CN201908202U - Three-dimensional knitting material - Google Patents

Abstract

The utility model relates to a three-dimensional knitting material, which is characterized in that: a knitted geometric structure of the knitting material is a structure that is knitted by extending in a three-dimensional space and presents in a continuous yarn, yarn sections in a representative volume element of the knitted geometric structure satisfy the symmetry of points described by a space point group, and the knitted structure integrally presents in a three-dimensional knitted fabric which is obtained by interweaving representative volume elements which are translated by utilizing the translational symmetric operation described by a space group. The knitting material adopts the representative volume element satisfying the point group symmetry as a basic structural element to derive a novel three-dimensional knitted geometric structure satisfying the symmetric of the space group, and a novel three-dimensional knitting material variety with an excellent geometric structure and an excellent performance is obtained by researching the technical feasibility and predicting the percent of fiber volume of correspondent three-dimensional fabric. A knitting material array adopts a regular hexagon, so the movement orbit of a yarn carrier is convenient to realize, and the production is easy to organize.

Description

The 3 D weaving material

Technical field

The utility model relates to a kind of 3 D weaving material.

Background technology

D braided composites obtains the extensive concern of industries such as Aero-Space, national defence and medical treatment with its excellent mechanical property.Because be subject to processing the restriction of factors such as technology, the kind of D braided composites is very few, working (machining) efficiency is low and technology cost height.Obtain the better D braided composites of combination property, be badly in need of the more 3 D weaving technology of exploitation.Most at present researchs concentrate on four step rule and two kinds of braid methods of two step method, and the Study on Forecast of relevant three dimensional knitting method also is in the starting stage.

The crystal of different lattice structures shows different performances, adopts the crystal symmetric group crystal geometry can be classified.With reference to the research method of symmetric group, to the in addition inductive research of the cell geometry of braided material, the three-dimensional yarn crossovers method that the symmetry operation of describing according to space point group and space group pushes away newly in a large number.Yet technological feasibility and performance study as new 3 D weaving material do not launch as yet.From satisfying the space point group

Be the HM symbolic notation), deriving on the basis of all symmetry operation obtains a kind of unit cell of new yarn crossovers geometry.This unit cell is put into the space lattice that satisfies it can obtain yarn continuous three-dimensional yarn crossovers geometry.

The utility model content

The purpose of this utility model is to provide a kind of 3 D weaving material.

The technical solution of the utility model is to have adopted a kind of 3 D weaving material, the braiding geometry of this braided material is for extending the structure that is continuous yarn that is woven at three dimensions, and the yarn line segment in the representative volume unit in the braiding geometry satisfies the space point group The symmetry of the point of describing, braided structure presents on the whole with representative volume unit space group

The translation symmetry behaviour who describes carries out be interweaved together 3 D weaving fabric of three dimensions that translation obtains.

Described have a point group

Symmetric representative volume unit, it is derived based on point group

The symmetry operation described of group element be

(n is 1～6) can be expressed as

$s_{6z}=c_{6z}{\mathrm{\&sigma;}}_{\mathrm{xy}}=[\frac{x}{2}-\frac{\sqrt{3}}{2}y,\frac{\sqrt{3}}{2}x+\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^2(x,y,z)=[-\frac{x}{2}-\frac{\sqrt{3}}{2}y,\frac{\sqrt{3}}{2}x-\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^3\left(\text{x,y,z}\right)\text{=}(-x,-y,z)$

$s_{6z}^4(x,y,z)=[-\frac{x}{2}+\frac{\sqrt{3}}{2}y,-\frac{\sqrt{3}}{2}x-\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^5(x,y,z)=[\frac{x}{2}+\frac{\sqrt{3}}{2}y,-\frac{\sqrt{3}}{2}x+\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^6(x,y,z)=E$

(x, y z) are transformed to the symmetry operation of putting behind the equal sign with the point on a certain yarn line segment axis in expression.

Described space group

The translation symmetry behaviour who describes is in the xyz coordinate system, with point group

Described yarn line segment is combined in and makes following mode in the three dimensions

T _i=ux _i+ vy _i+ wz _i(u, v, w are base vector)

The translation symmetry operation.

The yarn line segment combination of described representative volume unit has z to thickness t, reaches in the parallel with it bundle of planes space group of representative volume unit at the xoy coordinate surface

The translation symmetry behaviour space group of describing The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing The translation symmetry behaviour cross section of describing is a hexagonal section, the translation of representative volume unit is with the cornerwise integral multiple translation of the hexagonal section of positive six prisms, along z to integral multiple translation with 2t, the pairing dot matrix in representative volume unit is simple hexagonal lattice in the 3 D weaving material, and final formation has space group

Symmetric a kind of new space continuous yarn intersection geometry.

Described each yarn line segment combination unit cell has surperficial representative volume unit, representative volume unit, bight and inner representative volume unit, individual layer knitted body representative volume unit sum

N＝＝3n ²-3n+1 (1)

Representative volume unit, bight N _cSpace group

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour and the facial representative volume unit number N that describe _fBe respectively

N _c＝6，N _f＝6(n-2) (2)

Inner representative volume unit number N _iFor

N _i＝N-N _f-N _c (3)

N is that braided fabric cross section regular hexagon Bian Shang represents gonosome product unit number.

Described each establishment yarn line segment combination center is provided with axial yarn.

Braided material of the present utility model is to satisfy point group

Symmetric representative volume unit be basic structural unit derive satisfy space group

Symmetric new 3 D weaving geometry by to the research of its technological feasibility with to the prediction of the fiber volume percentage composition of corresponding three-dimensional braid, has obtained the new 3 D weaving description of materials of geometry and function admirable.This braided material array has adopted regular hexagon, makes the movement locus of taking the yarn device be convenient to realize that tissue is produced easily.

Description of drawings

Fig. 1 is the front view of the utility model braided material section;

Fig. 2 is the right view of Fig. 1;

Fig. 3 is the vertical view of Fig. 1;

Fig. 4 is the stereogram of Fig. 1;

Fig. 5 is the three-dimensional cutaway view of Fig. 1;

Fig. 6 is the structural representation of minimum yarn line segment among Fig. 1;

Fig. 7 is the yarn line segment combination single cell structure schematic diagram by yarn line segment translation design shown in Figure 6;

Fig. 8 is the residing hexagonal-lattice schematic diagram of each unit cell in the braided material;

Fig. 9 is each unit cell regional structure schematic diagram of living in the braided material;

Figure 10 is surperficial single cell structure schematic diagram;

Figure 11 is a bight single cell structure schematic diagram;

Figure 12 is inner single cell structure schematic diagram;

Figure 13 is the view that interweaves of the part braiding yarn that surrounds of three adjacent yarn;

Figure 14 is the structural representation of β for the yarn braid angle of braiding geometry;

Figure 15 is the variation diagram of the distortion situation in the braid angle of the fiber percentage composition of braided fabric and weaving textile yarn and cross section.

The specific embodiment

Concrete structure of the present utility model is described below:

1, yarn line segment combination single cell structure is described

The space point group

Group element be

(n is 1～6), group's generator is s ₆Corresponding symmetry operation can be expressed as

$s_{6z}=c_{6z}{\mathrm{\&sigma;}}_{\mathrm{xy}}=[\frac{x}{2}-\frac{\sqrt{3}}{2}y,\frac{\sqrt{3}}{2}x+\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^2(x,y,z)=[-\frac{x}{2}-\frac{\sqrt{3}}{2}y,\frac{\sqrt{3}}{2}x-\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^3\left(\text{x,y,z}\right)\text{=}(-x,-y,z)$

$s_{6z}^4(x,y,z)=[-\frac{x}{2}+\frac{\sqrt{3}}{2}y,-\frac{\sqrt{3}}{2}x-\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^5(x,y,z)=[\frac{x}{2}+\frac{\sqrt{3}}{2}y,-\frac{\sqrt{3}}{2}x+\frac{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">y</figure-callout>}}{2},z]$

$s_{6z}^6(x,y,z)=E$

(x, y z) are transformed to the symmetry operation of putting behind the equal sign with the point on a certain yarn line segment axis in expression.

There is point group in the yarn line segment that is in position shown in Figure 6 in yarn line segment combination shown in Figure 7 and the coordinate system

Symmetry operation relation.This combination pattern is as the representative volume unit (abbreviation unit cell) of new 3 D weaving geometry.

2 satisfy space group

Symmetric 3 D weaving geometry

2.1 corresponding space group The simple hexagonal lattice in space

The corresponding simple hexagonal lattice (as shown in Figure 8) of the space lattice that the crystal symmetric group is described, the space point group Coordinate with it.To express with a lattice point by the representative volume unit (as shown in Figure 7) that this point group is derived, put into hexagonal lattice.Consider the continuity of yarn, promptly obtain a kind of space group that satisfies

Symmetric new space continuous yarn intersection geometry (as shown in Figure 4).

Consider the feasibility that technology realizes, the z in above-mentioned figure is to having added axial yarn.

2.2 space group

Corresponding structure (obtaining) by translation representative volume unit

Set up coordinate system xyz, be in three-dimensional translation symmetry operation

T _i=ux _i+ vy _i+ wz _i(u, v, w are base vector)

The yarn line segment combination shown in Figure 7 through translation can obtain Fig. 1 to three-dimensional yarn crossovers geometry shown in Figure 5.

If the combination z of individual layer yarn line segment shown in Figure 7 is t to thickness.In xoy coordinate surface and parallel with it bundle of planes, the translation of unit cell is the cornerwise integral multiple translation of hexagonal section of positive six prisms that relied on point group yarn changing section, along z to integral multiple translation with 2t.

2.3 space group Corresponding new 3 D weaving geometry

Use the space point group

Symmetry operation push away the unit cell of this new 3 D weaving geometry, with the translation symmetry operation this unit cell is carried out translation, can obtain possible 3 D weaving interior geometry.Consider the continuity requirement of border yarn in the actual braiding process, and its rule is studied, and then obtain a kind of brand-new 3 D weaving geometry (as shown in Figure 4).

3, the geometrical analysis model of new 3 D weaving material

New 3 D weaving geometry is expected to be used to make the prefabricated component of new D braided composites material.As a kind of new 3 D weaving material, its performance prediction is the important content of basic research.

3.1 basic assumption

(1) cross section of fabric braiding yarn is assumed to be ellipse, and two-semiaxle is respectively a/2, b/2;

(2) z is a regular hexagon to yarn cross section, can be covered with the hexagon space with the extruding of braiding yarn;

(3) all braiding yarns have identical performance, do not consider to weave factor such as yarn physical damnification and the difference of the performance that causes;

(4) braided structure inside, surface and folding corner region have the geometry of stable and consistent.

3.2 the zone of 3 D weaving fabric is divided and unit cell

Braided fabric is divided into interior zone, surf zone and folding corner region.Corresponding unit cell is called inner unit cell (Interior Unit), surperficial unit cell (Face Unit) and bight unit cell (Corner Unit) (as shown in Figure 9).

Inner unit cell is cut apart by shown in Figure 12; Surface unit cell and bight unit cell are cut apart shown in Figure 10,11.

3.3 describe the geometric parameter of 3 D weaving fabric

(1) the unit cell number of individual layer braided fabric

If n is a unit cell number on the regular hexagon limit, braided fabric cross section.Individual layer knitted body unit cell sum

N＝＝3n ²-3n+1 (1)

Bight unit cell N _cCount N with facial unit cell _fBe respectively

N _c＝6，N _f＝6(n-2) (2)

Inner unit cell is counted N _IFor

N _i＝N-N _f-N _c (3)

(2) braiding yarn and the axially geometrical relationship of yarn

By pass of trying to achieve between axial yarn and the knitting yarn geometric parameter shown in Figure 13 be

$R=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">b</figure-callout>}}^2+3a^2}-\frac{\sqrt{3}}{3}a---\left(4\right)$

(3) braid angle β

The yarn braid angle of describing the braiding geometry is β, can be got by geometrical relationship shown in Figure 14

$\mathrm{tg\&beta;}=t/(R+\frac{a}{\sqrt{3}})---\left(5\right)$

Push away by formula (4) and (5)

$t=\mathrm{tg\&beta;}\sqrt{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">b</figure-callout>}}^2+3a^2}---\left(6\right)$

(4) cross-sectional area A of 3 D weaving fabric and one deck unit-cell volume U

If the length of side of the regular hexagonal section of axial yarn is R; The cornerwise length in the cross section of 3 D weaving material is D, and the thickness of individual layer unit cell is 2t.Can get

$D=2D_{d}R+(N_d+3)a/\cos \frac{\mathrm{\&pi;}}{6}2(N_{d}R+\frac{N_d+3}{\sqrt{3}}a)---\left(7\right)$

$A=\frac{\sqrt{3}}{2}{(5\sqrt{3}R+8a)}^2---\left(8\right)$

The cumulative volume of 3 D weaving fabric one deck unit cell is

$U=2\mathrm{At}=\sqrt{3}{(5\sqrt{3}R+8a)}^{2}t---\left(9\right)$

(5) volume of yarn calculates in the 3 D weaving fabric

Being located at thickness is in the 2t braided fabric, and axially the volume of yarn is U _CyThe volume of inner single unit cell braiding yarn is The volume of facial single unit cell braiding yarn is

The volume of the single unit cell braiding in bight yarn is

Can push away

$U_{\mathrm{cy}}=N\&times;6\&times;\frac{1}{2}\&times;\frac{\sqrt{3}}{2}{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">R</figure-callout>}}^2\&times;2t=57\sqrt{3}{R}^{2}t---\left(10\right)$

Can get simultaneously

$U_{\mathrm{by}}^i=6\mathrm{\&pi;<figure-callout\; id="2"\; label="ab\; t"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">ab</figure-callout>}\sqrt{t^{}}\sqrt{{}^2+\frac{4}{3}{a}^2},$ $U_{\mathrm{by}}^f=7\mathrm{\&pi;<figure-callout\; id="2"\; label="ab\; t"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">ab</figure-callout>}\sqrt{t^{}}\sqrt{{}^2+\frac{4}{3}{a}^2},$

$U_{\mathrm{by}}^c=8\mathrm{\&pi;<figure-callout\; id="2"\; label="ab\; t"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">ab</figure-callout>}\sqrt{t^{}}\sqrt{{}^2+\frac{4}{3}{a}^2}---\left(11\right)$

The cumulative volume U of knitting yarn in the individual layer unit cell braided fabric _By

$U_{\mathrm{by}}=N_I{U}_{\mathrm{by}}^I+N_F{U}_{\mathrm{by}}^F+N_C{U}_{\mathrm{by}}^C=132\mathrm{\&pi;<figure-callout\; id="2"\; label="ab\; t"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">ab</figure-callout>}\sqrt{t^{}}\sqrt{{}^2+\frac{4}{3}{a}^2}---\left(12\right)$

The cumulative volume U of yarn in the individual layer unit cell braided fabric _y

$U_y=U_{\mathrm{by}}+U_{\mathrm{cy}}=132\mathrm{\&pi;<figure-callout\; id="2"\; label="ab\; t"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">ab</figure-callout>}\sqrt{t^{}}\sqrt{{}^2+\frac{4}{3}{a}^2}+57\sqrt{3}{R}^{2}t---\left(13\right)$

(6) the fiber volume percentage composition of 3 D weaving fabric:

$V=\frac{U_y}{U}\&times;100\%---\left(14\right)$

Formula (9) and (13) substitution following formula are got

$V=\frac{\mathrm{\&pi;}(44\mathrm{\&pi;<figure-callout\; id="2"\; label="ab\; t"\; filenames="HSA00000397596700042.png"\; state="\{\{state\}\}">ab</figure-callout>}\sqrt{t^{}}\sqrt{{}^2+4a^2/3}+19\sqrt{3}{R}^{2}t)}{2{(5\sqrt{3}R+8a)}^{2}t}---\left(15\right)$

By formula (5), (6) and (15) can push away

V＝f(a，b，β) (16)

Make λ=a/b, can get V=f (λ, β).

(7) relation of braiding geometry and fiber volume percentage composition

The oval cross section that the braiding yarn of same cross section is corresponding different with the difference of urgent degree, the fiber percentage composition of braided fabric is relevant with the distortion situation in the braid angle of weaving textile yarn and cross section.

Get ab=1, a/b ∈ [1/4,4] can get the Changing Pattern of the fiber volume percentage composition V of 3 D weaving fabric shown in Figure 15 with λ and β.

Last figure as can be seen, the excursion of fabric fibre percentage composition is 34～68%.When the λ value was constant, the fabric fibre percentage composition increased with the increase of angle of weave β, and amplitude of variation is not obvious.And the variation that shrivels coefficient lambda=a/b of yarn is very big to its percentage composition influence; As seen, the knitting yarn in the braiding process z to press more " flat " then might form fine and close braided fabric more.

Claims (6)

1. the 3 D weaving material is characterized in that, the braiding geometry of this braided material is for extending the structure that is continuous yarn that is woven at three dimensions, and the yarn line segment in the representative volume unit in the braiding geometry satisfies the space point group The symmetry of the point of describing, braided structure presents on the whole with representative volume unit space group

The translation symmetry behaviour who describes carries out be interweaved together 3 D weaving fabric of three dimensions that translation obtains.

2. 3 D weaving material according to claim 1 is characterized in that, described have a point group

Symmetric representative volume unit, it is derived based on point group

The symmetry operation described of group element be

(n is 1～6) can be expressed as

$s_{6z}=c_{6z}{\mathrm{\&sigma;}}_{\mathrm{xy}}=[\frac{x}{2}-\frac{\sqrt{3}}{2}y,\frac{\sqrt{3}}{2}x+\frac{y}{2},z]$

$s_{6z}^2(x,y,z)=[-\frac{x}{2}-\frac{\sqrt{3}}{2}y,\frac{\sqrt{3}}{2}x-\frac{y}{2},z]$

$s_{6z}^3\left(\text{x,y,z}\right)\text{=}(-x,-y,z)$

$s_{6z}^4(x,y,z)=[-\frac{x}{2}+\frac{\sqrt{3}}{2}y,-\frac{\sqrt{3}}{2}x-\frac{y}{2},z]$

$s_{6z}^5(x,y,z)=[\frac{x}{2}+\frac{\sqrt{3}}{2}y,-\frac{\sqrt{3}}{2}x+\frac{y}{2},z]$

$s_{6z}^6(x,y,z)=E$

(x, y z) are transformed to the symmetry operation of putting behind the equal sign with the point on a certain yarn line segment axis in expression.

3. 3 D weaving material according to claim 2 is characterized in that, described space group

The translation symmetry behaviour who describes is in the xyz coordinate system, with point group

Described yarn line segment is combined in and makes following mode in the three dimensions

T _i=ux _i+ vy _i+ wz _i(u, v, w are base vector)

The translation symmetry operation.

4. 3 D weaving material according to claim 3 is characterized in that, the yarn line segment combination of described representative volume unit has z to thickness t, reaches in the parallel with it bundle of planes space group of representative volume unit at the xoy coordinate surface

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour cross section of describing is a hexagonal section, the translation of representative volume unit is with the cornerwise integral multiple translation of the hexagonal section of positive six prisms, along z to integral multiple translation with 2t, the pairing dot matrix in representative volume unit is simple hexagonal lattice in the 3 D weaving material, and final formation has space group Symmetric a kind of new space continuous yarn intersection geometry.

5. 3 D weaving material according to claim 4 is characterized in that, described each yarn line segment combination unit cell has surperficial representative volume unit, representative volume unit, bight and inner representative volume unit, individual layer knitted body representative volume unit sum

N＝＝3n ²-3n+1 (1)

Representative volume unit, bight N _cSpace group

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour space group of describing

The translation symmetry behaviour and the facial representative volume unit number N that describe _fBe respectively

N _c＝6，N _f＝6(n-2) (2)

Inner representative volume unit number N _iFor

N _i＝N-N _f-N _c (3)

N is that braided fabric cross section regular hexagon Bian Shang represents gonosome product unit number.

6. according to 3 D weaving material according to claim 5, it is characterized in that described each establishment yarn line segment combination center is provided with axial yarn.

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