CN109376497A - A kind of acquisition methods of minimal surface continuous gradient porous structure - Google Patents
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Abstract
The invention belongs to porous structure fields, and disclose a kind of acquisition methods of minimal surface continuous gradient porous structure.This method includes the following steps: that (a) establishes Euler's three-dimensional spatial area and carry out grid dividing to it, obtains the coordinate of each node on grid, chooses multiple nodes within network nodes as characteristic point, the characteristic value of each characteristic point is set as (x, y, z, a, t)；(b) it is required according to the gradient of required minimal surface porous structure porosity, assignment is carried out to a the and t value in the characteristic value of each characteristic point；(c) minimal surface model is obtained according to the corresponding characteristic value fitting of each characteristic point, generates the porous structure of minimal surface in three-dimensional spatial area according to the model of the minimal surface, required continuous gradient minimal surface porous structure is obtained with this.Through the invention, the disadvantage for overcoming conventional uniform hole porous structure performance single produces the gradient porous material suitable for complicated mechanical environment.
Description
Technical field
The invention belongs to porous structure fields, more particularly, to a kind of obtaining for minimal surface continuous gradient porous structure
Take method.
Background technique
Porous material is widely used in navigating since it is with the Good All-around Properties such as shock resistance, energy-absorbing, heat-insulated, sound-absorbing
The light-weight design of the industries such as empty space flight, medical treatment, communications and transportation.Raising and integrated design however as properties of product
Demand, simple lightweight and energy absorption characteristics are no longer satisfied the demand of high-performance component, such as current most study
Uniform porous lattice material, mechanical property is single and is difficult to change, and can not match the mechanical property demand of " profile-followed variation ",
Data as 3D printing input, and CAD has attracted domestic and foreign scholars widely to pay close attention to, and enrich more
The porous structure of sample is devised for lightweight, wherein three period minimal surfaces (TPMS) are especially noticeable, as one
Minimal surface is planted, each point average curvature is zero on TPMS curved surface, smooth surface fairing, the period on three directions of theorem in Euclid space
Distribution is mutually communicated between Kong Yukong, in addition, by modification TPMS implicit function expression argument, may be implemented porous size and
The accurate control of shape is particularly suitable for design gradient porous material.
To sum up, most of porous structure is uniform pores structure at present, and the porous structure parameter of design is non-adjustable, hole
Diameter and bar parameter can not change with spatial position, it is difficult to meet mechanical property demand in complex environment.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of minimal surface continuous gradient is porous
The acquisition methods of structure, by establishing three-dimensional spatial area and in this region feature points, according to required gradient porous
Requirement of the structure to porosity carries out assignment to the characteristic value of each characteristic point, obtains minimal surface model, last basis with this
The minimal surface model generates continuous gradient minimal surface porous structure, overcomes conventional uniform hole porous structure performance is single to lack
Point produces the gradient porous material suitable for complicated mechanical environment.
To achieve the above object, it is proposed, according to the invention, provide a kind of acquisition side of minimal surface continuous gradient porous structure
Method, which is characterized in that this method includes the following steps:
(a) Euler's three-dimensional spatial area is established, which is subjected to grid dividing, obtains the three-dimensional of gridding
The coordinate of each node on area of space and the grid, chooses multiple nodes as characteristic point in the network node, if
Determining the corresponding characteristic value of each characteristic point is (x, y, z, a, t), wherein x, y and z are characteristic point respectively in X, the seat of Y and Z-direction
Scale value, a are pore sizes, and t is porosity；
(b) it is required according to the gradient of required minimal surface porous structure porosity, to the characteristic value of each characteristic point
In a and t value carry out assignment so that a the and t value of the characteristic point in the three-dimensional spatial area changes in gradient；
(c) the corresponding characteristic value of characteristic point each in three-dimensional spatial area is fitted and obtains the minimal surface model
F (x, y, z, a, t)=0 generates the porous knot of minimal surface according to the model of the minimal surface in the three-dimensional spatial area
Structure obtains required continuous gradient minimal surface porous structure with this.
It is further preferred that in step (a), when carrying out grid dividing to the described three-dimensional spatial area, each direction
Number of grid be preferably no less than 50.
It is further preferred that a the and t value in each mesh point coordinate is assigned in step (b)
Value, it is preferred to use interpolation method.
It is further preferred that the model according to the minimal surface is in the three-dimensional spatial area in step (c)
The porous structure of minimal surface is generated, the wall thickness of porous structure is preferably first set, then by the minimal surface according to described pre-
If wall thickness thicken, can be obtained the porous structure of the minimal surface.
It is further preferred that the model according to the minimal surface is in the three-dimensional spatial area in step (c)
The porous structure of minimal surface is generated, preferably as follows:
In the three-dimensional spatial area, identify the entity part and aperture sections in the minimal surface, i.e., described three
Dimension space region is divided into entity part and aperture sections by the minimal surface；
Entity boundary area encompassed is filled, can be obtained required minimal surface porous structure.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, can obtain down and show
Beneficial effect:
1, the gradient porous structure that obtains of the present invention, solves that the porosity porous structural mechanical property of conventional uniform is single to be lacked
Point, gradient porous material that can be different according to different application Environment Design, use scope are wide；
2, the minimal surface model that the present invention constructs, after modifying to pore size therein and porosity
The porous structure of different porosities is generated, there is very big design freedom, calculating process is simple, and it is short high-efficient to calculate the time.
Detailed description of the invention
Fig. 1 is the acquisition methods of minimal surface continuous gradient porous structure constructed by preferred embodiment according to the invention
Flow chart.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
The present invention is to establish Euler space and to spatial gridding, and according to Practical Project requirement definition characteristic point, pass through
Interpolation algorithm obtains the control function value of spatially each point, and is joined using variable in this space lattice control minimal surface equation
Several values.The uniform gradient minimal surface porous structure of pore size and controlled porosity is constructed, complex engineering application is used for.
Fig. 1 is the acquisition methods of minimal surface continuous gradient porous structure constructed by preferred embodiment according to the invention
Flow chart, as shown in Figure 1, a kind of acquisition methods of minimal surface continuous gradient porous structure, specifically comprise the following steps:
(1) establish Euler space region, and area grid division carried out to three-dimensional space, establish spatial function f (x, y, z,
A, t)=0, wherein a indicates that pore size, t indicate porosity.
It specifically includes: according to Practical Project demand, establishing Euler space R, grid dividing is carried out according to its coordinate value, it is proposed that
The grid in each direction is no less than 50, to obtain accurate model；Each spatial point be corresponding with a pore size a and
The initial value of porosity t, a and t are 0.
(2) according to Practical Project demand, porous structure is defined in three-dimensional space in different spatial A, B, C, D etc., and
Define each point pore size and porosity A (x1, y1, z1, a1, t1), B (x2, y2, z2, a2, t2), C (x3, y3, z3, a3,
t3),D(x4,y4,z4,a4,t4)；
(3) according to the characteristic point of the definition in step (2), using interpolation algorithm, generate at three-dimensional space each point f (x,
y,z,a,t)；
It specifically includes: according to the defining point in step (2), interpolation calculation is carried out before each point, allow between spatial points
Pore size and porosity even transition, and by the value of a and t of obtained each spatial point substitute into before define f (x, y,
Z, a, t) in function.
(4) mathematical modeling that minimal surface is carried out according to the f (x, y, z, a, t) at spatial points, parses different type pole
The implicit function equation of small curved surface, such as the equation of Schoen Gyroid porous structure are as follows:
Wherein, a indicates cell size；The volume fraction of t control porous structure.
(5) porous structure is generated in three-dimensional spatial area according to minimal surface model foundation, it is specific there are two types of mode, first
Kind is that direct curved surface adds a wall thickness, and another kind is the pore region and entity that three-dimensional spatial area is divided by identification minimal surface
Region will fill side region and produce entity.
It can be obtained required continuous gradient minimal surface porous structure after above-mentioned steps.
Below with reference to several examples, the invention will be further described.
Example 1:
(1) spatial dimension R is established, wherein 0≤x≤20,0≤y≤20,0≤z≤20, and grid dividing is carried out to space,
Subdivision is carried out for cell size with 0.05, then there are 400 units, 401 nodes in each direction of R.Establish spatial function f (x,
Y, z, a, t), initial value 0 is assigned a value of to a and t of each node.
(2) define the characteristic point of porous structure at different locations in three-dimensional space: A (0,0,0,2.8,0.05), B (20,
20,0,2.8,0.05)、C(0,0,20,2.25,0.2)、D(20,20,20,2.25,0.2)。
(3) characteristic point according to defined in step (2) acquires the function f value of intermediate each point, such as AC1 using interpolation algorithm
(0,0,5,2.663,0.0875)、AC2(0,0,10,2.525,0.125)、AC3(0,0,15,2.3875,0.1625)。
(4) mathematical modeling of Schoen Gyroid porous structure is carried out according to the f (x, y, z, a, t) at spatial points, it is public
The value of b=5 in formula (1), t at each point can use formula
F (x, y, z, a, t)=0.9015+0.4115*z-t (2)
It indicates, by formula (1) and (2) simultaneous, constructs continuous gradient minimal surface porous structure.
(5) porous structure is generated in three-dimensional spatial area according to minimal surface model foundation, minimal surface is obtained with this
Porous structure.
Example 2:
(1) spatial dimension R is established, wherein 0≤x≤20,0≤y≤20,0≤z≤20, and grid dividing is carried out to space,
Subdivision is carried out for cell size with 0.05, then there are 400 units, 401 nodes in each direction of R.Establish spatial function f (x,
Y, z, a, t), initial value 0 is assigned a value of to a and t of each node.
(2) characteristic point of porous structure at different locations in three-dimensional space: A (0,0,0,2.65,0.075), B is defined
(20,20,0,2.65,0.075)、C(0,0,20,2.25,0.2)、D(20,20,20,2.25,0.2)。
(3) characteristic point according to defined in step (2) acquires the function f value of intermediate each point, such as AC1 using interpolation algorithm
(0,0,5,2.55,0.10625)、AC2(0,0,10,2.45,0.1375)、AC3(0,0,15,2.35,0.16875)。
(4) mathematical modeling of Schoen Gyroid porous structure is carried out according to the f (x, y, z, a, t) at spatial points, it is public
The value of b=5 in formula (1), t at each point can use formula
F (x, y, z, a, t)=0.9015+0.3455*z-t (2)
To indicate.By formula (1) and (2) simultaneous, continuous gradient minimal surface porous structure is constructed.
(5) porous structure is generated in three-dimensional spatial area according to minimal surface model foundation, minimal surface is obtained with this
Porous structure.
Example 3:
(1) spatial dimension R is established, wherein 0≤x≤20,0≤y≤20,0≤z≤20, and grid dividing is carried out to space,
Subdivision is carried out for cell size with 0.05, then there are 400 units, 401 nodes in each direction of R.Establish spatial function f (x,
Y, z, a, t), initial value 0 is assigned a value of to a and t of each node.
(2) define the characteristic point of porous structure at different locations in three-dimensional space: A (0,0,0,2.55,0.1), B (20,
20,0,2.55,0.1)、C(0,0,20,2.25,0.2)、D(20,20,20,2.25,0.2)。
(3) characteristic point according to defined in step (2) acquires the function f value of intermediate each point, such as AC1 using interpolation algorithm
(0,0,5,2.475,0.125)、AC2(0,0,10,2.4,0.15)、AC3(0,0,15,2.325,0.175)。
(4) mathematical modeling of Schoen Gyroid porous structure is carried out according to the f (x, y, z, a, t) at spatial points, it is public
The value of b=5 in formula (1), t at each point can use formula
F (x, y, z, a, t)=0.9015+0.2798*z-t (2)
To indicate.By formula (1) and (2) simultaneous, continuous gradient minimal surface porous structure is constructed.
(5) porous structure is generated in three-dimensional spatial area according to minimal surface model foundation, minimal surface is obtained with this
Porous structure.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (5)
1. a kind of acquisition methods of minimal surface continuous gradient porous structure, which is characterized in that this method includes the following steps:
(a) Euler's three-dimensional spatial area is established, which is subjected to grid dividing, obtains the three-dimensional space of gridding
The coordinate of each node on region and the grid chooses multiple nodes as characteristic point in the network node, and setting is every
The corresponding characteristic value of a characteristic point is (x, y, z, a, t), wherein x, y and z are characteristic point respectively in X, the coordinate of Y and Z-direction
Value, a is pore size, and t is porosity；
(b) it is required according to the gradient of required minimal surface porous structure porosity, to a in the characteristic value of each characteristic point
Assignment is carried out with t value, so that a the and t value of the characteristic point in the three-dimensional spatial area changes in gradient；
(c) the corresponding characteristic value of characteristic point each in three-dimensional spatial area is fitted obtain the minimal surface model f (x,
Y, z, a, t)=0, the porous structure of minimal surface is generated in the three-dimensional spatial area according to the model of the minimal surface, with
This obtains required continuous gradient minimal surface porous structure.
2. a kind of acquisition methods of minimal surface continuous gradient porous structure as described in claim 1, which is characterized in that in step
Suddenly in (a), when carrying out grid dividing to the described three-dimensional spatial area, the number of grid in each direction is preferably no less than 50.
3. a kind of acquisition methods of minimal surface continuous gradient porous structure as claimed in claim 1 or 2, which is characterized in that
In step (b), a the and t value in each mesh point coordinate carries out assignment, it is preferred to use interpolation method.
4. a kind of acquisition methods of minimal surface continuous gradient porous structure as described in claim 1-3, which is characterized in that
In step (c), the model according to the minimal surface generates the porous structure of minimal surface in the three-dimensional spatial area,
It is preferred that first setting the wall thickness of porous structure, the minimal surface is thickened according to the preset wall thickness then, can be obtained institute
State the porous structure of minimal surface.
5. a kind of acquisition methods of minimal surface continuous gradient porous structure as described in claim 1-4, which is characterized in that
In step (c), the model according to the minimal surface generates the porous structure of minimal surface in the three-dimensional spatial area,
It is preferred that as follows:
In the three-dimensional spatial area, the entity part and aperture sections in the minimal surface, i.e., the described three-dimensional space are identified
Between region entity part and aperture sections be divided by the minimal surface；
Entity boundary institute enclosing region is filled, can be obtained required minimal surface porous structure.
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