Conformal vibratory smoothing polishing method for conic optical elements and optical elements

Abstract

The application discloses a kind of conformal vibration smooth polishing method and optical element for conical surface optical element, the method of the application includes the conical surface of conical surface optical element to be processed is divided into concentric n ring zone, respectively to each ring zone test obtains corresponding removal function;Measure the surface shape data of conical surface optical element to be processed;For each ring zone, respectively according to the surface shape data of conical surface optical element to be processed and its removal function, carry out the residence time calculation in polishing process;For each ring zone of conical surface optical element to be processed, in turn using the processing parameters set, corresponding removal function and the residence time calculated to carry out polishing disc conformal vibration smooth polishing until surface shape data meets requirements.The application aims to protect the low-frequency surface shape of conical surface optical element, while quickly and effectively inhibiting the medium-frequency error remaining on the original processing surface, to achieve the purpose of realizing the collaborative control of processing efficiency and surface shape precision of conical surface optical element.

Description

Technical Field

[0001] This invention relates to the field of optical element processing technology, specifically to a conformal vibration smoothing polishing method for conical optical elements and the optical element itself. Background Technology

[0002] Complex curved surface optical elements are widely used in fields such as spectral analysis, laser communication, integrated circuit manufacturing, and astronomical observation. Ultra-precision manufacturing technology for such optical elements with complex curved shapes has always been a research hotspot in the field of optical manufacturing, and researchers have conducted a series of studies. Conical optical elements, as an important type of complex curved surface optical element, possess unique beam transformation capabilities, capable of shaping incident beams into Bessel beams. Bessel beams exhibit near-diffraction-free characteristics, long depth of focal length, and self-healing properties, and are widely used in laser processing, biomedicine, and optical imaging. As the requirements for the manufacturing precision of core optical elements in optical systems continue to increase, the demand for conical optical elements is becoming increasingly apparent.

[0003] Currently, in the field of ultra-precision optical manufacturing, most methods for controlling the surface shape error of conical optical elements still rely on iterative processing using a combination of multiple processes. This involves using different processes to address surface shape errors at different frequency bands. For example, magnetorheological polishing is first used to correct low-frequency errors on the optical surface, ensuring the low-frequency surface shape meets acceptable standards. However, this process also introduces various types of residual mid-frequency errors into the processed surface. Often, large-aperture or full-aperture polishing tools are then used to smooth the residual mid-frequency errors. During this process, due to the drastic changes in the curvature of the conical surface, it is difficult to maintain the surface shape of the conical optical element effectively. Therefore, iterative processing is required until the errors in each frequency band of the processed surface converge to acceptable levels. This method is complex, time-consuming, and costly, making it difficult to simultaneously achieve coordinated control of low- and mid-frequency surface shape errors of conical optical elements. Consequently, it struggles to meet the demands of large-scale market applications and facilitate mass production. Existing methods for controlling the surface shape error of conical optical elements using different processes to handle surface shape errors in different frequency bands have the following problems: (1) Low processing efficiency: Multiple polishing processes with multiple processes will lead to a longer processing cycle and introduce errors in multiple processing and inspection stages, resulting in a decrease in accuracy; (2) Distortion function distortion: During processing, ordinary polishing tools will cause contact removal deformation due to the characteristics of the high steepness and continuous curvature of the conical surface, which will lead to distortion of the removal function and reduce the certainty and predictability of processing; (3) Limited surface shape correction frequency band: When using sub-aperture polishing tools to process conical elements, the low-frequency surface shape of the element is often destroyed due to poor bonding effect. In addition, some existing technologies have proposed using non-contact CO2 laser polishing methods to process conical optical elements, but this method will inevitably produce thermal effects on the processed surface, especially at the cone tip of the conical surface, which will lead to rounding and passivation phenomena, failing to provide high-quality conical surface shape results. How to achieve improved processing efficiency and surface shape accuracy control for conical optical elements has become an urgent technical problem to be solved. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a conformal vibration smoothing polishing method and optical element for conical optical elements, which addresses the above-mentioned problems of the prior art. The present invention aims to protect the low-frequency surface shape of the conical optical element while quickly and effectively suppressing the mid-frequency error remaining on the original processed surface, thereby achieving the purpose of improving processing efficiency and surface shape accuracy of the conical optical element.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A conformal vibration smoothing polishing method for conical optical elements includes the following steps: S101, based on the concentric circle polishing trajectory of the processed conical optical element, the conical surface of the processed conical optical element is divided into n concentric rings, and the corresponding removal function is obtained by testing each ring. S102, Measure the surface shape data of the processed conical optical element; S103, for each ring of the conical optical element being processed, the dwell time during the polishing process is calculated based on the current surface shape data of the conical optical element being processed and its removal function; S104, for each ring of the conical optical element being processed, the polishing disk is used sequentially for conformal vibration smoothing polishing using the set processing parameters, the corresponding removal function and the calculated dwell time; S105, measure the surface shape data of the processed conical optical element. If the surface shape data meets the requirements, the process ends and exits; otherwise, adjust the processing parameters and jump to step S103 to continue the iteration.

[0006] Optionally, in step S101, when testing each ring to obtain the corresponding removal function, the process includes conducting a dwelling spot experiment on each ring on a test piece under the same conditions as the processed conical optical element, and using a measuring instrument to obtain the removal function of the corresponding ring on the test piece, thereby obtaining the removal function corresponding to each ring.

[0007] Optionally, the dwell time calculation during the polishing process in step S103 includes: S201, Based on the current surface shape data of the processed conical optical element, obtain the required material removal thickness for each sampling point in the current surface shape data of the processed conical optical element: ; in, For the kth sampling point Required material removal thickness, For the kth sampling point Surface data, For the ideal shape surface values, , This represents the total number of sampling points; S202, will any number of The radius of the circumference of the ring to the center of the ring is denoted as . , , To determine the total number of rings, determine the number of rings. Number of stations on each ring And the number of residence points in each annulus Increasing from the center outwards; determining the first... Any 1st ring band The polar angle of each station and rectangular coordinates for: ; ; in, The polar angle of the first station. For the index of the residence point, ; and The first Any 1st ring band The x and y coordinates of each station; S203, bring all N rings onto the rings. Each station is sequentially numbered; S204, transform the removal function of each ring zone in polar coordinates to global coordinates to obtain the amount of material removed per unit time at each residence point; ; ; in, For the first The first ring band The coordinates of each dwelling point in the global coordinate system The amount of material removed per unit time at a location. For the first The first ring band The polar angle of each station The result obtained by the rotation transformation function Coordinates in the global coordinate system The column vector at position, in the superscript Indicates transpose; For the first The first ring band Cartesian coordinates of each station point For rotation transformation function, is the independent variable of the rotation transformation function; S205, according to The sequential number of each station and the index of the station on each circumference There exists a unique one-to-one mapping relationship, which determines all the first... The first station for the first sampling points Material removal rate per unit time : ; in, For the first The first ring band The coordinates of each dwelling point in the global coordinate system The amount of material removed per unit time at a location. Coordinates in the global coordinate system The column vector at that position; S206, all the first The first station for the first sampling points Material removal rate per unit time Build Dimensional material removal matrix per unit time Construct a system of linear equations for the residence time: ; in, for The total material removal matrix of dimension, Let M be the dwell time at each of the M stops. ~ These represent the dwell times at the 1st to Mth stops, respectively. For the K sampling points, the required material thickness vector to be removed. ~ Let the required material removal thicknesses be the thicknesses required for the first to K sampling points, respectively; solve the linear equations for the dwell time to obtain the dwell time for the M dwell points.

[0008] Optionally, during the conformal vibration smoothing polishing of the polishing disc in step S104, the conical optical element to be processed is fixed on the fixture of the machine tool. The yaw motion of the yaw cradle mechanism of the fixture adjusts the generatrix on one side of the conical optical element to be processed to a horizontal state, drives the conical optical element to rotate around the axis, and then drives the conical optical element to reciprocate along the horizontal direction through the vibration mechanism of the fixture. The polishing disc on the machine tool is controlled to make radial feed motion along the horizontal direction in sequence in each ring. Using the set processing parameters, the corresponding removal function and the calculated dwell time, the polishing disc is used to perform conformal vibration smoothing polishing.

[0009] Optionally, in step S104, the set processing parameters include some or all of the following: the vibration frequency of the polishing disc, the vibration amplitude, the feed distance, the polishing pressure, the material removal depth of a single wheel, and the number of polishing wheels.

[0010] Optionally, in step S104, during conformal vibration smoothing polishing of the polishing disk, the polishing disk used is a fan-shaped structure cocentric with the conical optical element being processed, and polishing disks with different parameters are used for different annular zones, and for any... i The ring band includes: obtaining the first iThe starting and ending coordinates of the annular band removal area along the generatrix direction of the conical optical element being processed are calculated. The distance between the midpoint of the annular band width segment between these starting and ending coordinates and the center of the conical optical element being processed is then used as the center design distance of the corresponding polishing pad. ; Get the i The length of the line segment in the direction of the generatrix of the cone surface of the processed conical optical element, representing the removal region of the first ring, is taken as the obtained length of the first ring. i The actual radial width of the first ring will be the first i The actual radial width of each ring is used as the fan edge length of the corresponding polishing pad. Design distance based on the center of the polishing pad and fan edge length Determine the central angle of the corresponding polishing pad. : ; in, The target aspect ratio coefficient is the ratio of the outer edge arc length to the fan edge length of the polishing pad.

[0011] Optionally, the polishing pad includes a conformal transition layer, a flexible deformation layer and a polishing pad layer arranged in sequence. The top surface of the conformal transition layer is provided with a ball joint mechanism for connecting the polishing pad. The polishing pad layer is used to contact the surface of the conical optical element being processed to achieve polishing of the conical optical element being processed.

[0012] Optionally, the material used in the flexible deformable layer has an elastic modulus in the range of 10-50 MPa and a Poisson's ratio in the range of 0.45-0.49.

[0013] Optionally, the thickness of the polishing pad layer is 1-2 mm.

[0014] The present invention also provides a conical optical element, wherein the conical optical element is formed by processing using the conformal vibration smoothing polishing method for conical optical elements.

[0015] Compared with existing technologies, the present invention mainly achieves the following beneficial effects: The method of the present invention includes dividing the conical surface of the conical optical element to be processed into n concentric rings, and testing and obtaining the corresponding removal function for each ring; measuring the surface shape data of the conical optical element to be processed; calculating the dwell time during the polishing process for each ring based on the current surface shape data of the conical optical element to be processed and its removal function; and performing conformal vibration smoothing polishing on a polishing disk for each ring of the conical optical element to be processed using set processing parameters, the corresponding removal function, and the calculated dwell time until the surface shape data meets the requirements. The present invention can protect the low-frequency surface shape of the conical optical element while quickly and effectively suppressing the mid-frequency error remaining on the original processed surface, achieving the goal of improving processing efficiency and surface shape accuracy of the conical optical element in a coordinated manner. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of the ring zone division and its corresponding removal function according to an embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram of the conical conformal vibration polishing principle according to an embodiment of the present invention.

[0019] Figure 4 This is a schematic diagram of the structural parameters of the polishing disc in an embodiment of the present invention.

[0020] Figure 5 This is a three-dimensional exploded view of the polishing disc in an embodiment of the present invention.

[0021] Legend: 1. Conformal transition layer; 2. Flexible deformation layer; 3. Polishing pad layer. Detailed Implementation

[0022] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0023] like Figure 1 As shown, the conformal vibration smoothing polishing method for conical optical elements in this embodiment includes the following steps: S101, based on the concentric circular polishing trajectory applied to the processed conical optical element, the conical surface of the processed conical optical element is divided into n concentric rings, such as... Figure 2 The figures show the first to nth annular zones, respectively. The corresponding removal function is obtained by testing each annular zone. Figure 2The right side illustrates the removal functions for the 1st to nth rings, where darker colors represent areas where material is removed more deeply, and lighter colors represent areas where material is removed less deeply. S102, Measure the surface shape data of the processed conical optical element; S103, for each ring of the conical optical element being processed, the dwell time during the polishing process is calculated based on the current surface shape data of the conical optical element being processed and its removal function; S104, for each ring of the conical optical element being processed, the polishing disk is used sequentially for conformal vibration smoothing polishing using the set processing parameters, the corresponding removal function and the calculated dwell time; S105: Measure the surface shape data of the processed conical optical element. If the surface shape data meets the requirements, the process ends and exits; otherwise, adjust the processing parameters and jump to step S103 to continue iteration. If the surface shape of the polished conical element does not meet the requirements, modify the polishing processing parameters based on the surface shape detection data feedback, and perform local shaping or overall smoothing on the conical element.

[0024] In step S101 of this embodiment, when testing each ring band to obtain the corresponding removal function, the following steps are taken: a dwelling spot test is performed on each ring band on a test piece with the same conditions (same material, same size) as the processed conical optical element; the removal function of the corresponding ring band on the test piece is obtained using a measuring instrument; and the removal function corresponding to each ring band is obtained. Preliminary experiments are then conducted to obtain the accurate removal function of different ring bands.

[0025] In this embodiment, step S103 includes calculating the dwell time during the polishing process: S201, in this embodiment, a concentric circle polishing trajectory is used to process the conical element. The surface of the conical element to be processed is divided into multiple concentric ring removal regions, and the corresponding removal function is matched in the removal function library to solve the problem of solving the residence time equation involving time-varying removal functions. The initial surface shape data obtained by measuring equipment such as a white light interferometer is discretized to obtain discrete sampling points. ,in , This represents the total number of sampling points. Based on the current surface shape data of the processed conical optical element, the required material removal thickness for each sampling point in the current surface shape data of the processed conical optical element is obtained: ; in, For the kth sampling point Required material removal thickness, For the kth sampling point Surface data, For the ideal shape surface values, , This represents the total number of sampling points; S202, will any number of The radius of the circumference of the ring to the center of the ring is denoted as . , , To determine the total number of rings, determine the number of rings. Number of stations on each ring And the number of residence points in each annulus Increasing from the center outwards; determining the first... Any 1st ring band The polar angle of each station and rectangular coordinates for: ; ; in, The polar angle of the first station. For the index of the residence point, ; and The first Any 1st ring band The x and y coordinates of each station; S203, bring all N rings onto the rings. Each station is sequentially numbered; S204, transform the removal function of each ring zone in polar coordinates to global coordinates to obtain the amount of material removed per unit time at each residence point; ; ; in, For the first The first ring band The coordinates of each dwelling point in the global coordinate system The amount of material removed per unit time at a location. For the first The first ring band The polar angle of each station The result obtained by the rotation transformation function Coordinates in the global coordinate system The column vector at position, in the superscript Indicates transpose; For the first The first ring band Cartesian coordinates of each station point For rotation transformation function, is the independent variable of the rotation transformation function; S205, based on the principle of material removal superposition, the total removal amount generated by the combined effect of all retention points is distributed as follows: ; in, For the first The length of stay at each stop, For the removal function in the first... The removal matrix of each resident point; therefore, it can be determined according to The sequential number of each station and the index of the station on each circumference There exists a unique one-to-one mapping relationship, which determines all the first... The first station for the first sampling points Material removal rate per unit time : ; in, For the first The first ring band The coordinates of each dwelling point in the global coordinate system The amount of material removed per unit time at a location. Coordinates in the global coordinate system The column vector at that position; S206, all the first The first station for the first sampling points Material removal rate per unit time Build Dimensional material removal matrix per unit time Construct a system of linear equations for the residence time: ; in, for The total material removal matrix of dimension, Let M be the dwell time at each of the M stops. ~ These represent the dwell times at the 1st to Mth stops, respectively. For the K sampling points, the required material thickness vector to be removed. ~ Let the required material removal thicknesses be the thicknesses required for the first to K sampling points, respectively; solve the linear equations for the dwell time to obtain the dwell time for the M dwell points.

[0026] The polishing process in this embodiment employs conical conformal vibration polishing, such as... Figure 3As shown, in step S104, during conformal vibration smoothing polishing, the conical optical element to be processed is fixed to the machine tool fixture. The oscillation motion of the fixture's oscillating cradle mechanism adjusts the generatrix of one side of the conical optical element to a horizontal state, driving the conical optical element to rotate around its axis. Then, the fixture's vibration mechanism drives the conical optical element to reciprocate along the horizontal direction, while the polishing disc on the machine tool is controlled to perform radial feed motion along the horizontal direction, sequentially moving through each ring. Using the set processing parameters, the corresponding removal function, and the calculated dwell time, the polishing disc performs conformal vibration smoothing polishing. In this embodiment, a processing method that oscillates the generatrix of the conical element to a horizontal position is adopted. This method is beneficial for decoupling the mechanical behavior between the polishing disc and the processed surface during polishing, achieving loading control of normal compressive stress and vibration control of tangential shear stress respectively. Secondly, it eliminates the complex relative posture analysis between the oscillating tool and the workpiece, as well as the problems of stress field tilting and torsion. This processing method also reduces the requirements for the interpolation motion performance of the machine tool. The feed space motion trajectory of the end effector of the polishing equipment is a straight line, which is closer to the ideal processing trajectory. In this embodiment, a yaw cradle mechanism is used to provide the yaw motion of the vertical section where the generatrix of the conical optical element is located for the processed conical optical element. The specific yaw degree is related to the half-apex angle of the conical element to be processed. The high-frequency and high-speed vibration motion of the polishing disc can generate a higher relative motion speed at the contact point, providing a higher material removal efficiency to the processed surface. Adjusting to the accurate processing position includes accurately mounting the conical element to be processed on a special fixture and matching it with the corresponding reference point, and using a dial indicator to check the alignment accuracy between the cone center and the rotation center of the rotary mechanism.

[0027] In step S104 of this embodiment, the set processing parameters include some or all of the following: the vibration frequency, vibration amplitude, feed distance, polishing pressure, single-wheel material removal depth, and number of polishing wheels of the polishing disc. The polishing pressure is monitored in real time by the force control unit of the polishing tool. The force control unit controls the polishing pressure with an accuracy of ±0.1N, smoothing pressure fluctuations ≤10%, and a maximum pressure ≥50N.

[0028] In step S104 of this embodiment, during conformal vibration smoothing polishing of the polishing disk, the polishing disk used is a fan-shaped structure that is concentric with the conical optical element being processed, such as... Figure 4 As shown, a is the polishing disk and b is the conical optical element being processed.

[0029] Existing technologies for sub-aperture polishing generally use full-diameter polishing discs to achieve fit to the machined curved surface shape; traditional flexible sub-aperture polishing tools such as airbags and magnetorheological polishers are used to achieve fit to complex curved surfaces. However, full-diameter polishing tools lack the ability to locally modify the machined surface and protect its structure. For components with singular points at the cone tip, such as conical surfaces, vibration of the full-diameter polishing disc cannot protect the cone tip structure and may even generate continuous impact, resulting in a decrease in machining quality. Traditional flexible sub-aperture polishing tools such as airbags and magnetorheological polishers lack the ability to adapt to surfaces with varying curvature. The removal function on the machined surface of the conical surface will be severely distorted, and it will be unable to effectively suppress mid-frequency errors. Regular toolpaths may even introduce mid-frequency errors into the machined surface. To solve the above technical problems, this embodiment uses polishing discs with different parameters for different annular zones, and for any... i The ring band includes: obtaining the first i The starting and ending coordinates of the annular band removal area along the generatrix direction of the conical optical element being processed are calculated. The distance between the midpoint of the annular band width segment between these starting and ending coordinates and the center of the conical optical element being processed is then used as the center design distance of the corresponding polishing pad. ; Get the i The length of the line segment in the direction of the generatrix of the cone surface of the processed conical optical element, representing the removal region of the first ring, is taken as the obtained length of the first ring. i The actual radial width of the first ring will be the first i The actual radial width of each ring is used as the fan edge length of the corresponding polishing pad. Design distance based on the center of the polishing pad and fan edge length Determine the central angle of the corresponding polishing pad. : ; in, The target aspect ratio coefficient for the effective working surface of the polishing pad is the ratio of the outer edge arc length to the fan edge length. The three contouring design factors mentioned above affect the variation in the contact area between the polishing pad and the conical surface at different radial positions. This sub-aperture conical contouring polishing pad allows for a small degree of edge over-polishing when polishing at the edge or cone tip, enabling thorough polishing and protection of the cone tip structure.

[0030] In this embodiment, the conformal design of the polishing pad improves its fit during the polishing of the conical surface, thereby maintaining the accuracy of the low-frequency surface shape when smoothly polishing the surface of the conical element. Figure 5As shown, in this embodiment, the polishing pad includes a conformal transition layer 1, a flexible deformation layer 2, and a polishing pad layer 3 arranged in sequence. The top surface of the conformal transition layer 1 is provided with a ball joint mechanism for connecting the polishing pad. The polishing pad layer 3 is used to contact the surface of the processed conical optical element to achieve polishing of the processed conical optical element.

[0031] In this embodiment, the conformal transition layer 1 serves as the main load-bearing structure of the polishing pad. The top surface is designed with a ball joint mechanism to connect with the upper unit, so as to realize high-precision vibration motion transmission under different frequencies and amplitudes. Materials such as aluminum alloy can be selected.

[0032] In this embodiment, the elastic modulus of the material used in the flexible deformable layer 2 is in the range of 10-50 MPa, and the Poisson's ratio is between 0.45 and 0.49. The material can be polyurethane or silicone rubber.

[0033] In this embodiment, the thickness of the polishing pad 3 is 1-2mm. It is shaped according to the characteristic dimensions of the conical element to be processed so that the contour of its lower surface is close to the curvature of the workpiece surface, so as to take into account both material removal performance and surface compliance. Materials such as polyurethane, asphalt, velvet or viscoelastic polymer are selected.

[0034] Furthermore, this embodiment also provides a conical optical element, which is formed by processing using the conformal vibration smoothing polishing method for conical optical elements in this embodiment.

[0035] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A conformal vibration smoothing polishing method for conical optical elements, characterized in that, Includes the following steps: S101, based on the concentric circle polishing trajectory of the processed conical optical element, the conical surface of the processed conical optical element is divided into n concentric rings, and the corresponding removal function is obtained by testing each ring. S102, Measure the surface shape data of the processed conical optical element; S103, for each ring of the conical optical element being processed, the dwell time during the polishing process is calculated based on the current surface shape data of the conical optical element being processed and its removal function; S104, for each ring of the conical optical element being processed, the polishing disk is used sequentially for conformal vibration smoothing polishing using the set processing parameters, the corresponding removal function and the calculated dwell time; S105, measure the surface shape data of the processed conical optical element. If the surface shape data meets the requirements, the process ends and exits; otherwise, adjust the processing parameters and jump to step S103 to continue the iteration.

2. The conformal vibration smoothing polishing method for conical optical elements according to claim 1, characterized in that, In step S101, when testing each ring band to obtain the corresponding removal function, the process includes conducting a dwelling spot experiment on each ring band on a test piece under the same conditions as the processed conical optical element, and using a measuring instrument to obtain the removal function of the corresponding ring band on the test piece, thereby obtaining the removal function corresponding to each ring band.

3. The conformal vibration smoothing polishing method for conical optical elements according to claim 1, characterized in that, Step S103 includes calculating the dwell time during the polishing process, which includes: S201, Based on the current surface shape data of the processed conical optical element, obtain the required material removal thickness for each sampling point in the current surface shape data of the processed conical optical element: ； in, For the kth sampling point Required material removal thickness, For the kth sampling point Surface data, For the ideal shape surface values, , This represents the total number of sampling points; S202, will any number of The radius of the circumference of the ring to the center of the ring is denoted as . , , To determine the total number of rings, determine the number of rings. Number of stations on each ring And the number of residence points in each annulus Increasing from the center outwards; determining the first... Any 1st ring band The polar angle of each station and rectangular coordinates for: ； ； in, The polar angle of the first station. For the index of the residence point, ; and The first Any 1st ring band The x and y coordinates of each station point; S203, bring all N rings onto the rings. Each station is sequentially numbered; S204, transform the removal function of each ring zone in polar coordinates to global coordinates to obtain the amount of material removed per unit time at each residence point; ； ； in, For the first The first ring band The coordinates of each dwelling point in the global coordinate system The amount of material removed per unit time at a location. For the first The first ring band The polar angle of each station The result obtained by the rotation transformation function Coordinates in the global coordinate system The column vector at position, in the superscript Indicates transpose; For the first The first ring band Cartesian coordinates of each station point For rotation transformation function, is the independent variable of the rotation transformation function; S205, according to The sequential number of each station and the index of the station on each circumference There exists a unique one-to-one mapping relationship, which determines all the first... The first station for the first sampling points Material removal rate per unit time : ； in, For the first The first ring band The coordinates of each dwelling point in the global coordinate system The amount of material removed per unit time at a location. Coordinates in the global coordinate system The column vector at that position; S206, all the first The first station for the first sampling points Material removal rate per unit time Build Dimensional material removal matrix per unit time Construct a system of linear equations for the residence time: ； in, for The total material removal matrix of dimension, Let M be the dwell time at each of the M stops. ~ These represent the dwell times at the 1st to Mth stops, respectively. For the K sampling points, the required material thickness vector to be removed. ~ Let the required material removal thicknesses be the thicknesses required for the first to K sampling points, respectively; solve the linear equations for the dwell time to obtain the dwell time for the M dwell points.

4. The conformal vibration smoothing polishing method for conical optical elements according to claim 1, characterized in that, In step S104, during conformal vibration smoothing polishing, the conical optical element to be processed is fixed on the machine tool fixture. The yaw motion of the yaw cradle mechanism of the fixture adjusts the generatrix on one side of the conical optical element to be processed to a horizontal state, drives the conical optical element to rotate around the axis, and then drives the conical optical element to reciprocate along the horizontal direction through the vibration mechanism of the fixture. The polishing disk on the machine tool is controlled to make radial feed motion along the horizontal direction in sequence in each ring. Using the set processing parameters, the corresponding removal function and the calculated dwell time, the polishing disk is used to perform conformal vibration smoothing polishing.

5. The conformal vibration smoothing polishing method for conical optical elements according to claim 1, characterized in that, In step S104, the set processing parameters include some or all of the following: the vibration frequency of the polishing disc, the vibration amplitude, the feed distance, the polishing pressure, the material removal depth of a single wheel, and the number of polishing wheels.

6. The conformal vibration smoothing polishing method for conical optical elements according to claim 1, characterized in that, In step S104, during conformal vibration smoothing polishing, the polishing disk used is a fan-shaped structure cocentric with the conical optical element being processed. Different parameters are used for different ring zones, and for any given ring zone... i The ring band includes: obtaining the first... i The starting and ending coordinates of the annular band removal area along the generatrix direction of the conical optical element being processed are calculated. The distance between the midpoint of the annular band width segment between these starting and ending coordinates and the center of the conical optical element being processed is then calculated. This distance is used as the center design distance of the corresponding polishing pad. ; Get the i The length of the line segment in the direction of the generatrix of the cone surface of the processed conical optical element, representing the removal region of the first ring, is taken as the obtained length of the first ring. i The actual radial width of the first ring will be the first i The actual radial width of each ring is used as the fan edge length of the corresponding polishing pad. Design distance based on the center of the polishing pad and fan edge length Determine the central angle of the corresponding polishing pad. : ； in, The target aspect ratio coefficient is the ratio of the outer edge arc length to the fan edge length of the polishing pad.

7. The conformal vibration smoothing polishing method for conical optical elements according to claim 1, characterized in that, The polishing pad includes a conformal transition layer (1), a flexible deformation layer (2), and a polishing pad layer (3) arranged in sequence. The top surface of the conformal transition layer (1) is provided with a ball joint mechanism for connecting the polishing pad. The polishing pad layer (3) is used to contact the surface of the processed conical optical element to achieve polishing of the processed conical optical element.

8. The conformal vibration smoothing polishing method for conical optical elements according to claim 7, characterized in that, The elastic modulus of the material used in the flexible deformable layer (2) is in the range of 10-50 MPa, and the Poisson's ratio is between 0.45 and 0.

49.

9. The conformal vibration smoothing polishing method for conical optical elements according to claim 7, characterized in that, The thickness of the polishing pad (3) is 1-2 mm.

10. A conical optical element, characterized in that, The conical optical element is formed by the conformal vibration smoothing polishing method for conical optical elements as described in any one of claims 1 to 9.

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