纤维增强复材C形圆台壳件固化变形的预测方法

陶裕梅; 郑子君; 邵家儒

doi:10.11868/j.issn.1005-5053.2021.000198

纤维增强复材C形圆台壳件固化变形的预测方法

doi: 10.11868/j.issn.1005-5053.2021.000198

重庆理工大学机械工程学院, 重庆 400054

基金项目: 国家自然科学基金青年项目（11702046）；重庆市教委科学研究项目（KJ1600910）

详细信息

通讯作者:
邵家儒（1986—），男，博士，副教授，主要从事机械CAE设计、流固耦合动力学方面的研究，联系地址：重庆市巴南区李家沱红光大道69号，E-mail:shaojiaru@cqut.edu.cn

中图分类号: TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2021-11-30
- 修回日期: 2022-01-10
- 网络出版日期: 2022-04-22

Prediction method for curing deformation of conical C-shaped shell of fiber reinforced composite

College of Mechanical Engineering, Chongqing University of Technology, Chongqing, 400054, China

摘要

摘要: 采用热压罐固化成形的纤维增强复合材料工件在脱模后通常与模具形状有一定出入，影响成型的精度和质量。为研究曲面零件固化变形规律，将C形圆台壳件的几何形状用母线长度、半高处半径、圆心角、半顶角、厚度五个参数表征，并基于虚功原理和小变形假设推导由于固化工艺中温度改变导致的形状变化公式。结果表明：固化后此类工件的厚度变薄，半高处半径缩小、圆心角增大、母线变短、顶角变小。与有限元模拟正交实验对比，验证了本公式的正确性；给出了基于path-dependent本构关系的固化变形有限元模拟的简化实现方案，与文献相比可以减少80%的计算时间，且实现难度较低。分别用本公式、热弹性有限元模型、path-dependent有限元模型计算某小型固定翼飞机的机头罩固化变形，预测半跨长平均缩小量分别是8.1 mm、7.6 mm、6.1 mm，均与实测值7.7 mm基本吻合；计算结果可以解释该零件的装配变形现象。
- 复合材料 /
- 热压罐 /
- 固化变形 /
- 虚功原理 /
- 热应变
Abstract: The shape of fiber-reinforced composite work-piece cured in autoclave usually deviates from the original design after demoulding, which influences the product quality. In order to study the cure deformation law of curved parts, the geometry of conical C-shaped shell was described by only five parameters: generatrix length, radius at half height, center angle, half apex angle and shell thickness. Based on the virtual work principle and small deformation hypothesis, the analytic solution of the cure deformation caused by the temperature drop in the curing process was deduced. It is revealed that after curing, the thickness, half-height radius, generatrix length and apex angle decrease, while the center angle of the arc increases. Compared with the finite element simulation orthogonal test, which validates the analytical solution. A simplified scheme of finite element curing simulation by use of the path-dependent constitutive law is given. This simplified finite element deformation prediction method can cut the computing time by 80% and the implementation is much easier. By using this formula, thermoelastic finite element model and path-dependent finite element model, the curing deformation of the nose cover of a small fixed-wing aircraft is calculated, and the predicted average reduction of half-span length is 8.1mm,7.6mm and 6.1mm respectively, which are basically consistent with the measured value of 7.7mm. The assembly deformation characteristics of the part can also be explained based on the proposed analysis.
- composites /
- autoclave /
- curing deformation /
- virtual work principle /
- thermal strain

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图 1 固化温度工艺曲线以及固化参数随时间的变化

Figure 1. Curing temperature process curves and changes of curing parameters over time

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图 2 两种C形构件模型示意图　（a）圆壳模型；（b）圆台壳模型

Figure 2. Schematic diagrams of two C-shaped component models 　(a) round shell model； (b) round pedestal shell model

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图 3 C形圆台壳的1/2有限元模型

Figure 3. Symmetrical finite element model of C-shaped circular pedestal shell

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图 4 C形圆台壳件几何参数变量的公式预测结果与有限元对比

Figure 4. Comparison of formula prediction results of geometric parameter variables of C-shaped circular truncated shell and finite element

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图 5 path-dependent本构模型示意图

Figure 5. Schematic diagram of path-dependent constitutive model

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图 6 C型构件回弹预测结果与实验、文献对比　（a）（90）_n，（n=4,8,12,16）；（b）（90/0）_ns，（n=1,2,3,4）

Figure 6. Comparison of spring-in prediction results of C-shaped model with experiments and literatures　(a) (90)_n, (n=4,8,12,16); (b)(90/0)_ns, (n=1,2,3,4)

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图 7 某小型固定翼飞机机头罩几何模型

Figure 7. Geometric model of nose cover of a small fixed-wing aircraft

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图 8 机头罩1/2模型固化变形云图及实验测量点

Figure 8. Curing deformation contour and experimental measurement points of symmetrical model of nose cover

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图 9 不同变形轮廓与实验测量结果的对比

Figure 9. Comparison of different deformation profiles with experimental measurement results

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图 10 机头罩1/2模型装配对称轴与侧沿后的变形云图（放大8倍）

Figure 10. Deformation contour of half of nose cover model after assembling symmetry axis and side edges (8 times magnification)

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图 11 某小型固定翼飞机机头罩安装后照片

Figure 11. Photo of a small fixed-wing aircraft after the installation of the hood

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表 1 正交实验变量及对应水平选择

Table 1. Orthogonal test variables and corresponding level selections

Level	Generatrix length $h/{\text{mm}}$	Radius at half height $r/{\text{mm}}$	Center angle $\theta /\left( {^{\text{o}}} \right)$	Half apex angle $\phi /\left( {^{\text{o}}} \right)$
	A	B	C	D
1	100	100	30	5
2	200	200	60	10
3	300	300	90	15

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表 2 玻璃纤维增强树脂基复材(Hexcel7781/LY5052/ HY5052,$ V_{f}=0.49 $)的等效力学性能

Table 2. Equivalent mechanical properties of glass fiber reinforced resin-based composite material (Hexcel7781/LY5052/HY5052, $ V_{r}=0.49 $)

State	E_τ/GPa	En/GPa	G_ττ/GPa	G_τn/GPa	ν_ττ	ν_τn	α_τ10^–6/°C	α_n10^–6/°C	dβ_τ/∆X_τ	dβ_n/∆X_n
Rubbery	18.7	2.3	0.03	0.03	0.002	0.845	5.54	264.8	–7.95×10^–5	–3.5×10^–2
Glassy	22.95	8.4	2.55	2.43	0.1	0.455	15.2	66.4	–3.65×10^–4	–2.2×10^–2

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表 3 3 mm厚C形模型的不同本构模型运行时间对比

Table 3. Comparison of time costs of different constitutive laws for C-section with 3 mm thickness

Model	Time cost/s
CHILE(α)	182
CHILE(T_g)	185
Path-dependent	149
Viscoelastic	157
Proposed model	32

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表 4 机头罩简化几何模型参数

Table 4. Simplified geometric model parameters of nose cover

Radius	Generatrix length, h/mm	radius at half height, r/mm	center angle， θ/(°)	half apex angle， φ/(°)
Minor radius	782	1315	12	8
Long radius		278.5	80

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