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.