Theoretical Stability Analysis of Self-Excited Vibration in a Thin Film Wrapped Around an Air-Turn Bar

This paper deals with a theoretical stability analysis of a self-excited vibration generated in a film wrapped around an air-turn bar. In this paper, firstly, vibration characteristics of the self-excited vibration are examined experimentally, and it is shown that two different types of self-excited vibration, which are low-frequency and high-frequency modes, occur in the film. Secondly, stability of the low-frequency mode is examined theoretically. A theoretical model of the film wrapped around the air-turn bar is developed. Basic equations of the air flow in the gap between the film and air-turn bar, and pressurized air flow inside the air-turn bar are derived. The characteristics equation of the system is derived from the basic equations of motion of the film coupled with the air flow. Instability condition in which the self-excited vibration occurs is shown as a function of air flow rate and tension applied to the film. Moreover, instability mechanism of the self-excited vibration is discussed based on the theoretical model.