A Numerical method for computing the periodic solutions of the ring-spinning balloon equations^∗

^∗ Work supported by CNR, Rome, Italy.

Abstract

The ring-spinning process is the last phase of the manufacturing process of textile yarn, where a loop of yarn rotates rapidly about a fixed axis and twisting occurs while the yarn is wound onto the bobbin. The surface generated by the rotating loop of the yarn is called a balloon. In this paper a numerical method is developed for the calculation of periodic solutions of a non-stationary mathematical model of the ring-spinning process recently proposed in the technical literature. Some results are given, from which the method seems to be very efficient and reliable in the simulation of realistic process.

Keywords:

• Non-stationary ring-spinning models
• Finite-Segments method
• univariate minimisation
• Brent's method
• Secant method

C.R. Categories:

• G1.8
• G1.6

^∗ Work supported by CNR, Rome, Italy.

^∗ Work supported by CNR, Rome, Italy.

Notes

^∗ Work supported by CNR, Rome, Italy.