CN114117833A - Sierpinski curve path planning method based on additive manufacturing post-processing - Google Patents
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Abstract
The invention relates to a path planning method based on a Sierpinski curve, which is suitable for performing material reduction and finish machining after additive manufacturing, and comprises the following steps: classifying the mapping regions according to the geometric characteristics of the model; solving a Sierpinski path in a mapping plane; and mapping the Sierpinski path to the curved surface to obtain a finish machining path. The method adopts an advanced material reduction manufacturing path for the complex additive manufacturing model, improves the processing orderless, eliminates intermediate frequency and high frequency errors and eliminates polishing textures; the processing efficiency and the quality are improved; judging the type of the mapping region according to the geometric characteristics of the curved surface, and selecting a proper mapping region to ensure that no unprocessed residual region and repeated region exist; the order is set according to the removal precision, and the processing path is required to be short and the efficiency is required to be high on the premise of ensuring the quality; the path planning mode effectively prevents the operation in a single direction, eliminates intermediate frequency and high frequency errors, and realizes efficient precision machining.
Description
Technical Field
The invention relates to the technologies of computer graphics, material increase/decrease manufacturing processing, trajectory planning and the like, in particular to a method which is suitable for performing precision processing on a curved surface after material increase manufacturing and obtaining a curved surface mapping trajectory after planning a Sierpinski path by adopting a plane area.
Background
The additive manufacturing technology can print complex components, the manufacturing method of layer-by-layer accumulative processing can manufacture parts with excellent mechanical properties, and compared with material reduction manufacturing, the additive manufacturing method has the advantages of saving processing materials, avoiding processing stress concentration and the like. The parts manufactured by additive processing have the advantages of high rigidity, easiness in manufacturing and the like, so that the parts have wide application prospects in the fields of space optics, automobiles, aerospace and the like. Particularly in the field of national military defense, such as some key components with high strength of high-speed guided weapons, the processing quality of the components directly influences the use quality of the whole equipment. Furthermore, for these military components, the final surface quality will even determine their physical properties and accuracy; even for consumer products, an aesthetically smooth surface quality is important.
However, the surface quality of the workpiece manufactured by additive manufacturing, particularly the workpiece processed by laser powder feeding, is often very poor, and precision processing is required. The invention aims at the bottleneck problems that the traditional material reducing manufacturing path is applied to a polishing process and generates medium-frequency and high-frequency errors due to single direction of the path, and the processing efficiency and the quality are always difficult to solve.
The disadvantages of the conventional material reducing path planning method at the present stage are obvious: firstly, unprocessed residual regions and repeated regions easily exist, polygons are various in shape, the traditional path is not ideal in coverage of boundaries mostly, the path is sparse and uneven, and partial regions are easily processed and partial regions are not processed; the traditional equidistant contour offset path (CPO) or reciprocating cutting path (Zig-Zag) is not efficient, wastes time and labor, and the reciprocating operation of the latter is easy to cause a saw-tooth boundary, so that the processing precision is not high; conventional paths, which are mostly run in a single direction, result in a large amount of mid-frequency, high-frequency errors, and machining in this manner results in a large amount of machined texture.
The existing path planning mode needs to be improved and innovated to realize the precise machining of the additive manufacturing post-processing, and the mapping scheme can be adaptively selected according to the geometric characteristics and a path with constantly changing direction is the core of the efficient and high-precision machining of the additive manufacturing post-processing.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a precise material reduction trajectory planning method for additive manufacturing post-processing based on Sierpinski path mapping.
The technical scheme adopted by the invention for realizing the purpose is as follows: the Sierpinski curve path planning method based on additive manufacturing post-processing comprises the following steps:
step 1: determining the shape of a plane mapping area corresponding to the curved surface by adopting a fixed boundary surface parameterization method according to the geometric characteristics of the curved surface;
step 2: in the plane mapping area, determining parameters of a corresponding Sierpinski path according to the mapping area and the size of the curved surface;
and step 3: determining a triangular patch of a Sierpinski path in the plane mapping area;
and 4, step 4: and mapping the triangular patch processing path in the plane mapping area to the curved surface to obtain a detection processing track.
And the mapping domain is divided into a unit circle domain and a square domain by calculating the circularity of the projection region according to the geometric characteristics of the curved surface by adopting a fixed boundary surface parameterization method.
The circularity is defined as a proportional relationship between the area and the circumference and is unitized, and the value of circularity is closer to 1 and closer to a circle.
The circularity value is 4 times the area divided by the circumference squared.
The parameter for determining the corresponding Sierpinski path according to the mapping area and the curved surface size comprises the following steps:
the line spacing is in direct proportion to the order of the Sierpinski path, and the size of the order is adjusted to obtain the proper line spacing;
and the step length is interpolated between every two points on the Sierpinski curved surface path by a chord height difference method.
The triangular patch of the Sierpinski path in the determined area is as follows:
and dividing the unit circular domain or the square domain into a plurality of triangular patches, filling the patches by a Sierpinski path, and covering the whole unit circular domain or the whole square domain.
The mapping of the triangular patch processing path in the plane mapping area to the curved surface comprises:
in the plane mapping area, sequentially calculating the barycentric coordinates of each triangular patch divided according to the Sierpinski path in the plane mapping area under the condition that the processing order of the Sierpinski path is decreased, and sequentially storing the barycentric coordinates;
in the curved surface, the sequence of barycentric coordinates is used as the processing sequence of the path on the curved surface, and the Sierpinski path is used as the processing track for filling each curved surface patch.
Coordinates (x) of the center of gravity point q on the triangular patchq，yq) The calculation formula is as follows:
xq＝{I xp1+J xp2+K xp3|I+J+K＝1,I,J,K≥0}，
yq＝{I yp1+J yp2+K yp3|I+J+K＝1,I,J,K≥0}；
wherein, the coordinates of three vertexes of the triangular patch are p respectively1(xp1，yp1)、p2(xp2，yp2)、p3(xp3，yp3) And I, J, K are weighting coefficients.
The invention has the following beneficial effects and advantages:
1. the method adopts a precise material reduction trajectory planning method based on the additive manufacturing post-treatment of Sierpinski path mapping, can ensure that the processing paths have no intersection and the direction is constantly changed, and improves the processing efficiency and quality.
2. The invention adopts the method for judging the roundness of the projection surface of the curved surface, can realize the selection of the mapping unit circular domain and the unit square domain, and can greatly improve the boundary precision.
3. According to the method, the projection domain and the curved surface are unified through the barycentric coordinate system, and the order of the surface patches of the projection domain is adjusted to ensure that the clockwise direction and the counterclockwise direction of the vertexes of the two surface patches are consistent, so that the difficulty of path planning can be greatly simplified.
Drawings
FIG. 1 is a flow chart of the method steps of the present invention.
FIG. 2 is an illustration of rectangular and circular fields of a mesh surface.
FIG. 3 is a mapping plane rectangular field, circular field of a model.
FIG. 4 is a mapping plane rectangular domain, circular domain of another model.
Fig. 5 is a schematic diagram of barycentric coordinates on a planar mesh patch.
Fig. 6 is a schematic triangular subdivision.
Fig. 7 planar rectangular domain, circular domain partitioning, and xierbius trajectory generation.
FIG. 8 illustrates a face area of a rectangular field and a circular field being divided and generated by a Sierpinski trajectory.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Example (b): the invention relates to a path planning method based on material increase post-processing of a Sierpinski curve.
The specific path planning method based on the Sierpinski curve for additive post-processing comprises the following steps:
parameterization is performed on the surfaces, and a one-to-one mapping from the appropriate parameter domain to the surfaces is found.
The purpose of parameterizing the surface mesh is to find a one-to-one mapping rule from the planar mesh to the surface of the triangular mesh. A good mapping rule needs to comply with the rule that angular deformation (conformal parameterization) or area deformation (isoparametric parameterization) is minimized. The present invention uses a fixed boundary method.
Fixed boundary surface parameterization is a method of defining a set of constrained boundary parameterizations, i.e. each vertex along the boundary is defined by two u, v coordinates. When selecting a boundary parameterization scheme for a fixed boundary method, the present invention provides two different options:
(1) the boundary parameterization can be chosen in two general methods: uniform or parametric in arc length. Even, i.e. equally spaced, boundary parameterization, while producing poor visual impact, is more stable. In order to better comply with the principle of reducing machining errors, we use the arc length frame parameterization method by default.
(2) The boundary shape of the planar domain is represented by one of two standard shapes: circular or square. It is clear that square boundary parameterization is typically used to approximate rectangles. The circular boundary parameterization corresponds to a projection that approximates a circle.
The invention can obtain the area outline by projecting the curved surface mesh onto the plane, judge the shape according to the numerical value of the calculation circularity and select the boundary parameterization type, and divide the mapping domain into a unit circle domain and a square domain, as shown in figure 2.
The circularity is unitized by the proportional relationship between the area and the circumference, and approaches 1 (is a standard circle) to a standard circle.
The circularity is calculated as follows:
Circularity＝4×Area/Length2 (1)
wherein, circulation is a Circularity value; area is the Area enclosed by the outline of the projection Area; length is the contour Length of the projection area.
For example, a curved surface is projected, the circularity of the projection region is calculated, and if the circularity exceeds 0.8, the projection region is mapped in a circular domain; otherwise, if the mapping is less than 0.8, mapping is carried out according to the square domain.
Determining the parameters of the corresponding Sierpinski path according to the dimensions of the curved surface: the standard of the selected parameter comprises a line spacing which is in direct proportion to the order of the Sierpinski path, and the line spacing can be judged by a simulation result, and the order is adjusted, so that the proper line spacing is obtained; the step length is determined by a chord height difference method: and (3) interpolating the distance between every two points on the Sierpinski curved surface path to obtain the step length with proper chord height difference precision.
Determining the number and the size of triangular areas of the Sierpinski path in the area: and dividing the unit circle domain or the square domain, filling the unit circle domain or the square domain by a Sierpinski path, and determining the number of triangles on the premise of meeting the boundary coverage. The more the number of the divisions is, the closer the boundary formed by the triangles is to the circle, and the better the coverage of the outer boundary is; at the same time, the calculation time will be increased.
Mapping the path in the mapping area to the curved surface to obtain a detection processing track as follows: the conversion of the consistency of the sequence of the surface patches in the unit domain of the plane and the sequence of the corresponding surface patches is completed through a barycentric coordinate system.
The barycentric coordinates are proportional to the areas of the three sub-triangles divided by the barycentric and the vertices, so that the area ratio of each sub-triangle can be obtained as the sum of the areas, as shown in fig. 5.
Mapping a Sierpinski path in a plane domain to a mesh surface by a mapping principle: since the path points cannot be guaranteed to be at the vertices or edges of the triangle (i.e. on the triangle surface in most cases), the coordinates of the path points on the surface patch corresponding to the mesh surface can be obtained through barycentric coordinate conversion.
With reference to the definition of 2D generalized barycentric coordinates, it provides an efficient and robust implementation of generalized barycentric coordinates in two-dimensional closed form of simple two-dimensional triangle definitions. The patch order of the mapping planes is adjusted to be the same as the original surface mesh, as shown in fig. 3 and 4.
Calculating the plane domain according to the following formulaCoordinate (x) of gravity point q on triangle patchq，yq) See fig. 4:
xq＝{I xp1+J xp2+K xp3|I+J+K＝1,I,J,K≥0}，
yq＝{I yp1+J yp2+K yp3|I+J+K＝1,I,J,K≥0}； (2)
wherein, the coordinates of three vertexes of the triangular patch are p respectively1(xp1，yp1)、p2(xp2，yp2)、p3(xp3，yp3) I, J, K is a weighting coefficient;
with the method of expressing q as a weighted average of the vertices of the triangle patch, as described above, the index of the flat domain follows a one-to-one mapping rule and is the same as the original surface mesh, and the point q corresponds to a coordinate of a point in the upper patch of the flat domain of the original surface mesh, which coordinate can be calculated by equation 2.
The method of triangular iterative subdivision is adopted to divide a triangular patch into a circular domain or a square domain, and then the following algorithm 1 is executed:
the algorithm name is: gensierp (x1, x2, x3, n)
The input is as follows: x1, x2, x3, Sierpinski curve order n;
the output is: barycentric coordinate point collection verticales (2-dimension)
1. If n is 0, directly calculating barycentric coordinates by using the public (2) and outputting verticals;
2. if n ≠ 0, solving for bisector point x4 in the triangular subdivision scheme of FIG. 6;
3. recursively invoking an iterative function
A, recursively invoking gensierp (x1, x3, x4, n-1);
b, recursive calling gensierp (x3, x2, x4, n-1);
4. sequentially storing the points calculated in the step 3 into verticals
5. And executing 3-4 until n is 0, and stopping the program.
And (3) performing triangle segmentation on the circular domain or the square domain by adopting a triangle iterative subdivision method, and then executing the algorithm 1, as shown in fig. 7.
The larger the number of the divided triangular patches is, the better the boundary coverage of the circular domain is; meanwhile, the larger the number of triangle patches, the more time is required for calculation.
Fig. 8 is a diagram illustrating a mapping track obtained by mapping a complex surface, and a square domain and a circular domain are given as examples in this patent. Compared with the mapping track of a circular domain, the mapping track of a square domain has more ideal boundary coverage; the projection surface of the complex curved surface has lower circularity and is closer to a rectangle, so that the mapping track obtained by square domain mapping is more ideal.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (8)
1. The Sierpinski curve path planning method based on additive manufacturing post-processing is characterized by comprising the following steps of:
step 1: determining the shape of a plane mapping area corresponding to the curved surface by adopting a fixed boundary surface parameterization method according to the geometric characteristics of the curved surface;
step 2: in the plane mapping area, determining parameters of a corresponding Sierpinski path according to the mapping area and the size of the curved surface;
and step 3: determining a triangular patch of a Sierpinski path in the plane mapping area;
and 4, step 4: and mapping the triangular patch processing path in the plane mapping area to the curved surface to obtain a detection processing track.
2. The Sierpinski curve path planning method based on additive manufacturing post-processing according to claim 1, wherein a fixed boundary surface parameterization method is adopted according to the geometric characteristics of the curved surface, and a mapping domain is divided into a unit circle domain and a square domain by calculating the circularity of a projection region.
3. The method of claim 2, wherein the circularity is defined as a proportional relationship between area and perimeter and is unitized, and the circularity value is closer to 1 and closer to a circle.
4. The method of claim 3, wherein the circularity has a value of 4 times area divided by circumference squared.
5. The method of claim 1, wherein the determining parameters of the corresponding Sierpinski path according to the mapping region and the surface dimension comprises:
the line spacing is in direct proportion to the order of the Sierpinski path, and the size of the order is adjusted to obtain the proper line spacing;
and the step length is interpolated between every two points on the Sierpinski curved surface path by a chord height difference method.
6. The method for schelkimpflug curve path planning based on additive manufacturing post-processing according to claim 1, wherein the triangular patches of the scheimpflug curve path in the determined region are:
and dividing the unit circular domain or the square domain into a plurality of triangular patches, filling the patches by a Sierpinski path, and covering the whole unit circular domain or the whole square domain.
7. The method of claim 1, wherein the mapping the triangular patch toolpath within the planar mapping region onto a curved surface comprises:
in the plane mapping area, sequentially calculating the barycentric coordinates of each triangular patch divided according to the Sierpinski path in the plane mapping area under the condition that the processing order of the Sierpinski path is decreased, and sequentially storing the barycentric coordinates;
in the curved surface, the sequence of barycentric coordinates is used as the processing sequence of the path on the curved surface, and the Sierpinski path is used as the processing track for filling each curved surface patch.
8. The method of claim 1, wherein coordinates (x) of a center of gravity point q on the triangular patch are determined by a Sierpinski curve path planning method based on additive manufacturing post-processingq，yq) The calculation formula is as follows:
xq＝{Ixp1+Jxp2+K xp3|I+J+K＝1,I,J,K≥0}，
yq＝{Iyp1+Jyp2+K yp3|I+J+K＝1,I,J,K≥0}；
wherein, the coordinates of three vertexes of the triangular patch are p respectively1(xp1，yp1)、p2(xp2，yp2)、p3(xp3，yp3) And I, J, K are weighting coefficients.
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