate distribution is converted into a map, where j is the local current density, M is the molar mass of silver, z is the valence, F is the Faraday constant, and ρ is the density of silver. The generated spatially correlated random perturbation field is used as a multiplicative perturbation factor and multiplied point-by-point with the above coating normal growth rate distribution to obtain the corrected surface growth rate distribution. This corrected surface growth rate distribution includes both the growth trend determined by the macroscopic electric field and the uncertainties of crystal nucleation and growth at the microscopic scale.

[0058] Using mesh deformation technology, each mesh node on the surface of the GIS conductive arm is moved a distance along the normal direction. This distance is equal to the modified surface growth rate of that mesh node multiplied by the current time step. After all mesh nodes have been moved, the resulting new surface is the updated 3D geometric model of the GIS conductive arm. The maximum increment of the coating thickness within the current time step is found by traversing all surface mesh nodes. This maximum increment is then compared with a preset maximum allowable single-step increment threshold, for example, 0.1. The results are compared. If the actual maximum increment is greater than the threshold, the next time step is shortened proportionally; conversely, if it is much smaller than the threshold, the next time step is increased, thereby improving simulation efficiency while ensuring computational stability.

[0059] In an optional embodiment, based on the local curvature and silver ion concentration gradient of the GIS conductive arm surface at the previous time step, a local conductivity decay matrix is ​​calculated to correct the electric field model, including:

[0060] For each surface mesh node of the 3D geometric model, the Gaussian curvature is calculated using information from adjacent nodes;

[0061] The silver ion concentration at each node was obtained by solving the problem using the finite element method, and the normal gradient was calculated.

[0062] The local conductivity of each node satisfies the following relationship: ;

[0063] in, Local conductivity; The bulk conductivity of the electrolyte; The curvature is Gaussian, and its unit is . ; The normal gradient is expressed in units of . ; The curvature influence coefficient; The concentration gradient influence coefficient;

[0064] The local conductivity of all nodes is combined to form the local conductivity attenuation matrix.

[0065] Specifically, let the curvature influence coefficient be... The concentration gradient influence coefficient is At the start of each simulation time step, geometric and physical field analyses are performed on each grid node on the surface of the GIS conductive arm. For the geometric analysis, taking a node P as an example, all directly connected neighboring nodes P1, P2...P... of node P are obtained. n The coordinates of node P are determined. Based on the spatial location of node P, a local quadratic surface is fitted to approximate the real surface around that point. The two principal curvatures of this surface are calculated using differential geometry principles, and multiplied together to obtain the Gaussian curvature. For the physical field analysis, the finite element solver of the simulation software has obtained the silver ion concentration distribution throughout the entire electrolyte domain based on the calculation results of the previous time step. The concentration value of each grid node on the surface of the GIS conductive arm is extracted, and the normal gradient of the concentration field at that point is calculated. The magnitude of this gradient reflects the ease or difficulty of ion replenishment.

[0066] Assume the bulk conductivity of the electrolyte is 6.5. For a mesh node located in the tip region, the calculated Gaussian curvature is as high as 0.8. Meanwhile, due to rapid ion consumption and a large concentration gradient, for example, the normal concentration is 0.2. According to the formula, substitute the values ​​to perform the calculation: This value indicates that the electrolyte conductivity decreased by 6% near this point. The local conductivity values ​​calculated for all surface mesh nodes are aggregated to form a decay matrix or vector corresponding to each surface mesh node. This matrix is ​​then input into the electric field model as a spatially variable material property for solving the electric field distribution in the next time step, thus making the current distribution calculation closer to the real physical process.

[0067] In an optional embodiment, the segmented anode current adjustment vector is calculated based on the deviation between the target thickness distribution and the current simulated thickness distribution, including:

[0068] The surface of the GIS conductive arm is divided into N regions corresponding to N segmented anodes, and the average deviation between the simulated thickness and the target thickness of all grid nodes in each region is calculated.

[0069] The proportional-integral control algorithm is used to calculate the current adjustment of each anode, and the current adjustment satisfies the following relationship: ;

[0070] in, Let be the current adjustment amount of the j-th segment anode at time t, j=1,…,N; This is the proportionality coefficient. The integral coefficient; The average deviation of the j-th region at time t;

[0071] Add the current adjustment amount to the anode current of the previous time step to obtain the total anode current of each segment used for electric field solution in the current time step.

[0072] Specifically, the target coating thickness is set to 20. The uniformity requirement is ±2. The proportionality coefficient is The integral coefficient is The control objective is clearly defined as achieving 20 on the surface of the GIS conductive arm. A uniform coating is achieved. Continuing with the previous example, there are eight segmented anodes and eight corresponding regions. Therefore, in the simulation model, the entire surface of the GIS conductive arm is divided into eight control regions based on its relative position to the eight segmented anodes. For example, the surface region of the GIS conductive arm directly opposite anode number 1 is defined as region 1. After each simulation time step, the average coating thickness of all grid nodes within each region is calculated. Assuming that at the current time t, the simulated average thickness of region 3 is 18.5... The thickness deviation is then calculated as the target value minus the actual value, i.e. A positive thickness deviation indicates that the coating in that area is too thin.

[0073] The calculated thickness deviation value is input into the proportional-integral controller of the corresponding anode. For region 3, the region current adjustment consists of two parts. The proportional part is... A, it can respond quickly to the current deviation. Integral part The accumulated historical deviation is then used to eliminate steady-state error. Assume that the cumulative deviation integral value for region 3 so far is 10. Therefore, the contribution of the integral part is 0.1A. Thus, the total current adjustment is... A. Add this current adjustment to the current value of anode 3 in the previous time step. If the current value in the previous time step was 5.0A, then the new anode current is... A. Perform the above process simultaneously on all 8 anodes to generate a new current vector, which will serve as the boundary condition for the electric field calculation in the next time step. This optimizes the uniformity of the coating thickness by enhancing the current in the under-plated region and weakening the current in the over-plated region.

[0074] In an optional embodiment, the Markov chain model is updated based on the surface current density distribution, and the model is used to generate a spatially correlated random perturbation field, including:

[0075] Each grid node on the surface of the GIS conductive arm is defined as a state unit, and the state of the state unit is either lattice growth or lattice vacancy.

[0076] At each time step, the probability of each grid node being classified as a lattice growth state is determined to be related to the current density at the grid node, and satisfies the following relationship: ;

[0077] in, The probability of determining it as a lattice growth state; Current density, in units of ; This represents the current time step, in seconds (s). These are probability conversion coefficients;

[0078] All grid nodes on the surface of the GIS conductive arm are randomly determined according to this probability, and a two-dimensional random field consisting of +1 corresponding to lattice growth and -1 corresponding to lattice vacancies is generated as a spatially correlated random perturbation field.

[0079] Specifically, let the probability transformation coefficient be... Each grid node on the surface of the GIS conductive arm is abstracted as a unit that can exist in one of two states: lattice growth or lattice vacancy. The transition between these two states is modeled as a Markov process, with the core being the determination of the transition probability. This probability is related to a macroscopic physical quantity, namely the local current density at that grid node. The current density is calculated by electrochemical simulation at each time step. The probability of lattice growth occurring at a grid node within the current time step is given by a formula, reflecting the physical intuition that higher current density leads to more active ion deposition and a higher growth probability.

[0080] At each time step, a random perturbation field is generated for all grid nodes on the surface of the GIS conductive arm: with a time step length of... Taking point A, which has a higher current density on the surface, as an example, , Now consider point B, where the current density is lower. The growth probability is A Monte Carlo simulation is performed on each grid node. A random number between 0 and 1 is generated for point A. Due to the extremely high probability of growth, this random number is almost certainly less than 0.99995, so point A is classified as +1, representing lattice growth. The random number generated for point B has approximately a 67% chance of being greater than 0.3297. If so, point B is classified as -1, representing a lattice vacancy. Combining the +1 and -1 values ​​obtained from this random simulation of all grid nodes on the surface forms a two-dimensional random perturbation field covering the entire surface of the GIS conductive arm.

[0081] In an optional embodiment, the spatially correlated random perturbation field is superimposed on the base growth rate determined by the surface current density distribution to obtain a modified surface growth rate distribution that incorporates the randomness of microlattice growth, including:

[0082] According to Faraday's law of electrolysis, the basic growth rate is calculated from the surface current density.

[0083] The modified surface growth rate satisfies the following relationship: ,in, To correct the surface growth rate; Basic growth rate; Let p be a spatially correlated random perturbation field, and p be any grid node on the surface of the GIS conductive arm. A is the dimensionless amplitude coefficient.

[0084] Specifically, assuming a dimensionless amplitude coefficient of 0.05, according to Faraday's law of electrolysis, the basic growth rate of the coating surface is proportional to the local current density, as shown in the following equation: Where M is the molar mass of silver, z is the valence of the silver ion, and F is the Faraday constant. That is the density of silver. For any point on the surface... The simulation software will use this formula to derive a basic growth rate based on the calculated current density. For example, if the current density at a certain point is... Then the corresponding basic growth rate can be calculated, for example, 0.005. This rate represents the average growth under ideal, uniform conditions.

[0085] The spatially correlated random perturbation field generated in the previous step, consisting of +1 and -1, is applied to the base growth rate using a correction formula. Continuing with the example above, if the base growth rate at this point is 0.005... If the value of this point in the random perturbation field is +1, then the corrected growth rate is... This is 5% faster than the base growth rate. Conversely, if the random value corresponding to this point is -1, then the corrected growth rate is... This is 5% slower than the base growth rate. By performing this operation on all grid nodes on the surface, the originally smooth base growth rate distribution is transformed into a modified growth rate distribution with small random fluctuations, closely resembling the actual crystal growth pattern, such as... Figure 4 As shown.

[0086] In an optional embodiment, adjusting the next time step size based on the maximum coating increment at the current time step includes:

[0087] After the simulation at the current time step is completed, traverse all grid nodes on the surface of the GIS conductive arm to find the actual maximum coating increment.

[0088] Calculate the next time step, which satisfies the following relationship: ;in, Set the next time step and set the value range to between 0.5 seconds and 10 seconds; This is the current time step; The maximum permissible increment of the coating at any location within each time step; This represents the actual maximum coating increment.

[0089] Specifically, a control parameter is set such that the maximum allowable growth thickness at any point on the coating surface within a single time step is 0.1. This limitation prevents mesh distortion or computational divergence caused by excessive growth in a single step. After completing the calculation for a time step, for example, the current time step is 5.0s, the evaluation phase begins. In this phase, all mesh nodes on the surface of the GIS conductive arm are traversed, and the newly added coating thickness on each mesh node in the past 5.0s is checked.

[0090] Find and determine the largest value among all the thickness increments of the mesh nodes, denoted as . For example, in a tip region with particularly high current density, the actual coating increment could reach 0.25. This far exceeds the target value. The step size for the next time step is calculated using the formula. Substituting the data, we get... Since the actual increment is 2.5 times the target increment, the next time step is shortened to 0.4 times the original to simulate changes in the rapid growth region. Conversely, if the actual coating increment is only 0.05... The calculated new step size will be 10 seconds, thus accelerating the simulation process when growth is slow. For the calculated... Limit the range to ensure the value falls within a reasonable range of 0.5s to 10s. 2.0s falls within this range, so it is adopted; if the calculated result is less than 0.5s, then take 0.5s; if it is greater than 10s, then take 10s.

[0091] S3, repeat the multi-time-step iterative simulation until the total electroplating time is reached, and integrate the segmented anode current adjustment vectors generated by all time steps to form a time-segmented anode current control sequence to guide the actual electroplating process.

[0092] Specifically, the total electroplating time, for example, is set to 3600 seconds, as the termination condition for the iterative loop. At each time step, the duration of the current time step and the calculated absolute current value applied to each segment of the anode are recorded. The simulation ends when the cumulative simulation time reaches 3600 seconds. The time step lengths and corresponding segmented anode current vectors recorded for all time steps are organized chronologically to form a detailed control list. This list specifies the exact current output of each controlled anode power supply during each time period of the electroplating process, such as from 0 to 30 seconds, or from 30 to 58 seconds. This list is a time-segmented control sequence of the anode current that can be directly input into a multi-channel programmable power supply to control the actual electroplating production process.

[0093] In addition, in the description of this specification, "multiple" means at least two, such as two, three or more, etc., unless otherwise expressly and specifically defined.

Claims

1. A method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation, characterized in that, Includes the following steps: S1. Establish an electrochemical simulation environment that includes the initial three-dimensional geometric model of the GIS conductive arm, segmented anodes, and electrolyte; S2, in the multi-time-step iterative simulation, the following operations are performed in each time step: Based on the local curvature and silver ion concentration gradient of the GIS conductive arm surface in the previous time step, calculate the local conductivity decay matrix to correct the electric field model; based on the deviation between the target thickness distribution and the current simulated thickness distribution, calculate the piecewise anode current adjustment vector, and solve the corresponding surface current density distribution under the corrected electric field model; update the Markov chain model according to the surface current density distribution, and use this model to generate a spatially correlated random perturbation field; superimpose the spatially correlated random perturbation field onto the basic growth rate determined by the surface current density distribution to obtain a corrected surface growth rate distribution containing the randomness of micro-lattice growth; update the three-dimensional geometric model of the GIS conductive arm according to the corrected surface growth rate distribution, and adjust the next time step size according to the maximum coating increment of the current time step; S3, repeat the multi-time-step iterative simulation until the total electroplating time is reached, and integrate the segmented anode current adjustment vectors generated by all time steps to form a time-segmented anode current control sequence to guide the actual electroplating process.

2. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to claim 1, characterized in that, An electrochemical simulation environment was established, including an initial three-dimensional geometric model of the GIS conductive arm, segmented anodes, and electrolyte, comprising: A 3D laser scanner was used to scan the GIS conductive arm to generate point cloud data, which was then processed by reverse engineering software to construct an initial 3D geometric model. N columnar soluble silver anodes are arranged in a ring array around the GIS conductive arm as segmented anodes; The electrolyte is set to be an aqueous solution of silver nitrate.

3. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to claim 2, characterized in that, The surface mesh element size of the initial 3D geometric model is 0.5 mm.

4. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to claim 2, characterized in that, There are 8 columnar soluble silver anodes, each with a diameter of 20 mm.

5. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to claim 2, characterized in that, The concentration of silver ions in the silver nitrate aqueous solution is 50 g / L, and the concentration of sodium dodecyl sulfate additive is 100 mg / L.

6. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to claim 1, characterized in that, Based on the local curvature and silver ion concentration gradient of the GIS conductive arm surface in the previous time step, the local conductivity decay matrix is ​​calculated to correct the electric field model, including: For each surface mesh node of the 3D geometric model, the Gaussian curvature is calculated using information from adjacent nodes; The silver ion concentration at each node was obtained by solving the problem using the finite element method, and the normal gradient was calculated. The local conductivity of each node satisfies the following relationship: ; in, Local conductivity; The bulk conductivity of the electrolyte; The curvature is Gaussian, and its unit is . ; The normal gradient is expressed in units of . ; The curvature influence coefficient; The concentration gradient influence coefficient is used; the local conductivity of all nodes is combined to form the local conductivity attenuation matrix.

7. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to claim 1, characterized in that, Based on the deviation between the target thickness distribution and the current simulated thickness distribution, the segmented anode current adjustment vector is calculated, including: dividing the GIS conductive arm surface into N regions corresponding to N segmented anodes, and calculating the average deviation between the simulated thickness and the target thickness of all grid nodes in each region; The proportional-integral control algorithm is used to calculate the current adjustment of each anode, and the current adjustment satisfies the following relationship: ; in, Let be the current adjustment amount of the j-th segment anode at time t, j=1,…,N; This is the proportionality coefficient. The integral coefficient; The average deviation of the j-th region at time t; Add the current adjustment amount to the anode current of the previous time step to obtain the total anode current of each segment used for electric field solution in the current time step.

8. The method for controlling the thickness of the silver plating layer of a GIS conductive arm based on dynamic electric field simulation according to any one of claims 1-7, characterized in that, The Markov chain model is updated based on the surface current density distribution, and the spatially correlated random perturbation field is generated using this model, including: Each grid node on the surface of the GIS conductive arm is defined as a state unit, and the state of the state unit is either lattice growth or lattice vacancy. At each time step, the probability of each grid node being classified as a lattice growth state is determined to be related to the current density at the grid node, and satisfies the following relationship: ; in, The probability of determining it as a lattice growth state; Current density, in units of ; This is the current time step, in seconds. These are probability conversion coefficients; All grid nodes on the surface of the GIS conductive arm are randomly determined according to this probability, and a two-dimensional random field consisting of +1 corresponding to lattice growth and -1 corresponding to lattice vacancies is generated as a spatially correlated random perturbation field.

9. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to claim 8, characterized in that, The spatially correlated random perturbation field is superimposed onto the base growth rate determined by the surface current density distribution to obtain a modified surface growth rate distribution that incorporates the randomness of microlattice growth, including: According to Faraday's law of electrolysis, the basic growth rate is calculated from the surface current density. The modified surface growth rate satisfies the following relationship: ,in, To correct the surface growth rate; Basic growth rate; Let p be a spatially correlated random perturbation field, and p be any grid node on the surface of the GIS conductive arm. A is the dimensionless amplitude coefficient.

10. The method for controlling the thickness of the silver plating layer on a GIS conductive arm based on dynamic electric field simulation according to any one of claims 1-7, characterized in that, Adjust the next time step size based on the maximum coating increment at the current time step, including: After the simulation at the current time step is completed, traverse all grid nodes on the surface of the GIS conductive arm to find the actual maximum coating increment. Calculate the next time step, which satisfies the following relationship: ;in, Set the next time step and set the value range to between 0.5 seconds and 10 seconds; This is the current time step; The maximum permissible increment of the coating at any location within each time step; This represents the actual maximum coating increment.

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