Modeling of Curling of Plain-Knitted Fabrics toward Its Suppression

卷曲是指平纹针织物的边缘卷曲的现象，它妨碍了织物的有效缝纫。由于卷曲程度与纱线性能和/或针织参数之间的定量关系不清楚，因此需要对卷曲进行分析。首先，基于微分几何和静力学变分原理，建立了平纹针织物的组织模型。然后，卷曲被视为变形的线圈，以减少其势能。接下来，考虑重力效应，在2D空间中对整个织物的卷曲进行建模。最后，它表明，由于织物的刚度的差异，织物的卷曲形状的差异可以模拟。我们将能够从纱线的性质和编织参数来估计织物的卷曲，而无需实际编织。这将通过控制这些属性/参数来抑制卷曲。

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.