Anode surface material etching simulation method based on plasma discharge channel

Abstract

The invention discloses an anode surface material etching simulation method based on a plasma discharge channel, and belongs to the field of thermal plasma simulation modeling. The problems that existing material etching simulation depends on a hypothetical heat source, the influence of the transient evolution process of a plasma channel on material etching cannot be fully considered, and the simulation prediction precision is low are solved. By considering multi-physical field coupling and a transient process, high-precision key data of anode surface pressure distribution and heat flux density distribution can be provided, errors caused by a traditional assumed heat source model are overcome, and the corrosion removal process of an anode surface material is accurately simulated. The simulation result not only can accurately reflect the anode surface temperature field distribution, but also can predict the geometric contour, diameter and depth of the anode surface pit in detail. The method is mainly applied to material etching simulation of the plasma discharge channel.

Description

Technical Field

[0003] This invention belongs to the field of thermal plasma simulation modeling. Background Technology

[0005] Electrical Discharge Machining (EDM) is one of the most widely used special machining technologies. Its ability to process high-hardness materials, complex surfaces, and micro-aperture holes makes it widely applicable in mold manufacturing, aerospace, and automotive industries. EDM generates a transient high-temperature plasma discharge channel through pulsed spark discharge between the tool electrode and the workpiece, causing localized melting or vaporization of the workpiece material, thus achieving material removal. With the increasing demands for precision and efficiency in micro-hole machining, complex surface forming, and high-hardness alloy machining, the precise control and optimization of EDM have become increasingly important. Numerical simulation technology plays an increasingly crucial role in revealing the discharge mechanism, optimizing process parameters, and reducing experimental costs.

[0006] In electrical discharge machining (EDM), after a pulsed voltage is applied, a transient electric field is generated between the tool electrode and the workpiece. When the electric field strength at a certain point reaches approximately 10... 5 At V / mm, the dielectric ionizes, electrons are emitted and accelerated by the electric field to collide with surrounding dielectric molecules, leading to dielectric breakdown and the formation of a discharge channel. The temperature within the discharge channel can instantly rise to thousands or even tens of thousands of Kelvin, creating a high-intensity heat source that rapidly melts and vaporizes the electrode material. Simultaneously, the magnetic field generated by the current within the channel radially compresses the plasma channel through the Lorentz force, affecting the flow rate and pressure of the interelectrode medium and further influencing heat transfer and fluid motion during the discharge process. Furthermore, the Joule heating generated when the current passes through the plasma causes a sharp increase in plasma temperature, which in turn affects the plasma's electrical conductivity, thermal conductivity, and other physical properties. Therefore, each discharge process in electrical discharge machining is a coupled evolutionary process involving the interaction of multiple physical fields: the current field, electromagnetic field, heat transfer field, and flow field.

[0007] The material removal process in electrical discharge machining (EDM) is characterized by the accumulation of pits due to continuous discharge. Therefore, the erosion mechanism of pit formation by a single discharge has significant fundamental research value. Existing material removal simulations mostly rely on hypothetical heat sources, typically setting the energy distribution ratio and heat source radius as empirical values ​​and equivalent channel radii, respectively. However, these parameters dynamically change with discharge waveforms, process parameters, and discharge time. Static assumptions often fail to accurately reflect the complex changes in the actual machining process, leading to large prediction errors and making it difficult to meet the requirements of high-precision machining. Therefore, traditional heat source assumption models cannot fully consider the transient evolution of the plasma channel, resulting in difficulty in accurately predicting the anodic material removal process and low prediction accuracy. These problems urgently need to be solved. Summary of the Invention

[0009] To address the problem that existing material erosion simulations rely on assumed heat sources and cannot fully consider the impact of the transient evolution of the plasma channel on material erosion, resulting in low simulation prediction accuracy, this invention provides a simulation method for anodic surface material erosion based on a plasma discharge channel.

[0010] A simulation method for anolyte surface material etching based on plasma discharge channels, the method comprising:

[0011] S1. Based on the geometric characteristics of the actual discharge device, a two-dimensional axisymmetric geometric model of the plasma discharge channel is established using simulation software. This two-dimensional axisymmetric geometric model includes three regions: cathode, inter-electrode medium, and anode.

[0012] S2. Based on the coupling relationship between the multiphysics fields, construct the governing equations for each physics field, and apply the multiphysics field governing equations to the two-dimensional axisymmetric geometric model to obtain the multiphysics field coupling simulation model; the multiphysics field consists of four physics fields, namely the flow field, heat transfer field, current field and electromagnetic field;

[0013] S3. Set the material properties, physical boundary conditions and initial environmental conditions of each region in the multiphysics coupling simulation model;

[0014] S4. Mesh the multiphysics coupling simulation model;

[0015] S5. Based on the transient solver, the multiphysics coupling simulation model after meshing is simulated to obtain the heat flux density distribution, pressure distribution, pressure radius distribution, and heat flux density radius distribution on the anode surface.

[0016] S6. Substitute the maximum values ​​of the heat flux density distribution and pressure distribution on the anode surface, as well as the pressure radius distribution and heat flux density radius distribution on the anode surface, into the material erosion simulation model to calculate the temperature field distribution on the anode surface.

[0017] S7. Based on the temperature field distribution on the anode surface, obtain the geometric contour, diameter, and depth of the pits on the anode surface.

[0018] Preferably, the flow field governing equations include:

[0019] Continuity equation:

[0020] (1);

[0021] Momentum conservation equation:

[0022] (2);

[0023] in, For density, It is a velocity vector. For time, It is the identity matrix. For dynamic viscosity, For Hamiltonian operators, For matrix transpose, To calculate the current density in the computational domain, For magnetic flux, It is the acceleration due to gravity. For pressure.

[0024] Preferably, the governing equations for the heat transfer field are:

[0025] (3);

[0026] in, For density, For constant pressure heat capacity, For temperature, For time, It is a velocity vector. For Hamiltonian operators, Thermal conductivity, For electric field, Boltzmann's constant, For electron charge, To calculate the current density in the computational domain, This is the net volumetric emissivity.

[0027] Preferably, the governing equation for the current field is:

[0028] (4);

[0029] (5);

[0030] (6);

[0031] In the formula, For Hamiltonian operators, For electric potential, To calculate the electrical conductivity of the material in the computational domain, To calculate the current density in the computational domain, It is an electric field.

[0032] Preferably, the electromagnetic field governing equations are:

[0033] (7);

[0034] (8);

[0035] in, For Hamiltonian operators, Relative permeability The magnetic vector potential, To calculate the electrical conductivity of the material in the computational domain, For electric potential, It represents magnetic flux.

[0036] Preferably, in step S2, the multiphysics governing equations are applied to the two-dimensional axisymmetric geometric model in the following manner:

[0037] The flow field control equation is applied to the interelectrode medium region, while the heat transfer field control equation, current field control equation, and electromagnetic field control equation are all applied to the regions where the cathode, interelectrode medium, and anode are located.

[0038] Preferably, in step S3, setting the material properties for each region includes:

[0039] The cathode material is set to tungsten, the anode material to stainless steel, and the inter-electrode medium to air, with constraints imposed on the conductivity of the inter-electrode medium;

[0040] The constraint is: when season ;when ,make ;

[0041] in, Indicates temperature The conductivity of the inter-electrode dielectric under the following conditions =1 S / m, which is the set minimum conductivity;

[0042] The physical boundary conditions for each region are as follows:

[0043] Set the upper, lower, left, and right boundaries of the region where the cathode is located as AB, GHI, AG, and BI, respectively;

[0044] Set the upper, lower, left, and right boundaries of the anode region as EF, DC, ED, and FC, respectively;

[0045] The left and right boundaries of the region where the inter-electrode medium is located are set as GE and IF, respectively; and GHI and EF are also used as the upper and lower boundaries of the region where the inter-electrode medium is located, respectively.

[0046] Of all the boundaries, boundary GHI is composed of a curve and a straight line, and all the remaining boundaries are straight lines. Boundaries AG, GE and ED are on the same straight line, and boundaries BI, IF and FC are on the same straight line.

[0047] In the flow field, boundaries GHI and EF are no-slip boundaries, where the fluid velocity is 0, and boundary IF is in an open state.

[0048] In the temperature field, the temperatures of boundaries AB, DC, BI, IF, and FC are all set to 1000 K, and an energy exchange term between the cathode and the plasma discharge channel is set on boundary GHI. An energy exchange term between the anode and the plasma discharge channel is set on the boundary EF. ;and

[0049] (9);

[0050] (10);

[0051] (11);

[0052] (12); among which, For electron current density, The ion current density, The work function of the cathode material. For electric field, The ionization potential of the plasma is denoted as . The emission coefficient of the cathode surface, The Stefan-Boltzmann constant is given. For temperature;

[0053] To calculate the current density in the computational domain, Let be the work function of the anode material. The anode surface emissivity;

[0054] The thermionic emission current density, The thermionic emission constant of the cathode, For electron charge, Work function of cathode material This is an electric field correction term. Boltzmann's constant, For electric field, The vacuum permittivity, It is a unit vector;

[0055] In a current field, the boundary DC is considered as the current flowing into the boundary, and its input current density is... ,in, For the magnitude of the current, The anode radius is defined, with boundary DC and FC connected to power supply ground, and boundary BI and IF electrically insulated. ;

[0056] In the electromagnetic field, the boundaries AB, BI, IF, FC, and DC are all magnetically insulated, that is... ;

[0057] Initial environmental conditions include: initial flow velocity of 0, initial flow pressure of standard atmosphere, initial temperature of 293.15 K, reference impedance of current field of 50 Ω, initial electric potential of current field of 0 Ω, and initial magnetic vector potential of electromagnetic field of 0 Ω.

[0058] Preferably, the specific implementation method for meshing the multiphysics coupled simulation model in step S4 is as follows:

[0059] When meshing the regions containing the cathode and anode, the range of side lengths for the resulting polygonal mesh is as follows: to ;

[0060] When meshing is performed in the region containing the interpolar medium, the range of side lengths for the resulting polygonal mesh is as follows: to ;

[0061] The surrounding areas of boundaries GHI and EF are further refined, and the side lengths of the resulting polygonal mesh range from [value missing]. to .

[0062] Preferably, in step S6, the method for obtaining the temperature field distribution on the anode surface is as follows:

[0063] The maximum heat flux density and the radius distribution of the heat flux density on the anode surface are input into the heat source term of the material erosion simulation model, and the maximum pressure on the anode surface and the radius distribution of the pressure on the anode surface are input into the volume force term of the material erosion simulation model to obtain the temperature field distribution on the anode surface.

[0064] Preferably, the method for obtaining the geometric contour, diameter, and depth of the pit on the anode surface based on the temperature field distribution on the anode surface in step S7 is as follows:

[0065] Solid regions are identified within the surface temperature field distribution, and the contours of these solid regions serve as the geometric contours of the pits on the anode surface. The solid fraction of the material in these solid regions is... ;

[0066] The geometric contour of the pit on the anode surface is projected, and the diameter of the equivalent circle of the projection surface is taken as the diameter of the pit.

[0067] The depth of the pit is defined as the depth of the center point within the geometric contour of the pit on the anode surface.

[0068] The beneficial effects of this invention are:

[0069] The plasma discharge channel-based simulation method for anolyte surface material removal described in this invention, by considering multi-physics coupling and transient processes, can provide high-precision key data on the pressure distribution and heat flux density distribution of the anode surface. This overcomes the errors introduced by traditional hypothetical heat source models and accurately simulates the anolyte surface material removal process. The simulation results not only accurately reflect the temperature field distribution on the anode surface but also predict in detail the geometric contour, diameter, and depth of pits on the anode surface, improving the simulation accuracy of electrical discharge machining (EDM) anode surface material removal simulation and enhancing the accuracy of simulation predictions.

[0070] By establishing a coupled simulation model involving four physical fields—flow, heat transfer, current, and electromagnetic fields—the transient evolution of a plasma discharge channel can be accurately simulated. A transient solver is used to solve the meshed multiphysics coupled simulation model, yielding crucial data on the heat flux density and pressure distribution on the anode surface. This data will be further applied to a material erosion simulation model to accurately predict the temperature field distribution on the anode surface, thereby calculating the geometric contour, diameter, and depth of the pits on the anode surface. This dynamic calculation method overcomes the limitations of existing static assumption methods, making the simulation results more reliable and improving the accuracy of simulation predictions.

[0071] This invention eliminates uncertainties in traditional heat source assumptions by capturing the physical characteristics of the discharge process in real time, and directly applies transient simulation data to the material erosion model, thereby improving the accuracy and reliability of anode material processing performance prediction. Compared with existing methods, this invention can provide more accurate discharge process simulation, thereby optimizing the process parameters of electrical discharge machining and improving processing accuracy and efficiency.

[0072] The innovation of this invention lies in its realization of a closed-loop integrated simulation from the physical process of discharge to the material erosion mechanism, which can provide strong technical support for the optimization of high-precision and high-efficiency electrical discharge machining processes. In particular, its application in the processing of complex materials will significantly improve processing quality and production efficiency.

[0073] Furthermore, the simulation method for erosion of anode surface materials based on plasma discharge channels of the present invention is applicable to the prediction of processing performance of different anode materials. It is not only applicable to the processing of conventional materials, but also to the processing of difficult-to-machine materials, meeting the needs of modern industry for high-precision and high-efficiency processing. Attached Figure Description

[0075] Figure 1 This is a flowchart of the simulation method for erosion of anode surface material based on plasma discharge channel described in this invention;

[0076] Figure 2 This is a schematic diagram of a two-dimensional axisymmetric geometric model;

[0077] Figure 3 It is a multiphysics coupling simulation model after mesh generation;

[0078] Figure 4 This is a schematic diagram of the temperature field distribution of the anode surface material at different times during the etching process;

[0079] Figure 5 It is a curve formed by the maximum heat flux density on the anode surface of the plasma discharge channel at different times. Detailed Implementation

[0081] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0082] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0083] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0084] This invention simulates the erosion of anode surface materials using a plasma discharge channel based on multiphysics, solving the technical problems of existing material erosion simulation models that rely on statically set heat source parameters and ignore the influence of transient changes in the plasma channel on material erosion. By capturing the physical characteristics during the discharge process in real time, this invention eliminates the uncertainties in traditional heat source assumptions and directly applies transient simulation data to the material erosion model, thereby improving the accuracy and reliability of anode material processing performance prediction. By considering multiphysics coupling and transient processes, it can provide high-precision key data on anode surface pressure distribution and heat flux density distribution, overcoming the errors caused by traditional assumed heat source models and accurately simulating the erosion process of anode surface materials. The specific implementation method is as follows:

[0085] Specific Implementation Method 1: Combination Figure 1 As shown, this invention provides a simulation method for anolyte surface material etching based on a plasma discharge channel. The method includes:

[0086] S1. Based on the geometric characteristics of the actual discharge device, a two-dimensional axisymmetric geometric model of the plasma discharge channel is established using simulation software. This two-dimensional axisymmetric geometric model includes three regions: cathode, inter-electrode medium, and anode. (See [link]). Figure 2 ;

[0087] S2. Based on the coupling relationship between the multiphysics fields, construct the governing equations for each physics field, and apply the multiphysics field governing equations to the two-dimensional axisymmetric geometric model to obtain the multiphysics field coupling simulation model; the multiphysics field consists of four physics fields, namely the flow field, heat transfer field, current field and electromagnetic field;

[0088] Because of the coupling between the flow field, the current field, and the electromagnetic field: the fluid velocity affects the distribution of the current in the fluid, the current generates an electromagnetic field, and the electromagnetic field generates the Lorentz force. Acting on the flow field, it changes the motion state of the fluid. The motion of the fluid in the flow field will change the current distribution, which in turn affects the electromagnetic field. The coupling of the three is described by combining the control equations of the flow field, current field and electromagnetic field.

[0089] There is coupling between the heat transfer field and the current field: Joule heating is generated when the current flows through the interelectrode medium. The distribution of current directly affects the temperature distribution of the inter-electrode medium, and changes in temperature affect material properties, thereby altering the current field distribution.

[0090] There is coupling between the heat transfer field and the flow field: temperature is closely related to the material properties of the fluid, temperature changes affect fluid motion, and fluid motion, in turn, alters the temperature distribution; therefore...

[0091] In practical applications, the flow field governing equations include:

[0092] Continuity equation:

[0093] (1);

[0094] Momentum conservation equation:

[0095] (2);

[0096] in, For density, It is a velocity vector. For time, It is the identity matrix. For dynamic viscosity, For Hamiltonian operators, For matrix transpose, To calculate the current density in the computational domain, For magnetic flux, It is the acceleration due to gravity. For pressure;

[0097] Because of the coupling between the flow field, current field, and electromagnetic field, the Lorentz force generated by the electromagnetic field... It is gravity.

[0098] The constructed flow field governing equations fully consider the influence of Lorentz force and gravity on fluid flow in the plasma discharge channel. By accurately simulating the pressure gradient and velocity field distribution, these governing equations can more accurately reflect the flow state in the discharge channel, improving the reliability of the simulation results.

[0099] In practical applications, the governing equations for the heat transfer field are:

[0100] (3);

[0101] in, For density, For constant pressure heat capacity, For temperature, For time, It is a velocity vector. For Hamiltonian operators, Thermal conductivity, For electric field, Boltzmann's constant, For electron charge, To calculate the current density in the computational domain, The net volumetric emissivity;

[0102] Joule heating is generated by the current field due to the coupling between the current field and the heat transfer field. Indicates enthalpy transfer; This represents the net radiation loss by volume.

[0103] The constructed heat transfer field governing equations comprehensively consider the heat generation and transfer processes in electrical discharge machining (EDM). Joule heating simulates the heat generated by current passing through plasma, enthalpy transfer describes the diffusion of heat in different regions, and net volumetric radiation loss accounts for radiation loss in high-temperature plasma. By considering these processes, the accuracy of temperature field prediction and the reliability of material removal simulation results are improved.

[0104] In practical applications, the current field control equation is:

[0105] (4);

[0106] (5);

[0107] (6);

[0108] In the formula, For Hamiltonian operators, For electric potential, To calculate the electrical conductivity of the material in the computational domain, To calculate the current density in the computational domain, It is an electric field.

[0109] The constructed current field control equations comprehensively consider the distribution characteristics of current in the plasma discharge channel, including electric field distribution, dielectric conductivity variation, and spatial distribution of current density, and can accurately predict the changes in current during the discharge process.

[0110] In practical applications, the electromagnetic field control equations are as follows:

[0111] (7);

[0112] (8);

[0113] in, For Hamiltonian operators, Relative permeability The magnetic vector potential, To calculate the electrical conductivity of the material in the computational domain, For electric potential, It represents magnetic flux.

[0114] The constructed electromagnetic field control equations can accurately calculate the electromagnetic field distribution, ensuring simulation accuracy.

[0115] Furthermore, the implementation method for applying multiphysics governing equations to a two-dimensional axisymmetric geometric model is as follows:

[0116] The flow field control equation is applied to the interelectrode medium region, while the heat transfer field control equation, current field control equation, and electromagnetic field control equation are all applied to the regions where the cathode, interelectrode medium, and anode are located.

[0117] The reason for setting different application regions lies in the differences in the characteristics and range of influence of each physical field. First, the flow field governing equations apply to the interelectrode medium region because the flow field mainly describes the flow behavior within the medium. The flow characteristics during plasma discharge mainly occur within the medium, and the influence of the Lorentz force on the flow is also reflected in this region. Therefore, the flow field equations are mainly used to describe the flow state of the medium, thereby affecting temperature and pressure parameters. Second, the heat transfer field governing equations, current field governing equations, and electromagnetic field governing equations apply to the regions where the cathode, interelectrode medium, and anode are located because these regions all involve the generation and transfer of heat, the flow of current, and the effect of magnetic fields.

[0118] This regional division allows for a precise description of the physical phenomena and interactions within each region, thereby improving the accuracy and reliability of the simulation model. The flow field equations ensure accurate simulation of the medium flow, while the heat transfer, current, and electromagnetic field equations guarantee that the interactions of heat, current, and electromagnetic effects are fully considered in all involved regions, providing a precise physical basis for the final material removal process.

[0119] S3. Set the material properties, physical boundary conditions, and initial environmental conditions for each region in the multiphysics coupling simulation model; specifically...

[0120] Setting the material properties for each region includes:

[0121] The cathode material is set to tungsten, the anode material to stainless steel, and the inter-electrode medium to air, with constraints imposed on the conductivity of the inter-electrode medium;

[0122] The constraint is: when season ;when ,make ;

[0123] in, Indicates temperature The conductivity of the inter-electrode dielectric varies with temperature. =1S / m, which is the set minimum conductivity;

[0124] The physical boundary conditions for each region are as follows:

[0125] Set the upper, lower, left, and right boundaries of the region where the cathode is located as AB, GHI, AG, and BI, respectively;

[0126] Set the upper, lower, left, and right boundaries of the anode region as EF, DC, ED, and FC, respectively;

[0127] The left and right boundaries of the region where the inter-electrode medium is located are set as GE and IF, respectively; and GHI and EF are also used as the upper and lower boundaries of the region where the inter-electrode medium is located, respectively.

[0128] Of all the boundaries, boundary GHI is composed of a curve and a straight line, and all the remaining boundaries are straight lines. Boundaries AG, GE and ED are on the same straight line, and boundaries BI, IF and FC are on the same straight line.

[0129] In the flow field, boundaries GHI and EF are no-slip boundaries, where the fluid velocity is 0, and boundary IF is in an open state.

[0130] In the temperature field, the temperatures of boundaries AB, DC, BI, IF, and FC are all set to 1000K, and an energy exchange term between the cathode and the plasma discharge channel is set on boundary GHI. An energy exchange term between the anode and the plasma discharge channel is set on the boundary EF. ;and

[0131] (9);

[0132] (10);

[0133] (11);

[0134] (12);

[0135] in, For electron current density, The ion current density, The work function of the cathode material. For electric field, The ionization potential of the plasma is denoted as . The emission coefficient of the cathode surface, The Stefan-Boltzmann constant is given. For temperature;

[0136] To calculate the current density in the computational domain, Let be the work function of the anode material. The anode surface emissivity;

[0137] The thermionic emission current density, The thermionic emission constant of the cathode, For electron charge, Work function of cathode material This is an electric field correction term. Boltzmann's constant, For electric field, The vacuum permittivity, It is a unit vector;

[0138] In a current field, the boundary DC is considered as the current flowing into the boundary, and its input current density is... ,in, For the magnitude of the current, The anode radius is defined, with boundary DC and FC connected to power supply ground, and boundary BI and IF electrically insulated. ;

[0139] In the electromagnetic field, the boundaries AB, BI, IF, FC, and DC are all magnetically insulated, that is... ;

[0140] Initial environmental conditions include: initial flow velocity of 0, initial flow pressure of standard atmosphere, initial temperature of 293.15K, reference impedance of current field of 50Ω, initial electric potential of current field of 0Ω, and initial magnetic vector potential of electromagnetic field of 0Ω.

[0141] S4. Mesh the multiphysics coupling simulation model;

[0142] For details, see Figure 3 The specific implementation method for mesh generation of the multiphysics coupled simulation model is as follows:

[0143] When meshing the regions containing the cathode and anode, the range of side lengths for the resulting polygonal mesh is as follows: to ;

[0144] When meshing is performed in the region containing the interpolar medium, the range of side lengths for the resulting polygonal mesh is as follows: to ;

[0145] The surrounding areas of boundaries GHI and EF are further refined, and the side lengths of the resulting polygonal mesh range from [value missing]. to .

[0146] During mesh generation, refining the interelectrode medium region and some boundaries can significantly improve simulation accuracy, especially in regions where physical properties such as current, electric field, and temperature gradient change drastically. By refining the mesh, local variations can be captured more accurately, improving the calculation accuracy of key parameters such as heat flux density and pressure distribution. Furthermore, refining the mesh only in areas of significant physical change improves computational efficiency and avoids resource waste.

[0147] S5. Based on the transient solver, the multiphysics coupling simulation model after meshing is simulated to obtain the heat flux density distribution, pressure distribution, pressure radius distribution, and heat flux density radius distribution on the anode surface.

[0148] In practical applications, when the transient solver performs simulation calculations, the time step of the output data is set using a piecewise strategy, specifically as follows:

[0149] Greater than or equal to and less than or equal to Within the time interval, the time step of the output data is ;

[0150] In greater than and less than or equal to Within the time interval, the time step of the output data is ;

[0151] In greater than Within the time interval, the time step of the output data is ;

[0152] The above-mentioned preferred method adopts a segmented strategy, which can dynamically adjust the calculation accuracy and efficiency according to different stages of the discharge process.

[0153] S6. Substitute the maximum values ​​of the heat flux density distribution and pressure distribution on the anode surface, as well as the pressure radius distribution and heat flux density radius distribution on the anode surface, into the material erosion simulation model to calculate the temperature field distribution on the anode surface.

[0154] Figure 4 A schematic diagram of the temperature field distribution of the anode surface material at different times during the etching process is given;

[0155] Specifically, the method for obtaining the temperature field distribution on the anode surface is as follows:

[0156] The maximum heat flux density and the radius distribution of the heat flux density on the anode surface are input into the heat source term of the material erosion simulation model, and the maximum pressure on the anode surface and the radius distribution of the pressure on the anode surface are input into the volume force term of the material erosion simulation model to obtain the temperature field distribution on the anode surface; wherein, the material erosion simulation model is the existing technology.

[0157] Figure 5 The curves showing the maximum heat flux density on the anode surface of the plasma discharge channel at different times are presented.

[0158] S7. Based on the temperature field distribution on the anode surface, obtain the geometric contour, diameter, and depth of the pits on the anode surface; specifically,

[0159] Solid regions are identified within the surface temperature field distribution, and the contours of these solid regions serve as the geometric contours of the pits on the anode surface. The solid fraction of the material in these solid regions is... ;

[0160] The geometric contour of the pit on the anode surface is projected, and the diameter of the equivalent circle of the projection surface is taken as the diameter of the pit.

[0161] The depth of the pit is defined as the depth of the center point within the geometric contour of the pit on the anode surface.

[0162] This preferred method can accurately reflect the temperature field and solid region contour changes of the material at different times, and accurately obtain the geometric contour of the pit. In addition, the use of projection to calculate the pit diameter and the use of the depth value of the pit center point as the pit depth ensures the accurate quantification of the pit morphology, which helps to more realistically simulate the etching effect in the electrical discharge machining process.

[0163] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for simulation of anode surface material erosion based on a plasma discharge channel, characterized in that, The method comprises: S1. According to the geometric characteristics of an actual discharge device, a two-dimensional axisymmetric geometric model of a plasma discharge channel is established by using simulation software, the two-dimensional axisymmetric geometric model comprising three regions of a cathode, an inter-electrode medium and an anode; S2. According to a multi-physical field coupling relationship, a physical field control equation is constructed, and the multi-physical field control equation is applied to the two-dimensional axisymmetric geometric model to obtain a multi-physical field coupling simulation model; the multi-physical field is four physical fields, which are a flow field, a heat transfer field, a current field and an electromagnetic field; S3. Material properties of each region in the multi-physical field coupling simulation model, physical boundary conditions of each region and initial environmental conditions are set; S4. The multi-physical field coupling simulation model is meshed; S5. The meshed multi-physical field coupling simulation model is simulated based on a transient solver to obtain anode surface heat flux density distribution, anode surface pressure distribution, anode surface pressure radius distribution and anode surface heat flux density radius distribution; S6. Maximum values in the anode surface heat flux density distribution and the anode surface pressure distribution, and the anode surface pressure radius distribution and the anode surface heat flux density radius distribution are substituted into a material ablation simulation model for calculation to obtain anode surface temperature field distribution; S7. According to the anode surface temperature field distribution, a geometric profile of an anode surface pit, a diameter of the pit and a depth of the pit are obtained.

2. The method of claim 1, wherein the method is performed by a computer system. The flow field control equation comprises: a continuity equation: （1）； a momentum conservation equation: （2）； wherein is the density, is the velocity vector, is the time, is the identity matrix, is the dynamic viscosity, is the Hamiltonian operator, is the matrix transpose, is the current density of the computational domain, is the magnetic flux, is the gravitational acceleration, is the pressure.

3. The method of claim 1, wherein the method is performed by a computer system. the heat transfer field control equation is: （3）； where, is the density, is the constant pressure heat capacity, is the temperature, is the time, is the velocity vector, is the Hamiltonian operator, is the thermal conductivity, is the electric field, is the Boltzmann constant, is the electron charge, is the current density in the computational domain, is the volume net radiation coefficient.

4. The method of claim 1, wherein the method is performed by a computer system. the current field control equation is: （4）； （5）； （6）； wherein is a Hamiltonian operator, is an electric potential, is a conductivity of the material of the calculation domain, is a current density of the calculation domain, is an electric field.

5. The method of claim 1, wherein the method further comprises: the electromagnetic field control equation is: （7）； （8）； wherein, is a Hamiltonian operator, is a relative magnetic permeability, is a magnetic vector potential, is a conductivity of the material of the calculation domain, is an electric potential, is a magnetic flux.

6. The method of claim 1, wherein the method is performed by a computer system. In step S2, the multi-physical field control equation is applied to the two-dimensional axisymmetric geometric model in the following manner: the flow field control equation is applied to the inter-electrode medium region, and the heat transfer field control equation, the current field control equation and the electromagnetic field control equation are all applied to the regions of the cathode, the inter-electrode medium and the anode.

7. The method of claim 1, wherein the method is performed by a computer system. In step S3, the material properties of each region are set as follows: the cathode material is tungsten, the anode material is stainless steel, the inter-electrode medium is air, and the conductivity of the inter-electrode medium is constrained; the constraint condition is: When time, cause ; When , let ; wherein represents the temperature under which the inter-electrode medium conductivity, = 1 S / m, is the set minimum conductivity; the physical boundary conditions of each region are: the upper, lower, left and right boundaries of the region where the cathode is located are set as AB, GHI, AG and BI respectively; the upper, lower, left and right boundaries of the region where the anode is located are set as EF, DC, ED and FC respectively; the left and right boundaries of the region where the inter-electrode medium is located are set as GE and IF respectively; and GHI and EF are also set as the upper and lower boundaries of the region where the inter-electrode medium is located respectively; of all the boundaries, boundary GHI is a combination of a curve and a straight line, and all the remaining boundaries are straight lines, and boundaries AG, GE and ED are on the same straight line, and boundaries BI, IF and FC are on the same straight line; in the flow field, boundaries GHI and EF are no-slip boundaries, and the fluid motion velocity value thereon is 0, and boundary IF is in an open state; In the temperature field, the temperature of the boundaries AB, DC, BI, IF, FC is set to 1000 K, the energy exchange term between the cathode and the plasma discharge channel is set on the boundary GHI , the energy exchange term between the anode and the plasma discharge channel is set on the boundary EF ; and （9）； （10）； （11）； （12）； wherein is the electron current density, is the ion current density, is the work function of the cathode material, is the electric field, is the ionization potential of the plasma, is the cathode surface emission coefficient, is the Stefan-Boltzmann constant, is the temperature; is the current density in the domain, is the work function of the anode material, is the anode surface emission coefficient; is the thermionic emission current density, is the cathode thermionic emission constant, is the electron charge, is the cathode material work function, is the electric field correction term, is the Boltzmann constant, is the electric field, is the vacuum permittivity, is the unit vector; In the current field, the boundary DC is taken as the current inflow boundary, and the current density input by it wherein, is the current size, is the anode radius size, the boundary DC and FC are connected to the power supply ground, and the boundaries BI and IF are electrically insulated; in the electromagnetic field, boundaries AB, BI, IF, FC and DC are magnetically insulated. Initial environmental conditions: including the initial velocity of the flow field is 0, the initial pressure of the flow field is standard atmospheric pressure, the initial temperature of the heat field is 293.15 K, the reference impedance of the current field is 50, the initial potential of the current field is 0, and the initial magnetic vector potential of the electromagnetic field is 0.

8. The method of claim 1, wherein the method is performed by a computer system. The specific implementation manner of the grid division on the multi-physical field coupling simulation model in step S4 is as follows: When the area where the cathode and the anode are located is meshed, the length of each side of the polygonal mesh formed ranges from to ; When the region where the inter-electrode medium is located is meshed, the length of each side of the polygonal mesh formed ranges from to ; The peripheral regions of the boundary GHI and EF are further refined, and the length of each side of the polygonal mesh formed thereby is in the range of to .

9. The method of claim 1, wherein the method is performed by a computer system. The implementation manner of obtaining the anode surface temperature field distribution in step S6 is as follows: The maximum value of the anode surface heat flux density and the anode surface heat flux density radius distribution are input into the heat source term of the material erosion simulation model, the maximum value of the anode surface pressure and the anode surface pressure radius distribution are input into the volume force term of the material erosion simulation model, and the anode surface temperature field distribution is obtained.

10. The method of claim 1, wherein the method is performed by a computer system. The implementation manner of obtaining the geometric profile of the anode surface pit, the diameter of the pit and the depth of the pit according to the anode surface temperature field distribution in step S7 is as follows: identifying a solid state region in the surface temperature field distribution, and the contour of the solid state region as the geometric contour of the anode surface crater, the solid state region material solid phase fraction ; The geometric profile of the anode surface pit is projected, and the equivalent circle diameter of the projection plane is taken as the pit diameter; The depth value of the center point in the geometric profile of the anode surface pit is taken as the pit depth.

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