Magneto-rheological polishing polyhedral co-body element integrated machining pose calculation method

Abstract

The invention relates to the technical field of optical processing, in particular to a magneto-rheological polishing polyhedral co-body element integrated processing pose calculation method, which comprises the following steps of: determining a track fragment corresponding to each mirror body during processing according to the surface of each mirror body in a to-be-processed polyhedral co-body element; an ideal polishing track during machining is obtained by combining the track fragments corresponding to the mirror bodies; setting a polishing gap of a machining tool during machining, and determining a normal of each point of a mirror body in the multi-surface common-body element; according to the polishing gap and the normal of each point, the actual polishing track of the machining tool and the machining posture of the machining tool are obtained, and the machining posture of the machining tool is obtained. According to the invention, the integrated processing pose control of the coaxial multi-surface common-body element is realized, and the multi-section processing redundant manufacturing time is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical processing, and particularly relates to a method for calculating the pose of an integrated machining of a magnetorheological polishing multi-faceted co-body element. Background Art

[0002] Nowadays, most high-performance imaging optical systems in the world adopt multi-mirror reflective optical systems, which can be divided into coaxial systems and off-axis systems. Common ones are off-axis three-mirror and coaxial three-mirror types. However, the alignment and adjustment of single-element systems are difficult and costly, and the volume and mass of opto-mechanical structural parts are large. Therefore, a multi-faceted co-body design scheme has emerged. For the integration of the primary and secondary mirrors of off-axis three-mirror, see the paper "Design of an Off-Axis Three-Mirror Optical System with Integrated Primary and Secondary Mirrors" published in Infrared and Laser Engineering. For the integration of the primary and secondary mirrors of coaxial three-mirror, see the paper "Fabrication of the LSST Monolithic Primary-Tertiary Mirror" published in Modern Technologies in Space- and Ground-based Telescopes and Instrumentation II. In this paper, the multi-faceted co-body surface is polished using a stress disk tool, and its removal function size is relatively large and has no obvious directionality. Therefore, there is more flexibility in the process to control.

[0003] In the modification stage of large-aperture optical elements, the magnetorheological polishing scanning removal processing method is becoming more and more mainstream, and the magnetorheological polishing removal function is relatively small and directional. The processing mode of magnetorheological polishing needs to evaluate the processing cycle. The off-axis multi-faceted co-body mirror can adopt two processes to scan and process the main mirror and the secondary mirror respectively, without generating too much redundant manufacturing time. For the coaxial multi-faceted co-body mirror, if the grating trajectory is still used and the main mirror and the secondary mirror are scanned and processed in two processes respectively, during the scanning of the main mirror, there will be an idle running time between the central hole and the secondary mirror, which will cause too much redundant manufacturing time. If the main mirror and the secondary mirror are regarded as one process, it is necessary to accurately control the pose change at the joint of the main mirror and the secondary mirror, thus increasing the difficulty of program development. If a circular trajectory is adopted and the workpiece rotates, the design of the mirror body support and the rotating mechanical structure is complex, increasing the additional design cost. If the tool rotates, the machine tool, as the carrier of the magnetorheological tool, has a high degree of freedom requirement, thus requiring a high-precision calculation method and the support of a high-performance multi-degree-of-freedom machine tool. Summary of the Invention

[0004] In view of this, the present invention aims to provide a method for calculating the machining position and posture of an integrated machining of a magnetorheological polishing multi-faceted coaxial element, obtaining the trajectory segments of the surfaces of each mirror body in the multi-faceted coaxial element to be machined, and then determining the total polishing trajectory during machining; according to the set polishing gap and the normal vectors of each point of the mirror body in the multi-faceted coaxial element, obtaining the machining position and machining posture of the machining tool, and combining the total polishing trajectory, the machining position of the machining tool and the machining posture, realizing the integrated machining position and posture control of the coaxial multi-faceted coaxial element, and reducing the redundant manufacturing time of multi-stage machining.

[0005] To achieve the above object, the technical solution of the present invention is realized as follows: A method for calculating the machining position and posture of an integrated machining of a magnetorheological polishing multi-faceted coaxial element, comprising: S1: Determine the trajectory segments corresponding to each mirror body during machining according to the surfaces of each mirror body in the multi-faceted coaxial element to be machined; combine the trajectory segments corresponding to each mirror body to obtain the ideal polishing trajectory during machining; S2: Set the polishing gap during machining of the machining tool and determine the normal vectors of each point of the mirror body in the multi-faceted coaxial element; S3: According to the ideal polishing trajectory obtained in step S1, and the polishing gap and the normal vectors of each point obtained in step S2, obtain the actual polishing trajectory of the machining tool and the machining posture of the machining tool; S4: Combine the actual polishing trajectory and the machining posture obtained in step S3 to obtain the machining position and posture of the machining tool.

[0006] Further, step S1 includes: S11: Obtain the surface equations of the main mirror body and the slave mirror body in the multi-faceted coaxial element; S12: Generate the first trajectory segment with the single-side one-ring arm of the main mirror body as a reference; S13: Generate the second trajectory segment with the remaining ring arms of the main mirror body except the ring arm in S12 as a reference; S14: Generate the third trajectory segment with the slave mirror body as a reference; S15: According to the first trajectory segment, the second trajectory segment and the third trajectory segment obtained in steps S12 to S14, obtain the ideal polishing trajectory.

[0007] Further, step S11 includes: Obtain the surface equation f 1 (x, y); Obtain the surface equation f 3 (x, y); Obtain the central hole equation f h (x, y); Based on the surface equation f 1(x, y), from the surface equation f of the body mirror 3 (x, y) and the central hole equation f h (x, y), to determine the coordinate vectors of each point in the multi - surface co - body element , where the sagittal height z is: ; Back up the sagittal height z three times to obtain the first sagittal height z, the second sagittal height z, and the third sagittal height z.

[0008] Furthermore, in step S12, based on the first sagittal height z, generate the first trajectory segment through the following formula: ; where z 1 represents the first sagittal height z, R 3 represents the semi - aperture of the body mirror, None represents a null value, Pathize represents a function to make a point set into a grating trajectory, (ε 1 , η 1 , γ 1 ) represents the coordinate values in the first trajectory segment.

[0009] Furthermore, in step S13, based on the second sagittal height z, generate the second trajectory segment through the following formula: ; where z 2 represents the second sagittal height z, (ε 2 , η 2 , γ 2 ) represents the coordinate values in the second trajectory segment.

[0010] Furthermore, in step S14, based on the third sagittal height z, generate the third trajectory segment through the following formula: ; where z 3 represents the third sagittal height z, (ε 3 , η 3 , γ 3 ) represents the coordinate values in the third trajectory segment, and R h represents the semi - aperture of the central hole.

[0011] Furthermore, in step S15, splice the first trajectory segment, the second trajectory segment, and the third trajectory segment through the following formula: ; where (ε, η, γ) represents the coordinate of each trajectory point in the ideal polishing trajectory, and cat represents a function to link parameter vectors.

[0012] Furthermore, the process of determining the normals of each point of the mirror body in the polyhedral common body element in step S2 includes: establishing a global processing coordinate system when processing the polyhedral common body element, the intersection of the body mirror surface and the reference horizontal plane in the polyhedral common body element is the origin of the global processing coordinate system; the common rotation axis of the polyhedral common body element is the Z axis of the global processing coordinate system, the direction in which the cosine of the angle between the normal of each point in the polyhedral common body mirror surface is positive is the positive direction of the global Z axis, and the X axis and Y axis of the processing coordinate system of the processing tool itself are the X axis and Y axis of the global processing coordinate system; and calculating the normals of each point of the mirror body in the polyhedral common body element in the global processing coordinate system.

[0013] Furthermore, the machining coordinate system is translated relative to the global machining coordinate system in the Z-axis direction , It represents the normal line of each point of the mirror body in the multi-faceted co-body element, and Δ represents the polishing gap.

[0014] Furthermore, in step S3, the coordinates of each track point in the actual polishing track are determined by the following formula: ; in, Represents the coordinates of each track point in the actual polishing track, Represents the coordinates of each track point in the ideal polishing track, ; The processing posture is determined by the following formula: ; in, Indicates the processing posture.

[0015] Compared with the prior art, the invention can achieve the following beneficial effects: The present invention creates the magnetorheological polishing multi-faceted co-body component integrated processing posture calculation method, and the multi-faceted co-body partitioned scanning processing in the same working section, that is, the main mirror and the secondary mirror are processed in a scanning trajectory, which effectively avoids the problem of processing the posture conversion at the joint and the problem of excessive requirements on equipment and algorithms. In addition, the present invention adopts a loop arm (that is, the main mirror and the secondary mirror are a ring in the top view, and the loop arm is a part of this ring) detour trajectory strategy, which avoids redundant processing time, does not need to consider the concentric and coaxial tolerance requirements of the multi-faceted co-body component for high trajectory consistency, and does not require too high algorithms and equipment, and shortens the manufacturing cycle for the polishing of large-caliber multi-faceted co-body components. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings: Figure 1Schematic flowchart of the pose calculation method for integrated machining of the magnetorheological polishing multi-faceted co-body element according to the embodiments of the present invention; Figure 2 Schematic diagram of the first trajectory segment according to the embodiments of the present invention; Figure 3 Schematic diagram of the second trajectory segment according to the embodiments of the present invention; Figure 4 Schematic diagram of the third trajectory segment according to the embodiments of the present invention; Figure 5 Schematic diagram of the polishing trajectory according to the embodiments of the present invention; Figure 6 Coordinate system relationship diagram according to the embodiments of the present invention; Figure 7 Tool pose vector diagram according to the embodiments of the present invention. Detailed implementation manners

[0017] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, rather than limiting the present invention.

[0018] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0019] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0020] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be a direct connection or an indirect connection through an intermediate medium, and it may be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0021] The present invention will be described in detail below with reference to the drawings and in conjunction with embodiments.

[0022] As Figure 1 shown, the pose calculation method for integral machining of a magnetorheological polishing multi-faceted co-body element according to an embodiment of the present invention includes: S1: Determine the trajectory segments corresponding to each mirror body during machining according to the surfaces of each mirror body in the multi-faceted co-body element to be machined; combine the trajectory segments corresponding to each mirror body to obtain the ideal polishing trajectory during machining.

[0023] In some embodiments, step S1 includes: S11: Obtain the surface equations of the main mirror and the slave mirror in the multi-faceted co-body element. Specifically, step S11 includes: Obtain the surface equation f 1 (x, y); Obtain the surface equation f 3 (x, y); Obtain the central hole equation f h (x, y) of the multi-faceted co-body element; Based on the surface equation f 1 (x, y) of the main mirror, the surface equation f 3 (x, y) of the slave mirror, and the central hole equation f h (x, y), determine the coordinate vectors of each point in the multi-faceted co-body element, where the sagittal height z is: ; Back up the sagittal height z three times to obtain the first sagittal height z, the second sagittal height z, and the third sagittal height z.

[0024] S12: Generate the first trajectory segment with the unilateral one-ring arm of the main mirror as a reference. Specifically, based on the first sagittal height z, generate the first trajectory segment through the following formula: ; where z 1 represents the first sagittal height z, and R 3Represents the semi-aperture of the body mirror, None represents a null value, Pathize represents a function that makes the point integration into a grating trajectory, (ε 1 ,η 1 ,γ 1 ) represents the coordinate value in the first trajectory segment.

[0025] In one embodiment, the structure of the function of point integration as a raster trajectory is as follows: Set three empty vectors abc, scan the rows and columns of the vector height z matrix, if i in the i-th row is an odd number, scan forward, and append the non-empty data (x, y, z) of the row to the end of the abc vector in sequence. If i in the i-th row is an even number, scan backward, and append the non-empty data (x, y, z) of the row to the end of the abc vector in sequence.

[0026] S13: Using the remaining loop arms of the main mirror except the loop arm in S12 as a reference, generate a second trajectory segment. Specifically, based on the second vector height z, the second trajectory segment is generated by the following formula: ; Among them, z 2 represents the second vector height z, (ε 2 ,η 2 ,γ 2 ) represents the coordinate value in the second trajectory segment.

[0027] S14: Generate a third trajectory segment with the slave mirror as a reference. Specifically, based on the third vector height z, the third trajectory segment is generated by the following formula: ; Among them, z 3 represents the third vector height z, (ε 3 ,η 3 ,γ 3 ) represents the coordinate value in the third trajectory segment, R h Indicates the semi-diameter of the center hole.

[0028] S15: According to the first trajectory segment, the second trajectory segment and the third trajectory segment obtained in steps S12 to S14, an ideal polishing trajectory is obtained. Specifically, the first trajectory segment, the second trajectory segment and the third trajectory segment are spliced ​​by the following formula: ; Among them, (ε, η, γ) represents the coordinates of each trajectory point in the ideal polishing trajectory, and cat represents the function of linking the parameter vector.

[0029] S2: Set the polishing gap of the processing tool during processing, and determine the normal lines of each point of the mirror body in the multi-faceted common body component.

[0030] In some embodiments, the process of determining the normal vectors of each point on the mirror body in the multi-faceted coaxial element includes: establishing a global machining coordinate system when machining the multi-faceted coaxial element, wherein, the intersection point of the body mirror surface and the reference horizontal plane in the multi-faceted coaxial element is the origin of the global machining coordinate system; the common rotation axis of the multi-faceted coaxial element is the Z-axis of the global machining coordinate system, the direction with a positive cosine of the angle between the Z-axis and the normal vectors of each point on the multi-faceted coaxial mirror surface is the positive direction of the global Z-axis, and the X-axis and Y-axis of the machining coordinate system of the machining tool itself are the X-axis and Y-axis of the global machining coordinate system. The machining coordinate system is translated in the Z-axis direction relative to the global machining coordinate system , denotes the normal vectors of each point on the mirror body in the multi-faceted coaxial element, and Δ denotes the polishing gap.

[0031] Calculate the normal vectors of each point on the mirror body in the multi-faceted coaxial element in the global machining coordinate system.

[0032] S3: Based on the ideal polishing trajectory obtained in step S1, as well as the polishing gap and the normal vectors of each point obtained in step S2, obtain the actual polishing trajectory of the machining tool and the machining posture of the machining tool. Specifically, the machining position is determined by the following formula: ; wherein, denotes the coordinates of each trajectory point in the actual polishing trajectory, denotes the coordinates of each trajectory point in the ideal polishing trajectory, ; The machining posture is determined by the following formula: ; wherein, denotes the machining posture.

[0033] In a certain embodiment, it is necessary to set the initial pose of the machining tool, and the initial pose includes the initial machining position , and the initial machining posture . During the actual machining process, first control the machining tool to adjust to the initial pose. After the initial pose is set, new machining positions and machining postures are obtained according to the formulas for determining the machining position and machining posture for machining.

[0034] S4: Combine the actual polishing trajectory and the machining posture obtained in step S3 to obtain the machining pose of the machining tool.

[0035] During the optical processing, the processing position and orientation of the processing tool include the processing position of the processing tool and the processing orientation of the processing tool. The processing position of the processing tool is the coordinate of each trajectory point in the actual polishing trajectory of the processing tool. Therefore, when the actual polishing trajectory and the processing orientation of the processing tool are determined, the processing position and orientation of the processing tool during the processing can be directly obtained.

[0036] To clearly illustrate the method for calculating the integrated processing position and orientation of the magnetorheological polishing multi-faceted coaxial body element provided by the present invention, an embodiment is provided.

[0037] Embodiment: The method for calculating the integrated processing position and orientation of the magnetorheological polishing multi-faceted coaxial body element described in this embodiment includes: S1: According to the surfaces of each mirror body in the multi-faceted coaxial body element to be processed, determine the corresponding trajectory segments during processing; combine the corresponding trajectory segments of each mirror body to obtain the ideal polishing trajectory during processing.

[0038] In this embodiment, step S1 includes: S11: Obtain the surface equations of the main mirror body and the secondary mirror body in the multi-faceted coaxial body element. Specifically, step S11 includes: Obtain the surface equation f 1 (x, y) of the main mirror body as: ; Obtain the surface equation f 3 (x, y) of the secondary mirror body as: ; Obtain the central hole equation f h (x, y) in the multi-faceted coaxial body element as: ; Based on the surface equation f 1 (x, y) of the main mirror body, the surface equation f 3 (x, y) of the secondary mirror body, and the central hole equation f h (x, y), determine the coordinate vector of each point in the multi-faceted coaxial body element, where the sagittal height z is: ; Back up the sagittal height z three times to obtain the first sagittal height z, the second sagittal height z, and the third sagittal height z.

[0039] S12: Taking the single-side one-ring arm of the main mirror body as a reference, generate the first trajectory segment. Specifically, based on the first sagittal height z, generate the first trajectory segment as shown in Figure 2 through the following formula: ; where the semi-aperture R 3= 1000, the pseudo-code of the function Pathize for the point set to become the raster trajectory can be as follows:

[0040] Among them, z.rows is the number of rows of the sagittal height z matrix, and z.cols is the number of columns of the sagittal height z matrix.

[0041] S13: Using the remaining arms of the main mirror except for the ring arms in S12 as a reference, generate the second trajectory segment. Specifically, based on the second sagittal height z, generate the second trajectory segment as shown by the following formula: Figure 3 The second trajectory segment shown: .

[0042] S14: Using the slave mirror as a reference, generate the third trajectory segment. Specifically, based on the third sagittal height z, generate the third trajectory segment as shown by the following formula: Figure 4 The third trajectory segment shown: ; Among them, the semi-aperture R of the central hole h = 500.

[0043] S15: According to the first trajectory segment, the second trajectory segment, and the third trajectory segment obtained in steps S12 to S14, obtain the ideal polishing trajectory as shown by Figure 5 the following. Specifically, splice the first trajectory segment, the second trajectory segment, and the third trajectory segment by the following formula: ; If the traditional method of processing the main mirror and the slave mirror in two separate work sections is adopted, according to the previous overall processing strategy, there will be redundant time: ; Among them, T m represents the minimum dwell time for each dwell point due to the machine tool movement performance limitation, P represents the number of idle running dwell points, and the number of idle running dwell points P increases as the semi-aperture R of the slave mirror 3 = 1000 increases, and the redundant processing time increases in a quadratic trend. That is, when the semi-aperture R of the slave mirror 3 = 2000, the redundant time T ry ≈ 8.72 h.

[0044] S2: Set the polishing gap during processing of the processing tool, and determine the normal vectors of each point of the mirror body in the multi-faceted co-body component.

[0045] In this embodiment, the polishing gap Δ is set to 2. The intersection point of the coaxial mirror of the multi-faceted coaxial element and the curved surface of the secondary mirror is taken as the tool origin, and the coaxial axis of the coaxial mirror is taken as the global Z-axis. The direction with the positive cosine of the angle between the normal vectors of each point on the coaxial mirror surface and the global Z-axis is taken as the positive direction of the global Z-axis. Combining the X-axis and Y-axis of the machining coordinate system of the machining tool itself, the global machining coordinate system for machining the multi-faceted coaxial element as shown in Figure 6 is determined. Figure 6 In w , S T represents the global machining coordinate system, and S ; where represents the unnormalized surface normal, and F 1 = f 1 (x, y) - z, F 3 = f 3 (x, y) - z, F 1x , F 1y , F 1z , are the partial derivatives of the equation F 1 with respect to x, y, and z, and F 3x , F 3y , F 3z , are the partial derivatives of the equation F 3 with respect to x, y, and z. The equation F is defined as: .

[0046] where the Z-axis direction of the machining coordinate system is translated by .

[0047] S3: According to the ideal polishing trajectory obtained in step S1, the polishing gap and the normal vectors of each point obtained in step S2, the actual polishing trajectory of the machining tool and the machining posture of the machining tool are obtained.

[0048] In this embodiment, the initial pose of the machining tool is first set. The initial pose includes the initial machining position , and the initial machining posture .

[0049] The machining position is determined by the following formula: ; where F x , F y and F z are the partial derivatives of the equation F with respect to x, y, and z respectively; The machining posture is determined by the following formula: 。

[0050] S4: Combine the actual polishing trajectory and the machining posture obtained in step S3 to obtain the machining pose of the machining tool. The discretized pose obtained in this embodiment is as Figure 7 shown.

[0051] It should be understood that various forms of the processes shown above can be used, reordering, adding or deleting steps. For example, the steps described in the disclosure of the present invention can be executed in parallel, sequentially or in a different order, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and no limitation is made herein.

[0052] The above specific embodiments do not constitute a limitation to the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub - combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the processing posture of a multi-faceted component in a magnetorheological polishing process, characterized in that: include: S1: according to the surface of each mirror body in the multi-faceted common body component to be processed, determine the trajectory segments corresponding to each mirror body during processing; combine the trajectory segments corresponding to each mirror body to obtain the ideal polishing trajectory during processing; S2: setting the polishing gap of the processing tool during processing, and determining the normal lines of each point of the mirror body in the multi-faceted common body element; S3: according to the ideal polishing trajectory obtained in step S1, and the polishing gap and normal lines of each point obtained in step S2, the actual polishing trajectory of the processing tool and the processing posture of the processing tool are obtained; S4: Combining the actual polishing trajectory and processing posture obtained in step S3, the processing posture of the processing tool is obtained.

2. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 1 is characterized in that: Step S1 includes: S11: Obtaining surface equations of the main mirror and the secondary mirror in the multi-faceted common body element; S12: Taking the single-side ring arm of the main mirror as a reference, generating a first trajectory segment; S13: using the remaining ring arms of the main mirror except the ring arm in S12 as a reference, generating a second trajectory segment; S14: generating a third trajectory segment with the slave body mirror as a reference; S15: Obtain the ideal polishing trajectory according to the first trajectory segment, the second trajectory segment and the third trajectory segment obtained in steps S12 to S14.

3. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 2 is characterized in that: Step S11 includes: Get the main mirror surface equation f1(x,y); Get the surface equation f3(x,y) from the body mirror; Get the center hole equation f in the polyhedral common body element h (x,y); Based on the main mirror surface equation f1(x, y), the secondary mirror surface equation f3(x, y) and the center hole equation f h (x, y), determine the coordinate vector of each point in the polyhedral co-body element , where the arrow height z is: ； The arrow height z is backed up three times to obtain a first arrow height z, a second arrow height z and a third arrow height z.

4. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 3 is characterized in that: In step S12, based on the first vector height z, the first trajectory segment is generated by the following formula: ； Among them, z1 represents the first vector height z, R3 represents the semi-aperture of the slave mirror, None represents a null value, Pathize represents a function that integrates points into a grating trajectory, and (ε1, η1, γ1) represents the coordinate value in the first trajectory segment.

5. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 4 is characterized in that: In step S13, based on the second vector height z, the second trajectory segment is generated by the following formula: ； Among them, z2 represents the second vector height z, and (ε2, η2, γ2) represents the coordinate value in the second trajectory segment.

6. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 5 is characterized in that: In step S14, based on the third vector height z, the third trajectory segment is generated by the following formula: ； Wherein, z3 represents the third vector height z, (ε3, η3, γ3) represents the coordinate value in the third trajectory segment, R h It represents the semi-diameter of the central hole.

7. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 6 is characterized in that: In step S15, the first trajectory segment, the second trajectory segment and the third trajectory segment are spliced ​​using the following formula: ； Wherein, (ε, η, γ) represents the coordinates of each track point in the ideal polishing track, and cat represents the function for linking parameter vectors.

8. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 7 is characterized in that: The process of determining the normal lines of each point of the mirror body in the multi-faceted common body element in step S2 includes: A global machining coordinate system is established when machining the multifaceted common body element, wherein the intersection of the body mirror curved surface and the reference horizontal plane in the multifaceted common body element is the origin of the global machining coordinate system; the common rotation axis of the multifaceted common body element is the Z axis of the global machining coordinate system, the direction in which the cosine of the angle between the normal line of each point in the multifaceted common body mirror curved surface is positive is the positive direction of the global Z axis, and the X axis and Y axis of the machining coordinate system of the machining tool itself are the X axis and Y axis of the global machining coordinate system; Calculate the normal of each point of the mirror body in the multi-faceted common body element in the global processing coordinate system.

9. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 8 is characterized in that: The processing coordinate system is translated relative to the global processing coordinate system in the Z-axis direction , represents the normal line of each point of the mirror body in the multi-faceted co-body element, and Δ represents the polishing gap.

10. The method for calculating the integrated processing posture of a multi-faceted common body component by magnetorheological polishing according to claim 9 is characterized in that: In step S3, the coordinates of each track point in the actual polishing track are determined by the following formula: ； in, represents the coordinates of each track point in the actual polishing track, represents the coordinates of each track point in the ideal polishing track, ; The processing posture is determined by the following formula: ； in, Indicates the processing posture.

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