基于分数阶模型的纱线蠕变性能模拟与预测

doi:10.13475/j.fzxb.20211005006

纺织学报 ›› 2022, Vol. 43 ›› Issue (11): 46-51.doi: 10.13475/j.fzxb.20211005006

基于分数阶模型的纱线蠕变性能模拟与预测

李杨¹, 彭来湖¹^,²(), 郑秋扬¹, 胡旭东¹

1.浙江理工大学浙江省现代纺织装备技术重点实验室, 浙江杭州 310018
2.浙江理工大学龙港研究院, 浙江温州 325802

收稿日期:2021-10-22 修回日期:2022-03-15 出版日期:2022-11-15 发布日期:2022-12-26
通讯作者: 彭来湖
作者简介:李杨(1994—),男,博士生。主要研究方向为纱线张力控制技术。
基金资助:
浙江省博士后科研项目特别资助项目(ZJ2020004)

Simulation and prediction of yarn creep performance based on fractional model

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

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 Published:2022-11-15 Online:2022-12-26
Contact: PENG Laihu

摘要/Abstract

摘要：

针对现有纱线拉伸力学模型描述不准确问题,以分数阶微积分模型对纱线拉伸行为进行分析。首先,引入分数阶微积分理论改进的黏壶模型建立了分数阶纱线蠕变模型,使用XL-2型纱线强伸度仪对不同线密度及不同张力纱线进行蠕变实验,获得纱线蠕变的全过程曲线。通过对不同线密度下的试验曲线进行回归分析得到了模型参数以及蠕变模型参数与施加张力大小的变化关系。最后,利用不同模型对不同张力的纱线蠕变曲线进行拟合和预测。结果表明:分数阶纱线蠕变模型,相比于三元件模型、整数阶模型和Burgers模型,具有结构简单、参数少的特点,并且对纱线蠕变的拟合和预测也具备较高的精度。

关键词: 纱线蠕变模型, 线密度, 分数阶微积分, 纱线蠕变性能预测

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

中图分类号:

TS184.1

李杨, 彭来湖, 郑秋扬, 胡旭东. 基于分数阶模型的纱线蠕变性能模拟与预测[J]. 纺织学报, 2022, 43(11): 46-51.

LI Yang, PENG Laihu, ZHENG Qiuyang, HU Xudong. Simulation and prediction of yarn creep performance based on fractional model[J]. Journal of Textile Research, 2022, 43(11): 46-51.

图/表 12

图1

图2

图3

图4

表1

图5

表2

实验2的参数拟合结果"

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

表2

图6

图7

表3

实验2的模型拟合精度评价"

蠕变模型	均方差MSE		相关系数 $R 2$
蠕变模型	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

表3

图8

表4

模型拟合精度评价"

蠕变模型	均方差MSE		相关系数 $R 2$
蠕变模型	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

表4

参考文献 12

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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

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基于分数阶模型的纱线蠕变性能模拟与预测

Simulation and prediction of yarn creep performance based on fractional model

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