Modeling of dual-chamber pneumatic spring and application to transmissibility design of vibration isolation table

Abstract

Pneumatic vibration isolation table typically consisting of dual-chamber pneumatic springs and a rigid table are widely employed for proper operation of precision instruments such as optical devices or nano-scale equipments owing to their low stiffness- and high damping- characteristics. As environmental vibration regulations for precision instruments become more stringent, it is required to improve further the isolation performance. This thesis will discuss about transmissibility design method of pneumatic vibration isolation table for an efficient improvement of its performance based on accurate modeling of the isolator. Experimental observations for the complex stiffness of dual-chamber pneumatic spring, a major component in pneumatic vibration isolation system, were firstly made. Measurement results exhibit significantly amplitude dependent behavior, which cannot be described by linear models taken in previous researches. In this thesis, an improvement for the complex stiffness model of dual-chamber pneumatic spring is proposed by taking two major considerations. One is to consider the amplitude dependent complex stiffness of diaphragm necessarily employed for prevention of air leakage. The other is to employ a nonlinear model for the air flow in capillary tube connecting the two pneumatic chambers. The proposed complex stiffness model reflecting the dependency on both frequency and excitation amplitude is shown to be valid by comparison with experimental measurements. Another important observation for the complex stiffness of dual-chamber pneumatic spring is existence of inherent coupling between stiffness- and damping- characteristics, which implies the need of optimization for the transmissibility design of pneumatic vibration isolation table. For this purpose, the volume ratio of bottom- to top- chamber and the equivalent flow restriction coefficient both which relate the stiffness of pneumatic chamber and the damping of capillary tube respect...