A New Elliptical Cross-Section Mathematical Model of Woven Fabric Based on Jacobian Transformation

• Published in: 东华大学学报（英文版） Vol. 29; no. 5; pp. 434 - 438
• Main Author: 杨育林 谷大鹏 齐效文 陈素文
• Format: Journal Article
• Language: English
• Published: Key Laboratory of Fundamental Science of Mechanical Structure and Material Science under Extreme Condition for National Defence, Yanshan University, Qinhuangdao 066004, China%College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China 2012
• Subjects: 理论; 纺织工业; 纺织数学; 设计; mathematical model; elliptical cross-section; woven fabric; 3D simulation; Matlab
• ISSN: 1672-5220

In order to give a true reflection of the spatial structure of woven fabric, a circular mathematical model is established based on the Peirce＇s model and the principle of the coordinate transformation. The circular model uses arcs and tangent lines as the yarn flexion shape and selects the circle as the yarn cross-section. Then, a new elliptical cross-section mathematical model is rapidly built by the Jaeobian transformation of the circular model. The Matiab software is used for the 3D simulation. It is shown that 3D simulations of woven fabrics with different weft and warp yarn counts, weft and warp densities, structure phases, weaves and flattening coefficients are successfully realized by Matiab basing on the elliptical mathematical model.