Modeling of Curling of Plain-Knitted Fabrics toward Its Suppression

卷边是平针织物的边缘卷曲的现象，它妨碍织物的有效缝纫。由于卷曲程度与纱线性能和/或针织参数之间的定量关系尚不清楚，因此需要对卷曲进行分析。首先，基于微分几何和变分静力学原理对平针织物的针脚进行了建模。然后，将卷边视为针迹的变形，以降低针迹的势能。其次，考虑重力效应，对整个织物在二维空间中的卷曲进行建模。最后表明，可以模拟出由于织物刚度的不同而导致的织物卷曲形状的差异。我们将能够在没有实际编织的情况下，从纱线的性质和编织参数来估计织物的卷曲。通过控制这些属性/参数，可以抑制卷曲。

Curling is a phenomenon that edges of a plain-knitted fabric are curled and it prevents efficient sewing of the fabric. As quantitative relationship between the magnitude of curling and properties of a yarn and/or knitting parameters is unclear, analysis of curling has been required. First, a knitted stitch in a plain-knitted fabric is modeled based on the differential geometry and the variational principle of statics. Then, curling is regarded as deformation of the stitch to reduce its potential energy. Next, curling of the whole fabric in 2D space is modeled considering the gravitational effect. Finally, it is shown that the difference of the curled shape of the fabric due to the difference of the rigidity of the fabric can be simulated. We will be able to estimate curling of a fabric from properties of a yarn and knitting parameters without actually knitting. It will lead to suppression of curling by controlling such properties/parameters.