CN109376497B - Method for obtaining continuous gradient porous structure of extremely-small curved surface - Google Patents
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Abstract
The invention belongs to the field of porous structures, and discloses a method for acquiring a continuous gradient porous structure with a tiny curved surface. The method comprises the following steps: (a) Establishing an Euler three-dimensional space region and carrying out grid division on the Euler three-dimensional space region to obtain coordinates of each node on a grid, selecting a plurality of nodes from network nodes as characteristic points, and setting the characteristic value of each characteristic point as (x, y, z, a, t); (b) Assigning values of a and t in the characteristic values of each characteristic point according to the gradient requirement of the porosity of the required minimum curved surface porous structure; (c) And fitting according to the characteristic value corresponding to each characteristic point to obtain a minimal curved surface model, and generating a porous structure of the minimal curved surface in a three-dimensional space area according to the minimal curved surface model so as to obtain the required continuous gradient minimal curved surface porous structure. The invention overcomes the defect of single performance of the traditional uniform pore porous structure and manufactures the gradient porous material suitable for complex mechanical environment.
Description
Technical Field
The invention belongs to the field of porous structures, and particularly relates to a method for acquiring a continuous gradient porous structure with a minimum curved surface.
Background
The porous material has excellent comprehensive properties of impact resistance, energy absorption, heat insulation, sound absorption and the like, and is widely applied to lightweight design in the industries of aerospace, medical treatment, transportation and the like. However, with the improvement of product performance and the demand of integrated design, the simple light weight and energy absorption characteristics can not meet the demand of high performance components, such as the most studied uniform porous lattice material at present, which has single mechanical property and is difficult to change, and can not match the mechanical property demand of shape change,
as data input of 3D printing, computer aided design attracts wide attention of scholars at home and abroad, various porous structures are designed for light weight, a three-cycle extremely-small curved surface (TPMS) is particularly attractive, as the extremely-small curved surface, the average curvature of each point on the TPMS curved surface is zero, the surface is smooth and smooth, the three points are periodically distributed in three directions of a European space, holes are communicated with one another, in addition, the precise control of the size and the shape of the porous structure can be realized by modifying implicit function expression parameters of the TPMS, and the method is particularly suitable for designing gradient porous materials.
In summary, most of the existing porous structures are uniform pore structures, the designed porous structure parameters are not adjustable, the pore diameter and the rod parameters cannot be changed along with the spatial position, and the mechanical property requirements in complex environments are difficult to meet.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a method for acquiring a continuous gradient porous structure with a tiny curved surface, which comprises the steps of establishing a three-dimensional space area, defining characteristic points in the area, assigning a value to a characteristic value of each characteristic point according to the porosity requirement of the required gradient porous structure, thus obtaining a tiny curved surface model, and finally generating the continuous gradient tiny curved surface porous structure according to the tiny curved surface model.
In order to achieve the above object, according to the present invention, there is provided a method for obtaining a continuous gradient porous structure of an extremely small curved surface, the method comprising the steps of:
(a) Establishing an Euler three-dimensional space region, carrying out grid division on the three-dimensional space region to obtain a gridded three-dimensional space region and coordinates of each node on the grid, selecting a plurality of nodes from the network nodes as characteristic points, and setting characteristic values corresponding to each characteristic point as (X, Y, Z, a, t), wherein X, Y and Z are coordinate values of the characteristic points in X, Y and Z directions respectively, a is the size of a pore, and t is the porosity;
(b) Assigning values of a and t in the characteristic values of each characteristic point according to the gradient requirement of the porosity of the required minimum curved surface porous structure, so that the values of a and t of the characteristic points in the three-dimensional space region are in gradient change;
(c) And fitting the characteristic value corresponding to each characteristic point in the three-dimensional space region to obtain the minimum curved surface model f (x, y, z, a, t) =0, and generating a porous structure of the minimum curved surface in the three-dimensional space region according to the model of the minimum curved surface so as to obtain the required continuous gradient minimum curved surface porous structure.
Further preferably, in the step (a), when the three-dimensional space region is subjected to grid division, the number of grids in each direction is preferably not less than 50.
Further preferably, in step (b), the values of a and t in each grid node coordinate are assigned, preferably by interpolation.
Further preferably, in step (c), the porous structure of the minimum curved surface is generated in the three-dimensional space region according to the model of the minimum curved surface, and preferably, the wall thickness of the porous structure is set first, and then the minimum curved surface is thickened according to the preset wall thickness, so that the porous structure of the minimum curved surface is obtained.
Further preferably, in step (c), the porous structure of the minimal curved surface is generated in the three-dimensional space region according to the model of the minimal curved surface, preferably according to the following manner:
in the three-dimensional space region, identifying a solid part and a pore part in the minimal curved surface, namely the three-dimensional space region is divided into the solid part and the pore part by the minimal curved surface;
and filling the area surrounded by the solid boundary to obtain the required tiny curved surface porous structure.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. the gradient porous structure obtained by the invention overcomes the defect of single mechanical property of the traditional uniform pore porous structure, can design different gradient porous materials according to different application environments, and has wide application range;
2. the extremely-small curved surface model constructed by the method can generate porous structures with different porosities by modifying the pore size and the porosity in the extremely-small curved surface model, and has the advantages of great design freedom, simple calculation process, short calculation time and high efficiency.
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FIG. 1 is a flow chart of a method for obtaining a continuous gradient porous structure with a very small curved surface constructed according to a preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention. In addition, the technical features involved in the respective embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention establishes Euler space and gridds the space, defines characteristic points according to actual engineering requirements, obtains control function values of each point on the space through an interpolation algorithm, and controls the value of variable parameters in a minimal curved surface equation by using the space grid. And constructing a uniform gradient minimum curved surface porous structure with controllable pore size and porosity for complex engineering application.
Fig. 1 is a flowchart of a method for obtaining a continuous gradient porous structure with a very small curved surface according to a preferred embodiment of the present invention, and as shown in fig. 1, the method for obtaining a continuous gradient porous structure with a very small curved surface specifically includes the following steps:
(1) Establishing an Euler space region, performing region meshing on a three-dimensional space, and establishing a space function f (x, y, z, a, t) =0, wherein a represents the pore size and t represents the porosity.
The method specifically comprises the following steps: establishing an Euler space R according to actual engineering requirements, and carrying out grid division according to coordinate values of the Euler space R, wherein not less than 50 grids in each direction are suggested so as to obtain an accurate model; each spatial point corresponds to a pore size a and an initial value of porosity t, a and t being 0.
(2) According to actual engineering requirements, defining porous structures in a three-dimensional space at different spatial positions A, B, C, D and the like, and defining the pore sizes and the porosities A (x 1, y1, z1, a1, t 1), B (x 2, y2, z2, a2, t 2), C (x 3, y3, z3, a3, t 3) and D (x 4, y4, z4, a4, t 4) of all points;
(3) Generating f (x, y, z, a, t) at each point of the three-dimensional space by adopting an interpolation algorithm according to the defined characteristic points in the step (2);
the method specifically comprises the following steps: and (3) according to the defined points in the step (2), carrying out interpolation calculation before each point to ensure that the pore size and the porosity between each point in the space are in uniform transition, and substituting the obtained values of a and t of each space point into the previously defined f (x, y, z, a, t) function.
(4) Performing mathematical modeling on the minimal curved surfaces according to f (x, y, z, a, t) at each point in space, and analyzing implicit function equations of different types of minimal curved surfaces, such as an equation of a Schoen Gyroid porous structure:
wherein a represents a cell size; t controls the volume fraction of the porous structure.
(5) The porous structure is generated in a three-dimensional space region according to an extremely-small curved surface model, and the porous structure is generated in two ways, namely, a direct curved surface is added with a wall thickness, and the other way is to identify a pore region and an entity region which are formed by dividing the three-dimensional space region by the extremely-small curved surface, and fill the entity side region to generate an entity.
The required continuous gradient minimum curved surface porous structure can be obtained through the steps.
The invention is further described below with reference to several examples.
Example 1:
(1) Establishing a space range R, wherein x is more than or equal to 0 and less than or equal to 20, y is more than or equal to 0 and less than or equal to 20, z is more than or equal to 0 and less than or equal to 20, meshing the space, and dividing by taking 0.05 as the size of a unit, so that each direction of R has 400 units and 401 nodes. And establishing a space function f (x, y, z, a, t), and assigning an initial value of 0 to a and t of each node.
(2) Defining characteristic points of the porous structure at different positions in the three-dimensional space: a (0, 2.8, 0.05), B (20, 0,2.8, 0.05) C (0, 20,2.25, 0.2), D (20, 2.25, 0.2).
(3) And (3) calculating the function f value of each point in the middle by adopting an interpolation algorithm according to the characteristic points defined in the step (2), such as AC1 (0, 5,2.663, 0.0875), AC2 (0, 10,2.525, 0.125) and AC3 (0, 15,2.3875, 0.1625).
(4) The mathematical modeling of the Schoen Gyroid porous structure is carried out according to f (x, y, z, a, t) at each point in space, and the value of b =5,t at each point in formula (1) can be represented by formula
f(x,y,z,a,t)＝0.9015+0.4115*z-t (2)
And (3) representing that the continuous gradient minimum curved surface porous structure is constructed by combining the formulas (1) and (2).
(5) And establishing a three-dimensional space region according to the extremely-small curved surface model to generate a porous structure, so as to obtain the porous structure of the extremely-small curved surface.
Example 2:
(1) Establishing a space range R, wherein x is more than or equal to 0 and less than or equal to 20, y is more than or equal to 0 and less than or equal to 20, z is more than or equal to 0 and less than or equal to 20, carrying out grid division on the space, and subdividing by taking 0.05 as the size of a unit, wherein each direction of R has 400 units and 401 nodes. And establishing a space function f (x, y, z, a, t), and assigning an initial value of 0 to a and t of each node.
(2) Defining characteristic points of the porous structure at different positions in the three-dimensional space: a (0, 2.65, 0.075), B (20, 0,2.65, 0.075) C (0, 20,2.25, 0.2), D (20, 2.25, 0.2).
(3) And (3) calculating the function f value of each intermediate point, such as AC1 (0, 5,2.55, 0.10625), AC2 (0, 10,2.45, 0.1375) and AC3 (0, 15,2.35, 0.16875) by adopting an interpolation algorithm according to the characteristic points defined in the step (2).
(4) The mathematical modeling of Schoen Gyroid porous structure is performed according to f (x, y, z, a, t) at each point in space, and the value of b =5,t at each point in formula (1) can be formulated as
f(x,y,z,a,t)＝0.9015+0.3455*z-t (2)
To indicate. And (3) establishing a continuous gradient minimum curved surface porous structure by combining the formulas (1) and (2).
(5) And establishing a three-dimensional space region according to the extremely-small curved surface model to generate a porous structure, so as to obtain the porous structure of the extremely-small curved surface.
Example 3:
(1) Establishing a space range R, wherein x is more than or equal to 0 and less than or equal to 20, y is more than or equal to 0 and less than or equal to 20, z is more than or equal to 0 and less than or equal to 20, meshing the space, and dividing by taking 0.05 as the size of a unit, so that each direction of R has 400 units and 401 nodes. And establishing a spatial function f (x, y, z, a, t), and assigning an initial value of 0 to a and t of each node.
(2) Defining characteristic points of the porous structure at different positions in the three-dimensional space: a (0, 2.55, 0.1), B (20, 0,2.55, 0.1) C (0, 20,2.25, 0.2), D (20, 2.25, 0.2).
(3) And (3) calculating the function f value of each intermediate point, such as AC1 (0, 5,2.475, 0.125), AC2 (0, 10,2.4, 0.15) and AC3 (0, 15,2.325, 0.175) by adopting an interpolation algorithm according to the characteristic points defined in the step (2).
(4) The mathematical modeling of the Schoen Gyroid porous structure is carried out according to f (x, y, z, a, t) at each point in space, and the value of b =5,t at each point in formula (1) can be represented by formula
f(x,y,z,a,t)＝0.9015+0.2798*z-t (2)
To indicate. And (3) combining the formulas (1) and (2) to construct a continuous gradient minimum curved surface porous structure.
(5) And establishing a three-dimensional space region according to the extremely-small curved surface model to generate a porous structure, so as to obtain the porous structure of the extremely-small curved surface.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A method for obtaining a continuous gradient porous structure of a very small curved surface is characterized by comprising the following steps:
(a) Establishing an Euler three-dimensional space region, carrying out grid division on the three-dimensional space region to obtain a gridded three-dimensional space region and coordinates of each node on the grid, selecting a plurality of nodes from the network nodes as characteristic points, and setting a characteristic value corresponding to each characteristic point as (X, Y, Z, a, t), wherein X, Y and Z are coordinate values of the characteristic points in X, Y and Z directions respectively, a is the size of a pore, and t is the porosity;
(b) According to the gradient requirement of the porosity of the porous structure of the required minimum curved surface, assigning values of a and t in the characteristic values of each characteristic point, so that the values of a and t of the characteristic points in the three-dimensional space region are in gradient change;
(c) And fitting the characteristic value corresponding to each characteristic point in the three-dimensional space region to obtain the extremely-small curved surface model, and generating a porous structure of the extremely-small curved surface in the three-dimensional space region according to the extremely-small curved surface model so as to obtain the required continuous gradient extremely-small curved surface porous structure.
2. The method for obtaining a continuous gradient cellular structure with an extremely small curved surface according to claim 1, wherein in the step (a), when the three-dimensional space region is subjected to grid division, the number of grids in each direction is not less than 50.
3. The method for obtaining a continuous gradient porous structure with a very small curved surface as claimed in claim 1 or 2, wherein in step (b), the values of a and t in each node coordinate of the mesh are assigned by interpolation.
4. The method for obtaining a continuous gradient porous structure with an extremely small curved surface as claimed in claim 1 or 2, wherein in step (c), the porous structure with an extremely small curved surface is generated in the three-dimensional space region according to the model with the extremely small curved surface, and the porous structure with the extremely small curved surface is obtained by first setting the wall thickness of the porous structure and then thickening the extremely small curved surface according to the preset wall thickness.
5. The method for obtaining a continuous gradient porous structure with an extremely small curved surface as claimed in claim 1 or 2, wherein in the step (c), the porous structure with the extremely small curved surface is generated in the three-dimensional space region according to the model of the extremely small curved surface according to the following modes:
identifying a solid part and a pore part in the minimal curved surface in the three-dimensional space region, namely the three-dimensional space region is divided into the solid part and the pore part by the minimal curved surface;
and filling the area surrounded by the solid boundary to obtain the required tiny curved surface porous structure.
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