Dynamics and stability of pneumatically isolated systems

Abstract

Pneumatic vibration isolation is the most widespread effective method for creating vibration-free environments that are vital for precise experiments and manufacturing operations in optoelectronics, life sciences, microelectronics, nanotechnology and other areas. The modeling and design principles of a dual-chamber pneumatic vibration isolator continue to attract attention of researchers. On the other hand, behavior of systems of such isolators was never explained in the literature in sufficient detail. After a brief summary of the theory and a model of a single standalone isolator, the dynamics of a system of isolators supporting a payload is considered with main attention directed to three aspects of their behavior: first, the static stability of payloads with high positions of the center of gravity; second, role of gravity terms in the vibration transmissibility; third, the dynamic stability of the feedback system formed by mechanical leveling valves. The direct method of calculating the maximum stable position of the center of gravity is presented and illustrated by three-dimensional stability domains. A numerical method for feedback stability analysis of self-leveling valve systems is provided, and the results are compared with the analytical estimates for a single isolator. The relation between the static and dynamic phenomena is discussed.