基于分数阶模型的纱线蠕变性能模拟与预测

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。

Simulation and prediction of yarn creep performance based on fractional model

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.