CN113119451B

CN113119451B - 3D printing path planning method for curved surface cladding porous lightweight structure

Info

Publication number: CN113119451B
Application number: CN202110375409.1A
Authority: CN
Inventors: 沈楷; 陈正颖; 熊旭辉; 刘州鹏; 刘文杰; 刘浩; 田威; 廖文和
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2021-04-08
Filing date: 2021-04-08
Publication date: 2022-05-06
Anticipated expiration: 2041-04-08
Also published as: CN113119451A

Abstract

The invention discloses a 3D printing path planning method of a curved surface cladding porous lightweight structure, which comprises the following steps: step 1: separating a cladding curved surface from a surface area of a work surface, wherein the cladding curved surface comprises a plurality of layers of cladding surfaces; step 2: fitting the cladding curved surface into a plane pi, and taking two mutually perpendicular directions n on the plane pi₀And n₁(ii) a And step 3: for the cladding surface of the adjacent layer, the normal vector direction is n₀And n₁The section group of the laser cladding surface is connected with the intersection points of the section and the cladding surface to obtain a series of parallel section curves; and 4, step 4: and adjusting the distance between the section curves on the cladding surface to ensure that the distance between the adjacent section curves is the width of the cladding path, wherein the adjusted section curve is the cladding path of the cladding surface. The invention solves the problem that the porous lightweight structure is complex and difficult to achieve in the curved surface cladding process, and provides an effective solution for the 3D printing path planning problem of the curved surface cladding porous lightweight structure.

Description

3D printing path planning method for curved surface cladding porous lightweight structure

Technical Field

The invention relates to a 3D printing path planning method for a curved surface cladding porous lightweight structure, and belongs to the field of application and design of 3D printing software.

Background

With the continuous development of three-dimensional printing manufacturing technology, people have higher and higher requirements on energy conservation, consumption reduction and rapid manufacturing, and light-weight structures aiming at weight reduction and high performance are paid more and more attention. At present, light-weight structure generation methods based on a three-dimensional printing technology mainly comprise the following two types: the first type is the design of lightweight structures of the model by using geometric solid modeling before slicing, such as pores or complex hole structures designed in the model. The second type is to perform path planning after the model is sliced, and to realize the printing of a lightweight structure by filling regular mesh paths (such as honeycomb paths, rhombic paths, fractal scanning paths, etc.) in the slice layer.

The Fused Deposition Modeling (FDM) -based 3D printing technology is one of the traditional printing technologies in the 3D printing field, and is popular with numerous device developers and users because the Fused Deposition Modeling (FDM) based 3D printing technology is simple in principle and easy to implement, and can be applied to printing various complex physical models and artware. The curved surface cladding belongs to a part of 3D printing technology based on fused deposition modeling, the representation methods of the curved surfaces are various, such as a continuous curved surface and a discrete curved surface, the commonly used continuous curved surface is a Bezier curved surface or a B-spline curved surface, and the discrete curved surface representation mainly comprises a three-dimensional mesh. Due to the complexity of curved surfaces, digital geometry mainly uses three-dimensional point clouds (fig. 1) or three-dimensional meshes (fig. 2) as the main expression.

The three-dimensional mesh is characterized by rich expression capability, capability of expressing complex geometric shapes, simple associated structure, direct drawing means of mesh models, suitability for modeling complex three-dimensional shapes and most extensive application of surface expression. Cladding on a complex curved surface based on a triangular mesh surface cladding technology is always a hot point of research in the technical field of 3D printing. The method is used for carrying out fusion cladding on the complex curved surface, the number of layers to be clad and the distance between cladding layers can be controlled according to requirements, and a porous structure can exist between the cladding layers.

The porous lightweight structure has many advantages, can hold redundant materials in the cladding process, ensures the printing quality, can save materials and reduce resource waste, and meets the requirement of lightweight. In the process of cladding a complex curved surface, planning of a curved surface cladding path and generation of the cladding path are hot spots of current research, are also requirements for saving resources and protecting the environment, and can meet the current environmental requirements. Therefore, the research on the related technology of complex curved surface cladding is very important.

Disclosure of Invention

In order to solve the problem of 3D printing path planning for cladding on a curved surface to achieve a porous lightweight structure, the invention aims to provide a 3D printing path planning method for cladding the porous lightweight structure on the curved surface, effectively solves the problem that the porous lightweight structure is complex and difficult to achieve in the process of cladding the curved surface, and provides an effective solution for the problem of 3D printing path planning for cladding the porous lightweight structure on the curved surface.

The complex surface modeling mode of the invention adopts a triangular mesh to express, the simplest expression method of the triangular mesh is to store a single triangular patch in a set, and some data exchange formats use the expression form as a basic characteristic. The STL format is the most common data format for existing representation triangulated mesh, supporting both binary and ASCII code formats. Compared with other data files, the main advantages of such files are the simplicity of data format and good cross-platform performance, and various types of spatial curved surfaces can be output. The triangular mesh model is a piecewise linear curved surface formed by connecting vertexes and edges in a three-dimensional space, wherein each edge is contained in two triangles at most, and the triangular mesh represents a typical description: (V, K), where V denotes the mesh shape defined by the geometric position of the set of points in three-dimensional space; k is a simple complex shape, expresses a connection relation of points, edges and surfaces, and determines the topology type of the grid.

In order to clearly show connectivity of a mesh, vertex and related data overlap and to clearly show topological relation of a midpoint, an edge and a face of an STL triangular mesh model, a half-edge data structure is adopted, each edge of a triangular patch is divided into two directed half edges in opposite directions, the half edge which conforms to the right-hand spiral direction according to a normal vector belongs to the current triangular patch, each triangular patch is composed of 3 directed half edges, and the connection relation of the face and the face is established through pointers of the adjacent half edges of the topological half edges.

The invention provides a 3D printing path planning method facing a curved surface cladding porous lightweight structure, which is characterized in that an STL format model is converted into a triangular plate model mesh, a slicing theory is adopted, firstly, a curved surface is segmented to separate a required curved surface from the surface of a workpiece, a 0-layer segmented curved surface is arranged, the distance between the ith cladding surface and i-1 cladding surfaces is a constant s, and cladding is arranged from the 1 st layer. And fitting the curved surface into a plane by adopting a slicing theory, and constructing a group of plane slice family cladding curved surfaces with the thickness of 0 and the direction vertical to the track to obtain a series of parallel section curves to form a cladding track.

Based on a complex curved surface of a triangular mesh, the invention provides a 3D printing path planning method facing a curved surface cladding porous lightweight structure by adopting an STL data format, and the specific process is as follows: firstly, the curved surface is divided, namely, the area to be divided is separated from the surface of the workpiece by adopting the existing curved surface dividing method. And secondly, assuming that the cladding surface of the 0 th layer is the divided curved surface, the distance between the ith cladding surface and the (i-1) th cladding surface is a constant s, and cladding starts from the cladding surface of the 1 st layer. Thirdly, fitting the cladding curved surface into a plane pi, and taking a direction n on the plane pi₀. Fourthly, for the ith cladding surface, the cladding path width d can be set by referring to but not limited to the diameter of the cladding nozzle. Then a series of intervals d and normal vector directions n are constructed₀The cladding curved surface is cut by the parallel plane to obtain a row of parallel section curves. And fifthly, adjusting by adopting a segmentation adjustment method, adjusting the distance between the jth curve and the jth curve on the curved surface by taking the jth-1 section curve as a reference on the curved surface, so that the distance between the jth curve and the jth curve is d, and assuming that the 0 th section curve is fixed. Sixthly, taking a direction n on the plane II₁，n₀And n₁Are perpendicular to each other. Then change the direction to n₁And repeating the operations of the fourth step and the fifth step. And seventhly, increasing the value of the layer number i by 1 and continuing cladding. For the above operation steps, the user can adjust the path distance d, and set a smaller interface curve distance, i.e. the cladding path width d, for the first k cladding layers and the last k cladding layers so as to increase or decrease the adhesion degree of the cladding layers and the matrix layer and the attractive layer degree of cladding, whereinA larger cladding layer path width is provided therebetween so as to form a porous structure.

Drawings

FIG. 1 is a three-dimensional point cloud representation; FIG. 2 is a three-dimensional mesh representation; FIG. 3 is a flow chart of curved surface segmentation; FIG. 4 illustrates several layers of cladding surfaces; FIG. 5 is a surface fit to a plane; FIG. 6 is a series of n₀Intercepting a cladding curved surface by a directional slice family; FIG. 7 shows n₀A cladding path generated by directional slicing; FIG. 8 is a graph of the sum of n₀N in a vertical direction₁Direction; FIG. 9 is a series of n₁Intercepting a cladding curved surface by a directional slice family; FIG. 10 is n₁A cladding path generated by directional slicing; FIG. 11 illustrates several cladding paths; FIG. 12 is a path planning procedure; FIG. 13 is a path of X-direction slice generation; FIG. 14 is a path of Y-direction slice generation; fig. 15 is a two-layer cladding curved surface path; FIG. 16 is a porous lightweight structure; fig. 17 shows a porous lightweight structure.

Detailed Description

In order to achieve the purpose of cladding on a curved surface to achieve a porous lightweight structure, the invention provides an effective path planning method, which adopts the following technical scheme:

firstly, a curved surface is segmented, namely, an area to be segmented is separated from the surface of a workpiece by adopting the existing curved surface segmentation method. The process of segmenting the mesh surface mainly comprises six parts: firstly, carrying out topology reconstruction on the STL model, converting the STL model into a half-edge data structure, and establishing topology information. And secondly, carrying out sub-region division, and dividing the model into a plurality of sub-regions by identifying the characteristic edges of the model. And thirdly, generating control points of the boundary of the sub-regions, and simplifying subsequent grid splicing. And fourthly, reducing the dimensions of the sub-regions, mapping the three-dimensional sub-regions into two-dimensional regions, and generating two-dimensional grids. And fifthly, reflecting the two-dimensional grids to a three-dimensional space, and completing the grid division of the three-dimensional sub-area. And sixthly, combining the meshes of all the sub-regions to obtain a final mesh curved surface. The specific flow is shown in fig. 3.

And secondly, assuming that the cladding surface of the 0 th layer is the divided curved surface, the distance between the ith cladding surface and the (i-1) th cladding surface is a constant s, and cladding starts from the cladding surface of the 1 st layer. As shown in fig. 4, there are several layers of cladding curved surfaces.

Thirdly, fitting the cladding curved surface into a plane pi, and randomly selecting one direction n on the plane pi₀，n₀And the cladding curved surface is positioned on the plane pi and is vertical to the normal vector direction of the plane pi, so that a reference coordinate system related to the plane pi is obtained, the position and the direction of the plane pi are determined, and the plane fitting of the cladding curved surface is realized by a least square method. The least squares approach brings the fitted object closer to the final object by minimizing the sum of the squares of the errors. The fusion covering curved surface is discretized into triangular surface patches, each triangular surface patch is provided with three vertexes, coordinates of a series of space discrete points are obtained, the space discrete points are fitted into a plane, the optimization process is achieved, the plane is found, the Euclidean distance from all data points to the fitting plane is the minimum, and the problem that the distance from the points to the fitting plane is the minimum is solved. Knowing a priori, that is, the mean value of a large number of discrete points of a fitted plane, requires finding the normal vector of the plane. According to SVD transformation of the covariance matrix, the singular vector corresponding to the minimum singular value is the normal direction of the fitting plane. And solving a fitting plane by using SVD (singular value decomposition), wherein the principle of the SVD is as follows:

1. knowing coordinates (x) of several three-dimensional points_i,y_i,z_i) The fitting plane equation is set as ax + by + cz-e (1) and the constraint condition is a²+b²+c²＝1 (2)

The goal is to have as many points as possible on a plane that minimizes the sum of the distances of all points.

2. All points have an average coordinate of

Constructing equations

3. By subtracting the formula (1) and the formula (3), the product can be obtained

4. Hypothesis matrix

Column matrix

Then formula (4) is equivalent to AX 0 (5)

5. Ideally, all points are on a plane, and equation (5) holds; in practical situations, some points are out of plane, the fitting aims at the distance from the plane to all points as small as possible, so that the target function is min | | AX | (6) the constraint condition is | | | X | | | | | | (1 (7))

If A can be singular value decomposed: a ═ UDV^TWhere D is a diagonal matrix and U and V are both unitary matrices. Then AX | | | | UDV^TX||＝||DV^TX|| (9)

Wherein V^TX is a column matrix, and | | | V^TX||＝||X||＝1 (10)

Since the diagonal elements of D are singular values, the last diagonal element is assumed to be the smallest singular value, if and only if

When the value of the equation (9) is the minimum value, the equation (6) is satisfied. At this time

Therefore, the optimal solution of the objective function (6) under the constraint condition (7) is X ═ a, b, c ═ v_n,1,v_n,2,v_n,3) In summary, (13) when singular value decomposition is performed on the matrix a, the eigenvector corresponding to the smallest singular value is the coefficient vector of the fitting plane. As shown in fig. 5, the surface is fitted to a plane using the least squares method.

Fourthly, for the ith cladding surface, the cladding path width d can be set by referring to but not limited to the diameter of the cladding nozzle. Then a series of intervals d and normal vector directions n are constructed₀The parallel planes of the cladding curved surface are cut off, and the series of planes are flatThe row plane is the slice family and d is the distance between slice layers, as shown in fig. 6. The slices in the slice group and the triangular meshes of the cladding curved surface generate intersection points, and a series of parallel section curves can be obtained by connecting the intersection points in sequence. The direction of the slice is vertical to the cladding surface, and the direction of the generated slice family is the moving direction of the spray head. In the third step, the direction n has already been defined₀，n₀I.e. the direction of the slice family. To be convenient and feasible, a fixed one of the coordinate axes is usually defined as the direction of the slice family.

Fifthly, because the cladding surface is a curved surface, the distances between section curves obtained by cutting the cladding surface by using a slice group with the constant distance d in a fixed direction may be different, and the distances between a series of parallel section curves obtained are not necessarily d, the distances between the section curves are adjusted by adopting a segmentation adjustment method, so that the distances between the section curves are d. And (3) adjusting the distance between the jth section curve and the jth-1 section curve on the curved surface by taking the jth-1 section curve as a reference on the curved surface so that the distance between the jth section curve and the jth-1 section curve is d, and assuming that the 0 th section curve is fixed. The distance between each adjusted section curve is d, and n is generated₀The cladding path resulting from the directional slicing is shown in fig. 7.

Sixthly, taking another direction n on the plane II₁So that n is₁And n₀Perpendicular to each other as shown in fig. 8. Then changing the orientation of the slice family to n₁Repeating the fourth and fifth steps on the next cladding layer to obtain a series of parallel section curves in the other direction, and generating a cladding path in the other direction by adjusting the distance between the section curves in a segmented manner, as shown in fig. 9 and 10.

And seventhly, increasing the value of the layer number i by 1 and continuing cladding. For the above operation steps, the user can adjust the path distance d, set a smaller section curve distance for the first k cladding layers and the last k cladding layers so as to increase or decrease the adhesion degree of the cladding layers and the matrix layer and the aesthetic layering degree of cladding, and set a larger cladding path width for the middle cladding layer so as to form a porous structure. FIG. 11 shows the formation of several layers of cladding paths, and the distance d between the paths can be freely adjusted to form a porous lightweight structure.

A flowchart of the steps of the overall process is shown in fig. 12.

By the method for planning the cladding path of the curved surface, the cladding path is successfully planned on the curved surface, the required cladding path can be successfully generated, the width d of the cladding path and the distance s between the cladding curved surfaces can be freely changed according to the different sizes of cladding nozzles, and the number of layers of the cladding layer can be controlled according to the requirements.

The free-form surface is clad by the path planning method of the invention, assuming that the total number of clad layers is 2, fig. 13 is a diagram for planning the path of the surface of the first clad layer, setting the direction of the slice family as the X direction of the fixed coordinate axis, cutting a series of slice planes with the normal vector direction as the X axis direction to obtain a series of parallel section curves, adjusting the distance between the section curves by adopting a sectional adjustment method to ensure that the distance between the section curves is d, and then generating the clad path. And (3) performing cladding path planning on the second layer, changing the direction of the slice group, setting the direction of the other slice group to be vertical to the X axis, namely setting the direction to be the Y axis, and intercepting the cladding layer by using a series of slice planes with normal vector directions in the Y axis direction to obtain a series of parallel section curves to generate a cladding path in the other direction, as shown in fig. 14. The distance between a series of section curves is the cladding path width d, and can be freely adjusted. The distance between the two cladding layers is the interlayer thickness s, which can be freely adjusted, as shown in fig. 15, for a two-layer cladding curved surface path.

The invention relates to a 3D printing path planning method facing a curved surface cladding porous lightweight structure, which can generate the porous lightweight structure as required and freely adjust the space between cladding layers, namely the interlayer thickness s and the path width D on a single cladding layer. For the first k cladding layers and the last k cladding layers, slicing in multiple directions is carried out on the same cladding layer, a smaller section curve interval, namely the cladding path width d, is set, and multiple-direction cladding paths are generated, so that the adhesion degree of the cladding layers and the matrix layers and the attractive layering degree of cladding are increased and decreased. In the same way for the intermediate cladding layer, a larger cladding path width d is set in order to form a porous structure.

As shown in fig. 16 and 17, the path is a cladding path cladding on a cylindrical surface, and assuming that the total number of cladding layers is m, the spacing between the cladding layers is a constant s. Setting a smaller cladding path width d for the front k layers, wherein the cladding path directions between the layers are different and coexist in two directions: the first is along the axis of the cylinder and the second is along the circumferential direction of the cylinder. Cladding is carried out alternately in cladding paths in two directions, and the adhesion degree with a matrix layer is increased. Starting from the (k + 1) th layer, setting a larger cladding path width d, wherein the cladding path directions between the layers are different, and the cladding paths coexist in two directions: the first is along the axis of the cylinder and the second is along the circumferential direction of the cylinder. Cladding is carried out alternately on cladding paths in two directions until cladding is finished to the k + t layer, the t layers are counted, the interlayer spacing is constant s, a porous structure is formed, and the purposes of light weight, material saving and redundant material containing are achieved. From the (k + t + 1) th layer, setting a smaller cladding path width d, wherein the cladding path directions between the layers are different and coexist in two directions: the first is along the axis of the cylinder and the second is along the circumferential direction of the cylinder. Cladding is carried out alternately on cladding paths in the two directions until the cladding is finished to the mth layer, the distance between the layers is constant s, and the attractiveness of cladding is improved.

Claims

1. A3D printing path planning method of a curved surface cladding porous lightweight structure is characterized by comprising the following steps:

step 1: separating a cladding area from a workpiece surface area, wherein the cladding area comprises a plurality of layers of cladding curved surfaces, and the 0 th layer of cladding curved surface is the workpiece surface;

step 2: fitting the cladding curved surface into a plane pi, and taking two mutually perpendicular directions n on the plane pi₀And n₁；

And step 3: for the cladding surface of the adjacent layer, the normal vector direction is n₀And n₁Cutting and cladding curved surface of the slice group, and cutting and cladding curved surfaceThe crossing points are connected to obtain a series of parallel section curves;

and 4, step 4: adjusting the interval of the cross-section curves on the cladding curved surface to ensure that the interval between the adjacent cross-section curves is the width of the cladding path, wherein the adjusted cross-section curve is the cladding path of the cladding curved surface;

n in step 2₀The vector is positioned on the plane pi and is vertical to the normal vector direction of the plane pi;

in the step 3, the distance between adjacent slices in the slice family is the width of a cladding path;

in the step 2, a least square method is used for fitting the cladding curved surface into a plane pi;

and the section curve interval of the front k-layer cladding curved surface and the last k-layer cladding curved surface is smaller than that of the middle-layer cladding curved surface, and the k value is set according to the requirement.