A domain-force co-controlled spindle-shaped lattice polishing tool and its design method

Abstract

This invention discloses a domain-force co-controlled spindle-shaped lattice polishing tool and its design method, comprising a spindle-shaped sphere, two fixed shafts, two rotating sleeves, and a polishing outer layer. The lower part of the spindle-shaped sphere has several structured flow channels, which are distributed in a fan shape along the circumference. Each structured flow channel has a serpentine reciprocating structure, and electrodes are placed on the structured flow channels. All the structured flow channels and all the electrodes constitute a lattice system. This invention proposes a domain-force co-controlled spindle-shaped lattice polishing tool, using polydimethylsiloxane 3D printing to create a lattice system with structured flow channels. The internal flow channels of the polishing tool, combined with interdigitated electrodes, form lattice units. Each lattice unit is coupled to form a lattice system, enabling independent control of the contact stress of each lattice unit within the lattice system. This achieves the ideal contact stress distribution required for material removal, enabling controllable and on-demand material removal.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision machining technology, specifically to a domain-force co-controlled spindle-shaped dot matrix polishing tool and its design method. Background Technology

[0002] The frequency, time, and energy domain characteristics or parameters created by high-performance lasers make them an indispensable tool for cutting-edge scientific research in fields such as inertial confinement fusion, aerospace, astronomical observation, and new materials. To obtain high-performance lasers, it is essential to ensure the precision manufacturing level of the core component of high-power lasers—the aspherical optical element—that is, the accuracy of full-frequency error control.

[0003] Existing polishing technologies can effectively control low-frequency surface shape errors and significantly reduce high-frequency roughness, but effective control of mid-frequency errors remains a pressing issue. Stress-disk polishing uses computer-controlled dynamic polishing to manage stress distribution on the component surface, but its limitation lies in controlling the strain of the polishing disc by adjusting the tension of the connecting wires. This results in poor surface shape adaptability during deformation and regionalized stress changes on the disc surface, meaning the stress control area is limited. Such regional variations also lead to irregular distribution of surface contact stress, limiting the smoothing effect on mid-frequency errors. Flexible polishing tools adapt to the workpiece contour by adjusting the tool's surface shape and simultaneously control the tool's stiffness, enabling control of mid-frequency errors in different frequency bands. However, controlling mid-frequency errors caused by random fluctuations in contact stress during processing remains challenging, and relevant control methods require further breakthroughs. The aforementioned polishing methods have limitations in tool surface shape adaptation and contact stress control, particularly in achieving independent, real-time, and rapid control of the contact stress of the lattice units while simultaneously achieving an ideal distribution of contact stress across the entire lattice system of the polishing tool to remove mid-frequency errors, thus failing to achieve controllable material and on-demand removal. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a domain-force co-controlled spindle-shaped lattice polishing tool and its design method, aiming to achieve independent, real-time and rapid adjustment of the contact stress of the lattice units to achieve an ideal distribution, thereby reducing the influence of random fluctuations in contact stress, and realizing the functions of surface shape self-adaptation and suppression of periodic vibration.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A domain-force co-controlled spindle-shaped dot matrix polishing tool includes a spindle-shaped sphere, two fixed shafts respectively connected to the left and right ends of the spindle-shaped sphere, two rotating sleeves respectively rotatably sleeved on the left and right fixed shafts, and a polishing outer layer connected between the left and right rotating sleeves and covering the outer wall of the spindle-shaped sphere. The lower part of the spindle-shaped sphere has several structured flow channels, which are distributed in a fan shape along the circumference. Each structured flow channel has a serpentine reciprocating structure. The side of the structured flow channel facing the lower outer wall of the spindle-shaped sphere has several inflection points. The inflection points are close to the lower outer wall of the spindle-shaped sphere and are spaced apart along the outer wall of the spindle-shaped sphere in the axial direction. Electrodes are set on the structured flow channels. All the structured flow channels and all the electrodes constitute a dot matrix system.

[0007] Furthermore, an axial channel is provided on both the shuttle-shaped sphere and the fixed shaft, and the two ends of the structured flow channel are respectively connected to the axial channel.

[0008] Furthermore, a drive gear is rotatably sleeved on the fixed shaft, and the drive gear is connected to a rotating sleeve on the same side.

[0009] A design method for a domain-force co-controlled, spindle-shaped lattice polishing tool as described above includes:

[0010] Step 1: Combine the curvature characteristics of the entire surface of the aspherical optical element to obtain the design criteria for the geometric parameters of the spindle-shaped sphere, and establish a universal spindle-shaped shape feature;

[0011] Step 2: Based on the stress distribution model of different flow channel structures, optimize the structured flow channel configuration inside the simulated shuttle-shaped sphere;

[0012] Step 3: Based on the influence of electrode spacing and arrangement characteristics on electric field strength, combined with the flow channel construction and lattice close packing direction, an electrode topology with ideal electroosmosis driving effect is obtained.

[0013] Step 4: Combine the structured flow channel configuration and electrode topology to divide the lattice units for local region control;

[0014] Step 5: Establish the coupling relationship between lattice units using the theory of continuum mechanics to obtain a lattice system that conforms to the structured flow channel configuration;

[0015] Step 6: Establish the overall three-dimensional model of the polishing tool. The spindle-shaped sphere is made of polydimethylsiloxane viscoelastic material. Based on the constitutive model of polydimethylsiloxane viscoelastic material, the dynamic deformation response behavior of the lattice system is studied using the dynamic analysis module in the finite element method to obtain the contour-following characteristics of the polishing tool.

[0016] Step 7: Using the modal analysis module of the finite element method, study the transient dynamic characteristics of the polishing tool structure and analyze the control effect of the polishing tool on vibrations in different time and frequency domains;

[0017] Step 8: Optimize the dot matrix system of the polishing tool based on the contouring characteristics and vibration control effect;

[0018] Step 9: Repeat steps 5-8 until the best optimization result is obtained;

[0019] Step 10: Create a polishing tool based on the best optimization results.

[0020] Further, step 1 includes:

[0021] The curvature features of the entire surface of the aspherical optical element are extracted using 3D design software. Then, the geometric parameters of a series of polishing tools are determined based on the relationship between the polishing tool and the workpiece size.

[0022] Furthermore, step 3 includes:

[0023] The distribution of electric field intensity under different electrode arrangements and electrode spacings was analyzed using the finite element method. Based on the structured flow channel construction and the arrangement of electrodes in the close packing direction of the lattice, an electrode topology with sufficient electric field intensity and range was obtained.

[0024] Furthermore, step 5 includes:

[0025] The structured flow channel consists of several direct flow channels, which are regarded as three-dimensional Euler-Bernoulli beams, taking into account axial, bending and torsional degrees of freedom.

[0026] Axial stiffness The calculation formula is as follows:

[0027]

[0028] Where E represents the elastic modulus of the material, A represents the cross-sectional area of ​​the flow channel at that location, and L represents the length of the flow channel;

[0029] Bending stiffness The calculation formula is as follows:

[0030]

[0031] Where I represents the moment of inertia of the flow channel section;

[0032] Torsional stiffness The calculation formula is as follows:

[0033]

[0034] Where J represents the torsional constant and G represents the shear modulus;

[0035] Local stiffness matrix of the flow channel The calculation formula is as follows:

[0036]

[0037] In the formula, This represents the combined matrix of the bending stiffness and torsional stiffness of the flow channel.

[0038] Furthermore, step 5 also includes:

[0039] Perform a coordinate transformation on the local stiffness matrix of the flow channel to obtain the local stiffness matrix in the local coordinate system. Transform to the global coordinate system using the rotation matrix R:

[0040]

[0041] in, The stiffness of the flow channel in the global coordinate system is given by T, which represents the transpose.

[0042] Treating this flow channel segment as a node, the degrees of freedom of the node are assigned, and the displacement formula of the node is as follows:

[0043]

[0044] in, These represent the displacements of the node in the x, y, and z directions of the global coordinate system, respectively. These represent the rotation angles of the node about the global coordinate system axes x, y, and z, respectively. The displacement matrix representing the six degrees of freedom of a single node;

[0045] By combining boundary constraints, fixing the inlet and outlet of the flow channel, and considering the gravity load F of the lattice system, the Newton-Raphson method is used to solve the equations, yielding the following results:

[0046]

[0047]

[0048] in, Let represent the instantaneous stiffness matrix of the k-th iteration. This is expressed as the displacement increment at the k-th time. This represents the equivalent nodal stress inside the material caused by displacement in the k-th iteration. , This represents the displacement at the k-th and (k+1)-th iterations.

[0049] Furthermore, step 5 also includes:

[0050] From the global stiffness matrix Extracting off-diagonal matrix blocks ;

[0051] After solving for the coupling relationship of the lattice elements, the influence relationship of each internal element and the lattice system are obtained.

[0052] Furthermore, step 6 includes:

[0053] By combining the constitutive model of PDMS viscoelastic materials with fractional derivatives and introducing variable fractional integral theory, the constitutive equation of polydimethylsiloxane viscoelastic materials is established:

[0054]

[0055] in, For stress, For strain, t is a time variable. For material coefficients, Where is the viscoelastic coefficient, and , For operators of varying fractional order, a definition of the varying fractional section integral operator is proposed using Coimbra:

[0056]

[0057] in, For the Gamma function, Represents the different values ​​of the interval (0~t). Indicate strain about The first derivative, This indicates the degree to which the viscoelastic properties of a material change over time, and the range is (0~1).

[0058] After obtaining the constitutive equation of polydimethylsiloxane viscoelastic material, the relevant parameters are set using the finite element dynamics analysis module to analyze the response behavior of the dynamic deformation of the lattice system and obtain the conformal characteristics of the polishing tool.

[0059] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention proposes a domain-force co-controlled spindle-shaped lattice polishing tool, which uses polydimethylsiloxane 3D printing to form a lattice system with structured flow channels. The internal flow channels of the polishing tool and the interdigitated electrodes form lattice units. Each lattice unit is coupled to form a lattice system, realizing independent control of the contact stress of each lattice unit within the lattice system, achieving the ideal contact stress distribution required for material removal, and realizing controllable and on-demand material removal. In addition, its viscoelastic material properties and the structured design of the internal flow channels of the lattice system can adapt to the tool surface shape and reduce periodic vibration, controlling the generation of mid-frequency errors. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the usage state of a domain-force co-controlled spindle-shaped dot matrix polishing tool according to the present invention.

[0061] Figure 2 This is a schematic diagram of the axial cross-sectional structure of a domain-force co-controlled spindle-shaped lattice polishing tool according to the present invention.

[0062] Figure 3 This is a schematic diagram of the longitudinal cross-sectional structure of the middle part of a domain-force co-controlled spindle-shaped dot matrix polishing tool according to the present invention.

[0063] Figure 4 This is a schematic diagram of a domain-force co-controlled spindle-shaped dot matrix polishing tool according to the present invention. The outer polishing layer is not shown in the figure.

[0064] Figure 5 This is a schematic diagram of the flow channel unit structure in a domain-force co-controlled spindle-shaped dot matrix polishing tool according to the present invention.

[0065] Figure 6 This is a flowchart illustrating the design method of a domain-force co-controlled simulated shuttle-shaped dot matrix polishing tool according to the present invention.

[0066] In the diagram: 1 is the fixed shaft; 2 is the drive gear; 3 is the central shaft; 4 is the axial channel; 5 is the polished outer layer; 6 is the rotating sleeve; 7 is the bearing; 8 is the flow channel inlet; 9 is the electrode; 10 is the structured flow channel; 1000 is the first DC channel; 1001 is the second DC channel; 1002 is the third DC channel; 11 is the flow channel outlet; 12 is the lattice unit; 13 is the drive gear belt; 14 is the linkage shaft; 15 is the robotic arm mounting frame; 16 is the motor; 17 is the motor mounting plate; 18 is the motor belt; 19 is the stress control domain; 20 is the spindle-shaped sphere. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Please see Figures 1-5 A domain-force coordinated spindle-shaped dot matrix polishing tool includes a spindle-shaped sphere 20, two fixed shafts 1 respectively connected to the left and right ends of the spindle-shaped sphere 20, two rotating sleeves 6 respectively rotatably sleeved on the left and right fixed shafts, and a polishing outer layer 5 connected between the left and right rotating sleeves 6 and covering the outer wall of the spindle-shaped sphere 20. The lower part of the spindle-shaped sphere 20 has several structured flow channels 10, all of which are fan-shaped distributed circumferentially, with an angle range of 20°-45° to ensure full coverage of the contact area. The remaining parts have no flow channel structure. Figure 3As shown, the fan-shaped angle in this invention is preferably 30°. Each structured flow channel 10 is a serpentine reciprocating structure. The structured flow channel 10 has several inflection points 1003 on the side facing the lower outer wall of the imitation spindle-shaped sphere 20. The several inflection points 1003 are close to the lower outer wall of the imitation spindle-shaped sphere 10 and are spaced apart along the outer wall of the imitation spindle-shaped sphere 10 in the axial direction. Electrodes 9 are provided on the structured flow channel 10. All the structured flow channels and all the electrodes on the imitation spindle-shaped sphere 20 constitute a dot matrix system.

[0069] The polishing outer layer 5 is preferably an organic fabric layer, on which a thin layer of elastomer is coated and abrasive grains are adhered. The function of the organic fabric layer is to effectively transfer the output stress of the polishing tool to the contact area without changing the stress distribution trend. The organic fabric layer is fixed on the rotating sleeve 6. The spindle-shaped sphere 20 is made of polydimethylsiloxane (PDMS) viscoelastic material.

[0070] Continue reading Figure 1 A drive gear 2 is rotatably sleeved on a fixed shaft 1 via a bearing 7. The drive gear 2 is fixedly connected to a rotating sleeve 6 on the same side. When the drive gear 2 rotates, it drives the polishing outer layer 5 to rotate via the rotating sleeve 6, while the spindle-shaped sphere 20 does not rotate. The polishing tool of the present invention is used in conjunction with a drive device. The function of the drive device is to drive the polishing tool to rotate. The structure of the drive device is known technology. The following is one embodiment adopted by the present invention: The drive device includes a drive gear belt 13, a linkage shaft 14, a robotic arm mounting frame 15, a motor 16, a motor mounting plate 17, and a motor belt 18. The motor mounting plate 17 is mounted on the robotic arm mounting frame 15, and the motor 16 is mounted on the motor mounting plate 17. The linkage shaft 14 is also rotatably mounted on the robotic arm mounting frame 15. The end of the linkage shaft 14 is connected to the output shaft of the motor 16 via the motor belt 18 and a corresponding pulley. Pulleys are also sleeved at both ends of the linkage shaft 14. The linkage shaft 14 is connected to the drive gears 2 at both ends of the polishing tool via the drive gear belt 13 through the pulleys.

[0071] Continue reading Figure 2 An axial channel 21 is provided on both the spindle-shaped sphere 20 and the fixed shaft 1, and both ends of the structured flow channel 10 are connected to the axial channel 21. Specifically, one of the fixed shafts 1 is fixedly connected to a central shaft 3 protruding towards the spindle-shaped sphere 20. The central shaft 3 passes through the spindle-shaped sphere 20 and is connected to the other fixed shaft 1 by a thread. The two fixed shafts 1 clamp the spindle-shaped sphere 20 in the middle. The axial channel 21 is formed by the through holes at the center of the fixed shaft 1 and the central shaft 3, and it is used to supply liquid to the structured flow channel 10.

[0072] Continue reading Figure 2 and 5 The structured flow channel 10 consists of several such Figure 5The flow channel unit shown (excluding the beginning and end) consists of 6 DC channels. Specifically, the flow channel unit includes two third DC channels 1003 forming a V-shape. Each third DC channel 1003 connects to a vertically arranged first DC channel 1000. The two first DC channels 1000 are arranged in parallel, and the first DC channels 1000 are inclined outwards to connect to a second DC channel 1001. The two second DC channels 1001 form an inverted V-shape. The electrodes of this invention are preferably interdigitated electrodes, which are respectively arranged on the left and right sides of the flow channel unit. Each flow channel unit corresponds one-to-one with the left and right sides of the positive and negative electrodes of the interdigitated electrodes, achieving a large-area strong electric field coverage. The interdigitated electrodes and the flow channel unit are combined to form a lattice unit 12.

[0073] During polishing, the drive device drives the drive gear 2 to rotate, and the drive gear 2 drives the outer polishing layer 5 to rotate through the rotating sleeve 6, while the imitation shuttle-shaped sphere 20 does not rotate. The area with the structured flow channel 10 on the imitation shuttle-shaped sphere 20 is always facing the workpiece.

[0074] Please see Figure 6 A design method for a domain-force co-controlled lattice polishing tool as described above, comprising:

[0075] Step 1: Based on the full-surface curvature characteristics of aspherical optical elements, design criteria for the geometric parameters of a spindle-shaped sphere are obtained, establishing universally applicable spindle-shaped shape features, including:

[0076] The curvature features of the entire surface of the aspherical optical element are extracted using 3D design software. Then, the geometric parameters of a series of polishing tools are determined based on the relationship between the polishing tool and the workpiece size.

[0077] Step 2: Based on the stress distribution model of different flow channel structures, optimize the structured flow channel configuration inside the spindle-shaped sphere.

[0078] Step 3: Based on the influence of electrode spacing and arrangement characteristics on electric field strength, and combined with channel construction and lattice close packing direction, an electrode topology with ideal electroosmosis driving effect is obtained, including:

[0079] The distribution of electric field intensity under different electrode arrangements and electrode spacings was analyzed using the finite element method. Based on the structured flow channel construction and the arrangement of electrodes in the close packing direction of the lattice, an electrode topology with sufficient electric field intensity and range was obtained.

[0080] Step 4: Combine the structured flow channel configuration and electrode topology to divide the lattice units for local region control;

[0081] Step 5: Establish the coupling relationship between lattice units using continuum mechanics theory to obtain a lattice system conforming to the structured flow channel configuration, including:

[0082] To calculate the coupling relationship of the lattice elements, the flow channel structure must first be simplified and the stiffness of each part of the flow channel calculated. The structured flow channel consists of several direct current channels, which are regarded as three-dimensional Euler-Bernoulli beams, taking into account axial, bending and torsional degrees of freedom.

[0083] Axial stiffness The calculation formula is as follows:

[0084]

[0085] Where E represents the elastic modulus of the material, A represents the effective cross-sectional area of ​​the flow channel at that location, and L represents the length of the flow channel;

[0086] Bending stiffness The calculation formula is as follows:

[0087]

[0088] Where I represents the moment of inertia of the flow channel section.

[0089] Torsional stiffness The calculation formula is as follows:

[0090]

[0091] Where J represents the torsional constant and G represents the shear modulus.

[0092] Therefore, the local stiffness matrix of the flow channel The calculation formula is as follows:

[0093]

[0094] In the formula, This represents the combined matrix of the bending stiffness and torsional stiffness of the flow channel.

[0095] Subsequently, a coordinate transformation is performed on the local stiffness matrix of the flow channel to obtain the local stiffness matrix in the local coordinate system. Transform to the global coordinate system using a rotation matrix R, where R is determined by the direction cosine of the beam element's axis direction:

[0096]

[0097] in, This represents the stiffness of the flow channel in the global coordinate system, with the superscript T indicating transpose.

[0098] Treating this flow channel segment as a node and assigning its degrees of freedom, the displacement formula for the node is as follows:

[0099]

[0100] Each node contains six degrees of freedom. These represent the displacements of the node in the x, y, and z directions of the global coordinate system, respectively. These represent the rotation angles of the node about the global coordinate system axes x, y, and z, respectively. This represents the displacement matrix for a single node with six degrees of freedom.

[0101] By combining boundary constraints, fixing the inlet and outlet of the flow channel, and considering the gravity load F of the lattice system, the Newton-Raphson method is used to solve the equations, yielding the following results:

[0102]

[0103]

[0104] in, Let represent the instantaneous stiffness matrix of the k-th iteration. This is expressed as the displacement increment at the k-th time. This represents the equivalent nodal stress inside the material caused by displacement in the k-th iteration. This represents the displacement in the k-th iteration. This represents the displacement in the (k+1)th iteration;

[0105] Subsequently, from the global stiffness matrix Extracting off-diagonal matrix blocks , Indicates the coupling stiffness between node i and node j:

[0106]

[0107] in, This represents the constraint force generated by node i in the x-direction when node j undergoes displacement in the x-direction; This represents the constraint force generated in the x direction by node i when node j is displaced in the y direction; This represents the constraint force generated by node i in the x direction when node j is displaced in the z direction; This indicates that when node j rotates about the x-axis When i is in the x-direction, the constraint force generated thereon; This indicates that when node j rotates about the z-axis When i is in the x-direction, the constraint force generated thereon; This represents the constraint force generated by node i in the y direction when node j is displaced in the x direction; This represents the constraint force generated by node i in the y direction when node j undergoes displacement in the y direction; This represents the constraint force generated by node i in the y direction when node j is displaced in the z direction.

[0108] After solving for the coupling relationship of the lattice elements, the influence relationship of each internal element and the lattice system are obtained.

[0109] Step 6: Establish a three-dimensional model of the polishing tool. The spindle-shaped sphere is made of polydimethylsiloxane viscoelastic material. Based on the constitutive model of polydimethylsiloxane viscoelastic material, the dynamic deformation response behavior of the lattice system is studied using the dynamic analysis module in the finite element method to obtain the conformal characteristics of the polishing tool, including:

[0110] Combining the constitutive model of polydimethylsiloxane viscoelastic materials with fractional derivatives, and introducing variable fractional integral theory, the constitutive equation of polydimethylsiloxane viscoelastic materials is established:

[0111]

[0112] in, For stress, For strain, t is a time variable. For material coefficients, Where is the viscoelastic coefficient, and , For operators of varying fractional order, a definition of the varying fractional section integral operator is proposed using Coimbra:

[0113]

[0114] in, For the Gamma function, Represents the different values ​​of the interval (0~t). Indicate strain about The first derivative, This indicates the degree to which the viscoelastic properties of a material change over time, and the range is (0~1).

[0115] After obtaining the constitutive equation of polydimethylsiloxane viscoelastic material, the relevant parameters are set using the finite element dynamics analysis module to analyze the response behavior of the dynamic deformation of the lattice system and obtain the conformal characteristics of the polishing tool.

[0116] Step 7: Using the modal analysis module of the finite element method, study the transient dynamic characteristics of the polishing tool structure and analyze the control effect of the polishing tool on vibrations in different time and frequency domains.

[0117] Step 8: Optimize the dot matrix system of the polishing tool based on the contouring characteristics and vibration control effect.

[0118] Step 9: Repeat steps 5-8 until the best optimization result is obtained. The best optimization result is determined based on the conformal performance and vibration control effect.

[0119] Step 10: Create a polishing tool based on the best optimization results.

[0120] The working principle of the polishing tool of this invention is as follows: Before polishing, the mid-frequency error of the entire workpiece surface is extracted to obtain the ideal contact stress distribution for removing the mid-frequency error. During polishing, a solution is injected into the structured flow channel inside the spindle-shaped sphere. By applying the voltage value corresponding to the ideal contact stress, the internal stress of the lattice unit is precisely controlled. The generated internal stress of the lattice unit is transferred from the spindle-shaped sphere to the outer polishing layer, forming contact stress in the tool-workpiece contact area. Under the rotation of the polishing outer layer with attached abrasive grains, material is removed from the workpiece surface. By planning the movement trajectory of the tool across the entire workpiece surface, the voltage is adjusted in real time to obtain the ideal contact stress distribution in the contact area, ultimately achieving on-demand material removal from the entire workpiece surface and effectively controlling the mid-frequency error.

[0121] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A domain-force co-controlled spindle-shaped dot matrix polishing tool, characterized in that, It includes a spindle-shaped sphere, two fixed shafts connected to the left and right ends of the spindle-shaped sphere, two rotating sleeves rotatably fitted onto the two fixed shafts, and a polished outer layer connected between the two rotating sleeves and covering the outer wall of the spindle-shaped sphere. The lower part of the spindle-shaped sphere has several structured flow channels, which are distributed in a fan shape along the circumference. Each structured flow channel has a serpentine reciprocating structure. The side of the structured flow channel facing the lower outer wall of the spindle-shaped sphere has several inflection points. These inflection points are close to the lower outer wall of the spindle-shaped sphere and are spaced apart along the outer wall of the spindle-shaped sphere in the axial direction. Electrodes are set on the structured flow channels. All the structured flow channels and all the electrodes constitute a lattice system.

2. The domain-force co-controlled spindle-shaped dot matrix polishing tool according to claim 1, characterized in that, An axial channel is provided on both the spindle-shaped sphere and the fixed shaft, and the two ends of the structured flow channel are connected to the axial channel respectively.

3. The domain-force co-controlled spindle-shaped dot matrix polishing tool according to claim 1, characterized in that, A drive gear is rotatably sleeved on a fixed shaft, and the drive gear is connected to a rotating sleeve on the same side.

4. A design method for a domain-force co-controlled spindle-shaped dot matrix polishing tool as described in any one of claims 1-3, characterized in that, include: Step 1: Combine the curvature characteristics of the entire surface of the aspherical optical element to obtain the design criteria for the geometric parameters of the spindle-shaped sphere, and establish a universal spindle-shaped shape feature; Step 2: Based on the stress distribution model of different flow channel structures, optimize the structured flow channel configuration inside the simulated shuttle-shaped sphere; Step 3: Based on the influence of electrode spacing and arrangement characteristics on electric field strength, combined with the flow channel construction and lattice close packing direction, an electrode topology with ideal electroosmosis driving effect is obtained. Step 4: Combine the structured flow channel configuration and electrode topology to divide the lattice units for local region control; Step 5: Establish the coupling relationship between lattice units using the theory of continuum mechanics to obtain a lattice system that conforms to the structured flow channel configuration; Step 6: Establish the overall three-dimensional model of the polishing tool. The spindle-shaped sphere is made of polydimethylsiloxane viscoelastic material. Based on the constitutive model of polydimethylsiloxane viscoelastic material, the dynamic deformation response behavior of the lattice system is studied using the dynamic analysis module in the finite element method to obtain the contour-following characteristics of the polishing tool. Step 7: Using the modal analysis module of the finite element method, study the transient dynamic characteristics of the polishing tool structure and analyze the control effect of the polishing tool on vibrations in different time and frequency domains; Step 8: Optimize the dot matrix system of the polishing tool based on the contouring characteristics and vibration control effect; Step 9: Repeat steps 5-8 until the best optimization result is obtained; Step 10: Create a polishing tool based on the best optimization results.

5. The design method according to claim 4, characterized in that, Step 1 includes: The curvature features of the entire surface of the aspherical optical element are extracted using 3D design software. Then, the geometric parameters of a series of polishing tools are determined based on the relationship between the polishing tool and the workpiece size.

6. The design method according to claim 4, characterized in that, Step 3 includes: The distribution of electric field intensity under different electrode arrangements and electrode spacings was analyzed using the finite element method. Based on the structured flow channel construction and the arrangement of electrodes in the close packing direction of the lattice, an electrode topology with sufficient electric field intensity and range was obtained.

7. The design method according to claim 4, characterized in that, Step 5 includes: The structured flow channel consists of several direct flow channels, which are regarded as three-dimensional Euler-Bernoulli beams, taking into account axial, bending and torsional degrees of freedom. Axial stiffness The calculation formula is as follows: Where E represents the elastic modulus of the material, A represents the cross-sectional area of ​​the flow channel at that location, and L represents the length of the flow channel; Bending stiffness The calculation formula is as follows: Where I represents the moment of inertia of the flow channel section; Torsional stiffness The calculation formula is as follows: Where J represents the torsional constant and G represents the shear modulus; Local stiffness matrix of the flow channel The calculation formula is as follows: In the formula, This represents the combined matrix of the bending stiffness and torsional stiffness of the flow channel.

8. The design method according to claim 7, characterized in that, Step 5 also includes: Perform a coordinate transformation on the local stiffness matrix of the flow channel to obtain the local stiffness matrix in the local coordinate system. Transform to the global coordinate system using the rotation matrix R: in, The stiffness of the flow channel in the global coordinate system is given by T, which represents the transpose. Treating this flow channel segment as a node, the degrees of freedom of the node are assigned, and the displacement formula of the node is as follows: in, These represent the displacements of the node in the x, y, and z directions of the global coordinate system, respectively. These represent the rotation angles of the node about the global coordinate system axes x, y, and z, respectively. The displacement matrix representing the six degrees of freedom of a single node; By combining boundary constraints, fixing the inlet and outlet of the flow channel, and considering the gravity load F of the lattice system, the Newton-Raphson method is used to solve the equations, yielding the following results: in, Let represent the instantaneous stiffness matrix of the k-th iteration. This is expressed as the displacement increment at the k-th time. This represents the equivalent nodal stress inside the material caused by displacement in the k-th iteration. , This represents the displacement in the k-th and (k+1)-th iterations.

9. The design method according to claim 8, characterized in that, Step 5 also includes: From the global stiffness matrix Extracting off-diagonal matrix blocks ; After solving for the coupling relationship of the lattice elements, the influence relationship of each internal element and the lattice system are obtained.

10. The design method according to claim 4, characterized in that, Step 6 includes: By combining the constitutive model of PDMS viscoelastic materials with fractional derivatives and introducing variable fractional integral theory, the constitutive equation of polydimethylsiloxane viscoelastic materials is established: in, For stress, For strain, t is the time variable. For material coefficients, Where is the viscoelastic coefficient, and , For operators of varying fractional order, a definition of the varying fractional section integral operator is proposed using Coimbra: in, For the Gamma function, Represents the different values ​​of the interval (0~t). Indicate strain about The first derivative, This indicates the degree to which the viscoelastic properties of a material change over time, and the range is (0~1). After obtaining the constitutive equation of polydimethylsiloxane viscoelastic material, the relevant parameters are set using the finite element dynamics analysis module to analyze the response behavior of the dynamic deformation of the lattice system and obtain the conformal characteristics of the polishing tool.

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