Mathematical Model For The Siro-Spinning Yarn System

Siro-spinning technology is a very effective and economical method for producing composite yarns, and it has become a hot subject in recent years. Mathematical model is a key point for interpreting the spinning procedure. Though much research has been conducted experimentally and theoretically, its mathematical model is still far from perfect possibly due to the nonlinear phenomena and complex properties involved in the proposes, and many factors affecting the procedure such as the distance of the rollers, the convergence point, the force of the yarns, the twist of the yarns, densities of the two strands and the spun yarn, the velocities of the two strands and the spun yarn. In this thesis a complete model is established which can be used to optimize the system parameters, and reveal how to control its instability.The convergence angle is a major parameter of the spinning system which determines whether the composite yarns could have fine properties. Using force balance and basic laws in fluid mechanics, e.g., the mass conservation, and the momentum conservation, we can identify the convergent point with ease, while some other known models require experimental data to determine the convergence angle.A dynamical model is established by suitable choice of a control volume where the center of mass focuses on the convergent point. The variational iteration method is applied to solve analytically the nonlinear system, the obtained results show that there is an optimal condition for the system, and resonance arises for some special cases which should be avoided in engineering applications.We design a three-strand yarn spinning system where exist possibly one or two convergent points depending on the spinning conditions. A description of stable working conditions for three-strand yarn is also given, and the conditions for single or two convergent points are obtained, which are essential to determine the dynamical properties of the spinning system.