Design and preparation method of small tool and polishing device for achieving uniform material removal

Abstract

This invention belongs to the field of ultra-precision machining technology, specifically relating to a method for designing and manufacturing a small tool and a polishing device for achieving uniform material removal. The method includes: calculating the amount of material removed at each point in the contact area within a dwell time T using the Preston equation, given the contact stress and relative velocity distribution between the polishing tool and the workpiece; determining the material properties and structural characteristics of the initial ordinary small tool and the workpiece; obtaining the circumferential stress distribution characteristics of the contact area between the tool and the workpiece based on quasi-static stress simulation results of an ordinary small tool with a material mass ratio of 30%–90% pressing down 0.1–2 mm on the workpiece surface; calculating the angular distribution of contact areas with different radii; and fabricating a corresponding mold based on the cross-sectional curve data of the small tool, and then manufacturing the small tool using the mold. This invention, through structural design and appropriate pressing down and rotation speed, ensures that the amount of material removed at each point in the contact area larger than a certain radius is as consistent as possible during point grinding.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision machining technology, and more specifically, to a method and apparatus for designing and manufacturing a small tool to achieve uniform material removal. Background Technology

[0002] With the rapid development of high technology, hard and brittle materials, such as sapphire, single-crystal silicon, and optical glass, are increasingly widely used in aerospace, optoelectronics, and microelectronics. Besides their high strength and hardness, these materials offer better thermal insulation and chemical stability than other materials, along with good heat resistance and corrosion resistance, making them widely applicable across various fields. The surface accuracy and quality of hard and brittle materials have a crucial impact on the quality and lifespan of devices. Currently, processing methods for these hard and brittle materials mainly include chemical mechanical polishing, stress plate polishing, CCOS, magnetic flux conversion, ion beam polishing, and jet polishing. While breakthroughs have been achieved, problems remain, such as uneven material removal and poor quality control, making it impossible to further suppress mid-to-high frequency errors without compromising workpiece surface accuracy.

[0003] Computer-controlled optical surface treatment (CCOS) has undergone many years of development, with researchers primarily focusing on processing techniques based on simple polishing tools (disc-type small tools, spherical small grinding heads, etc.), such as trajectory planning and dwell time calculation. Many scholars have also conducted research and design on the characteristics of these small tools, such as tool posture, materials, and three-dimensional structure. For example, Chinese invention patent CN111070080B, entitled "A Series of Processing Processes for the Surface of Sub-Aperture Center-Supply Optical Elements," discloses a center-supply disc-type small tool. By changing different grinding and polishing pads, it achieves a successive recursive suppression process of low-frequency, mid-frequency, and high-frequency errors on the optical surface. Another example is foreign invention patent WO2020018018A1, which 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 altered, verifying the influence of tool flexibility on material removal.

[0004] Currently, there is no design for small tools that can achieve uniform material removal. Therefore, based on the Preston equation, a small tool with a special cross-sectional shape is designed to achieve uniform removal of material at fixed points. It is driven by a small tool polishing device to perform high-speed rotation and trajectory planning, and is applied to hard and brittle material workpieces to achieve rapid and uniform removal of large areas of material. Summary of the Invention

[0005] The purpose of this invention is to solve the problems of uneven material removal and unstable surface quality in existing processing technologies. It proposes a small tool design and preparation method and polishing device to achieve uniform material removal, which has the advantages of uniform and controllable material removal depth and good processing effect.

[0006] This invention achieves the above objective through the following technical solution: a method for designing and preparing a small tool to achieve uniform material removal, specifically including the following steps:

[0007] Step 1: Based on the Preston equation, given the known contact stress and relative velocity distribution between the tool and the workpiece, calculate the amount of material removed at each point in the contact area within the dwell time T.

[0008] Step 2: Determine the material properties and structural characteristics of the initial general-purpose tool and workpiece;

[0009] Step 3: Based on the quasi-static stress simulation results of ordinary small tools with a material mass ratio of 30% to 90% pressing down 0.1 to 2 mm on the workpiece surface, obtain the circumferential stress distribution characteristics of the contact area between the tool and the workpiece;

[0010] Step 4: Calculate the angular distribution of contact areas with different radii;

[0011] Step 5: Based on the cross-sectional curve data of the tool, make the corresponding mold, and then use the mold to make the tool.

[0012] Furthermore, step one specifically includes:

[0013] The formula for calculating the material removal amount ΔZ(x,y) is:

[0014]

[0015] Substitution of variables in equation (1):

[0016]

[0017] Where θ is the total angle rotated by the tool. Let ω be the angle through which the tool rotates at a certain moment, and let V be the angular velocity of the tool. The velocity V depends only on the radius r and the angular velocity ω, i.e., V = rω. Simplify equation (2):

[0018]

[0019] Assuming the circumferential equivalent stress is Right now Then equation (3) can be further simplified to:

[0020]

[0021] Under given operating conditions, if the Preston coefficient K is a constant, then:

[0022]

[0023] Where, constant

[0024] Furthermore, step two includes:

[0025] A composite material with silicone as the matrix and 1000-mesh silicon carbide abrasive grains as the reinforcing phase is used as the main material of the small tool. The mass ratio of silicon carbide abrasive grains to silicone is positively correlated with the elastic modulus of the composite material. A small tool with a central liquid supply disc with a flow channel design is used as the structural feature of a common small tool.

[0026] Furthermore, in step two, the radius of the liquid supply center hole of the small tool is set to x mm, the outer diameter of the small tool is set to β mm, the annular area outside the radius α mm is set as the design range for uniform removal, the flow channel design divides the small tool symmetrically into four parts, the width of the flow channel is 1 mm, the overall thickness of the ordinary small tool is 6-10 mm, the depth of the flow channel is 3 mm, and K9 glass is used as the material for processing the workpiece.

[0027] Furthermore, step three specifically includes:

[0028] Based on quasi-static stress simulation results of ordinary small tools with material mass ratios of 30%–90% pressing down 0.1–2 mm on the workpiece surface, the circumferential stress distribution characteristics of one-quarter of the tool-workpiece contact area are obtained. The circumferential stress curve of the area beyond radius α mm is integrated and divided by the arc length to obtain the equivalent contact stress for different radii. Equivalent contact stress Multiply by radius r to get The distribution characteristics of the product along the radius, for Curve fitting is performed on discrete points to obtain... The equation of the curve; determine the value of the constant C:

[0029]

[0030] Furthermore, step four specifically includes:

[0031] Calculate the angular distribution of contact areas with different radii according to formulas (5) and (6); symmetrically divide the tool into four parts, each part corresponding to two boundary curves. The equations of the boundary curves in the polar coordinate system are:

[0032]

[0033] Through numerical calculation and coordinate transformation, x = rcosθ, y = rsinθ, the coordinates of the data points of the boundary curve in the Cartesian coordinate system are:

[0034]

[0035] Numerical calculation tools are used to obtain data points for the boundary curves. These data points are then imported into modeling software to generate a model of the novel structural tool. Simulations are performed again to solve the problem, and the uniformity of the tool is evaluated. Determine if it meets the uniform removal design requirements; if it does, proceed to step four; if it does not, modify the material properties and boundary conditions of the tool, and repeat steps two through four; or compensate. For the discrete point values, re-fit the curve and repeat steps three and four.

[0036] Furthermore, step five includes:

[0037] Based on the cross-sectional curve data of the tool, the mold is modeled and made using 3D printing or wire cutting. A composite material with room temperature vulcanizing silicone as the matrix and 1000-mesh silicon carbide abrasive grains as the reinforcing phase is used as the main material of the tool. After standing at room temperature for 3 hours, the tool is demolded and trimmed.

[0038] The present invention also provides a polishing device, including a multi-degree-of-freedom robotic arm and an actuator disposed on the multi-degree-of-freedom robotic arm. The actuator includes a small tool, which is manufactured using the design and preparation method described above.

[0039] Furthermore, the actuator also includes a servo motor, a hollow spindle, and a high-speed rotary joint. The servo motor is driven by the hollow spindle to rotate. The small tool is located at the lower end of the hollow spindle, and the high-speed rotary joint is fitted with the upper end of the hollow spindle. The high-speed rotary joint, the hollow spindle, and the small tool form a hollow channel for the flow of polishing fluid, allowing the polishing fluid to enter from the high-speed rotary joint and flow out from the lower end of the small tool to polish the workpiece.

[0040] Furthermore, it also includes a workpiece clamping platform, comprising a water tank, a pressure sensor, and a Z-axis micro-motion platform. The water tank clamps the workpiece via a clamping assembly, the pressure sensor detects the pressure applied to the workpiece by the actuator, and the Z-axis micro-motion platform enables micro-motion of the workpiece.

[0041] The technical concept of this invention is: based on the Preston equation The material removal coefficient K is a constant under the conditions of workpiece processing requirements and mechanical properties of polishing tools. Therefore, the amount of material removed depends on the normal stress P, relative linear velocity V, and residence time T on the workpiece contact surface. The amount of material removed can be equivalently understood as the cumulative amount of contact stress at different radii as the rotation angle increases. By changing the residence time T at different radii through structural design, the integral value of the three can be kept constant to achieve uniform removal of the workpiece and achieve the ideal removal effect.

[0042] The beneficial effects of this invention are as follows: The material removal tool used in this invention, through its structural design and in conjunction with the corresponding downward pressure and rotation speed, can ensure that the amount of material removed from each point in the contact area larger than a certain radius is as consistent as possible during the fixed-point grinding process; at the same time, a polishing device is designed, which, when used with the tool, can perform path planning with a trajectory offset slightly smaller than the diameter of the tool, thereby achieving rapid and uniform removal of material over a large area, improving processing efficiency and quality, and providing an important foundation for subsequent large-scale production and precision machining. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of a small tool structure manufactured using the design and preparation method of the present invention for achieving uniform material removal;

[0044] Figure 2 This is a schematic diagram of a common small tool structure used in the design and preparation method of a small tool for achieving uniform material removal according to the present invention.

[0045] Figure 3 This is a schematic flowchart illustrating the design and fabrication method of a small tool for achieving uniform material removal according to the present invention.

[0046] Figure 4 This is a schematic diagram showing the relationship between the mass ratio of silicon carbide abrasive particles to silicone A adhesive involved in this invention and the elastic modulus of the composite material.

[0047] Figure 5 This is a schematic diagram of the contact model of a common small tool involved in this invention.

[0048] Figure 6 This is a schematic diagram of the circumferential stress distribution characteristics of a quarter contact area of ​​a common small tool involved in this invention.

[0049] Figure 7 This is what the present invention relates to. Schematic diagram of the curve.

[0050] Figure 8 This is a schematic diagram of the boundary curve involved in this invention in the polar coordinate system.

[0051] Figure 9This is a schematic diagram of the cross-sectional features of the small tool involved in this invention in the Cartesian coordinate system.

[0052] Figure 10 This is a comparison chart of the material removal uniformity index of ordinary and small tools involved in this invention.

[0053] Figure 11 This is one of the structural schematic diagrams of a polishing device according to the present invention.

[0054] Figure 12 This is the second schematic diagram of a polishing device according to the present invention.

[0055] Figure 13 for Figure 12 Enlarged view of point A in the middle.

[0056] Figure 14 This is a schematic diagram of the actuator structure in a polishing device according to the present invention.

[0057] Figure 15 This is a cross-sectional schematic diagram of the actuator in a polishing device according to the present invention.

[0058] Figure 16 This is a schematic diagram of a workpiece clamping platform in a polishing apparatus according to the present invention.

[0059] Figure 17 This is a schematic diagram of the water tank, pressure sensor, workpiece placement plate, and workpiece connection structure in a polishing device of the present invention.

[0060] In the diagram, 100 - multi-DOF robotic arm, 200 - actuator, 201 - small tool, 2011 - fluid supply center hole, 2012 - narrow groove, 2013 - arc groove, 202 - small tool bonding plate, 203 - small tool connector, 204 - rigid coupling, 205 - synchronous pulley, 206 - spindle fixing platform, 207 - spindle sleeve, 208 - hollow spindle, 209 - high-speed rotary joint, 210 - joint fixing bracket, 211 - shock absorber, 212 - Servo motor, 213-motor mounting bracket, 214-synchronous belt, 300-workpiece clamping platform, 301-optical flat plate, 302-No. 1 adapter plate, 303-Z-axis micro-motion platform, 304-No. 2 adapter plate, 305-pressure sensor, 306-aluminum plate with long hole, 307-water tank, 3071-acrylic adapter plate, 308-No. 1 rubber sealing ring, 309-No. 2 rubber sealing ring, 310-workpiece placement plate, 311-workpiece, 312-limiting plate. Detailed Implementation

[0061] The present invention will be further described below with reference to the accompanying drawings:

[0062] like Figure 1-10As shown, a method for designing and fabricating a small tool to achieve uniform material removal includes the following steps:

[0063] Step 1: According to the Preston equation, given the contact stress and relative velocity distribution between the tool and the workpiece, the material removal amount ΔZ(x,y) at each point in the contact area within the dwell time T can be calculated:

[0064]

[0065] The small tool performs a cyclical rotation. With one full rotation, the tool removes the same amount of material at every point within the same radius area of ​​the workpiece (i.e., the circumferential path). Therefore, the material removal amount is evenly distributed along the circumferential path within the same radius. It is necessary to consider the time it takes for the tool to rotate one full circle (i.e.,...) ω is the rotational speed of the small tool. Through structural design, the amount of material removed in the radial direction is uniformly distributed. Substitute the variables in equation (1):

[0066]

[0067] Where θ is the total angle rotated by the tool. Let ω be the angle through which the tool rotates at a certain moment, and let V be the angular velocity of the tool. The velocity V depends only on the radius r and the angular velocity ω, i.e., V = rω. Simplify equation (2):

[0068]

[0069] Therefore, the amount of material removed can be equivalently understood as the cumulative amount of contact stress at different radii as the rotation angle increases.

[0070] Assuming the circumferential equivalent stress is Right now Then equation (3) can be further simplified to:

[0071]

[0072] Under given operating conditions, if the Preston coefficient K is a constant, then:

[0073]

[0074] Where, constant θ represents the angular distribution of the contact areas with different radii on the cross-section of the small tool;

[0075] Step Two: Determine the material properties and structural features of the initial general-purpose tool and workpiece. This invention uses a composite material with silicone as the matrix and 1000-mesh silicon carbide abrasive grains as the reinforcing phase as the main material of the tool. The mass ratio of silicon carbide abrasive grains to silicone is positively correlated with the elastic modulus of the composite material. A central liquid supply disc type tool with a flow channel design is used as the structural feature of the general-purpose tool. From an illustrative perspective, this invention sets the radius of the central liquid supply hole of the tool to 2mm, the outer diameter of the tool to 12mm, and the annular region with a radius of 6mm to 12mm as the design range for uniform removal. The flow channel design symmetrically divides the tool into four sections, with a flow channel width of 1mm. The overall thickness of the general-purpose tool is 6mm, and the depth of the flow channel is 3mm. This invention uses K9 glass as the material for processing the workpiece, and a planar surface is used as an example of the structural feature of the processed workpiece.

[0076] Step 3: Based on the quasi-static stress simulation results of a common small tool (30% of the mass) pressing 0.4 mm onto the workpiece surface, obtain the circumferential stress distribution characteristics of one-quarter of the contact area between the tool and the workpiece. Integrate the circumferential stress curves with radii from 6 mm to 12 mm, and divide by the arc length to obtain the equivalent contact stress for different radii. Equivalent contact stress Multiply by radius r to get The distribution characteristics of the product along the radius, for Curve fitting is performed on discrete points to obtain... Curve equation; Since this invention uniformly removes a region with a radius of 6mm to 12mm, the value of the constant C can be determined as follows:

[0077]

[0078] Step 4: Calculate the angular distribution of contact areas with different radii according to formulas (5) and (6); This invention symmetrically divides the tool into four parts, each corresponding to two boundary curves. The equations of the boundary curves in the polar coordinate system are:

[0079]

[0080] Through numerical calculation and coordinate transformation, x = rcosθ, y = rsinθ, the coordinates of the data points of the boundary curve in the Cartesian coordinate system are:

[0081]

[0082] The boundary curve data points were obtained using the numerical computation tool Matlab, imported into the modeling software Solidworks to generate a model of the novel structural tool, and then simulated and solved again. The uniformity evaluation index of the tool was used as the basis for the solution. Determine if it meets the uniform removal design requirements; if it does not meet the uniform removal effect, modify the material properties (such as elastic modulus) and boundary conditions (such as indentation) of the tool, and repeat steps two to four above; or compensate. For discrete point values, re-fit the curve and repeat steps three and four.

[0083] Step 5: Based on the cross-sectional curve data of the tool, model the mold and make the corresponding mold by 3D printing or metal wire cutting. Use room temperature vulcanizing silicone as the matrix and 1000-mesh silicon carbide abrasive as the reinforcing phase as the main material of the tool. After standing at room temperature for 3 hours, demold the tool and trim it at the same time.

[0084] The uniform removal characteristic of the tool is achieved through structural design, which regularly reduces the amount of material removed in areas larger than a certain radius (6mm), resulting in a uniform distribution of material removal in areas larger than a certain radius (6mm). This avoids the problem of uneven material removal caused by excessive removal near the edge of the tool in traditional tools.

[0085] The common small tool is a disc-shaped tool, which is divided into a solid tool and a center-supply tool. The solid tool has a center rotation speed of zero and no flow channel design. Due to the high rotation speed at the edge, the amount of material removed from the edge is too large. Moreover, the centrifugal effect caused by the high rotation speed makes it difficult for polishing fluid or coolant to enter the polishing area of ​​the solid tool. Therefore, this invention is based on the optimized design of a center-supply tool with a flow channel design.

[0086] The main body of the tool is particle-reinforced silicone, with added particles being 1000-mesh silicon carbide abrasive grains. The silicone is room temperature vulcanizing silicone. A and B components are mixed at a mass ratio of 10:1 and then solidified at room temperature to form an elastomer. Different mass ratios of silicon carbide abrasive grains and silicone component A result in composite materials with different elastic moduli. To improve the tool's ability to remove hard and brittle materials, cerium oxide, alumina, or silicon carbide slurry can be injected into the center of the tool to allow free abrasives to process the workpiece. Alternatively, diamond resin abrasive cloth, cut to size according to the surface shape, can be attached to its surface. The thickness of the abrasive cloth is ~0.30mm. Tools with 1500-mesh diamond resin abrasive cloth are used in the grinding stage, while those with 5000-mesh diamond resin abrasive cloth are used in the fine polishing stage. In this case, deionized water can be selected as the slurry injected into the center.

[0087] The applicable processing objects of the small tool design and preparation method for achieving uniform material removal include, but are not limited to, planar workpieces, as well as spherical workpieces, aspherical workpieces, etc., and the surface shape of the workpiece needs to be modified to the corresponding workpiece surface shape in step two.

[0088] like Figure 11-17As shown, a polishing device, using a small tool prepared according to the above design method, achieves rapid and uniform removal of hard and brittle materials. It includes a multi-degree-of-freedom robotic arm 100, an actuator 200, a workpiece clamping platform 300, and a worktable 400. The workpiece 311 is fixed to the optical flat plate 310 via four elongated aluminum plates 306.

[0089] The multi-degree-of-freedom robotic arm 100 drives the actuator 200 to plan the grating path trajectory. Due to manufacturing precision errors, the trajectory offset can be slightly smaller than the diameter of the small tool 201 to achieve rapid material removal in a large area.

[0090] The actuator 200 includes a small tool 201, a small tool bonding plate 202, a small tool connector 203, a rigid coupling 204, a timing pulley 205, a spindle fixing platform 206, a spindle sleeve 207, a hollow spindle 208, a high-speed rotary joint 209, a joint fixing bracket 210, a shock absorber 211, a servo motor 212, a motor fixing bracket 213, and a timing belt 214. The motor fixing bracket 213 and the spindle fixing platform 206 are fixed to the mounting frame assembly, which is connected to the multi-degree-of-freedom robotic arm 100, thereby realizing the installation of the actuator 200. The servo motor 212 is fixed on the motor mounting bracket 213. The hollow spindle 208 is mounted on the spindle sleeve 207 via two deep groove ball bearings. The spindle sleeve 207 is fixed on the spindle mounting bracket 206. The servo motor 212 is connected to the hollow spindle 208 via a synchronous belt 214 and a synchronous pulley 205, and transmits torque to the hollow spindle 208. The hollow spindle 208 is connected to the small tool connector 203 via a rigid coupling 204, and transmits torque to the small tool connector 203. A small tool bonding plate 202 is provided at the lower end of the small tool connector 203. A small tool 201 is provided at the lower end of the small tool bonding plate 202. The small tool 201 is made using the above-described design and manufacturing method. The small tool connector 203 and the small tool bonding plate 202 are connected and fixed by screws. The small tool bonding plate 202 and the small tool 201 are bonded by silicone instant adhesive. The upper end of the hollow spindle 208 is connected to the high-speed rotary joint 209. The high-speed rotary joint 209 is connected to the shock absorber 211 through the joint fixing bracket 210. The shock absorber 211 is connected to the mounting bracket assembly. The hollow spindle 208 rotates under the drive of the servo motor 212, while the high-speed rotary joint 209 does not rotate with it.

[0091] Among them, the small tool 201 has a disc structure with a liquid supply center hole 2011 in the center. Several narrow grooves 2012 are evenly arranged around the bottom surface. The narrow grooves 2012 are connected to the liquid supply center hole 2011. An arc-shaped groove 2013 is formed at the end of the narrow groove 2012 near the edge of the small tool 201. The arc-shaped groove 2013 is nearly triangular in shape, and its width gradually increases from the end connected to the narrow groove 2012 towards the end near the edge of the small tool 201.

[0092] A flow channel 2092 is opened inside the high-speed rotary joint 209, and a liquid inlet 2091 connected to the flow channel 2092 is opened on the side. The lower end of the flow channel 2092 is connected to the hollow cavity of the hollow spindle 208. The small tool connector 203, small tool adhesive plate 202 and small tool 201 at the lower end of the hollow cavity are all annular structures, so that the hollow cavity of the hollow spindle 208 is connected to the liquid supply center hole 2011 of the small tool 201.

[0093] When the small tool 201 is in use, the polishing slurry flows from the inlet hole to the space between the lower surface of the small tool 201 and the workpiece 311. The small tool 201 rotates and polishes the workpiece 311 through the lower surface and the polishing slurry.

[0094] The workpiece fixture platform 300 is installed on the worktable 400 and includes an optical flat plate 301, a No. 1 adapter plate 302, a Z-axis micro-motion platform 303, a No. 2 adapter plate 304, a pressure sensor 305, an aluminum plate with a long hole 306, a water tank 307, an acrylic adapter plate 3071, a No. 1 rubber sealing ring 308, a No. 2 rubber sealing ring 309, a workpiece placement plate 310, and a workpiece 311. The optical flat plate 301, adapter plate 1 302, Z-axis micro-motion platform 303, adapter plate 2 304, pressure sensor 305, and water tank 307 are arranged sequentially from bottom to top. The pressure sensor 305 is installed on the water tank 307. The workpiece placement plate 310 is installed inside the water tank 307 and is connected to the upper end of the pressure sensor 305. An acrylic adapter plate 3071 is also installed on the bottom wall inside the water tank 307. The acrylic adapter plate 3071 is connected to the lower end of the workpiece placement plate 310 by fasteners. Rubber sealing ring 1 308 and rubber sealing ring 2 309 are also installed between the workpiece placement plate 310 and the acrylic adapter plate 3071. The workpiece 311 is placed on the upper surface of the workpiece placement plate 310. Multiple limiting plates 312 are installed on the workpiece placement plate 310 by fasteners. The limiting plates 312 are located around the workpiece 311 and abut against the side of the workpiece 311, which serves to limit the workpiece 311 in the horizontal direction.

[0095] The technical concept of this invention is: based on the Preston equation The material removal coefficient K is a constant under the conditions of workpiece processing requirements and mechanical properties of polishing tools. Therefore, the amount of material removed depends on the normal stress P, relative linear velocity V, and residence time T on the workpiece contact surface. The amount of material removed can be equivalently understood as the cumulative amount of contact stress at different radii as the rotation angle increases. By changing the residence time T at different radii through structural design, the integral value of the three can be kept constant to achieve uniform removal of the workpiece and achieve the ideal removal effect.

[0096] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the technical solutions of the present invention. Any technical solution that can be implemented based on the above embodiments without creative effort should be considered to fall within the scope of protection of the patent of the present invention.

Claims

1. A method for designing and fabricating a small tool to achieve uniform material removal, characterized in that, Specifically, the steps include the following: Step 1: Based on the Preston equation, given the known contact stress and relative velocity distribution between the tool and the workpiece, calculate the amount of material removed at each point in the contact area within the dwell time T. Step 2: Determine the material properties and structural characteristics of the initial general-purpose tool and workpiece; Step 3: Based on the quasi-static stress simulation results of ordinary small tools with a material mass ratio of 30% to 90% pressing down 0.1 to 2 mm on the workpiece surface, obtain the circumferential stress distribution characteristics of the contact area between the tool and the workpiece; Step 4: Calculate the angular distribution of contact areas with different radii; Step 5: Based on the cross-sectional curve data of the tool, make the corresponding mold, and then use the mold to make the tool.

2. The method for designing and preparing a small tool for uniform material removal according to claim 1, characterized in that, Step one specifically includes: The formula for calculating the material removal amount ΔZ(x,y) is: Substitution of variables in equation (1): Where θ is the total angle rotated by the tool. Let ω be the angle through which the tool rotates at a certain moment, and let V be the angular velocity of the tool. The velocity V depends only on the radius r and the angular velocity ω, i.e., V = rω. Simplify equation (2): Assume the circumferential equivalent stress is Right now Then equation (3) can be further simplified to: Under given operating conditions, if the Preston coefficient K is a constant, then: Where, constant 3. The method for designing and preparing a small tool for uniform material removal according to claim 2, characterized in that, Step two includes: A composite material with silicone as the matrix and 600-2000 mesh silicon carbide abrasive grains as the reinforcing phase is used as the main material of the small tool. The mass ratio of silicon carbide abrasive grains to silicone is positively correlated with the elastic modulus of the composite material. A central liquid supply disc type small tool with a flow channel design is used as the structural feature of the ordinary small tool.

4. The method for designing and preparing a small tool for uniform material removal according to claim 3, characterized in that, In step two, the radius of the liquid supply center hole of the small tool is set to x mm, the outer diameter of the small tool is set to β mm, and the annular area outside the radius α mm is set as the design range for uniform removal. The flow channel design divides the small tool symmetrically into four parts, where the width of the flow channel is a mm, the overall thickness of the ordinary small tool is b mm, and the depth of the flow channel is c mm.

5. The method for designing and preparing a small tool for uniform material removal according to claim 4, characterized in that, Step three specifically includes: Based on quasi-static stress simulation results of ordinary small tools with material mass ratios of 30%–90% pressing down 0.1–2 mm on the workpiece surface, the circumferential stress distribution characteristics of one-quarter of the tool-workpiece contact area are obtained. The circumferential stress curve of the area beyond radius α mm is integrated and divided by the arc length to obtain the equivalent contact stress for different radii. Equivalent contact stress Multiply by radius r to get The distribution characteristics of the product along the radius, for Curve fitting is performed on discrete points to obtain... The equation of the curve; determine the value of the constant C:

6. The method for designing and preparing a small tool for uniform material removal according to claim 5, characterized in that, Step four specifically includes: Calculate the angular distribution of contact areas with different radii according to formulas (5) and (6); symmetrically divide the tool into four parts, each part corresponding to two boundary curves. The equations of the boundary curves in the polar coordinate system are: Through numerical calculation and coordinate transformation, x = rcosθ, y = rsinθ, the coordinates of the data points of the boundary curve in the Cartesian coordinate system are: Numerical calculation tools are used to obtain data points for the boundary curves. These data points are then imported into modeling software to generate a model of the novel structural tool. Simulations are performed again to solve the problem, and the uniformity of the tool is evaluated. Determine if it meets the uniform removal design requirements; if it does, proceed to step four; if it does not, modify the material properties and boundary conditions of the tool, and repeat steps two through four; or compensate. For the discrete point values, re-fit the curve and repeat steps three and four.

7. The method for designing and preparing a small tool for uniform material removal according to claim 6, characterized in that, Step five includes: Based on the cross-sectional curve data of the tool, a mold is modeled, and the corresponding mold is made by 3D printing or metal wire cutting. A composite material with room temperature vulcanizing silicone as the matrix and 600-2000 mesh silicon carbide abrasive grains as the reinforcing phase is used as the main material of the tool. After standing at room temperature for 3-8 hours, the tool is demolded and trimmed at the same time.

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