Design and preparation method of gradient lattice composite structure tool based on electroosmotic driving

Abstract

The application belongs to the technical field of ultra-precision machining, and discloses a design and preparation method of a gradient lattice composite structure small tool based on electroosmotic driving, which comprises the following steps: establishing an electroosmotic driving control equation and a non-Newtonian fluid constitutive model, analyzing dynamic and static contact stress distribution characteristics, deducing a theoretical material removal function on the basis, and establishing a material deterministic removal evaluation index. Then, stress analysis of the tool structure is carried out, the overall tool structure deformation characteristics are calculated, the lattice structure size distribution in the gradient layer of the small tool is obtained by using a numerical calculation method, the modeling of the three-dimensional structure of the small tool is carried out, the dynamic simulation of the specific machining process is carried out, the corresponding material removal model is established, the coefficient of the theoretical material removal function is corrected, then the deterministic evaluation is carried out, and if the evaluation index is met, the preparation of the small tool and the arrangement design of the electrode layer are carried out. The application can improve the uniformity of the material removal amount distribution and promote the material deterministic removal.

Description

Technical Field

[0001] This invention belongs to the field of ultra-precision machining technology, specifically relating to a method for designing and fabricating small tools based on electroosmosis-driven gradient lattice composite structures. Background Technology

[0002] As high-end equipment gradually leads the development of advanced technologies, research on ultra-precision machining technology and equipment for high-end optical components plays a vital role. Ultra-precision machining technology for laser optical components is a core technology in fields such as high-power lasers, ultra-short intense lasers, and laser countermeasures, and is an important indicator of a nation's development level and potential in both civilian and military equipment.

[0003] Currently, Computer-Controlled Optical Surface Technology (CCOS) based on small polishing discs is the main method for high-precision and high-efficiency processing of laser optical components. Some researchers have disclosed a new method for uniform removal of hard and brittle materials based on gradient-function polishing discs. This method involves solidifying abrasives, polymers, and binders into a five-gradient polishing disc with different volume ratios. The workpiece (adsorbed under negative pressure) contacts the disc with a certain downward pressure for polishing, achieving good uniform material removal. Many researchers have also studied and designed small tools based on their characteristics, such as tool posture, materials, and three-dimensional structure. For example, the foreign invention patent "A Polishing Tool" with authorization publication number WO2020018018A1 discloses a disc-shaped active flexible small tool with retractable reinforcing ribs. By changing the position of the reinforcing ribs, the stiffness of the small tool is changed, verifying the influence of tool flexibility on material removal.

[0004] Electroosmotic drive utilizes an external electric field to directly drive and control the flow of fluid within microchannels without damaging mechanical components. It offers advantages such as high efficiency and convenience in control and integration. Furthermore, based on the characteristics of non-Newtonian fluids—that is, a slightly viscous liquid under normal conditions, its apparent viscosity increases sharply when subjected to impact, exhibiting the impact resistance of a solid—it returns to its original flexible state after the impact force disappears.

[0005] Currently, existing polishing technologies based on controllable flexible terminals, such as airbag polishing and non-Newtonian fluid grinding disc polishing, still suffer from drawbacks such as weak local polishing correction capabilities, susceptibility to edge effects, and high equipment costs. These drawbacks can increase the surface shape error in the original frequency band of the workpiece surface, thus failing to guarantee the surface shape accuracy of the processed workpiece. To achieve deterministic material removal and ensure the surface shape accuracy of the processed workpiece, this invention proposes a method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a technical solution for the design and fabrication of small tools based on electroosmosis-driven gradient lattice composite structures.

[0007] A method for designing and fabricating small tools based on electroosmosis-driven gradient lattice composite structures includes the following steps:

[0008] Step 1: Establish the electroosmosis driving control equations and the non-Newtonian fluid constitutive model based on the electroosmosis driving principle and the characteristics of non-Newtonian fluids.

[0009] Step 2: Considering the interface friction and damping characteristics, use simulation software to simulate and calculate the dynamic and static contact stress distribution on the tool-workpiece surface under different working conditions, and establish dynamic and static contact stress distribution models based on the simulation results.

[0010] Step 3: Based on the electroosmotic drive control equation, obtain the influence model of different voltage drives on the actual contact stress distribution differences.

[0011] Step 4: Use the Princeton equation to derive the theoretical material removal function and establish a deterministic material removal evaluation index;

[0012] Step 5: Based on the existing contact stress distribution, perform stress analysis on the tool to obtain the size distribution characteristics of the internal crystal structure of the tool, and establish the corresponding tool model;

[0013] Step 6: Conduct simulation experiments using the established tool model to obtain the corresponding material removal model.

[0014] The model is compared with the theoretical materials, and the corresponding coefficients are adjusted to verify the feasibility of the theoretical model. Then, a deterministic evaluation is performed. If the evaluation is satisfied, the next step is carried out. If the evaluation is not satisfied, step 5 is repeated.

[0015] Step 7: Prepare the small tool based on the tool model;

[0016] Step 8: Use the prepared small tool to conduct process experiments and compare and verify the actual material removal function with the theoretical material removal function.

[0017] Further, step 1 includes:

[0018] Step 1.1, assume that the width of the unit lattice is W, the height is H, and the length is L;

[0019] Based on the Poisson-Nernst-Planck equation, the electroosmotic drive control equation in cylindrical coordinates is established. The position coordinates of a point in space are described by (r, θ, z), where r represents the distance from the point to the z-axis (r≥0), θ represents the angle with the z-axis, and z has the same meaning as the Z-axis in the rectangular coordinate system.

[0020]

[0021] In the formula This is the double-layer potential. ρ is the difference in double-layer potential as a function of position. e Static charge density per unit volume, ε r ε is the relative permittivity, ε0 ​​is the vacuum permittivity, and c i It is the ion concentration of the i-th type of ion in the electrolyte solution. χ is the gradient of ion concentration over time, where t is the fluid flow time. i Here, ei is the ionic valence of the i-th ion, e0 is the charge carried by the electron, and K is the charge carried by the i-th ion. B Here, T is the Boltzmann constant, v is the fluid velocity, and D is the fluid velocity. i Let be the diffusion coefficient of the i-th component ion;

[0022] The expressions for each component of the fluid velocity were derived using numerical calculations.

[0023] Step 1.2: Based on the fluid momentum equation, establish a constitutive model for the non-Newtonian fluid:

[0024]

[0025] In the formula, ρ refers to the solution density, p refers to the fluid pressure, ▽p refers to the pressure gradient distribution, μ refers to the viscosity coefficient, F refers to the electric field force, and Δv refers to the velocity change.

[0026] Assuming the pressure gradient within a single lattice in the gradient layer is zero, the force expression within the lattice is:

[0027]

[0028] In the formula F r F θ F z This represents the component of the electric field force experienced by the fluid within a single crystal lattice.

[0029] Based on this, the components of the electric force within a single lattice can be determined, and a matrix of all lattice electric force components [F] can be established using the coordinates of the lattice body center. r ]、[F θ ]、[F z Substitute it into equation (2) to obtain the pressure gradient distribution.

[0030] Further, step 3 includes:

[0031] Based on the fluid velocity component expressions obtained from the electroosmotic driving control equations and the pressure gradient distribution derived from the non-Newtonian fluid constitutive model, Obtain a model showing the influence of different voltage driving forces on the actual contact stress distribution differences.

[0032] Further, step 4 includes:

[0033] Based on the Preston equation, given the contact stress distribution and velocity field distribution, and assuming the Preston coefficient K remains constant under a certain working condition, the theoretical material removal function is:

[0034]

[0035] In the formula, MRR refers to the amount of material removed during the polishing process. This refers to the distribution of contact stress at different locations under different electric potentials at various time points. This refers to the velocity distribution at different locations under different electric potentials at various points in time.

[0036] The boundary conditions of the tool are substituted into numerical solutions to analyze the differences in the distribution of dynamic and static material removal amounts, and a deterministic material removal index is established, namely the mean of the peak and trough values ​​of material removal amount.

[0037] Further, step 5 includes:

[0038] Step 5.1, perform unit lattice force analysis:

[0039] Considering interfacial compatibility conditions, and based on the concept of effective stress in elastic porous media, it is assumed that the total stress within a unit lattice consists of effective stress and fluid pressure, i.e.:

[0040] σ=σ e +αpI

[0041]

[0042] In the formula, σ is the total stress, σ e Where p is the effective stress, I is the fluid pressure, α is the Biot coefficient, and C is the effective stress. s C is the compressibility coefficient of a solid. m The compression coefficient of the gradient layer;

[0043] Effective stress σ within unit lattice of tool gradient layer e for:

[0044] σ e =σ s (1-φ)

[0045]

[0046] In the formula σ s The average stress on the gradient layer skeleton particles is φ, where φ is porosity and V is V. p V is the pore volume. b The volume of the elastic layer is its external appearance.

[0047] Therefore, the total dependent variable of the tool gradient layer is ε = ε e +ε s ;

[0048] Where the bulk strain ε e =f e (σ e ), structural strain ε s =f s (p);

[0049] f e (σ e f is the functional expression of the bulk strain with respect to the effective stress. s (p) is the functional expression of structural strain with respect to fluid pressure;

[0050] When a unit lattice structure is subjected to three-dimensional stress, the stress and strain it experiences are expressed in tensors as follows:

[0051]

[0052] Where σ ii The magnitude of the principal stresses on each plane, τ ij ε refers to the magnitude of the shear stress in each direction on each plane. ii The normal strain on each plane, γ ij This refers to the magnitude of tangential strain on each plane;

[0053] Step 5.2, perform overall force integration within the tool:

[0054] Based on the principle of small deformation in mechanics of materials, assuming that the strut lattice within the gradient layer is a compressive elastic rod, the deformation gradient of the overall structure within the gradient layer, according to the Lagrange formula, is:

[0055]

[0056] in and These refer to the current and initial line elements, respectively, and are vectors;

[0057] According to the right Cauchy-Green deformation tensor:

[0058] C = F T F = U 2 (9)

[0059] Where C is the right Cauchy-Green deformation tensor and U is the right elongation tensor;

[0060] To obtain zero-based deformation measurements, the equivalent tensor needs to be subtracted from C to obtain the Green-Lagrange strain tensor E:

[0061]

[0062] Step 5.3, Solve for the internal structural dimensions of the tool:

[0063] E = πED 2 (11)

[0064] Solve for the diameter tensor D, and each component of it is the structural diameter at each location;

[0065] Substituting equations (5) to (10) into equation (11), and using numerical solution methods, we can obtain the distribution characteristics of the column cross-section size, i.e., the column cross-section diameter d.

[0066] Furthermore, in step 7, a three-layer composite structure of rigid layer-gradient layer-homogeneous layer is used as the basic structure of the tool. The tool includes a gradient layer, electrode layers are arranged on the upper and lower bottom surfaces of the gradient layer, and an insulating layer is set outside the electrode layer. The gradient layer of the tool is prepared by 3D printing. The preparation process of the gradient layer includes:

[0067] S100 is used to prepare a 3D printing matrix material by uniformly mixing liquid photopolymer resin with 600-2000 mesh silicon carbide abrasive particles.

[0068] S101, the gradient layer structure of the tool is divided into two parts, including the lower matrix structure and the upper capping structure. The lower matrix structure includes the internal lattice structure and the circumferential and bottom surrounding structures. The two parts of the gradient layer structure are exported as three-dimensional model files and sliced ​​in 3D printing slicing software.

[0069] S102: Use a 3D printer to print the lower base structure and the upper capping structure. After printing, clean the surface of the part to remove uncured resin, then cure it with ultraviolet light. Then, inspect and evaluate the internal lattice structure. If the error between the support column size and the design size is within a reasonable range, the part is considered qualified and a gradient layer entity with a basic structure is obtained for subsequent operations. If the requirements are not met, adjust the 3D printer parameters and repeat S100-S102.

[0070] In step S103, a non-Newtonian fluid with a water-cassava starch mass ratio of 1:0.8-1:1.5 is filled into the lower matrix structure through the gradient layer fluid exchange inlet. This fluid serves as the electroosmotic driving fluid while simultaneously improving the overall impact resistance of the tool. Both the fluid exchange inlet and outlet remain sealed when no operation is being performed to ensure airtightness. At this point, the tool gradient layer preparation is complete.

[0071] Furthermore, in step 7, the electrode layer is configured as follows: the electrode layer includes several electrodes, the electrodes are flexible electrodes, distributed in a ring array around the gradient layer, the electrode layers on both sides of the gradient layer are symmetrically distributed, two electrodes located on different electrode layers correspond to a set of control electrodes, and an insulating layer covers the electrode layer as leakage protection.

[0072] Further, in step 7, the electrode layer is configured as follows: the electrode layer includes several electrodes, the electrodes are flexible electrodes, both electrode layers include several electrode components, each electrode component includes multiple electrodes distributed at linear intervals, the two electrode layers have the same number of electrode components and are distributed in a * shape, so that the electrode layers are distributed in a ring array around the gradient layer, the positions of the electrode components on the two electrode layers correspond one-to-one, but the positions of the electrodes on the two corresponding electrode components are staggered, so that the connection line of the electrodes on the two corresponding electrode components forms a W-shaped structure. In this W-shaped structure, except for the electrodes at both ends, each of the remaining electrodes and the two connected electrodes form a group of control electrodes, and the insulating layer covers the electrode layer as leakage protection.

[0073] Compared with the prior art, the beneficial effects of the present invention are:

[0074] This invention utilizes the effective dissipation of external impacts by a gradient lattice structure and the damping absorption characteristics of non-Newtonian fluids to effectively suppress vibrations in the processing system. Based on this, it uses the principle of electroosmosis to actively regulate the flow characteristics of non-Newtonian fluids within the lattice structure, thereby changing the viscoelasticity of the non-Newtonian fluids to compensate for differences in contact stress distribution at the processing interface under various working conditions, improving the uniformity of material removal distribution, and promoting deterministic material removal. Attached Figure Description

[0075] Figure 1 This is a flowchart of the present invention;

[0076] Figure 2 This is a schematic diagram of the gradient lattice under stress in this invention;

[0077] Figure 3 This is a schematic diagram of the structure of the small tool in this invention;

[0078] Figure 4 This is a schematic diagram of the gradient layer structure of the small tool in this invention;

[0079] Figure 5 This is a schematic diagram of the internal structure of the gradient layer of the small tool in this invention;

[0080] Figure 6 This is one of the schematic diagrams of the lower base structure of the small tool in this invention;

[0081] Figure 7This is the second schematic diagram of the lower base structure of the small tool in this invention;

[0082] Figure 8 This is a schematic diagram of the electrode layer structure in the first embodiment of the present invention;

[0083] Figure 9 This is a schematic diagram of the electrode layer structure in the second embodiment of the present invention.

[0084] In the diagram: 200 is the rigid layer; 201 is the gradient layer; 202 is the homogeneous layer; 203 is the electrode layer; 204 is the insulating layer; 205 is the central liquid supply channel; 300 is the central liquid supply hole; 301 is the liquid exchange outlet; 302 is the upper capping structure; 303 is the liquid exchange inlet; and 304 is the lower substrate structure. Detailed Implementation

[0085] The invention will now be further described with reference to the accompanying drawings.

[0086] Please see Figures 1-9 A method for designing and fabricating small tools based on electroosmosis-driven gradient lattice composite structures includes the following steps:

[0087] Step 1: Based on the electroosmosis driving principle and the characteristics of non-Newtonian fluids, establish the electroosmosis driving control equations and the non-Newtonian fluid constitutive model, specifically including:

[0088] Step 1.1, assume that the width of the unit lattice is W, the height is H, and the length is L;

[0089] Based on the Poisson-Nernst-Planck equations, the electroosmotic driving control equations in cylindrical coordinates are established. The position coordinates of a point in space are described by (r, θ, z), where r represents the distance from the point to the z-axis (r≥0), θ represents the angle with the z-axis, and z has the same meaning as the Z-axis in the rectangular coordinate system.

[0090]

[0091] In the formula This is the double-layer potential. ρ is the difference in double-layer potential as a function of position. e Static charge density per unit volume, ε r εi is the relative permittivity, ε0 is the vacuum permittivity, and ci is the concentration of the i-th ion in the electrolyte solution. χ is the gradient of ion concentration over time, where t is the fluid flow time. i Here, ei is the ionic valence of the i-th ion, e0 is the charge carried by the electron, and K is the charge carried by the i-th ion. B Here, T is the Boltzmann constant, v is the fluid velocity, and D is the fluid velocity. iLet be the diffusion coefficient of the i-th component ion;

[0092] Numerical calculations were used to derive the expressions for each component of the fluid velocity.

[0093] Step 1.2: Based on the fluid momentum equation, establish a constitutive model for the non-Newtonian fluid:

[0094]

[0095] In the formula, ρ refers to the solution density, p refers to the fluid pressure, ▽p refers to the pressure gradient distribution, μ refers to the viscosity coefficient, F refers to the electric field force, and Δv refers to the velocity change.

[0096] Assuming the pressure gradient within a single lattice in the gradient layer is zero, the force expression within the lattice is:

[0097]

[0098] In the formula F r F θ F z This represents the component of the electric field force experienced by the fluid within a single crystal lattice.

[0099] Based on this, the components of the electric force within a single lattice can be determined, and a matrix of all lattice electric force components [F] can be established using the coordinates of the lattice body center. r ]、[F θ ]、[F z Substitute it into equation (2) to obtain the pressure gradient distribution ▽p.

[0100] Step 2: Considering the interface friction and damping characteristics, use MATLAB simulation software to simulate and calculate the dynamic and static contact stress distribution on the tool-workpiece surface under different working conditions, such as different rotational speeds, pressure, feed rates, and trajectory parameters. Based on the simulation results, establish dynamic and static contact stress distribution models.

[0101] Step 3: Based on the electroosmotic drive control equation, obtain the influence model of different voltage drives on the actual contact stress distribution differences. Specifically, it includes:

[0102] Based on the fluid velocity component expressions obtained from the electroosmotic driving control equations and the pressure gradient distribution derived from the non-Newtonian fluid constitutive model, Obtain a model showing the influence of different voltage driving forces on the actual contact stress distribution differences.

[0103] Step 4: Derive the theoretical material removal function using the Preston equation and establish a deterministic material removal evaluation index, specifically including:

[0104] Based on the Preston equation, given the contact stress distribution and velocity field distribution, and assuming the Preston coefficient K remains constant under a certain working condition, the theoretical material removal function is:

[0105]

[0106] In the formula, MRR refers to the amount of material removed during the polishing process. This refers to the distribution of contact stress at different locations under different electric potentials at various time points. This refers to the velocity distribution at different locations under different electric potentials at various points in time.

[0107] The boundary conditions of the tool are substituted into numerical solutions to analyze the differences in the distribution of dynamic and static material removal amounts, and a deterministic material removal index is established, namely the mean of the peak and trough values ​​of material removal amount.

[0108] Step 5: Based on the existing contact stress distribution, perform stress analysis on the tool to obtain the size distribution characteristics of the internal crystal structure of the tool, and establish the corresponding tool model, specifically including:

[0109] Step 5.1, as follows Figure 2 As shown, a unit lattice force analysis is performed:

[0110] Considering interfacial compatibility conditions, and based on the concept of effective stress in elastic porous media, it is assumed that the total stress within a unit lattice consists of effective stress and fluid pressure, i.e.:

[0111] σ=σ e +αpI

[0112]

[0113] In the formula, σ is the total stress, σ e Where p is the effective stress, I is the fluid pressure, α is the Biot coefficient, and C is the effective stress. s C is the compressibility coefficient of a solid. m The compression coefficient of the gradient layer;

[0114] Effective stress σ within unit lattice of tool gradient layer e for:

[0115] σ e =σ s (1-φ)

[0116]

[0117] In the formula σ s The average stress on the gradient layer skeleton particles is φ, where φ is porosity and V is V. p V is the pore volume. b The volume of the elastic layer is its external appearance.

[0118] Therefore, the total dependent variable of the tool gradient layer is ε = ε e +ε s ;

[0119] Where the bulk strain ε e =f e (σ e ), structural strain ε s =f s (p);

[0120] f e (σ e f is the functional expression of the bulk strain with respect to the effective stress. s (p) is the functional expression of structural strain with respect to fluid pressure;

[0121] When a unit lattice structure is subjected to three-dimensional stress, the stress and strain it experiences are expressed in tensors as follows:

[0122]

[0123] Where σ ii The magnitude of the principal stresses on each plane, τ ij ε refers to the magnitude of the shear stress in each direction on each plane. ii The normal strain on each plane, γ ij This refers to the magnitude of tangential strain on each plane;

[0124] Step 5.2, perform overall force integration within the tool:

[0125] Based on the principle of small deformation in mechanics of materials, assuming that the strut lattice within the gradient layer is a compressive elastic rod, the deformation gradient of the overall structure within the gradient layer, according to the Lagrange formula, is:

[0126]

[0127] in and These refer to the current and initial line elements, respectively, and are vectors;

[0128] According to the right Cauchy-Green deformation tensor:

[0129] C = F T F = U 2 (9)

[0130] Where C is the right Cauchy-Green deformation tensor and U is the right elongation tensor;

[0131] To obtain zero-based deformation measurements, the equivalent tensor needs to be subtracted from C to obtain the Green-Lagrange strain tensor E:

[0132]

[0133] Step 5.3, Solve for the internal structural dimensions of the tool:

[0134] E = πED 2 (11)

[0135] Solve for the diameter tensor D, and each component of it is the structural diameter at each location;

[0136] Substituting equations (5) to (10) into equation (11), and using numerical solution methods, we can obtain the distribution characteristics of the column cross-section size, i.e., the column cross-section diameter d.

[0137] Step 6: Use the established tool model to conduct simulation experiments to obtain the corresponding material removal model. Compare it with the theoretical material removal model and make corresponding coefficient corrections to verify the feasibility of the theoretical model. Then, conduct a deterministic evaluation. If the evaluation is satisfied, proceed to the next step. If not, repeat step 5.

[0138] Step 7: Prepare the small tool based on the tool model, such as... Figures 3-7 As shown, a three-layer composite structure of rigid layer-gradient layer-homogeneous layer is used as the basic structure of the tool. The tool includes a gradient layer, with electrode layers arranged on the top and bottom surfaces of the gradient layer, and an insulating layer outside the electrode layer. The gradient layer of the tool is fabricated using 3D printing. The fabrication process of the gradient layer includes:

[0139] S100 is used to prepare a 3D printing matrix material by uniformly mixing liquid photopolymer resin with 600-2000 mesh silicon carbide abrasive particles.

[0140] S101, the gradient layer structure of the tool is divided into two parts, including the lower matrix structure and the upper capping structure. The lower matrix structure includes the internal lattice structure and the circumferential and bottom surrounding structures. The two parts of the established gradient layer structure are exported as three-dimensional model files and sliced ​​in the Preform software.

[0141] S102: Use a 3D printer to print the lower base structure and the upper capping structure. After printing, clean the surface of the part to remove uncured resin, then cure it with ultraviolet light. Then, inspect and evaluate the internal lattice structure. If the error between the support column size and the design size is within a reasonable range, the part is considered qualified and a gradient layer entity with a basic structure is obtained for subsequent operations. If the requirements are not met, adjust the 3D printer parameters and repeat S100-S102.

[0142] In step S103, a non-Newtonian fluid with a water-cassava starch mass ratio of 1:0.8-1:1.5 is filled into the lower matrix structure through the fluid exchange inlet. This serves as the electroosmotic driving fluid while simultaneously improving the overall impact resistance of the tool. Both the fluid exchange inlet and outlet remain sealed when no specific operation is performed to ensure airtightness. At this point, the tool gradient layer preparation is complete.

[0143] Step 7 also includes: Figure 8 This is one implementation of a flexible electrode distribution on an electrode layer. The electrode layer includes several flexible electrodes arranged in a ring array around the gradient layer with a radial spacing of 15 mm. The two electrode layers are symmetrically distributed, primarily for applications where the surface curvature of the component to be processed has minimal variation. Figure 8 Electrodes 1-2 in section b form a control electrode group, followed by 3-4, 5-6, and so on, which are named electrode groups {1, 2, 3...}. The contact stress on the tool surface is managed by zones, with the corresponding areas named {block 1, block 2, block 3...}. The voltage values ​​of each control electrode group are rationally set based on the curvature variation characteristics of the surface of the component to be processed. An insulating layer covers the electrode layer as leakage protection.

[0144] Figure 9 Another implementation of the flexible electrode distribution on the electrode layer includes several electrodes, which are flexible electrodes. Both electrode layers include several electrode assemblies, and each electrode assembly includes multiple electrodes distributed at linear intervals with a radial spacing of 15 mm. The two electrode layers have the same number of electrode assemblies and are distributed in a * shape, so that the electrode layers are distributed in a ring array around the gradient layer. The positions of the electrode assemblies on the two electrode layers correspond one-to-one, but the positions of the electrodes on the two corresponding electrode assemblies are staggered, so that the connection line of the electrodes on the two corresponding electrode assemblies forms a W-shaped structure. In this W-shaped structure, except for the electrodes at both ends, each electrode and the two connected electrodes form a group of control electrodes. An insulating layer covers the electrode layer as leakage protection.

[0145] Specifically, this implementation method is mainly aimed at situations where the surface curvature of the component to be processed varies greatly. Figure 9 Electrodes 1, 2, and 3 in section b form a group of control electrodes, and 2, 3, 4, 3, 4, 5, etc., are arranged sequentially as other control electrode groups, named electrode groups {1, 2, 3, 4...}. The contact stress on the tool surface is managed in zones, and the regions corresponding to the electrode groups are named {block 1, block 2, block 3, block 4...}. The asymmetrically distributed control electrodes exhibit a more pronounced gradient in electric field change, resulting in higher relative sensitivity of the electroosmotic drive. This allows it to adapt to workpieces with rapidly changing surface curvature and provides a smooth transition. An insulating layer covers the electrode layer as a leakage current protection layer.

[0146] Step 8: Use the prepared small tool to conduct process experiments and compare and verify the actual material removal function with the theoretical material removal function.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing and fabricating small tools based on electroosmosis-driven gradient lattice composite structures, characterized in that, The steps include the following: Step 1: Establish the electroosmosis driving control equations and the non-Newtonian fluid constitutive model based on the electroosmosis driving principle and the characteristics of non-Newtonian fluids. Step 2: Considering the interface friction and damping characteristics, use simulation software to simulate and calculate the dynamic and static contact stress distribution on the tool-workpiece surface under different working conditions, and establish dynamic and static contact stress distribution models based on the simulation results. Step 3: Based on the electroosmotic drive control equation, obtain the influence model of different voltage drives on the actual contact stress distribution differences. Step 4: Use the Princeton equation to derive the theoretical material removal function and establish a deterministic material removal evaluation index; Step 5: Based on the existing contact stress distribution, perform stress analysis on the tool to obtain the size distribution characteristics of the internal crystal structure of the tool, and establish the corresponding tool model; Step 6: Use the established tool model to conduct simulation experiments to obtain the corresponding material removal model. Compare it with the theoretical material removal model and make corresponding coefficient corrections to verify the feasibility of the theoretical model. Then, conduct a deterministic evaluation. If the evaluation is satisfied, proceed to the next step. If not, repeat step 5. Step 7: Prepare the small tool based on the tool model; Step 8: Use the prepared small tool to conduct process experiments and compare and verify the actual material removal function with the theoretical material removal function.

2. The method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure according to claim 1, characterized in that, Step 1 includes: Step 1.1, assume that the width of the unit lattice is W, the height is H, and the length is L; Based on the Poisson equation, the electroosmotic drive control equation in cylindrical coordinates is established. The position coordinates of a point in space are described by (r, θ, z), where r represents the distance from the point to the z-axis, θ represents the angle with the z-axis, and z has the same meaning as the Z-axis in the rectangular coordinate system. In the formula This is the double-layer potential. ρ is the difference in double-layer potential as a function of position. e Static charge density per unit volume, ε r ε is the relative permittivity, ε0 ​​is the vacuum permittivity, and c i It is the ion concentration of the i-th type of ion in the electrolyte solution. χ is the gradient of ion concentration over time, where t is the fluid flow time. i It is the ionic valence of the i-th ion, e0 is the charge carried by the electron, e i K represents the charge of the i-th ion. B Here, T is the Boltzmann constant, v is the fluid velocity, and D is the fluid velocity. i Let be the diffusion coefficient of the i-th component ion; The expressions for each component of the fluid velocity were derived using numerical calculations. Step 1.2: Based on the fluid momentum equation, establish a constitutive model for the non-Newtonian fluid: In the formula, ρ refers to the solution density, and p refers to the fluid pressure. The pressure gradient distribution refers to μ, the viscosity coefficient refers to F, the electric force refers to Δv, and the velocity change refers to Δv. Assuming the pressure gradient within a single lattice in the gradient layer is zero, the force expression within the lattice is: In the formula F r F θ F z This represents the component of the electric field force experienced by the fluid within a single crystal lattice. Based on this, the components of the electric force within a single lattice can be determined, and a matrix of all lattice electric force components [F] can be established using the coordinates of the lattice body center. r ]、[F θ ]、[F z Substitute it into equation (2) to obtain the pressure gradient distribution ▽p.

3. The method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure according to claim 2, characterized in that, Step 3 includes: Based on the fluid velocity component expressions obtained from the electroosmotic driving control equations and the pressure gradient distribution derived from the non-Newtonian fluid constitutive model, Obtain a model showing the influence of different voltage driving forces on the actual contact stress distribution differences.

4. The method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure according to claim 3, characterized in that, Step 4 includes: Based on the Preston equation, given the contact stress distribution and velocity field distribution, and assuming the Preston coefficient K remains constant under a certain working condition, the theoretical material removal function is: In the formula, MRR refers to the amount of material removed during the polishing process. This refers to the distribution of contact stress at different locations under different electric potentials at various time points. This refers to the velocity distribution at different locations under different electric potentials at various points in time. The boundary conditions of the tool are substituted into numerical solutions to analyze the differences in the distribution of dynamic and static material removal amounts, and a deterministic material removal index is established, namely the mean of the peak and trough values ​​of material removal amount.

5. The method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure according to claim 4, characterized in that, Step 5 includes: Step 5.1, perform unit lattice force analysis: Considering interfacial compatibility conditions, and based on the concept of effective stress in elastic porous media, it is assumed that the total stress within a unit lattice consists of effective stress and fluid pressure, i.e.: In the formula, σ is the total stress, σ e Where p is the effective stress, I is the fluid pressure, α is the Biot coefficient, and C is the effective stress. s C is the compressibility coefficient of a solid. m The compression coefficient of the gradient layer; Effective stress σ within unit lattice of tool gradient layer e for: In the formula σ s The average stress on the gradient layer skeleton particles is φ, where φ is porosity and V is V. p V is the pore volume. b The volume of the elastic layer is its external appearance. Therefore, the total dependent variable of the tool gradient layer is ε = ε e +ε s ; Where the bulk strain ε e =f e (σ e ), structural strain ε s =f s (p); f e (σ e f is the functional expression of the bulk strain with respect to the effective stress. s (p) is the functional expression of structural strain with respect to fluid pressure; When a unit lattice structure is subjected to three-dimensional stress, the stress and strain it experiences are expressed in tensors as follows: Where σ ii The magnitude of the principal stresses on each plane, τ ij ε refers to the magnitude of the shear stress in each direction on each plane. ii The normal strain on each plane, γ ij This refers to the magnitude of tangential strain on each plane; Step 5.2, perform overall force integration within the tool: Based on the principle of small deformation in mechanics of materials, assuming that the strut lattice within the gradient layer is a compressive elastic rod, the deformation gradient of the overall structure within the gradient layer, according to the Lagrange formula, is: in and These refer to the current and initial line elements, respectively, and are vectors; According to the right Cauchy-Green deformation tensor: C=F T F=U 2 (9) Where C is the right Cauchy-Green deformation tensor and U is the right elongation tensor; To obtain zero-based deformation measurements, the equivalent tensor needs to be subtracted from C to obtain the Green-Lagrange strain tensor E, i.e.: Step 5.3, Solve for the internal structural dimensions of the tool: E=πED 2 (11) Solve for the diameter tensor D, and each component of it is the structural diameter at each location; Substituting equations (5) to (10) into equation (11), and using numerical solution methods, we can obtain the distribution characteristics of the column cross-section size, i.e., the column cross-section diameter d.

6. The method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure according to claim 1, characterized in that, In step 7, a three-layer composite structure of rigid layer-gradient layer-homogeneous layer is used as the basic structure of the tool. Electrode layers are arranged on the top and bottom surfaces of the gradient layer, and an insulating layer is set outside the electrode layer. The gradient layer of the tool is prepared by 3D printing. The preparation process of the gradient layer includes: S100 is used to prepare a 3D printing matrix material by uniformly mixing liquid photopolymer resin with 600-2000 mesh silicon carbide abrasive particles. S101, the gradient layer structure of the tool is divided into two parts, including the lower matrix structure and the upper capping structure. The lower matrix structure includes the internal lattice structure and the circumferential and bottom surrounding structures. The two parts of the gradient layer structure are exported as three-dimensional model files and sliced ​​in 3D printing slicing software. S102: Use a 3D printer to print the lower base structure and the upper capping structure. After printing, clean the surface of the part to remove uncured resin, then cure it with ultraviolet light. Then, inspect and evaluate the internal lattice structure. If the error between the support column size and the design size is within a reasonable range, the part is considered qualified and a gradient layer entity with a basic structure is obtained for subsequent operations. If the requirements are not met, adjust the 3D printer parameters and repeat S100-S102. S103, a non-Newtonian fluid with a water-cassava starch mass ratio of 1:0.8-1:1.5 is filled into the lower matrix structure from the gradient layer fluid exchange inlet. This fluid serves as an electroosmotic driving fluid and improves the overall impact resistance of the tool. The fluid exchange inlet and outlet remain sealed when no specific operation is performed to ensure airtightness. At this point, the tool gradient layer preparation is complete.

7. The method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure according to claim 6, characterized in that, In step 7, the electrode layer is configured as follows: the electrode layer includes several electrodes, the electrodes are flexible electrodes, and they are distributed in a ring array around the gradient layer. The electrode layers on both sides of the gradient layer are symmetrically distributed. Two electrodes located on different electrode layers constitute a set of control electrodes. An insulating layer is covered on the electrode layer as leakage protection.

8. The method for designing and fabricating a small tool based on an electroosmosis-driven gradient lattice composite structure according to claim 6, characterized in that, In step 7, the electrode layer is configured as follows: the electrode layer includes several electrodes, the electrodes are flexible electrodes, both electrode layers include several electrode components, each electrode component includes multiple electrodes distributed at linear intervals, the two electrode layers have the same number of electrode components and are distributed in a * shape, so that the electrode layer is distributed in a ring array around the gradient layer, the positions of the electrode components on the two electrode layers correspond one-to-one, but the positions of the electrodes on the two corresponding electrode components are staggered, so that the connection line of the electrodes on the two corresponding electrode components forms a W-shaped structure. In this W-shaped structure, except for the electrodes at both ends, each of the other electrodes and the two connected electrodes form a group of control electrodes, and the insulating layer covers the electrode layer as leakage protection.

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