On the Vibration of a Translating String Coupled to Hydrodynamic Bearings

Abstract

The vibration of a translating string, controlled through hydrodynamic bearing forces, is analyzed by the transfer function method. Interactions between the string response and the bearing film are described by the bearing impedance function. This function depends on the string translation speed, the frequency of the film thickness variation, and the spatial location of the bearings. The control system consists of the translating string, bearings, actuators and sensors, and feedback elements. An integral formulation of the controlled system response is proposed that leads to the closed-loop transfer function. The frequency response of the control system is studied in the system parameter space. The feasibility of adding active control to improve the bearing force control is also considered.