Mathematical Modeling of Yarn Dynamics in a Generalized Twisting System

Area of Science:

• Textile Engineering
• Materials Science
• Applied Mathematics

Background:

• Yarn formation relies on twisting short fibers, which dictates yarn structure and properties.
• Understanding yarn dynamics during twisting is crucial for textile manufacturing.

Purpose of the Study:

• To develop a novel theoretical model for yarn dynamics in generalized twisting systems.
• To simultaneously analyze twist generation and propagation phenomena.

Main Methods:

• Established equations of yarn motion.
• Numerically solved boundary value problems using the Newton-Raphson method.
• Validated simulation results through experimental comparisons.

Main Results:

• Demonstrated good agreement between simulation and experimental results for a moving rigid cylinder system.
• Quantified influences of parameters like wrap angle and yarn tension on the twisting process.
• Revealed variations in yarn torsional rigidity with twisting parameters.

Conclusions:

• The proposed model accurately captures yarn dynamics during twisting.
• Wrap angle and yarn tension are critical factors influencing twist efficiency and propagation.
• The study provides new insights into controlling yarn properties through optimized twisting parameters.