Journal of Textile Research ›› 2023, Vol. 44 ›› Issue (04): 55-62.doi: 10.13475/j.fzxb.20220403708

• Textile Engineering • Previous Articles     Next Articles

Fractal-based modeling of whiskers and simulation of drafting process

XIE Penghao1, LI Yong2, CHEN Xiaochuan1(), WANG Jun3   

  1. 1. College of Mechanical Engineering, Donghua University, Shanghai 201620, China
    2. College of Mechanical and Electronic Engineering, Tarim University,Alar, Xinjiang 843300, China
    3. College of Textiles, Donghua University, Shanghai 201620, China
  • Received:2022-04-11 Revised:2022-11-16 Online:2023-04-15 Published:2023-05-12

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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

CLC Number: 

  • TS101

Fig. 1

Initial graph and transformation process of top view. (a) Initial set graph; (b)n=1"

Fig. 2

Front view initial graphics and transformation process. (a) Initial set graph; (b)n=1; (c) n=2"

Tab. 1

IFS transformation of fractal whisker elements in top view"

Ti ωi
T1 x'=x-2.4 y'=y
T2 x'=x+2.4 y'=y
T3 x'=x y'=y+2.68

Tab. 2

IFS codes of fractal whiskers in top view"

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

Fig. 3

Basic unit of fractal whisker aggregate model"

Fig. 4

Fist mirror structure diagram"

Fig. 5

Second mirror structure"

Fig. 6

Schematic diagram of cut part in second mirror structure"

Fig. 7

3-D models of fractal whiskers with different quantities"

Tab. 3

Whisker quantitative error"

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

Fig. 8

Stress contour of each quantitative stretch"

Tab. 4

Model quantitative tensile force and experimental draft force"

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/%
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

Fig. 9

Model's stretch and stretch polylines"

Tab. 5

Comparison of calculated and experimental values of drafting force"

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

Fig. 10

Simulated draft force for different draft ratios"

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