纱线结构中纤维形态的数学表征

 根据空间几何学基本原理，采用曲率、挠率以及相对转角对纤维的形态结构进行表征，用于衡量纤维的弯曲变形和扭转变形，改变了以往纤维形态研究只考虑其空间曲线特性的局限，从而建立了纤维的空间弹性曲杆模型。分别对纱线捻回角与纤维扭转数进行数学推导，分析了两者之间的统一关系。并指出纱线捻回角是纤维弯曲变形和扭转变形的综合反映，而纤维扭转数则可以将纤维的弯曲变形和扭转变形加以区别，从而能够突出纤维本身扭转性能的重要性。

Mathematical characterization of fiber morphology in yarn assembly

According to the basic principle of space geometry,the fiber morphology is characterized by the curvature,torsion and relative rotation for measuring the bend deformation and torsion deformation of fiber.In doing so,the limitation of previous researches of fiber morphology only considering the characteristics of space curve is changed,and the space elastic rod model of fiber is built.At the same time,the yarn twist angle and the fiber twisting number are studied by mathematical deduction,and their relationship is analyzed.As a result,the twist angle is the integrated reflection of bend deformation and torsion deformation,but the twisting number can be used to distinguish the bend deformation and the torsion deformation,so the importance of torsion performance of fiber itself can be emphasized.