An improved Capstan equation including power-law friction and bending rigidity for high performance yarn

• A modified Capstan including bending rigidity and power-law friction was developed.
• The effects of bending rigidity and power-law friction on tension ratio were analyzed.
• The modified curve has an approximate agreement with the experimental and fitted one.

The tension of high performance yarn in the weaving region has influence on uniformity and pattern effect of fabric, which is difficult to be predicted in weaving process. In this paper, a modified Capstan equation including bending rigidity and power-law friction effects was developed, and solved numerically. The effects of the bending rigidity and power-law friction on tension ratio were analyzed. The experimental results were compared with the classical Capstan equation and modified one, showing that there was an approximate agreement between the modified tension ratio and experimental values. And therefore, the modified tension ratio could be used to characterize the tension variation and provide theoretical support for precisely controlling of yarn tension.

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