Design method of working tooth and profile of large-caliber gun deep rifling electrolytic machining cathode

Abstract

The application belongs to the technical field of electrolytic processing, and particularly relates to a large-caliber gun deep rifling electrolytic processing cathode working tooth and profile design method. The tail fin section is arranged at the end of the large end of the working tooth, the end face of the tail fin section is inwardly recessed to form a tail fin shape, and the circular arc line of the recessed part is tangent to the circumferential surface of the cathode body. The application improves the deep rifling R angle forming precision, completes the rifling size design precision, improves the large-caliber barrel rifling electrolytic processing cathode design precision, shortens the tail fin cathode profile design cycle, reduces the development cost, improves the consistency of the anode surface current density distribution and the actual processing working condition, provides a more reliable physical basis for the cathode design, effectively reduces the iteration times, significantly shortens the cathode design cycle, and guarantees the design precision and reduces the development cost.

Description

Technical Field

[0001] This invention belongs to the field of electrolytic machining technology, specifically relating to a method for electrolytic machining of cathode working teeth and profile design for deep rifling of large-caliber artillery. Background Technology

[0002] In modern warfare, artillery barrels possess core functions integrating precision strikes, fire suppression, system integration, and strategic deterrence, far exceeding any previous era. As a key component for achieving high-speed, stable projectile rotation, the rifling precision directly impacts artillery firing accuracy, significantly affecting barrel erosion, wear resistance, and lifespan. To meet the high-precision, high-stability, and long-life requirements of next-generation artillery barrels under extreme service conditions, ultra-high-strength and high-toughness gun steel has become the preferred material for large-caliber artillery barrels. However, mechanical broaching of new ultra-high-strength and high-toughness gun steel suffers from low processing efficiency, severe tool wear, and unsatisfactory barrel bore surface quality, making it difficult to meet the urgent needs of new large-caliber weapon systems.

[0003] Electrolytic machining, as an advanced special machining technology based on electrochemical anodic dissolution, has advantages such as zero tool cathode wear, high processing efficiency, no burrs, good surface quality, and low batch processing cost. It has important military application value and broad market application prospects in fields such as weaponry, oil drilling and extraction, and aerospace.

[0004] The structure of a conventional rifling electrolytic machining cathode includes a cathode body, a front guide, a liquid supply hole, an insulating sleeve, working teeth, and a rear guide. The working teeth are typically cylindrical structures with gradually changing dimensions, and their end faces are flat. Patent publication number "CN116673553B" discloses a "Multi-tooth Segmented Electrolytic Machining Cathode and Tooling for Large-caliber Artillery Barrel Rifling," providing a multi-tooth segmented cathode working tooth structure. Different segments of the working teeth have different profile parameters and are fixed in series via wedge keyways and wedge keys. Because the segmented structure relies solely on wedge keys for connection, it lacks measures to ensure the continuity of the profile between segments, leading to axial misalignment or radial steps between adjacent segments of the working teeth, resulting in a decrease in rifling machining accuracy. Patent publication number "CN108672855B" discloses a "Replaceable Working Teeth Large-caliber Complex Helical Electrolytic Machining Cathode," whose working teeth are three-sided feed cone structures, evenly distributed circumferentially, and mounted on the cathode body for complete replacement. Because the replaceable structure lacks self-positioning or error-proofing design, the alignment of the new tooth with the front and rear guides after replacing the working tooth depends on assembly precision, which can easily lead to misalignment and affect machining quality. Patent publication number "CN108746900B" discloses a "High-Efficiency Precision Electrolytic Machining Cathode for Titanium Alloy Barrel Rifling," which provides an integral conical working tooth with an increasing diameter from front to back, and tooth side inclination angles α=10°~15° on both sides forming a three-sided feed structure; the front end of the working tooth has an inverted conical step that cooperates with the front guide wedge-shaped positioning ring. Since this design is only for titanium alloys, its applicability to other materials such as gun steel and high-temperature alloys has not been verified, resulting in unclear material versatility and limiting the widespread application of the cathode.

[0005] Meanwhile, existing technologies also have the following problems in the design of the cathode structure. Patent publication number "CN116372290B" discloses a "Method for Designing the Cathode Profile of the Stator Electrolytic Machining of All-Metal Oil Screw Drill Tool," which adopts... "The spline inner contour integration method is used to design the stator cathode profile of an all-metal oil screw drill bit. However, this method only fits the geometric gap and curvature compliance, without considering the coupling effects of multiple physical fields such as electric field, flow field, and temperature field in electrolytic machining. This results in a disconnect between the gap design and the actual electrochemical dissolution process. Patent publication number CN121118343A discloses a method for designing a precision electrolytic machining cathode under multi-field coupling. This method uses multi-physics co-simulation to predict changes in machining gap and optimize the cathode design. However, the two-dimensional multi-physics simulation model along the flow direction cannot fully reflect the complex changes in electrolyte flow, bubble distribution, and temperature gradient in three-dimensional space, resulting in oversimplification and insufficient simulation accuracy. Patent publication number CN117680782B..." The document "A Precision Electrolytic Machining Cathode Profile Design Optimization Method for Aero-engine Blades" discloses a method that uses multi-physics coupled simulation to solve for the current density distribution. The method uses the average and variance of the current density around the blade profile as the objective function and employs a differential evolution algorithm to optimize the offset of the control points on the cathode profile curve. However, the differential evolution algorithm suffers from problems such as high iteration count and computational cost when the number of control points is large, and the lack of geometric continuity constraints on the cathode profile changes during optimization, leading to slow convergence and the potential for discontinuous profile structures.

[0006] In summary, existing electrolytic machining cathode profile design methods fail to adequately consider the concentrated effect of the electric field at the tooth edge and the dynamic evolution characteristics of the flow field during machining. This results in a significant structural mismatch between the cathode profile and the actual physical field, leading to low rifling forming accuracy. Furthermore, during the electrolytic machining of deep rifling in large-caliber artillery, the small machining gap, complex flow field in the machining area, and significant coupling effects of multiple physical fields such as electric field, flow field, and temperature field make it difficult to guarantee the forming accuracy of deep rifling.

[0007] Therefore, there is an urgent need to provide a new type of cathode working tooth and a precise profile design method to ensure the forming accuracy of deep rifling in the electrolytic machining process of large-caliber artillery. Summary of the Invention

[0008] This invention addresses the shortcomings of existing technologies in effectively improving the forming accuracy of large-caliber deep rifling by proposing a method for designing the cathode working teeth and profile of deep rifling in large-caliber artillery through electrolytic machining.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: a cathode working tooth for electrolytic machining of deep rifling in a large-caliber artillery, wherein a tail fin section is extended at the end of the large end of the working tooth, the end face of the tail fin section is concave inward to form a tail fin shape, and the arc of the concave part is tangent to the circumferential surface of the cathode body.

[0010] Furthermore, the above-mentioned method for designing the cathode working tooth profile of electrolytic machining for deep rifling in large-caliber artillery includes the following steps:

[0011] Step 1: Perform 3D parametric modeling of the working teeth:

[0012] In the simulation software, a three-dimensional parametric model corresponding to the working tooth is established based on the defined design variables. The working tooth includes a body segment and a tail fin segment located at the tail end of the body segment. The design variable vector is defined as follows:

[0013]

[0014] in, This refers to the axial length of the body segment. The width of the small end of the body segment. The width of the larger end of the body segment. The radius of the small end of the body segment. The radius of the large end of the body segment. This refers to the axial length of the caudal fin segment. H is the arc length of the inward concavity of the caudal fin segment, H is the depth of the large end of the working tooth, and h is the depth of the small end of the working tooth. The semi-cone angle of the working teeth. The inward angle of the working tooth of the tail fin cathode;

[0015] Step 2: Use the coefficient of variation of the current density on the anode surface as the objective function;

[0016] Step 3: First, establish a multiphysics mathematical model, including the electric field control equation, the flow field control equation, and the temperature field control equation, and then modify the multiphysics mathematical model.

[0017] Step 4: Introduce adjoint variables into the multiphysics mathematical model Constructing the Lagrange functional:

[0018]

[0019] Through the Find the variational derivation of the adjoint equation and boundary conditions. The adjoint equation is: The accompanying boundary conditions include those on the anode boundary. At the cathode boundary On the insulating boundary ;

[0020] Step 5: Based on the adjoint theory, derive the sensitivity expression of the objective function with respect to the design variables, and obtain the cathode surface sensitivity density function and gradient formula:

[0021]

[0022]

[0023] in The normal potential gradient of the cathode surface. The adjoint field gradient is the normal direction of the cathode surface, where The geometric sensitivity of the cathode surface normal displacement to design variables;

[0024] Step 6: Establish a three-dimensional multiphysics coupled simulation model, set the boundary conditions of each physical field, iteratively solve to obtain the current density distribution on the anode surface, solve the accompanying problem to obtain the accompanying field distribution, and calculate the gradient of the objective function with respect to the design variables.

[0025] Step 7: Update the design variables and iterate until the convergence condition is met to obtain the optimized design variables.

[0026] Furthermore, in step two above, the coefficient of variation of the current density at the anode surface is:

[0027]

[0028] in This represents the total number of sampling points on the anode surface. For the first Normal current density at each sampling point This is the average current density at all sampling points.

[0029] Furthermore, in step three above, the formula for the mathematical model of electrolyte conductivity based on multiphysics correction is as follows:

[0030]

[0031] in, The initial electrolyte conductivity, This represents the volume fraction of hydrogen bubbles. This refers to the concentration of the solid product. For temperature coefficient, This is the initial electrolyte temperature.

[0032] Furthermore, in step six above, the specific steps for establishing the three-dimensional multiphysics coupled simulation model are as follows:

[0033] Step 6.1: Set boundary conditions for each physics field: Add relevant simulation parameters and control variables, and define the control variables under the defined node:

[0034] The formula for adding the objective function integral operator is:

[0035]

[0036] in For the integral operator defined on the anode surface, The local normal current density on the anode surface. This represents the average current density at the anode surface.

[0037] Step 6.2: Based on the three-dimensional cathode profile model generated in Step 1, an electrolyte fluid domain is generated on the upper surface of the cathode using the equal gap theory. The upper surface of the fluid domain represents the anode boundary.

[0038] Step 6.3: Set the boundary conditions and relevant simulation parameters for the electric-current-thermal physical field:

[0039] Electrolyte conductivity in electric field model Set to:

[0040]

[0041] The boundary conditions include the applied operating voltage at the anode. The cathode is grounded, and the remaining boundaries are set to insulation; the flow field model adopts a three-phase gas-liquid-solid turbulent flow model.

[0042] The relevant simulation parameters include the cathode hydrogen evolution mass source. Solid product quality source :

[0043] The cathode hydrogen evolution mass source Set by the following formula:

[0044]

[0045] The solid product quality source Set by the following formula:

[0046]

[0047] in Here is the molar mass of hydrogen. The normal current density at the cathode boundary. The molar mass of the solid product. The local current density on the anode surface. The number of electrons in the reaction. The constant is Faraday's constant; the flow field boundary conditions include inlet pressure p and outlet pressure p. The remaining boundaries are set as walls with no slip, i.e., u is 0; the temperature field model adopts the Joule heating model, and the boundary conditions include the inlet temperature. Other boundaries are set to thermal insulation;

[0048] Step 6.4: Mesh generation. The cathode domain uses a tetrahedral mesh, and the electrolyte fluid domain uses a dense hexahedral mesh. Boundary layer meshes are set on the upper surface of both the cathode domain and the upper surface of the electrolyte fluid domain.

[0049] Step 6.5: Set up the research steps. Add a steady-state node and an associated sensitivity analysis node under the research steps. Under the associated sensitivity analysis node, set the design variables in Step 6.1 as control variables and set initial values ​​and boundary constraints. Solve separately. The steady-state node extracts the anode surface current density, and the associated sensitivity analysis node extracts the anode surface associated field gradient.

[0050] Furthermore, the specific steps in step seven above are as follows:

[0051] Step 7.1: Set initial design variables And give boundary constraints for each variable. Choose the initial step size Convergence tolerance Maximum number of iterations Line search for contraction factor Maximum number of iterations for linear search minimum step size , prevent zero small amount ;

[0052] Step 7.2: Execute step six to obtain the gradient under the current design variables. A backtracking search is used to determine a suitable step size, thus determining the optimal step size. ;

[0053] Step 7.3: Update design variables and project them onto the boundary:

[0054] First, calculate the trial point, determined by the following formula:

[0055]

[0056] Then, boundary projection is performed on each component, and its boundary constraints are determined by the following equation:

[0057]

[0058] Step 7.4: Calculate the relative change of the objective function, determined using the following formula:

[0059]

[0060] in, In the new design variables If the value obtained in step six is ​​not satisfied by any of the following convergence conditions, then continue executing step six; otherwise, if any of the following conditions are satisfied, then stop iterating:

[0061]

[0062]

[0063] Obtain the optimized design variables.

[0064] Compared with the prior art, the beneficial effects of the present invention are:

[0065] 1. This invention proposes a tail fin-type cathode working tooth. A tail fin-type working tooth is designed at the tail end of the conventional rifling electrolytic machining cathode working tooth. Because the sharp corner of the tail fin-type working tooth has a small radius of curvature, it can generate an electric field concentration effect in this local area. According to electromagnetic field theory, the electric field strength on the conductor surface is inversely proportional to the radius of curvature, and the electric field strength at the sharp corner is significantly increased. When the tail fin-type working tooth passes through the rifling radius (R-angle) region, the local current density increases sharply, resulting in high-speed dissolution of the residual material at the root. This profile structure allows for secondary processing of the already formed rifling radius (R-angle) region after the rifling body section has been formed, further reducing the R-angle and thus improving the forming accuracy of the deep rifling radius (R-angle), achieving the desired rifling dimensional design accuracy.

[0066] 2. This invention proposes a design method for the working tooth profile of the cathode in electrolytic machining of deep rifling in large-caliber artillery. This method improves the design accuracy of cathodes in electrolytic machining of large-caliber barrel rifling, shortens the design cycle of tail fin cathode profiles, and reduces development costs. This method constructs an electro-current-thermal multiphysics coupled model through strong coupling solution, simulating the dynamic distribution of current density, electrolyte flow rate, bubble volume fraction, solid product concentration, and temperature within the machining gap. It also introduces nonlinear corrections for conductivity based on bubble rate, solid product concentration, and temperature, thus more realistically reflecting the dynamic changes in gap conductivity during electrolytic machining. This improves the consistency between the current density distribution on the anode surface and the actual machining conditions, providing a more reliable physical basis for cathode design. Based on this, the precise gradient of the objective function with respect to design variables is obtained based on the current density distribution on the anode surface. Iterative optimization of cathode geometric parameters effectively reduces the number of iterations, significantly shortening the cathode design cycle while ensuring design accuracy and reducing development costs. Attached Figure Description

[0067] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0068] Figure 2 This is a cross-sectional view of the gun barrel rifling, where L is the width of the groove; R is the radius of the groove's R-angle; R 阴 R is the radius of the bearish line. 阳 The radius of the bullish candlestick;

[0069] Figure 3 The diagram shows the working teeth of the tail fin cathode, with each design variable marked. The working teeth of the tail fin section are concave inward to form an arc-shaped profile.

[0070] Figure 4 This is a schematic diagram of a tail fin cathode.

[0071] The attached diagram is labeled as follows: 1-Cathode body, 2-Front guide, 3-Sealing ring, 4-Liquid supply hole, 5-Insulating sleeve, 6-Working tooth, 7-Rear guide, 8-Pyramid. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0073] See Figure 4 A cathode for electrolytic machining of deep rifling in a large-caliber artillery piece has a conventional structure including 1. a cathode body; 2. a front guide; 3. a sealing ring; 4. a liquid supply hole; 5. an insulating sleeve; 6. a working tooth; 7. a rear guide; and 8. a prism. This invention features a structural design for the working tooth 6, which includes a body section and a tail fin section at the tail end of the body section. The body section has a tapered diameter structure, including a large end and a small end. The tail fin section extends from the large end of the working tooth 6, and its end face is concave inward to form a tail fin shape. The arc of the concave area is tangent to the circumferential surface of the cathode body 1.

[0074] Based on the structural improvement of the core structure - working tooth 6, the design idea for its profile is: to construct a multi-physics coupled simulation model, define design variables, take the uniformity of current density on the anode surface as the objective function, use the adjoint theory to quickly calculate the gradient of key geometric parameters, and achieve quantitative optimization of key geometric parameters of the tail fin cathode through iterative optimization, thereby effectively improving the forming accuracy.

[0075] This invention proposes a method for designing the cathode profile of the tail fin type in electrolytic machining of deep rifling in large-caliber artillery, such as... Figure 1 As shown, the specific steps are as follows:

[0076] Step 1: Perform 3D parametric modeling of the working teeth:

[0077] The working tooth 6 includes a body segment and a caudal fin segment at the large end of the body segment. The design variable vector is defined as follows:

[0078]

[0079] like Figure 3 As shown, where The axial length of the working tooth 6. The width of the small end of the working tooth is 6. The width of the large end of the body section of the working tooth 6 is... The radius of the small end of the body segment of the working tooth 6 is... The main working teeth have a large end radius of 6. The axial length of working tooth 6 in the caudal fin segment. H represents the arc length of the inward concavity formed by the surface of the working tooth 6 in the caudal fin segment; H represents the depth of the large end of the main working tooth 6; and h represents the depth of the small end of the main working tooth 6. The semi-cone angle of the working tooth 6 of the tail fin cathode. The potential angle of the working tooth of the tail fin cathode.

[0080] Set the initial values ​​for the design variables and the boundary constraints, where the initial values ​​are respectively taken as follows: 40mm 2mm 4mm 154mm It is 154.5mm. 12mm H is 15mm, H is 2mm, and h is 1.5mm. 2.5° The angle is 15°; the boundary constraints are respectively taken as follows: mm mm mm mm mm mm mm mm mm , mm.

[0081] Step 2: Use the coefficient of variation of the current density at the anode surface as the objective function;

[0082] The coefficient of variation of the current density on the anode surface is in the form of:

[0083]

[0084] in, This represents the total number of sampling points on the anode surface. For the first Normal current density at each sampling point This is the average current density across all sampling points.

[0085] Step 3: First, establish a multi-physics coupled mathematical model, including the electric field control equation, the flow field control equation, and the temperature field control equation. Due to the small processing gap, complex flow field state, and large amount of erosion in deep rifling electrolytic machining, and considering the influence of bubble rate, solid product concentration, and temperature on conductivity, the mathematical model is then modified.

[0086] 3.1 Establishing a multiphysics coupling mathematical model:

[0087] The governing equation for the electric field is the Laplace equation:

[0088]

[0089] in For gradient operators, The electrolyte conductivity, The electric potential is used; the governing equations for the flow field are the Navier-Stokes equations for incompressible fluids:

[0090]

[0091] in The electrolyte density, For flow velocity vectors, Electrolyte pressure, Let be the dynamic viscosity. The governing equation for the temperature field is:

[0092]

[0093] in Here, T represents the specific heat capacity of the electrolyte, and T represents the electrolyte temperature. Thermal conductivity, This is the Joule heat source term.

[0094] 3.2 Modified Mathematical Model:

[0095] The corrected mathematical model for electrolyte conductivity is as follows:

[0096]

[0097] in The initial electrolyte conductivity, This represents the volume fraction of hydrogen bubbles. This refers to the concentration of the solid product. For temperature coefficient, This represents the initial electrolyte temperature.

[0098] Step 4: Introduce adjoint variables into the multiphysics mathematical model Constructing the Lagrange functional:

[0099]

[0100] Through the Find the variational derivation of the adjoint equation and boundary conditions. The adjoint equation is: The accompanying boundary conditions include those on the anode boundary. At the cathode boundary On the insulating boundary ;

[0101] Step 5: Based on the adjoint theory, derive the sensitivity expression of the objective function in Step 2 with respect to the design variables, and obtain the cathode surface sensitivity density function and gradient formula:

[0102]

[0103]

[0104] in The normal potential gradient of the cathode surface. The adjoint field gradient is the normal direction of the cathode surface, where This represents the geometric sensitivity of the cathode surface normal displacement to design variables.

[0105] Step 6: Establish a three-dimensional multiphysics coupled simulation model, set the boundary conditions for each physics field, iteratively solve to obtain the current density distribution on the anode surface, solve the adjoint problem to obtain the adjoint field distribution, and calculate the gradient of the objective function with respect to the design variables; specifically including the following sub-steps:

[0106] Step 6.1: Add relevant simulation parameters and control variables. Define the control variables under the definition node and add the objective function integration operator, set by the following formula:

[0107]

[0108] in For the integral operator defined on the anode surface, The local normal current density on the anode surface. This represents the average current density at the anode surface.

[0109] Step 6.2: Based on the three-dimensional cathode profile model generated in Step 1, an electrolyte fluid domain is generated on the upper surface of the cathode using the equal gap theory. The upper surface of the fluid domain represents the anode boundary.

[0110] Step 6.3: Set the boundary conditions and relevant simulation parameters for the electric-current-thermal physical field:

[0111] Electrolyte conductivity in electric field model Set to:

[0112]

[0113] The boundary conditions include the applied operating voltage at the anode. Cathode grounded, all other boundaries set as insulation, operating voltage 12V, initial conductivity It is 20 S / m.

[0114] The flow field model adopts a three-phase gas-liquid-solid turbulent flow model, with the inlet pressure p set between 1 MPa and 1.2 MPa, and the bubble diameter being [missing information]. m, the diameter of the solid product is m,

[0115] The relevant simulation parameters include the cathode hydrogen evolution mass source. Solid product quality source :

[0116] The cathode hydrogen evolution mass source Set by the following formula:

[0117]

[0118] The solid product quality source Set by the following formula:

[0119]

[0120] in Here is the molar mass of hydrogen. The normal current density at the cathode boundary. The molar mass of the solid product. The local current density on the anode surface. The number of electrons in the reaction. ρ is the Faraday constant. The flow field boundary conditions include the inlet pressure p and the outlet pressure p. The remaining boundaries are set as walls with no slip, i.e., u is 0. The temperature field model adopts the Joule heating model, and the boundary conditions include the inlet temperature. Other boundaries are set to adiabatic, and the inlet temperature is... It is 293K.

[0121] Step 6.4: Mesh generation. Tetrahedral mesh is used for the cathode domain, and a dense hexahedral mesh is used for the electrolyte fluid domain. Boundary layer meshes are set on the upper surface of both the cathode domain and the electrolyte fluid domain.

[0122] Step 6.5: Set up the research step. Under the research step, add a steady-state node and an associated sensitivity analysis node. Under the associated sensitivity analysis node, set the design variables from Step 6.1 as control variables, and set initial values ​​and boundary constraints. Solve separately. The steady-state node extracts the anode surface current density, and the associated sensitivity analysis node extracts the associated field gradient at the anode surface.

[0123] Step 7: Update the design variables, iterate and optimize until the convergence condition is met, and obtain the optimized design variables. The specific steps are as follows:

[0124] Step 7.1: Set initial design variables And give boundary constraints for each variable. Choose the initial step size The convergence tolerance is 0.1. for Maximum number of iterations The shrinkage factor is 30, and the line search is performed. The maximum number of iterations for the line search is 0.5. The minimum step size is 10. , prevent zero small amount for .

[0125] Step 7.2: Execute step 6 to obtain the gradient under the current design variables. A backtracking search is used to determine a suitable step size, thus determining the optimal step size. .

[0126] Step 7.3: Update design variables and project them onto the boundary:

[0127] First, calculate the trial point, determined by the following formula:

[0128]

[0129] Then, boundary projection is performed on each component, and its boundary constraints are determined by the following equation:

[0130]

[0131] Step 7.4: Calculate the relative change of the objective function from Step 2, using the following formula:

[0132]

[0133] in In the new design variables If the value obtained from step 6 is not satisfied by any of the following convergence conditions, then continue executing step 6; otherwise, if any of the following conditions are satisfied, then stop iterating:

[0134]

[0135]

[0136] Obtain the optimized design variables.

[0137] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A cathode working tooth for electrolytic machining of deep rifling in a large-caliber artillery piece, characterized in that: A tail fin section is provided at the end of the large end of the working tooth (6). The end face of the tail fin section is concave inward to form a tail fin shape. The arc of the concave part is tangent to the circumferential surface of the cathode body (1).

2. The method for designing the cathode working tooth profile of electrolytic machining for deep rifling in large-caliber artillery according to claim 1, characterized in that: Includes the following steps: Step 1: Perform three-dimensional parametric modeling of the working tooth (6): In the simulation software, a three-dimensional parametric model corresponding to the working tooth (6) is established according to the defined design variables. The working tooth (6) includes a body segment and a tail fin segment located at the tail end of the body segment. The design variable vector is defined as follows: in, This refers to the axial length of the body segment. The width of the small end of the body segment. The width of the larger end of the body segment. The radius of the small end of the body segment. The radius of the large end of the body segment. This refers to the axial length of the caudal fin segment. H is the arc length of the inward concavity of the caudal fin segment, H is the depth of the large end of the working tooth (6), and h is the depth of the small end of the working tooth (6). The semi-cone angle of the working tooth (6), The inward angle of the working tooth (6) of the tail fin cathode; Step 2: Use the coefficient of variation of the current density on the anode surface as the objective function; Step 3: First, establish a multiphysics mathematical model, including the electric field control equation, the flow field control equation, and the temperature field control equation, and then modify the multiphysics mathematical model. Step 4: Introduce adjoint variables into the multiphysics mathematical model Constructing the Lagrange functional: Through the Find the variational derivation of the adjoint equation and boundary conditions. The adjoint equation is: The accompanying boundary conditions include those on the anode boundary. At the cathode boundary On the insulating boundary ; Step 5: Based on the adjoint theory, derive the sensitivity expression of the objective function with respect to the design variables, and obtain the cathode surface sensitivity density function and gradient formula: in The normal potential gradient of the cathode surface. The adjoint field gradient is the normal direction of the cathode surface, where The geometric sensitivity of the cathode surface normal displacement to design variables; Step 6: Establish a three-dimensional multiphysics coupled simulation model, set the boundary conditions of each physical field, iteratively solve to obtain the current density distribution on the anode surface, solve the accompanying problem to obtain the accompanying field distribution, and calculate the gradient of the objective function with respect to the design variables. Step 7: Update the design variables and iterate until the convergence condition is met to obtain the optimized design variables.

3. The method for designing the cathode working tooth profile of electrolytic machining for deep rifling in large-caliber artillery according to claim 2, characterized in that: In step two, the coefficient of variation of the current density at the anode surface is: in This represents the total number of sampling points on the anode surface. For the first Normal current density at each sampling point This is the average current density at all sampling points.

4. The method for designing the cathode working tooth profile of electrolytic machining for deep rifling in large-caliber artillery according to claim 3, characterized in that: In step three, the formula for the mathematical model of electrolyte conductivity based on multiphysics correction is as follows: in, The initial electrolyte conductivity, This represents the volume fraction of hydrogen bubbles. This refers to the concentration of the solid product. For temperature coefficient, This is the initial electrolyte temperature.

5. The method for designing the cathode working tooth profile of electrolytic machining for deep rifling in large-caliber artillery according to claim 4, characterized in that: In step six, the specific steps for establishing the three-dimensional multiphysics coupled simulation model are as follows: Step 6.1: Set boundary conditions for each physics field: Add relevant simulation parameters and control variables, and define the control variables under the defined node: The formula for adding the objective function integral operator is: in For the integral operator defined on the anode surface, The local normal current density on the anode surface. This represents the average current density at the anode surface. Step 6.2: Based on the three-dimensional cathode profile model generated in Step 1, an electrolyte fluid domain is generated on the upper surface of the cathode using the equal gap theory. The upper surface of the fluid domain represents the anode boundary. Step 6.3: Set the boundary conditions and relevant simulation parameters for the electric-current-thermal physical field: Electrolyte conductivity in electric field model Set to: The boundary conditions include the applied operating voltage at the anode. The cathode is grounded, and the remaining boundaries are set to insulation; the flow field model adopts a three-phase gas-liquid-solid turbulent flow model. The relevant simulation parameters include the cathode hydrogen evolution mass source. Solid product quality source : The cathode hydrogen evolution mass source Set by the following formula: The solid product quality source Set by the following formula: in Here is the molar mass of hydrogen. The normal current density at the cathode boundary. The molar mass of the solid product. The local current density on the anode surface. The number of electrons in the reaction. The constant is Faraday's constant; the flow field boundary conditions include inlet pressure p and outlet pressure p. The remaining boundaries are set as walls with no slip, i.e., u is 0; the temperature field model adopts the Joule heating model, and the boundary conditions include the inlet temperature. Other boundaries are set to thermal insulation; Step 6.4: Mesh generation. The cathode domain uses a tetrahedral mesh, and the electrolyte fluid domain uses a dense hexahedral mesh. Boundary layer meshes are set on the upper surface of both the cathode domain and the upper surface of the electrolyte fluid domain. Step 6.5: Set up the research steps. Add a steady-state node and an associated sensitivity analysis node under the research steps. Under the associated sensitivity analysis node, set the design variables in Step 6.1 as control variables and set initial values ​​and boundary constraints. Solve separately. The steady-state node extracts the anode surface current density, and the associated sensitivity analysis node extracts the anode surface associated field gradient.

6. The method for designing the cathode working tooth profile of electrolytic machining for deep rifling in large-caliber artillery according to claim 5, characterized in that: The specific steps in step seven are as follows: Step 7.1: Set initial design variables And give boundary constraints for each variable. Choose the initial step size Convergence tolerance Maximum number of iterations Line search for contraction factor Maximum number of iterations for linear search minimum step size , prevent zero small amount ; Step 7.2: Execute step six to obtain the gradient under the current design variables. A backtracking search is used to determine a suitable step size, thus determining the optimal step size. ; Step 7.3: Update design variables and project them onto the boundary: First, calculate the trial point, determined by the following formula: Then, boundary projection is performed on each component, and its boundary constraints are determined by the following equation: Step 7.4: Calculate the relative change of the objective function, determined using the following formula: in, In the new design variables If the value obtained in step six is ​​not satisfied by any of the following convergence conditions, then continue executing step six; otherwise, if any of the following conditions are satisfied, then stop iterating: Obtain the optimized design variables.

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