Modeling of nonlinear complex stiffness of dual-chamber pneumatic spring for precision vibration isolations

Dual-chamber pneumatic springs are widely in the vibration isolation systems for precision instruments such as optical devices or nano-scale equipments owing to their superior stiffness- and damping-characteristics. In order to facilitate their design optimization or active control, a more accurate mathematical model or complex stiffness is needed. So far nonlinearities have not been dealt with. Experimental results we obtained rigorously for a dual-chamber pneumatic spring exhibit significantly amplitude dependent nonlinear behavior, which cannot be described by linear models in earlier researches. In this paper, an improvement for the complex stiffness model is presented 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 use a dynamic model for oscillating flow in capillary tube connecting the two pneumatic chambers instead of unidirectional flow model. The proposed nonlinear complex stiffness model, which reflects dependency on both frequency and excitation amplitude is shown to be very valid by comparison with the experimental measurements. Such an accurate nonlinear model for the dual-chamber pneumatic springs would contribute to more effective design or control of vibration isolation systems.