圆顶形层联机织预制体参数化几何建模

doi:10.7527/S1000-6893.2023.29556

Abstract

Abstract:

Dome-shaped Multi-layer Interlock Woven Preform （DIWP） prepared by integrated copying weaving technology has the characteristics of good design， stable structure and strong bearing capacity. Therefore， it is crucial to investigate the microstructure of DIWP and construct its parametric geometric model for predicting the mechanical properties of DIWP and guiding its process design. The construction method of DIWP parametric model is comprehensively studied based on the preform macro-structure characteristics and weaving process parameters， and the solid geometric model is established by using SolidWorks software. The results show that the relationship between the spatial coordinates and the motion path of DIWP yarn can be described by introducing the weft inclination. The assumption of parabolic convex lens yarn section in the form of quadratic function with one variable is applicable to DIWP. Three kinds of DIWP parametric models with different meso-structures are discussed， and subsequently， the theory of DIWP parametric model construction with systematic， reliable and universal research value is further obtained. The analytical formulas of the model are entirely derived by MATLAB software， and they are solvable and unique. The parametric model can effectively characterize the spatial topology relationship of DIWP and calculate the fiber volume content. Compared with the measured values， the error is -3.43%. The results provided a theoretical basis for the simulation of DIWP and had guiding significance for the design of the actual preparation process.

Key words: dome-shaped, multi-layer interlock woven preform, parametric model, weft inclination, quadratic function of one variable, fiber volume fraction

CLC Number:

Changlong ZHANG, Li CHEN, Jing WANG, Wanli YUE, Xiaoping SHI. Parametric geometric modeling of dome⁃shaped multi⁃layer interlock woven preform[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(16): 429556-429556.

Figures/Tables 17

Fig.1

Fig.2

Table 1

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Table 2

Coordinates of binder yarns path nodes of P2 and P3 type

参考点	P2型		P3型
参考点	x坐标	y坐标	x坐标	y坐标
$A 1$	$x A 1 P 2$	$y A 1 P 2$	$x A 1 P 3$	$y A 1 P 3$
$A 2$	$x A 2 P 2$	$y A 2 P 2$	$x A 2 P 3$	$y A 2 P 3$
$E 1$	$x E 1 P 2$	$y E 1 P 2$	$x E 1 P 3$	$y E 1 P 3$
$A 3$	$x A 3 P 2$	$y A 3 P 2$	$x A 3 P 3$	$y A 3 P 3$
$A 4$	$x A 4 P 2$	$y A 4 P 2$	$x A 4 P 3$	$y A 4 P 3$
$E 2$	$x E 2 P 2$	$y E 2 P 2$
$A 5$	$x A 5 P 2$	$y A 5 P 2$
$A 6$	$x A 6 P 2$	$y A 6 P 2$	$x A 6 P 3$	$y A 6 P 3$
$E 3$	$x E 3 P 2$	$y E 3 P 2$	$x E 3 P 3$	$y E 3 P 3$
$A 7$	$x A 7 P 2$	$y A 7 P 2$	$x A 7 P 3$	$y A 7 P 3$
$A 8$	$x A 8 P 2$	$y A 8 P 2$	$x A 8 P 3$	$y A 8 P 3$

Table 2

Table 3

Expression of binder yarns straight segment length of P2 and P3 type

直线段	类型	解析式
$l A 2 E 1$	P2型	$(x E 1 P 2 - x A 2 P 2) 2 + (y A 2 P 2 - y E 1 P 2) 2$
$l A 2 E 1$	P3型	$(x E 1 P 3 - x A 2 P 3) 2 + (y A 2 P 3 - y E 1 P 3) 2$

$l E 1 A 3$	P2型	$(x A 3 P 2 - x E 1 P 2) 2 + (y E 1 P 2 - y A 3 P 2) 2$
$l E 1 A 3$	P3型	$(x A 3 P 3 - x E 1 P 3) 2 + (y E 1 P 3 - y A 3 P 3) 2$

$l A 4 E 2$	P2型	$(x E 2 P 2 - x A 4 P 2) 2 + (y A 4 P 2 - y E 2 P 2) 2$

$l E 2 A 5$	P2型	$(x A 5 P 2 - x E 2 P 2) 2 + (y E 2 P 2 - y A 5 P 2) 2$

$l A 6 E 3$	P2型	$(x E 3 P 2 - x A 6 P 2) 2 + (y A 6 P 2 - y E 3 P 2) 2$
$l A 6 E 3$	P3型	$(x E 3 P 3 - x A 6 P 3) 2 + (y A 6 P 3 - y E 3 P 3) 2$

$l E 3 A 7$	P2型	$(x A 7 P 2 - x E 3 P 2) 2 + (y E 3 P 2 - y A 7 P 2) 2$
$l E 3 A 7$	P3型	$(x A 7 P 3 - x E 3 P 3) 2 + (y E 3 P 3 - y A 7 P 3) 2$

Table 3

Table 4

Expression of binder yarns curve segment length of P2 and P3 type

参考点	类型	解析式
参考点	类型	$L$	$F$
$l A 1 A 2$	P2型	$2 x A 2 P 2$	$y A 1 P 2 - y A 2 P 2$
$l A 1 A 2$	P3型	$2 x A 2 P 3$	$y A 1 P 3 - y A 2 P 3$

$l A 3 T 2$	P2型	$- 2 x A 3 P 2$	$y A 3 P 2 - y T 2 P 2$

$l A 4 T 2$	P2型	$- 2 x A 4 P 2$	$y A 4 P 2 - y T 2 P 2$

$l A 3 A 4$	P3型	$- 2 x A 3 P 3$	$y A 3 P 3 - y A 4 P 3$

$l A 5 T 3$	P2型	$2 x A 5 P 2$	$y T 3 P 2 - y A 5 P 2$

$l A 6 T 3$	P2型	$2 x A 6 P 2$	$y T 3 P 2 - y A 6 P 2$

$l A 4 A 6$	P3型	$2 x A 6 P 3$	$y A 4 P 3 - y A 6 P 3$

$l A 7 A 8$	P2型	$- 2 x A 7 P 2$	$y A 7 P 2 - y A 8 P 2$
$l A 7 A 8$	P3型	$- 2 x A 7 P 3$	$y A 7 P 3 - y A 8 P 3$

Table 4

Fig.10

Fig.11

Table 5

DIWP sample input parameter information

变量	数值	变量	数值
$w$	5	$δ f *$ /（g·cm^-3）	1.8
$ρ *$ /（根·cm^-1）	3	$λ$	4.8
$R 0$ /mm	50	$D w$ /mm	0.52
$θ$ /（°）	52.85	$A j$ /mm	2.2
$η w$ /tex	990	$D j$ /mm	0.56
$η j$ /tex	990	$A b$ /mm	1.4
$η b$ /tex	495	$D b$ /mm	0.38

Table 5

Table 6

Parametric model calculation results

类别	$V w$ /mm³	$V b$ /mm³	$V j$ /mm³	V/mm³	$V f$ /%
理论值	7.304	4.124	7.333	55.159 0	34.01
实测值	6.930	3.795	7.183	50.848 8	35.22

Table 6

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Parametric geometric modeling of dome⁃shaped multi⁃layer interlock woven preform

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