A complex mold cavity arc additive trajectory generation method

Abstract

This invention discloses a method for generating arc additive manufacturing trajectories for complex mold cavities. The method involves layering and slicing the arc additive manufacturing target model to obtain polygonal data of the additive cavity cross-section; dividing the maximum envelope rectangle into m rows and n columns horizontally and vertically to obtain the background mesh of the maximum envelope rectangle; calculating the level set function value of the background mesh nodes using a signed distance function, where the level set function value is positive when the background mesh node is inside the cross-sectional polygon, and negative otherwise; and calculating the maximum value ψ of this function. max and in [0,ψ max The process involves dividing the material into equal parts with a spacing equal to the fill spacing L, resulting in a sequence of equal parts. Each element in this sequence is then traversed to obtain the corresponding horizontal set function contour line. This contour line represents the additive trajectory of the complex cross-section, offset by a certain distance. This invention avoids complex polygon operations such as polygon intersection, difference, and union, greatly simplifying the process of generating equidistant additive trajectories for complex cross-sectional contours and improving the efficiency of additive trajectory generation in arc additive manufacturing.

Description

Technical Field

[0001] This invention relates to the field of arc additive manufacturing and remanufacturing technology for molds, and specifically to a method for generating arc additive manufacturing trajectories for complex mold cavities based on level set functions. Background Technology

[0002] In additive manufacturing and machining technologies, the generation of infill trajectories for arbitrary polygonal cross-sections has always been a core issue, especially in arc-wire additive manufacturing based on layer-by-layer additive manufacturing, where this problem has received considerable research and attention. To address this issue, researchers both domestically and internationally have conducted extensive work and developed various infill strategies, such as contour parallel equidistant infill, grating infill, zigzag infill, and spiral infill. However, the trajectories generated by grating and zigzag infill strategies consist of long straight line segments, resulting in large turning angles, significant impact on equipment, and numerous arc interruptions, which are detrimental to the stable combustion of the welding arc. Spiral infill strategies are generally only suitable for simple cross-sectional shapes, while fractal infill strategies often lead to complex trajectories, making them unsuitable for generating trajectories for complex cross-sectional shapes.

[0003] Therefore, the contour parallel equidistant filling strategy has become a common choice. The generated trajectory is parallel to the polygon boundary, exhibiting good stability and continuity, making it suitable for fields such as CNC machining and arc-fused-wire additive manufacturing. Equidistant filling strategies include offset strategies and Voronoi diagram strategies. However, offset strategies require handling polygon intersections, crosses, and unions, and suffer from polygon divergence problems, resulting in high algorithm complexity and complex programming. Voronoi diagrams, on the other hand, require constructing multiple Voronoi polygons, which is difficult for complex cross-sections. Summary of the Invention

[0004] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a method for generating arc additive trajectories in complex mold cavities, simplifying the process of generating parallel and equidistant additive trajectories for arbitrary complex cross-sectional polygonal contours, and improving the efficiency of generating parallel and equidistant arc additive trajectories.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for generating electric arc additive manufacturing trajectories for complex mold cavities includes the following steps:

[0007] S1. Slice the electric arc additive target model into layers to obtain the polygonal data of the additive cavity cross section. The polygonal cross section has multiple holes and multiple islands, and the outer contour polygons are arranged counterclockwise and the inner contour polygons are arranged clockwise.

[0008] The cross-sectional polygon data of the layered slices is used as one of the input data of this invention. In addition, the equidistant offset distance L, the horizontal segmentation data m and the vertical segmentation data n are also input.

[0009] S2. Generate the background mesh for the input cross-section polygon;

[0010] S3. Calculate the level set function value of the background mesh nodes using the signed distance function. The calculation formula is as follows: Where x' and y' represent the coordinates of points on the cross-sectional polygon, x and y represent the coordinates of background grid nodes, and ψ represents the level set function value. The level set function value is positive when the background grid node is inside the cross-sectional polygon, and negative otherwise. The maximum envelope rectangle of the cross-sectional polygon data is calculated, and the maximum envelope rectangle covers all vertices of the cross-sectional polygon.

[0011] S4. Calculate the maximum value ψ(x,y) of the level set function. max and in [0,ψ max Divide the material into equal parts according to the spacing L, and obtain an equal part sequence; traverse each element of the sequence and obtain the contour line of the horizontal set function corresponding to the element. The contour line is the additive trajectory of the corresponding complex cross section offset by a certain distance.

[0012] S5. Calculate the contour lines of the horizontal set function for each element in the contour sequence. During the calculation, each rectangular sub-grid in the background grid is transformed into two triangular grids and the horizontal set value is used as the height component value. Construct the STL surface model of the surface, and then call the STL model slicing algorithm to quickly obtain the contour lines.

[0013] S6. Combine the contour lines of each element in the equally divided sequence; form a set of contour lines corresponding to all filling heights of the horizontal set function, which is the equidistant filling trajectory of the complex cross-section contour;

[0014] S7. Determine if the filling is complete; if yes, proceed to S8; otherwise, return to S4.

[0015] S8, outputs an equidistant fill path.

[0016] Furthermore, step S1 obtains polygonal data of the additive cavity cross section, including ordered point coordinate data of the cross section boundary polygon, equidistant offset distance L, lateral segmentation data m, and longitudinal segmentation data n.

[0017] Furthermore, in step S3, the maximum envelope rectangle can be any of the polygons of a cross section, or a cross section can be decomposed into multiple cross sections containing an outer contour polygon and multiple inner contour polygons for filling. There are no restrictions on the shape of the cross section to be filled, that is, any complex cross section shape can be filled at equal intervals. The complexity of the cross section shape does not affect the calculation efficiency of the method, and it can quickly and efficiently fill any complex cross section with parallel contours at equal intervals.

[0018] Furthermore, in step S3, the level set function ψ(x,y) is a discrete function on the background grid, and its calculation formula should use the discrete calculation formula in practical applications. Where i and j represent the row and column indices of the background mesh, respectively, and k represents the index of all vertices of the cross-sectional polygons. When the level set function point (x i ,y j The horizontal set function is positive when inside the polygon, zero when on the boundary, and negative otherwise; the solution domain of the horizontal set function is the background grid rectangular region.

[0019] Furthermore, in step S5, when solving for the contour lines of the horizontal set function, a rectangular grid can be divided into two triangles to construct a spatial STL model of the horizontal set function. Then, the contour lines can be quickly solved by directly calling the STL model slicing algorithm. In this way, the mature STL model slicing algorithm can be called, and the problem of parallel equidistant or non-equidistant filling of the contour of any complex cross section can be transformed into a mature and stable STL model slicing problem, which greatly simplifies the problem of generating the contour parallel filling trajectory.

[0020] In step S4, the filling spacing L is usually half the weld width, which can realize the generation of equidistant filling paths for any complex cross-section. In addition, if the filling spacing is not a fixed value, non-equidistant filling paths for parallel contour filling can be generated, thereby realizing the generation of variable width filling trajectories for any complex cross-section.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1. This invention proposes an efficient, fast, and simple method for generating parallel equidistant or non-equidistant additive trajectories for arbitrary complex polygonal cross-sections. This method greatly simplifies the process of generating parallel equidistant additive trajectories for arbitrary complex polygonal cross-sections and improves the efficiency of generating parallel equidistant trajectories for arc additive profiles. By constructing a level set function ψ(x,y) for a certain cross-section once, and then calling the target STL model slicing algorithm multiple times, all contour parallel equidistant filling trajectories are generated, greatly improving computational efficiency and reducing algorithm complexity. That is, after generating the level set function, the number of filling trajectories has a negligible impact on the solution time, while the complexity of traditional geometric offset algorithms is directly related to the number of filling trajectories.

[0023] 2. This invention calculates the background mesh of the maximum envelope rectangle of the profile based on the information of the cross-sectional contour and generates a horizontal set function surface. The additive path is the contour lines of several sets of horizontal set function surfaces. Compared with the traditional contour geometric offset algorithm, the computational efficiency of the horizontal set algorithm is independent of the shape of the cross-sectional contour polygon and only related to the number of horizontal and vertical equal divisions of the background mesh of the maximum envelope rectangle. In contrast, the computational complexity of the traditional geometric offset algorithm is highly dependent on the shape complexity of the cross-sectional polygon. Furthermore, there are no restrictions on the shape of the mold cavity cross-section to be filled, meaning that equidistant filling can be performed on any complex cross-sectional shape. At the same time, the number of equal divisions of the maximum envelope rectangle in the horizontal and vertical directions is not explicitly specified; the division data is determined only by the required accuracy. That is, the larger the number of divisions m and n, the higher the accuracy of the additive trajectory. Reasonable values ​​can be selected according to the accuracy requirements of additive manufacturing.

[0024] 3. This invention effectively solves the problems of poor arc stability and large equipment impact in traditional raster filling strategies, Z-shaped filling strategies, and spiral filling strategies, as well as the problems of polygon intersection, difference, and union operations and polygon divergence in traditional contour equidistant offset filling strategies. Compared with traditional contour geometric offset algorithms, it is convenient to operate, has a clear algorithm flow, and does not require handling polygon self-intersection, polygon intersection, difference, and union operations. Attached Figure Description

[0025] Figure 1 A flowchart illustrating the generation of a parallel and equidistant filling trajectory using the method of this invention;

[0026] Figure 2 This is a schematic diagram illustrating the generation of the cavity cross-sectional contour polygon, the maximum envelope rectangle, the background mesh, the horizontal set function surface, and the equidistant fill lines in Embodiment 1 of the present invention.

[0027] Figure 3 This is a schematic diagram of the contour parallel filling lines with different parallel distances and the corresponding horizontal set function surfaces in Embodiment 1 of the present invention.

[0028] In the figure, 1 - enveloping rectangle, 2 - cross-sectional profile, 3 - background grid, 4 - horizontal set function surface, and 5 - filling trajectory (horizontal set function contour lines). Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0030] It should be noted that similar reference numerals and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the figures, or the orientation or positional relationship commonly used when the product is in use. They are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of this invention should be included within the scope of protection of this invention.

[0031] See Figure 1 This invention provides a method for generating electric arc additive manufacturing trajectories for complex mold cavities, comprising the following steps:

[0032] S1. The target model of electric arc additive manufacturing is sliced ​​into layers to obtain the polygonal data of the cross-section of the additive cavity. The polygonal cross-section may contain multiple holes and multiple islands, and the outer contour polygons are arranged in counterclockwise order and the inner contour polygons are arranged in clockwise order. The polygonal data of the sliced ​​cross-section is used as one of the input data of this invention. In addition, the equidistant offset distance L, the horizontal segmentation data m and the vertical segmentation data n are also input.

[0033] S2. Generate the background mesh for the input cross-section polygon;

[0034] S3. Calculate the level set function value of the background mesh nodes using the signed distance function. The calculation formula is as follows: Where x' and y' represent the coordinates of a point on the cross-sectional polygon, x and y represent the coordinates of a background mesh node, and ψ represents the value of the horizontal set function. The value of the horizontal set function is positive when the background mesh node is inside the cross-sectional polygon, and negative otherwise.

[0035] S4. Calculate the maximum value ψ(x,y) of the level set function. max and in [0,ψ max Divide the sequence into equal parts with a spacing equal to the padding spacing L to obtain an equally divided sequence;

[0036] S5. Calculate the contour lines of the horizontal set function for each element in the contour sequence. During the calculation, each rectangular sub-grid in the background grid is transformed into two triangular grids and the horizontal set value is used as the height component value. Construct the STL surface model of the surface, and then call the STL model slicing algorithm to quickly obtain the contour lines.

[0037] S6. Contour lines of each element in the combined equally divided sequence;

[0038] S7. Determine if the filling is complete; if yes, proceed to S8; otherwise, return to S4.

[0039] S8, outputs an equidistant fill path.

[0040] Example 1

[0041] In the arc additive remanufacturing repair process of crankshaft failure molds, the cross-sectional shape of the crankshaft mold cavity is highly complex and irregular, making it difficult to generate parallel and equidistant filling trajectories. This embodiment applies the method of the present invention to achieve the generation of parallel and equidistant filling trajectories, mainly including the following steps:

[0042] 1) See Figure 2 Figure (a) shows that the STL model of the target material for the arc additive remanufacturing of a failed automobile crankshaft mold is sliced ​​to obtain the cross-sectional contour data 2 at a certain height. The polygonal cross-section may have a hole, and the outer contour is sorted counterclockwise and the inner contour is sorted clockwise.

[0043] 2) Solve for the maximum envelope rectangle (minimum bounding rectangle) 1 of the contour data. This maximum envelope rectangle covers all vertices of the cross-sectional polygon.

[0044] 3) Divide the maximum envelope rectangle into 50 rows and 50 columns in both the horizontal and vertical directions to obtain the background grid 3 of the maximum envelope rectangle. Each grid vertex is a node of the background grid, with a total of 2500 nodes (50×50).

[0045] 4) Calculate the level set function value of the background mesh nodes using the signed distance function. The calculation formula is as follows: Where x k 'and yk 'Represents the coordinates of a point on the cross-sectional polygon, x, y i and y i The coordinates of the background mesh nodes and ψ represent the horizontal set function value. The horizontal set function value is positive when the background mesh node is inside the cross-sectional polygon, and negative otherwise. In this implementation case, the maximum values ​​of i and j are both 50.

[0046] 5) After obtaining the level set function ψ(x,y), calculate the maximum value ψ of this function. max =20, and divide [0,20] into equal parts with a spacing of L=1.5, to obtain an equal-divided sequence. Traverse each element in the sequence and obtain the corresponding horizontal set function contour line. This contour line is the filling trajectory of the corresponding complex cross-section offset by a certain distance. See Figure 3 ;

[0047] 6) Form a set of contour lines corresponding to all fill heights of the horizontal set function; this is the equidistant fill trajectory of the complex cross-sectional profile. See [link / reference]. Figure 2 (c) As can be seen from the figure, the filling trajectory has the feature of being parallel to the outline of the cross-section polygon and has fewer arc breaks. For additive manufacturing processes, fewer arc breaks can improve the stability of the additive process. The filling trajectory has no large turning points and has high movement stability.

[0048] See Figure 3 As shown in (a)-(c), the parallel fill lines of the profile are 1.5, 3, and 4.5 mm away from the cross-sectional profile, respectively. It can be seen that the fill trajectory still maintains an inner profile and an outer profile. At this time, the method can automatically determine the number of polygons of the fill line according to the actual situation.

[0049] See Figure 3 As shown in (d)-(i), the parallel filling trajectories of the contour are 6, 7.5, 9, 10.5, 12, and 13.5 mm away from the cross-sectional contour, respectively. It can be seen that the algorithm can automatically split the original cross-sectional polygon into multiple polygons according to the actual situation, and the splitting process does not require the use of polygon intersection and union operations.

[0050] See Figure 3 As shown in (j)-(l), these are parallel filling trajectories of the contour with a fill line distance of 15, 16.5, and 18 mm from the cross-sectional contour, respectively. It can be seen that the algorithm can automatically transform the original cross-sectional polygon into multiple polygons and then into a small number of polygons according to the actual situation, which greatly simplifies the problem of merging the offset of complex cross-sectional polygons.

[0051] In summary, this invention constructs a specific level set function, whose contour lines serve as the equidistant filling trajectory. This avoids the complex polygon operations such as polygon intersection, difference, and union found in conventional contour offset filling algorithms, greatly simplifying the generation process of equidistant additive trajectories for complex cross-sectional contours and improving the efficiency of additive trajectory generation in arc additive manufacturing. The method features simple structure, high computational efficiency, and ease of programming. The process of obtaining contour lines solely through cutting the level set function automatically avoids polygon splitting, merging, and difference operations present in geometric offset algorithms. It eliminates the need for polygon splitting, merging, and difference operations, automatically performing these operations, significantly simplifying the generation process of parallel equidistant additive trajectories for arbitrarily complex cross-sectional polygon contours and improving the efficiency of generating parallel equidistant additive trajectories for arc additive manufacturing.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described with reference to preferred embodiments, those skilled in the art should understand that various changes in form and detail can be made. All obvious changes derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for generating arc additive manufacturing trajectories in complex mold cavities, characterized in that, Includes the following steps: S1. Slice the electric arc additive target model into layers to obtain the polygonal data of the additive cavity cross section. The polygonal cross section contains multiple holes and multiple islands, and the outer contour polygons are arranged counterclockwise and the inner contour polygons are arranged clockwise. Use the polygonal data of the sliced ​​cross section as one of the input data. In addition, the equidistant offset distance L, the horizontal segmentation data m, and the vertical segmentation data n are also input. S2. Generate the background mesh for the input cross-section polygon; S3. Calculate the level set function value of the background mesh nodes using the signed distance function. The calculation formula is as follows: Where x' and y' represent the coordinates of a point on the cross-sectional polygon, x and y represent the coordinates of a background mesh node, and ψ represents the value of the horizontal set function. The value of the horizontal set function is positive when the background mesh node is inside the cross-sectional polygon, and negative otherwise. Calculate the maximum envelope rectangle of the cross-sectional polygon data, where the maximum envelope rectangle covers all vertices of the cross-sectional polygon; S4. Calculate the maximum value ψ(x,y) of the level set function. max and in [0,ψ max Divide the material into equal parts according to the spacing L, and obtain an equal part sequence; traverse each element of the sequence and obtain the contour line of the horizontal set function corresponding to the element. The contour line is the additive trajectory of the equidistant offset distance L of the corresponding complex cross section. S5. Calculate the contour lines of the horizontal set function for each element in the contour sequence. During the calculation, each rectangular sub-grid in the background grid is transformed into two triangular grids and the horizontal set value is used as the height component value. Construct the STL surface model of the surface, and then call the STL model slicing algorithm to quickly obtain the contour lines. S6. Combine the contour lines of each element in the equally divided sequence; form a set of contour lines corresponding to all filling heights of the horizontal set function, which is the equidistant filling trajectory of the complex cross-section contour; S7. Determine if the filling is complete; if yes, proceed to S8; otherwise, return to S4. S8, outputs an equidistant fill path.

2. The method for generating arc additive manufacturing trajectories for complex mold cavities according to claim 1, characterized in that, Step S1 obtains polygonal data of the additive cavity cross section, including ordered point coordinate data of the cross section boundary polygon, equidistant offset distance L, lateral segmentation data m, and longitudinal segmentation data n.

3. The method for generating arc additive manufacturing trajectories for complex mold cavities according to claim 1, characterized in that, In step S3, the maximum envelope rectangle can be any of the polygons of a cross section, or a cross section can be decomposed into multiple cross sections containing an outer contour polygon and multiple inner contour polygons for filling. There are no restrictions on the shape of the cross section to be filled, that is, any complex cross section shape can be filled at equal intervals.

4. The method for generating arc additive manufacturing trajectories for complex mold cavities according to claim 1, characterized in that, In step S3, the level set function ψ(x,y) is a discrete function on the background grid, and its calculation formula should use the discrete calculation formula in practical applications. Where i and j represent the row and column indices of the background mesh, respectively, and k represents the index of all vertices of the cross-sectional polygons. When the level set function point (x i ,y j The horizontal set function is positive when inside the polygon, zero when on the boundary, and negative otherwise; the solution domain of the horizontal set function is the background grid rectangular region.

5. The method for generating arc additive manufacturing trajectories for complex mold cavities according to claim 1, characterized in that, In step S5, when solving for the contour lines of the horizontal set function, a rectangular grid is divided into two triangles to construct a spatial STL model of the horizontal set function. The contour lines can then be quickly solved by directly calling the STL model slicing algorithm.

6. The method for generating arc additive manufacturing trajectories for complex mold cavities according to claim 1, characterized in that, In step S4, the filling spacing L is 1 / 2 of the weld width.

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