CN116705209B - High-precision calculation method for surface force of molten pool under selective laser melting technology - Google Patents

Abstract

The invention relates to the field of metal additive manufacturing, and in particular to a high-precision calculation method for the surface force of a molten pool under selective laser melting technology. It is used to solve the problem that the existing technology requires a full field when calculating the surface force of a molten pool under selective laser melting technology. The problem of large amount of calculation caused by solving the free interface evolution equation and the problem of low accuracy when solving the surface force by the material point method include the following steps: using the preset calculation parameters to divide the calculation domain into a calculation grid, At the same time, the entire material domain is discretized into material points, and the material points are used to initialize the calculation grid; based on the mass field of the background grid node in the material point method, the free surface grid is searched in the initialized calculation grid, And establish a free surface virtual grid based on the free surface grid; perform smooth reconstruction and volume correction on the rough free interface of the free surface virtual grid to obtain a smooth free interface; solve the melt pool on the smooth free interface surface force.

Description

A high-precision calculation method for the surface force of the molten pool in selective laser melting technology

Technical Field

The present invention relates to the field of metal additive manufacturing, and in particular to a high-precision calculation method for molten pool surface force under selective laser melting technology.

Background Art

In recent years, additive manufacturing technology has attracted widespread attention from the industrial community at home and abroad. Additive manufacturing technology is a revolutionary manufacturing technology that uses high-energy heat beams to melt materials one by one and deposit them layer by layer, which can achieve "near-net" forming of any complex shape. Unlike traditional subtractive and equal-material manufacturing technologies such as turning, additive manufacturing obtains complex part configurations by melting and depositing layer by layer, and has unique advantages such as short cycle, low cost, and material saving. Among them, selective laser melting technology is one of the common metal additive manufacturing technologies.

However, most of the current free interface capture methods require full-field solution of additional equations and particle search algorithms. For example, the VOF method requires reconstruction of the normal vector and intercept based on the volume fraction in each unit, and the Level set method requires full-field solution of the signed distance function and additional reinitialization at each step. The SPH method in the meshless method requires searching for the neighboring relationship of surface particles, which affects the computational efficiency. The free interface of the standard material point method is stepped, which requires further improvement of accuracy and establishment of an accurate model for the surface force in metal additive manufacturing problems.

Summary of the invention

In view of the defects in the prior art, the present invention provides a high-precision calculation method for the surface force of the molten pool under the selective laser melting technology.

In order to achieve the above-mentioned purpose, the present invention provides a high-precision calculation method for the surface force of the molten pool under the selective laser melting technology, the method comprising the following steps: using preset calculation parameters to divide the calculation domain into a calculation grid, and at the same time discretizing the entire material domain into material points, and using the material points to initialize the calculation grid; searching for free surface grids in the initialized calculation grid according to the mass field of the background grid nodes in the material point method, and establishing a free surface virtual grid based on the free surface grid; smoothing and reconstructing the rough free interface of the free surface virtual grid and volume correction to obtain a smooth free interface; solving the surface force of the molten pool on the smooth free interface. The present invention reduces the amount of calculation when calculating the surface force of the molten pool under the selective laser melting process, solves the "step-shaped" liquid surface problem described by the background grid in the standard material point method, and improves the accuracy of solving the surface force of the molten pool.

Optionally, searching for a free surface grid in the initialized computational grid according to the mass field of the background grid nodes in the material point method, and establishing a free surface virtual grid according to the free surface grid comprises the following steps:

Mapping the mass of the material point to the background grid nodes;

Loop through all empty grids in the entire computational domain. When the mass at the node of any empty grid is not zero, the node is a free surface node, and the non-empty grid connected to it is a free surface grid.

Based on the free surface mesh obtained by searching, a free surface virtual mesh that coincides with it is established.

Furthermore, establishing a free surface virtual grid that overlaps with the free surface grid is beneficial to the smooth reconstruction of the interface at a small number of free surface grids, which can effectively improve the efficiency of surface capture.

Optionally, the step of smoothly reconstructing and volume-correcting the rough free interface of the free surface virtual grid to obtain a smooth free interface comprises the following steps:

Set the smoothing threshold and vector field convergence condition;

Taking the position of each node on the virtual grid of the free surface as the initial value of the iteration, combining the smoothing number threshold to iteratively calculate the position of each node on the rough free interface, and obtaining the middle position of each node on the rough free interface;

Performing volume correction on the intermediate position to obtain a corrected intermediate position;

Calculating the vector field of the corrected intermediate position, and when the vector field does not satisfy the vector field convergence condition, using the corrected intermediate position calculated this time as the iteration initial value to calculate the next corrected intermediate position, iteratively calculating until the vector field satisfies the vector field convergence condition, and using the final corrected intermediate position as the final node position;

The smooth free interface is obtained according to the final node position.

Furthermore, by setting the smoothing number threshold and vector field convergence condition, the rough free interface of the free surface virtual grid is smoothly reconstructed and volume corrected multiple times to obtain a smooth free interface, which solves the "step-shaped" liquid surface problem described by the background grid in the standard material point method and is beneficial to improving the solution accuracy of the surface force of the molten pool.

Optionally, the step of taking the position of each node on the virtual grid of the free surface as an initial value of the iteration, and iteratively calculating the position of each node on the rough free interface in combination with the smoothing number threshold, to obtain the middle position of each node on the rough free interface comprises the following steps:

Using the position of each node on the virtual grid of the free surface as the iterative initial value for the first smoothing of the rough free interface, and then calculating the unit external normal vector and smooth displacement of each node on the rough free interface;

Calculating the position of each node on the rough free interface using the unit external normal vector and the smooth displacement, and recording it as a preliminary position;

If the number of smoothing times for the rough free interface is less than the smoothing times threshold, the preliminary position calculated this time is used as the next preliminary position of the iteration initial value, and the iterative calculation is performed until the number of smoothing times for the rough free interface is not less than the smoothing times threshold, and the final preliminary position is used as the intermediate position.

Optionally, performing volume correction on the intermediate position to obtain a corrected intermediate position comprises the following steps:

Update the unit external normal vector according to the intermediate position to obtain a spare unit external normal vector;

The middle position is volume-corrected using the spare unit external normal vector to obtain a corrected middle position.

Optionally, solving the surface force of the molten pool on the smooth free interface comprises the following steps:

Calculating the mixing area at each node on the smooth free interface;

The average curvature at each node on the smooth free interface is calculated using the mixed area and the unit external normal vector, and the average curvature is smoothed using a weighted average method to obtain a smooth curvature;

Establishing a molten pool surface force model according to the mixed area, the unit external normal vector and the smooth curvature;

The surface force at each node on the smooth free interface is solved according to the molten pool surface force model, and the surface force is mapped to the material point using a volume averaging method.

Furthermore, the surface force of the molten pool can be solved with higher accuracy on the smooth free interface, and mapping the surface force to material points can further derive the surface force at each material point, which is conducive to introducing the surface force into the calculation of the background grid node force.

Optionally, the unit external normal vector and the smooth displacement respectively satisfy the following relationship:

,

,

in, The unit external normal vector of node I on the rough free interface, is the area vector of node I on the rough free interface; is the smooth displacement generated by the node I on the rough free interface calculated by the kth iteration, J is the neighbor node of the node I on the rough free interface, is the set of neighbor nodes, is the weight factor of node I at neighboring node J on the rough free interface, The position of neighbor node J in the kth iteration calculation, is the initial position of node I on the rough free interface calculated in the kth iteration.

Optionally, when iteratively acquiring the intermediate position, the preliminary position satisfies the following relationship:

in, is the initial position of node I on the rough free interface, is the initial position of node I on the rough free interface calculated at the k+1th iteration, is the initial position of node I on the rough free interface calculated at the kth iteration, is the coefficient for controlling node movement, is the relaxation factor, is the unit external normal vector of node I on the rough free interface calculated at the kth iteration, It is the smooth displacement generated by the node I on the rough free interface obtained by k-th iterative calculation.

Optionally, the smooth curvatures satisfy the following relationships:

in, is the smooth curvature at node I on the smooth free interface, J is the neighbor node of I on the smooth free interface, is the set of neighbor nodes, is the weight factor for curvature smoothing, is the average curvature at node I on the smooth free interface, is the average curvature of the neighboring nodes of node I on the smooth free interface.

Furthermore, the smooth curvature at each node on the smooth free table is obtained after smoothing the average curvature using the weighted averaging method, wherein the average curvature at each node on the smooth free table is solved based on the discrete average form of the Laplace operator. The adopted average curvature effectively avoids the accuracy loss of multiple derivations in the prior art, reduces the amount of calculation when calculating the surface force of the molten pool under the selective laser melting process, and smoothing the average curvature can improve the accuracy of the surface force solution.

Optionally, the molten pool surface force model satisfies the following relationship:

in, is the molten pool surface force at node I on the smooth free interface, is the surface tension coefficient, is the smooth curvature at node I on the smooth free interface, is the unit external normal vector, is the mixing area at node I on the smooth free interface.

In summary, the present invention solves the "step-shaped" liquid surface problem described by the background grid in the standard material point method, effectively improves the efficiency of capturing the free surface of the molten pool, reduces the amount of calculation when calculating the surface force of the molten pool under the selective laser melting process, and realizes high-precision calculation of the surface force of the molten pool under the selective laser melting technology, and the accuracy of the prediction results is good.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

FIG1 is a schematic flow chart of a method for high-precision calculation of molten pool surface force under the selective laser melting technology according to an embodiment of the present invention;

FIG2 is a schematic diagram of a free surface mesh according to an embodiment of the present invention;

FIG3 is a schematic diagram of smooth reconstruction according to an embodiment of the present invention;

FIG4 is a schematic diagram of a simplified process for obtaining the final node position according to an embodiment of the present invention;

FIG5 is a schematic diagram of solving a unit external normal vector according to an embodiment of the present invention;

FIG6 is a schematic diagram of a free surface mesh smoothing process according to an embodiment of the present invention;

FIG7 is a schematic diagram of a volume correction process according to an embodiment of the present invention;

FIG8 is a schematic diagram of geometrically dividing virtual grid units according to an embodiment of the present invention;

FIG. 9 is a schematic diagram of calculating polygonal areas and mixed areas at free surface nodes according to an embodiment of the present invention.

DETAILED DESCRIPTION

The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are only for illustration and are not intended to limit the present invention. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not have to be adopted to implement the present invention. In other examples, in order to avoid confusing the present invention, known circuits, software or methods are not specifically described.

Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and/or subcombination. In addition, it should be understood by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale.

It should be noted in advance that, in an optional embodiment, except for independent explanations, the same symbols or letters appearing in all formulas have the same meanings and values.

In addition, no matter on which interface, for a fixed node I, the set of its neighbor nodes is unchanged. Therefore, in this embodiment, "J is the neighbor node of node I on the smooth free interface", "J is the neighbor node of node I on the rough free interface" or similar statements only indicate that the position of the node has changed after processing, and does not mean that the node target has changed, that is, the neighbor nodes referred to as "neighbor nodes of node I on the smooth free interface", "neighbor nodes of node I on the rough free interface" and "neighbor nodes of node I on the reconstructed interface" are the same in target.

In an optional embodiment, referring to FIG. 1 , the present invention provides a high-precision calculation method for the surface force of a molten pool under the selective laser melting technology, the method comprising the following steps:

S1. Use preset calculation parameters to divide the calculation domain into calculation grids, discretize the entire material domain into material points, and use the material points to initialize the calculation grid.

Specifically, in this embodiment, the computational domain is divided into computational grids according to preset computational parameters, and the entire material domain is discretized into material points, and then the physical quantities carried by the grid units and the physical quantities carried by the material points are initialized. This is a prior art, and the standard material point method can be specifically referred to, and will not be described in detail here.

Furthermore, the preset calculation parameters include the length of the grid unit and the number of initial material points in the unit.

S2. searching for a free surface grid in the initialized computational grid according to the mass field of the background grid nodes in the material point method, and establishing a free surface virtual grid according to the free surface grid.

Among them, S2 specifically includes the following steps:

S21. Mapping the mass of the material point to the background grid nodes.

Specifically, in this embodiment, the mass of the material point is mapped to the background grid nodes in the form of a function. This is a prior art, and specific reference may be made to the standard material point method, which will not be described in detail here.

S22. Loop through all empty grids in the entire computational domain. When the mass at the node of any empty grid is not zero, the node is a free surface node, and the non-empty grid connected to it is a free surface grid.

Specifically, in this embodiment, in the standard material point method, the tracking of the free surface can be achieved through the mass field of the background grid node. Please refer to Figure 2. The hollow points on the four vertices of the square represent massless nodes; the solid black points on the four vertices of the square represent nodes with non-zero mass, that is, free surface nodes, hereinafter referred to as nodes; the small black dots in the square represent material points, the squares without material points are empty cells, the squares containing material points and having interfaces with empty cells are free surface cells, the interface between the free surface cells and the empty cells is the free surface of the molten pool, the squares containing material points but having no interfaces with empty cells are the fluid cells of the molten pool, and the grid where the free surface is located is the free surface grid.

Furthermore, it is not difficult to see from Figure 2 that the free surface tracking strategy in the standard material point method obtains a "step-like" rough free interface, which cannot accurately describe the free surface morphology of the molten pool, and cannot obtain the accurate normal vector and curvature of each node on the free surface, thus affecting the accuracy of the surface force solution.

S23. A free surface virtual grid that coincides with the free surface grid obtained by searching is established.

Specifically, in this embodiment, the free surface virtual grid coincides with the free surface grid obtained by the search, and both are determined by the free surface nodes. However, unlike the free surface grid, the free surface virtual grid only carries geometric information, normal vectors, curvature, surface tension and other information, which facilitates the reconstruction of the rough free interface.

S3. Smoothly reconstruct and volume correct the rough free interface of the free surface virtual grid to obtain a smooth free interface.

Specifically, in this embodiment, please refer to FIG3. For the free surface of the spherical molten pool, the free interface formed by the virtual grid of the free surface established at the beginning is actually a "step-shaped" rough free interface, as shown in FIG3 (a). After smooth reconstruction, the rough free interface is closer to the actual situation in shape, but it brings about a deviation in volume, as shown in FIG3 (b). Therefore, it is necessary to perform volume correction on the rough free interface after smooth reconstruction, so as to obtain a smooth free interface that is closest to the actual situation, as shown in FIG3 (c).

More specifically, S3 includes the following steps:

S31. Set the smoothing times threshold and the vector field convergence condition.

Specifically, in this embodiment, see FIG4 , the smoothing times threshold is used to determine whether to perform iterative smoothing reconstruction on the rough free interface, and the vector field convergence condition is used to determine whether to perform iterative volume correction on the rough free interface after smoothing reconstruction. The advantage is that the rough free interface can be restored to the free interface closest to the actual situation, that is, the smooth free interface.

Furthermore, the smoothing threshold is 20 times, and the vector field convergence condition is:

Where L is the number of nodes on the rough free interface, that is, the number of free surface nodes on the rough free interface; is the converged residual; is the field vector including all free surface nodes The 2-norm of , taking free surface node I as an example:

in, is the field vector at free surface node I, is the node position of free surface node I after the jth volume repair, is the node position of free surface node I after the j-1th volume repair.

Furthermore, in other optional embodiments, other smoothing number thresholds may be selected and other convergence conditions may be designed, which are not specifically listed here.

S32, taking the position of each node on the virtual grid of the free surface as the initial value of the iteration, combining the smoothing number threshold to iteratively calculate the position of each node on the rough free interface, and obtaining the middle position of each node on the rough free interface.

Among them, S32 specifically includes the following steps:

S321, taking the position of each node on the virtual grid of the free surface as the iterative initial value for the first smoothing of the rough free interface, and then calculating the unit external normal vector and smooth displacement of each node on the rough free interface.

Specifically, in this embodiment, referring to FIG. 5 , the positions of the nodes on the virtual grid of the free surface are used as the initial values of the first smoothing iteration of the rough free interface, where I, , and They represent the four nodes on the rough free interface.

On a rough free interface, the unit external normal vector of node I is Satisfies the following relationship:

Unit external normal vector Used to determine the smooth reference direction of node I on the rough free interface.

is the area vector of node I on the rough free interface, Satisfies the following relationship:

in, is the set of triangles around node I on the rough free interface, is the area vector of the Kth triangle in the triangle set.

Area Vector It can be calculated by the following method:

,

,

,

in, and Two vectors representing the two sides of the Kth triangle in the triangle set, , , and They are node I, , and In Figure 5, Direction and nodes To Node The same direction, Direction and nodes The direction to node I is the same.

The smooth displacement of node I on the rough free interface satisfies the following relationship:

in, is the smooth displacement of node I on the rough free interface calculated by the kth iteration, J is the neighbor node of node I on the rough free interface, is the set of neighbor nodes, is the weight factor of node I at neighboring node J on the rough free interface, The position of neighbor node J in the kth iteration calculation, is the initial position of node I on the rough free interface obtained in the kth iteration calculation. In the first iteration calculation, k=1. Can be recorded as .

Weight Factor Satisfies the following relationship:

in, is the area vector of the neighboring node J of node I on the rough free interface, The calculation method and The calculation method is the same as is the smoothing weight factor, and .

Furthermore, FIG. 5 is only for the convenience of explanation, and does not mean that the position and scene of node I or any node on the rough free interface are fixed. This should be understood.

S322. Calculate the position of each node on the rough free interface using the unit external normal vector and the smooth displacement, and record them as preliminary positions.

Specifically, in this embodiment, the initial position satisfies the following relationship:

in, is the initial position of node I on the rough free interface, is the initial position of node I on the rough free interface calculated at the k+1th iteration, is the coefficient for controlling node movement, , is the relaxation factor, , is the unit external normal vector of node I on the rough free interface obtained by the kth iterative calculation. In the first iterative calculation, k=1.

Further, please refer to Figure 6, in which is the position of the neighbor node J of node I on the rough free interface, is the position of node I on the rough free interface. The closed area surrounded by the dotted line represents the free surface mesh without smooth reconstruction, and the closed area surrounded by the real line represents the free surface mesh after smooth reconstruction.

S323. If the number of smoothing times for the rough free interface is less than the smoothing times threshold, the preliminary position calculated this time is used as the next preliminary position of the iteration initial value, and the iterative calculation is performed until the number of smoothing times for the rough free interface is not less than the smoothing times threshold, and the final preliminary position is used as the intermediate position.

Specifically, in this embodiment, please refer to Figure 4. Once the preliminary positions of all nodes on the rough free interface are calculated, a smooth reconstruction is completed. If the number of smoothing times for the rough free interface does not reach 10 times, the preliminary positions of each node on the rough free interface calculated this time are fed back to step S321 as the initial value of the iteration for the next smooth reconstruction, until the number of smoothing times for the rough free interface reaches 10 times. S32 This method for smooth reconstruction of the rough free interface is a weighted Laplacian smoothing method. This method is different from the traditional Laplace smoothing method. The smoothing weight at the neighbor node used by the weighted Laplacian smoothing method is not a constant, but considers the distance between the neighbor node and the current node. The distance is measured by the area represented by the neighbor node. Its advantage is that it can restore the real situation of the free surface to the greatest extent, improve the efficiency of capturing the free surface of the molten pool, and thus improve the accuracy of the calculation of the molten pool surface force under the selective laser melting technology.

S33, performing volume correction on the intermediate position to obtain a corrected intermediate position.

After multiple smooth reconstructions in step S32, the rough free interface is closest to the actual situation in shape. For ease of distinction, the free surface determined by the nodes in the middle position is named the reconstructed interface. However, it should be understood that the reconstructed interface is essentially a rough free interface that has undergone multiple smooth reconstructions.

Furthermore, S33 specifically includes the following steps:

S331. Update the unit external normal vector according to the intermediate position to obtain a spare unit external normal vector.

Specifically, in this embodiment, please refer to Figure 4, S32 only obtains and outputs the middle position of each node on the rough free interface, but the unit external normal vector corresponding to the middle position of each node on the rough free interface is not updated. Therefore, it is necessary to update the unit external normal vector of each node on the rough free interface according to the middle position, and the updated result is recorded as the spare unit external normal vector, which provides a data basis for volume correction of the middle position of each node on the rough free interface.

S332. Perform volume correction on the middle position using the spare unit external normal vector to obtain a corrected middle position.

Specifically, in this embodiment, it is first necessary to calculate the volume correction displacement of each node on the reconstructed interface according to the middle position of each node on the reconstructed interface and the weight factor, and then calculate the corrected middle position of each node on the reconstructed interface according to the volume correction displacement and the spare unit external normal vector. The volume correction displacement and the corrected middle position of each node on the reconstructed interface respectively satisfy the following relationship:

,

,

in, To reconstruct the volume correction displacement of node I on the interface, To reconstruct the position of the neighbor node J of node I on the interface, is the position of the neighbor node J of node I on the reconstruction interface when smooth reconstruction is not performed; To reconstruct the corrected intermediate positions of each node on the interface, is the volume correction factor, , is the spare unit external normal vector at node I on the reconstructed interface.

Furthermore, the weight factor in this step It is calculated based on the middle position of each node on the reconstructed interface. The calculation method thereof refers to the content of step S321.

Furthermore, based on FIG. 6 , please refer to FIG. 7 , in which the closed area surrounded by solid lines is a free surface mesh after volume correction.

S34, calculating the vector field of the corrected intermediate position, and when the vector field does not satisfy the vector field convergence condition, using the corrected intermediate position calculated this time as the iteration initial value to calculate the next corrected intermediate position, iteratively calculating until the vector field satisfies the vector field convergence condition, and using the final corrected intermediate position as the final node position.

Specifically, in this embodiment, the reconstructed interface determined by each free surface node at the intermediate position of the correction is recorded as the correction interface. , calculate the field vector of each node on the correction interface according to the field vector calculation method provided in step S31 and determine whether the field vector of the node on the correction interface meets the vector field convergence condition provided in step S31. If not, the position of each node on the correction interface is fed back to step S32 as an iterative initial value for recalculation. Repeat the operations of step S32 to step S34 until the field vector of the node on the correction interface meets the vector field convergence condition provided in step S31, thereby obtaining the final node position of the free surface node.

S35. Obtain the smooth free interface according to the final node position.

Specifically, in this embodiment, the final node position is the position of each node on the smooth free interface, so a smooth free interface, that is, a smooth free surface of the molten pool, can be obtained according to the final node position.

S4. Solving the surface force of the molten pool on the smooth free interface.

Among them, S4 specifically includes the following steps:

S41, calculating the mixing area at each node on the smooth free interface.

Specifically, in this embodiment, this step obtains the mixed area at each node on the smooth free interface. After obtaining the smooth free interface, the curvature of each node needs to be calculated for subsequent calculation of the surface force.

Further, please refer to FIG8. In order to calculate the curvature of each node on the smooth free surface, it is necessary to geometrically divide the virtual grid unit, which is the free surface unit after constructing the virtual grid of the free surface. First, the quadrilateral facets of the virtual grid unit in FIG8 (a) are triangulated to obtain a series of triangular facets without any gaps or overlaps, as shown in FIG8 (b). Triangulation is to cut each quadrilateral facet along its shorter diagonal, as shown by the dotted line in FIG8 (b). Subsequently, the surface composed of the triangular facets is decomposed into a set of polygons according to the construction idea of the Voronoi diagram, as shown in FIG8 (c). These polygons are composed of the circumcenter or the center of the edge of the triangle. The specific method is shown in FIG9. Each polygon represents the area of a node, which is referred to as the mixed area below. The polygons do not overlap with each other, and the total area of all polygons is equal to the area of the free surface in FIG8 (a) or FIG8 (b).

Further, see Figure 9. On a smooth free interface, the mixed area at the free surface node I is the sum of the areas of the polygons around the node. Before calculating the area of each polygon, we must first consider the type of each triangle it contains and the internal angle of each triangle at the node I. Therefore, we need to consider the following three cases: triangle non-obtuse triangle; triangle is an obtuse triangle, and Obtuse angle; triangle is an obtuse triangle, and is an acute angle. The three cases are shown in (a), (b), and (c) in Figure 9. Therefore, the area of the i-th polygon at the free surface node I is Satisfies the following relationship:

in, and For triangle The two interior angles of and For triangle The two side vectors of , and The triangle The positions of the three vertices, the edge vector The direction of the vertex To the top Direction, edge vector The direction of the vertex To the top direction.

Furthermore, on the smooth free interface, the mixing area at node I is Satisfies the following relationship:

in, is the set of polygons around node I on the smooth free interface.

S42, using the mixed area and the unit external normal vector to calculate the average curvature at each node on the smooth free interface, and using a weighted average method to smooth the average curvature to obtain a smooth curvature.

Specifically, in this embodiment, the average curvature at the node I on the smooth free interface is Satisfies the following relationship:

See Figure 9, is the position of node I on the smooth free interface, is the position of the neighbor node J of node I on the smooth free interface, and Respectively with the edge Two opposite interior angles of a triangle.

Use weighted average method to average curvature The smooth curvature obtained by smoothing satisfies the following relationship:

in, is the smooth curvature of node I on the smooth free interface, J is the neighbor node of node I on the smooth free interface, is the weight factor for curvature smoothing, , is the average curvature of the neighboring nodes of node I on the smooth free interface, The calculation method and is calculated in the same way.

S43, establishing a molten pool surface force model according to the mixed area, the unit external normal vector and the smooth curvature.

Specifically, in this embodiment, the molten pool surface force model satisfies the following relationship:

in, is the surface force of the molten pool at node I on the smooth free interface, is the surface tension coefficient, is the unit external normal vector. Can be replaced by , and the node I on the smooth free interface is the same as the node I on the virtual grid of the free surface, so It is also the surface force of the molten pool at node I on the virtual grid of the free surface.

S44. Solve the surface force at each node on the smooth free interface according to the molten pool surface force model, and map the surface force to the material point using a volume averaging method.

Specifically, in this embodiment, the , S41 obtained and S42 calculated By bringing it into the molten pool surface force model of S43, the surface force at node I on the molten pool can be calculated, that is, the surface force of the molten pool at node I on the smooth free interface .

Furthermore, since the virtual free surface mesh completely overlaps with the free surface mesh before smooth reconstruction, they share the same mesh node number, and the surface force of each node on the virtual free surface mesh can be directly assigned to the background mesh node, that is:

in, is the surface force at node I of the background mesh.

Next, the surface force at the background grid node is mapped to the grid center of the free surface unit to become the surface force of the free surface unit. Finally, the surface force of the free surface unit is evenly distributed to each material point in the free surface unit in the form of body force per unit mass, and the surface force of each material point is obtained. The surface force of the free surface unit and the surface force of each material point satisfy the following relationship:

,

,

in, is the surface force of free surface element C, is the set of free surface nodes contained in the free surface element C, is the number of free surface elements containing background grid node I; is the surface force at each material point in the free surface element C, is the unit mass of the free surface element C, is the number of material points in the free surface element C.

It should be noted that, in some cases, the actions described in the specification can be performed in a different order and still achieve the desired results. In this embodiment, the order of steps given is only to make the embodiment appear clearer and easier to explain, rather than to limit it.

In summary, the present invention utilizes the characteristic of the material point method that the background grid is easy to track the free surface. First, the free surface grid and its nodes are identified through the mass field of the background grid nodes, and then a free surface virtual grid that coincides with the free surface grid is established. The free interface is smoothly reconstructed on the free surface virtual grid, and the volume correction method is used to correct the smoothed interface to obtain a smooth free interface, which solves the "step-shaped" liquid surface problem described by the background grid in the standard material point method, and effectively improves the efficiency of free surface capture of the molten pool; then, the curvature and surface force are solved on the free surface with higher precision, and the average curvature used effectively avoids the precision loss of multiple derivations in the prior art, and reduces the amount of calculation when calculating the surface force of the molten pool under the selective laser melting process; finally, the volume averaging method is used to establish the mapping relationship between the free surface virtual grid and the material point method, and the surface force of each material point is obtained. This method has good conservation and stability. The present invention realizes the high-precision calculation of the surface force of the molten pool under the selective laser melting technology, and the accuracy of the prediction results is good.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims (10)

1. A high-precision calculation method for the surface force of a molten pool under selective laser melting technology, characterized in that it comprises the following steps: The calculation domain is divided into a calculation grid using preset calculation parameters, and the entire material domain is discretized into material points, and the calculation grid is initialized using the material points; Searching for a free surface grid in the initialized computational grid according to the mass field of the background grid node in the material point method, and establishing a free surface virtual grid according to the free surface grid; Smoothly reconstructing and volume correcting the rough free interface of the free surface virtual grid to obtain a smooth free interface; The surface force of the molten pool is solved on the smooth free interface. 2. According to the method for high-precision calculation of molten pool surface force in selective laser melting technology of claim 1, it is characterized in that the free surface grid is searched in the initialized calculation grid according to the mass field of the background grid node in the material point method, and the free surface virtual grid is established according to the free surface grid, which comprises the following steps: Mapping the mass of the material point to the background grid nodes; Loop through all empty grids in the entire computational domain. When the mass at the node of any empty grid is not zero, the node is a free surface node, and the non-empty grid connected to it is a free surface grid. Based on the free surface mesh obtained by searching, a free surface virtual mesh that coincides with it is established. 3. According to the high-precision calculation method of the molten pool surface force under the selective laser melting technology of claim 2, it is characterized in that the smoothing reconstruction and volume correction of the rough free interface of the free surface virtual grid to obtain a smooth free interface comprises the following steps: Set the smoothing threshold and vector field convergence condition; The position of each node on the virtual grid of the free surface is used as an iterative initial value, and the position of each node on the rough free interface is iteratively calculated in combination with the smoothing number threshold to obtain the middle position of each node on the rough free interface; Performing volume correction on the intermediate position to obtain a corrected intermediate position; Calculating the vector field of the corrected intermediate position, and when the vector field does not satisfy the vector field convergence condition, using the corrected intermediate position calculated this time as the iteration initial value to calculate the next corrected intermediate position, iteratively calculating until the vector field satisfies the vector field convergence condition, and using the final corrected intermediate position as the final node position; The smooth free interface is obtained according to the final node position. 4. According to a high-precision calculation method for the surface force of the molten pool under the selective laser melting technology of claim 3, it is characterized in that the position of each node on the virtual grid of the free surface is used as the initial value of the iteration, and the position of each node on the rough free interface is iteratively calculated in combination with the smoothing number threshold to obtain the middle position of each node on the rough free interface, which includes the following steps: Using the position of each node on the virtual grid of the free surface as the iterative initial value for the first smoothing of the rough free interface, and then calculating the unit external normal vector and smooth displacement of each node on the rough free interface; Calculating the position of each node on the rough free interface using the unit external normal vector and the smooth displacement, and recording it as a preliminary position; If the number of smoothing times for the rough free interface is less than the smoothing times threshold, the preliminary position calculated this time is used as the next preliminary position of the iteration initial value, and the iterative calculation is performed until the number of smoothing times for the rough free interface is not less than the smoothing times threshold, and the final preliminary position is used as the intermediate position. 5. The high-precision calculation method for the surface force of the molten pool in the selective laser melting technology according to claim 4 is characterized in that the volume correction of the intermediate position to obtain the corrected intermediate position comprises the following steps: Update the unit external normal vector according to the intermediate position to obtain a spare unit external normal vector; The middle position is volume-corrected using the spare unit external normal vector to obtain a corrected middle position. 6. The high-precision calculation method for the surface force of the molten pool under the selective laser melting technology according to claim 5 is characterized in that the step of solving the surface force of the molten pool on the smooth free interface comprises the following steps: Calculating the mixing area at each node on the smooth free interface; The average curvature at each node on the smooth free interface is calculated using the mixed area and the unit external normal vector, and the average curvature is smoothed using a weighted average method to obtain a smooth curvature; Establishing a molten pool surface force model according to the mixed area, the unit external normal vector and the smooth curvature; The surface force at each node on the smooth free interface is solved according to the molten pool surface force model, and the surface force is mapped to the material point using a volume averaging method. 7. The high-precision calculation method for the surface force of the molten pool in the selective laser melting technology according to claim 6 is characterized in that the unit external normal vector and the smooth displacement respectively satisfy the following relationship: , , in, The unit external normal vector of node I on the rough free interface, is the area vector of node I on the rough free interface; is the smooth displacement generated by the node I on the rough free interface calculated by the kth iteration, J is the neighbor node of the node I on the rough free interface, is the set of neighbor nodes, is the weight factor of node I at neighboring node J on the rough free interface, The position of neighbor node J in the kth iteration calculation, is the initial position of node I on the rough free interface calculated in the kth iteration. 8. The high-precision calculation method for the surface force of the molten pool in the selective laser melting technology according to claim 7 is characterized in that when iteratively obtaining the intermediate position, the preliminary position satisfies the following relationship: , in, is the initial position of node I on the rough free interface, is the initial position of node I on the rough free interface calculated at the k+1th iteration, is the initial position of node I on the rough free interface calculated at the kth iteration, is the coefficient for controlling node movement, is the relaxation factor, is the unit external normal vector of node I on the rough free interface calculated at the kth iteration, It is the smooth displacement generated by the node I on the rough free interface obtained by k-th iterative calculation. 9. The high-precision calculation method for the surface force of the molten pool in the selective laser melting technology according to claim 8 is characterized in that the smooth curvatures satisfy the following relationship: , in, is the smooth curvature at node I on the smooth free interface, J is the neighbor node of I on the smooth free interface, is the set of neighbor nodes, is the weight factor for curvature smoothing, is the average curvature at node I on the smooth free interface, is the average curvature of the neighboring nodes of node I on the smooth free interface. 10. The high-precision calculation method for the molten pool surface force in the selective laser melting technology according to claim 9, characterized in that the molten pool surface force model satisfies the following relationship: , in, is the molten pool surface force at node I on the smooth free interface, is the surface tension coefficient, is the smooth curvature at node I on the smooth free interface, is the unit external normal vector, is the mixing area at node I on the smooth free interface.