CN116705209B - High-precision calculation method for surface force of molten pool under selective laser melting technology - Google Patents
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Abstract
The application relates to the field of metal additive manufacturing, in particular to a high-precision calculation method for the surface force of a molten pool under a selective laser melting technology, which is used for solving the problems of large calculation amount caused by the need of solving a free interface evolution equation in a full field when the surface force of the molten pool under the selective laser melting technology is calculated and the problem of lower precision when the surface force is solved by a material point method in the prior art, and comprises the following steps: dividing a calculation grid by using preset calculation parameters, dispersing the whole material domain into object points, and initializing the calculation grid by using the object points; searching a free surface grid in the initialized calculation grid according to a mass field of a background grid node in an object point method, and establishing a free surface virtual grid according to the free surface grid; carrying out smooth reconstruction and volume correction on the rough free interface of the free surface virtual grid to obtain a smooth free interface; and solving the surface force of the molten pool on the smooth free interface.
Description
Technical Field
The application relates to the field of metal additive manufacturing, in particular to a high-precision calculation method for the surface force of a molten pool under a selective laser melting technology.
Background
In recent years, additive manufacturing technology has attracted widespread attention in the domestic and foreign industries. The additive manufacturing technology is a revolutionary manufacturing technology which adopts high-energy heat beams to melt materials layer by layer and accumulate the materials layer by layer and can realize near net shape forming of any complex shape. Unlike traditional turning and other material reducing and equal material producing technology, the material adding process obtains complicated part configuration in layer-by-layer smelting and accumulating mode and has the advantages of short period, low cost, saving in material, etc. Among them, selective laser melting technology is one of the common metal additive manufacturing technologies.
However, most of the current free interface capturing methods require full-field solving of additional equations and particle search algorithms, such as the VOF method requires reconstructing normal vectors and intercepts from the volume fraction in each cell, and the Level set method requires full-field solving of the symbol distance function and additional reinitialization at each step. The SPH method in the gridless method needs to search for the proximity relation of surface particles, which affects the calculation efficiency, while the free interface of the standard mass point method is stepped, which needs to further improve the precision and establish an accurate model for the surface force in the metal additive manufacturing problem.
Disclosure of Invention
Aiming at the defects in the prior art, the application provides a high-precision calculation method for the surface force of a molten pool under a selective laser melting technology.
In order to achieve the above purpose, the application provides a high-precision calculation method for the surface force of a molten pool under a selective laser melting technology, which comprises the following steps: dividing a calculation grid by using preset calculation parameters, dispersing the whole material domain into object points, and initializing the calculation grid by using the object points; searching a free surface grid in the initialized calculation grid according to a mass field of a background grid node in an object point method, and establishing a free surface virtual grid according to the free surface grid; carrying out smooth reconstruction and volume correction on the rough free interface of the free surface virtual grid to obtain a smooth free interface; and solving the surface force of the molten pool on the smooth free interface. The application reduces the calculated amount when calculating the surface force of the molten pool under the selective laser melting process, solves the problem of the stepped liquid level described by the background grid in the standard mass point method, and improves the solving precision of the surface force of the molten pool.
Optionally, the searching the free surface grid in the initialized calculation grid according to the mass field of the background grid node in the object point method, and establishing the free surface virtual grid according to the free surface grid includes the following steps:
mapping the mass of the object points to the background grid nodes;
all the empty grids in the whole calculation domain are circulated, when the quality of the node of any empty grid is not zero, the node is a free surface node, and meanwhile, the non-empty grid connected with the node is a free surface grid;
and establishing a free surface virtual grid overlapped with the free surface grid according to the free surface grid obtained by searching.
Furthermore, the virtual grid of the free surface, which is coincident with the grid of the free surface, is established, so that smooth reconstruction of the interface is facilitated at a small number of grids of the free surface, and the efficiency of surface capturing can be effectively improved.
Optionally, the step of performing smooth reconstruction and volume correction on the rough free interface of the virtual grid of the free surface to obtain a smooth free interface includes the following steps:
setting a smoothing frequency threshold and a vector field convergence condition;
taking the positions of all nodes on the virtual grid of the free surface as iteration initial values, and carrying out iterative computation on the positions of all nodes on the rough free interface by combining the smoothing frequency threshold value to obtain the intermediate positions of all nodes on the rough free interface;
performing volume correction on the intermediate position to obtain a corrected intermediate position;
calculating a vector field of the corrected intermediate position, when the vector field does not meet the vector field convergence condition, calculating the next corrected intermediate position by taking the corrected intermediate position obtained by the calculation as the iteration initial value, carrying out iterative calculation until the vector field meets the vector field convergence condition, and taking the final corrected intermediate position as a final node position;
and obtaining the smooth free interface according to the final node position.
Furthermore, the rough free interface of the virtual grid of the free surface is subjected to repeated smooth reconstruction and volume correction by setting a smooth frequency threshold value and vector field convergence conditions, so that a smooth free interface is obtained, the problem of the stepped liquid level described by the background grid in the standard mass point method is solved, and the solving precision of the surface force of a molten pool is improved.
Optionally, using the positions of the nodes on the virtual grid of the free surface as iteration initial values, and iteratively calculating the positions of the nodes on the rough free interface in combination with the smoothing frequency threshold value to obtain the intermediate positions of the nodes on the rough free interface, where the steps include:
taking the positions of all nodes on the virtual grid of the free surface as the iteration initial values for carrying out first smoothing on the rough free interface, and further calculating the unit external normal vector and smooth displacement of all the nodes on the rough free interface;
calculating the position of each node on the rough free interface by using the unit external normal vector and the smooth displacement, and marking the position as a preliminary position;
and if the smoothing times of the rough free interface is smaller than the smoothing times threshold, taking the preliminary position obtained by the calculation as the next preliminary position of the iteration initial value, carrying out iterative calculation until the smoothing times of the rough free interface is not smaller than the smoothing times threshold, and taking the final preliminary position as the intermediate position.
Optionally, the step of performing volume correction on the intermediate position to obtain a corrected intermediate position includes the following steps:
updating the unit external normal vector according to the intermediate position to obtain a standby unit external normal vector;
and carrying out volume correction on the intermediate position by using the spare unit external normal vector to obtain a corrected intermediate position.
Optionally, the solving for the surface force of the molten pool at the smooth free interface comprises the steps of:
calculating the mixing area of each node on the smooth free interface;
calculating the average curvature of each node on the smooth free interface by using the mixed area and the unit external normal vector, and smoothing the average curvature by using a weighted average method to obtain a smooth curvature;
establishing a molten pool surface force model according to the mixing area, the unit external normal vector and the smooth curvature;
and solving the surface force at each node on the smooth free interface according to the molten pool surface force model, and mapping the surface force to the material point by adopting a volume average method.
Furthermore, the accuracy of solving the surface force of the molten pool on the smooth free interface is higher, and the surface force at each object point can be further obtained by mapping the surface force to the object point, so that the calculation of introducing the surface force into the background grid node force is facilitated.
Optionally, the unit external normal vector and the smooth displacement satisfy the following relationships, respectively:
，
，
wherein ,said extra-unit normal vector of node I on said rough free interface,/and a method of making said node I>The area vector of the node I on the rough free interface is the area vector of the node I on the rough free interface;For the smooth displacement generated by the node I on the rough free interface obtained by the kth iterative computation, J is the neighbor node of the node I on the rough free interface, and +.>For the set of neighbor nodes, +.>For the weight factor of node I at neighbor node J on the rough free interface, +.>Position of neighbor node J in kth iterative computation,/->And calculating the obtained preliminary position of the node I on the rough free interface in the kth iteration.
Optionally, when the intermediate position is obtained iteratively, the preliminary position satisfies the following relationship:
wherein ,for said preliminary position of node I on said rough free interface,For the preliminary position of node I on the rough free interface calculated in the k+1st iteration,/for the rough free interface>For the preliminary position of node I on the rough free interface calculated at the kth iteration,/I>For controlling the coefficients of node movement, +.>For relaxation factor, ++>For the unit external normal vector of the node I on the rough free interface obtained by the kth iterative computation,/and the like>And (3) calculating the smooth displacement generated by the node I on the rough free interface for the kth iteration.
Optionally, the smooth curvatures satisfy the following relationships, respectively:
wherein ,j is the neighbor node of the node I on the smooth free interface, which is the smooth curvature of the node I on the smooth free interface,For the set of neighbor nodes, +.>For curvature smoothed weighting factor, +.>For the mean curvature at node I on the smooth free interface, +.>Is the average curvature at the neighbor node of node I on the smooth free interface.
Further, the smooth curvature at each node on the smooth free surface is obtained after the average curvature is smoothed by adopting a weighted average method, wherein the average curvature at each node on the smooth free surface is obtained by solving according to the discrete average form of the Laplacian operator, the adopted average curvature effectively avoids the precision loss of multiple derivation in the prior art, the calculated amount of calculating the surface force of a molten pool under the selective laser melting process is reduced, and the precision of solving the surface force can be improved by smoothing the average curvature.
Optionally, the molten pool surface force model satisfies the following relationship:
wherein ,for the bath surface force at the junction I on the smooth free interface +.>As a function of the surface tension coefficient,for the smooth curvature at node I on the smooth free interface,For the unit external normal vector, +.>Is the mixing area at node I on the smooth free interface.
In summary, the application solves the problem of the 'stepped' liquid level described by the background grid in the standard mass point method, effectively improves the free surface capturing efficiency of the molten pool, reduces the calculated amount when calculating the surface force of the molten pool under the selective laser melting technology, realizes the high-precision calculation of the surface force of the molten pool under the selective laser melting technology, and has better accuracy of the prediction result.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for calculating the surface force of a molten pool with high precision under a selective laser melting technology according to an embodiment of the application;
FIG. 2 is a schematic view of a free surface mesh in accordance with an embodiment of the present application;
FIG. 3 is a schematic view of a smooth reconstruction according to an embodiment of the present application;
FIG. 4 is a simplified flowchart of a method for obtaining a final node position according to an embodiment of the present application;
FIG. 5 is a schematic diagram of a solution of an external normal vector unit according to an embodiment of the present application;
FIG. 6 is a schematic diagram of a free surface mesh smoothing process according to an embodiment of the present application;
FIG. 7 is a schematic diagram of a volume correction process according to an embodiment of the present application;
FIG. 8 is a schematic diagram of geometrically partitioning virtual grid cells according to an embodiment of the present application;
FIG. 9 is a schematic diagram of polygon area and blended area calculations at free surface nodes in accordance with an embodiment of the present application.
Detailed Description
Specific embodiments of the application will be described in detail below, it being noted that the embodiments described herein are for illustration only and are not intended to limit the application. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one of ordinary skill in the art that: no such specific details are necessary to practice the application. In other instances, well-known circuits, software, or methods have not been described in detail in order not to obscure the application.
Throughout the specification, references to "one embodiment," "an embodiment," "one example," or "an example" mean: a particular feature, structure, or characteristic described in connection with the embodiment or example is included within at least one embodiment of the application. Thus, the appearances of the phrases "in one embodiment," "in an embodiment," "one example," or "an example" in various places throughout this specification are not necessarily all referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics may be combined in any suitable combination and/or sub-combination in one or more embodiments or examples. Moreover, those of ordinary skill in the art will appreciate that the illustrations provided herein are for illustrative purposes and that the illustrations are not necessarily drawn to scale.
It should be noted in advance that in an alternative embodiment, the same symbols or alphabet meaning and number are the same as those present in all formulas, except where separate descriptions are made.
In addition, no matter on which interface, the set of the neighbor nodes is unchanged for the fixed node I, so that the references of "J is the neighbor node of the node I on the smooth free interface", "J is the neighbor node of the node I on the rough free interface", or the like in this embodiment only indicate that the position of the node is changed after the node is processed, and do not represent that the node target is changed, i.e. the neighbor nodes referred to by "the neighbor node of the node I on the smooth free interface", "the neighbor node of the node I on the rough free interface", and "the neighbor node of the node I on the reconstructed interface" are the same on the target.
In an alternative embodiment, referring to fig. 1, the present application provides a method for calculating the surface force of a molten pool under a selective laser melting technique with high precision, the method comprising the steps of:
s1, dividing a calculation grid by using preset calculation parameters, dispersing the whole material domain into object points, and initializing the calculation grid by using the object points.
Specifically, in this embodiment, the calculation grid is divided according to preset calculation parameters, and the whole material domain is discretized into object particles, and then the physical quantity carried by the grid unit and the physical quantity carried by the particles are initialized. Reference is made specifically to the standard particle method, which is not described in detail herein.
Further, the preset calculation parameters comprise the length of the grid unit and the number of initial substance points in the unit.
S2, searching a free surface grid in the initialized calculation grid according to a quality field of a background grid node in an object point method, and establishing a free surface virtual grid according to the free surface grid.
Wherein, S2 specifically further comprises the following steps:
s21, mapping the mass of the object points to the background grid nodes.
Specifically, in this embodiment, the mass of the object particles is mapped onto the background grid nodes in a functional form, which is known in the art, and reference may be made to the standard object particle method, which is not described in detail herein.
S22, circulating all the empty grids in the whole calculation domain, wherein when the mass of the node of any empty grid is not zero, the node is a free surface node, and meanwhile, the non-empty grid connected with the free surface node is the free surface grid.
Specifically, in this embodiment, tracking of the free surface in the standard particle method can be achieved by the mass field of the background grid nodes. Referring to fig. 2, the open dots on the four vertices of the square represent no mass nodes; solid black dots on four vertexes of the square represent nodes with non-zero mass, namely free surface nodes, and are hereafter called nodes for short; the small black dots in the square represent the material dots, the square not containing the material dots is an empty cell, the square containing the material dots and having an interface with the empty cell is a free surface cell, the interface of the free surface cell and the empty cell is the free surface of the molten pool, the square containing the material dots but not having an interface with the empty cell is a fluid cell of the molten pool, and the grid of the free surface is the free surface grid.
Further, as can be seen from fig. 2, the free surface result obtained by the free surface tracking strategy in the standard mass particle method is a "step-like" rough free interface, which cannot accurately describe the free surface morphology of the molten pool, and further cannot obtain accurate normal vectors and curvatures of nodes on the free surface, thereby affecting the accuracy of solving the surface force.
S23, establishing a free surface virtual grid overlapped with the free surface grid according to the free surface grid obtained by searching.
Specifically, in this embodiment, the free surface virtual grid coincides with the free surface grid obtained by searching, and is determined by the free surface nodes, but unlike the free surface grid, the free surface virtual grid only carries geometric information, normal vector, curvature, surface tension and other information, so that the reconstruction of a rough free interface is facilitated.
And S3, carrying out smooth reconstruction and volume correction on the rough free interface of the free surface virtual grid to obtain a smooth free interface.
Specifically, in this embodiment, referring to fig. 3, for the free surface of the spherical molten pool, the free interface formed by the virtual grid of the free surface initially established is also actually a "stepped" rough free interface, as in (a) of fig. 3. The rough free interface is closer in shape to reality after smooth reconstruction, but brings about a volumetric deviation, as in (b) of fig. 3. It is therefore necessary to make a volume correction of the rough free interface after smooth reconstruction, so that a smooth free interface closest to the actual situation is obtained, as in fig. 3 (c).
More specifically, S3 specifically further includes the following steps:
s31, setting a smoothing frequency threshold value and vector field convergence conditions.
Specifically, in this embodiment, please refer to fig. 4, the smoothing frequency 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 the smoothing reconstruction. This has the advantage that the rough free interface can be restored to the free interface closest to the actual situation, i.e. the smooth free interface.
Further, the smoothing frequency threshold is 20 times, and the vector field convergence condition is:
wherein L is the number of nodes on the rough free interface, namely the number of nodes on the free surface of the rough free interface;is a converging residual error;For a field vector comprising all free surface nodes +.>Taking the free surface junction I as an example:
wherein ,a field being the free surface junction IVector (S)>For the junction position of the free surface junction I after the jth volume repair,/th time>Is the junction location of free surface junction I after the j-1 th volume repair.
Still further, in alternative embodiments, other smoothing frequency thresholds and other convergence conditions may be selected and designed, as such, are not specifically recited herein.
S32, taking the positions of all nodes on the virtual grid of the free surface as iteration initial values, and carrying out iterative computation on the positions of all nodes on the rough free interface by combining the smoothing frequency threshold value to obtain the intermediate positions of all nodes on the rough free interface.
Wherein, S32 specifically further comprises the following steps:
s321, taking the positions of all nodes on the virtual grid of the free surface as the iteration initial value for carrying out first smoothing on the rough free interface, and further calculating the unit external normal vector and smooth displacement of all the nodes on the rough free interface.
Specifically, in this embodiment, referring to fig. 5, the positions of nodes on the virtual grid of the free surface are used as initial iteration values for performing first smoothing on the rough free interface, where I,、 andRepresenting four nodes on the rough free interface, respectively.
On the rough free interface, the unit external normal vector of the node IThe following relationship is satisfied:
unit external normal vectorFor determining a smooth reference direction for the junction I at the rough free interface.
For the area vector of node I on the rough free interface, +.>The following relationship is satisfied:
wherein ,is a set of triangles surrounding node I on the rough free interface, +.>Is the area vector of the kth triangle in the triangle set.
Area vectorThe method can be calculated by the following method:
，
，
，
wherein , andTwo vectors representing the two sides of the kth triangle in the triangle set, respectively, +.>、、 andNode I, & I, respectively>、 andIs a position of (c). In FIG. 5, < >>Direction and junction->To node->Is the same in direction (I)>Direction and junction->The direction to node I is the same.
The smooth displacement of the node I on the rough free interface satisfies the following relationship:
wherein ,for the smooth displacement generated by the node I on the rough free interface obtained by the kth iterative computation, J is the neighbor node of the node I on the rough free interface, +.>For the set of neighbor nodes, +.>Is the weight factor of node I at neighbor node J on the rough free interface, +.>Position of neighbor node J in kth iterative computation,/->For the preliminary position of node I on the rough free interface, calculated at the kth iteration, k=1,/in the first iteration>Can be recorded as +.>。
Weighting factorThe following relationship is satisfied:
wherein ,area vector of neighbor node J of node I on rough free interface, +.>Is calculated by the method and->Is calculated in the same way,Is a smooth weight factor, and->。
Further, fig. 5 is for convenience of description only, and is not to be construed as illustrating the location of the node I or any one of the nodes on the rough free interface and the scene where it is located.
S322, calculating the positions of all nodes on the rough free interface by using the unit external normal vector and the smooth displacement, and marking the positions as preliminary positions.
Specifically, in the present embodiment, the preliminary position satisfies the following relationship:
wherein ,for said preliminary position of node I on the rough free interface,/for the first time>For the preliminary position of node I on the rough free interface calculated at the (k+1) th iteration,/for the preliminary position>For controlling the coefficients of node movement, +.>，For relaxation factor, ++>，And (3) obtaining a unit external normal vector of the node I on the rough free interface by the kth iterative calculation, wherein k=1 in the first iterative calculation.
Further, please refer to fig. 6, in whichIs the position of the neighbor node J of node I on the rough free interface, +.>Is the location of node I on the rough free interface. The enclosed area enclosed by the dashed line represents the free surface mesh that has not been smoothly reconstructed, and the enclosed area is implemented to represent the free surface mesh that has been smoothly reconstructed.
And S323, if the smoothing times of the rough free interface is smaller than the smoothing times threshold, taking the preliminary position obtained by the calculation as the next preliminary position of the iteration initial value, carrying out iterative calculation until the smoothing times of the rough free interface are not smaller than the smoothing times threshold, and taking the final preliminary position as the intermediate position.
Specifically, in this embodiment, referring to fig. 4, a smooth reconstruction is completed without calculating the preliminary positions of all nodes on the rough free interface once, and if the number of times of smoothing the rough free interface does not reach 10 times, the preliminary positions of all nodes on the rough free interface obtained by this calculation are fed back to step S321 as the iteration initial value to perform the next smooth reconstruction until the number of times of smoothing the rough free interface reaches 10 times. The method for carrying out smooth reconstruction on the rough free interface is a weighted Laplacian smoothing method, and the method is different from the traditional Laplacian smoothing method, and the smoothing weight at the neighbor node used by the weighted Laplacian smoothing method is not constant, but the distance between the neighbor node and the current node is considered, and the distance is measured by the area represented by the neighbor node. The method has the advantages that the method can restore the real situation of the free surface to the greatest extent, improves the efficiency of capturing the free surface of the molten pool, and further improves the precision of calculating the surface force of the molten pool under the selective laser melting technology.
And S33, performing volume correction on the intermediate position to obtain a corrected intermediate position.
After the multiple smooth reconstructions of step S32, the rough free interface has been closest in shape to the actual situation, and for ease of distinction, the free surface determined by the nodes at the intermediate positions is referred to as the reconstructed interface, but it should be understood that the reconstructed interface is in essence a rough free interface after the multiple smooth reconstructions.
Further, S33 specifically further includes the following steps:
s331, updating the unit external normal vector according to the intermediate position to obtain a standby unit external normal vector.
Specifically, in this embodiment, referring to fig. 4, S32 only obtains and outputs the intermediate positions of the nodes on the rough free interface, however, the unit external normal vector corresponding to the intermediate positions of the nodes on the rough free interface is not updated, so that the unit external normal vector of each node on the rough free interface needs to be updated according to the intermediate positions, and the update result is recorded as a spare unit external normal vector, so as to provide a data basis for performing volume correction on the intermediate positions of the nodes on the rough free interface.
And S332, performing volume correction on the intermediate position by using the standby unit external normal vector to obtain a corrected intermediate position.
Specifically, in this embodiment, first, volume correction displacement of each node on the reconstruction interface is calculated according to the intermediate position and the weight factor of each node on the reconstruction interface, then, correction intermediate positions of each node on the reconstruction interface are calculated according to the volume correction displacement and the external normal vector of the standby unit, and the volume correction displacement and the correction intermediate positions of each node on the reconstruction interface respectively satisfy the following relationships:
，
，
wherein ,volume-corrected displacement of node I on the reconstruction interface, +.>Position of neighbor node J of node I on the reconstruction interface, < >>Reconstructing the position of a neighbor node J of the node I on the interface when the smooth reconstruction is not performed;Modified intermediate positions of the nodes on the reconstruction interface, < >>For volume correction factor, ++>，And reconstructing the outside normal vector of the standby unit at the node I on the interface.
Further, the weight factor in this stepIs calculated on the basis of the intermediate positions of the respective nodes on the reconstruction interface, and the calculation method thereof refers to the content of step S321.
Further, referring to fig. 7, based on fig. 6, the enclosed area surrounded by the solid line is a free surface grid subjected to volume correction.
And S34, calculating a vector field of the corrected intermediate position, and when the vector field does not meet the vector field convergence condition, using the corrected intermediate position obtained by calculation at the time as the iteration initial value to calculate the next corrected intermediate position, carrying out iterative calculation until the vector field meets the vector field convergence condition, and using the final corrected intermediate position as a final node position.
Specifically, in the present embodiment, the reconstructed interface determined by each free surface node at the correction intermediate position is referred to as a correction interface. Calculated according to step S332And (3) calculating the field vector of each node on the correction interface according to the field vector calculation mode provided in the step (S31), judging whether the field vector of each node on the correction interface meets the vector field convergence condition provided in the step (S31), and if not, feeding back the position of each node on the correction interface to the step (S32) as an iteration initial value for recalculation. Repeating the operations from 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.
And S35, obtaining the smooth free interface according to the final node position.
Specifically, in this embodiment, the positions of the nodes on the smooth free interface are the positions of the final nodes, so that the smooth free interface, that is, the smooth free surface of the molten pool, can be obtained according to the positions of the final nodes.
S4, solving the surface force of the molten pool on the smooth free interface.
Wherein, S4 specifically further comprises the following steps:
s41, calculating the mixing area at each node on the smooth free interface.
Specifically, in this embodiment, the mixing area at each node is obtained on the smooth free interface in this step. After a smooth free interface is obtained, the curvature of each node needs to be calculated in order to calculate the surface force later.
Further, referring to fig. 8, in order to calculate the curvature of each node on the smooth free surface, the virtual grid cells, that is, the free surface cells after the free surface virtual grid is constructed, need to be geometrically divided. First, the quadrangular face piece of the virtual grid cell in (a) of fig. 8 is triangulated to obtain a series of triangular face pieces without any gaps or overlapping, as shown in (b) of fig. 8. Triangulation is the cutting of each quadrilateral panel along its shorter diagonal, as indicated by the dashed line in fig. 8 (b). Subsequently, the curved surface constituted by the triangular patches is decomposed into a set of polygons in accordance with the constitution idea of the Voronoi diagram, as shown in (c) of fig. 8. The polygons consist of the outer centers of triangles or the centers of sides, as shown in fig. 9, each polygon representing the area of a node, hereinafter referred to as the blend area, and the polygons do not overlap each other, and the total area of all the polygons is equal to the area of the free surface in fig. 8 (a) or 8 (b).
Further, referring to fig. 9, on a smooth free interface, the blending area at the free surface node I is the sum of the polygonal areas around the node. Before calculating the area of each polygon, the types of the triangles contained in each polygon and the internal angle of each triangle at the node I are considered first. The following three cases need to be considered: triangle-shapedA non-obtuse triangle; triangle->Is an obtuse triangle and is->Is an obtuse angle; triangle->Is an obtuse triangle and is->Is an acute angle. The three cases are shown as (a) and (b) in FIG. 9 respectivelyAnd (c) is shown. Thus, the ith polygonal area +_at free surface node I>The following relationship is satisfied:
wherein , andIs triangle->Is> andIs triangle->Is>、 andRespectively triangle +.>Is the position of the three vertices of (1), edge vector +.>Is oriented as vertex->To the vertex +.>Direction, edge vector->Is oriented as vertex->To the vertex +.>Direction.
Further, on a smooth free interface, the mixing area at node IThe following relationship is satisfied:
wherein ,is a collection of polygons around node I on a smooth free interface.
S42, calculating average curvature at each node on the smooth free interface by using the mixed area and the unit external normal vector, and smoothing the average curvature by using a weighted average method to obtain a smooth curvature.
Specifically, in the present embodiment, the average curvature at the node I on the smooth free interfaceThe following relationship is satisfied:
in which, referring to FIG. 9,is a node on a smooth free interfaceI position,/-)>Is the position of neighbor node J of node I on the smooth free interface, +.> andRespectively is->Two opposite triangular inner corners.
Using weighted average to average curvatureThe smooth curvature obtained by performing the smoothing process satisfies the following relationship:
wherein ,for the smooth curvature of the junction I on the smooth free interface, J is the neighbor junction of the junction I on the smooth free interface,/and J is the one of the two>For curvature smoothed weighting factor, +.>，For the average curvature at the neighbor node of node I on the smooth free interface, +.>Is calculated by the method and->The same way of calculation.
S43, establishing a molten pool surface force model according to the mixing area, the unit external normal vector and the smooth curvature.
Specifically, in this embodiment, the molten pool surface force model satisfies the following relationship:
wherein ,for the surface force of the bath at the junction I on the smooth free interface +.>Is the surface tension coefficient +.>Is the unit external normal vector. During calculation +.>Can be replaced by->And the node I on the smooth free interface is the same node as the node I on the virtual grid of the free surface, thus +.>Is also the surface force of the molten pool at node I on the free surface virtual grid.
S44, solving the surface force at each node on the smooth free interface according to the molten pool surface force model, and mapping the surface force to the material point by adopting a volume average method.
Specifically, in the present embodiment, S331 is obtainedS41 is->And S42 meterCalculated and obtainedThe surface force of the molten pool at the junction I on the molten pool can be calculated by bringing the surface force into the molten pool surface force model of S43, namely the surface force of the molten pool at the junction I on the smooth free interface +.>。/>
Further, since the free surface virtual grid and the free surface grid before smooth reconstruction are completely overlapped, they share the same grid node number, and the surface force of each node on the free surface virtual grid can be directly distributed to the background grid node, namely:
wherein ,is the surface force at background grid junction I.
Then, mapping the surface force at the background grid node to the surface force of the free surface unit at the grid center of the free surface unit, and finally uniformly distributing the surface force of the free surface unit to each object point in the free surface unit in the form of physical force of unit mass to obtain the surface force of each object point, wherein the surface force of the free surface unit and the surface force of each object point respectively meet the following relation:
，
，
wherein ,is the surface force of the free surface unit C +.>Is the set of free surface nodes contained in free surface unit C, < > and>the number of free surface elements that are the inclusion of background mesh nodes I;For the surface force of each object point in the free surface unit C +.>Is the unit mass of the free surface unit C +.>Is the number of material particles in free surface unit C.
It should be noted that, in some cases, the actions described in the specification may be performed in a different order and still achieve desirable results, and in this embodiment, the order of steps is merely provided to make the embodiment more clear, and it is convenient to describe the embodiment without limiting it.
In summary, the application utilizes the characteristic that the object particle method is easy to track the free surface by means of the background grid, firstly identifies the free surface grid and the nodes thereof through the mass field of the background grid nodes, then establishes a free surface virtual grid overlapped with the free surface grid, carries out smooth reconstruction of a free interface on the free surface virtual grid, carries out volume correction on the smooth and heavy interface by adopting the volume correction method to obtain a smooth free interface, solves the problem of the stepped liquid level described by the background grid in the standard object particle method, and effectively improves the free surface capturing efficiency of a molten pool; then, the curvature and the surface force are solved on the free surface with higher precision, wherein the average curvature adopted effectively avoids the precision loss of multiple derivation in the prior art, and reduces the calculated amount when the surface force of a molten pool under the selective laser melting process is calculated; finally, a mapping relation between the free surface virtual grid and a substance point method is established by adopting a volume average method, and the surface force of each object point is obtained. The application realizes high-precision calculation of the surface force of the molten pool under the selective laser melting technology, and the accuracy of the prediction result is better.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the application, and are intended to be included within the scope of the appended claims and description.
Claims (10)
1. A high-precision calculation method of the surface force of a molten pool under a selective laser melting technology is characterized by comprising the following steps:
dividing a calculation grid by using preset calculation parameters, dispersing the whole material domain into object points, and initializing the calculation grid by using the object points;
searching a free surface grid in the initialized calculation grid according to a mass field of a background grid node in an object point method, and establishing a free surface virtual grid according to the free surface grid;
carrying out smooth reconstruction and volume correction on the rough free interface of the free surface virtual grid to obtain a smooth free interface;
and solving the surface force of the molten pool on the smooth free interface.
2. The method for high-precision calculation of molten pool surface force under selective laser melting technology as set forth in claim 1, wherein said searching free surface grids in said initialized calculation grids according to mass fields of background grid nodes in object particle method, and establishing free surface virtual grids according to said free surface grids comprises the steps of:
mapping the mass of the object points to the background grid nodes;
all the empty grids in the whole calculation domain are circulated, when the quality of the node of any empty grid is not zero, the node is a free surface node, and meanwhile, the non-empty grid connected with the node is a free surface grid;
and establishing a free surface virtual grid overlapped with the free surface grid according to the free surface grid obtained by searching.
3. The method for calculating the surface force of the molten pool under the selective laser melting technology according to claim 2, wherein the step of performing smooth reconstruction and volume correction on the rough free interface of the virtual grid of the free surface to obtain a smooth free interface comprises the following steps:
setting a smoothing frequency threshold and a vector field convergence condition;
taking the positions of all nodes on the virtual grid of the free surface as iteration initial values, and carrying out iterative computation on the positions of all nodes on the rough free interface by combining the smoothing frequency threshold value to obtain the intermediate positions of all nodes on the rough free interface;
performing volume correction on the intermediate position to obtain a corrected intermediate position;
calculating a vector field of the corrected intermediate position, when the vector field does not meet the vector field convergence condition, calculating the next corrected intermediate position by taking the corrected intermediate position obtained by the calculation as the iteration initial value, carrying out iterative calculation until the vector field meets the vector field convergence condition, and taking the final corrected intermediate position as a final node position;
and obtaining the smooth free interface according to the final node position.
4. The method for high-precision calculation of molten pool surface force under selective laser melting technology as claimed in claim 3, wherein said iterative calculation of the positions of nodes on said rough free interface by using the positions of nodes on said free surface virtual grid as iteration initial values and combining said smoothing frequency threshold value to obtain the intermediate positions of the nodes on said rough free interface comprises the steps of:
taking the positions of all nodes on the virtual grid of the free surface as the iteration initial values for carrying out first smoothing on the rough free interface, and further calculating the unit external normal vector and smooth displacement of all the nodes on the rough free interface;
calculating the position of each node on the rough free interface by using the unit external normal vector and the smooth displacement, and marking the position as a preliminary position;
and if the smoothing times of the rough free interface is smaller than the smoothing times threshold, taking the preliminary position obtained by the calculation as the next preliminary position of the iteration initial value, carrying out iterative calculation until the smoothing times of the rough free interface is not smaller than the smoothing times threshold, and taking the final preliminary position as the intermediate position.
5. The method for calculating the surface force of the molten pool under the selective laser melting technology according to claim 4, wherein the step of performing the volume correction on the intermediate position to obtain the corrected intermediate position comprises the following steps:
updating the unit external normal vector according to the intermediate position to obtain a standby unit external normal vector;
and carrying out volume correction on the intermediate position by using the spare unit external normal vector to obtain a corrected intermediate position.
6. The method for high-precision calculation of the surface force of a molten pool under a selective laser melting technology according to claim 5, wherein the step of solving the surface force of the molten pool on the smooth free interface comprises the following steps:
calculating the mixing area of each node on the smooth free interface;
calculating the average curvature of each node on the smooth free interface by using the mixed area and the unit external normal vector, and smoothing the average curvature by using a weighted average method to obtain a smooth curvature;
establishing a molten pool surface force model according to the mixing area, the unit external normal vector and the smooth curvature;
and solving the surface force at each node on the smooth free interface according to the molten pool surface force model, and mapping the surface force to the material point by adopting a volume average method.
7. The method for high-precision calculation of molten pool surface force under selective laser melting technology as set forth in claim 6, wherein said unit external normal vector and said smooth displacement satisfy the following relations:
，
，
wherein ,said extra-unit normal vector of node I on said rough free interface,/and a method of making said node I>The area vector of the node I on the rough free interface is the area vector of the node I on the rough free interface;For the smooth displacement generated by the node I on the rough free interface obtained by the kth iterative computation, J is the neighbor node of the node I on the rough free interface, and +.>For the set of neighbor nodes, +.>Is saidWeight factor of node I at neighbor node J on coarse free interface, < >>Position of neighbor node J in kth iterative computation,/->And calculating the obtained preliminary position of the node I on the rough free interface in the kth iteration.
8. The method for high-precision calculation of molten pool surface force under selective laser melting technology as set forth in claim 7, wherein said preliminary position satisfies the following relationship when said intermediate position is obtained iteratively:
，
wherein ,for said preliminary position of node I on said rough free interface,For the preliminary position of node I on the rough free interface calculated in the k+1st iteration,/for the rough free interface>For the preliminary position of node I on the rough free interface calculated at the kth iteration,/I>For controlling the coefficients of node movement, +.>For relaxation factor, ++>For the unit external normal vector of the node I on the rough free interface obtained by the kth iterative computation,/and the like>And (3) calculating the smooth displacement generated by the node I on the rough free interface for the kth iteration.
9. The high-precision calculation method for the surface force of a molten pool under the selective laser melting technology according to claim 8, wherein the smooth curvatures respectively satisfy the following relations:
，
wherein ,j is the neighbor node of the node I on the smooth free interface, which is the smooth curvature of the node I on the smooth free interface,For the set of neighbor nodes, +.>For curvature smoothed weighting factor, +.>For the mean curvature at node I on the smooth free interface, +.>Is the average curvature at the neighbor node of node I on the smooth free interface.
10. The high-precision calculation method for the surface force of the molten pool under the selective laser melting technology according to claim 9, wherein the model of the surface force of the molten pool meets the following relation:
，
wherein ,for the bath surface force at the junction I on the smooth free interface +.>Is the surface tension coefficient +.>For the smooth curvature at node I on the smooth free interface,For the unit external normal vector, +.>Is the mixing area at node I on the smooth free interface.
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| 廉艳平 等.物质点法的理论和应用.力学进展.2013,第43卷(第2期),第237-264页. * |
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