An electric field simulation method, system, computer device and storage medium

Abstract

This invention provides an electric field simulation method, system, computer equipment, and storage medium, belonging to the field of electrochemical processing simulation and multiphysics numerical calculation of particle systems. The method includes: describing the contact mechanical behavior between particles based on a discrete element simulation platform, deriving contact parameters by solving for particle motion states; constructing particle contact resistance and volume resistance models by combining the Holm contact model and the Archie rock electric model to achieve mechanical-electric coupling; treating the particle system as a conductive network, establishing a global conductivity matrix equation based on Kirchhoff's current law, and solving for the potential distribution at each node using a sparse matrix algorithm; and achieving synchronous calculation and result feedback of the dynamics and electrical modules through a data interface. This invention can simulate 10... 5 Dynamic, high-fidelity electric field simulations of particle systems of orders of magnitude and above provide an effective quantitative tool for the electromechanical coupling analysis and process optimization of material removal behavior in the DECP process.

Description

Technical Field

[0001] This invention belongs to the field of electrochemical processing simulation and multiphysics numerical calculation of particulate systems, specifically involving an electric field simulation method, system, computer equipment and storage medium. Background Technology

[0002] Dry electrochemical polishing (DECP) is a surface treatment technology that utilizes porous solid electrolyte particles to adsorb electrolyte, initiating an electrochemical reaction at the localized contact point between the particles and the workpiece surface, thereby achieving selective dissolution of the material. Compared to traditional liquid-phase electrochemical polishing, DECP can achieve localized dissolution only at the peaks of microscopic protrusions on the workpiece surface, significantly improving its surface quality while maintaining the workpiece's macroscopic geometry. This technology offers advantages such as strong localization of material removal, high selectivity, low electrolyte consumption, and environmental friendliness, making it particularly suitable for precision machining of complex curved surfaces and localized morphology reshaping.

[0003] This study aims to accurately predict and visualize the electric field and current distribution during the DECP process using numerical methods, thereby revealing the microscopic interaction mechanism, establishing a quantitative relationship between process parameters and processing quality, and guiding process optimization and equipment design. Existing technologies for simulating and analyzing the conductivity behavior of particulate systems during DECP mainly rely on the following categories:

[0004] Macroscopic homogenization methods are the most typical examples of methods that fail to preserve the physical realism at the particle scale. These methods simplify a system of tens of thousands of discrete particles into a continuous homogeneous medium with equivalent conductivity. Although computationally efficient and capable of handling up to 10-1 particles... 5 While it can handle particle systems of orders of magnitude and above, its model inherently discards particle-scale details, completely ignoring the discrete contact relationships between particles, the dynamic changes at contact points, and the differences in local contact resistance. Therefore, it is inherently unable to predict local current concentrations and electric field distortions caused by individual poor contacts or changes in contact force. These microscopic phenomena are the direct causes of pitting, burning, and uneven removal in the DECP process.

[0005] On the other hand, the Discrete Element Method (DEM) is a particle-scale numerical method that, by solving the equations of motion for each particle, can realistically simulate the dynamic behaviors of particles, such as translation, rotation, collision, contact, and separation. It possesses inherent physical realism in simulating particle motion, accumulation, and forces. However, when attempting to establish a coupled circuit network model to describe conductivity, existing methods are limited by computational scale, typically handling only systems with tens to hundreds of particles, a far cry from the high-density (10^10) particles found in actual DECP processes. 5 The particle size is far from that of particles of orders of magnitude and above. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides an electric field simulation method, system, computer equipment, and storage medium.

[0007] To achieve the above objectives, the present invention provides an electric field simulation method, comprising: A simulation system comprising an anode workpiece, a cathode electrolytic cell, and porous electrolyte particles is constructed. A three-dimensional dynamic model of the porous electrolyte particle system is established, and the Hertz-Mindlin JKR contact model is used to obtain the motion state of all particles and the contact information between particles in the three-dimensional dynamic model. The contact information includes the contact radius and normal overlap between particles.

[0008] Based on the contact radius, the Holm contact model is used to obtain the contact resistance between particles; based on the normal overlap, the Archie rock electric model is used and the volume resistance of each particle in the contact direction is obtained by differentiation; the anode workpiece, cathode electrolytic cell and electrolyte particles in the simulation system are abstracted as circuit nodes, and the contact resistance between any two contacting particles is connected in series with the volume resistance of each of the two particles to serve as the branch resistance connecting the circuit nodes. A conductive network is constructed based on all nodes and branch resistances.

[0009] Based on the conductive network, a set of current balance equations is established for each node according to Kirchhoff's current law, and the set of current balance equations is assembled into a global conductive matrix equation with the node potential as the unknown quantity. The global conductive matrix equation is solved using a sparse matrix algorithm to obtain the potential distribution of all nodes and the current distribution of each branch. Based on the potential distribution and current distribution, the electric field simulation of the workpiece and electrolyte particle system is realized.

[0010] Preferably, the three-dimensional dynamic model is established based on a discrete element simulation platform, which is EDEM or an equivalent simulation environment; when establishing the three-dimensional dynamic model, the material property parameters of the particles need to be initialized, including density, elastic modulus, Poisson's ratio, surface energy, friction coefficient and coefficient of restitution.

[0011] Preferably, the Hertz-Mindlin JKR contact model is used to obtain the motion state of all particles and the contact information between particles in the three-dimensional dynamic model. Specifically, this includes: calculating the normal contact force and tangential contact force between any pair of contacting particles based on the material property parameters of the particles; the normal contact force includes the normal elastic component determined by the normal overlap based on Hertz theory, the normal damping component determined by the equivalent damping model, and the adhesion force component based on JKR theory; the tangential contact force includes the tangential elastic component determined by the tangential displacement based on Mindlin theory and the corresponding tangential damping component; calculating the resultant force and resultant torque on each particle based on all contact forces; using the resultant force and resultant torque, updating the position and velocity of all particles by explicit time integration to obtain the motion state; and calculating the contact radius in the contact information based on the normal contact force and particle material properties.

[0012] Preferably, the step of using the Archie rock electric model and obtaining the volume resistance of each particle in the contact direction by differentiation specifically includes: dividing the particle into multiple differential units along the current conduction path from the geometric center to the contact surface; determining the resistivity of each differential unit based on the Archie rock electric model, and calculating its differential resistance in combination with the geometric dimensions of the differential unit; and obtaining the volume resistance of each particle in the contact direction by integrating all differential resistances along the entire conduction path.

[0013] Preferably, the sparse matrix solving algorithm uses a row-compressed sparse format to store the conductivity matrix, and keeps the fixed potential boundary conditions of the anode and cathode nodes unchanged during the solving process; the convergence criterion and maximum number of iterations of the solver are preset through the configuration file, and the potential values ​​of all particle nodes and the current values ​​of each contact branch are output after solving.

[0014] Preferably, the method is applicable to particle number scales greater than or equal to 10. 5 The system of electrolyte particles is visualized, and the spatiotemporal evolution results, including the potential field distribution cloud map and the current field vector map, are output.

[0015] The present invention also provides an electric field simulation system, comprising: The model building module is used to construct a simulation system that includes an anode workpiece, a cathode electrolytic cell, and porous electrolyte particles; a three-dimensional dynamic model of the porous electrolyte particle system is established, and the Hertz-Mindlin JKR contact model is used to obtain the motion state of all particles in the three-dimensional dynamic model and the contact information between particles. The contact information includes the contact radius and normal overlap between particles.

[0016] The network construction module is used to obtain the contact resistance between particles based on the contact radius using the Holm contact model; to obtain the volume resistance of each particle in the contact direction using the Archie rock electric model and the differential method based on the normal overlap; to abstract the anode workpiece, cathode electrolytic cell and electrolyte particles in the simulation system as circuit nodes; to connect the contact resistance between any two contacting particles in series with the volume resistance of each of the two particles as the branch resistance connecting the circuit nodes; and to construct a conductive network based on all nodes and branch resistances.

[0017] The calculation module is used to establish a set of current balance equations for each node based on the conductive network and Kirchhoff's current law, and assemble the set of current balance equations into a global conductive matrix equation with the node potential as the unknown quantity; solve the global conductive matrix equation using a sparse matrix algorithm to obtain the potential distribution of all nodes and the current distribution of each branch; and realize the electric field simulation of the workpiece and electrolyte particle system based on the potential distribution and current distribution.

[0018] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any one of the electric field simulation methods.

[0019] The present invention also provides a computer-readable storage medium storing a computer program that, when loaded by a processor, can execute any of the steps in the electric field simulation method.

[0020] The electric field simulation method provided by this invention has the following beneficial effects: This invention accurately characterizes the motion and contact details (contact radius, normal overlap) of each particle based on the discrete element method and the Hertz-Mindlin JKR model, and dynamically drives the Holm contact resistance model and the Archie rock electric resistance model, achieving a true mapping from particle-scale mechanical state to electrical response. Furthermore, the entire system is abstracted into a conductive network with particles as nodes and contact resistance and volume resistance connected in series as branches, transforming the complex physical field problem into a circuit problem. Finally, utilizing the inherent sparsity of this network, a sparse matrix algorithm is used for solution, achieving a solution for 10-1 particles without losing any particle-scale details. 5 The system enables efficient calculation of electric field distribution in particle systems of orders of magnitude and above, achieving a fundamental breakthrough in the balance between simulation realism, scale, and efficiency. Attached Figure Description

[0021] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of an electric field simulation method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the particle contact dynamics model used in the embodiments of the present invention; Figure 3 This is a schematic diagram illustrating the solution for the normal overlap caused by the contact between any two particles in an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the definition of all nodes in this embodiment of the invention; Figure 5 This is a flowchart illustrating the implementation of an embodiment of the present invention in an equivalent simulation environment; Figure 6 A schematic diagram illustrating a specific numerical simulation implementation scenario for verifying the embodiments of the present invention; Figure 7 To verify the simulated implementation effect of different particle stacking heights in the embodiments of the present invention, Figure 7 (a) is 20mm in height. Figure 7 (b) has a height of 40mm. Figure 7 (c) is 60mm in height; Figure 8 This is a simulation result of the electric field distribution under real working conditions, based on an embodiment of the present invention. Figure 8 (a) represents the current field distribution. Figure 8 (b) represents the electric potential field distribution. Detailed Implementation

[0023] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0024] This invention provides an electric field simulation method, specifically: an electric field simulation method applicable to DECP electrolyte particle systems. The workpiece acts as the anode, forming a potential difference with the cathode electrolytic cell. Electrolyte particles (which become conductive after adsorbing the electrolyte) form a dynamic conductive network through multi-directional contacts: "particle-particle," "particle-workpiece (anode)," and "particle-cathode electrolytic cell." The potential difference is transmitted through this network, generating an electric field. This electric field drives electrochemical reactions at the particle-workpiece contact points, achieving selective dissolution and polishing of the workpiece surface. This satisfies the requirement for accurate simulation of the electric field of the electrolyte particle system under all time and space conditions at the particle scale. Specifically, as follows... Figure 1 As shown, it includes:

[0025] S1. Construct a simulation system that includes an anode workpiece, a cathode electrolytic cell, and porous electrolyte particles; establish a three-dimensional dynamic model of the porous electrolyte particle system, and use the Hertz-Mindlin JKR contact model to obtain the motion state of all particles in the three-dimensional dynamic model and the contact information between particles, including the contact radius and normal overlap between particles.

[0026] A three-dimensional dynamic model of the electrolyte particle system is established based on a discrete element simulation platform (such as EDEM or an equivalent simulation environment). The mechanical contact relationship between the particles is described using the Hertz-Mindlin JKR model. Specifically, this includes initializing particle properties according to parameters such as particle material density, elastic modulus, Poisson's ratio, surface energy, and frictional recovery coefficient.

[0027] The translational and rotational angular displacements of global particles are solved by time integration (explicit time stepping). Any number of particles in contact are identified by querying the particle spatial coordinates. The normal compression and elastic normal force are calculated based on Hertz theory. The tangential force and stick-slip history are calculated by combining Mindlin theory. The adhesion effect is compensated according to the JKR model to calculate the contact radius, adhesion force and effective contact area. The dynamic behavior parameters of global particles with contact relationships are derived simultaneously.

[0028] A discrete electrolyte particle dynamics equation is defined, which describes the translational, slip, adhesion, and rotational motion states of the particles, thereby calculating the global particle trajectory data. The contact motion state of any particle in the discrete multibody motion field conforms to the description of Hertz-Mindlin JKR theory, and the geometric relationships between particles are as follows: Figure 2 As shown: (1) (2) The normal force generated during particle contact is denoted as . The resulting tangential force is denoted as Furthermore, normal force Elastic component in the normal direction Damping component in the normal direction Together they constitute the sum of vectors; the tangential force Elastic component in the tangential direction and the damping component in the tangential direction Together they constitute the sum of vectors.

[0029] Any pair of particles that come into contact i With particles j The elastic component in the normal direction between them is defined as ,in i , j This serves as an index for the different particles in the particle system. Similarly, any pair of particles in contact... i With particles j The elastic component in the tangential direction between them is defined as The particles i With particles j The damping components in the tangential and normal directions between them are defined as The following is an explanation:

[0030] (3) (4) (5) in, The elastic stiffness is in the tangential direction. This refers to the displacement in the tangential direction (contact overlap). For equivalent Young's modulus, The equivalent radius of curvature, Based on equivalent quality and The damping coefficient, These are the relative velocity components in the normal and tangential directions, respectively. For particle surface energy, denoted as the contact radius between particles.

[0031] In the adhesion forces of electrolyte particles, the maximum pull-out force that breaks the adhesion relationship. The following is an equivalent definition: (6) (7) Among them, any pair of particles that come into contact i With particles j The geometric mean radius between them is The reaction of particles i Particle size With particles j Particle size The contact structure scale between them i , j This serves as an index for different particles in the particulate system. The surface tension of the electrolyte is defined as... The solid-liquid contact angle between the particles and the electrolyte is defined as... In the implementation of specific numerical simulations, and The particle surface energy is confirmed by experimental fitting and equivalent relationship, and the function is loaded into the call chain of the particle contact mechanics calculation module to replace the calculation logic of the preset model.

[0032] S2. Based on the contact radius, the Holm contact model is used to obtain the contact resistance between particles; based on the normal overlap, the Archie rock electric model is used and the volume resistance of each particle in the contact direction is obtained by differentiation; the anode workpiece, cathode electrolytic cell and electrolyte particles in the simulation system are abstracted as circuit nodes, and the contact resistance between any two contacting particles is connected in series with the volume resistance of each of the two particles to serve as the branch resistance connecting the circuit nodes. A conductive network is constructed based on all nodes and branch resistances.

[0033] Based on the particle contact radius, an electrolyte particle contact resistance model based on the Holm contact model is established. The equivalent contact resistance is calculated for any pair of particles in contact, and the changes in contact resistance are explained based on differences in particle motion and contact state. An electrolyte particle conductivity model is established based on the Holm contact model, the Archie rock-electric model, and Ohm's law, combined with differential and geometric solutions. Simplified structural and charge transfer assumptions are made when establishing the electrolyte particle conductivity model. The electrolyte particle structure is simplified to a homogeneous porous structure, and the contact area between particles is calculated based on the contact mechanics model, ignoring the microscopic non-contact situation between contact surfaces caused by differences in surface roughness. The influence of Joule heating on contact resistance and particle bulk resistance is simplified. The saturation of the electrolyte adsorbed by the electrolyte particles is consistent. The influence of the surface state of non-metallic materials and other surface layers on conductivity is simplified.

[0034] S201, Calculation of Particle Contact Resistance The conductivity of the porous electrolyte particles can be expressed, according to the modified Archie model, as follows: (8) in, For effective conductivity Regarding porosity The function expression, Defined as electrolyte conductivity, m The Archie index, obtained through experimental fitting, allows us to define the conductivity of two-phase materials containing electrolyte particles.

[0035] No. i and the j The conductivity of the particles is defined by formula (8), and it is assumed that any first particle has a conductivity of 0. i With the j All electrolyte particles have the same conductivity, and any pair of particles that come into contact... i With particles j The contact resistance generated between them, according to Holm's description of contact resistance, is defined as follows: (9) In the formula, Particles i With particles j The contact resistance generated during the contact behavior; Defined as the effective resistivity function of global electrolyte particles based on porosity variables, and the effective conductivity function They are reciprocals of each other; The actual contact radius between the two particles under the action of the elastic component of the normal contact force, and the subscripts in the above variables. i , j This serves as an index for the different particles in the particle system.

[0036] S202, Calculation of Particle Volume Resistivity The calculation of particle volume resistivity conforms to Ohm's law. Assuming that the electrolyte particles are composed of several thin-film resistors connected in series, for any of these thin-film resistors, their volume resistance satisfies the following formula: (10) in, dR The bulk resistance of the arbitrary thin-film resistor is given. dz The thickness of the arbitrary thin-film resistor is given. r The radius of the particle itself, which is composed of the thin-film resistor.

[0037] For any pair of particles in contact i With particles j The two have a normal overlap in the normal direction. Solving for the geometric relationship is as follows: Figure 3 As shown, the following equation is satisfied: (11) (12) (13) like Figure 3 As shown, the included angle , , and and the normal overlap between particle i and particle j and It is only used for deriving intermediate geometric relationships, as a transitional parameter in the derivation process, and is not used as an independent parameter of the method of this invention, nor as an external input variable in the solution process of the embodiments of this invention. It is defined as the amount of normal overlap generated by particle i and particle j during contact behavior.

[0038] Any pair of particles that come into contact i With particles j The geometric center distance between them is defined as The following equation is satisfied: (14) in, The particle is defined as i Spatial geometric coordinates, The particle is defined as j Spatial geometric coordinates.

[0039] The particles are solved geometrically. i and granules j Each normal overlap and Satisfy the following formula: (15) (16) Based on particle normal overlap A volume resistance model between particles is established for any pair of particles that are in contact and undergo elastic deformation. i With particles j The geometric center distance It should be smaller than the particle size. i With particles j The sum of radii; using the differential method, the particle is equivalent to several cylindrical resistive sheets of thickness dl connected in series, and the volume resistance integral domain of any particle is defined by the particle radius and the normal overlap. According to the differential method analysis, the particle i With particles j Under elastic deformation, the volume resistance of each component along the contact path satisfies the following equation:

[0040] (17) (18) In the above formula, and Each is defined as the particle i With particles j The volume resistance of the path from the geometric center to the contact surface, wherein the volume resistance is considered as a number of thicknesses. dz The equivalent resistance of a porous resistive sheet under series connection conditions; z Based on the coordinates of the particles in a two-dimensional projection, with values ​​ranging from (0, r), this method is used to solve for the resistance of the sheet resistor at different coordinate positions. dR ; It is used to calculate the actual contact area and particle radius collapse degree generated by the elastic deformation of particles, but does not represent the actual geometric penetration. and Each is defined as the particle i With particles j The geometric radius; the subscripts of the above variables i , j This serves as an index for the different particles in the particle system.

[0041] Due to the porous nature of electrolyte particles, the bulk resistance of electrolyte particles is described based on the Archie rock-electric model, and the equivalent resistance of the porous resistive sheet is... dR The conductivity of the electrolyte Porosity and empirical parameters m The above design embeds contact resistance and volume resistance models into the discrete electrolyte particle system, coupling the complex multibody dynamics and electrical properties of the electrolyte particle system. This allows the contact and adhesion behavior between particles to be reflected mathematically in terms of their corresponding electrical properties, thereby achieving a unified description of the particle's mechanical state and conductivity. This provides a foundation for establishing a global electric field matrix model and solving for the potential distribution.

[0042] S3. Based on the conductive network, establish a set of current balance equations for each node according to Kirchhoff's current law, and assemble the set of current balance equations into a global conductive matrix equation with the node potential as the unknown quantity; use the sparse matrix algorithm to solve the global conductive matrix equation to obtain the potential distribution of all nodes and the current distribution of each branch; based on the potential distribution and current distribution, realize the electric field simulation of the workpiece and electrolyte particle system.

[0043] Based on Kirchhoff's current law and current balance equations, and combined with nodal analysis, environmental assumptions are made, and the electrolyte particle conductivity matrix equation is established, such as... Figure 4As shown, the node analysis method assumes that any electrolyte particle in the dry electrochemical polishing system is considered a separate node, and the anode workpiece and the cathode electrolytic cell are each considered a separate node; the Kirchhoff current law and current balance equation assume that in the circuit composed of all nodes in the dry electrochemical polishing system, for any node in the circuit, the inflow current is considered positive and the outflow current is considered negative, and the sum of the currents flowing into the node is equal to the sum of the currents flowing out of the node; the environmental factors assume that the ambient temperature and electrochemical effects have no effect on the charge transport of all nodes.

[0044] The entire electrolyte particle system is considered as a conductive network composed of independent particle nodes and their contact relationships. Each node contains its own volume resistance property, and any pair of contacting particles are connected by the contact resistance calculated above. By calling the data interface in the DEM simulation platform, the particle node and contact pair information is automatically extracted to generate node numbers and contact relationship data, which are used to characterize the current conduction path in the system and serve as the input basis for solving the global electric field matrix.

[0045] Based on the accessed global particle conductivity network information, treating each particle as an independent node, and following Kirchhoff's current law, a current balance equation is formulated for any node in the system, where the algebraic sum of the inflow and outflow currents at any node is zero. Combining all the node equations yields a global conductivity matrix equation, which uses the unknown potential, contact resistance, and volume resistance of each node as unknowns of conductivity. This matrix equation describes the current and potential distribution relationship of the entire particle system. The electrolyte particle conductivity matrix equation is expressed as follows:

[0046] (19) in, It is a conductivity matrix defined by the volume resistance and contact resistance of the particle contact system. Defined as the nodal potential vector, It is defined as a current source vector, and the potential distribution of each node in the system is obtained by using a sparse matrix numerical solution algorithm.

[0047] (20) For nodes 0 to n, the relations are defined in DECP as follows: Figure 4 As shown, the current balance equations for each node are constructed as follows: Node 0 (Anode): ;(twenty one) Node 1 (Cathode): ;(twenty two) Node i: ;(twenty three) Node n: ;(twenty four) Wherein, node 0 is the cathode electrolytic cell, node 1 is the anode workpiece, and node... i , i+1 ... n-1 , n Representing all electrolyte particles; the conductivity matrix G From self-conductivity G ii ( i = i ) and mutual conductance G ij ( i ≠ j It consists of two variables. i , j The index is the number of different particles in the particle system, and the relationship between the two is as described in formula (25); self-conductance is the sum of the conductances of all branches formed by a node and all nodes that produce contact behavior, and mutual conductance is the conductance of the branches formed by two nodes that produce contact behavior; the conductance G With resistance R The relationships are reciprocals of each other.

[0048] (25) The self-conductivity G ii The following relation is satisfied: Assume that at any time step, the arbitrary... i Particles and the first j, j+1, ..., j+ n Each particle simultaneously engages in contact behavior. Assume any pair of particles in contact... i With particles j Taking this as an example, mutual conduction G ij and self-conductivity G ii Equations (26) and (27) show that the total resistance in the contact path can be defined as the contact resistance. R c，ij and volume resistance R bulk The sum of series.

[0049] (26) (27) Through the above design, a network-based representation and matrix-based solution of the conductivity behavior of electrolyte particle systems are realized, transforming the complex and massive multi-contact relationships in the particle system into a computable circuit topology. While preserving the physical characteristics of the contacts, this method can efficiently solve for the potential and current distribution at each node in the system, providing a core computational framework for further evaluation of quantitative indicators such as macroscopic electric field distribution and current density distribution.

[0050] This invention is compiled using C++ and solves the electric field of the electrolyte particle system through the Edem API interface. The electrical calculation API is deployed as an independent module within the simulation project directory and is called by the simulation control module according to a preset coupling rhythm. The specific process is as follows: Figure 5 As shown, specifically, as described below: Dynamic numerical input solution stage Before the simulation begins, material properties are assigned to all electrolyte particles, including density, elastic modulus, Poisson's ratio, surface energy, coefficient of friction, and coefficient of restitution. These material properties are obtained through experimental measurements. During the kinetic solution process, the contact kinetic data and contact duration of the electrolyte particles are updated in explicit time steps and serve as the input basis for the following process.

[0051] External data receiving stage When the simulation control module is triggered at a specified coupling step, it transmits the particle contact data of the current time step to the API. The contact data is exported by Edem itself and includes contact pair identifiers, contact radii, normal overlap, contact pressure, particle radius, and particle coordinates; the data is delivered to the API in the form of structured binary records or structured text records.

[0052] Static parameter loading phase The API synchronously receives data and reads the electrical parameter configuration file in the project directory; the input values ​​in the configuration file include anode potential, cathode potential, effective conductivity of electrolyte particles, anode conductivity, and cathode conductivity; the input values ​​are loaded and cached as global constants for all subsequent calculations.

[0053] Resistance calculation stage Calculate the contact resistance for all contact pairs formed by global particles. The contact resistance is calculated based on the contact radius and contact pressure extracted during the data reception phase; and the volume resistance is simultaneously calculated for each pair of contact particles, which is calculated from the effective conduction path length defined by the particle radius and normal overlap; generate the conductance of each contact path and record it in the form of nodes.

[0054] Conductivity matrix construction stage The API assembles a conductivity matrix based on the aforementioned conductivity data. The non-zero entries in the matrix are generated by the path resistance between particles, and the matrix row and column indices are consistent with the particle numbers. The conductivity of all connected paths of each node is accumulated and the corresponding entries are written into the matrix synchronously. The matrix is ​​stored in a row-compressed sparse format, and the fixed potential boundary conditions of the anode and cathode nodes are written into the matrix structure.

[0055] Potential solution stage After the conductivity matrix is ​​constructed and assembled, a sparse iterative solver is called to solve for the node potentials. The convergence criterion and maximum number of iterations of the solver are determined by the selected configuration, and the convergence of the results is judged. During the process, the potential constraints of the boundary nodes remain unchanged. After the solution is completed, the potential values ​​of all particle nodes are output.

[0056] Current output stage Based on the potential solution results, the current value of the path is calculated according to the node potential difference between any contact particle pair and the equivalent resistance of the corresponding path. The current calculation covers all effective contact pairs. The current record adopts a structured data format, which includes node number, current value, direction attribute and path index.

[0057] Data post-processing and return stage After the potential calculation stage and the current output stage are completed, the potential records and current records are exported and returned to the software simulation control module in the form of structured data. After receiving the data, the control module writes the node potential into the data field of the corresponding particle object and writes the path current into the data field of the particle contact relationship. The post-processing interface displays and exports the particle node potential distribution, contact path current distribution and their time evolution results in a graphical and structured data format.

[0058] This specific embodiment is based on the verification process of the simulation method, and is used to illustrate the executability of the electrolyte particle conductivity simulation method. A simulation scenario of natural accumulation of electrolyte particles is constructed according to the aforementioned steps, and the global potential solution and the current distribution of the global contact path are completed. Specifically, the insulating boundary 1 constrains the electrolyte particles 3, and the electrolyte particles 3 are set with natural accumulation heights of 20mm, 40mm, and 60mm respectively in the container. The upper end of the electrolyte particles 3 contacts the positive electrode 2, and the lower end contacts the cathode 4. An axial static load is applied to the upper part of the positive electrode 2. In the above scenario, the electrolyte particles 3, the positive electrode 2, and the negative electrode 4 constitute an equivalent resistance, as detailed in [link to documentation]. Figure 6The equivalent resistance values ​​of the above-mentioned electrolyte particle accumulation samples were measured using the two-electrode method under the conditions of accumulation heights of 20 mm, 40 mm, and 60 mm. Simultaneously, the theoretical equivalent resistance values ​​under the same conditions were numerically simulated using the aforementioned simulation method. The actual measured values ​​and theoretical calculation values ​​were compared to verify the accuracy of the simulation method. For the verification results under the accumulation height conditions of 20 mm, 40 mm, and 60 mm, please refer to [link to relevant documentation]. Figure 7 (a)- Figure 7 (c).

[0059] Figure 7 In the figure, the three trend lines are roughly parallel and close to the diagonal, indicating that for different stacking heights (i.e., different particle system sizes and contact complexities), the simulation results of this invention can systematically reflect the same resistance variation trend as actual measurements. This proves that the core method of coupling particle contact mechanics (Hertz-Mindlin JKR) with the electrical model (Holm + Archie) in this invention is consistent with physical reality and can accurately convert mechanical states (contact radius, overlap) into electrical parameters (resistance).

[0060] Figure 7 All numerical simulation results are distributed near the peaks of the experimental discrete data distribution, indicating that the simulated predictions fall within a reasonable range of experimental data dispersion. This demonstrates that the prediction error of the method is acceptable, possesses engineering practical value, and provides a reliable quantitative tool for process analysis. Furthermore, the simulation results, encompassing three heights and covering different particle numbers and contact network complexities, maintain consistent correlation with experimental data in all cases, proving the effectiveness of this invention for particle systems of different sizes. This lays a solid empirical foundation for its application in the quantitative analysis and optimization of DECP processes.

[0061] To improve the representativeness of the verification results, the particle electrical parameters were referenced from the actual DECP operating conditions during the above verification process, as shown in Table 1. Table 1 Electrolyte particle electrical parameters under numerical simulation during the verification process Table 1 shows that the equivalent resistance at different electrolyte particle stacking heights exhibits a consistent trend of nonlinear variation between numerical simulation and experimental measurements, with the model prediction relative error remaining within 24%-48%. Therefore, the simulation method constructed in this invention demonstrates high accuracy in characterizing the electrical properties of discrete electrolyte particle systems under dynamic field conditions. Furthermore, based on the full-scene simulation of the DECP under real-world operating conditions and the numerical simulation results, the visualization distribution of the global particle potential and current fields is shown below. Figure 8As shown, Current represents electric current, and Electrical potential represents voltage. Figure 8 (a) shows the current field distribution, with contour lines indicating current intensity (unit: A). Figure 8 (b) shows the electric potential field distribution, with contour lines indicating the potential values ​​(unit: V). The initial conditions in the scenario include an anode voltage of 60V, a particle count of 35W, a Rayleigh percentage of 20%, and a fixed Rayleigh time step of 1.0552e-06s. Figure 8 The dense and tortuous shape of the mean squares intuitively reflects the non-uniformity and local abrupt changes of the electric field in the particle contact network, which contrasts sharply with the smooth and uniform distribution obtained by traditional continuous domain simulation methods (shown in the lower part of the figure).

[0062] This invention provides, for the first time, an electric field simulation method applicable to DECP electrolyte particle systems. This method reveals the electric field distribution of the entire particle system from the perspective of a single electrolyte particle, correlates the dynamic relationships such as particle contact and adhesion with conductivity, and constructs mathematical relationships. This provides theoretical support for the force-electric coupling field-controlled material removal behavior in DECP electrolyte particle systems and offers a quantitative tool for designing polishing uniformity and electric field optimization schemes. Unlike static electric field solutions that homogenize particle systems, this invention allows for complete customization of the material's electrical and mechanical properties and enables simulation on a desktop platform. 5 This method enables dynamic solving of the electric field of particle systems of orders of magnitude and above. It can achieve high-fidelity replication of the number, size, and spatiotemporal relationship of particles under real-world conditions, and accurately simulate the local and global electric field distribution within the electrolytic cell space.

[0063] Based on the same inventive concept, the present invention also provides an electric field simulation system, comprising: The model building module is used to construct a simulation system that includes an anode workpiece, a cathode electrolytic cell, and porous electrolyte particles; a three-dimensional dynamic model of the porous electrolyte particle system is established, and the Hertz-Mindlin JKR contact model is used to obtain the motion state of all particles in the three-dimensional dynamic model and the contact information between particles. The contact information includes the contact radius and normal overlap between particles.

[0064] The network construction module is used to obtain the contact resistance between particles based on the contact radius using the Holm contact model; to obtain the volume resistance of each particle in the contact direction using the Archie rock electric model and the differential method based on the normal overlap; to abstract the anode workpiece, cathode electrolytic cell and electrolyte particles in the simulation system as circuit nodes; to connect the contact resistance between any two contacting particles in series with the volume resistance of each of the two particles as the branch resistance connecting the circuit nodes; and to construct a conductive network based on all nodes and branch resistances.

[0065] The calculation module is used to establish a set of current balance equations for each node based on the conductive network and Kirchhoff's current law, and assemble the set of current balance equations into a global conductive matrix equation with the node potential as the unknown quantity; solve the global conductive matrix equation using a sparse matrix algorithm to obtain the potential distribution of all nodes and the current distribution of each branch; and realize the electric field simulation of the workpiece and electrolyte particle system based on the potential distribution and current distribution.

[0066] This invention also provides a computer device, which, at the hardware level, includes a processor, an internal bus, a network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to implement the electric field simulation method provided above.

[0067] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the electric field simulation method provided above.

[0068] Specific limitations regarding the electric field simulation method calculation system can be found in the limitations of the electric field simulation method described above, and will not be repeated here. Each module in the above electric field simulation system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of the computer device in hardware form or independent of it, or stored in the memory of the computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0069] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. Furthermore, the above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. An electric field simulation method, characterized in that, include: A simulation system comprising an anode workpiece, a cathode electrolytic cell, and porous electrolyte particles is constructed; a three-dimensional dynamic model of the porous electrolyte particle system is established, and the Hertz-Mindlin JKR contact model is used to obtain the motion state of all particles and the contact information between particles in the three-dimensional dynamic model, wherein the contact information includes the contact radius and normal overlap between particles; Based on the contact radius, the Holm contact model is used to obtain the contact resistance between particles; Based on the normal overlap, the Archie rock electric model is used and the volume resistance of each particle in the contact direction is obtained by differential method. The anode workpiece, cathode electrolytic cell and electrolyte particles in the simulation system are abstracted as circuit nodes. The contact resistance between any two contacting particles is connected in series with the volume resistance of each of the two particles to serve as the branch resistance connecting the circuit nodes. A conductive network is constructed based on all nodes and branch resistances. Based on the conductive network, a set of current balance equations is established for each node according to Kirchhoff's current law, and the set of current balance equations is assembled into a global conductive matrix equation with the node potential as the unknown. The global conductivity matrix equation is solved using a sparse matrix algorithm to obtain the potential distribution of all nodes and the current distribution of each branch; based on the potential and current distributions, the electric field simulation of the workpiece and electrolyte particle system is realized.

2. The electric field simulation method according to claim 1, characterized in that, The three-dimensional dynamic model is established based on a discrete element simulation platform, which is EDEM or an equivalent simulation environment. When establishing the three-dimensional dynamic model, the material property parameters of the particles need to be initialized, including density, elastic modulus, Poisson's ratio, surface energy, friction coefficient, and coefficient of restitution.

3. The electric field simulation method according to claim 1, characterized in that, The Hertz-Mindlin JKR contact model is used to obtain the motion state of all particles and the contact information between particles in the three-dimensional dynamic model. Specifically, this includes: calculating the normal and tangential contact forces between any pair of contacting particles based on the particle material properties; the normal contact force includes the normal elastic component determined by the normal overlap based on Hertz theory, the normal damping component determined by the equivalent damping model, and the adhesion force component based on JKR theory; the tangential contact force includes the tangential elastic component determined by the tangential displacement based on Mindlin theory and the corresponding tangential damping component; calculating the resultant force and resultant torque on each particle based on all contact forces; using the resultant force and resultant torque, updating the position and velocity of all particles by explicit time integration to obtain the motion state; and calculating the contact radius in the contact information based on the normal contact forces and particle material properties.

4. The electric field simulation method according to claim 1, characterized in that, The method of obtaining the volume resistance of each particle in the contact direction using the Archie rock electric model and the differential method specifically includes: dividing the particle into multiple differential units along the current conduction path from the geometric center to the contact surface; determining the resistivity of each differential unit based on the Archie rock electric model, and calculating its differential resistance in combination with the geometric dimensions of the differential unit; and obtaining the volume resistance of each particle in the contact direction by integrating all differential resistances along the entire conduction path.

5. The electric field simulation method according to claim 1, characterized in that, The sparse matrix solving algorithm uses a row-compressed sparse format to store the conductivity matrix. During the solving process, the fixed potential boundary conditions of the anode and cathode nodes remain unchanged. The convergence criterion and maximum number of iterations of the solver are preset through the configuration file. After solving, the potential values ​​of all particle nodes and the current values ​​of each contact branch are output.

6. The electric field simulation method according to claim 1, characterized in that, The method is applicable to particle size greater than or equal to 10. 5 The system of electrolyte particles is visualized, and the spatiotemporal evolution results, including the potential field distribution cloud map and the current field vector map, are output.

7. An electric field simulation system, characterized in that, include: The model building module is used to construct a simulation system that includes an anode workpiece, a cathode electrolytic cell, and porous electrolyte particles; a three-dimensional dynamic model of the porous electrolyte particle system is established, and the Hertz-Mindlin JKR contact model is used to obtain the motion state of all particles in the three-dimensional dynamic model and the contact information between particles, including the contact radius and normal overlap between particles; The network construction module is used to obtain the contact resistance between particles based on the contact radius using the Holm contact model; Based on the normal overlap, the Archie rock electric model is used and the volume resistance of each particle in the contact direction is obtained by differential method. The anode workpiece, cathode electrolytic cell and electrolyte particles in the simulation system are abstracted as circuit nodes. The contact resistance between any two contacting particles is connected in series with the volume resistance of each of the two particles to serve as the branch resistance connecting the circuit nodes. A conductive network is constructed based on all nodes and branch resistances. The calculation module is used to establish a set of current balance equations for each node based on the conductive network and Kirchhoff's current law, and to assemble the set of current balance equations into a global conductive matrix equation with the node potential as the unknown quantity. The global conductivity matrix equation is solved using a sparse matrix algorithm to obtain the potential distribution of all nodes and the current distribution of each branch; based on the potential and current distributions, the electric field simulation of the workpiece and electrolyte particle system is realized.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is loaded by the processor, it is able to perform the steps of the method according to any one of claims 1 to 6.

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