CN114488943A - Random multi-region efficient polishing path planning method oriented to cooperation condition - Google Patents

Random multi-region efficient polishing path planning method oriented to cooperation condition Download PDF

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CN114488943A
CN114488943A CN202210016548.XA CN202210016548A CN114488943A CN 114488943 A CN114488943 A CN 114488943A CN 202210016548 A CN202210016548 A CN 202210016548A CN 114488943 A CN114488943 A CN 114488943A
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CN114488943B (en
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张小俭
吴毅
陈巍
严思杰
丁汉
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Huazhong University of Science and Technology
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00Programme-control systems
    • G05B19/02Programme-control systems electric
    • G05B19/18Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
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    • G05B2219/34093Real time toolpath generation, no need for large memory to store values
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Abstract

The invention discloses a random multi-region efficient polishing path planning method under a matching working condition, which comprises the steps of S100, measuring and obtaining point cloud data of a soft mold and a hard mold matching surface, carrying out principal component analysis on the point cloud data to align, fitting the point cloud data of a reinforced wall plate to the surface and taking a complementary set, matching the point cloud data of a sacrificial layer, and taking a difference value in the height direction to obtain a height map to be processed of the surface of the sacrificial layer; s200, extracting the maximum height and the minimum height of the height map to be processed, and planning a processing sequence and a single processing depth according to the maximum height difference, the removal depth model of the polishing head and the matching precision requirement of the surface of the workpiece; s300, optimizing the processing sequence and the polishing path of each region simultaneously through an immune genetic algorithm; s400, dispersing the grinding path and the transition path according to the requirement of the maximum step length to obtain a series of tool contacts, and calculating a tool axis vector and tool position point data according to the feeding direction and the surface normal vector to obtain a tool position track planning path.

Description

Random multi-region efficient polishing path planning method oriented to cooperation condition
Technical Field
The invention belongs to the technical field of advanced manufacturing, and particularly relates to a random multi-region efficient polishing path planning method under a coordination working condition.
Background
In the traditional integral forming and manufacturing process of rib/skin of large-scale composite material reinforced wall board, in order to meet the precision of profile matching, the technology of matching hard films and soft films (mostly made of rubber materials) with moulds is often adopted, wherein the precision processing of the soft films is a difficult point. The currently commonly used methods are manual measurement and polishing operations. Firstly, daubing red lead powder on the surface of a hard die, attaching the red lead powder by using a soft die, marking a region to be processed, carrying out grinding and polishing processing, and repeating the detection and processing processes until the two surfaces are accurately attached. Because of the need of many times of grinding and polishing and repeated measurement, the quality and the efficiency of the manual operation are difficult to guarantee, the manual operation belongs to the manufacturing process with low efficiency, and the processing precision and the processing efficiency are seriously influenced. In order to solve the problems, high-precision non-contact scanning is adopted to replace Hongdan powder to detect a region to be processed, a robot grinding and polishing technology is adopted to replace manual grinding and polishing, and automation of detection and processing is achieved. The area to be processed of the soft mold has the characteristics of random quantity, random distribution, random shape and the like because the area to be processed of the soft mold is obtained by matching with the hard film. In order to realize the rapid measurement-grinding and polishing integrated automatic operation of the robot on the basis of accurately measuring the to-be-processed area, an efficient grinding and polishing path planning method needs to be provided for a plurality of random to-be-processed areas of the soft mold under the matching working condition.
For planning a grinding path of a random-shaped area, patent document CN112947309A discloses a robot grinding path planning method based on an equal-residual-height end face, which is used for constructing a bounding box of an area to be processed, acquiring an initial grinding path of the bounding box, and performing discretization according to a given step length. And determining the processing line spacing according to the limitation of the radius of the polishing head, the surface curvature of the workpiece and the residual height, sequentially extrapolating discrete knife contacts to obtain interpolation points of adjacent polishing paths, and deleting the interpolation points outside the boundary of the surrounding box, thereby obtaining the interpolation point coordinates of the planned polishing path. In addition, for planning of polishing paths in randomly distributed areas, patent document CN107932505A discloses an optimal polishing task path planning method based on an articulated arm robot, which is based on a simulated annealing algorithm and sequentially includes steps of data input, path generation, path point calculation, path update, iterative control, temperature control processing, and the like to obtain an optimal polishing task path. Patent document CN111203788A discloses a wall surface polishing path planning method, which scans a wall surface, obtains protruding points of the wall surface to be polished through obtained point cloud data, and calculates a processing order of the protruding points through a variation of a greedy algorithm.
However, the method in CN112947309A only addresses a single region to be processed, and does not consider the problem of transition of processing order and connection in multiple regions when there are multiple regions, and thus cannot be applied to multiple regions. Both the task path planning methods disclosed in patent documents CN107932505A and CN111203788A have the problem of abstracting the region to be processed into one point rather than a real region, and the methods proposed in the documents are difficult to apply when the region to be processed is large and the planning of the processing path in the region has a large influence on the idle stroke length.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a random multi-region efficient grinding path planning method under a coordination working condition, a height map to be processed is quickly converted into a map of an area to be processed corresponding to each processing depth through simple image processing, fine hole holes and islands of the area to be processed caused by measurement data fluctuation are removed, a processing sequence and a grinding path of each area are simultaneously optimized through an immune genetic algorithm, the grinding path and a transition path are dispersed according to a maximum step requirement to obtain a series of tool contacts, and a tool shaft vector and tool position data are calculated according to a feeding direction and a surface normal vector, so that a tool position path planning path is obtained.
In order to achieve the purpose, the invention provides a random multi-region efficient grinding path planning method facing to a matching working condition, which comprises the following steps:
s100, measuring to obtain point cloud data of the matching surfaces of the soft mold and the hard mold, carrying out principal component analysis on the point cloud data to correctly place, fitting the point cloud data of the reinforced wall plate to the surface and taking a complementary set to match with the point cloud data of the sacrificial layer, and taking a difference value in the height direction to obtain a height map to be processed of the surface of the sacrificial layer;
s200, extracting the maximum height and the minimum height of the height map to be processed, and planning a processing sequence and a single processing depth according to the maximum height difference, the removal depth model of the polishing head and the matching precision requirement of the surface of the workpiece;
s300, planning a polishing path of each region to be processed, and simultaneously optimizing a processing sequence and the polishing path of each region through an immune genetic algorithm;
s400, dispersing the grinding path and the transition path according to the requirement of the maximum step length to obtain a series of cutter contacts, and calculating cutter axis vectors and cutter position point data according to the feeding direction and the surface normal vector to obtain a cutter position track planning path.
Further, in step S100, for n-dimensional random variables
X=(X1,X2,…,XN)TThe covariance matrix is:
Figure BDA0003461181680000031
wherein c isij=COV(Xi,Xj) I, j ═ 1,2, …, n denotes the component X of XiAnd XjThe covariance of (a).
Further, in step S100, the rotation matrix R of the point cloud normal vector of the soft mold and the hard mold matching surface rotated to be perpendicular to the yoz plane is:
Figure BDA0003461181680000032
wherein n ═ n (n)x,ny,nz) The normal vector of the plane where the point cloud is located is equal to the unit vector of the eigenvector corresponding to the minimum singular value of the covariance matrix.
Further, step S200 further includes:
s201: carrying out gray level binarization processing on the height map to be processed by taking the target height at each processing time as a threshold value, wherein the gray level binarization processing process comprises the following steps:
Figure BDA0003461181680000041
the Binary (i, j) represents the Gray level of the corresponding position of the image after the Gray level binarization, the Gray (i, j) represents the Gray level of the corresponding position of the original Gray level image, and the Threshold represents the Threshold used in the Gray level binarization process.
Further, step S200 further includes:
s202: merging islands close to the edge of a region to be processed through expansion corrosion, eliminating fine jitter of the boundary, and then carrying out corrosion expansion to eliminate independent fine noise points;
the expansion corrosion treatment process comprises the following steps:
Figure BDA0003461181680000042
where a represents a non-zero set of pixels in the binary image and B represents a structural element, i.e. a structural element.
Further, step S200 further includes:
s203: and extracting the boundary of all the gray binary images to obtain boundary curves of all the areas to be processed, placing the boundary curves in the same coordinate system, and judging the inclusion relationship of each curve.
Further, the determining the inclusion relationship of each curve includes:
s204: let the point taken be PcFor the set of boundary points { PePoint P ini、Pi+1Calculating the included angle, and recording PcPiAnd PcPi+1The included angle between is thetaiPositive counterclockwise and negative clockwise, the cumulative angle increment α is:
Figure BDA0003461181680000043
s205: when α approaches ± 360 °, then the point is inside the curve, and when it approaches 0 °, then the point is outside the curve.
Further, step S300 includes:
s301: calculating all eigenvalues and eigenvectors of each covariance matrix of the point set of the area to be processed, and obtaining the direction of the point set with the maximum spread by taking the eigenvector corresponding to the maximum eigenvalue, wherein the direction is approximate to the processing direction which enables the number of row cutting paths to be the minimum;
s302: calculating the maximum distance of the area to be processed, which is vertical to the processing direction, determining the cutting speed and the applied pressure adopted by the grinding and polishing operation according to the single processing depth so as to obtain a ground removal profile, and determining the line spacing by combining the distance of the area to be processed, which is vertical to the processing direction;
s303: and generating a series of parallel lines according to the line spacing, and solving intersection points with the boundary curve to be used as path points of the polishing path.
Further, step S300 includes:
s304: through a nested genetic algorithm, the outer layer optimizes the processing sequence of the regions to be processed, and the inner layer optimizes the path trend of each region to achieve the optimization goal of enabling the total length of the paths to be processed to be shortest.
Further, step S400 includes:
s401: let point P be the knife contact point and coordinate P (P)x,Py,Pz) The point of the path O is the center point of the tool, and the coordinate is O (O)x,Oy,Oz) Let the unit vector of the motion direction of the processing track where the processing point is located be r ═ r (r)i,rj,rk) The unit normal vector of the surface is n ═ (n)i,nj,nk) The diameter of the polishing disc is R, the axis inclination angle of the polishing disc is theta, and the width of a contact area obtained through simulation after polishing pressure is set is L, so that the calculation formula of the center point of the polishing disc is as follows:
O=P+(R-L)(r cosθ+n sinθ) (7)
s402: the corresponding arbor vectors are:
c=n cosθ-r sinθ (8)
s403: and obtaining a planned cutter position file after the steps are completed, obtaining a rapid program for polishing machining through post-processing, and completing the planning of the random multi-region efficient polishing path.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. the method of the invention rapidly converts the height map to be processed into the map of the area to be processed corresponding to each processing depth through simple image processing, removes the fine hole and island of the area to be processed caused by the fluctuation of the measured data, optimizes the processing sequence and the grinding path of each area simultaneously through the immune genetic algorithm, disperses the grinding path and the transition path according to the maximum step length requirement to obtain a series of tool contacts, and calculates the tool shaft vector and the tool position data according to the feeding direction and the surface normal vector, thereby obtaining the tool position path planning path.
2. The method of the invention rapidly calculates the direction with the least number of the line cutting paths of each area by a principal component analysis method, and realizes the rapid line cutting path planning of the random area by the intersection of parallel lines and the area to be processed.
3. According to the method, the inclusion relation of adjacent height layer curves projected on the same plane is judged through accumulated angle increment, a relation tree between areas to be processed is established and added to path planning as constraint, and the sequence of layered processing is guaranteed in the path planning of random multiple areas.
4. The method optimizes the random multi-region processing sequence and optimizes the path trend in the region through the nested immune genetic algorithm, and is more suitable for the condition that the area of the random to-be-processed region is not negligible relative to the total area of the to-be-processed workpiece compared with other methods for abstracting the to-be-processed region into mass points.
Drawings
Fig. 1 is a working flow of a random multi-zone grinding path planning method according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a height of a hard film of a sacrificial layer to be processed according to an embodiment of the present invention;
FIG. 3 is a diagram of a height to be processed of a rubber pad surface of a sacrificial layer according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating the height of the sacrificial layer to be processed according to one embodiment of the present invention;
FIG. 5 is a depth map with depth removed according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of marking the region to be processed with 1/3 as the threshold of the maximum removal depth in the embodiment of the present invention;
FIG. 7 is a schematic view of a region to be processed in the embodiment of the present invention;
FIG. 8 is a schematic illustration of an expansion operation performed in an embodiment of the present invention;
FIG. 9 is a schematic illustration of an etching operation performed in an embodiment of the present invention;
FIG. 10 is a diagram illustrating selection of different starting points for a row-cutting path according to an embodiment of the present invention;
FIG. 11 is a flow chart of a nested immunogenetic algorithm according to an embodiment of the present invention;
FIG. 12 is a diagram illustrating a random multi-zone row-cut path planning according to an embodiment of the present invention;
FIG. 13 is a schematic diagram of a beveled end face grinding operation in accordance with an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, an embodiment of the present invention provides a method for planning a random multi-region efficient polishing path under a coordination condition, taking an IRB6700 robot as an example, and the method mainly includes the following steps:
(1) measuring is needed before a path is planned, point cloud data of the matching surfaces of the soft mold and the hard mold are obtained through high-precision non-contact scanning, and a covariance matrix is obtained through point cloud data calculation:
for n-dimensional random variable X ═ X (X)1,X2,…,XN)TThe covariance matrix is:
Figure BDA0003461181680000071
wherein c isij=COV(Xi,Xj) I, j ═ 1,2, …, n denotes the component X of XiAnd XjThe covariance of (a).
And for the covariance matrix, carrying out SVD (singular value decomposition) transformation to obtain a minimum singular value and a corresponding eigenvector, wherein the eigenvector is a normal vector of a plane where the point cloud is located. Let the normal vector be n ═ n (n)x,ny,nz) Then the rotation matrix R that rotates the surface point cloud normal vector to be perpendicular to the yoz plane is:
Figure BDA0003461181680000072
fitting the point cloud data of the ribbed wall plate to the surface and taking a complementary set, matching the point cloud data with the point cloud data of the sacrificial layer, and taking a difference value in the height direction to obtain a height map to be processed of the surface of the sacrificial layer, as shown in fig. 2-4.
(2) And extracting the maximum height and the minimum height from the height map, and planning the machining times and the single machining depth according to the maximum height difference, the removal depth model of the grinding head and the matching precision requirement of the surface of the workpiece. And (3) carrying out gray level binarization processing on the height map by taking the target height during each processing as a threshold value, setting the points with the height higher than the threshold value as black to obtain a group of black-white binary images corresponding to different processing heights, and marking the area to be processed by using the black. The gray level binarization processing process comprises the following steps:
Figure BDA0003461181680000081
wherein Binary (i, j) represents the Gray level of the corresponding position of the image after the Gray level binarization, Gray (i, j) represents the Gray level of the corresponding position of the original Gray level image, and Threshold represents the Threshold used in the Gray level binarization process, as shown in fig. 5 and 6.
(3) Due to fluctuation of data obtained by non-contact measurement, many fine islands or holes can exist after the data are converted into a gray binary image, islands close to the edge of a region to be processed can be combined through expansion corrosion, fine jitter of the boundary is eliminated, and then corrosion expansion is carried out to eliminate independent fine noise points. The structural elements of the expansion and corrosion operations adopt the shape and size of the contact area of the polishing head. The calculation processes of expansion and corrosion are respectively as follows:
Figure BDA0003461181680000082
where a represents a non-zero set of pixels in a binary image and B represents a structural element, i.e. a structuring element. The set resulting from expanding A with B is the set of the origin positions of B after translating B so that B intersects A, and the set resulting from eroding A with B is the set of the origin positions of B when B is completely included in A after translating B. Taking the operation process of fig. 6 of step (2) as an example, the original fine holes are removed after the expansion and etching operations, and the boundary is slightly smooth, as shown in fig. 7-9.
And performing boundary extraction on all the gray binary images to obtain boundary curves of all the regions to be processed. And placing the boundary curves in the same coordinate system, and calculating the inclusion relation of the curves. In the subsequent hierarchical processing path planning process, if two boundary curves have an inclusion relationship, the processing order relationship of the two boundary curves corresponding to the areas to be processed needs to be determined, and the areas with higher heights need to be processed before the areas with lower heights. When the inclusion relation is judged, one point in the curve can be selected, and the accumulated angle increment is obtained by the boundary curve of the previous layer area. Let the point taken be PcFor the set of boundary points { PePoint P ini、Pi+1Calculating the included angle, and recording PcPiAnd PcPi+1The included angle between is thetaiPositive counterclockwise and negative clockwise, the cumulative angle increment α is:
Figure BDA0003461181680000091
points are shown inside the curve when alpha is near 360 deg. and points are shown outside the curve when alpha is near 0 deg.. The distance between the selected point and the curve is also judged while the accumulated angle increment is calculated, and the two curves can be determined to have an inclusion relation when the distance is smaller than the radius of the expansion structural element.
(4) And (4) performing line cutting path planning on each region to be processed, calculating all characteristic values and characteristic vectors of the covariance matrix, and obtaining the direction of the point set with the maximum dispersion by taking the characteristic vector corresponding to the maximum characteristic value. The direction in which the point set dispersion is greatest can be viewed approximately as the machine direction in which the number of row-cut paths is minimized.
And calculating the maximum distance of the area to be processed, which is vertical to the processing direction. And determining the cutting speed and the applied pressure adopted by the grinding and polishing operation according to the single processing depth so as to obtain a ground removal profile, and determining the line spacing by combining the distance of the area to be processed, which is vertical to the processing direction. And then generating a series of parallel lines according to the line spacing, and solving an intersection point with the boundary curve to be used as a path point of the polishing path. And recording two end points of the two outermost paths to obtain the starting points of the processing paths in the four selectable areas. When the area of the region to be processed is not negligible in relation to the total surface area, the beginning and end points of the processing path in the region to be processed have a large influence on the total path length. In the subsequent path optimization process, the selection of the starting point and the ending point of the processing path of each region to be processed needs to be taken into consideration, as shown in fig. 10.
(5) The optimization process can be similar to the Traveling Salesman (TSP) problem by simultaneously optimizing the processing order and the path trend of each region through a nested immunogenetic algorithm, the flow of which is shown in fig. 11.
The cost function between each node is a definite value when the original genetic algorithm solves the TSP problem, and for the path planning on multiple random areas, the selection of the starting point of the processing path in each area has a large influence on the idle stroke length between the areas. When the number of the areas to be processed is n, the empty routes between the areas are listed as a consumption matrix,the matrix will have 4nIn such a state, when the number of the regions is large, it is difficult to determine the optimal starting point of the processing path of each region by traversal. Through a nested genetic algorithm, the outer layer optimizes the processing sequence of the regions to be processed, and the inner layer optimizes the path trend of each region to achieve the optimization goal of enabling the total length of the paths to be processed to be shortest. To test the optimization effect of the selected algorithm, regions of random shape were randomly generated and optimized by the selected algorithm, as shown in the left diagram of fig. 12, and the resulting path is shown in the right diagram of fig. 12.
(6) And dispersing the grinding path and the transition path according to the maximum step length requirement to obtain a series of cutter contacts, and calculating a cutter axis vector and cutter position point data according to the feeding direction and the surface normal vector to obtain a cutter position track. Fig. 13 is a schematic diagram of the angled face grinding process, defining the midpoint P of the boundary between the abrasive disk and the workpiece surface as the point of contact of the blade.
The method for calculating the tool bit data according to the tool contact is as follows:
let point P be the knife contact point and coordinate P (P)x,Py,Pz) The point of the path O is the center point of the tool, and the coordinate is O (O)x,Oy,Oz) Let the unit vector of the motion direction of the processing track where the processing point is located be r ═ r (r)i,rj,rk) The unit normal vector of the surface is n ═ (n)i,nj,nk) The diameter of the polishing disc is R, the axis inclination angle of the polishing disc is theta, and the width of a contact area obtained through simulation after polishing pressure is set is L, so that the calculation formula of the center point of the polishing disc is as follows:
O=P+(R-L)(r cosθ+n sinθ) (7)
the corresponding arbor vectors are:
c=n cosθ-r sinθ (8)
and obtaining a planned cutter position file after the steps are completed, obtaining a rapid program which can be used for actual processing through post-processing, and completing the planning of the random multi-region efficient polishing path.
The method of the invention rapidly converts the height map to be processed into the map of the area to be processed corresponding to each processing depth through simple image processing, removes the fine hole and island of the area to be processed caused by the fluctuation of the measured data, optimizes the processing sequence and the grinding path of each area simultaneously through the immune genetic algorithm, disperses the grinding path and the transition path according to the maximum step length requirement to obtain a series of tool contacts, and calculates the tool shaft vector and the tool position data according to the feeding direction and the surface normal vector, thereby obtaining the tool position path planning path. The inclusion relation of adjacent height layer curves projected on the same plane is judged through accumulated angle increment, a relation tree between areas to be processed is established and added to path planning as constraint, and the sequence of layered processing is ensured in the path planning of random multiple areas. Through a nested immune genetic algorithm, the path trend in the region is optimized while the random multi-region processing sequence is optimized, and compared with other methods for abstracting the region to be processed into mass points, the method is more suitable for the condition that the area of the random region to be processed is not negligible relative to the total area of the workpiece to be processed.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A random multi-zone efficient grinding path planning method oriented to the cooperation working condition is characterized by comprising the following steps:
s100, measuring to obtain point cloud data of the matching surfaces of the soft mold and the hard mold, performing principal component analysis on the point cloud data to align, fitting the point cloud data of the reinforced wall plate to the surface and taking a complementary set, matching the complementary set with the point cloud data of the sacrificial layer, and taking a difference value in the height direction to obtain a height map to be processed of the surface of the sacrificial layer;
s200, extracting the maximum height and the minimum height of the height map to be processed, and planning a processing sequence and a single processing depth according to the maximum height difference, the removal depth model of the polishing head and the matching precision requirement of the surface of the workpiece;
s300, planning a polishing path of each region to be processed, and simultaneously optimizing a processing sequence and the polishing path of each region through an immune genetic algorithm;
s400, dispersing the grinding path and the transition path according to the requirement of the maximum step length to obtain a series of cutter contacts, and calculating cutter axis vectors and cutter position point data according to the feeding direction and the surface normal vector to obtain a cutter position track planning path.
2. The method for planning the random multi-zone efficient grinding path under the cooperative working condition according to claim 1, wherein in step S100, for an n-dimensional random variable X ═ X (X ═ X)1,X2,…,XN)TThe covariance matrix is:
Figure FDA0003461181670000011
wherein c isij=COV(Xi,Xj) I, j ═ 1,2, …, n denotes the component X of XiAnd XjThe covariance of (a).
3. The method for planning the random multi-region efficient grinding path under the matching condition according to claim 2, wherein in the step S100, the rotation matrix R of the point cloud normal vector of the matching surface of the soft mold and the hard mold to the plane perpendicular to the yoz is:
Figure FDA0003461181670000021
wherein n ═ n (n)x,ny,nz) The normal vector of the plane where the point cloud is located is equal to the unit vector of the eigenvector corresponding to the minimum singular value of the covariance matrix.
4. The method for planning the random multi-zone efficient grinding path under the cooperative working condition according to any one of claims 1 to 3, wherein the step S200 further comprises:
s201: carrying out gray level binarization processing on the height map to be processed by taking the target height at each processing time as a threshold value, wherein the gray level binarization processing process comprises the following steps:
Figure FDA0003461181670000022
the Binary (i, j) represents the Gray level of the corresponding position of the image after the Gray level binarization, the Gray (i, j) represents the Gray level of the corresponding position of the original Gray level image, and the Threshold represents the Threshold used in the Gray level binarization process.
5. The method for planning the random multi-region efficient grinding path under the cooperative working condition according to claim 4, wherein the step S200 further comprises:
s202: merging islands close to the edge of a region to be processed through expansion corrosion, eliminating fine jitter of the boundary, and then carrying out corrosion expansion to eliminate independent fine noise points;
the expansion corrosion treatment process comprises the following steps:
Figure FDA0003461181670000023
where a represents a non-zero set of pixels in a binary image and B represents a structural element, i.e. a structural element.
6. The method for planning the random multi-region efficient grinding path under the cooperative working condition according to claim 5, wherein the step S200 further comprises:
s203: and extracting the boundary of all the gray binary images to obtain boundary curves of all the areas to be processed, placing the boundary curves in the same coordinate system, and judging the inclusion relationship of each curve.
7. The method for planning the random multi-region efficient grinding path under the coordination condition according to claim 6, wherein the judging of the inclusion relationship of each curve comprises:
s204: let the point taken be PcFor the set of boundary points { PePoint P ini、Pi+1Calculating the included angle, and recording PcPiAnd PcPi+1The included angle between is thetaiPositive counterclockwise and negative clockwise, the cumulative angle increment α is:
Figure FDA0003461181670000031
s205: when α approaches ± 360 °, then the point is inside the curve, and when it approaches 0 °, then the point is outside the curve.
8. The method for planning the random multi-region efficient grinding path under the coordination condition according to claim 6, wherein the step S300 comprises:
s301: for the point set of each region to be processed, calculating all eigenvalues and eigenvectors of the point set by taking a covariance matrix, and obtaining the direction in which the point set is most spread by taking the eigenvector corresponding to the largest eigenvalue, wherein the direction is approximate to the processing direction in which the number of row-cutting paths is the least;
s302: calculating the maximum distance of the area to be processed perpendicular to the feeding direction, determining the cutting speed and the applied pressure adopted by the grinding and polishing operation according to the single processing depth so as to obtain a ground removal profile, and determining the processing line distance according to the distance of the area to be processed perpendicular to the processing direction;
s303: and generating a series of parallel lines according to the line spacing, and solving intersection points with the boundary curve to be used as path points of the polishing path.
9. The method for planning the random multi-region efficient grinding path under the coordination condition according to claim 8, wherein the step S300 comprises:
s304: through a nested genetic algorithm, the outer layer optimizes the processing sequence of the regions to be processed, and the inner layer optimizes the path trend of each region to achieve the optimization goal of enabling the total length of the paths to be processed to be shortest.
10. The method for planning the random multi-zone efficient grinding path under the cooperative working condition according to any one of claims 1 to 4, wherein the step S400 comprises:
s401: let point P be the knife contact point and coordinate P (P)x,Py,Pz) The point of the path O is the center point of the tool, and the coordinate is O (O)x,Oy,Oz) Let the unit vector of the motion direction of the processing track where the processing point is located be r ═ r (r)i,rj,rk) The unit normal vector of the surface is n ═ (n)i,nj,nk) The diameter of the polishing disc is R, the axis inclination angle of the polishing disc is theta, and the width of a contact area obtained through simulation after polishing pressure is set is L, so that the calculation formula of the center point of the polishing disc is as follows:
O=P+(R-L)(rcosθ+nsinθ) (7)
s402: the corresponding arbor vectors are:
c=ncosθ-rsinθ (8)
s403: and obtaining a planned cutter position file after the steps are completed, obtaining a rapid program for polishing machining through post-processing, and completing the planning of the random multi-region efficient polishing path.
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