Processing path-based lattice structure performance homogenization calculation method

Abstract

The invention relates to a lattice structure performance homogenization calculation method based on a processing path. The lattice structure performance homogenization calculation method comprises the following steps: constructing a track morphology field based on bounding box size information of lattice cells, processing path information and a processing path process database; carrying out pixel / voxelization on the bounding box of the lattice cells; calculating the area / volume fraction of the unit based on the function value of each node in the trajectory morphology field, and obtaining a finite element grid after screening; the processing path is used as input, so that tedious model format conversion, curved surface subdivision and line cluster intersection operation are avoided; the finite element grids are numbered, and material attributes of units are calculated according to an SIMP mode to construct a finite element grid topological relation; a grid containing an area fraction is used as a homogenization representative volume unit, under the loading condition of considering six unit strain inputs, microscopic strain is substituted into a homogenization integral formula, and a macroscopic equivalent elastic tensor is calculated, so that the convergence speed and precision can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, and more specifically to a method for calculating the uniformity of performance of lattice structures based on processing paths. Background Technology

[0002] Additive manufacturing technology offers unprecedented freedom in the design of lattice structures. When performing macroscopic predictions on additively manufactured lattice structures, existing technologies employ homogenization methods to calculate the equivalent performance of lattice material elements in order to reduce the complexity of finite element simulations. However, existing methods often focus on optimizing the lattice topology while neglecting the coupling effect of the processing path on structural performance, leading to deviations between the geometric characteristics of the formed structure and its actual performance. Furthermore, due to the complexity of lattice structures, finite element simulations require the generation of numerous meshes and the solving of these meshes, resulting in low efficiency and high computational costs. Additionally, existing homogenization methods all require first constructing a geometric model of the lattice structure and then discretizing the mesh through voxelization or binarization, leading to lengthy processes, low boundary accuracy, and difficulty in directly reflecting the actual morphological features introduced by the processing path during additive manufacturing. Therefore, a processing path-based homogenization calculation method for lattice structure performance is urgently needed to address these issues. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the uniformity of the performance of lattice structures based on processing paths. By directly designing the processing path of the lattice structure instead of its geometric model, this method solves the problems of geometric distortion and lengthy processes in existing methods, and enables the prediction of the performance of lattice structures.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for calculating the performance uniformity of a lattice structure based on the processing path, comprising the following steps: S1. Construct a trajectory topography field based on the bounding box size information, processing path information, and processing path technology database of lattice cells; S2. Pixelate / voxelize the bounding box of the lattice cells; S3. Calculate the area / volume fraction of the element based on the function value of each node in the trajectory topography field, and obtain the finite element mesh after filtering. S4. Number the finite element mesh, and calculate the material properties of the elements according to the SIMP method to construct the finite element mesh topology. S5. Using the mesh containing area fraction as the homogenized representative volume element, and considering the loading conditions of six unit strain inputs, the micro-strain is substituted into the homogenized integral formula to calculate the macroscopic equivalent elastic tensor.

[0005] Preferably, in S1, the topography field mesh is initialized based on the bounding box size information; the trajectory shape parameters and process parameters in the processing path information are extracted; and the molten pool shape function is constructed based on the processing path process database.

[0006] Preferably, the trajectory shape parameters include the molten pool width, molten pool penetration depth, molten pool spherical height, and spherical radius; the process parameters include the laser power P and the scanning speed v.

[0007] Preferably, in S2, the bounding box region of the lattice cells with quadrilateral / hexahedral mesh size is pixelated / voxelized.

[0008] Preferably, in S3, the largest single connected component in the pixel / voxel structure is retained in the pixel / voxel unit where the area / volume fraction is not zero.

[0009] Preferably, the finite element mesh is numbered with element numbers, local node numbers, and node numbers in the global coordinate system.

[0010] Preferably, the finite element mesh topology is constructed using the SIMP method, and the calculation formula is as follows: ; in, Let e ​​be the Young's modulus. This is the area fraction or volume fraction of unit e. The Young's modulus of the unit raw material. Young's modulus constant It is a punishment factor.

[0011] Beneficial effects: This invention designs the processing path of the lattice structure directly, rather than its geometric model; it avoids cumbersome model format conversion, surface subdivision, and intersection operations of line clusters; and it does not require the construction of a geometric model of the lattice, but directly establishes a quadrilateral or hexahedral mesh model of the lattice from the implicit field for finite element analysis; in addition, when performing homogenization calculations on lattice cells, this invention uses the SIMP method, which effectively improves the convergence speed and accuracy. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method for calculating the uniformity of performance of a lattice structure based on the processing path according to the present invention. Figure 2 This is a finite element mesh diagram of the lattice cells in an embodiment of the present invention; Figure 3 This is a diagram illustrating the impact of pixel / voxel resolution on the equivalent mechanical properties of lattice cells in an embodiment of the present invention. Figure 4This diagram shows the typical three shape function sign values ​​for the four vertices of unit e in an embodiment of the present invention. Detailed Implementation

[0013] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe a method for calculating the uniformity of lattice structure performance based on processing paths, or several specific implementation methods, and does not strictly limit the scope of protection specifically claimed by this invention.

[0014] Example: Figure 1 As shown, a method for calculating the performance uniformity of a lattice structure based on the processing path includes the following steps: Step 1: Construct a trajectory topography field based on the bounding box size information of the lattice cells, the machining path information, and the machining path process database; specifically, initialize the topography field mesh based on the bounding box size information; extract trajectory shape parameters and process parameters from the machining path information; and construct the melt pool shape function based on the machining path process database, including: Topographic field mesh initialization is essentially lattice cell initialization: constructing the bounding boxes of the lattice cells and initializing the mesh information of the space containing the lattice cells based on these bounding boxes; obtaining mesh accuracy. bounding box of lattice cells ; ; in, This represents the smallest point of the bounding box of the lattice cell. This represents the maximum point of the bounding box of the lattice cell, where x, y, and z represent the coordinates of the lattice cell along the x-axis, y-axis, and z-axis, respectively. The subscripts min and max indicate the minimum and maximum points on their respective coordinate axes. Initialize the mesh of the lattice cells: ; in, A three-dimensional mesh representing lattice cells. This represents a point in the i-th row, j-th column, k-th layer of the grid; The trajectory shape parameters include the molten pool width, molten pool penetration depth, molten pool spherical height, and spherical radius; the process parameters include laser power and scanning speed. Define the upper half of the molten pool as a spherical cap and the lower half as a paraboloid of revolution. The shape function of the molten pool is: ; in, This refers to the height of the spherical cap portion of the molten pool; Let the radius of the molten pool spherical cap be . This represents the height of the upper half of the molten pool. The coordinates of the current point. The point's molten pool region satisfies ; The width of the molten pool; The depth of the molten pool. The radius of the spherical cap. : ; First, the trajectory shape parameters are determined, and then the molten pool shape parameters are gradually constructed by solving the molten pool geometric parameters, thereby generating the trajectory topography field; Step 2: Pixelate / Voxelize the bounding box of the raster cell: Pixelate / Voxelize the bounding box region according to the bounding box size of the raster cell using a quadrilateral / hexahedral mesh size; Step 3: Calculate the area / volume fraction of the element based on the function value of each node in the trajectory topography field. In pixel / voxel elements where the area / volume fraction is not 0, only the largest single connected domain in the pixel / voxel structure is selected as the finite element mesh. Taking a two-dimensional dot matrix cell as an example, the specific method for calculating the area fraction of its pixel unit is as follows: According to the MS algorithm, the shape function values ​​of the four vertices of the 2D unit e are... There are 16 possible signs for the positive or negative sign of the integer part. For each of these 16 cases, the area fraction of the unit can be calculated. Examples are given below. Figure 4 The calculation results for the three cases are shown below. Black dots indicate that the value is greater than or equal to 0, meaning the point is within the lattice structure's solid domain; hollow dots indicate that the value is less than 0, meaning the point is outside the lattice structure's solid domain. The area fraction results for these three cases are shown in the following formula: ; In the formula, , and Corresponding to Figure 4 The area fraction of the unit under cases (a), (b), and (c); Step 4: Number the elements, local nodes, and nodes in the global coordinate system of the finite element mesh; The finite element mesh topology is constructed using the SIMP method, and the calculation formula is as follows: ; in, Let e ​​be the Young's modulus. This is the area fraction or volume fraction of unit e. The Young's modulus of the unit raw material. Young's modulus constant It is a punishment factor Step 5: Using the area fraction mesh as the homogenized representative volume element, and considering the loading conditions of six unit strain inputs, substitute the micro-strain into the homogenized integral formula to calculate the macroscopic equivalent elastic tensor: Based on asymptotic homogenization, the equivalent elastic tensor of a periodic lattice material composed of discrete units... This can be expressed as: ; In the formula, It is a locally varying elastic tensor that depends on the lattice elements. Material distribution in; It is the area (2D lattice) or volume (3D lattice) of a lattice cell. It is the strain of the initially defined macroscopic unit; The local strain is obtained by solving the linear elastic equation with y-periodicity, and the calculation formula is as follows; ; In the formula, This represents the virtual displacement field belonging to the y-periodic Sobolev functional space; in the implementation of finite element analysis, the lattice cell uses... The mesh is discretized from finite element units to compute the homogenized elastic tensor, which is the sum of integrals defined over the finite element region, and the strain tensor. The calculation formula is as follows: ; In the formula, It is the displacement field under the weak form of the equilibrium equation; For ease of calculation, the formula is modified to matrix form, as follows: ; First, use the strain-displacement matrix. The strain in the above formula is represented as... Thus, the homogenized elasticity matrix expressed in terms of displacement is obtained, as shown below: ; in,{ } is the displacement field with an initial given unit strain, { This is the auxiliary displacement field, strain-displacement matrix, obtained by solving problems with periodic boundary conditions in linear elastic equations. It is a matrix composed of derivatives of shape functions as elements. When the displacement has been determined, the homogenized elastic matrix... The terms can be represented as: ; In the formula, The element stiffness matrix, The formula is obtained through... The displacement information of each finite element is used to calculate the homogenized equivalent elastic tensor, where The displacement is unknown. In the implementation of the finite element method, this displacement is obtained by considering the following six unit strain input loading conditions; ; For a three-dimensional lattice material, its homogenized equivalent elastic tensor is a symmetric matrix with the following general form: .

[0015] In a specific case: BCC and Gyroid cells were selected, and homogenization was performed using NTopology software, with the results compared to those of the present invention; the results are shown in Table 1. Table 1 shows that for the BCC structure, the calculation results of the present invention and NTopology are consistent, with errors in all parameters within 3%, demonstrating the accuracy of the method. For the G structure, the results differ; the lattice cells constructed in the present invention are based on the actual processing path, while conventional methods are entirely based on geometric solutions. The homogenization equivalent results of conventional structures cannot represent the performance of real objects.

[0016] Table 1. Comparison of homogenized equivalent elastic tensors of BCC and Gyroid lattice cells in different software.

[0017] In one specific embodiment: Reference Figure 2 As shown, the dimensions of the two-dimensional lattice cell and the three-dimensional lattice cell are selected as follows: and The mesh resolution (i.e., lattice cell size / finite element size) was 20, 40, 60, 80, 100, 120, 150, and 200. Homogenization calculations were performed for these cases, and the results were statistically analyzed and compared with conventional binarization methods. The statistical results of the lattice cell homogenization analysis are as follows: Figure 3 As shown.

[0018] The results show that as the grid resolution increases, the various computational metrics gradually converge; Figure 3As can be seen in (a), for 2D lattice cells, all parameters calculated using the SIMP method begin to converge when the mesh resolution is 100. Although higher mesh resolutions lead to more accurate calculation results, the computation time increases. Therefore, based on the numerical analysis results, the mesh resolution for the remaining 2D lattice structure homogenization calculations in this invention is 100. Furthermore, although the calculation results using the binarization method also converge, their performance is far inferior to that of the SIMP method; from... Figure 3 As can be seen in (a), the area of ​​the lattice structure after discretization deviates from the original lattice structure area, and it cannot accurately handle the boundary of the model. However, the SIMP method can retain the accurate lattice structure area while fuzzily describing the boundary of the lattice model. Therefore, compared with the SIMP method, binarization has a poorer convergence speed. Figure 3 It can be observed that for 3D lattice cells, all parameters calculated using the SIMP method begin to converge when the mesh resolution is 80. To maintain consistency with the calculation of 2D lattice cells, the mesh resolution is set to 100 for the homogenization calculation of the remaining 3D lattice cells in this invention. Similar to the homogenization calculation of 2D lattice cells, the convergence speed of the SIMP method is better than that of the binarization method. Likewise, the volume of the lattice cells after binarization discretization deviates from the original lattice cell volume; only when the resolution is 150 or higher does the volume discretization result of binarization approach the result of the SIMP method.

[0019] The embodiments of the present invention have been described in detail above with reference to the examples. However, the present invention is not limited to the above embodiments. For those skilled in the art, after learning the contents described in the present invention, several equivalent changes and substitutions can be made without departing from the principle of the present invention. These equivalent changes and substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for calculating the performance uniformity of a lattice structure based on the processing path, characterized in that, Includes the following steps: S1. Construct a trajectory topography field based on the bounding box size information, processing path information, and processing path technology database of lattice cells; S2. Pixelate / voxelize the bounding box of the lattice cells; S3. Calculate the area / volume fraction of the element based on the function value of each node in the trajectory topography field, and obtain the finite element mesh after filtering. S4. Number the finite element mesh, and calculate the material properties of the elements according to the SIMP method to construct the finite element mesh topology. S5. Using the mesh containing area fraction as the homogenized representative volume element, and considering the loading conditions of six unit strain inputs, the micro-strain is substituted into the homogenized integral formula to calculate the macroscopic equivalent elastic tensor.

2. The method for calculating the uniformity of performance of a lattice structure based on processing path according to claim 1, characterized in that: In S1, the topography field mesh is initialized based on the bounding box size information; the trajectory shape parameters and process parameters in the machining path information are extracted; and the molten pool shape function is constructed based on the machining path process database.

3. The method for calculating the uniformity of performance of a lattice structure based on processing path according to claim 1, characterized in that: The trajectory shape parameters include the molten pool width, molten pool penetration depth, molten pool cap height, and cap radius; the process parameters include laser power P and scanning speed v.

4. The method for calculating the uniformity of performance of a lattice structure based on processing path according to claim 1, characterized in that: In S2, pixelation / voxelization is performed on bounding box regions of quadrilateral / hexahedral mesh-sized lattice cells.

5. The method for calculating the uniformity of performance of a lattice structure based on a processing path according to claim 4, characterized in that: In S3, the largest single connected component in the pixel / voxel structure is preserved in pixel / voxel units where the area / volume fraction is not zero.

6. The method for calculating the uniformity of performance of a lattice structure based on a processing path according to claim 5, characterized in that: The finite element mesh is numbered with element numbers, local node numbers, and node numbers in the global coordinate system.

7. The method for calculating the uniformity of performance of a lattice structure based on processing path according to claim 1, characterized in that: The finite element mesh topology is constructed using the SIMP method, and the calculation formula is as follows: ； in, Let e ​​be the Young's modulus. This is the area fraction or volume fraction of unit e. The Young's modulus of the unit raw material. Young's modulus constant It is a punishment factor.

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