A design method for gradient hollow filling structure suitable for additive manufacturing

Abstract

A design method for gradient hollow-filled structures suitable for additive manufacturing is disclosed. This method divides the original two-dimensional filling region into multiple triangular mesh regions, determines the corresponding scalar field, and performs expansion deformation on the original two-dimensional filling region according to the defined scalar field, establishing a one-to-one mapping relationship between the original two-dimensional filling region and any position in the expanded region. A uniform hollow-filling pattern is designed in the expanded region, and the density of the hollow-filling pattern is controlled by setting its length parameter. Based on the established mapping relationship, an inverse mapping operation is performed on the uniform hollow-filling structure filling the expanded region to obtain a gradient-filled non-uniform hollow-filling structure in the original two-dimensional filling region. The structure generated by this invention, under the same material conditions, can effectively improve the load-bearing performance compared to uniform hollow filling.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing optimization technology, specifically to a design method for a gradient hollow filling structure suitable for additive manufacturing. Background Technology

[0002] Hollow-filled structures, such as honeycomb structures, are widely used in aerospace and other fields with extreme lightweight requirements. In recent years, the development of additive manufacturing technology has provided new solutions for the design and fabrication of complex hollow-filled structures. Traditional hollow-filled structures typically use uniform grids, such as hexagonal honeycomb structures and square grids. While uniform grid structures are simple, their load-bearing capacity is often poor, and material utilization is low. Gradient grids can effectively solve this problem by adaptively increasing the density of the filling grid in critical load-bearing areas and rationally decreasing the density of the filling structure in non-load-bearing areas, thus effectively balancing requirements for lightweighting, load-bearing capacity, and shape preservation. However, existing technologies mostly rely on experience or manual methods to design gradient-filled structures, lacking automated design methods that can quantitatively control the grid filling density. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a design method for a gradient hollow-filled structure suitable for additive manufacturing. The structure generated by this invention can effectively improve the load-bearing performance of the structure compared to uniform hollow filling, under the same material conditions.

[0004] To achieve the above technical objectives, the adopted technical solution is: a design method for a gradient hollow-filled structure suitable for additive manufacturing, comprising the following steps:

[0005] Step 1: Given a two-dimensional original filling region, divide the two-dimensional original filling region into multiple triangular mesh regions, and determine the scalar field representing the gradient filling structure density of each triangular mesh region based on topology optimization.

[0006] Step 2: Perform expansion deformation on the two-dimensional filled region according to the determined scalar field. The degree of expansion in the neighborhood of any position in the original two-dimensional filled region is positively correlated with the scalar field defined at that location. At the same time, establish a one-to-one mapping relationship between any position in the original two-dimensional filled region and the expanded region.

[0007] Step 3: Design a uniform hollow filling pattern in the expansion area, and adjust the density of the hollow filling pattern by setting the length parameter of the hollow filling pattern.

[0008] Step 4: Perform an inverse mapping operation on the uniform hollow filling pattern of the expanded region based on the established mapping relationship to obtain a gradient-filled non-uniform hollow filling structure in the original two-dimensional filling region. The specific implementation method is as follows:

[0009] Step 4.1: For any point p on the uniformly hollow-filled pattern of the expansion region... e A kd-tree search can be used to find the distance p in the dilated region. e The nearest triangular mesh region f i ;

[0010] Step 4.2, Distance p e The nearest triangular mesh region f i The vertex coordinates are respectively Calculate point p using formula (1) e Relative to vertex area weight The specific calculations are as follows:

[0011]

[0012] Step 4.3, Triangular mesh region f i The vertex coordinates in the original two-dimensional filled region are: With p e The corresponding point is p n The calculation can be performed using formula (2), and the specific calculation is as follows:

[0013]

[0014] Step 4.4: Based on the mapping equation (2) in step 4.3, calculate all points in the filling pattern. Then, the uniform filling pattern planned in the expansion region in step 3 is mapped to the original filling region to form a non-uniform gradient hollow filling pattern.

[0015] The specific implementation steps of step 2 of this invention are as follows:

[0016] Step 2.1: Based on the scalar field defined on each triangular mesh region, define two mutually orthogonal vectors p on each triangular mesh region. i and q i ;

[0017] Step 2.2: Assume the coordinates of the i-th vertex of the expanded filling region are... Then the gradient of the coordinates of the three vertices of each triangular mesh region should be equal to p. i or q i This can be expressed as formula (3), and the specific calculation is as follows:

[0018]

[0019] Where i, j, and k are the indices of the vertices of the l-th triangular mesh region, and m is the total number of triangular mesh regions in the original two-dimensional filled region;

[0020] Step 2.3: Further transform formula (3) into matrix form formula (4), and the specific calculation is as follows:

[0021]

[0022] Among them, A 2m×n It is the gradient matrix, 2m >> n. n is the total number of vertices in the triangular mesh region;

[0023] Step 2.4, Calculate the solution φ of the system of equations (4). p and φ q The least squares solution of the system of equations is calculated using formula (4), and the specific calculation is as follows:

[0024]

[0025] Ultimately, φ p and φ q This forms an expanding filling region, the degree of which is positively correlated with the scalar field.

[0026] This invention uses two mutually orthogonal vectors p i and q i The calculation method is as follows:

[0027]

[0028] Where λ is a user-defined expansion coefficient, exp(λρ) i The value of ) represents the expansion size of the i-th triangular mesh region; m is the total number of triangular mesh regions in the original two-dimensional filled region, ρ i Let represent the scalar field of the i-th triangular mesh region.

[0029] The beneficial effects of this invention are:

[0030] (1) Users can quantitatively control the density of gradient hollow filling by defining the density field, adjusting the side length of the filling pattern and adjusting the expansion coefficient.

[0031] (2) The non-uniform hollow filling structure designed by the gradient grid filling structure design method has better mechanical properties and enhanced load-bearing capacity than the uniform filling structure under the same filling rate. Attached Figure Description

[0032] Figure 1 This is a flowchart of the technical solution of the present invention;

[0033] Figure 2 The original two-dimensional filling area of ​​this invention is divided into multiple triangular grid areas.

[0034] Figure 3 This is a diagram illustrating the generation process of the gradient-filled structure of the present invention;

[0035] Figure 4 To adopt Figure 1 The technical solution in the diagram verifies the influence of the expansion coefficient and grid side length on the grid density.

[0036] Figure 5 Comparison of printed samples from force-displacement experiments;

[0037] Figure 6 for Figure 4 Relevant parameter diagrams for the printed sample;

[0038] Figure 7 A diagram of a three-point bending mechanics experiment for a printed sample;

[0039] Figure 8 For is Figure 5 Force-displacement comparison diagram of the sample undergoing a three-point bending mechanical test. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0041] This invention discloses a design method for gradient hollow infill structures suitable for additive manufacturing. This method, for a given infill region and a scalar field indicating the infill density, allows for quantitative control of the infill density of the structure by adjusting relevant parameters. The structure generated by this invention, using the same materials, effectively improves the load-bearing capacity compared to a uniform grid.

[0042] like Figure 1 As shown, the present invention discloses a design method for a gradient hollow-filled structure suitable for additive manufacturing, which mainly includes the following steps:

[0043] Step 1: Given a 2D original filled region, divide the 2D original filled region into multiple triangular mesh regions, such as... Figure 2 As shown, each triangular mesh region has a scalar field representing the gradient-filled structure density as input. Specifically, it includes the following steps:

[0044] (11) Given a two-dimensional original filled region, divide it into multiple triangular mesh regions, such as Figure 2As shown, it can be represented by a triangular mesh M(V,F), where V and F represent the set of vertices and triangular faces, respectively.

[0045] (12) Under a certain working condition, topology optimization design is performed on the original two-dimensional filling region. In this example, a simply supported beam structure is selected, and the midpoint of the top of the workpiece is subjected to a concentrated load. Based on the results of the topology optimization, a scalar field representing the gradient filling structure density ρ∈[0,1] corresponding to each triangular mesh region is obtained, for example, such as Figure 3 As shown in (a), the yellow color has a high density, close to 1, while the blue color is close to 0.

[0046] Step two: The original filled region is subjected to expansion deformation processing based on the scalar field to construct the expanded filled region. The calculation results are as follows: Figure 3 As shown in (b), the specific steps include the following:

[0047] (21) Based on the scalar field defined on each triangular mesh region, define two mutually orthogonal vectors p on each triangular mesh region. i and q i It is calculated using formula (1), which is as follows:

[0048]

[0049] Where λ is the expansion coefficient, which can be defined by the user. For the correlation between the expansion coefficient and the density of the fill, please refer to [reference needed]. Figure 4 ;exp(λρ i The value of ) represents the expansion size at the i-th triangular mesh region; ρ i represents the scalar field of the i-th triangular mesh region; m is the total number of triangular mesh regions in the filled region.

[0050] (22) Assume the coordinates of the i-th vertex of the expanded filling region are Then the gradient of the coordinates of the three vertices of each triangular mesh region should be equal to p. i or q i This can be expressed as formula (2), which is as follows:

[0051]

[0052] Where i, j, and k are the indices of the l-th triangle vertex, and m is the total number of triangular mesh regions in the filled region.

[0053] (23) To facilitate the calculation of the vertex coordinates of the expanded filling region, formula (2) is further transformed into matrix form, as shown in formula (3). Formula (3) is as follows:

[0054]

[0055] Among them, A 2m×n It is the gradient matrix. m is the total number of triangular mesh regions in the filled area, and n is the total number of vertices of the triangular mesh regions.

[0056] (24) Calculation formula (3) Solution φ of the system of equations p and φ q In formula (3), 2m >> n is usually an inconsistency matrix. Therefore, the least squares solution of the system of equations can be calculated using formula (4), which is as follows:

[0057]

[0058] Ultimately, φ p and φ q This forms an expanded filling region, and the degree of expansion is positively correlated with the filling density.

[0059] Step 3: Design a uniform hollow filling pattern in the expansion area, as shown in the following figure. Figure 3 As shown in (c), the hollow fill pattern can be defined by the user, including but not limited to grid structures, honeycomb structures, etc. Users can adjust the density of the hollow fill pattern by setting the hollow fill pattern length parameter. The correlation between the hollow fill pattern length parameter and the fill density is shown in [reference needed]. Figure 4 .

[0060] Step four: Perform an inverse mapping operation on the uniformly hollow-filled pattern filling the expansion region to obtain a gradient-filled, non-uniformly hollow-filled structure, such as... Figure 3 As shown in (d), the specific steps include the following:

[0061] (41) For any point p on the uniformly filled pattern of the expansion region e A kd-tree search can be used to find the distance p in the dilated region. e The nearest triangular mesh region f i .

[0062] (42) Distance p e The nearest triangular mesh region f i The vertex coordinates in the expansion region are respectively Point p can be calculated using formula (3) and formula (5). e Relative to vertex area weight Formula (5) is as follows:

[0063]

[0064] (43) Triangular mesh region f in the two-dimensional original filled region i The vertex coordinates are The coordinates of the vertices of the originally divided triangular mesh region are p. e The corresponding point is p n The calculation can be performed using formula (6), which is as follows:

[0065]

[0066] (44) Based on the mapping equation (6) in step (43), all points in the filling pattern are calculated, and the uniform filling pattern planned in the expansion region can be mapped to the original filling region to form a non-uniform gradient filling pattern.

[0067] Furthermore, to verify the beneficial effects of the technical solution proposed in this invention, the following comparative experiments were conducted:

[0068] (1) Users can quantitatively control the density of the gradient grid by defining a scalar field, adjusting the side length of the fill pattern and adjusting the expansion coefficient.

[0069] like Figure 4 As shown, different grid side lengths and expansion coefficients were set, and the correlation between the expansion coefficient and the fill density was verified through simulation comparison. The simulation comparison results show that in the design method disclosed in this invention, the fill rate is negatively correlated with the grid side length parameter and positively correlated with the expansion coefficient parameter. Therefore, users can independently set the fill density by adjusting parameters such as grid side length and expansion coefficient.

[0070] (2) The non-uniform grid structure designed using the gradient grid filling structure design method described above has better mechanical properties than the uniformly filled grid structure under the same filling rate.

[0071] like Figure 5 , Figure 6 As shown, by adjusting design parameters such as pattern side length and expansion coefficient, several experimental sample structural designs with different densities were created. Corresponding non-uniform infill samples were then printed using 3D printing technology. Figure 6 As shown in (b)(d)(f). Simultaneously, a uniformly distributed grid structure with a material filler mass ratio approximately equal to that of the non-uniformly filled structure was designed, and a corresponding uniformly filled sample was printed using 3D printing technology, such as... Figure 6 As shown in (a)(c)(e). Then, three-point bending mechanics tests were conducted on the non-uniformly infilled and uniformly infilled samples, as follows: Figure 7 As shown in the figure. The final result is a comparison of the corresponding force-displacement curves, as shown in the figure. Figure 8 As shown. From Figure 8As can be seen, the non-uniform grid structure designed using the gradient grid filling structure design method described in this invention has significantly improved stiffness and load-bearing capacity compared to a uniformly filled grid structure.

[0072] This invention discloses a design method for gradient hollow-filled structures suitable for additive manufacturing. This method, for a given filling region and a scalar field indicating the grid filling density, allows for quantitative control of the grid filling density by adjusting relevant parameters. The structure generated by this invention, using the same materials, effectively improves the load-bearing performance compared to a uniform grid.

[0073] The above are merely preferred embodiments of the present invention and are not intended to limit or restrict the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection declared by the present invention.

Claims

1. A design method for a gradient hollow-filled structure suitable for additive manufacturing, characterized by: Includes the following steps: Step 1: Given a two-dimensional original filling region, divide the two-dimensional original filling region into multiple triangular mesh regions, and determine the scalar field representing the gradient filling structure density of each triangular mesh region based on topology optimization. Step 2: Perform expansion deformation processing on the two-dimensional filling region according to the determined scalar field. The degree of expansion in the neighborhood of any position in the original two-dimensional filling region is positively correlated with the scalar field defined at the position. At the same time, establish a one-to-one mapping relationship between the original two-dimensional filling region and any position in the expansion region. The specific implementation method of step 2 is as follows: Step 2.1: Based on the scalar field defined on each triangular mesh region, define two mutually orthogonal vectors on each triangular mesh region; Step 2.2, assuming the expansion filling region is... Given the coordinates of the three vertices, the gradient of the coordinates of the three vertices in each triangular mesh region should be equal to the two mutually orthogonal vectors defined. Step 2.3: Convert the equation relationship between the gradient of the three vertex coordinates of each triangular mesh region described in Step 2.2 and the two defined mutually orthogonal vectors into matrix form; Step 2.4: Calculate the solution to the system of equations in matrix form. and By calculating the least squares solution of the system of equations, the final and This forms an expanding, filling region, the degree of which is positively correlated with the scalar field. Step 3: Design a uniform hollow filling pattern in the expansion area, and adjust the density of the hollow filling pattern by setting the length parameter of the hollow filling pattern. Step 4: Perform an inverse mapping operation on the uniform hollow filling pattern of the expanded region based on the established mapping relationship to obtain a gradient-filled non-uniform hollow filling structure in the original two-dimensional filling region. The specific implementation method is as follows: Step 4.1: For any point on the uniformly hollow-filled pattern in the expansion region... Distance can be found in the dilated region using a kd-tree search. The nearest triangular grid area ; Step 4.2, Distance The nearest triangular grid area The vertex coordinates are respectively The point is calculated using formula (1). Relative to vertex area weight The specific calculations are as follows: Step 4.3, Triangular Mesh Area The vertex coordinates in the original two-dimensional filled region are: ,and The corresponding points are The calculation can be performed using formula (2), and the specific calculation is as follows: Step 4.4: Based on the mapping equation (2) in step 4.3, calculate all points in the filling pattern. Then, the uniform filling pattern planned in the expansion region in step 3 is mapped to the original filling region to form a non-uniform gradient hollow filling pattern.

2. The design method for a gradient hollow infill structure suitable for additive manufacturing as described in claim 1, characterized in that: The specific implementation steps of step 2 are as follows: Step 2.1: Based on the scalar field defined on each triangular mesh region, define two mutually orthogonal vectors on each triangular mesh region. and ; Step 2.2, assuming the expansion filling region is... The coordinates of the vertices are Then the gradient of the coordinates of the three vertices of each triangular mesh region should be equal to or This can be expressed as formula (3), and the specific calculation is as follows: in, , and It is the first The indices of the vertices of a triangular mesh region. It is the total number of triangular mesh regions in the original two-dimensional filled region; Step 2.3: Further transform formula (3) into matrix form formula (4), and the specific calculation is as follows: in, It is the gradient matrix. , , This represents the total number of vertices in the triangular mesh region. Step 2.4: Calculate the solution of the system of equations (4). and The least squares solution of the system of equations is calculated using formula (5), and the specific calculation is as follows: final, and This forms an expanding, filling region, the degree of which is positively correlated with the scalar field.

3. The design method for a gradient hollow-filled structure suitable for additive manufacturing as described in claim 2, characterized in that: Two mutually orthogonal vectors and The calculation method is as follows: in, For a custom expansion coefficient, The value represents the first The expansion size of each triangular grid region; It is the total number of triangular mesh regions in the original two-dimensional filled region. Indicates the first scalar field of a triangular grid region.

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