Journal of Textile Research ›› 2022, Vol. 43 ›› Issue (11): 46-51.doi: 10.13475/j.fzxb.20211005006

• Textile Engineering • Previous Articles     Next Articles

Simulation and prediction of yarn creep performance based on fractional model

LI Yang1, PENG Laihu1,2(), ZHENG Qiuyang1, HU Xudong1   

  1. 1. Key Laboratory of Modern Textile Machinery & Technology of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China
    2. Longgang Institute of Zhejiang Sci-Tech University, Wenzhou, Zhejiang 325802, China
  • Received:2021-10-22 Revised:2022-03-15 Online:2022-11-15 Published:2022-12-26
  • Contact: PENG Laihu E-mail:laihup@zstu.edu.cn

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Abstract:

Aiming of the inaccuracy in existing yarn stretch mechanics models, the yarn extension behavior is analyzed by the fractional calculus model. The fractional order calculus theory with improved glue-pot model is introduced for the establishment of the fractional order yarn creep model. XL-2 tensile tester was used to measure the yarn elongation for creep with yarns under the same tension and of different linear density and with yarns under different tensions but of the same linear density, obtaining the creep curve for the whole process. The yarn creep test curves for yarns with different linear densities were selected for regression, and the model parameters were obtained. The relationship between creep model parameters and applied tension was also obtained. Finally, different models were used to fit and predict the yarn creep curve under different tension. The results show that the fractional order yarn creep model proposed in this paper is not only simple in structure and involving less parameters than the three-component model, integer order model and Burgers model, but also has high precision in the fit and prediction of yarn creep.

Key words: yarn creep model, line density, fractional calculus, prediction of yarn creep performance

CLC Number: 

  • TS184.1

Fig.1

Fractional order M‖N yarn creep model"

Fig.2

Creep test result of yarn with different linear densities"

Fig.3

Creep tests of cotton yarn with different tensile forces"

Fig.4

Fractional order M‖N fitting curve of yarn creep model to test 1"

Tab.1

Fitting results of fractional order M‖N yarn creep model to test 1"

线密度/tex τ0 E1 η1 β1 η2 β2 R2
14.5 34.156 98.13 3226.4 0.157 52.11 0.10 0.986
19.4 47.325 80.91 17435.1 0.149 26.89 0.10 0.985
27.0 50.729 60.45 50713.1 0.468 18.65 0.10 0.987
32.0 53.246 48.85 15393.1 0.536 13.28 0.10 0.986

Fig.5

Relationship between model parameters and applied loads in test 1"

Tab.2

Fitting results of test 2"

载荷/cN τ 0 E 1 η 1 β 1 η 2 β 2 R 2
100 48.156 86.53 2376.7 0.323 23.27 0.10 0.996
120 59.458 54.60 11813.4 0.459 13.82 0.10 1.000
140 67.629 32.37 43215.2 0.582 7.05 0.10 0.998
160 70.751 21.25 91175.6 0.674 5.28 0.10 0.994

Fig.6

Fitting results of fractional order M‖N yarn creep model to test 2"

Fig.7

Fitting effect curves of different models to test 2"

Tab.3

Model fitting accuracy evaluation for test 2"

蠕变模型 均方差MSE 相关系数 R 2
100 cN 140 cN 100 cN 140 cN
本文模型 0.412 0.528 0.984 0.978
三元件模型 3.736 2.624 0.628 0.733
M‖N模型 1.358 0.632 0.917 0.958
Bergers模型 2.133 0.954 0.928 0.964

Fig.8

Prediction of yarn creep by model under different tension in Test 2"

Tab.4

Model fitting accuracy evaluation"

蠕变模型 均方差MSE 相关系数 R 2
120 cN 160 cN 120 cN 160 cN
本文模型 0.456 0.489 0.989 0.972
三元件模型 1.168 1.160 0.965 0.958
M‖N模型 0.537 0.612 0.979 0.981
Bergers模型 2.350 2.164 0.750 0.664
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