Simulation and processing method of magnetorheological polishing of complex curved optical components

Abstract

The present invention is applicable to the field of ultra-precision polishing of optical complex curved surface components, and provides a simulation and processing method for magnetorheological polishing of complex curved surface optical components, including the following steps: H1: Calculate the initial surface shape error according to the detection image of the interferometer and the expected surface shape after processing; H2: Select a suitable polishing trajectory according to the component type and the initial surface shape error; H3: Divide the surface shape error into non-spherical areas, obtain the position, size, spherical radius and spherical center coordinates of each divided area, and obtain the removal function of each divided area; H4: Perform a magnetorheological polishing spot sampling experiment to obtain the three-dimensional morphology of the actual polishing spot under the current processing conditions, and calculate the polishing spot removal function of each divided area; H5: Allocate dwell points and calculate the dwell time matrix. This method can achieve high-precision magnetorheological polishing effect and provide theoretical support for the magnetorheological polishing process.

Description

Technical Field

[0001] The invention relates to the field of ultra-precision polishing of optical complex curved surface elements, and in particular to a simulation and processing method of magnetorheological polishing of complex curved surface optical elements. Background Art

[0002] As early as 2001, foreign scholars have carried out magnetorheological polishing experiments and analyzed the material removal mechanism of magnetorheological polishing of optical components. Its characteristics are that the magnetorheological fluid is adsorbed by the magnetic field, and the liquid is driven by the polishing wheel to achieve shear removal of surface materials. Because magnetorheological polishing has the advantages of low subsurface damage, high processing efficiency, high removal stability and high surface accuracy, and can obtain smaller flexible polishing spots, magnetorheological polishing is suitable for ultra-precision processing of optical components with small period and complex curved surfaces.

[0003] Under the same processing parameters, the morphology and size of the spherical polishing spot and the plane polishing spot are different. When processing aspheric optical elements, the local fitting spherical radius and polishing spot morphology at different positions on the surface are also different. In order to ensure that the correct polishing spot can be obtained during magnetorheological polishing of aspheric elements, the movement direction of the magnetorheological fluid at the center point of contact between the polishing wheel and the element must coincide with the tangent plane at the local point of the element. Therefore, the polishing wheel posture corresponding to each point on the aspheric element is different during processing, resulting in the morphology of the polishing spot on the tangent plane being different from that on the XOY plane, which involves the transformation of the global coordinates and local coordinates of the polishing spot. Therefore, it is very necessary to perform global processing of local polishing spots and surface area division processing.

[0004] In actual processing, the morphology of the polishing spot changes every moment. The traditional magnetorheological polishing simulation and dwell time algorithm do not take into account the morphological differences of the polishing spots at different positions on the aspheric surface. Therefore, it is very meaningful to divide the aspheric surface into regions and ensure that the accuracy of the divided regions meets the standards. Of course, it is also necessary to simplify the magnetorheological polishing simulation process. Summary of the invention

[0005] The purpose of the present invention is to provide a processing simulation method for magnetorheological polishing of complex curved optical elements, so as to achieve high-precision processing of complex curved optical elements.

[0006] On the one hand, the present application provides a simulation method for magnetorheological polishing of a complex curved optical element, comprising the following steps:

[0007] H1: Calculate the initial surface shape based on the interferometer detection image and the expected surface shape after processing

[0008] error;

[0009] H2: Select the appropriate polishing trajectory according to the component type and initial surface error;

[0010] H3: Divide the surface error into non-spherical areas, obtain the position, size, spherical radius and spherical center coordinates of each divided area, and obtain the removal function of each divided area;

[0011] H4: Conduct magnetorheological polishing spot removal experiments to obtain the three-dimensional morphology of the actual polishing spot under the current processing conditions, and calculate the polishing spot removal function of each divided area;

[0012] H5: Assign dwell points and calculate the dwell time matrix.

[0013] Furthermore, in step H3, when the aspheric surface is divided into regions, the principle of division is that the larger the off-axis amount, the smaller the divided region.

[0014] Furthermore, in step H3, the local best sphere is calculated as follows:

[0015] A·t=b;

[0016] In the formula, the calculation expressions of A, t, and b are:

[0017]

[0018] In the formula, (x 0i ,y 0i ,z 0i ) is the initial sphere center coordinate, r 0i is the radius of the sphere, (x i ,y i ,z i ) is the original data coordinate, x 0i+1 =x 0i +Δx,y 0i+1 =y 0i +Δy、z 0i+1 =z 0i +Δz、r 0i+1 =r 0i +Δr, after multiple iterations, the spherical radius and center coordinates of each divided area can be obtained.

[0019] Furthermore, step H4 also includes projecting the polishing spots on the cutting plane into the global coordinate system to obtain the polishing spot morphology of each divided area:

[0020]

[0021] O(x, y, z) is the global coordinate of a point on the polishing spot, O′(x 0 ,y 0 ,z 0 ) is the local coordinate of a point on the polishing spot, O(x′, y′, z′) is the global coordinate corresponding to the center of the divided area; R y(α) is the coefficient matrix for rotating the y-axis by an angle of α, R x (β) is the coefficient matrix of the rotation angle β around the x-axis, and the corresponding equations are:

[0022]

[0023]

[0024] α is the angle between the local coordinate system and the global coordinate system in the XOZ plane, and β is the angle between the local coordinate system and the global coordinate system in the YOZ plane.

[0025] Furthermore, in step H5, a pulse iteration algorithm is used to solve the residence time matrix:

[0026] H(x,y)=R(x,y)*T(x,y)

[0027] Among them, H(x, y) is the residual matrix of the component, R(x, y) is the polishing spot removal function matrix, T(x, y) is the dwell time matrix, and * represents the convolution operation; when the RMS value of the residual error matrix of the component meets the requirements, the dwell time matrix is ​​derived, otherwise the iteration continues.

[0028] On the other hand, the present application also provides a method for magnetorheological polishing of complex curved optical components, which uses a simulation method for magnetorheological polishing of complex curved optical components as described above to obtain a polishing trajectory, a dwell point and a dwell time matrix, and then performs magnetorheological polishing.

[0029] The simulation and processing method of magnetorheological polishing of complex curved optical elements of the present application has at least the following beneficial effects compared with the prior art:

[0030] (1) The present application divides a complex aspheric surface into multiple small areas, and performs spherical fitting on each small area, using a spherical surface instead of a local aspheric surface for processing, thereby improving the accuracy of magnetorheological polishing of complex curved optical elements;

[0031] (2) The present application proposes that the influence of the off-axis value needs to be considered when performing area division, and the fitting calculation shows that the fitting error increases with the increase of the off-axis value. Therefore, when performing area division, the principle of division is that the larger the off-axis value, the smaller the divided area, thereby further improving the accuracy of magnetorheological polishing of complex curved optical elements;

[0032] (3) This application proposes a polishing spot coordinate transformation method, setting a region to correspond to a fixed polishing spot morphology, which greatly simplifies the simulation model;

[0033] (4) This application uses a pulse iteration algorithm to solve the residence time matrix. The smaller the iteration step is set, the higher the accuracy is. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments of the present invention or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 It is a schematic flow chart of a simulation method for magnetorheological polishing of a complex curved optical element according to Example 1 of the present application;

[0036] Figure 2 is the relationship curve between the off-axis amount and the fitting error;

[0037] Figure 3 It is a schematic diagram of the conversion between the local coordinate system and the global coordinate system in the polishing spot coordinate transformation of Example 1 of the present application;

[0038] Figure 4 It is a flow chart of the pulse iteration algorithm of Example 1 of the present application. DETAILED DESCRIPTION

[0039] The following description provides many different embodiments or examples for implementing different features of the present invention. The components and arrangements described in the following specific examples are only used to simplify the present invention and are only used as examples, not to limit the present invention.

[0040] Example 1

[0041] A simulation method for magnetorheological polishing of complex curved optical components, such as Figure 1 As shown, the following steps are included:

[0042] H1: Calculate the initial surface shape error based on the interferometer detection image and the expected surface shape after processing;

[0043] The initial surface shape error is calculated based on the initial surface shape and the designed surface shape after processing. The surface shape error is the surface shape contour that should be removed. This step is a prior art in this field and will not be described in detail here.

[0044] H2: Select the appropriate polishing trajectory according to the component type and initial surface error;

[0045] The simulation method of the present application is applicable to any polishing trajectory, among which the representative ones are grating trajectory, spiral trajectory, and random trajectory;

[0046] H3: Divide the surface error into non-spherical areas, obtain the position, size, spherical radius and spherical center coordinates of each divided area, and obtain the removal function of each divided area;

[0047] That is, the non-spherical area is divided into multiple small areas, and each small area is fitted and calculated according to the sphere to obtain the size, spherical radius and center coordinates of each small area, that is, the removal function of each small area is obtained.

[0048] When dividing the aspheric surface into regions, the principle of division is that the larger the off-axis value, the smaller the divided region. This is because when the applicant performed spherical surface fitting simulation on the aspheric surface, it was found that the larger the off-axis value, the larger the fitting error, that is, the lower the fitting accuracy. The relationship curve between the off-axis value and the fitting error is as follows: Figure 2 The size of the specific divided area is determined by the component type, material, polishing spot and other factors, so it is not limited here.

[0049] After being divided into multiple regions, a local optimal spherical surface fitting is performed for each region, and the fitted spherical surface is used as the local shape surface of the aspherical surface, thereby obtaining the removal function of each divided region.

[0050] The local best sphere is calculated as follows:

[0051] A·t=b;

[0052] In the formula, the calculation expressions of A, t, and b are:

[0053]

[0054] In the formula, (x 0i ,y 0i ,z 0i ) is the initial sphere center coordinate, r 0i is the radius of the sphere, (x i ,y i ,z i ) is the original data coordinate, x 0i+1 =x 0i +Δx,y 0i+1 =y 0i +Δy、z 0i+1 =z 0i +Δz、r 0i+1 =r 0i +Δr, after multiple iterations, the spherical radius and center coordinates of each divided area can be obtained.

[0055] H4: Conduct magnetorheological polishing spot removal experiments to obtain the three-dimensional morphology of the actual polishing spot under the current processing conditions, and calculate the polishing spot removal function of each divided area;

[0056] In this step, a light spot and color spot experiment is carried out according to the specified magnetorheological polishing process parameters, and the actual light spot obtained is the same as the light spot during actual processing. However, in the aspheric magnetorheological processing experiment, in order to ensure that the correct polishing spot can be obtained, the movement direction of the magnetorheological fluid at the center point of contact between the polishing wheel and the workpiece must coincide with the tangent plane at the local point of the workpiece. Therefore, during processing, the polishing wheel posture corresponding to each point on the aspheric surface is different, causing the morphology of the polishing spot on the tangent plane to be different from that on the XOY plane. This involves the transformation of the global coordinates and local coordinates of the polishing spot. The polishing wheel posture at a certain point during aspheric magnetorheological processing is as follows: Figure 3 As shown. The polishing spot of the cutting plane is projected into the global coordinate system to obtain the polishing spot morphology of each divided area:

[0057]

[0058] O(x, y, z) is the global coordinate of a point on the polishing spot, O′(x 0 ,y 0 ,z 0 ) is the local coordinate of a point on the polishing spot, O(x′, y′, z′) is the global coordinate corresponding to the center of the divided area; R y (α) is the coefficient matrix for rotating the y-axis by an angle of α, R x (β) is the coefficient matrix of the rotation angle β around the x-axis, and the corresponding equations are:

[0059]

[0060]

[0061] α is the angle between the local coordinate system and the global coordinate system in the XOZ plane, and β is the angle between the local coordinate system and the global coordinate system in the YOZ plane.

[0062] H5: Assign dwell points and calculate the dwell time matrix.

[0063] The dwell points are set according to the polishing trajectory and / or the user-specified position, and the dwell time matrix is ​​calculated based on the dwell points, the polishing spot removal function, and the removal function of each divided area.

[0064] Specifically, Figure 4 As shown, the pulse iteration algorithm is used to solve the residence time matrix. First, initialize the residence time matrix, which can be set to 0; then start the iterative calculation. In each iteration, the time increases by a fixed value Δt, and the residual matrix of the component is calculated according to the following formula:

[0065] H(x,y)=R(x,y)*T(x,y)

[0066] Among them, H(x,y) is the residual matrix of the component, R(x,y) is the polishing spot removal function matrix, T(x,y) is the dwell time matrix, and * represents the convolution operation; when the RMS value of the residual matrix of the component meets the requirements, the dwell time matrix is ​​derived, otherwise the iteration continues. During the iteration process, when the residual of the component has a negative value, the dwell time of the point is directly set to the time value of the previous step.

[0067] Thus, the simulation ends, and the polishing trajectory, dwell points, and the dwell time matrix corresponding to the dwell points are obtained.

[0068] Those skilled in the art can understand that different trajectory planning methods are selected during simulation, resulting in different allocation positions of dwell points and different dwell time matrices. During actual magnetorheological polishing, the morphology of the fitted spherical polishing spots corresponding to different positions is different, and the corresponding polishing spot projections are also different.

[0069] Example 2

[0070] This embodiment is an embodiment in which actual processing is performed after the simulation calculation in embodiment 1 is completed.

[0071] A processing method for magnetorheological polishing of complex curved optical elements, which uses a simulation method for magnetorheological polishing of complex curved optical elements as described in Example 1 to perform simulation, obtain polishing trajectory, dwell point and dwell time matrix, use process software to convert the polishing trajectory, dwell point and dwell time matrix into a numerical control code recognizable by a machine tool, and then perform magnetorheological polishing processing.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A simulation method for magnetorheological polishing of complex curved optical elements, characterized in that: The following steps are involved: H1: Calculate the initial surface shape error based on the interferometer detection image and the expected surface shape after processing; H2: Select the appropriate polishing trajectory according to the component type and initial surface error; H3: Divide the surface error into non-spherical areas, obtain the position, size, spherical radius and spherical center coordinates of each divided area, and obtain the removal function of each divided area; H4: Conduct magnetorheological polishing spot removal experiments to obtain the three-dimensional morphology of the actual polishing spot under the current processing conditions, and calculate the polishing spot removal function of each divided area; H5: Assign dwell points and calculate the dwell time matrix; In step H3, when the aspheric surface is divided into regions, the principle of division is that the larger the off-axis amount, the smaller the divided region; Step H4 also includes projecting the polishing spots on the cutting plane into the global coordinate system to obtain the polishing spot morphology of each divided area: ， is the global coordinate of a point on the polishing spot, is the local coordinate of a point on the polishing spot, is the global coordinate corresponding to the center of the divided area; Rotation around the y axis The coefficient matrix of angles, Rotation around the x-axis The coefficient matrix of the angle, the corresponding equations are: ， ， is the angle between the local coordinate system and the global coordinate system in the XOZ plane, is the angle between the local coordinate system and the global coordinate system in the YOZ plane; In step H5, the pulse iteration algorithm is used to solve the residence time matrix: ， Among them, H(x, y) is the residual matrix of the component, R(x, y) is the polishing spot removal function matrix, T(x, y) is the residence time matrix, Represents the convolution operation; when the RMS value of the element residual error matrix meets the requirements, the dwell time matrix is ​​derived, otherwise the iteration continues.

2. The method for simulating magnetorheological polishing of complex curved optical elements according to claim 1, characterized in that: In step H3, the local best sphere is calculated as follows: ； In the formula, the calculation expressions of A, t, and b are: ， In the formula, is the initial sphere center coordinate, is the radius of the sphere, is the original data coordinate, , , , , after multiple iterations, the spherical radius and center coordinates of each divided area can be obtained.

3. The simulation method for magnetorheological polishing of complex curved optical elements according to claim 1 or 2, characterized in that: The polishing track includes a grating track, a spiral track, and a random track.

4. The simulation method for magnetorheological polishing of complex curved optical elements according to claim 3, characterized in that: The dwell point is set according to the polishing trajectory and / or the user-specified position.

5. A method for magnetorheological polishing of complex curved optical components, characterized in that: A simulation method for magnetorheological polishing of a complex curved optical element as described in any one of claims 1 to 4 is used to perform simulation, obtain a polishing trajectory, a dwell point and a dwell time matrix, and then perform magnetorheological polishing processing.

6. The method for magnetorheological polishing of complex curved optical components according to claim 5, characterized in that: Also includes: Process software is used to convert the polishing trajectory, dwell point and dwell time matrix into NC codes that can be recognized by the machine tool.

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