Method for magnetorheological finishing of multi-faceted conformal element

Abstract

The application relates to the technical field of optical processing, in particular to a magnetorheological polishing multi-surface common element integrated processing method, which comprises the following steps: S1, decomposing a known actual grating track into a row coordinate according to a longitudinal coordinate mutation point; S2, splitting each row track into a main mirror first track segment, a slave mirror track segment and a main mirror second track segment according to a transition point circle diameter; S3, determining a transition point extension length according to a magnetorheological equipment removal function length; S4-S5, respectively extending the main mirror track segment and the slave mirror track segment and inserting new points; S6, obtaining three-dimensional coordinates by calculating z coordinates of each segment by using a corresponding surface equation; S7, splicing to generate a single-row ordered point sequence; and S8, combining all row tracks and rotating an angle to obtain a final track. θ Through the above scheme, the problems that multi-surface common element segmented processing has long redundant time, low efficiency, and the transition area joint is not accurately processed, the transition area of the optical element has a large range of edge, the effective aperture is reduced, and the imaging quality of the optical system is affected are solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of optical processing, and particularly relates to a magnetorheological polishing multi-surface common element integrated processing method. BACKGROUND

[0002] In the polishing processing field of multi-surface common mirrors, such as in the published paper Fabrication of the LSST monolithic primary tertiary mirror, the LSST project uses a 1.2-meter stress disc to polish the optical surface, but the current polishing technology mainly processes the primary mirror and the secondary mirror separately, and when the primary mirror is processed, the polishing equipment will run empty in the coverage range of the secondary mirror, resulting in redundant time and reducing the processing efficiency. In view of this, the patent application for an invention patent with the patent name of "magnetorheological polishing multi-surface common element integrated processing pose calculation method" with the patent publication number CN120055909A and the patent publication date of May 30, 2025 proposes an integrated processing calculation method, which optimizes the processing flow to a certain extent. However, the patent technology only focuses on the calculation of the processing pose and does not pay attention to the processing problem of the joint at the transition zone of the primary mirror and the secondary mirror. Further, when polishing the surface of a large-aperture optical element, due to the limitation of the performance of the C-axis of the machine tool, a spiral line or other annular trajectory cannot be used for processing, and more light grating type trajectories are used for scanning processing, but the existing light grating type trajectory processing scheme does not optimize the characteristics of the transition zone joint and cannot solve the problem of accurate processing of the transition zone of the primary mirror and the secondary mirror, which may further cause the range of the edge of the transition zone of the optical element to be too large, the effective aperture to be reduced, and finally affect the imaging quality of the optical system. SUMMARY

[0003] Therefore, the present application aims to provide a magnetorheological polishing multi-surface common element integrated processing method to solve the problems of long redundant time, low efficiency, and inaccurate processing of the transition zone joint in the segmented processing of the multi-surface common element, which causes the range of the edge of the transition zone of the optical element to be too large, the effective aperture to be reduced, and the imaging quality of the optical system to be affected.

[0004] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0005] A magnetorheological polishing multi-surface common element integrated processing method, the multi-surface common element comprising a primary mirror and a secondary mirror smoothly connected along the same continuous transition zone, comprising the following steps:

[0006] S1, for a known actual light grating type trajectory, the rows are decomposed according to the longitudinal coordinate mutation point position of the light grating type trajectory, and a two-dimensional trajectory arranged by rows is obtained;

[0007] S2, according to the diameter parameter of the transition point in the multi-faceted common element design to be processed, the two-dimensional trajectory coordinates of each row decomposed in step S1 are respectively decomposed into a first trajectory segment within the main mirror range, a trajectory segment within the body mirror range, and a second trajectory segment within the main mirror range;

[0008] S3, according to the removal function length of the magneto-rheological finishing equipment used for processing, the lengths of the first trajectory segment, the trajectory segment within the body mirror range, and the second trajectory segment to be extended at the transition point are determined , and the lengths are ensured to be greater than the removal function length;

[0009] S4, the first trajectory segment is extended from the truncation point A close to the body mirror by a length , and a first new point is inserted at the end of the extension ; the second trajectory segment is extended from the truncation point B close to the body mirror by a length , and a second new point is inserted at the end of the extension ; the dwell times of the first new point and the second new point are respectively defined as the dwell times at the points closest to the corresponding new points on the first trajectory segment and the second trajectory segment;

[0010] S5, the trajectory segment within the body mirror range is extended from the two side truncation points A and B close to the main mirror by lengths , and a third new point and a fourth new point are sequentially inserted at the ends of the extensions; the dwell times of the third new point and the fourth new point are respectively defined as the dwell times at the points closest to the corresponding new points on the trajectory segment within the body mirror range;

[0011] S6, the surface equations of the main mirror and the body mirror are obtained, the z coordinates of the points in the first trajectory segment and the second trajectory segment processed in step S4 are calculated using the surface equation of the main mirror, and the z coordinates of the points in the trajectory segment within the body mirror processed in step S5 are calculated using the surface equation of the body mirror, so as to obtain the complete three-dimensional coordinates of all the trajectory points in the first trajectory segment, the second trajectory segment, and the trajectory segment within the body mirror;

[0012] S7, the first trajectory segment, the trajectory segment within the body mirror, and the second trajectory segment processed in step S6 are sequentially spliced to generate an ordered point sequence of a single-row trajectory;

[0013] S8. Perform steps S2 to S7 on all rows of actual raster-like trajectories obtained from step S1 decomposition, then combine all row trajectories in the order of the polishing equipment's travel direction. Finally, rotate all the combined trajectory points with complete three-dimensional coordinates using a two-dimensional rotation matrix. The angle is used to obtain the final complete machining trajectory, where, This represents the rotation angle of the actual grating trajectory.

[0014] Furthermore, step S1 includes the following sub-steps:

[0015] S11. Suppose the rotation angle of the actual grating trajectory is known. The two-dimensional rotation matrix for:

[0016] ;

[0017] S12. The coordinates of the trajectory points of the known actual grating trajectory... Substituting into the following formula, we obtain the rotated two-dimensional coordinates. Make the grating lines of the known actual grating trajectory parallel to the x-axis:

[0018] ;

[0019] S13. Traverse all rotated 2D coordinate points according to the formula. Calculate the difference in ordinate between each point and the next point. ,in, For the first The ordinate of the two-dimensional coordinates of each point after rotation. For the first The ordinate of the two-dimensional coordinates of a point after rotation;

[0020] S14. Suppose the track gauge of the original grating trajectory, given the actual grating trajectory, is... ,when At that time, the first line of the original trajectory sequence of the known actual grating trajectory is... The dot is marked as the end point of the line, the first... The point is marked as the starting point of the next row, and a set of two-dimensional trajectory coordinates arranged in rows is obtained in this way.

[0021] Furthermore, step S2 includes the following sub-steps:

[0022] S21. Let the set of trajectory points of the known actual raster trajectory of the row to be processed be... The corresponding ordered sequence is , The total number of trajectory points of the known actual raster trajectory in the row to be processed; where any trajectory point of the known actual raster trajectory The coordinates can be represented as The radius of the seam between the stereoscope and the main mirror is ;

[0023] S22. Extract the starting point of the known actual raster trajectory in this row. coordinates Calculate the coordinates of the two points where the seam intersects with the known actual grating trajectory using the following formula:

[0024]

[0025] ;

[0026] S23, if Let the coordinates of point A be... The coordinates of point B are ,but:

[0027] ,

[0028] The set of known actual raster-like trajectory points for the first trajectory segment within the scope of the main mirror;

[0029] ,

[0030] For the known actual raster-like trajectory points of the trajectory segment within the scope of the stereoscope;

[0031] ,

[0032] The set of known actual raster-like trajectory points for the second trajectory segment within the scope of the main mirror;

[0033] like Let the coordinates of point A be... The coordinates of point B are ,but:

[0034] ,

[0035] The set of known actual raster-like trajectory points for the first trajectory segment within the scope of the main mirror;

[0036] ,

[0037] For the known actual raster-like trajectory points of the trajectory segment within the scope of the stereoscope;

[0038] ,

[0039] The set of known actual raster-like trajectory points for the second trajectory segment within the scope of the main mirror;

[0040] S24, Let The known number of actual grating trajectory points is , The known number of actual grating trajectory points is , The known number of actual grating trajectory points is Then the following conditions are met:

[0041] .

[0042] Furthermore, step S4 includes the following sub-steps:

[0043] S41. Obtain the starting point of the known actual grating trajectory from step S2. coordinates The coordinates of point A and the coordinates of point B;

[0044] S42, if ,but,

[0045] ,

[0046] ;

[0047] exist The corresponding known ordered sequence of actual grating trajectories The tail is inserted sequentially at the original cutoff point A and the first new point. Generate a new ordered sequence The Updated to The corresponding set of known actual raster trajectory points ;exist The corresponding known ordered sequence of actual grating trajectories Insert the second new point in the first order. Combined with the original cutoff point B, a new ordered sequence is generated. The Updated to The corresponding set of known actual raster trajectory points ;

[0048] S43, if ,but

[0049] ,

[0050] ;

[0051] exist The corresponding known ordered sequence of actual grating trajectories The tail is inserted sequentially at the original cutoff point A and the first new point. a new ordered sequence is generated , the is updated to corresponding known actual raster trajectory point set ; in corresponding ordered sequence the second new point is inserted in the head order and the original truncated point B, a new ordered sequence is generated , the is updated to corresponding known actual raster trajectory point set .

[0052] Further, step S5 includes the following sub-steps:

[0053] S51, if , then

[0054] ,

[0055] ;

[0056] S52, if , then

[0057] ,

[0058] ;

[0059] S53, in corresponding known actual raster trajectory ordered sequence the third new point is inserted in the head order point and the original truncated point A, the original truncated point B and the fourth new point are inserted in the tail order , a new ordered sequence is generated , the is updated to corresponding known actual raster trajectory point set .

[0060] Further, step S6 includes the following sub-steps:

[0061] S61, the surface equation of the main mirror of the multi-surface common element to be processed is obtained and the surface equation of the from mirror ;

[0062] S62, the z coordinate of each point in the first trajectory segment and the second trajectory segment processed in step S4 is calculated by using the surface equation of the main mirror ; the surface equation of the from mirror The z coordinate of each point in the trajectory segment within the scope of the objective mirror after the processing of step S5 is calculated;

[0063] S63, the coordinates of each trajectory point are updated as wherein, is the known actual grating trajectory coordinate, is the z coordinate calculated in step S62, and finally the complete three-dimensional coordinates of all trajectory points in the first trajectory segment and the second trajectory segment after the processing of step S4 and all trajectory points in the trajectory segment within the scope of the objective mirror after the processing of step S5 are obtained.

[0064] Further, in step S7, the ordered point sequence of the single-row trajectory is:

[0065] ,

[0066] wherein, is the known actual grating trajectory ordered sequence of the first trajectory segment after the processing of step S4, is the known actual grating trajectory ordered sequence of the trajectory segment within the scope of the objective mirror after the processing of step S5, is the known actual grating trajectory ordered sequence of the second trajectory segment after the processing of step S4, indicates the splicing operation in sequence;

[0067] The point set corresponding to the ordered point sequence of the single-row trajectory is :

[0068] ,

[0069] wherein, is any trajectory point in .

[0070] Compared with the prior art, the application can achieve the following beneficial effects:

[0071] By decomposing the known actual grating trajectory according to rows, and then decomposing each row of trajectory into the first trajectory segment within the scope of the objective mirror, the trajectory segment within the scope of the objective mirror and the second trajectory segment within the scope of the objective mirror according to the diameter parameter of the transition point of the multi-surface common element to be processed, and combining the removal function length of the magnetorheological polishing equipment used for processing to determine the extension length The trajectory segments are bidirectionally extended at the transition points and new points are inserted, finally the z coordinates of the trajectory points of each segment are calculated by the main mirror surface equation and the body mirror surface equation to obtain complete three-dimensional coordinates, and the trajectory is spliced and rotated in order of the first trajectory segment, the trajectory segment in the body mirror range and the second trajectory segment, which eliminates the redundant time of traditional segmented processing, solves the problems of long redundant time, low efficiency and inaccurate processing of the transition area joint in segmented processing of multi-surface common elements, effectively reduces the range of the transition area, avoids the reduction of the effective aperture of the optical element, and significantly improves the processing consistency of the multi-surface common element and the imaging quality of the optical system. BRIEF DESCRIPTION OF DRAWINGS

[0072] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of the application illustrated in the drawings, and their description, are presented to add generic scope to this application. In the drawings:

[0073] Figure 1 A flowchart of the magnetorheological polishing multi-surface common element integrated processing method provided by the embodiment of the application is shown in the figure;

[0074] Figure 2 A schematic diagram of the rotating rear grating processing trajectory provided by the embodiment of the application is shown in the figure;

[0075] Figure 3 A schematic diagram of the trajectory decomposition provided by the embodiment of the application is shown in the figure;

[0076] Figure 4 A schematic diagram of the main mirror trajectory single-row segment extension provided by the embodiment of the application is shown in the figure;

[0077] Figure 5 A schematic diagram of the body mirror trajectory single-row segment extension provided by the embodiment of the application is shown in the figure;

[0078] Figure 6 A schematic diagram of the combined single polishing trajectory on the mirror surface provided by the embodiment of the application is shown in the figure;

[0079] Figure 7 A schematic diagram of the combined single polishing trajectory on the mirror surface provided by the embodiment of the application is shown in the figure; Figure 6 A schematic diagram of the combined single polishing trajectory on the mirror surface provided by the embodiment of the application is shown in the figure; DETAILED DESCRIPTION

[0080] For the purpose of making the object, technical solutions and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and do not constitute a limitation on the present application. In different embodiments, similar elements are associated with similar element labels. In the following embodiments, many details are described in order to make the present application better understood. However, those skilled in the art can easily recognize that some features can be omitted in different cases, or can be replaced by other elements, materials, methods. In some cases, some operations related to the present application are not shown or described in the specification in order to avoid the core part of the present application being overwhelmed by too much description, and it is not necessary for those skilled in the art to describe these related operations in detail according to the description in the specification and general technical knowledge in the art.

[0081] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other to form various embodiments without conflict. At the same time, each step or action in the method description can also be sequentially adjusted or adjusted in a manner obvious to those skilled in the art. Therefore, the various sequences in the specification and drawings are only for the purpose of clearly describing a certain embodiment, and do not mean a necessary sequence, unless otherwise stated that a certain sequence must be followed.

[0082] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the purpose of facilitating the description of the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second" and the like are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features limited by "first", "second" and the like can explicitly or implicitly include one or more features. In the description of the present application, unless otherwise stated, the meaning of "a plurality of" is two or more.

[0083] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0084] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0085] like Figures 1 to 7 As shown, this embodiment provides a method for integrally fabricating a magnetorheological polishing multifaceted component. The multifaceted component includes a main mirror and a slave mirror smoothly connected along the same continuous transition zone, and includes the following steps:

[0086] Step S1: For the known actual grating trajectory, decompose the row according to the position of the abrupt change point of the grating trajectory to obtain the two-dimensional trajectory coordinates arranged in rows. Perform the decomposition operation on each actual grating trajectory that passes through the scope of the stereoscope.

[0087] Specifically, step S1 also includes the following sub-steps:

[0088] S11. Suppose the rotation angle of the actual grating trajectory is known. ,in The range of values ​​is ∈(-90°, 90°], and ≠0° (If the gate lines are already parallel to the x-axis in the initial state, i.e.) If the angle is 0°, then there is no need to perform the rotation operation in this step, and we can directly proceed to step S13 (which will be mentioned below) 2D rotation matrix. for:

[0089] ;

[0090] S12. The coordinates of the trajectory points of the known actual grating trajectory... Substituting into the following formula, we obtain the rotated two-dimensional coordinates. Make the grating lines of the known actual grating trajectory parallel to the x-axis:

[0091] ;

[0092] S13. Traverse all rotated 2D coordinate points according to the formula. Calculate the difference in ordinate between each point and the next point. ,in, For the first The ordinate of the two-dimensional coordinates of each point after rotation. For the first The ordinate of the two-dimensional coordinates of a point after rotation;

[0093] S14. Suppose the track gauge of the original grating trajectory, given the actual grating trajectory, is... ,when At that time, the first line of the original trajectory sequence of the known actual grating trajectory is... The dot is marked as the end point of the line, the first... The point is marked as the starting point of the next row, and a set of two-dimensional trajectory coordinates arranged in rows is obtained in this way.

[0094] Through a two-dimensional rotation matrix Correcting the known actual grating trajectory with angular offset to make the grating lines parallel to the x-axis can eliminate the interference of trajectory rotation on row decomposition and ensure that the division direction of the trajectory rows is adapted to the distribution of the main mirror and slave mirror of the multifaceted element; then using the original grating trajectory gauge of the known actual grating trajectory As the criterion, the difference in the vertical axis is used for judgment. Precisely marking the start and end points of rows can decompose continuous known actual raster trajectories into a regular set of two-dimensional trajectory coordinates arranged in rows. The same decomposition operation is performed on each known actual raster trajectories that pass through the scope of the stereoscope, providing a unified and accurate coordinate basis for the subsequent decomposition of trajectory segments in different scope areas, and avoiding misalignment in subsequent processing due to row decomposition deviations.

[0095] Step S2: Based on the circle diameter parameter of the transition point in the design of the multi-faceted coherent element to be processed, the two-dimensional trajectory coordinates obtained in step S1 are decomposed into a first trajectory segment within the scope of the main lens, a trajectory segment within the scope of the secondary lens, and a second trajectory segment within the scope of the main lens. The first trajectory segment, the trajectory segment within the scope of the secondary lens, and the second trajectory segment all come from the same complete known actual grating trajectory.

[0096] Specifically, step S2 includes the following sub-steps:

[0097] S21. Let the set of trajectory points of the known actual raster trajectory of the row to be processed be... The corresponding ordered sequence is , The total number of trajectory points of the known actual raster trajectory in the row to be processed; where any trajectory point of the known actual raster trajectory The coordinates can be represented as The radius of the seam between the stereoscope and the main mirror is And the radius of the joint It is half the diameter of the circle where the transition point of the multifaceted component to be processed is located;

[0098] S22, extract the starting point of the known actual grating track of the line coordinates of the point , calculate the coordinates of the two points where the seam intersects the known actual grating track according to the following formula:

[0099] ,

[0100] ;

[0101] S23, if , record the coordinates of point A as , and the coordinates of point B as , then:

[0102]

[0103] is the known actual grating track point set of the first track segment within the main mirror range;

[0104]

[0105] is the known actual grating track point set of the track segment within the from mirror range;

[0106] ,

[0107] is the known actual grating track point set of the second track segment within the main mirror range;

[0108] if , record the coordinates of point A as , and the coordinates of point B as , then:

[0109]

[0110] is the known actual grating track point set of the first track segment within the main mirror range;

[0111]

[0112] is the known actual grating track point set of the track segment within the from mirror range;

[0113] ,

[0114] is the known actual grating track point set of the second track segment within the main mirror range;

[0115] S24, let the number of known actual grating track points The known number of actual grating trajectory points is The known number of actual grating trajectory points is Then the following condition is met:

[0116] .

[0117] Based on the diameter parameter of the circle where the transition point of the multifaceted component to be processed is located, half of it is the joint radius between the stereo lens and the main lens. Combined with the known actual starting point of the grating trajectory x-coordinate The positive and negative distinction between the coordinates of points A and B allows for precise delineation of the boundaries of the first trajectory segment within the main lens area, the trajectory segment within the stereoscopic lens area, and the second trajectory segment within the main lens area. Furthermore, it clearly identifies that all three segments originate from the same complete, known actual grating trajectory, ensuring both trajectory continuity and precise isolation between different lens regions. Verification of quantitative relationships, among which, This represents the total number of trajectory points in the known actual raster trajectory of the row to be processed. for The number of trajectory points, for The number of trajectory points, for The number of trajectory points ensures that no known actual grating trajectory points are missed or repeated, providing a clear basis for the subsequent extended processing of trajectory segments in different ranges, and avoiding confusion between the first trajectory segment, the second trajectory segment and the trajectory segment in the scope of the main lens and the trajectory segment in the scope of the secondary lens, which could lead to processing deviations in the transition area.

[0118] Step S3: Based on the removal function length of the magnetorheological polishing equipment used in the processing, determine the length that the first trajectory segment, the trajectory segment within the scope of the stereoscope, and the second trajectory segment need to be extended at the transition point. and length It is greater than the length of the removal function.

[0119] Extend length Related to the removal function length of the magnetorheological polishing equipment used in the processing, and ensuring A length greater than the removal function length allows the commutation of the magnetorheological polishing wheel to be completed within the extended section detached from the mirror surface, avoiding damage to the mirror transition zone caused by sudden speed changes during commutation; simultaneously, The first trajectory segment in the main mirror range, the trajectory segment in the body mirror range and the second trajectory segment in the main mirror range are uniformly applied, which provides parameter support for the processing consistency at the transition points of each segment, prevents the processing quality from being uneven at the transition zone joints due to the length difference of different segments, and lays a unified standard for subsequent bidirectional extension processing.

[0120] Step S4, extending the length of the first trajectory segment from the truncation point A (the intersection point A of the joint and the trajectory determined in step S2) close to the body mirror to the body mirror direction , inserting a first new point at the end of the extension ; extending the length of the second trajectory segment from the truncation point B (the intersection point B of the joint and the trajectory determined in step S2) close to the body mirror to the body mirror direction , inserting a second new point at the end of the extension ; the residence time of the first new point is defined as the residence time on the first trajectory segment from the corresponding first new point closest point, and the residence time of the second new point is defined as the residence time on the second trajectory segment from the corresponding second new point closest point. It should be noted that the residence time refers to the residence time of the polishing wheel of the magnetorheological polishing device at the new point.

[0121] Specifically, step S4 includes the following sub-steps:

[0122] S41, obtaining the coordinates of the starting point of the known actual grating trajectory in step S2 , the coordinates of point A and the coordinates of point B;

[0123] S42, if then,

[0124] ,

[0125] ;

[0126] In the tail of the corresponding known actual grating trajectory ordered sequence insert the original truncation point A and the first new point , generate a new ordered sequence , update to the corresponding known actual grating trajectory point set ; in the head of the corresponding known actual grating trajectory ordered sequence insert the second new point ​and the original breakpoint B, to generate a new ordered sequence , the is updated to the corresponding known actual raster trajectory point set ;

[0127] S43, if

[0128] ,

[0129] ;

[0130] at the tail of the corresponding known actual raster trajectory ordered sequence insert the original breakpoint A and the first new point to generate a new ordered sequence , is updated to the corresponding known actual raster trajectory point set ; at the head of the corresponding ordered sequence insert the second new point and the original breakpoint B, to generate a new ordered sequence , is updated to the corresponding known actual raster trajectory point set .

[0131] According to the horizontal coordinate positive and negative difference of the known actual raster trajectory starting point , the first new point and the second new point coordinates are calculated respectively, wherein, is the horizontal coordinate of the intersection point of the seam and the known actual raster trajectory of the row, is the vertical coordinate of the intersection point, which can accurately control the extension position of the first trajectory segment (corresponding to ) and the second trajectory segment (corresponding to ) in the direction of the body mirror in the main body mirror range, and ensure that the extension section and the transition zone boundary are accurately connected; by inserting the original breakpoint A and the first new point at the tail of the corresponding known actual raster trajectory ordered sequence , and inserting the second new point and the original breakpoint B at the head of the corresponding known actual raster trajectory ordered sequence , a new ordered sequence is generated, , ​and update the trajectory point set , , the first trajectory segment and the second trajectory segment in the main mirror range are effectively covered to the transition area; the residence time of the new point is defined as the residence time of the nearest point to the new point on the first trajectory segment and the second trajectory segment, the continuity of the machining parameters of the extension segment and the original trajectory segment is ensured, and the discontinuity and unevenness of material removal in the transition area caused by parameter mutation is avoided.

[0132] Step S5, extending the trajectory segment in the body mirror range to the main mirror direction from the two side truncation points A and B of the main mirror , and sequentially inserting a third new point and a fourth new point at the extension ends. The residence time of the third new point and the fourth new point is respectively defined as the residence time of the nearest point to the corresponding third new point and the fourth new point on the trajectory segment in the body mirror range.

[0133] Specifically, step S5 includes the following sub-steps:

[0134] S51, if , then

[0135] ,

[0136] ;

[0137] S52, if , then

[0138] ,

[0139] ;

[0140] S53, if , then insert the third new point and the original truncation point A at the head of the corresponding known actual grating trajectory ordered sequence , and insert the original truncation point B and the fourth new point at the tail, to generate a new ordered sequence , update the corresponding known actual grating trajectory point set .

[0141] The third new point and the fourth new point are respectively calculated in combination with the horizontal coordinate Fourth new point Point coordinates, where, Let x be the x-coordinate of the intersection point between the seam and the known actual grating trajectory. Let be the ordinate of the intersection point, so that the trajectory segment within the scope of the stereoscope (corresponding to It can precisely extend the length towards the main mirror. This is consistent with the extension effect of the first and second trajectory segments within the main mirror range in step S4, achieving full coverage of the transition zone and completely eliminating the processing blind spot in the transition zone; through The corresponding known ordered sequence of actual grating trajectories Insert the third new point in the first order Insert the original cutoff point A and the tail sequentially into the original cutoff point B and the fourth new point. Generate a new ordered sequence And update the set of trajectory points This effectively expands the processing coverage of trajectory segments within the stereoscopic range in the transition zone; and the dwell time of a new point is defined as the dwell time of the trajectory segment within the stereoscopic range at the point closest to that new point, ensuring the extension segment ( Point A, Point B The continuity of the processing parameters between the point and the original trajectory segment is ensured to avoid discontinuous and uneven material removal in the transition zone due to abrupt parameter changes, thus providing a continuous and complete trajectory basis for subsequent three-dimensional coordinate calculations.

[0142] Step S6: Obtain the surface equations of the main mirror and the secondary mirror, and use the surface equations of the main mirror to calculate the z-coordinates of each point in the first and second trajectory segments after processing in step S4; use the surface equations of the secondary mirror to calculate the z-coordinates of each point in the trajectory segments within the range of the secondary mirror after processing in step S5, thereby obtaining the complete three-dimensional coordinates of all trajectory points in the first trajectory segment, the second trajectory segment, and the trajectory segments within the range of the secondary mirror.

[0143] Specifically, step S6 includes the following sub-steps:

[0144] S61. Obtain the surface equation of the main mirror of the multifaceted component to be processed. and the surface equation from the stereomicroscope ;

[0145] S62. Using the surface equation of the main mirror Calculate the z-coordinates of each point in the first and second trajectory segments after processing in step S4; use the surface equation from the stereoscope. Calculate the z-coordinates of each point in the trajectory segment within the scope of the stereoscope after processing in step S5;

[0146] S63. Update the coordinates of each trajectory point to... wherein, is the known actual grating trajectory coordinate, is the z coordinate calculated in step S62, and the complete three-dimensional coordinates of all trajectory points in the first trajectory segment and the second trajectory segment processed in step S4, and all trajectory points in the trajectory segment within the body mirror range processed in step S5 are ultimately obtained.

[0147] The surface equation of the main mirror of the multi-faceted solid element to be machined The surface equation of the body mirror The z coordinates of the points in the first trajectory segment (corresponding to ) processed in step S4, the second trajectory segment (corresponding to ) processed in step S4, and the trajectory segment within the body mirror range (corresponding to ) processed in step S5 are calculated respectively, which ensures the accurate matching of the z coordinates of the trajectory points in different trajectory segments in the main mirror region and the body mirror region with the actual surface shape of the multi-faceted solid element, and avoids the surface of the machined element not meeting the design requirements due to coordinate deviation; the coordinates of each trajectory point are updated uniformly as wherein, is the known actual grating trajectory coordinate, is the z coordinate calculated using the corresponding surface equation, which completely restores the spatial machining trajectory of the multi-faceted solid element, and provides accurate and directly callable three-dimensional coordinate data for subsequent trajectory splicing and machine tool machining.

[0148] In step S7, the first trajectory segment, the trajectory segment within the body mirror range, and the second trajectory segment processed in step S6 are spliced in order to generate an ordered point sequence of a single-row trajectory.

[0149] Specifically, in step S7, the ordered point sequence of the single-row trajectory is:

[0150] ,

[0151] wherein, is the known actual grating trajectory ordered sequence of the first trajectory segment processed in step S4, is the known actual grating trajectory ordered sequence of the trajectory segment within the body mirror range processed in step S5, is the known actual grating trajectory ordered sequence of the second trajectory segment processed in step S4, indicates the splicing operation in order;

[0152] The point set corresponding to the ordered point sequence of the single-row trajectory is:

[0153] , ​

[0154] wherein, is any trajectory point in

[0155] In the order of "first trajectory segment in the main mirror range after Step S6 processing, trajectory segment in the body mirror range, second trajectory segment in the main mirror range", the ordered point sequence of the single-row trajectory is generated by the "STITCH" splicing operation , realizing seamless connection of different mirror segments in the single-row trajectory, avoiding processing path confusion caused by incorrect splicing order; the point set corresponding to the ordered point sequence of the single-row trajectory clearly defines the range of the sequence, ensures that the single-row trajectory contains all necessary processing points, lays a regular single-row foundation for subsequent combination of all row trajectories in the order of the polishing equipment advancing direction to form a complete processing trajectory after performing Steps S2 to S7 on all actual grating-type trajectory rows decomposed in Step S1, and the unified sequence form also facilitates batch execution of the trajectory rotation operation by the two-dimensional rotation matrix in subsequent Step S8. Step S8, performing Steps S2 to S7 on all actual grating-type trajectory rows decomposed in Step S1, then combining all row trajectories in the order of the polishing equipment advancing direction, and finally rotating

[0156] all trajectory points with complete three-dimensional coordinates after combination by the two-dimensional rotation matrix by an angle of , to obtain the final complete processing trajectory, wherein is the rotation angle of the actual grating-type trajectory.

[0157] Performing Steps S2 to S7 on all known actual grating-type trajectory rows decomposed in Step S1 ensures that the trajectories of all processing areas on the surface of the multi-surface common element meet the transition zone optimization requirements, avoiding substandard processing quality in local areas due to non-processing; combining all row trajectories in the order of the original reciprocating advancing direction of each trajectory row (consistent with the alternating advancing logic of the known actual grating-type trajectory before Step S1 splitting, i.e., adjacent trajectory rows are sequentially advanced in opposite directions), relying on the ordered sequence of each trajectory row (i.e., the ordered point sequence of the single-row trajectory) to ensure the continuity of the overall trajectory after combination, avoiding advancing direction confusion; finally, rotating all trajectory points with complete three-dimensional coordinates after combination by the two-dimensional rotation matrix in Step S1 by an angle of , wherein is the rotation angle of the known actual grating-type trajectory, and the parameter in the two-dimensional rotation matrix To the same physical quantity), the trajectory is restored to the initial machining coordinate system, the influence of the rotation correction in step S1 is eliminated, and the final complete machining trajectory directly used for machine tool machining is obtained. Through accurate coverage processing of the transition area, the effective aperture of the element is effectively guaranteed, and continuous integrated machining of the multi-surface common element is realized, the time redundancy of traditional segmented machining is eliminated, and the machining efficiency is significantly improved.

[0158] Through the above technical solution, by decomposing the known actual grating type trajectory according to rows, and then according to the diameter parameter of the transition point of the to-be-machined multi-surface common element, each row of trajectory is decomposed into a first trajectory segment in the main mirror range, a trajectory segment in the slave mirror range and a second trajectory segment in the main mirror range, and the extension length is determined according to the removal function length of the magnetorheological polishing equipment used for machining , each trajectory segment is extended bidirectionally at the transition point and a new point is inserted, finally the z coordinate of each segment trajectory point is calculated through the main mirror surface equation and the slave mirror surface equation to obtain complete three-dimensional coordinates, and the trajectory is spliced and rotated in the order of the first trajectory segment, the trajectory segment in the slave mirror range and the second trajectory segment, which eliminates the redundant time of traditional segmented machining, avoids secondary machining of the transition area, reduces the machining cost, solves the problems of long redundant time and low efficiency of segmented machining of the multi-surface common element, and the transition area joint is not accurately machined, so that the edge of the transition area is removed more accurately and controllably, the edge effect is suppressed, the edge collapse or edge warping is reduced, the effective aperture of the multi-surface common optical element surface is effectively reduced, and the machining consistency of the multi-surface common element and the imaging quality of the optical system are finally significantly improved.

[0159] In addition, the machining logic of the present application can be further extended to a multi-surface common element (including a non-coaxial multi-surface common element) with a two-mirror body machining face normal consistent, no abrupt step structure and a continuous transition area: for this kind of multi-surface common element, only in step S2 when splitting the trajectory segment, the "diameter parameter of the transition point" is replaced by the corresponding "joint contour parameter of the main mirror and the slave mirror" according to the actual structure of the mirror body, and the calculation logic of the coordinates of points A and B is redefined based on the joint contour parameter, so that the accurate splitting of different trajectory segments can be completed; the subsequent steps S3-S8 can adaptively adjust the trajectory extension reference, the coordinate calculation adaptation logic and other details according to the structural characteristics of the element, and still realize the continuous integrated machining of the transition area, maintain high efficient machining and effective aperture guarantee.

[0160] Also can adopt respectively generate first subject mirror trajectory segment, from body mirror trajectory segment, subject mirror second trajectory segment corresponding machine tool basic execution code (include coordinate and residence time parameter) first, then according to the transition zone extension logic of this embodiment, add " extension segment execution code " in the end of two segment subject mirror code near from body mirror, from body mirror code near the two ends of subject mirror respectively, finally integrate three segment code according to " subject mirror first segment code, from body mirror segment code, subject mirror second segment code " order, can form complete integrated processing execution code, reach the same processing effect with original scheme, simplify trajectory coordinate and machine tool code conversion process simultaneously.

[0161] Although the embodiments of the present application have been shown and described above, it should be understood by those having ordinary skill in the art that the above embodiments are exemplary and should not be construed as limiting the present application. Those having ordinary skill in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present application.

[0162] The specific embodiments of the present application described above do not constitute a limitation of the protection scope of the present application. Any various other corresponding changes and modifications made according to the technical concept of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A method for integrally fabricating a magnetorheologically polished multifaceted co-element, the multifaceted co-element comprising: A main mirror and a secondary mirror that are smoothly connected along the same continuous transition zone are characterized by comprising the following steps: S1. For a known actual grating trajectory, decompose the rows according to the position of the abrupt change point of the vertical coordinate of the grating trajectory to obtain a two-dimensional trajectory arranged by rows. S2. Based on the circle diameter parameter of the transition point in the design of the multi-faceted coherent element to be processed, decompose each row of two-dimensional trajectory coordinates obtained in step S1 into the first trajectory segment within the scope of the main mirror, the trajectory segment within the scope of the secondary mirror, and the second trajectory segment within the scope of the main mirror. S3. Based on the removal function length of the magnetorheological polishing equipment used in the processing, determine the length that the first trajectory segment, the trajectory segment within the scope of the stereoscope, and the second trajectory segment need to be extended at the transition point. Ensure the length Greater than the length of the removal function; S4. Extend the length from the cutoff point A near the stereoscope of the first trajectory segment toward the stereoscope. Insert the first new point at the end of the extension. The length extending from the second trajectory segment near the cutoff point B of the stereoscope towards the stereoscope direction. Insert a second new point at the end of the extension. The first new point The second new point The dwell time is defined as the dwell time at the closest point to the corresponding new point on the first trajectory segment and the second trajectory segment, respectively. The coordinates of the cut-off points A and B are the coordinates of the two points that intersect with the known actual grating trajectory of the corresponding row through the seam of the main mirror and the slave mirror. The dwell time refers to the dwell time of the polishing wheel of the magnetorheological polishing device at the new point. S5. Extend the length from the two cutoff points A and B on both sides of the trajectory segment within the scope of the stereoscope toward the main mirror. Insert a third new point at the end of the extension. Fourth new point The third new point The fourth new point The dwell time is defined as the dwell time at the point closest to the corresponding new point on the trajectory segment within the scope of the stereoscope; S6. Obtain the surface equations of the main body mirror and the secondary body mirror, and use the surface equations of the main body mirror to calculate the z-coordinates of each point in the first trajectory segment and the second trajectory segment after processing in step S4; use the surface equations of the secondary body mirror to calculate the z-coordinates of each point in the trajectory segment within the range of the secondary body mirror after processing in step S5, thereby obtaining the complete three-dimensional coordinates of all trajectory points in the first trajectory segment, the second trajectory segment, and the trajectory segment within the range of the secondary body mirror. S7. The first trajectory segment processed in step S6, the trajectory segment within the scope of the stereoscope, and the second trajectory segment are sequentially spliced ​​together to generate an ordered point sequence of a single-line trajectory. S8. Perform steps S2 to S7 on all rows of actual raster-like trajectories obtained from step S1 decomposition, then combine all row trajectories in the order of the polishing equipment's travel direction. Finally, rotate all the combined trajectory points with complete three-dimensional coordinates using a two-dimensional rotation matrix. The angle is used to obtain the final complete machining trajectory, where, This represents the rotation angle of the actual grating trajectory.

2. The method for integral processing of multi-faceted co-element by magnetorheological polishing according to claim 1, characterized in that, Step S1 includes the following sub-steps: S11. Suppose the rotation angle of the actual grating trajectory is known. The two-dimensional rotation matrix for: ； S12. The coordinates of the trajectory points of the known actual grating trajectory... Substituting into the following formula, we obtain the rotated two-dimensional coordinates. Make the grating lines of the known actual grating trajectory parallel to the x-axis: ； S13. Traverse all rotated 2D coordinate points according to the formula. Calculate the difference in ordinate between each point and the next point. ,in, For the first The ordinate of the two-dimensional coordinates of each point after rotation. For the first The ordinate of the two-dimensional coordinates of a point after rotation; S14. Suppose the track gauge of the original grating trajectory, given the actual grating trajectory, is... ,when At that time, the first line of the original trajectory sequence of the known actual grating trajectory is... The dot is marked as the end point of the line, the first... The point is marked as the starting point of the next row, and a set of two-dimensional trajectory coordinates arranged in rows is obtained in this way.

3. The method for integral processing of magnetorheological polished multi-faceted co-element according to claim 1, characterized in that, Step S2 includes the following sub-steps: S21. Let the set of trajectory points of the known actual raster trajectory of the row to be processed be... The corresponding ordered sequence is , The total number of trajectory points of the known actual raster trajectory in the row to be processed; where any trajectory point of the known actual raster trajectory The coordinates can be represented as The radius of the seam between the stereoscope and the main mirror is ; S22. Extract the starting point of the corresponding row of known actual raster trajectory. coordinates Calculate the coordinates of the two points where the seam intersects with the known actual grating trajectory using the following formula: ， ； S23, if Let the coordinates of point A be... The coordinates of point B are ,but: ， The set of known actual raster-like trajectory points for the first trajectory segment within the scope of the main mirror; ， For the known actual raster-like trajectory points of the trajectory segment within the scope of the stereoscope; ， The set of known actual raster-like trajectory points for the second trajectory segment within the scope of the main mirror; like Let the coordinates of point A be... The coordinates of point B are ,but: ， The set of known actual raster-like trajectory points for the first trajectory segment within the scope of the main mirror; ， For the known actual raster-like trajectory points of the trajectory segment within the scope of the stereoscope; ， The set of known actual raster-like trajectory points for the second trajectory segment within the scope of the main mirror; S24, Let The known number of actual grating trajectory points is , The known number of actual grating trajectory points is , The known number of actual grating trajectory points is Then the following condition is met: 。 4. The method for integral processing of magnetorheological polished multi-faceted co-element according to claim 3, characterized in that, Step S4 includes the following sub-steps: S41. Obtain the starting point of the known actual grating trajectory from step S2. coordinates The coordinates of point A and the coordinates of point B; S42, if ,but, ， ； exist The corresponding known ordered sequence of actual grating trajectories The tail is inserted sequentially at the original cutoff point A and the first new point. Generate a new ordered sequence The Updated to The corresponding set of known actual raster trajectory points ;exist The corresponding known ordered sequence of actual grating trajectories Insert the second new point in the first order. Combined with the original cutoff point B, a new ordered sequence is generated. The Updated to The corresponding set of known actual raster trajectory points ; S43, if ,but ， ； exist The corresponding known ordered sequence of actual grating trajectories The tail is inserted sequentially at the original cutoff point A and the first new point. Generate a new ordered sequence The Updated to The corresponding set of known actual raster trajectory points ;exist The corresponding ordered sequence Insert the second new point in the first order. Combined with the original cutoff point B, a new ordered sequence is generated. The Updated to The corresponding set of known actual raster trajectory points .

5. The method for integral processing of magnetorheological polished multi-faceted co-element according to claim 3, characterized in that, Step S5 includes the following sub-steps: S51, if ,but ， ； S52, if ,but ， ； S53, in The corresponding known ordered sequence of actual grating trajectories Insert the third new point in the first order. Point A and the original cutoff point A are used as starting points. Then, the original cutoff point B and the fourth new point are inserted sequentially at the end. Generate a new ordered sequence The Updated to The corresponding set of known actual raster trajectory points .

6. The method for integral processing of multi-faceted co-element by magnetorheological polishing according to claim 1, characterized in that, Step S6 includes the following sub-steps: S61. Obtain the surface equation of the main mirror of the multifaceted component to be processed. and the surface equation from the stereomicroscope ; S62. Using the surface equation of the main mirror Calculate the z-coordinates of each point in the first and second trajectory segments after processing in step S4; utilize the surface equations from the stereoscope. Calculate the z-coordinates of each point in the trajectory segment within the scope of the stereoscope after processing in step S5; S63. Update the coordinates of each trajectory point to... ,in, Given the actual coordinates of the grating trajectory, The z-coordinates calculated in step S62 are used to obtain the complete three-dimensional coordinates of all trajectory points in the first trajectory segment and the second trajectory segment after processing in step S4, as well as all trajectory points in the trajectory segment within the scope of the stereoscope after processing in step S5.

7. The method for integral processing of magnetorheological polished multi-faceted co-element according to claim 1, characterized in that: In step S7, the ordered point sequence of the single-line trajectory: ， in, The known actual raster-type trajectory ordered sequence of the first trajectory segment after processing in step S4. This is the known actual raster-like ordered sequence of trajectory segments within the scope of the stereoscope after processing in step S5. The known actual raster-like ordered sequence of the second trajectory segment after processing in step S4. "Indicates sequential splicing operation; The set of points corresponding to the ordered sequence of points of a single trajectory for: ， in, for Any point on the trajectory in the array.

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