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The accurate modeling of the complex dynamic stiffness of inflated rubber diaphragms in pneumatic springs is necessary for an efficient design of vibration isolation tables for precision instruments, such as optical devices and nano-scale equipment. In addition to pressurized air, rubber diaphragms, essentially employed for the prevention of air leakage, make a significant contribution to the total complex stiffness. To reflect the effect of the dynamic stiffness of the inflated rubber diaphragm on the total complex stiffness during the initial design or design improvement stage, it is desirable to predict the complex stiffness of the inflated rubber diaphragm beforehand. In this paper, an estimation method for the complex stiffness of inflated rubber diaphragms using the commercial finite element method (e.g., ABAQUS) is proposed. The proposed method reflects their dynamic characteristics under the large static deformation by the Mooney-Rivlin and Morman's constitutive equations. The results of comparison with experimental results indicate that the predictions obtained by the proposed method are congruent with the experimental values of the diaphragm.

Estimation of the Complex Dynamic Stiffness of Inflated Rubber Diaphragms in Pneumatic Springs Using Finite Element Method