Multi-objective optimization of fiber orientation and grammage of recycled carbon fiber felt
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摘要: 废弃复合材料的回收再利用具有重要意义，传统回收方法能耗高且易损伤材料结构，回收纤维取向杂乱，无法进行高价值利用。本文采用团队研发的新型可回收环氧树脂制备Ⅳ型储氢气瓶废弃复合材料为对象，研究碳纤维的高效回收方法。自主搭建纤维湿法取向装置制备纤维毡，探究湿法取向过程各工艺对再生纤维毡制备效果包括取向度及克重的影响；利用响应面法(RSM)建立取向度和克重目标模型并进行可靠性分析，结合非支配排序遗传算法Ⅱ(NSGA-Ⅱ)对湿法取向工艺参数进行多目标优化；采用优劣解距离法(TOPSIS)决策选择最优解，实验验证多目标优化结果。结果表明：各工艺条件对纤维毡取向度影响大小为纤维长度>纤维含量>分散剂含量>滤网孔径；对纤维毡克重影响大小为纤维含量>分散剂含量>滤网孔径>纤维长度。目标函数模型具有较高的准确性；多目标优化纤维毡制备最佳工艺为纤维长度3 mm、纤维含量6.37 g/L、分散剂含量13.37 g/L、滤网孔径0.75 mm；验证实验制备纤维毡取向度81.08%，与遗传算法预测取向度(81.84%)误差0.94%；实验制备纤维毡克重42.86 g/m2，与遗传算法预测克重(42.57 g/m2)误差0.68%。Abstract: It is of great significance to realize the recycling and reuse of waste composite materials. Traditional recycling methods consume high energy and are easy to damage the material structure of the fibers. The recycled fibers are oriented in a disorderly manner and cannot be utilized for high value. In this research, the new recyclable epoxy resin developed by our team was used to manufacture type IV hydrogen storage vessel, and the efficient recycling method of carbon fiber from waste composite hydrogen cylinder was studied. The fiber wet orientation device was designed independently to prepare oriented fiber felt. The effects of various process in the wet orientation process on the quality of regenerated fiber felt samples, including orientation degree and weight, were explored. The response surface method (RSM) was used to establish the objective models related to the orientation and grammage of the fiber felt, and the reliability of the models were analyzed. Based on the models, the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) was used to perform multi-objective optimization of the parameters of fiber wet orientation process. The optimal solution was selected using technique for order preference by similarity to ideal solution (TOPSIS), and experiments were designed to verify the results of multi-objective optimization. The results show that the impact of various process conditions on the orientation of fiber felt is ranked as fiber length > fiber content > dispersant content > filter mesh hole size. And the order of the impact of various process conditions on the grammage of fiber felt is fiber content > dispersant content > filter mesh hole size > fiber length. The objective function models are very reliable for analyzing the orientation and grammage of the fiber felt. Through the multi-objective optimization algorithm, the optimal process parameters for the preparation of regenerated fiber felt are fiber length 3 mm, fiber content 6.37 g/L, dispersant content 13.37 g/L, and filter mesh hole size 0.75 mm. The orientation degree of the fiber felt prepared by verification experiment is 81.08%, with an error of 0.94% from the orientation degree(81.84%) predicted by genetic algorithm. The grammage of the fiber felt experimentally prepared is 42.86 g/m2, with an error of 0.68% from the grammage(42.57 g/m2) predicted by genetic algorithm.
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图 1 可回收Ⅳ型复合材料储氢气瓶制造-回收-再利用全流程
Figure 1. Recyclable type IV composite hydrogen storage cylinder manufacturing - recovery - recycle process
图 3 复合材料储氢气瓶及爆破后待回收储氢气瓶
Figure 3. Composite hydrogen storage cylinder and hydrogen storage cylinder to be recovered after blasting
图 5 再生纤维湿法取向装置及原理示意图
Figure 5. Regenerated fiber wet orientation device and schematic diagram of principle
图 7 纤维图像拍摄、前处理及取向定性定量分析
Figure 7. Fiber image shooting, pre-processing and orientation qualitative and quantitative analysis
图 10 不同工艺条件对纤维毡取向度的影响
Figure 10. Influence of different process conditions on orientation of fiber felt
图 11 不同工艺条件对纤维毡取向度的影响
Figure 11. Influence of different process conditions on grammage of fiber felt
图 12 取向度相关回归模型$ {Y}_{1} $可靠性分析
Figure 12. Reliability analysis of regression model $ {Y}_{1} $ related to the orientation
图 13 不同工艺条件对纤维毡取向度相关函数$ {Y}_{1} $的交互影响
Figure 13. Interaction effect of different process conditions on the function $ {Y}_{1} $ related to the orientation of fiber felt
图 14 克重相关回归模型$ {Y}_{2} $可靠性分析
Figure 14. Reliability analysis of regression model $ {Y}_{2} $ related to grammage
图 15 不同工艺条件对纤维毡克重相关函数$ {Y}_{2} $的交互影响
Figure 15. Interaction effect of different process conditions on the function $ {Y}_{2} $ related to the grammage of fiber felt
图 17 次序为1的解在Pareto前沿所处位置
Figure 17. The position of the first ranked solution on the Pareto front
图 18 验证实验制备纤维毡及其取向分布图
Figure 18. Fiber felts for verification experiments and its fiber orientation distribution.
表 1 EzCiclo RB240环氧树脂混合物基本属性
Table 1. The basic properties of EzCiclo RB240 epoxy resin mixtures
Property quantitative value Blending ratio of A and B (weight ratio) 100∶100(±2) Viscosity-25℃/cps 800~1200 Viscosity-40℃/cps 200~400 Liquid state density-25℃/(g·cm−3) 1.10~1.20 Density after curing-25℃/(g·cm−3) 1.15~1.25 Operable time-30℃/h >8 
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表 2 单因素实验方案设计及结果
Table 2. Single factor experimental scheme design and experimental results
$ {X}_{1} $/mm $ {X}_{2} $/(g·L−1) $ {X}_{3} $/(g·L−1) $ {X}_{4} $/mm $ {y}_{1} $/% $ {y}_{2} $/(g·m−2) 1 2 5 13 0.8 84.54 38.91 2 3 5 13 0.8 86.38 39.23 3 4 5 13 0.8 85.79 39.45 4 5 5 13 0.8 83.22 39.66 5 6 5 13 0.8 76.53 39.83 6 7 5 13 0.8 65.87 39.97 7 8 5 13 0.8 56.62 40.03 8 5 3 13 0.8 86.45 35.1 9 5 4 13 0.8 86.02 37.32 10 5 6 13 0.8 77.96 42.09 11 5 7 13 0.8 71.42 44.8 12 5 5 10 0.8 83.65 38.16 13 5 5 11 0.8 84.16 38.74 14 5 5 12 0.8 84.2 39.26 15 5 5 14 0.8 81.74 39.98 16 5 5 15 0.8 79.81 40.13 17 5 5 16 0.8 77.26 40.2 18 5 5 17 0.8 74.36 40.31 19 5 5 13 0.4 79.62 39.81 20 5 5 13 0.6 81.79 39.82 21 5 5 13 1.0 83.25 39.09 22 5 5 13 1.2 81.58 38.11 Notes：$ {X}_{1} $ is the length of the regenerated fiber; $ {X}_{2} $ is the content of fibers in the dispersing solution; $ {X}_{3} $ is the content of dispersant in the dispersing solution; $ {X}_{4} $ is the size of the filter mesh hole; $ {y}_{1} $ is the ratio of fiber orientation within ±10°; $ {y}_{2} $ is the grammage of the fiber felt
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表 3 再生纤维毡质量主要影响工艺参数取值范围
Table 3. The value range of process parameters which mainly affect the quality of recycled fiber felt
$ {X}_{1} $/mm $ {X}_{2} $/(g·L−1) $ {X}_{3} $/(g·L−1) $ {X}_{4} $/mm Value range 2~8 3~7 10~16 0.4~1.2 Notes：$ {X}_{1} $ is the length of the regenerated fiber; $ {X}_{2} $ is the content of fibers in the dispersing solution; $ {X}_{3} $ is the content of dispersant in the dispersing solution; $ {X}_{4} $ is the size of the filter mesh hole.
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表 4 取向工艺四因素三水平正交实验方案
Table 4. The orthogonal experiment scheme with four factors and three levels of orientation technology
$ {X}_{1} $/mm $ {X}_{2} $/(g·L−1) $ {X}_{3} $/(g·L−1) $ {X}_{4} $/mm $ {Y}_{1} $ $ {Y}_{2} $ 1 2 5 13 0.8 11.722 29.155 2 3 5 13 0.8 16.375 28.498 3 4 5 13 0.8 13.101 23.052 4 5 5 13 0.8 20.421 23.047 5 6 5 13 0.8 12.500 26.281 6 7 5 13 0.8 13.523 25.342 7 8 5 13 0.8 12.195 26.802 8 5 3 13 0.8 13.048 25.615 9 5 4 13 0.8 12.115 25.641 10 5 6 13 0.8 18.702 25.510 11 5 7 13 0.8 12.449 26.157 12 5 5 10 0.8 17.544 25.773 13 5 5 11 0.8 11.737 29.700 14 5 5 12 0.8 13.680 23.629 15 5 5 14 0.8 12.191 28.329 16 5 5 15 0.8 15.181 23.105 17 5 5 16 0.8 12.585 26.738 18 5 5 17 0.8 16.807 26.344 19 5 5 13 0.4 12.167 25.714 20 5 5 13 0.6 19.350 25.602 21 5 5 13 1.0 12.165 28.612 22 5 5 13 1.2 14.599 22.847 Notes：$ {X}_{1} $ is the length of the regenerated fiber; $ {X}_{2} $ is the content of fibers in the dispersing solution; $ {X}_{3} $ is the content of dispersant in the dispersing solution; $ {X}_{4} $ is the size of the filter mesh hole; $ {Y}_{1} $ is the regression function related to orientation ratio of fiber orientation within ±10°; $ {Y}_{2} $ is the regression function related to grammage of the fiber felt.
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表 5 取向度相关回归模型$ {Y}_{1} $方差分析
Table 5. Analysis of variance of the regression model $ {Y}_{1} $ related to the orientation
Source Sum of Squares df Mean Square F-value p-value Model 172.09 14 12.29 957.31 < 0.0001 $ {X}_{1} $ 102.43 1 102.43 7976.99 < 0.0001 $ {X}_{2} $ 19.51 1 19.51 1519.59 < 0.0001 $ {X}_{3} $ 2.96 1 2.96 230.20 < 0.0001 $ {X}_{4} $ 0.4233 1 0.4233 32.97 < 0.0001 $ {X}_{1}{X}_{2} $ 1.78 1 1.78 138.48 < 0.0001 $ {X}_{1}{X}_{3} $ 2.19 1 2.19 170.72 < 0.0001 $ {X}_{1}{X}_{4} $ 0.5562 1 0.5562 43.31 < 0.0001 $ {X}_{2}{X}_{3} $ 0.2746 1 0.2746 21.38 0.0006 $ {X}_{2}{X}_{4} $ 0.0015 1 0.0015 0.1155 0.7399 $ {X}_{3}{X}_{4} $ 0.0072 1 0.0072 0.5611 0.4683 $ {X}_1^2 $ 39.78 1 39.78 3098.24 < 0.0001 $ {X}_{2}^2 $ 2.80 1 2.80 218.21 < 0.0001 $ {X}_{3}^2 $ 1.01 1 1.01 78.41 < 0.0001 $ {X}_{4}^2 $ 1.00 1 1.00 78.00 < 0.0001 Residual 0.1541 12 0.0128 Lack of Fit 0.1488 10 0.0149 5.61 0.1607 Pure Error 0.0053 2 0.0027 Cor Total 172.25 26 R2 0.9991 R2Adj 0.9981 Notes：df is the degree of freedom; F is ratio between interclass variance and intraclass variance; p is used to evaluate the significance of the model and is related to F.
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表 6 克重相关回归模型$ {Y}_{2} $方差分析
Table 6. Analysis of variance of the regression model $ {Y}_{2} $ related to the grammage
Source Sum of Squares df Mean Square F-value p-value Model 119.37 14 8.53 1489.50 < 0.0001 $ {X}_{1} $ 1.54 1 1.54 269.04 < 0.0001 $ {X}_{2} $ 107.97 1 107.97 18861.72 < 0.0001 $ {X}_{3} $ 5.14 1 5.14 898.25 < 0.0001 $ {X}_{4} $ 2.58 1 2.58 450.13 < 0.0001 $ {X}_{1}{X}_{2} $ 0.0123 1 0.0123 2.14 0.1688 $ {X}_{1}{X}_{3} $ 0.0372 1 0.0372 6.49 0.0256 $ {X}_{1}{X}_{4} $ 0.0750 1 0.0750 13.11 0.0035 $ {X}_{2}{X}_{3} $ 0.1231 1 0.1231 21.50 0.0006 $ {X}_{2}{X}_{4} $ 0.0229 1 0.0229 4.00 0.0687 $ {X}_{3}{X}_{4} $ 0.0005 1 0.0005 0.0828 0.7784 $ {X}_{1}^2 $ 0.0786 1 0.0786 13.73 0.0030 $ {X}_{2} ^2$ 0.6247 1 0.6247 109.13 < 0.0001 $ {X}_{3}^2 $ 0.5321 1 0.5321 92.95 < 0.0001 $ {X}_{4}^2 $ 1.56 1 1.56 272.64 < 0.0001 Residual 0.0687 12 0.0057 Lack of Fit 0.0458 10 0.0046 0.3999 0.8684 Pure Error 0.0229 2 0.0115 Cor Total 119.44 26 R2 0.9994 $R_{{\rm{Adj}}}^2 $ 0.9988 Notes：df is the degree of freedom; F is ratio between interclass variance and intraclass variance; p is used to evaluate the significance of the model and is related to F.
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表 7 不同评估指标专家打分值
Table 7. Expert scores for different evaluation indicators
Expert number Indicator 1
(orientation)Indicator 2
(grammage)1 5 4 2 5 3 3 4 4 4 4 3 5 5 4 6 5 3 7 5 3 8 4 3 9 5 4 10 4 3
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表 8 Pareto最优解集中次序前10的解
Table 8. The top 10 solutions in the Pareto solution set
Ranking Process parameters Evaluation indicators $ {R}_{m} $ Fiber
Length/mmFiber
content/(g·L−1)Dispersant
content/(g·L−1)Filter mesh
hole size/mmFiber orientation
ratio within ±10°/%Grammage/
(g·m−2)1 3 6.37 13.37 0.75 81.84 42.57 0.85192 2 3 6.46 13.37 0.75 81.28 42.77 0.85157 3 3 6.46 13.71 0.75 81.01 42.87 0.85115 4 3 6.2 13.98 0.7 82.29 42.37 0.85072 5 3 6.2 13.37 0.75 82.88 42.18 0.85002 6 3 6.58 13.37 0.7 80.43 43.07 0.84926 7 3 6.47 13.07 0.8 81.37 42.64 0.84921 8 3 6.2 13.98 0.8 82.37 42.29 0.84906 9 3 6.1 13.71 0.75 83.22 42.05 0.84880 10 3 6.1 13.37 0.75 83.46 41.95 0.84747 Notes：$ {R}_{m} $ is the proximity index of each non-dominated solution to the optimal level.
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表 9 最优工艺参数实验验证结果
Table 9. Experimental verification results of optimal process parameters
Predicted value Fiber felt #1 Fiber felt #2 Fiber felt #3 Experimental mean Average error /% Fiber orientation ratio within ±10° /% 81.84 82.01 80.52 80.71 81.08 0.94% Grammage /(g·m−2) 42.57 41.85 43.57 43.16 42.86 0.68%
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