Optical processing non-grating track tool mark prediction method

Abstract

The invention relates to the technical field of optical processing, in particular to an optical processing non-grating track tool mark prediction method, which comprises the following steps of: obtaining a surface shape residual error and removal function distribution of a to-be-processed workpiece according to a surface shape and a processing technology of the to-be-processed workpiece; determining a non-grating processing track of the processing workpiece, and determining residence time of the processing workpiece according to the obtained surface shape residual error and removal function distribution; calculating a continuous tool influence function between adjacent residence points on the non-grating processing track by combining the obtained residence time based on the obtained removal function distribution; and calculating a predicted tool mark of a non-grating track according to the obtained continuous tool influence function. According to the method, correct dwell time is calculated according to requirements, sub-dwell points are established, sub-dwell time distribution is performed according to the dwell time, continuous simulation is performed, and then tool mark prediction under the non-grating track condition is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical processing, and particularly relates to a method for predicting non-grating trajectory tool marks in optical processing. Background Art

[0002] There have been numerous reports on the simulation of tool marks. In the paper "Toolmark prediction on the surface of large-aperture mirrors via magnetorheological finishing" published in the journal Optics Express, four prediction methods are given, namely the analytical method, the experimental method, the numerical method, and the AI prediction method. The invention patent application with the Chinese patent publication number CN116679622A and the publication date of October 3, 2023, and the patent name "Method for predicting surface shape tool mark error based on continuous tool function" gives a numerical method for predicting tool marks, which gives a method for simulating tool marks based on one-dimensional kinematics. The invention patent application with the Chinese patent publication number CN118821623A and the publication date of November 19, 2024, and the patent name "Method for predicting tool mark error on the surface of a polishing element based on a neural network" gives a neural network method for predicting tool marks, which requires a large amount of database support. The currently existing methods are all for predicting grating trajectories. There will be calculation errors if the above methods are used for predicting tool marks of non-grating trajectories. For example, the kinematic formula of a spiral trajectory needs to be considered in two dimensions and there is no large amount of data support. A method for simulating tool marks applicable to processing scenarios of various types of non-grating trajectories should be developed. In tool mark prediction, the method of dwell time allocation needs to be used. The invention patent application with the Chinese patent publication number CN117807816A and the publication date of April 2, 2024, and the patent name "Discrete form correction method for calculating dwell time by matrix method" gives a method for calculating the weighted corrected dwell time of an irregular grid (non-grating trajectory), which can compensate for the above errors; then considering the multi-dimensional kinematic formula of the non-grating trajectory and the calculation transformation of the optical processing pose, combining the three can calculate the accurate tool mark error. Summary of the Invention

[0003] In view of this, the present invention aims to provide a method for predicting non-grating trajectory tool marks in optical processing, so as to obtain the surface shape error, the removal function distribution, and the non-grating processing trajectory, calculate the correct dwell time according to requirements, establish sub-dwell points, allocate the sub-dwell time according to the dwell time, and perform continuous simulation. The method provided by the present invention can achieve the prediction of non-grating trajectory tool marks.

[0004] To achieve the above object, the technical solution of the present invention is realized as follows: An optical processing non-grating trajectory tool mark prediction method, comprising: S1: Obtain the surface shape residual and removal function distribution of the workpiece to be processed according to the surface shape and processing technology of the workpiece to be processed; S2: Determine the non-grating processing trajectory of the workpiece to be processed, and determine the dwell time of the workpiece to be processed according to the surface shape residual and removal function distribution obtained in step S1; S3: Based on the removal function distribution obtained in step S1, calculate the continuous tool influence function between adjacent dwell points on the non-grating processing trajectory in combination with the dwell time obtained in step S2; S4: Calculate the predicted tool marks of the non-grating trajectory according to the continuous tool influence function obtained in step S3.

[0005] Further, in step S2, the dwell time is calculated by the following formula: ; where, e i =E(x i , y i ), r ij =w(ξ j , η j )×R j (x i -ξ j , y i -η j ), t j =T(ξ j , η j ), E(x i , y i ) represents the surface shape residual of the i-th surface shape point (x i , y i ), 1≤i≤I, I represents the total number of surface shape points (x i , y i ), R j (x i -ξ j , y i -η j ) represents the removal function distribution at the j-th dwell point (ξ j , η j ), T(ξ j , η j ) represents the dwell time of the j-th dwell point (ξ j , η j ), 1≤j≤J, J represents the total number of dwell points (ξ j , η j ), w(ξ j , η j ) represents the j-th dwell point (ξj , η j The weight correction factor of

[0006] Furthermore, set P n sub-stay points between two adjacent stay points. The removal function distribution R j , η j at the j-th stay point (ξ j is obtained by the following formula: ; where Trans j () represents the attitude transformation function of the j-th stay point, and R represents the removal function distribution.

[0007] Furthermore, in step S3, set P n sub-stay points between two adjacent stay points, and calculate the continuous tool influence function by the following formula: ; where l represents the l-th sub-stay point, 1 ≤ l ≤ P n , m j represents the dwell segment between the j-th stay point and the (j + 1)-th stay point, 1 ≤ m j ≤ J - 1, represents the continuous tool influence function corresponding to the dwell segment m j , represents the continuous tool function slice of the l-th sub-stay point in the dwell segment m j , (α, β) represents the sub-stay point coordinates, and DT(l) represents the sub-stay time vector of the l-th sub-stay point.

[0008] Furthermore, the sub-stay time vector DT(l) is obtained by the following formula: ; where a represents the moving acceleration of the machining tool during the machining process, represents the starting moving speed of the machining tool in the dwell segment m j , represents the arc length of the machining tool moving from the l-th sub-stay point to the (l + 1)-th sub-stay point in the dwell segment m j .

[0009] Furthermore, the continuous tool function slice j of the l-th sub-stay point in the dwell segment m is obtained by the following formula: ; where supp() represents finding the region where the variable is not zero, \ represents the difference set, CD represents the dimension expansion range, represents the dwell segment mj The removal function distribution of the $l$-th sub-dwell point in it is obtained from the following formula: ; where represents the attitude transformation function of the $l$-th sub-dwell point in the dwell segment $m$ j in it.

[0010] Furthermore, in step S4: The continuous tool function between each surface point is calculated through the continuous tool influence function: The combined removal amount during the machining process is calculated according to the continuous tool function; The surface form residual is subtracted from the combined removal amount to obtain the predicted tool marks.

[0011] Furthermore, the process of calculating the continuous tool function between each surface point through the continuous tool influence function is as follows: ; where represents the global continuous tool function of the dwell segment $m$, and ED represents the global dimension expansion range. j in it.

[0012] Furthermore, during the process of calculating the combined removal amount during the machining process according to the continuous tool function, the continuous tool function is accumulated to obtain the combined removal amount.

[0013] Compared with the prior art, the present invention can achieve the following beneficial effects: In the optical machining non-grating trajectory tool mark prediction method of the present invention, by obtaining the surface form error, removal function distribution, and non-grating machining trajectory, calculating the correct dwell time according to requirements, establishing sub-dwell points, allocating sub-dwell times according to the dwell time, and performing continuity simulation, the tool mark prediction of the non-grating trajectory under any trajectory machining condition is realized. This method does not require a large amount of historical machining data support, and uses optical machining calculation transformation to obtain a more accurate dwell time, and then uses a more strict sub-dwell time allocation strategy, making the prediction model closer to the actual machining process and obtaining more accurate non-grating trajectory tool marks. Description of the Drawings

[0014] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings: Figure 1 is the flow schematic diagram of the optical machining non-grating trajectory tool mark prediction method described in the embodiment of the present invention; Figure 2 is the surface form residual diagram described in the embodiment of the present invention; Figure 3 The removal function graph described in the embodiment of the present invention Figure 4 The non-raster machining trajectory graph of the spiral line described in the embodiment of the present invention Figure 5 The final tool mark prediction graph described in the embodiment of the present invention Detailed implementation manners

[0015] In order to make the objectives, technical solutions and advantages of the present invention clearer, 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 and do not constitute a limitation to the present invention.

[0016] 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.

[0017] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying 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 should not be construed 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 number 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.

[0018] In the description of the present invention, it should be noted that, unless otherwise clearly defined and limited, the terms "mounted", "connected" and "connected" 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 directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0019] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0020] Such as Figure 1As shown in the figure, the optical processing non-grating trajectory tool mark prediction method described in the embodiment of the present invention includes: S1: Obtain the surface shape residual and removal function distribution of the workpiece to be processed according to the surface shape and processing technology of the workpiece to be processed.

[0021] In some embodiments, the surface shape of the workpiece to be processed is measured by an interferometer to obtain the surface shape residual of the workpiece to be processed, and the removal function distribution is determined according to the processing technology of the workpiece to be processed. The present invention is not limited to one process, and may be other deterministic polishing processes such as ion beam figuring and bladder polishing.

[0022] S2: Determine the non-grating processing trajectory of the workpiece to be processed, and determine the dwell time of the workpiece to be processed according to the surface shape residual and removal function distribution obtained in step S1. The present invention is not limited to one process, such as the magic angle process in magnetorheological processing, and is not limited to one trajectory, and can be used for random trajectories and maze trajectories, etc.

[0023] In some embodiments, in step S2, the dwell time is calculated by the following formula: ; where, e i = E(x i , y i ), r ij = w(ξ j , η j ) × R j (x i - ξ j , y i - η j ), t j = T(ξ j , η j ), E(x i , y i ) represents the surface shape residual of the i-th surface shape point (x i , y i ), 1 ≤ i ≤ I, I represents the total number of surface shape points (x i , y i ), w(ξ j , η j ) represents the weight correction factor of the j-th dwell point (ξ j , η j ) on the non-grating processing trajectory, R j (x i - ξ j , y i - η j ) represents the removal function distribution at the j-th dwell point (ξ j , η j ), T(ξ j, η j ) represents the residence time of the j-th residence point (ξ j , η j ), 1 ≤ j ≤ J, where J represents the total number of residence points (ξ j , η j ). The weight correction factor w(ξ j , η j ) is consistent with the weight correction factor provided in Chinese Patent Publication No. CN117807816A, publication date April 2, 2024, and patent name "Discrete Form Correction Method for Calculating Residence Time by Matrix Method".

[0024] Among them, P n sub-residence points are set between two adjacent residence points. The removal function distribution R j , η j ) at the j-th residence point (ξ j ) is obtained through the following formula: ; Among them, Trans j () represents the attitude transformation function of the j-th residence point, and R represents the removal function distribution. It can be seen from the above formula that the attitudes of the removal function distributions are different at different residence points.

[0025] S3: Based on the removal function distribution obtained in step S1, combined with the residence time obtained in step S2, calculate the continuous tool influence function between adjacent residence points on the non-grating machining trajectory.

[0026] In some embodiments, in step S3, P n sub-residence points are set between two adjacent residence points, and the continuous tool influence function is calculated through the following formula: ; Among them, l represents the l-th sub-residence point, 1 ≤ l ≤ P n , and the insertion method of the sub-residence points depends on the process requirements. m j represents the residence segment between the j-th residence point and the (j + 1)-th residence point, 1 ≤ m j ≤ J - 1, represents the continuous tool influence function corresponding to the residence segment m j , represents the continuous tool function slice of the l-th sub-residence point in the residence segment m j , (α, β) represents the sub-residence point coordinates, and DT(l) represents the sub-residence time vector of the l-th sub-residence point.

[0027] Specifically, the sub-residence time vector DT(1) of the l-th sub-residence point is obtained through the following formula: ; Among them, a represents the moving acceleration of the processing tool during the processing, represents the starting moving speed of the processing tool at the dwell segment m j ; represents the arc length of the processing tool moving from the l-th sub-dwell point to the (l + 1)-th sub-dwell point in the dwell segment m j , and the arc length is obtained according to different setting methods of the sub-dwell points.

[0028] The dwell segment m j The continuous tool function slice of the l-th sub-dwell point in it is obtained by the following formula: ; Among them, supp() represents finding the region where the variable is not 0, \ represents the difference set, CD represents the dimension expansion range, and the dimension expansion range CD only needs to enclose the two dwell points, that is: ; Among them, R ωmin represents the minimum value of the abscissa of the function distribution R after removal, and R ωmax represents the maximum value of the abscissa of the function distribution R after removal, s' ε represents the arc length projected along the abscissa direction of the dwell point on the non-grating processing trajectory, and s' η represents the arc length projected along the ordinate direction of the dwell point on the non-grating processing trajectory, and R vmin represents the minimum value of the ordinate of the function distribution R after removal, and R vmax represents the maximum value of the ordinate of the function distribution R after removal; represents the removal function distribution of the l-th sub-dwell point in the dwell segment m j and is obtained by the following formula: ; Among them, represents the attitude transformation function of the l-th sub-dwell point in the dwell segment m j .

[0029] S4: Calculate the predicted tool marks of the non-grating trajectory according to the continuous tool influence function obtained in step S3.

[0030] In some embodiments, in step S4: S41: Calculate the continuous tool function between each surface shape point through the continuous tool influence function. In a certain embodiment, the process is as follows: ; Among them, represents the dwell segment m jThe global continuous tool function, where ED represents the global dimension expansion range, which is related to the effective length of the removal function distribution R, i.e.: ; Among them, is the effective size area of the component.

[0031] S42: Calculate the synthetic removal amount during the machining process according to the continuous tool function. In a certain embodiment, specifically, accumulate the continuous tool function to obtain the synthetic removal amount, i.e.: ; Among them, FAR represents the synthetic removal amount; S43: Subtract the surface shape residual from the synthetic removal amount to obtain the predicted tool marks, i.e.: ; Among them, Res represents the predicted tool marks.

[0032] To clearly illustrate the optical machining non-grating trajectory tool mark prediction method described in the embodiments of the present invention, an embodiment is provided.

[0033] Embodiment 1: S1: Obtain the surface shape residual and removal function distribution of the workpiece to be machined according to the surface shape and machining process of the workpiece to be machined.

[0034] In this embodiment, the surface shape of the workpiece to be machined is measured by an interferometer to obtain the surface shape residual of the workpiece to be machined, as shown in Figure 2 . The workpiece to be machined is machined by magnetorheological polishing, and the corresponding removal function distribution is as shown in Figure 3 .

[0035] S2: Determine the non-grating machining trajectory of the workpiece to be machined, and determine the dwell time of the workpiece to be machined according to the surface shape residual and removal function distribution obtained in step S1.

[0036] In this embodiment, a non-grating machining trajectory of a spiral line as shown in Figure 4 is adopted, and the polar coordinate equation of the machining trajectory is:[[]]END]] ; Among them, Q = 4 / 2π, and the polar coordinates (ξ, η) of the dwell points of the machining trajectory are:[[]]END]] .

[0037] The machining process requirements used in this embodiment are that the flow direction of the magnetorheological fluid is always perpendicular to the tangent of the non-grating machining trajectory, and the machining trajectory is discretized, that is, the kth circle of the non-grating machining trajectory is discretized into γ k dwell points, and the number γ k of the dwell points in the kth circle is related to the number γk-1 Satisfy: γ k = γ k-1 (j / 2 + 1). Wherein, the number γ of the stationary points in the 0th circle 0 is 0, that is, γ 0 = 0, the number γ of the stationary points in the 1st circle 1 is 10, that is, γ 1 = 10.

[0038] Calculate the dwell time through the following formula: ; Among them, the total number J of the stationary points (ξ j , η j ) is: .

[0039] The removal function distribution R at the jth stationary point (ξ j , η j ) is obtained through the following formula: j Obtained through the following formula: ; Among them, Ts represents the translation function. In the above formula, Ts(R, ξ j , η j ) means translating the removal function distribution R to (ξ j , η j ), Rot represents the rotation function. In the above formula, Rot(Ts(R, ε j , η j ), ξ j , η j , θ j+1 -θ j ) means rotating Ts(R, ξ j , η j ) around the stationary point (ξ j , η j ) by the angle θ j+1 -θ j , θ j represents the angle of the removal function distribution R j at the jth stationary point. Through the above formula, it is ensured that during the magnetorheological machining process, the flow direction of the magnetorheological fluid is always perpendicular to the tangent of the non-grating machining trajectory, and an accurate dwell time is obtained.

[0040] S3: Based on the removal function distribution obtained in step S1, combine the dwell time obtained in step S2 to calculate the continuous tool influence function between adjacent stationary points on the non-grating machining trajectory.

[0041] In this embodiment, according to the process requirements, P is set at equal angular intervals between two adjacent stationary points nThe continuous tool influence function is calculated by the following formula: ; The sub-residence time vector DT(l) is obtained by the following formula: .

[0042] For the non-grating processing track of the spiral line in this embodiment, the moving speed , moving acceleration a, and the machining tool in the residence section m j The residence time at the jth residence point in Satisfies the following relationship: ; Arc Length It is obtained by the following formula: .

[0043] in, Indicates that the machining tool is in the residence section m j The starting processing angle in Indicates that the machining tool is in the residence section m j The machining angle at the lth sub-dwelling point in .

[0044] Resident segment m j Continuous tool function slices of the lth sub-residence point in From the following formula: ; In this embodiment, the resident segment m j The removal function distribution of the lth sub-residence point in Specifically: ; Among them, the resident segment m j The coordinates of the lth sub-residence point in for: .

[0045] S4: Calculate the predicted tool marks of the non-grating track according to the continuous tool influence function obtained in step S3. In step S4: S41: Calculate the continuous tool function between each face point through the continuous tool influence function, as follows: .

[0046] S42: Calculate the synthetic removal amount during the machining process according to the continuous tool function, that is: .

[0047] S43: Subtract the surface form residual from the synthetic removal amount to obtain the predicted tool marks, i.e.: .

[0048] The final tool mark prediction obtained by the above method is as Figure 5 shown. The surface form convergence rate of the final tool marks is 99.86%, the PV is 0.23013λ, where λ represents the wavelength of the light generated by the interferometer, and the RMS is 0.00029λ.

[0049] This method does not require a large amount of historical processing data support and is a specific analysis method for machining tasks with non-grating trajectories. As long as the process parameters and forms are determined for each machining task, the dwell time calculation at each location can be ensured to be accurate through optical machining calculation transformation (i.e., Trans pose transformation). Moreover, a more refined kinematic equation is considered, and then a more rigorous sub-dwell time allocation strategy is used, making the prediction model closer to the actual machining process and obtaining more accurate tool marks for non-grating trajectories.

[0050] It should be understood that various forms of the processes shown above can be used, with steps reordered, added, or deleted. For example, the steps recited 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 imposed herein.

[0051] The above specific embodiments do not constitute a limitation on 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 principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for predicting tool marks in optical machining non-grating tracks, characterized in that: include: S1: according to the surface shape and processing technology of the workpiece to be processed, obtaining the surface shape residual and removal function distribution of the workpiece to be processed; S2: determining the non-grating processing trajectory of the processed workpiece, and determining the residence time of the processed workpiece according to the surface shape residual and removal function distribution obtained in step S1; S3: calculating the continuous tool influence function between adjacent dwell points on the non-raster processing trajectory based on the removal function distribution obtained in step S1 and the dwell time obtained in step S2; S4: Calculate the predicted tool mark of the non-grating trajectory according to the continuous tool influence function obtained in step S3.

2. The optical machining non-grating track tool mark prediction method according to claim 1, characterized in that: In step S2, the residence time is calculated by the following formula: ； Among them, e i =E(x i ,y i ), r ij =w(ξ j ,η j )×R j (x i -ξ j ,y i -η j ), t j =T(ξ j ,η j ), E(x i ,y i ) represents the i-th surface point (x i ,y i ), 1≤i≤I, I represents the surface point (x i ,y i ), w(ξ j ,η j ) represents the jth dwell point (ξ) on the non-grating processing trajectory. j ,η j ) weight correction factor, R j (x i -ξ j ,y i -η j ) indicates that the removal function is distributed at the jth residence point (ξ j ,η j ) at the removal function distribution, T(ξ j ,η j ) represents the jth dwelling point (ξ j ,η j )'s residence time, 1≤j≤J, J represents the residence point (ξ j ,η j ) total number.

3. The optical machining non-grating track tool mark prediction method according to claim 2, characterized in that: The jth residence point (ξ j ,η j ) at the removal function distribution R j It is obtained by the following formula: ； Among them, Trans j () represents the posture transformation function of the j-th residence point, and R represents the removal function distribution.

4. The optical machining non-grating track tool mark prediction method according to claim 3, characterized in that: In step S3, a P is set between two adjacent dwell points. n Sub-dwelling points, the continuous tool influence function is calculated by the following formula: ； Where l represents the lth sub-residence point, 1≤l≤P n , m j represents the dwelling segment between the jth dwelling point and the j+1th dwelling point, 1≤m j ≤J-1, Indicates the resident segment m j The corresponding continuous tool impact function, Indicates the resident segment m j The continuous tool function slices of the l-th sub-residence point in , (α, β) represents the coordinates of the sub-residence point, and DT(l) represents the sub-residence time vector of the l-th sub-residence point.

5. The optical machining non-grating track tool mark prediction method according to claim 4, characterized in that: The sub-residence time vector DT(l) is obtained by the following formula: ； Where a represents the moving acceleration of the machining tool during the machining process, Indicates that the processing tool is in the residence section m j The starting moving speed, Indicates that the processing tool is in the residence section m j The arc length from the lth sub-residence point to the l+1th sub-residence point.

6. The optical machining non-grating track tool mark prediction method according to claim 4, characterized in that: Resident segment m j Continuous tool function slices of the lth sub-residence point in From the following formula: ； Among them, supp() means to find the area where the variable is not 0, \ means the difference set, and CD means the expansion range. Indicates the resident segment m j The removal function distribution of the l-th sub-residence point in is obtained by the following formula: ； in, Indicates the resident segment m j The posture transformation function of the lth sub-residence point in .

7. The optical machining non-grating track tool mark prediction method according to claim 6, characterized in that: In step S4: The continuous tool function between each surface point is calculated by the continuous tool influence function: calculating a resultant removal during machining according to the continuous tool function; The predicted tool mark is obtained by subtracting the surface shape residual from the synthetic removal amount.

8. The optical machining non-grating track tool mark prediction method according to claim 7, characterized in that: The process of calculating the continuous tool function between each face point through the continuous tool influence function is as follows: ； in, Indicates the resident segment m j The global continuous tool function ED represents the global dimensional expansion range.

9. The optical machining non-grating track tool mark prediction method according to claim 8, characterized in that: In the process of calculating the composite removal amount in the processing process according to the continuous tool function, the continuous tool function is accumulated to obtain the composite removal amount.

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