Abstract: The yarn winding process is an important part of the textile process and has a wide range of applications in the light industry and handicraft industry. In this paper, the yarn winding process is simplified as a string vibration process. The Fourier series method and the impulse theorem method are used to solve the fixed solution problem of the yarn winding problem, and then the vibration solution of the winding air loop is obtained. From the perspective of energy, the reason why the winding air loop is a standing wave is explained. With the aid of mathematical software, the motion state of the winding air loop is visualized. The shape of the winding air loop under different vibration wave velocities and unwinding angular velocities is investigated, and some interesting conclusions are obtained.

Key words: yarn winding problem, mathematical software, Fourier series method, the impulse theorem method