Tool mark prediction method for non-grating trajectory in optical machining

Abstract

The present invention relates to the field of optical processing technology, and in particular to a method for predicting tool marks for non-grating trajectories in optical processing. The method comprises: obtaining the surface shape residual and removal function distribution of the workpiece to be processed based on the surface shape and processing technology of the workpiece to be processed; determining the non-grating processing trajectory of the workpiece to be processed, and determining the dwell time of the workpiece to be processed based on the obtained surface shape residual and removal function distribution; calculating the continuous tool influence function between adjacent dwell points on the non-grating processing trajectory based on the obtained removal function distribution and the obtained dwell time; and calculating the predicted tool mark for the non-grating trajectory based on the obtained continuous tool influence function. The present invention calculates the correct dwell time according to demand, establishes sub-dwelling points, allocates sub-dwelling times based on the dwell time, and performs continuity simulation, thereby realizing tool mark prediction in the case of non-grating trajectories.

Description

Technical Field

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

[0002] There have been many 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 analytical method, experimental method, numerical method, and AI prediction method. The Chinese patent publication number is CN116679622A, the publication date is October 3, 2023, and the invention patent application named "Surface tool mark error prediction method based on continuous tool function" gives a numerical tool mark prediction method. This method gives a method of simulating tool marks based on one-dimensional kinematics. The Chinese patent publication number is CN118821623A, the publication date is November 19, 2024, and the invention patent application named "Prediction method of tool mark error on the surface of polishing element based on neural network" gives a neural network tool mark prediction method. This method requires a large number of databases for support. The current existing methods all predict grating trajectories. If the tool mark measurement of non-grating trajectories is carried out according to the above method, there will be calculation errors. For example, the kinematic formula of the spiral trajectory needs to be considered in two dimensions, and there is no large amount of data to support it. A method for tool mark simulation in processing scenarios that is applicable to various types of non-grating trajectories should be developed. A dwell time allocation method is required for tool mark prediction. The Chinese patent publication number is CN117807816A, and the publication date is April 2, 2024. The invention patent application named "Discrete Form Correction Method for Calculating Dwell Time by Matrix Method" provides a weighted correction dwell time calculation method for irregular grids (non-grating trajectories). This method can compensate for the above errors; then the multi-dimensional kinematic formula of the non-grating trajectory and the optical processing posture calculation transformation are taken into account, and the three are combined to calculate the accurate tool mark error. Summary of the Invention

[0003] In view of this, the present invention aims to provide a tool mark prediction method for non-grating trajectories in optical processing, so as to obtain surface error, removal function distribution and non-grating processing trajectory, calculate the correct dwell time according to demand, establish sub-dwelling points, allocate sub-dwelling times according to the dwell time, and perform continuity simulation. The method provided by the present invention can realize tool mark prediction of non-grating trajectories.

[0004] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0005] A method for predicting tool marks in optical machining non-grating tracks, comprising:

[0006] S1: According to the surface shape and machining process of the workpiece to be machined, the surface shape residual and removal function distribution of the workpiece to be machined are obtained;

[0007] S2: Determine the non-raster processing trajectory of the workpiece, and determine the dwell time of the workpiece according to the surface shape residual and removal function distribution obtained in step S1;

[0008] S3: Calculating the continuous tool influence function between adjacent dwell points on the non-raster machining trajectory based on the removal function distribution obtained in step S1 and the dwell time obtained in step S2;

[0009] S4: Calculate the predicted tool mark of the non-raster trajectory according to the continuous tool influence function obtained in step S3.

[0010] Furthermore, in step S2, the residence time is calculated by the following formula:

[0011] ;

[0012] 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 ), R j (x i -ξ j ,y i -η j ) represents the removal function distribution at the jth residence point (ξ j ,η j ) at the removal function distribution, T(ξ j ,η j ) represents the jth dwell point (ξ j ,η j)’s residence time, 1≤j≤J, J represents the residence point (ξ j ,η j ), w(ξ j ,η j ) represents the jth dwell point on the non-raster processing trajectory (ξ j ,η j ) weight correction factor.

[0013] Furthermore, P is set between two adjacent residence points. n Sub-residence points, the jth residence point (ξ j ,η j ) at the removal function distribution R j It is obtained by the following formula:

[0014] ;

[0015] Among them, Trans j () represents the posture transformation function of the jth residence point, and R represents the removal function distribution.

[0016] Further, in step S3, P is set between two adjacent residence points. n The continuous tool influence function is calculated by the following formula:

[0017] ;

[0018] Where l represents the lth sub-residence point, 1≤l≤P n , m j represents the dwell segment between the jth dwell point and the j+1th dwell point, 1≤m j ≤J-1, Indicates the resident segment m j The corresponding continuous tool influence 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.

[0019] Furthermore, the sub-residence time vector DT(l) is obtained by the following formula:

[0020] ;

[0021] Where a represents the moving acceleration of the machining tool during the machining process, Indicates that the machining tool is in the residence segment m j The starting moving speed, Indicates that the machining tool is in the residence segment m jThe arc length from the lth sub-residence point to the l+1th sub-residence point.

[0022] Furthermore, the resident segment m j Continuous tool function slices of the lth sub-residence point From the following formula:

[0023] ;

[0024] Among them, supp() means finding the area where the variable is not 0, \ means the difference set, and CD means the dimension expansion range. Indicates the resident segment m j The removal function distribution of the lth sub-residence point in is obtained by the following formula:

[0025] ;

[0026] in, Indicates the resident segment m j The posture transformation function of the lth sub-residence point in .

[0027] Furthermore, in step S4:

[0028] Calculate the continuous tool function between each face point through the continuous tool influence function:

[0029] Calculate the resultant removal during machining based on a continuous tool function;

[0030] The predicted tool mark is obtained by subtracting the surface shape residual from the synthetic removal amount.

[0031] Furthermore, the process of calculating the continuous tool function between each face point through the continuous tool influence function is as follows:

[0032] ;

[0033] in, Indicates the resident segment m j The global continuous tool function, ED represents the global dimension expansion range.

[0034] Furthermore, in the process of calculating the composite removal amount during the machining process according to the continuous tool function, the continuous tool function is accumulated to obtain the composite removal amount.

[0035] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0036] The present invention proposes a tool mark prediction method for optical machining non-grating trajectories. By acquiring surface shape errors, removal function distribution, and the non-grating machining trajectory, the correct dwell time is calculated as required, sub-dwell points are established, and sub-dwell times are allocated based on the dwell times. Continuous simulation is then performed to achieve tool mark prediction for non-grating trajectories under arbitrary trajectory machining conditions. This method does not require extensive historical machining data and utilizes optical machining computational transformations to obtain more accurate dwell times. Furthermore, a more rigorous sub-dwell time allocation strategy is employed, making the prediction model closer to the actual machining process and achieving more accurate tool marks for non-grating trajectories. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0038] Figure 1 A schematic diagram of the process of predicting tool marks for optical machining non-grating tracks according to an embodiment of the present invention;

[0039] Figure 2 To create the surface shape residual map described in the embodiment of the present invention;

[0040] Figure 3 The removal function diagram described in the embodiment of the present invention is created;

[0041] Figure 4 The non-grating processing trajectory diagram of the spiral line described in the embodiment of the present invention is created;

[0042] Figure 5 This is the final tool mark prediction diagram described in the embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 of the present invention.

[0044] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0045] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are 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 on the present invention. In addition, the terms "first", "second" and the like 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, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0046] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0047] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0048] like Figure 1 As shown, the optical machining non-grating track tool mark prediction method described in the embodiment of the present invention includes:

[0049] S1: According to the surface shape of the workpiece to be processed and the processing technology, the surface shape residual and removal function distribution of the workpiece to be processed are obtained.

[0050] In some embodiments, the surface shape of the workpiece to be processed is measured using an interferometer to obtain the surface shape residual of the workpiece to be processed. The removal function distribution is determined based on the processing technology of the workpiece to be processed. The present invention is not limited to a single process and can also be other deterministic polishing processes such as ion beam shaping and air bag polishing.

[0051] S2: Determine the non-raster machining trajectory of the workpiece and determine the dwell time of the workpiece based on the surface shape residual and removal function distribution obtained in step S1. The present invention is not limited to a single process, such as the magic angle process in magnetorheological fluid, or a single trajectory, and can be applied to random trajectories and maze trajectories.

[0052] In some embodiments, in step S2, the residence time is calculated by the following formula:

[0053] ;

[0054] 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 on the non-raster processing trajectory (ξ j ,η j ) weight correction factor, R j (x i -ξ j ,y i -η j ) represents the removal function distribution at the jth residence point (ξ j ,η j ) at the removal function distribution, T(ξ j ,η j ) represents the jth dwell point (ξ j ,η j )’s residence time, 1≤j≤J, J represents the residence point (ξ j ,η j ). Weight correction factor w(ξ j ,η j ) is consistent with the weight correction factor provided in Chinese patent publication number CN117807816A, publication date April 2, 2024, and patent name "Discrete form correction method for calculating residence time using matrix method".

[0055] Among them, P is set between two adjacent residence points. n Sub-residence points, the jth residence point (ξ j ,η j ) at the removal function distribution R j It is obtained by the following formula:

[0056] ;

[0057] Among them, Trans j () represents the posture transformation function of the jth dwell point, and R represents the removal function distribution. As can be seen from the above formula, the posture of the removal function distribution is different at different dwell points.

[0058] S3: Based on the removal function distribution obtained in step S1 and the dwell time obtained in step S2, a continuous tool influence function between adjacent dwell points on the non-raster machining trajectory is calculated.

[0059] In some embodiments, in step S3, a P is set between two adjacent dwell points. n The continuous tool influence function is calculated by the following formula:

[0060] ;

[0061] Where l represents the lth sub-residence point, 1≤l≤P n The insertion method of the sub-residence point depends on the process requirements, m j represents the dwell segment between the jth dwell point and the j+1th dwell point, 1≤m j ≤J-1, Indicates the resident segment m j The corresponding continuous tool influence 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.

[0062] Specifically, the sub-residence time vector DT(1) of the l-th sub-residence point is obtained as follows:

[0063] ;

[0064] Where a represents the moving acceleration of the machining tool during the machining process, Indicates that the machining tool is in the residence segment m j The starting moving speed, Indicates that the machining tool is in the residence segment m j The arc length from the lth sub-residence point to the l+1th sub-residence point is obtained according to different sub-residence point settings.

[0065] Resident segment m j Continuous tool function slices of the lth sub-residence point From the following formula:

[0066] ;

[0067] Among them, supp() means finding the area where the variable is not 0, \ means the difference set, and CD means the expansion range. The expansion range CD surrounds the two resident points, that is:

[0068] ;

[0069] Among them, R ωmin Indicates the minimum value of the horizontal axis of the removal function distribution R, R ωmax Indicates the maximum value of the horizontal coordinate of the removal function distribution R, s' ε Indicates arc length The projection of the dwell point along the non-raster machining trajectory in the horizontal coordinate direction, s' η Indicates arc length The projection of the dwell point along the non-raster machining trajectory in the ordinate direction, R vmin Indicates the minimum value of the vertical coordinate of the removal function distribution R, R vmax Indicates the maximum value of the ordinate of the removal function distribution R;

[0070] Indicates the resident segment m j The removal function distribution of the lth sub-residence point in is obtained by the following formula:

[0071] ;

[0072] in, Indicates the resident segment m j The posture transformation function of the lth sub-residence point in .

[0073] S4: Calculate the predicted tool mark of the non-raster trajectory according to the continuous tool influence function obtained in step S3.

[0074] In some embodiments, in step S4:

[0075] S41: Calculate the continuous tool function between each surface point through the continuous tool influence function. In one embodiment, the process is as follows:

[0076] ;

[0077] in, Indicates the resident segment m j The global continuous tool function, ED represents the global dimensional expansion range, which is related to the effective length of the removal function distribution R, that is:

[0078] ;

[0079] in, is the effective size area of ​​the component.

[0080] S42: Calculate the composite removal amount during the processing according to the continuous tool function. In one embodiment, specifically, the continuous tool function is accumulated to obtain the composite removal amount, that is:

[0081] ;

[0082] Wherein, FAR represents the synthetic removal amount;

[0083] S43: Subtract the surface shape residual from the synthetic removal amount to obtain the predicted tool mark, that is:

[0084] ;

[0085] Among them, Res represents the predicted knife mark.

[0086] In order to clearly illustrate the method for predicting tool marks of non-grating tracks in optical machining described in an embodiment of the present invention, an embodiment is provided.

[0087] Example 1:

[0088] S1: According to the surface shape of the workpiece to be processed and the processing technology, the surface shape residual and removal function distribution of the workpiece to be processed are obtained.

[0089] In this embodiment, 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, such as Figure 2 The workpiece to be processed is processed by magnetorheological polishing, and the corresponding removal function distribution is as follows. Figure 3 shown.

[0090] S2: Determine the non-raster processing trajectory of the workpiece, and determine the residence time of the workpiece according to the surface shape residual and removal function distribution obtained in step S1.

[0091] In this embodiment, the Figure 4 The non-grating machining trajectory of the spiral line shown in the figure has the polar coordinate equation as follows:

[0092] ;

[0093] Where Q = 4 / 2π, and the polar coordinates (ξ,η) of the dwell point of the machining trajectory are:

[0094] .

[0095] The processing technology used in this embodiment requires that the flow direction of the magnetorheological fluid is always perpendicular to the tangent of the non-grating processing track, and the processing track is discretized, that is, the k-th circle non-grating processing track is discretized into γ k The number of residence points in the kth circle is γ k and the number of stationary points in the k-1th circle γk-1 Satisfy: γ k =γ k-1 (j / 2+1). The number of stationary points in the 0th circle, γ0, is 0, i.e., γ0=0, and the number of stationary points in the 1st circle, γ1, is 10, i.e., γ1=10.

[0096] The dwell time is calculated by the following formula:

[0097] ;

[0098] Among them, the dwell point (ξ j ,η j The total number J of ) is:

[0099] .

[0100] The jth residence point (ξ j ,η j ) at the removal function distribution R j It is obtained by the following formula:

[0101] ;

[0102] Among them, Ts represents the translation function, in the above formula, Ts(R, ξ j ,η j ) means to shift 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 ) represents the conversion of Ts(R, ξ j ,η j ) around the stationary point (ξ j ,η j )Rotation angle θ j+1 -θ j ,θ j Represents the removal function distribution R of the jth residence point j The above formula ensures that the flow direction of the magnetorheological fluid is always perpendicular to the tangent of the non-grating machining track during the magnetorheological machining process, thereby obtaining an accurate dwell time.

[0103] S3: Based on the removal function distribution obtained in step S1 and the dwell time obtained in step S2, a continuous tool influence function between adjacent dwell points on the non-raster machining trajectory is calculated.

[0104] In this embodiment, according to the process requirements, P is set at equal angles between two adjacent dwell points.n The continuous tool influence function is calculated by the following formula:

[0105] ;

[0106] The sub-residence time vector DT(l) is obtained by the following formula:

[0107] .

[0108] For the non-grating processing trajectory 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 The following relationship is satisfied:

[0109] ;

[0110] Arc length It is obtained by the following formula:

[0111] .

[0112] in, Indicates that the machining tool is in the residence segment m j The starting processing angle in Indicates that the machining tool is in the residence segment m j The machining angle at the lth sub-dwelling point in .

[0113] Resident segment m j Continuous tool function slices of the lth sub-residence point From the following formula:

[0114] ;

[0115] In this embodiment, the resident segment m j The removal function distribution of the lth sub-residence point in Specifically:

[0116] ;

[0117] Among them, the resident segment m j The coordinates of the lth sub-station in for:

[0118] .

[0119] S4: Calculate the predicted tool mark of the non-raster track based on the continuous tool influence function obtained in step S3. In step S4:

[0120] S41: Calculate the continuous tool function between each face point through the continuous tool influence function, as follows:

[0121] .

[0122] S42: Calculate the composite removal amount during the machining process according to the continuous tool function, namely:

[0123] .

[0124] S43: Subtract the surface shape residual from the synthetic removal amount to obtain the predicted tool mark, that is:

[0125] .

[0126] The final tool mark prediction obtained by the above method is as follows Figure 5 As shown in the figure, the surface convergence rate of the final tool mark is 99.86%, the PV is 0.23013λ, λ represents the wavelength of the light generated by the interferometer, and the RMS is 0.00029λ.

[0127] This method does not require the support of a large amount of historical processing data, and is a specific analysis method for non-grating trajectory processing tasks. As long as the process parameters and form of each processing task are determined, the optical processing calculation transformation (i.e., Trans posture transformation) can be used to ensure the accurate calculation of the dwell time at each location. In addition, more sophisticated kinematic equations are taken into account, and a more stringent sub-dwell time allocation strategy is used, so that the prediction model is closer to the actual processing process and more accurate non-grating trajectory tool marks are obtained.

[0128] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0129] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for predicting tool marks in optical machining non-grating tracks, characterized in that: include: S1: obtaining a surface shape residual and a 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, and determine the residence time of the workpiece according to the surface shape residual and removal function distribution obtained in step S1; in step S2, 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, R represents the removal function distribution, the j-th residence point (ξ j ,η j ) at the removal function distribution R j The direction is the same as the normal direction of the non-raster processing trajectory; S3: Set P between two adjacent dwell points n Based on the removal function distribution obtained in step S1 and the dwell time obtained in step S2, 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 dwell segment between the jth dwell point and the j+1th dwell point, 1≤m j ≤J-1, J represents the dwell point (ξ j ,η j ), Indicates the resident segment m j The corresponding continuous tool influence 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, DT(l) represents the sub-residence time vector of the l-th sub-residence point; 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; Resident segment m j Continuous tool function slices of the lth sub-residence point From the following formula: ； Among them, supp() means finding the area where the variable is not 0, \ means the difference set, and CD means the dimension expansion range. Indicates the resident segment m j The removal function distribution of the lth 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; The expansion range CD can surround the two resident points, that is: ； Among them, R ωmin Indicates the minimum value of the horizontal axis of the removal function distribution R, R ωmax Indicates the maximum value of the horizontal coordinate of the removal function distribution R, s' ε Indicates arc length The projection of the dwell point along the non-raster machining trajectory in the horizontal coordinate direction, s' η Indicates arc length The projection of the dwell point along the non-raster machining trajectory in the ordinate direction, R vmin Indicates the minimum value of the vertical coordinate of the removal function distribution R, R vmax Indicates the maximum value of the ordinate of the removal function distribution R; S4: Calculating the predicted tool mark of the non-raster track according to the continuous tool influence function obtained in step S3; In step S4: The continuous tool function between each surface point is calculated by the continuous tool influence function, and the process is as follows: ； in, Represents the resident segment m j The global continuous tool function, ED represents the global dimensional expansion range, that is: ； in, is the effective size area of ​​the component; calculating a resultant removal during machining based on the continuous tool function; The predicted tool mark is obtained by subtracting the surface shape residual from the synthetic removal amount.

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 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 dwell point (ξ j ,η j )’s residence time, 1≤j≤J.

3. The optical machining non-grating track tool mark prediction method according to claim 1, 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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