基于分形的棉条建模及其牵伸过程的仿真

doi:10.13475/j.fzxb.20220403708

摘要/Abstract

摘要：

为分析计算棉条牵伸力的变化,以提高棉纤维牵伸的质量,依据分形理论的建模思想,将具有相同圆形截面的棉纤维按照分形理论进行排列,构建了新的棉须条模型。基于动态牵伸和静态牵伸的相似性,将该模型进行静态拉伸仿真,得出不同定量的棉条静态牵伸力。结果显示须条静态拉伸力与动态牵伸力的平均误差为5.66%,最大相对误差在12%以内。利用线性拟合求出动态牵伸力与静态牵伸力的关系式,成功预测了不同定量下的牵伸力。此外,得出了在定量为25.60 g/m时,静态牵伸力随牵伸倍数的变化曲线。结果表明仿真牵伸力与动态牵伸力的变化趋势基本一致。建立的分形须条模型有效,也为动态牵伸力的近似预测提供参考。

关键词: 棉须条, 分形结构, 动态牵伸力, 静态牵伸力, 牵伸质量

Abstract:

Objective In order to analyze and calculate the changes in the drawing force of cotton whiskers and improve the quality of the cotton drawing process, this paper analyzes and researches the drawing force. Using the finite element analysis to calculate the drawing force can greatly simplify the calculation process of the drawing force and improve the efficiency of the drawing process. The drawing force is the most important process parameter in the drawing process of cotton whiskers, and it has an important influence on the final yarn quality of the spinning process.
Method Fractology is an effective method used to describe the structure of irregular objects. Fractal theory is used to construct the complex form of whisker fibers, which can better reflect the structural characteristics of the whisker. Using the relationship between static stretching and dynamic drawing, static stretching is used instead of dynamic drawing to simulate and solve the drawing force. The simulated drawing force is fitted with the experimental data to obtain the fitting equation, which can be used to solve the drawing force.
Results The fractal whisker bar model constructed by the fractal method can better simulate the complex pore structure of cotton whiskers. The fractal graph generation algorithm used in this paper is the iterative function system algorithm (IFS). At the same time, the model uses a fiber bundle to represent the existence of several fibers, and the fiber bundle has a circular cross-sectional structure. ANSYS is used to perform finite element analysis and calculation of the fractal whisker bar model, and the simulation-calculated drawing force is obtained based on the post-processing results. (Tab. 4). The comparison results of the simulated drawing force and the experimental drawing force show that the average error between the static drawing force and the dynamic drawing force of the whisker strip is 5.66%, the maximum relative error is within 12%, and the relative error is within a reasonable range. These prove that the simulated drawing force can better reflect the drawing force in the drawing process to a certain extent. Using curve fitting, the relationship between the experimental drawing force and the simulated drawing force is obtained, and the size of the drawing force of the whiskers under different quantifications is successfully predicted. Under the quantitative 25.60 g/m whisker model, the simulated drawing force of the model under different drawing multiples is analyzed, and it is found that the simulated drawing force reached the critical maximum value when the drawing multiple was about 1.5, and then the drawing force decreased rapidly with the increase of the drawing multiple. The curve of the simulated drawing force with the multiple of drawing is also basically the same as the experimental curve. Finally, the comparison between the simulation results of the drawing force and the experimental data shows that the fractal whisker bar model can effectively solve the drawing force, and the model is reasonable.
Conclusion In this paper, the fractal method is used to construct a cotton whisker strip model, which provides a new idea for the three-dimensional modeling of the whisker strip. The fractal model can reflect the nonlinear structure of the whisker strip. The use of finite element simulation to solve the drawing force of the whisker strip can greatly improve the efficiency of solving the drawing force and save manpower and material resources. The simulation results of the drawing force of the whisker strip show the effectiveness of the fractal whisker strip model. The relationship between the simulated drawing force and the experimental drawing force can be used to predict the size of the drawing force and to pre-calculate the drawing force, which provides a reference for the setting of the drawing force in spinning. The curve of the simulated drawing force on the drawing multiple also proves the rationality of the fractal whisker model.

Key words: whiskers, fractal structure, dynamic drafting force, static drafting force, arawing quality

中图分类号:

TS101

谢鹏浩, 李勇, 陈晓川, 汪军. 基于分形的棉条建模及其牵伸过程的仿真[J]. 纺织学报, 2023, 44(04): 55-62.

XIE Penghao, LI Yong, CHEN Xiaochuan, WANG Jun. Fractal-based modeling of whiskers and simulation of drafting process[J]. Journal of Textile Research, 2023, 44(04): 55-62.

图/表 15

图1

图2

表1

表2

俯视图分形须条单元的IFS码"

i	$a i$	$c i$	$e i$	$f i$
(1)	1	2.4	1	0
(2)	1	2.4	1	0
(3)	1	0	1	2.68

表2

图3

图4

图5

图6

图7

表3

图8

表4

图9

表5

图10

参考文献 12

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T_i	ω_i
T₁	x'=x-2.4	y'=y
T₂	x'=x+2.4	y'=y
T₃	x'=x	y'=y+2.68

实验须条定量/(g·m^-1)	须条模型平均定量/(g·m^-1)	相对误差/%
8.96	6.40	28.57
13.44	12.80	4.76
17.92	19.20	7.14
26.88	25.60	4.76
31.36	32.00	2.04
35.84	38.40	7.14

须条定量/ (g·m^-1)	实验牵伸力/ cN	模型平均定量/ (g·m^-1)	仿真牵伸力/ cN	相对误差/%
须条定量/ (g·m^-1)	实验牵伸力/ cN	模型平均定量/ (g·m^-1)	仿真牵伸力/ cN	定量	牵伸力
8.96	56.210	6.40	52.146	28.57	7.23
13.44	71.369	12.80	79.690	-4.76	11.66
17.92	100.017	19.20	106.198	7.14	6.18
26.88	136.903	25.60	141.585	-4.76	3.42
31.36	156.236	32.00	157.627	2.04	0.89
35.84	175.269	38.40	183.279	7.14	4.57

须条定量/ (g·m^-1)	动态牵伸力的仿真/cN	动态牵伸力的计算值/cN	动态牵伸力的实验值/cN	相对误差/%
40.32	205.438	207.855	196.930	5.26
50.12	243.157	238.443	240.590	-0.90