Smoothing polishing path planning method and system with regional adaptability

Abstract

The present invention provides a smooth polishing path planning method and system with regional adaptability. First, contour lines are extracted from a dwell time density matrix and a contour tree is established. The contour tree is used to identify peaks and valleys of the surface to be removed. Then, a watershed segmentation algorithm is used to divide the entire surface into multiple sub-regions containing only independent peaks or valleys, and sub-region boundary information and adjacency relationships between sub-regions are obtained. Next, a backtracking method is used to obtain a Hamiltonian path traversing each sub-region. A variable-pitch double-helix path is planned within each sub-region, and the endpoints of sequentially adjacent sub-paths are connected. The present invention considers the influence of surface features on path generation and tool motion speed during polishing path planning, which is beneficial for improving tool motion speed smoothness and reducing speed fluctuations. Furthermore, even when the dynamic performance of the machine tool is limited, the tool motion trajectory tracking accuracy can still be guaranteed, thereby improving the processing accuracy of sub-aperture deterministic polishing.

Description

Technical Field

[0001] The present invention relates to the technical field of computer-controlled optical surface forming technology, and in particular to a smoothing polishing path planning method and system with regional adaptability. Background Art

[0002] At present, ultra-precision optical free-form surfaces play a vital role in many fields such as clean energy, microelectronics manufacturing, aerospace, astronomical observation, etc. Computer-controlled optical surface shaping technology (CCOS) is the main technology for ultra-precision polishing of optical free-form surfaces. Its core lies in the deterministic processing of optical free-form surfaces by computer-controlled small-diameter polishing tools. The material removal amount of CCOS can be regarded as the two-dimensional convolution between the tool influence function and the dwell time distribution along the polishing path. CCOS can be adjusted from three aspects: tool influence function, polishing path and dwell time distribution to accurately control the material removal effect and achieve the purpose of deterministic polishing.

[0003] Traditional deterministic polishing path planning methods, such as raster and spiral paths, don't consider the impact of surface shape variations on the polishing path. Instead, they simply calculate the polishing tool's velocity for each approximate straight segment along the path, tailored to the specific surface shape. Regions with steep height changes on the surface to be polished can cause sudden changes in the polishing tool's velocity. This can affect target trajectory tracking accuracy if the machine tool's dynamic performance is insufficient, leading to low-frequency errors on the polished workpiece surface.

[0004] The invention patent "Contour Path Planning Method for Sub-Aperture Polishing" (patent number CN107520683B) proposes a polishing path planning method based on the material removal amount contour line, which achieves efficient convergence of medium-frequency error and low-frequency error at the same time, but the planned path is not continuous, which is not convenient for continuous polishing processing. The invention patent "Full-band Convergence Path Planning Method for CCOS Polishing Process" (patent number CN106863136B) proposes a method for iteratively expanding the initial path on the processing speed distribution matrix to obtain a rate-stable processing trajectory, thereby achieving simultaneous convergence of low and medium-frequency errors. However, this method generates paths based on control points distributed in a discrete regular grid, which may cause frequent corners in the path, and has high requirements on the dynamic performance of the machine tool. In addition, it takes a long time to generate paths in an iterative manner.

[0005] Therefore, it is necessary to propose a new technical solution to improve the above technical problems. Summary of the Invention

[0006] In view of the defects in the prior art, the purpose of the present invention is to provide a smooth polishing path planning method and system with regional adaptability.

[0007] According to the present invention, a smooth polishing path planning method with regional adaptability is provided, the method comprising the following steps:

[0008] Step S1: Read in the residence time density matrix obtained by solving the target removal surface shape and the removal function;

[0009] Step S2: extracting contour lines from the dwell time density matrix and establishing a contour tree, using the contour tree to identify peaks and valleys of the surface to be removed;

[0010] Step S3: Divide the entire face into multiple sub-regions containing only independent peak regions or valley regions, and obtain sub-region boundary information and adjacency relationships between sub-regions;

[0011] Step S4: Based on the adjacency relationship between the sub-regions, a Hamiltonian path traversing each sub-region is obtained using a backtracking method, and a variable-pitch double-helix path is planned in each sub-region. The starting and ending positions of the spiral are adjusted so that the endpoints of sequentially adjacent sub-paths are connected.

[0012] Step S5: Connect the sub-paths of each area and perform smoothing and equidistant sampling; extract the coordinates of the trajectory control points and the dwell points from the path after equidistant sampling, calculate the dwell time corresponding to each dwell point, calculate the tool movement speed of each approximate straight line segment, and output the coordinates of each trajectory control point and the feed speed.

[0013] Preferably, the dwell time density matrix mentioned in step S1 can be replaced by a dwell time matrix corresponding to a square grid dwell point matrix with a spacing of unit length.

[0014] Preferably, step S2 includes the following steps:

[0015] Step S2.1: Extract contour lines from the residence time density matrix and build a contour tree, outputting a dictionary storing all contour line information, including the link relationship between each contour line;

[0016] Step S2.2: Identify the peaks and valleys of the surface to be removed using the contour tree, and output the outer contour contour point sequences corresponding to the peaks and valleys.

[0017] Preferably, step S3 includes the following steps:

[0018] Step S3.1: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and output a binary image with marked region segmentation lines;

[0019] Step S3.2: Obtain sub-region boundary information and adjacency relationships between sub-regions, and output a dictionary containing sub-region boundary line point sequences and adjacency relationships.

[0020] Preferably, step S4 includes the following steps:

[0021] Step S4.1: Construct an undirected connected graph based on the adjacency relationships of the sub-regions. Use recursive backtracking on the connected graph to find a Hamiltonian path that traverses each sub-region, and output a Hamiltonian path that traverses each sub-region.

[0022] Step S4.2: Obtaining nested circular contour lines for generating spiral lines;

[0023] Step S4.3: Interpolate points with equal parameters between adjacent contour lines of the nested annular contour line cluster to generate a single spiral trajectory, and output a double spiral trajectory point sequence after adjusting the starting point position of each sub-region.

[0024] Preferably, step S5 includes the following steps:

[0025] Step S5.1: After connecting the paths of each sub-region, the overall path is smoothed by B-spline fitting; the smoothed path is sampled with equal arc lengths, and a trajectory coordinate point sequence is output;

[0026] Step S5.2: Select the midpoint of the two trajectory coordinate points as the dwell point, calculate the dwell time corresponding to the dwell point, and output the polishing trajectory point sequence and the corresponding feed speed sequence.

[0027] The present invention also provides a smooth polishing path planning system with regional adaptability, the system comprising the following modules:

[0028] Module M1: reads in the residence time density matrix obtained by solving the target removal surface shape and removal function;

[0029] Module M2: Extract contour lines from the dwell time density matrix and build a contour tree to identify the peaks and valleys of the surface to be removed.

[0030] Module M3: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and obtain sub-region boundary information and adjacency relationships between sub-regions;

[0031] Module M4: Based on the adjacency relationship between sub-regions, the backtracking method is used to find the Hamiltonian path that traverses each sub-region. A variable-pitch double-helix path is planned in each sub-region, and the starting and ending positions of the spiral are adjusted so that the endpoints of sequentially adjacent sub-paths are connected.

[0032] Module M5: Connect the sub-paths of each area and perform smoothing and equidistant sampling; extract the coordinates of the trajectory control points and the dwell points from the path after equidistant sampling, calculate the dwell time corresponding to each dwell point, calculate the tool movement speed of each approximate straight line segment, and output the coordinates of each trajectory control point and the feed speed.

[0033] Preferably, the dwell time density matrix mentioned in the module M1 can be replaced by a dwell time matrix corresponding to a square grid dwell point matrix with a spacing of unit length;

[0034] The module M2 includes the following modules:

[0035] Module M2.1: Extract contour lines from the residence time density matrix and build a contour tree, outputting a dictionary storing all contour line information, including the link relationship between each contour line;

[0036] Module M2.2: Use the contour tree to identify the peaks and valleys of the surface to be removed, and output the outer contour contour point list corresponding to the peaks and valleys.

[0037] Preferably, the module M3 includes the following modules:

[0038] Module M3.1: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and output a binary image with the region segmentation lines marked;

[0039] Module M3.2: Obtain sub-region boundary information and adjacency relationships between sub-regions, and output a dictionary containing sub-region boundary point lists and adjacency relationships;

[0040] The module M4 includes the following modules:

[0041] Module M4.1: Construct an undirected connected graph based on the adjacency relationships of the subregions. Use recursive backtracking on the connected graph to find a Hamiltonian path that traverses each subregion, and output a Hamiltonian path that traverses each subregion.

[0042] Module M4.2: Obtaining nested circular contours for generating spirals;

[0043] Module M4.3: Interpolate points with equal parameters between adjacent contour lines of a nested annular contour line cluster to generate a single spiral trajectory, and output a double spiral trajectory point sequence after adjusting the starting point position of each sub-region.

[0044] Preferably, the module M5 includes the following modules:

[0045] Module M5.1: After connecting the sub-region paths, the overall path is smoothed by B-spline fitting; the smoothed path is sampled with equal arc lengths, and the trajectory coordinate point list is output;

[0046] Module M5.2: Select the midpoint of two trajectory coordinate points as the dwell point, calculate the dwell time corresponding to the dwell point, and output the polishing trajectory point sequence and the corresponding feed speed sequence.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The present invention generates a regionally adaptive variable-pitch smooth polishing path based on the dwell time density matrix. For different divided areas of the surface features to be machined, the path spacing is adjusted according to the different removal amounts in each area, so that the motion law of the tool during the sub-aperture deterministic polishing process is similar, which is beneficial to improving the smoothness of the tool movement speed and reducing speed fluctuations. Furthermore, under the condition of limited dynamic performance of the machine tool, the tool movement trajectory tracking accuracy can still be guaranteed, which is beneficial to improving the machining accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0050] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0051] Figure 2 is a density diagram of target removal surface type and residence time in an embodiment;

[0052] Figure 3 This is a simplified flow chart for step 2;

[0053] Figure 4 is an embodiment residence time density contour plot;

[0054] Figure 5 is a schematic diagram of a contour tree of an embodiment;

[0055] Figure 6 This is a simplified flowchart of step 3;

[0056] Figure 7 2. It is a schematic diagram of watershed segmentation in an embodiment;

[0057] Figure 8 Schematic diagram of the Hamiltonian path of the embodiment;

[0058] Figure 9 This is a schematic diagram of generating a variable spacing path in a sub-region of an embodiment;

[0059] Figure 10 It is a regional adaptive variable spacing path map generated by the embodiment. DETAILED DESCRIPTION

[0060] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, without departing from the scope of the present invention, a number of variations and improvements may be made by those skilled in the art. These all fall within the scope of protection of the present invention.

[0061] Example 1:

[0062] According to the present invention, a smooth polishing path planning method with regional adaptability is provided, the method comprising the following steps:

[0063] Step S1: Read in the dwell time density matrix obtained by solving the target removal surface shape and the removal function; the dwell time density matrix can be replaced by the dwell time matrix corresponding to the square grid dwell point matrix with a spacing of unit length.

[0064] Step S2: extracting contour lines from the dwell time density matrix and establishing a contour tree, using the contour tree to identify peaks and valleys of the surface to be removed;

[0065] Step S2.1: Extract contour lines from the residence time density matrix and build a contour tree, outputting a dictionary storing all contour line information, including the link relationship between each contour line;

[0066] Step S2.2: Identify the peaks and valleys of the surface to be removed using the contour tree, and output the outer contour contour point sequences corresponding to the peaks and valleys.

[0067] Step S3: Divide the entire face into multiple sub-regions containing only independent peak regions or valley regions, and obtain sub-region boundary information and adjacency relationships between sub-regions;

[0068] The step S3 comprises the following steps:

[0069] Step S3.1: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and output a binary image with marked region segmentation lines;

[0070] Step S3.2: Obtain sub-region boundary information and adjacency relationships between sub-regions, and output a dictionary containing sub-region boundary line point sequences and adjacency relationships.

[0071] Step S4: Based on the adjacency relationship between the sub-regions, a Hamiltonian path traversing each sub-region is obtained using a backtracking method, and a variable-pitch double-helix path is planned in each sub-region. The starting and ending positions of the spiral are adjusted so that the endpoints of sequentially adjacent sub-paths are connected.

[0072] Step S4.1: Construct an undirected connected graph based on the adjacency relationships of the sub-regions. Use recursive backtracking on the connected graph to find a Hamiltonian path that traverses each sub-region, and output a Hamiltonian path that traverses each sub-region.

[0073] Step S4.2: Obtaining nested circular contour lines for generating spiral lines;

[0074] Step S4.3: Interpolate points with equal parameters between adjacent contour lines of the nested annular contour line cluster to generate a single spiral trajectory, and output a double spiral trajectory point sequence after adjusting the starting point position of each sub-region.

[0075] Step S5: Connect the sub-paths of each region and perform smoothing and equal-interval sampling; extract the coordinates of the trajectory control points and the dwell points from the equally-sampled paths, calculate the dwell time corresponding to each dwell point, calculate the tool motion speed of each approximate straight line segment, and output the coordinates of each trajectory control point and the feed rate;

[0076] Step S5.1: After connecting the paths of each sub-region, the overall path is smoothed by B-spline fitting; the smoothed path is sampled with equal arc lengths, and a trajectory coordinate point sequence is output;

[0077] Step S5.2: Select the midpoint of the two trajectory coordinate points as the dwell point, calculate the dwell time corresponding to the dwell point, and output the polishing trajectory point sequence and the corresponding feed speed sequence.

[0078] The present invention also provides a smooth polishing path planning system with regional adaptability. The smooth polishing path planning system with regional adaptability can be implemented by executing the process steps of the smooth polishing path planning method with regional adaptability. That is, those skilled in the art can understand the smooth polishing path planning method with regional adaptability as a preferred implementation of the smooth polishing path planning system with regional adaptability.

[0079] Example 2:

[0080] Example 2 is a preferred example of Example 1 and is used to illustrate the present invention in more detail.

[0081] The present invention also provides a smooth polishing path planning system with regional adaptability, the system comprising the following modules:

[0082] Module M1: reads in the dwell time density matrix obtained by solving the removal function based on the target removal surface shape; the dwell time density matrix can be replaced by the dwell time matrix corresponding to the square grid dwell point array with a spacing of unit length;

[0083] Module M2: Extract contour lines from the dwell time density matrix and build a contour tree to identify the peaks and valleys of the surface to be removed.

[0084] Module M2.1: Extract contour lines from the residence time density matrix and build a contour tree, outputting a dictionary storing all contour line information, including the link relationship between each contour line;

[0085] Module M2.2: Use the contour tree to identify the peaks and valleys of the surface to be removed, and output the outer contour contour point list corresponding to the peaks and valleys.

[0086] Module M3: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and obtain sub-region boundary information and adjacency relationships between sub-regions;

[0087] Module M3.1: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and output a binary image with the region segmentation lines marked;

[0088] Module M3.2: Obtain sub-region boundary information and adjacency relationships between sub-regions, and output a dictionary containing sub-region boundary point lists and adjacency relationships;

[0089] Module M4: Based on the adjacency relationship between sub-regions, the backtracking method is used to find the Hamiltonian path that traverses each sub-region. A variable-pitch double-helix path is planned in each sub-region, and the starting and ending positions of the spiral are adjusted so that the endpoints of sequentially adjacent sub-paths are connected.

[0090] Module M4.1: Construct an undirected connected graph based on the adjacency relationships of the subregions. Use recursive backtracking on the connected graph to find a Hamiltonian path that traverses each subregion, and output a Hamiltonian path that traverses each subregion.

[0091] Module M4.2: Obtaining nested circular contours for generating spirals;

[0092] Module M4.3: Interpolate points with equal parameters between adjacent contour lines of a nested annular contour line cluster to generate a single spiral trajectory, and output a double spiral trajectory point sequence after adjusting the starting point position of each sub-region.

[0093] Module M5: Connects the sub-paths of each region and performs smoothing and equidistant sampling. It extracts the coordinates of the trajectory control points and dwell points from the equally sampled paths, calculates the dwell time corresponding to each dwell point, calculates the tool motion speed of each approximate straight line segment, and outputs the coordinates of each trajectory control point and the feed rate.

[0094] Module M5.1: After connecting the sub-region paths, the overall path is smoothed by B-spline fitting; the smoothed path is sampled with equal arc lengths, and the trajectory coordinate point list is output;

[0095] Module M5.2: Select the midpoint of two trajectory coordinate points as the dwell point, calculate the dwell time corresponding to the dwell point, and output the polishing trajectory point sequence and the corresponding feed speed sequence.

[0096] Example 3:

[0097] Example 3 is a preferred example of Example 1 and is used to illustrate the present invention in more detail.

[0098] In view of the defects in the prior art, the purpose of the present invention is to provide a smooth polishing path planning method with regional adaptability.

[0099] The method for planning a smooth polishing path with regional adaptability provided by the present invention comprises the following steps:

[0100] Step S1, reading in a dwell time density matrix obtained by solving a target removal surface shape and a removal function;

[0101] Step S2, extracting contour lines from the dwell time density matrix and establishing a contour tree, using the contour tree to identify peaks and valleys of the surface to be removed;

[0102] Step S3: using a watershed segmentation algorithm to divide the entire face into multiple sub-regions containing only independent peaks or valleys, and obtaining sub-region boundary information and adjacency relationships between sub-regions;

[0103] Step S4: Based on the adjacency relationship between the sub-regions, a Hamiltonian path traversing each sub-region is obtained using a backtracking method. A variable-pitch double-helix path is planned in each sub-region, and the starting and ending positions of the spiral are adjusted so that the endpoints of sequentially adjacent sub-paths are connected.

[0104] In step S5, the sub-paths of each area are connected and smoothed and sampled at equal intervals. The coordinates of the trajectory control points and the dwell points are extracted from the path after equal interval sampling, and the dwell time corresponding to each dwell point is calculated. Then, the tool movement speed of each approximate straight line segment is calculated, and the coordinates of each trajectory control point and the feed speed are output.

[0105] Preferably, the dwell time density matrix mentioned in step S1 can be approximately replaced by a dwell time matrix corresponding to a square grid dwell point array with a spacing of unit length.

[0106] Preferably, step S2 comprises the following steps:

[0107] Step S201: extract contour lines from the residence time density matrix and establish a contour line tree:

[0108] Extract the point list for each contour line in the dwell time density matrix, label its ID value, elevation value, and whether it is closed, and store it in a dictionary. Calculate the area enclosed by each contour line and sort the contour lines in descending order by area. Store the array in an area-sorted array. Add the map boundary to the end of the array as the contour line with the largest enclosed area.

[0109] For non-closed contour lines that cross the corner points of the map, corresponding corner points need to be added to the point column to facilitate the subsequent judgment of the contour line inclusion relationship.

[0110] Determine the containment relationship of each contour line: Take the line with the smallest enclosed area as the line to be processed, and search the area-sorted array in descending order until a line that encloses the line to be processed is found. This line is the parent line (parent node) of the line to be processed, and record the IDs of the parent and child lines. Take the next line in the array in descending order and process it until all contour lines have a parent line (the parent line may be the map boundary). Lines without child nodes are peak or valley lines. The height relationship between them and the parent node is used to distinguish peaks or valleys (if the parent node is the map boundary, it is defined as the peak).

[0111] The parent and child node information of all contour lines are traversed, that is, the tree structure formed by the mutual links between the contour lines is obtained.

[0112] This step outputs a dictionary that stores all contour line information, including the link relationship between each contour line.

[0113] Step S202: Identify the peaks and valleys of the surface to be removed using the contour tree:

[0114] Extract the outer contours of the peak area and valley area based on the contour tree, which will be used for subsequent regional division of the overall model. Take the peak top line and valley bottom line as the starting point of the search to determine whether its parent node has only a single child node:

[0115] If so, change the processing point to the parent node, and continue searching upward to see if the parent node of the processing point has only a single child node, until the result is no;

[0116] If not, determine whether the enclosed areas of the parent node's multiple child nodes differ significantly. If the areas of two or more child nodes differ by no more than 20% of the area of ​​the largest child node, the contour line corresponding to the current processing point is considered to be the outer contour of an independent peak or valley; otherwise, continue searching upward.

[0117] In this step, the outer contour point sequences corresponding to the peak area and valley area are output.

[0118] Preferably, step S3 comprises the following steps:

[0119] Step S301: Use the watershed segmentation algorithm to divide the entire face into multiple sub-regions containing only independent peaks or valleys.

[0120] The area enclosed by the outermost contours of the peaks and valleys on the surface output in step S202 is used as internal identifiers to generate a binary image. A watershed algorithm is applied to the binary image with internal identifiers to obtain a binary image marked with region segmentation lines. These region segmentation lines divide the entire image into multiple subregions containing only independent peaks or valleys.

[0121] This step outputs a binary image with the segmentation lines of the marked regions.

[0122] Step S302: Obtain sub-region boundary information and adjacency relationships between sub-regions:

[0123] Mark each sub-region ID and extract the boundary line point sequence of each sub-region; determine whether two sub-regions are adjacent by determining whether their boundary lines overlap.

[0124] This step outputs a dictionary containing the sub-region boundary line point list and adjacency relationships.

[0125] Preferably, step S4 comprises the following steps:

[0126] Step S401: construct an undirected connected graph based on the adjacency relationship of the sub-regions, and use recursive backtracking to find a Hamiltonian path that traverses each sub-region on the connected graph. There is usually more than one Hamiltonian path that meets the requirements, and any one of them can be used to proceed to the subsequent steps.

[0127] This step outputs a Hamiltonian path that traverses each sub-region as the sequence of subsequent path connections between sub-regions. Step S402: Obtain nested ring contour lines for generating spiral lines:

[0128] Discretely take grid points P in the area contained in the sub-area ij , construct a weighted undirected graph, and calculate the distance from each grid point to the boundary line point column B k The shortest distance of each grid point P is obtained, and the shortest boundary geodesic distance matrix SBG is obtained; at the same time, each grid point P is recorded ij The corresponding shortest distance boundary point Calculate the residence time density corresponding to each grid point The residence time density corresponding to the corresponding shortest distance boundary point The average of the average residence time density matrix The elements are:

[0129]

[0130] Construct a new approximate boundary residence time line integral matrix M, where the elements are:

[0131]

[0132] Draw contour lines on the matrix M and extract only the contour line Line1 closest to the boundary. The value k of the contour line can be determined according to the desired feed speed v wanted calculate.

[0133]

[0134] Use Line1 as the new boundary line and repeat the above process to get another contour line inward, thus obtaining a series of nested circular contour lines {Line k}.

[0135] In step S403, points are interpolated between adjacent contour lines of the nested annular contour cluster with equal parameters to generate a single helical trajectory. Points are then interpolated between adjacent single helices at equal intervals to generate a double helical trajectory with both endpoints on the subregion boundary. The starting point of the double helical trajectory is controlled by controlling the starting point of the interpolated points between the contour lines. The endpoint of the double helical trajectory can be changed by deleting or extending the helix along the subregion boundary after the interpolation is completed. Following the order of the Hamiltonian path, the starting point of the double helix in the subsequent subregion is adjusted to coincide with the endpoint of the spiral in the previous subregion.

[0136] This step outputs the double-helix trajectory point sequence of each sub-region after adjusting the starting point position.

[0137] Preferably, step S5 comprises the following steps:

[0138] In step S501, after connecting the sub-region paths, the overall path is smoothed by B-spline fitting, and the smoothed path is sampled with equal arc length.

[0139] This step outputs a column of trajectory coordinate points.

[0140] Step S502: Select the midpoint of the two trajectory coordinate points as the dwell point, and calculate the dwell time corresponding to the dwell point: obtain the Voronoi polygon corresponding to each dwell point and calculate its area S voronoi ; According to the coordinates of the residence point, interpolate in the residence time density matrix to obtain the residence time density t corresponding to the point dwellpoint The area of ​​the polygon multiplied by the dwell time density corresponding to the dwell point is considered as the dwell time T corresponding to the dwell point dwellpoint :

[0141] T dwellpoint ≈S voronoi ·t dwellpoint #(4)

[0142] The feed rate v in the straight line segment can be obtained by dividing the distance s between adjacent trajectory coordinate points by the dwell time of the corresponding dwell point:

[0143]

[0144] This step outputs the polishing trajectory point sequence and the corresponding feed speed sequence.

[0145] This embodiment provides a smooth polishing path planning method with regional adaptability, such as Figure 1 shown.

[0146] This embodiment implements smooth polishing path planning with regional adaptability through MATLAB programming, which specifically includes the following steps:

[0147] Step 1, read in data: read in the dwell time density matrix corresponding to the target removal surface, such as Figure 2 As shown;

[0148] The residence time density matrix is ​​obtained by deconvolution of the target removal surface and a removal function. The removal function is Gaussian, with a peak removal rate of 15 nm / s and a half-height width of 6 mm.

[0149] Step 2: Extract contour lines from the residence time density matrix, establish a contour tree, and obtain the outer contour contour point series of independent peak areas and valley areas through the contour tree.

[0150] The process flow chart of this step is as follows Figure 3 As shown in the figure, the criterion for judging whether the areas enclosed by multiple subnodes are significantly different is whether there are two or more subnodes whose areas differ by no more than 20% of the area of ​​the largest subnode. When extracting contour lines, the residence time density is divided into 20 layers, such as Figure 4 As shown. The contour tree established is as follows Figure 5 As shown, the map boundary is not considered when establishing the contour tree. The sequence numbers of the contour lines of the outer contours of the independent peaks and valleys extracted by the method are 20, 21, 23, and 26.

[0151] Step 3: Input the contour points of the independent peaks and valleys, use the enclosed areas as internal identifiers, and generate a binary image. Apply the watershed segmentation algorithm to this binary image to obtain a binary image with region segmentation lines. Label each subregion's ID and extract the boundary point list for each subregion. Determine whether two subregions are adjacent by determining whether their boundary lines overlap.

[0152] The process flow chart of this step is as follows Figure 6 The result of generating a binary image and performing watershed segmentation is shown in Figure 7 shown.

[0153] Step 4: construct an undirected connected graph based on the adjacency relationship of the sub-regions, and use the recursive backtracking method on the connected graph to find the Hamiltonian path that traverses each sub-region. Figure 8Takes nested circular contours for generating a spiral and interpolates points between them to generate a double helix that starts and ends on the boundary line.

[0154] Taking the first sub-region as an example, the grid points P are discretely taken in the area contained in the sub-region. ij , construct a weighted undirected graph, and calculate the distance from each grid point to the boundary line point column B k The shortest distance of , we get the shortest boundary geodesic distance matrix SBG, as Figure 9 (a); while recording each grid point P ij The corresponding shortest distance boundary point Calculate the residence time density corresponding to each grid point The residence time density corresponding to the corresponding shortest distance boundary point The average of the average residence time density matrix like Figure 9 (b) is shown, where the elements are:

[0155]

[0156] Construct a new approximate boundary residence time line integral matrix M, such as Figure 9 (c) shown, where the elements are:

[0157]

[0158] Draw contour lines on the matrix M and extract only the contour line Line1 closest to the boundary, such as Figure 9 As shown in (d), the value of the contour line k can be adjusted according to the desired feed speed v wanted calculate.

[0159]

[0160] In this embodiment, v wanted =1mm / s.

[0161] Use Line1 as the new boundary line and repeat the above process to get another contour line inward, thus obtaining a series of nested circular contour lines {Line k},like Figure 9 (e) shown.

[0162] By inserting points of equal parameters between adjacent contour lines of the nested annular contour line cluster, a single spiral trajectory is generated; then, by inserting points of equal spacing between adjacent single spiral lines, a double spiral trajectory is obtained with both endpoints on the sub-region boundary, such as Figure 9 (f) shown.

[0163] Step 5: Connect the paths of each sub-region in the order of the Hamiltonian path, use B-spline fitting to perform smoothing, and then perform equal-space sampling, as shown in the following example: Figure 10 In this embodiment, the sampling interval is 0.5 mm.

[0164] Select the midpoint of the two trajectory coordinate points as the dwell point and calculate the dwell time corresponding to the dwell point: obtain the Voronoi polygon corresponding to each dwell point and calculate its area S voronoi ; According to the coordinates of the residence point, interpolate in the residence time density matrix to obtain the residence time density t corresponding to the point dwellpoint The area of ​​the polygon multiplied by the dwell time density corresponding to the dwell point is considered as the dwell time T corresponding to the dwell point dwellpoint :

[0165] T dwellpoint ≈S voronoi ·t dwellpoint #(9)

[0166] The feed rate v in the straight line segment can be obtained by dividing the distance s between adjacent trajectory coordinate points by the dwell time of the corresponding dwell point:

[0167]

[0168] Finally, the polishing trajectory point sequence and the corresponding feed speed sequence are output.

[0169] A regionally adaptive smooth polishing path was compared with traditional grating and spiral polishing paths (0.5 mm pitch) to calculate the surface removal error under the consideration of the machine tool's dynamic performance. When considering the machine tool's dynamic performance, the tool's actual output path deviates from the input path. By calculating the actual output path and calculating the dwell time at a dwell point on it, the simulated surface removal error under the consideration of the machine tool's dynamic performance was obtained by convolving it with the removal function. The results show that the regionally adaptive variable-pitch path has the smallest surface removal error, only 9.6 nm. The errors of the grating path and spiral path are 23 nm and 72.1 nm, respectively, which are 2.38 and 7.46 times the errors of the variable-pitch path. Simulation results confirm that the regionally adaptive variable-pitch path based on the dwell time density matrix is ​​beneficial for improving the smoothness of the tool motion velocity and reducing velocity fluctuations. Furthermore, even when the machine tool's dynamic performance is limited, the tool's actual motion trajectory can still be guaranteed to not deviate from the input trajectory, which is beneficial for improving the machining accuracy of sub-aperture deterministic polishing.

[0170] The present invention provides a smoothing polishing path planning method with regional adaptability: a contour tree is established based on dwell time density information, and independent peaks and valleys of the surface to be machined are identified; each independent peak and valley is segmented using a watershed algorithm; an iterative backtracking method is used to obtain a Hamiltonian path traversing each sub-region, and variable-pitch machining paths are planned within each region; finally, the sub-region paths are connected, smoothed, and evenly spaced samples are taken, dwell times are calculated, approximate straight line segment velocities are converted, and a trajectory coordinate point sequence and feed rate sequence are output. This method is beneficial for improving the smoothness of tool motion speed and reducing speed fluctuations. Furthermore, even when the dynamic performance of the machine tool is limited, the tool motion trajectory tracking accuracy can still be guaranteed, and it is beneficial for improving the machining accuracy of sub-aperture deterministic polishing.

[0171] Those skilled in the art may understand this embodiment as a more specific description of Embodiment 1 and Embodiment 2.

[0172] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0173] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A smooth polishing path planning method with regional adaptability, characterized in that: The method comprises the following steps: Step S1: Read in the residence time density matrix obtained by solving the target removal surface shape and the removal function; Step S2: extracting contour lines from the dwell time density matrix and establishing a contour tree, using the contour tree to identify peaks and valleys of the surface to be removed; Step S3: Divide the entire face into multiple sub-regions containing only independent peak regions or valley regions, and obtain sub-region boundary information and adjacency relationships between sub-regions; Step S4: Based on the adjacency relationship between the sub-regions, a Hamiltonian path traversing each sub-region is obtained using a backtracking method, and a variable-pitch double-helix path is planned in each sub-region. The starting and ending positions of the spiral are adjusted so that the endpoints of sequentially adjacent sub-paths are connected. Step S5: Connect the sub-paths of each area and perform smoothing and equidistant sampling; extract the coordinates of the trajectory control points and the dwell points from the path after equidistant sampling, calculate the dwell time corresponding to each dwell point, calculate the tool movement speed of each approximate straight line segment, and output the coordinates of each trajectory control point and the feed speed.

2. The method for planning a smooth polishing path with regional adaptability according to claim 1, characterized in that: The dwell time density matrix mentioned in step S1 can be replaced by a dwell time matrix corresponding to a square grid dwell point matrix with a spacing of unit length.

3. The method for planning a smooth polishing path with regional adaptability according to claim 1, wherein: The step S2 comprises the following steps: Step S2.1: Extract contour lines from the residence time density matrix and build a contour tree, outputting a dictionary storing all contour line information, including the link relationship between each contour line; Step S2.2: Identify the peaks and valleys of the surface to be removed using the contour tree, and output the outer contour contour point sequences corresponding to the peaks and valleys.

4. The method for planning a smooth polishing path with regional adaptability according to claim 1, characterized in that: The step S3 comprises the following steps: Step S3.1: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and output a binary image with marked region segmentation lines; Step S3.2: Obtain sub-region boundary information and adjacency relationships between sub-regions, and output a dictionary containing sub-region boundary line point sequences and adjacency relationships.

5. The method for planning a smooth polishing path with regional adaptability according to claim 1, characterized in that: The step S4 comprises the following steps: Step S4.1: Construct an undirected connected graph based on the adjacency relationships of the sub-regions. Use recursive backtracking on the connected graph to find a Hamiltonian path that traverses each sub-region, and output a Hamiltonian path that traverses each sub-region. Step S4.2: Obtaining nested circular contour lines for generating spiral lines; Step S4.3: Interpolate points with equal parameters between adjacent contour lines of the nested annular contour line cluster to generate a single spiral trajectory, and output a double spiral trajectory point sequence after adjusting the starting point position of each sub-region.

6. The method for planning a smooth polishing path with regional adaptability according to claim 1, characterized in that: The step S5 comprises the following steps: Step S5.1: After connecting the paths of each sub-region, the overall path is smoothed by B-spline fitting; the smoothed path is sampled with equal arc lengths, and a trajectory coordinate point sequence is output; Step S5.2: Select the midpoint of the two trajectory coordinate points as the dwell point, calculate the dwell time corresponding to the dwell point, and output the polishing trajectory point sequence and the corresponding feed speed sequence.

7. A smooth polishing path planning system with regional adaptability, characterized in that: The system includes the following modules: Module M1: reads in the residence time density matrix obtained by solving the target removal surface shape and removal function; Module M2: Extract contour lines from the dwell time density matrix and build a contour tree to identify the peaks and valleys of the surface to be removed. Module M3: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and obtain sub-region boundary information and adjacency relationships between sub-regions; Module M4: Based on the adjacency relationship between sub-regions, the backtracking method is used to find the Hamiltonian path that traverses each sub-region. A variable-pitch double-helix path is planned in each sub-region, and the starting and ending positions of the spiral are adjusted so that the endpoints of sequentially adjacent sub-paths are connected. Module M5: Connect the sub-paths of each area and perform smoothing and equidistant sampling; extract the coordinates of the trajectory control points and the dwell points from the path after equidistant sampling, calculate the dwell time corresponding to each dwell point, calculate the tool movement speed of each approximate straight line segment, and output the coordinates of each trajectory control point and the feed speed.

8. The smooth polishing path planning system with regional adaptability according to claim 7, characterized in that: The dwell time density matrix mentioned in the module M1 can be replaced by a dwell time matrix corresponding to a square grid dwell point matrix with a spacing of unit length; The module M2 includes the following modules: Module M2.1: Extract contour lines from the residence time density matrix and build a contour tree, outputting a dictionary storing all contour line information, including the link relationship between each contour line; Module M2.2: Use the contour tree to identify the peaks and valleys of the surface to be removed, and output the outer contour contour point list corresponding to the peaks and valleys.

9. The smooth polishing path planning system with regional adaptability according to claim 7, characterized in that: The module M3 includes the following modules: Module M3.1: Divide the entire face into multiple sub-regions containing only independent peaks or valleys, and output a binary image with the region segmentation lines marked; Module M3.2: Obtain sub-region boundary information and adjacency relationships between sub-regions, and output a dictionary containing sub-region boundary point lists and adjacency relationships; The module M4 includes the following modules: Module M4.1: Construct an undirected connected graph based on the adjacency relationships of the subregions. Use recursive backtracking on the connected graph to find a Hamiltonian path that traverses each subregion, and output a Hamiltonian path that traverses each subregion. Module M4.2: Obtaining nested circular contours for generating spirals; Module M4.3: Interpolate points with equal parameters between adjacent contour lines of a nested annular contour line cluster to generate a single spiral trajectory, and output a double spiral trajectory point sequence after adjusting the starting point position of each sub-region.

10. The smooth polishing path planning system with regional adaptability according to claim 7, characterized in that: The module M5 includes the following modules: Module M5.1: After connecting the sub-region paths, the overall path is smoothed by B-spline fitting; the smoothed path is sampled with equal arc lengths, and the trajectory coordinate point list is output; Module M5.2: Select the midpoint of two trajectory coordinate points as the dwell point, calculate the dwell time corresponding to the dwell point, and output the polishing trajectory point sequence and the corresponding feed speed sequence.

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