Molten pool solidification interface simulation method for additive manufacturing and computer program

Abstract

The invention relates to the technical field of additive manufacturing, in particular to a molten pool solidification interface simulation method for additive manufacturing and a computer program. According to the molten pool area data, carrying out molten pool grid division on a molten pool area; the molten pool grid comprises a grid unit, a cell node, an edge node and a node node; obtaining a cellular score of the grid unit; determining a solid-liquid phase fraction of each node according to the cellular fraction; determining the solid-liquid phase fractions of the cell node and the edge node according to the solid-liquid phase fractions of the node; and determining a solidification interface of the molten pool area according to the solid-liquid phase fractions of the cell node, the edge node and the node node. According to the method, the molten pool solidification interface form in the DED forming process can be simulated under the condition of a large grid size, and the DED forming solidification microstructure can be analyzed and predicted in combination with temperature field data.

Description

Technical Field

[0001] The present application relates to the technical field of additive manufacturing, and particularly to a method for simulating a molten pool solidification interface for additive manufacturing and a computer program. Background Art

[0002] Direct energy deposition (DED) technology uses lasers, plasmas, arcs, electron beams, etc. as heat sources to generate a molten pool in the deposition area and move it quickly. Materials are fed into the high-temperature melting zone in the form of powder or wire, melted and solidified layer by layer, and accumulated layer by layer to finally form a part.

[0003] In direct energy deposition (DED) technology, the geometric profile of the molten pool, the area of the edge melting transition region, the depth, width, length, volume, cross-sectional area, and top surface area of the molten pool all affect the quality of the formed part. Appropriate molten pool solidification parameters and solidification interface morphology can reduce stress concentration, refine grains, and improve density.

[0004] In order to improve the quality and accuracy of parts prepared by direct energy deposition (DED) technology, the prior art conducts computer simulations on the solidification interface of the molten pool, and analyzes the grain forming process through the solidification interface obtained by the simulation.

[0005] Existing molten pool interface reconstruction algorithms isomorphicly construct a three-dimensional model of the molten pool and perform finite element analysis to simulate the solidification interface. In the solidification simulation of existing molten pool interface reconstruction algorithms, in order to ensure the accuracy of the molten pool interface, it is necessary to perform a sufficiently fine mesh division on the three-dimensional model of the molten pool. Excessively fine meshes affect the calculation efficiency during simulation and consume a long time.

[0006] In order to improve the numerical simulation efficiency of the DED forming process, the present application provides a method for simulating a molten pool solidification interface for additive manufacturing. Summary of the Invention

[0007] To overcome the problems existing in the related art, a first aspect of the present application provides a method for simulating a molten pool solidification interface for additive manufacturing, including:

[0008] Obtaining molten pool area data;

[0009] Performing molten pool mesh division on the molten pool area according to the molten pool area data; the molten pool mesh includes mesh units, cell nodes, edge nodes, and node nodes;

[0010] Obtaining the cell fraction of the mesh units;

[0011] Determining the solid-liquid fractions of each of the node nodes according to the cell fraction;

[0012] Determine the solid-liquid phase fractions of the cell nodes and the edge nodes according to the solid-liquid phase fraction of the node nodes;

[0013] Determine the solidification interface of the molten pool region according to the solid-liquid phase fractions of the cell nodes, the edge nodes and the node nodes.

[0014] In one embodiment, after determining the solid-liquid phase fractions of the respective node nodes according to the cell fractions, it further includes;

[0015] Divide the grid cell into M×M sub-grid cells, where M is an integer greater than or equal to 2.

[0016] In one embodiment, obtaining the cell fraction of the molten pool grid specifically includes:

[0017] Perform numerical simulation according to the molten pool region data to determine the cell fraction of the molten pool grid.

[0018] In one embodiment, determining the solid-liquid phase fraction of the node nodes according to the cell fraction specifically includes:

[0019] Obtain the cell fractions of the four molten pool grids around the node node;

[0020] Determine the solid-liquid phase fraction of the node node through the navgall algorithm;

[0021] In one embodiment, determining the solid-liquid phase fractions of the cell nodes and the edge nodes according to the solid-liquid phase fraction of the node nodes specifically includes:

[0022] Take the cell nodes and the edge nodes as interpolation points to be interpolated;

[0023] Interpolate the interpolation points to be interpolated according to the solid-liquid phase fractions of the four node nodes around the interpolation points to be interpolated to obtain the solid-liquid phase fractions of the interpolation points to be interpolated.

[0024] In one embodiment, interpolating the interpolation points to be interpolated according to the solid-liquid phase fractions of the four node nodes around the interpolation points to be interpolated to obtain the solid-liquid phase fractions of the interpolation points to be interpolated specifically includes:

[0025] Obtain the coordinates of the interpolation points to be interpolated and the four node nodes around them;

[0026] Interpolate the interpolation points to be interpolated in the x-axis direction and the y-axis direction respectively to obtain the solid-liquid phase fraction of the interpolation points.

[0027] In one embodiment, interpolation is performed on the point to be interpolated from the x-axis direction and the y-axis direction respectively to obtain the solid-liquid fraction of the interpolated point, which specifically includes:

[0028] The calculation formula for the point to be interpolated is:

[0029]

[0030]

[0031] wherein, the coordinates of the point P to be interpolated are (x, y), and the coordinates of the four node nodes Q 11 , Q 12 , Q 21 , Q 22 are (x1, y1), (x1, y2), (x2, y1), (x2, y2); f(Q 11 ), f(Q 12 ), f(Q 21 ), f(Q 22 ) are the solid-phase fractions or liquid-phase fractions of the four node nodes respectively.

[0032] In one embodiment, determining the solidification interface of the molten pool region according to the solid-liquid fractions of the cell node, the edge node and the node node specifically includes:

[0033] Compare the solid-phase fraction and the liquid-phase fraction of each node in the molten pool grid. If the solid-phase fraction is greater than the liquid-phase fraction, the node is determined as a solid-phase node; if the solid-phase fraction is less than the liquid-phase fraction, the node is determined as a liquid-phase node; if the solid-phase fraction is equal to the liquid-phase fraction, the node is determined as a solidification interface node;

[0034] Determine the solidification interface of the molten pool grid according to the solidification interface nodes.

[0035] The second aspect of the present application provides a computer program, and when the computer program is executed by a processor, it implements the steps in the molten pool solidification interface simulation method described in the first aspect of the present application.

[0036] The technical solution provided by the present application may include the following beneficial effects:

[0037] Based on the VOF method, in this application, edge nodes and cell nodes are defined on the grid cells as the points to be interpolated. The solid-liquid phase fractions of the grid cells are obtained from existing numerical simulation software, and the solid-liquid phase fractions of each grid intersection point (i.e., node) are calculated. Then, linear interpolation is performed on the points to be interpolated based on the nodes to obtain the solid-liquid phase fractions of all nodes on the molten pool grid. Finally, the solidification interface is reconstructed according to the solid-liquid phase fractions of each node. By performing node interpolation on the grid based on the existing grid structure of the solution, and using the nodes as the data points of the solidification interface for interface reconstruction. Therefore, compared with the existing solution, this application can obtain a solidification interface with higher accuracy and does not require setting small-sized grid cells in the grid division step, simplifying the calculation amount of the VOF method.

[0038] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit this application. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] By describing the exemplary embodiments of this application in more detail in conjunction with the drawings, the above and other objects, features, and advantages of this application will become more obvious. Among them, in the exemplary embodiments of this application, the same reference numerals generally represent the same components.

[0040] Figure 1 Schematic flowchart of the molten pool solidification interface simulation method shown in the embodiments of this application;

[0041] Figure 2 Schematic structural diagram of the molten pool grid;

[0042] Figure 3 Schematic interpolation diagram of the points to be interpolated in the molten pool grid;

[0043] Figure 4 Schematic solid-phase interpolation diagram of the molten pool grid;

[0044] Figure 5 Schematic liquid-phase interpolation diagram of the molten pool grid;

[0045] Figure 6 Schematic solidification interface diagram of the molten pool grid example. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] The preferred embodiments of this application will be described in more detail below with reference to the drawings. Although the preferred embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make this application more thorough and complete, and to fully convey the scope of this application to those skilled in the art.

[0047] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms "a", "the", and "said" used in this application and the appended claims are also intended to include the plural forms unless the context clearly dictates otherwise. It should also be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0048] It should be understood that although the terms "first", "second", "third", etc. may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of this application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of this application, the meaning of "a plurality" is two or more unless otherwise specifically defined.

[0049] Embodiment 1

[0050] The existing method for reconstructing the solidification interface of the molten pool is based on the VOF method, and a volume fraction for representing the solid phase ratio or the liquid phase ratio is defined inside the molten pool grid. The molten pool grid with a solid phase ratio greater than a preset threshold is used as a unit of the solidification interface.

[0051] The accuracy of the solidification interface depends on the size of the molten pool grid. However, increasing the meshing scale will cause a huge computational load in the grid division step and the volume fraction step of the grid, and it is impossible to reconstruct the solidification interface in real time during the printing process.

[0052] To solve the above technical problems, an embodiment of this application provides a method for simulating the solidification interface of a molten pool for additive manufacturing. This method is based on the VOF method and performs two-dimensional meshing on the molten pool.

[0053] It can be understood that the grid cells in the molten pool grid are voxels, and the voxels can be defined and assigned voxel fractions through numerical simulation software.

[0054] Specifically, the voxel fraction is a two-dimensional array, including the solid phase ratio and the liquid phase ratio.

[0055] As Figure 1 shown, the method for simulating the solidification interface of the molten pool according to the embodiment of this application includes the following steps:

[0056] S1. Obtain the data of the molten pool area;

[0057] S2. Divide the molten pool area into molten pool grids according to the data of the molten pool area;

[0058] S3. Obtain the cell fraction of the grid cell;

[0059] S4. Determine the solid-liquid fractions of each node according to the cell fraction;

[0060] S5. Determine the solid-liquid fractions of the cell node and the edge node according to the solid-liquid fractions of the node;

[0061] S6. Determine the solidification interface of the molten pool region according to the solid-liquid fractions of the cell node, the edge node, and the node.

[0062] Specifically, in step S2, the molten pool grid includes grid cells, cell nodes, edge nodes, and node nodes.

[0063] In the embodiment of the present application, as Figure 2 shown, the molten pool grid includes N grid cells, where N is an integer greater than or equal to 1.

[0064] Among them, the cell node represents the center of the grid cell, the edge node represents the midpoint of the boundary of the grid cell, and the node node represents the vertex of the grid cell. Further, in step S3, the cell fraction represents the ratio of solid phase and liquid phase in the grid cell. The value of the cell fraction ranges from [0, 1], representing the proportion of the solid phase or the liquid phase.

[0065] It can be understood that the cell fraction is obtained by cellular automata according to the simulation of the molten pool temperature field.

[0066] In step S4, the solid-liquid fraction of the node. It is calculated by the cell fraction before interpolation, and the solid-liquid fraction of the node is the average value of the cell fractions of adjacent grids.

[0067] In step S5, when the solid-liquid fractions of the node nodes of a grid cell are known, using the four node nodes as source data, linear interpolation is performed on the edge node and the cell node to determine the solid-liquid fractions of the edge node and the cell node.

[0068] In one interpolation method, the value of the edge node is equal to the average value of adjacent node nodes, and the value of the cell node is equal to the average value of the surrounding 4 node nodes.

[0069] Based on the VOF method, in the embodiments of the present application, edge nodes and cell nodes are defined on the grid cells as the points to be interpolated. The solid-liquid phase fractions of the grid cells are obtained from existing numerical simulation software, and the solid-liquid phase fractions of each grid intersection point (i.e., node) are calculated. Then, linear interpolation is performed on the points to be interpolated based on the node to obtain the solid-liquid phase fractions of all nodes on the molten pool grid. Finally, the solidification interface is reconstructed according to the solid-liquid phase fractions of each node. In the embodiments of the present application, by performing node interpolation on the grid based on the existing grid structure and using the nodes as the data points of the solidification interface for interface reconstruction. Therefore, compared with the existing solution, the embodiments of the present application can obtain a solidification interface with higher accuracy and do not require setting small-sized cell units in the cell division step, reducing the computational amount of the VOF method.

[0070] Embodiment 2

[0071] Based on Embodiment 1, the embodiments of the present application provide a multi-level grid division and node interpolation method.

[0072] The embodiments of the present application provide a method for simulating the solidification interface of a molten pool for additive manufacturing, including steps S1 - S6 in Embodiment 1.

[0073] Based on Embodiment 1, in the embodiments of the present application, instead of performing interpolation calculations for each grid one by one, interpolation is directly performed on the unknown data points from the known data points in the first-order grid cells, optimizing the structure of the calculation code, and thus quickly outputting the interpolation of the unknown data points.

[0074] Further, step S4 includes the following steps:

[0075] S401. Obtain the cell fractions of the four molten pool grids around the node;

[0076] S402. Determine the solid-liquid phase fraction of the node through the navgall algorithm.

[0077] Further, after step S4, it further includes:

[0078] S403. Divide the grid cell into M×M sub-grid cells, where M is an integer greater than or equal to 2.

[0079] In step S403, in order to improve the reconstruction accuracy of the solidification interface, a second-level division of the molten pool grid is performed.

[0080] Exemplarily, if Figure 2 the grid cell in is divided into 2×2 sub-grid cells. In this grid cell, there are 8 edge nodes and 4 cell nodes as the points to be interpolated.

[0081] In the embodiments of the present application, the node represents the vertex of the grid cell, that is, the intersection point of the grid cells. The navgall algorithm calculates by averaging the cell fractions of the four surrounding grid cells to obtain the solid-liquid fractions of the node.

[0082] In step S5, taking the node as the known value, regarding the cell node and the edge node as the interpolation points to be interpolated, and then performing bilinear interpolation on the interpolation points to be interpolated according to the solid-liquid fractions of the four node nodes around the interpolation points to be interpolated, so as to obtain the solid-liquid fractions of the interpolation points to be interpolated.

[0083] Specifically, step S5 includes:

[0084] S501. Obtain the coordinates of the interpolation point to be interpolated and the four surrounding node nodes;

[0085] S502. Perform interpolation on the interpolation point to be interpolated from the x-axis direction and the y-axis direction respectively to obtain the solid-liquid fractions of the interpolation point. Exemplarily, as Figure 3 shown, for the interpolation point P, in a grid cell (i.e., a cell), the node is Q 11 , Q 12 , Q 21 , Q 22 .

[0086] First, perform interpolation on the interpolation point P from the x-axis direction. Interpolate the value of point R1 through the solid-liquid fractions of Q 11 and Q 21 . The calculation formula (1) is:

[0087]

[0088] where f(Q 11 ) is the solid-phase fraction or liquid-phase fraction of node Q 11 , and f(Q 21 ) is the solid-phase fraction or liquid-phase fraction of node Q 21 .

[0089] Then, interpolate the value of point R2 through the solid-liquid fractions of Q 12 and Q 22 . The calculation formula (2) is:

[0090]

[0091] where f(Q 12 ) is the solid-phase fraction or liquid-phase fraction of node Q 12 , and f(Q 22 ) is the solid-phase fraction or liquid-phase fraction of node Q 22The solid fraction or liquid fraction of the node.

[0092] Then, determine the solid fraction or liquid fraction of the interpolation point P to be interpolated through the values of point R1 and point R2. The calculation formula (3) is:

[0093]

[0094] In the above calculation formula, the coordinates of the interpolation point P to be interpolated are (x, y), and the coordinates of the four node nodes Q 11 , Q 12 , Q 21 , Q 22 are (x1, y1), (x1, y2), (x2, y1), (x2, y2).

[0095] Substitute calculation formulas (1) and (2) into (3) to obtain the total calculation formula for the interpolation point to be interpolated as:

[0096]

[0097] In step S502, interpolate the solid fraction and liquid fraction of the interpolation point to be interpolated respectively through the total calculation formula of the interpolation point to be interpolated until the calculation of the interpolation points of the molten pool grid is completed.

[0098] Exemplarily, Figure 4 and Figure 5 are the solid phase interpolation schematic diagram and liquid phase interpolation schematic diagram of the molten pool grid example.

[0099] Specifically, step S6 includes:

[0100] S601. Compare the solid fraction and liquid fraction of each node in the molten pool grid. If the solid fraction is greater than the liquid fraction, determine the node as a solid phase node; if the solid fraction is less than the liquid fraction, determine the node as a liquid phase node; if the solid fraction is equal to the liquid fraction, determine the node as a solidification interface node;

[0101] S602. Determine the solidification interface of the molten pool grid according to the solidification interface node.

[0102] Exemplarily, Figure 6 is an example diagram of the solidification interface. Among them, the red area is the solid phase and the blue area is the liquid phase.

[0103] In the simulation method in Embodiment 1, improving the reconstruction accuracy requires calculating the interpolation points level by level. That is, performing interpolation operations on the grid cells and then on the sub-grid cells. Therefore, the more levels of grid cell division, the more interpolation points, which will inevitably increase the calculation load.

[0104] In the embodiment of the present application, by performing interpolation operations directly on the points to be interpolated in the grid cells and sub-grid cells through step S5, it is possible to avoid the calculation steps for the points to be interpolated at each level, thereby reducing the amount of calculation. Moreover, for regions with a relatively complex solid-liquid interface, grid divisions at multiple levels can obtain a more accurate solidification interface.

[0105] Embodiment III

[0106] A computer program, when executed by a processor, implements the steps in the molten pool solidification interface simulation method described in Embodiment I or Embodiment II.

[0107] Regarding the device in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments related to the method. Therefore, no further detailed description will be provided here.

[0108] The solution of the present application has been described in detail above with reference to the accompanying drawings. In the above embodiments, the descriptions of each embodiment have their own emphases. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments. Those skilled in the art should also be aware that the actions and modules involved in the specification are not necessarily essential to the present application.

[0109] In addition, it can be understood that the steps in the method embodiments of the present application can be adjusted, combined, and deleted according to actual needs, and the modules in the device embodiments of the present application can be combined, divided, and deleted according to actual needs.

[0110] In addition, the method according to the present application can also be implemented as a computer program or a computer program product. The computer program or computer program product includes computer program code instructions for performing some or all of the steps in the above method of the present application.

[0111] Alternatively, the present application can also be implemented as a non-transitory machine-readable storage medium (or computer-readable storage medium, or machine-readable storage medium), on which executable code (or computer program, or computer instruction code) is stored. When the executable code (or computer program, or computer instruction code) is executed by a processor of an electronic device (or an electronic device, a server, etc.), the processor is caused to execute some or all of the steps of the above method according to the present application.

[0112] Those skilled in the art will also understand that the various exemplary logical blocks, modules, circuits, and algorithm steps described in connection with the applications herein can be implemented as electronic hardware, computer software, or a combination of both.

[0113] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems and methods according to various embodiments of the present application. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a portion of code, which contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as combinations of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0114] The embodiments of the present application have been described above. The above description is exemplary and not exhaustive, and is also not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art in the technical field without departing from the scope and spirit of the described embodiments. The choice of terms used herein is intended to best explain the principles of the embodiments, the practical application, or the improvement of the technology in the market, or to enable other ordinary skill in the art in the technical field to understand the embodiments disclosed herein.

Claims

1. A method for simulating the solidification interface of a molten pool for additive manufacturing, characterized in that, Including: Obtaining data of the molten pool area; Performing molten pool grid division on the molten pool area according to the data of the molten pool area; the molten pool grid includes grid cells, cell nodes, edge nodes, and node nodes; Obtaining the cell fraction of the grid cells; Determining the solid-liquid fractions of each of the node nodes according to the cell fraction; Determining the solid-liquid fractions of the cell nodes and the edge nodes according to the solid-liquid fractions of the node nodes; Determining the solidification interface of the molten pool area according to the solid-liquid fractions of the cell nodes, the edge nodes, and the node nodes.

2. The method for simulating the solidification interface of a molten pool for additive manufacturing according to claim 1, wherein After determining the solid-liquid fractions of each of the node nodes according to the cell fraction, it further includes; Dividing the grid cells into M×M sub-grid cells, where M is an integer greater than or equal to 2.

3. A method for simulating the solidification interface of a molten pool for additive manufacturing according to claim 1, characterized in that, Obtaining the cell fraction of the molten pool grid, specifically including: Performing numerical simulation according to the data of the molten pool area to determine the cell fraction of the molten pool grid.

4. A method for simulating the solidification interface of a molten pool for additive manufacturing according to claim 1, characterized in that, Determining the solid-liquid fractions of the node nodes according to the cell fraction, specifically including: Obtaining the cell fractions of the four molten pool grids around the node node; Determining the solid-liquid fraction of the node node through the navgall algorithm.

5. A method for simulating the solidification interface of a molten pool for additive manufacturing according to claim 1, characterized in that, Determining the solid-liquid fractions of the cell nodes and the edge nodes according to the solid-liquid fractions of the node nodes, specifically including: Regarding the cell nodes and the edge nodes as interpolation points to be interpolated; Interpolating the interpolation points to be interpolated according to the solid-liquid fractions of the four node nodes around the interpolation points to be interpolated to obtain the solid-liquid fractions of the interpolation points to be interpolated.

6. The method for simulating the molten pool solidification interface for additive manufacturing according to claim 5, wherein Interpolating the interpolation points to be interpolated according to the solid-liquid fractions of the four node nodes around the interpolation points to be interpolated to obtain the solid-liquid fractions of the interpolation points to be interpolated, specifically including: Obtaining the coordinates of the interpolation points to be interpolated and the four node nodes around them; Interpolating the interpolation points to be interpolated respectively in the x-axis direction and the y-axis direction to obtain the solid-liquid fractions of the interpolation points.

7. A method for simulating the solidification interface of a molten pool for additive manufacturing according to claim 6, characterized in that Interpolating the interpolation points to be interpolated respectively in the x-axis direction and the y-axis direction to obtain the solid-liquid fractions of the interpolation points, specifically including: The calculation formula for the interpolation points to be interpolated is: Among them, the coordinates of the interpolation point P are (x, y), and the coordinates of the four node nodes Q 11 , Q 12 , Q 21 , Q 22 are (x1, y1), (x1, y2), (x2, y1), (x2, y2); f(Q 11 ), f(Q 12 ), f(Q 21 ), f(Q 22 ) are the solid phase fractions or liquid phase fractions of the four node nodes respectively.

8. A method for simulating a molten pool solidification interface for additive manufacturing according to claim 1, characterized in that, Determining the solidification interface of the molten pool area according to the solid-liquid fractions of the cell nodes, the edge nodes, and the node nodes, specifically including: Comparing the solid fractions and liquid fractions of each node in the molten pool grid. If the solid fraction is greater than the liquid fraction, the node is determined as a solid-phase node; if the solid fraction is less than the liquid fraction, the node is determined as a liquid-phase node; if the solid fraction is equal to the liquid fraction, the node is determined as a solidification interface node; Determining the solidification interface of the molten pool grid according to the solidification interface nodes.

9. A computer program, characterized in that, When the computer program is executed by a processor, it implements the steps in the molten pool solidification interface simulation method according to any one of claims 1 to 8.

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