CN108363835B - Porous sandwich structure based on T-spline surface and application - Google Patents
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Abstract
The invention discloses a T-spline surface-based porous sandwich structure, which is obtained by the following method: inputting two T spline surfaces, an implicit porous structure function expression, a surface discrete grid resolution and an interpolation grid resolution between the surfaces; dividing parameters such as two T spline surfaces into discrete meshes according to the resolution of the discrete meshes of the curved surfaces; generating an interpolation grid which is uniformly distributed between the two T spline surfaces according to the resolution of the interpolation grid between the surfaces and the discrete grid of the T spline surface; generating a porous structure by linear interpolation according to the interpolation grid and the implicit porous structure function expression; and finally, storing the generated porous sandwich structure in an STL format for output and storage. The invention discloses application of a porous sandwich structure based on a T-spline surface as a wing wall plate material.
Description
Technical Field
The invention belongs to the field of Computer-aided design (CAD), and particularly relates to a T-spline surface-based porous sandwich structure and application.
Background
The porous sandwich structure is a novel material structure widely applied in the engineering field, and the porous sandwich has important application in aerospace, buildings and other application occasions by virtue of the compression characteristic of the sandwich structure and the extension characteristic of the panel. Along with sandwich structures with different physical properties, the porous sandwich can be used as a functional structure for vibration absorption, sound insulation, light weight and the like, and the material consumption is maximally reduced while excellent mechanical properties are maintained. Skin skeleton structures widely used in aerospace vehicles are one of typical representatives of the application of porous sandwich structures. Common porous sandwiches include lattice sandwich structures, honeycomb sandwich structures, grid sandwich structures, foam sandwich structures, and the like, depending on the type of sandwich structure.
At present, the porous sandwich structure of the wing wall plate is mostly prepared by adopting the traditional manufacturing process including investment casting, stamping folding, stretching forming and the like, and the manufacturing process is complex and the cost is higher. The rapid forming technology provides an ideal solution for manufacturing the porous sandwich structure, and the porous sandwich with the complex topological morphology can be accurately manufactured layer by layer based on the idea of additive manufacturing. The accurate and reliable three-dimensional model is the basis for quickly forming and manufacturing the porous sandwich structure with excellent performance, the research on the porous sandwich structure at home and abroad focuses on the physical performance analysis and the traditional manufacturing process, the research on the digital design of the porous sandwich is less, a method for designing and generating the dot matrix sandwich between simple planes is preliminarily tried by a few researches, and the design research on the porous sandwich between large-area special-shaped free curved surfaces is less.
The invention patent with Chinese patent application number CN200910309127.0 discloses a dry preparation process of a fiber reinforced composite material tetrahedral lattice sandwich board; the invention patent with Chinese patent application number CN201510639359.8 discloses a design method of a pyramid-shaped composite material three-dimensional lattice sandwich structure, and the patents all realize the preparation of the sandwich structure by utilizing the traditional manufacturing process. In the academic thesis, Gorguarslan et al propose a design method of a lattice sandwich structure for additive manufacturing (see Gorguarslan R M, GandhiUN, et al, an improved lattice structure designing and designing structures [ J ]. Rapid modeling Journal,2017,23(2):305 and 319); chougoni et al propose a method to create a sandwich as succinctly as possible within a given entity to reduce the number of triangular patches used (see ChougoniL, percent J P, Veron P, et al, lattice structure light triangle definition for additional manufacturing [ J ]. Computer-aid Design,2017.)
According to literature analysis, the current published patents or literatures mainly aim at the design of the traditional manufacturing process method and the design method for generating a lattice porous structure inside some simple structural components, and are limited by the manufacturing process or the design method, and the porous sandwich structure is difficult to be generated efficiently between complex curved surfaces such as wing panels and the like.
Disclosure of Invention
The invention provides a T-spline surface-based porous sandwich structure and application thereof, in order to realize the manufacturing of the porous sandwich structure by utilizing a rapid forming technology.
In order to achieve the purpose, the invention provides the following technical scheme:
in one aspect, the invention provides a porous sandwich structure based on a T-spline surface, which is obtained by the following method:
step 1: inputting two T spline surfaces, an implicit porous structure function expression, a surface discrete grid resolution na and a surface interpolation grid resolution nb;
step 2: according to the resolution na of the curved surface discrete grid, dividing the parameters of the two T spline surfaces and the like into discrete grids;
and step 3: generating an interpolation grid which is uniformly distributed between two T spline surfaces according to the resolution nb of the interpolation grid between the surfaces and the discrete grid of the T spline surface;
and 4, step 4: generating a porous structure by linear interpolation according to an interpolation grid between two T spline surfaces and an implicit porous structure function expression;
and 5: and storing the generated porous sandwich structure in an STL format for output and storage.
According to the method, the T spline surface is used for modeling the appearance of the complex free-form surface, the parameter space characteristics of the T spline surface and the rapid construction of the interpolation grid between the surfaces are used for efficiently generating the internal design grid generation of the porous sandwich structure, and then the implicit porous structure characteristics are used for rapidly interpolating to generate the reliable sandwich structure between the T spline surfaces. The method for generating the porous sandwich structure is stable and reliable, the porous sandwich structure with different functional requirements can be designed and generated between the complex T-spline surfaces, and a reliable data basis is provided for the subsequent rapid forming process.
The formed porous sandwich structure fully utilizes the advantages of two T-spline surfaces as free surfaces, and can be flexibly designed and adjusted according to aerodynamic requirements or other design requirements. The T-spline curved surface has smooth surface and higher continuity and smoothness, the generated T-spline curved surface porous sandwich has the advantage of lightweight porous sandwich structure, the consumption of manufacturing materials is reduced on the basis of meeting the mechanical property requirement, and meanwhile, the T-spline curved surface porous sandwich has the smooth surface property of the T-spline curved surface, and the T-spline curved surface porous sandwich has wide application in the engineering field.
Preferably, in step 1, the T-spline surface expression is S (S, T), where S, T ∈ [0,1], and the implicit porous structure function expression is f (x, y, z) ═ c, where c is a critical value constant.
Preferably, the specific process of step 2 is:
firstly, isodyne lines of s-a/na (a-0, …, na) and T-b/na (b-0, …, na) are uniformly generated in the direction of s and T in a T-spline surface parameter domain, and the isodyne lines form isodyne meshes of the T-spline surface parameter domain;
then, according to the formula of the T-spline surface:
calculating to obtain a discrete grid corresponding to the Euclidean space T spline surface,
wherein n is the total number of control vertexes, i is the control vertex sequence number, PiFor the ith control vertex, wiIs the weight factor corresponding to the control vertex, BiAnd (s, t) is a mixing function corresponding to the control vertex.
Preferably, the specific process of step 3 is:
step 3.1: connecting vertexes of the discrete meshes generated by the two T spline surfaces in a one-to-one correspondence manner to generate a discrete mesh connecting line between the two T spline surfaces;
step 3.2: mesh resolution nb according to interpolation between surfaces, and discrete mesh link vertex coordinates P1 (x)1,y1,z1)、P2(x2,y2,z2) Generating coordinates of discrete grid connecting line dividing points by linear interpolation
Step 3.3: and connecting the grid connecting line dividing points in sequence to generate an interpolation grid uniformly distributed between the two T spline surfaces.
Preferably, the specific process of step 4 is:
respectively substituting the vertex coordinates of the interpolation grid into the implicit porous structure function expression, linearly interpolating and calculating a triangular patch intersected with the implicit porous structure and the interpolation grid, and for one vertex Ep of the triangular patch, using an edge vertex Ep1x of the intersected grid1,y1,z1)、Ep2x2,y2,z2) The coordinates of Ep are calculated:
on the other hand, the invention also provides application of the porous sandwich structure based on the T-spline surface as a wing wall plate material.
The porous sandwich structure provided by the invention has the advantage of light weight on the basis of meeting the mechanical property requirement of the wing wallboard, and can be applied to the wing wallboard.
Compared with the prior art, the invention has the limited effects that:
the method comprises the steps of utilizing a T spline surface to model a complex free-form surface, rapidly generating interpolation grids between the surfaces by means of parameter domain isoparametric segmentation and linear interpolation methods, and rapidly interpolating to generate a porous sandwich structure by utilizing a function expression of an implicit porous structure. The design method of the porous sandwich structure is accurate, stable and reliable, and provides a reliable method for generating the porous sandwich structure between complex curved surfaces, the generated porous sandwich structure not only has a complex and smooth free-form surface, can meet the design requirements of a large-sized airplane free-form surface wallboard, but also can achieve the aim of lightening the wing wallboard structure, and the consumption of manufacturing materials is reduced as much as possible on the basis of meeting other performance requirements such as mechanics and the like. Especially for important parts such as an aircraft wall plate, the light-weight wing wall plate can further reduce the energy consumption when the aircraft moves.
Drawings
FIG. 1 is a flow chart of a method for designing a porous sandwich structure based on a T-spline surface according to an embodiment;
FIG. 2 is a schematic diagram of an embodiment of generating a discrete mesh of a T-spline surface;
FIG. 3 is a schematic diagram of an embodiment of generating an interpolation grid between T-spline surfaces;
FIG. 4 is a schematic diagram illustrating a result of forming a porous sandwich between two T-spline surfaces provided in the example;
FIG. 5 shows the result of the porous sandwich structure of the vibration isolation layer of the mechanical part in example 1;
FIG. 6 shows the results of the production of the lightweight cellular sandwich structure of the wing panel of example 2.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the detailed description and specific examples, while indicating the scope of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
Fig. 1 is a flow chart of a method for designing a porous sandwich structure based on a T-spline surface according to an embodiment. Referring to fig. 1, the method for designing a porous sandwich structure based on a T-spline surface according to the embodiment includes:
step 101: inputting two T spline surfaces, an implicit porous structure function expression, a surface discrete grid resolution na and a surface interpolation grid resolution nb.
Specifically, two T-spline surfaces S (S, T) are input, where S, T ∈ [0,1], such as: the implicit porous structure function expression f (x, y, z) ═ 2x (cosx × cosy + cosy × cosz + cosz × cosx) - (cos (2 × x) + cos (2 × y) + cos (2 × z)) -0, the curved surface discrete grid resolution na ═ 10, and the curved surface interpolation grid resolution nb ═ 3.
Step 2: and dividing the parameters of the two T-spline surfaces and the like into discrete meshes according to the resolution na of the discrete mesh of the curved surface.
As shown in fig. 2, the specific process of step 2 is:
firstly, isodyne lines of s-a/na (a-0, …, na) and T-b/na (b-0, …, na) are uniformly generated in the parameter domains of the T- spline surfaces 201 and 202 along the directions of s and T, and the isodyne lines form isodyne meshes of the parameter domain of the T-spline surface;
then, according to the formula of the T-spline surface:
calculating to obtain a discrete grid 203 corresponding to the Euclidean space T spline surface,
wherein n is the total number of control vertexes, i is the control vertex sequence number, PiFor the ith control vertex, wiIs the weight factor corresponding to the control vertex, BiAnd (s, t) is a mixing function corresponding to the control vertex.
And step 3: and generating an interpolation grid which is uniformly distributed between the two T spline surfaces according to the resolution nb of the interpolation grid between the surfaces and the discrete grid of the T spline surface.
The specific process of the step 3 is as follows:
step 3.1: connecting vertexes of the discrete meshes generated by the two T spline surfaces in a one-to-one correspondence manner to generate a discrete mesh connecting line between the two T spline surfaces;
step 3.2: mesh resolution nb according to interpolation between surfaces, and discrete mesh link vertex coordinates P1 (x)1,y1,z1)、P2(x2,y2,z2) Generating coordinates of discrete grid connecting line dividing points by linear interpolation
Step 3.3: as shown in fig. 3, the mesh connecting line dividing points are sequentially connected to generate an interpolation mesh 301 uniformly distributed between two T-spline surfaces.
And 4, step 4: and linearly interpolating to generate the porous structure according to the interpolation grid between the two T spline surfaces and the implicit porous structure function expression.
Specifically, will insertRespectively substituting the vertex coordinates of the value meshes into the implicit porous structure function expression, linearly interpolating and calculating a triangular patch intersected with the implicit porous structure and the interpolation mesh, and regarding one vertex Ep of the triangular patch, using an edge vertex Ep1 (x) of the intersected mesh1,y1,z1)、Ep2(x2,y2,z2) The coordinates of Ep are calculated:
as shown in fig. 4, the final linear interpolation generates a porous sandwich structure between two T-spline surfaces.
And 5: and storing the generated porous sandwich structure in an STL format for output and storage.
Two exemplary embodiments of the invention are as follows:
example 1
A porous sandwich structure is designed and generated by selecting a vibration isolation layer of a special-shaped mechanical part, in order to be tightly attached to a complex special-shaped mechanical part, two surfaces of adjacent parts are modeled by utilizing a T spline surface, and the porous sandwich structure is generated between the surfaces of the two parts, so that the vibration isolation function between mechanical parts in a complex motion working condition can be realized. The implicit porous structure function expression is:
10×(cosxsiny+cosysinz+coszsinx)-0.5×[cos(2x)×cos(2y)+cos(2y)×cos(2z)+cos(2z)×cos(2x)]-14＝0，na＝80，nb＝80。
as shown in figure 5, an ordered porous sandwich structure is designed and generated between two T-spline free-form surfaces, and the generated structure is stored as an STL model and then manufactured by using a rapid prototyping technology to play an ideal vibration isolation role.
Example 2
Selecting a wing wall plate to generate a lightweight porous sandwich structure, modeling and designing complex free-form surfaces of an upper wall plate and a lower wall plate of the wing by using T spline surfaces respectively, and selecting an implicit porous structure function expression as follows: 0.5 × [ sin (2x) × cos (y) × sin (z) + sin (2y) × cos (z) × sin (x)) + sin (2z) × cos (x) × sin (y)) ] -0.5 × [ cos (2x) × cos (2y) + cos (2y) × cos (2z) + cos (2z) × cos (2x) ] +0.15 ═ 0, na ═ 80, nb ═ 80.
As shown in FIG. 6, a lightweight porous sandwich structure is formed between the free curved surfaces of the upper and lower wall plates of the wing by using the method of the invention, so that the material consumption and the energy consumption are reduced while the mechanical property is satisfied. The designed and generated sandwich structure is manufactured and molded by using an additive manufacturing technology, and compared with a solid wallboard structure with the same material and size, the porous sandwich structure designed and manufactured by using the method can reduce the part quality by 23.2 percent on the basis of keeping the mechanical properties such as compression resistance, bending resistance and the like basically required. Compared with the lattice sandwich structure provided by the literature method, the porous sandwich structure designed and manufactured by the method can further reduce the part quality by 8.6 percent.
The above-mentioned embodiments are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only the most preferred embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions, equivalents, etc. made within the scope of the principles of the present invention should be included in the scope of the present invention.
Claims (2)
1. A porous sandwich structure based on a T-spline surface is characterized in that the porous sandwich structure is provided with a free-form surface and is obtained by the following method:
step 1: inputting two T spline surfaces, wherein an implicit porous structure function expression is f (x, y, z) ═ c, c is a critical value constant, the discrete grid resolution na of the surfaces and the interpolation grid resolution nb between the surfaces;
step 2: according to the resolution na of the curved surface discrete grid, dividing the parameters of the two T spline surfaces and the like into discrete grids;
and step 3: according to the resolution nb of the interpolation grid between the curved surfaces and the discrete grid of the T spline curved surface, an interpolation grid which is uniformly distributed is generated between the two T spline curved surfaces, and the specific process is as follows:
step 3.1: connecting vertexes of the discrete meshes generated by the two T spline surfaces in a one-to-one correspondence manner to generate a discrete mesh connecting line between the two T spline surfaces;
step 3.2: according to the musicInter-surface interpolation mesh resolution nb, and discrete mesh link vertex coordinates P1 (x)1,y1,z1)、P2(x2,y2,z2) Generating coordinates of discrete grid connecting line dividing points by linear interpolation
Step 3.3: sequentially connecting the grid connecting line dividing points to generate an interpolation grid uniformly distributed between the two T spline surfaces;
and 4, step 4: generating a porous structure by linear interpolation according to an interpolation grid between two T spline surfaces and an implicit porous structure function expression;
and 5: storing the generated porous sandwich structure in an STL format for output and storage;
the specific process of the step 2 is as follows:
firstly, isoparametric lines of s-a/na and T-b/na are uniformly generated in the T-spline surface parameter domain along the directions of s and T, wherein a-0, …, na, b-0, …, na, isoparametric lines form isoparametric meshes of the T-spline surface parameter domain;
then, according to the formula of the T-spline surface:
calculating to obtain a discrete grid corresponding to the Euclidean space T spline surface,
wherein n is the total number of control vertexes, i is the control vertex sequence number, PiFor the ith control vertex, wiIs the weight factor corresponding to the control vertex, Bi(s, t) is a mixing function corresponding to the control vertex;
the specific process of the step 4 is as follows:
respectively substituting the vertex coordinates of the interpolation grids into the implicit porous structure function expression, linearly interpolating and calculating a triangular patch intersected with the implicit porous structure and the interpolation grids, and regarding one vertex Ep of the triangular patch, using an edge vertex Ep1 (x) of the intersected grid1,y1,z1)、Ep2(x2,y2,z2) The coordinates of Ep are calculated:
2. use of the T-spline surface based cellular core sandwich structure of claim 1 as a wing panel material.
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| CN112699455B (en) * | 2020-10-10 | 2021-11-16 | 北京航空航天大学 | Aircraft skin seamless forming method and device based on T-spline |
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