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The previous models of rolling-type mechanisms were built based on rigid contact and pure rolling motion, but when applied to ground microvibration isolation, a large error in the natural frequency was sometimes observed in the experiments. A new model of a common mechanism based on completely elastic contact is developed, and the expression of the natural frequency is provided under a microvibration condition. The experiments and analysis show that the proposed model is more accurate than the previous model, and the natural frequency is independent of the payload. The analysis shows that the proposed model is only suitable in the range of completely elastic contact, and the load range is provided after comparing the experimental results with existing theory.

The elastomeric diaphragm is widely used in pneumatic vibration isolators, and the relevant model is often ignored due to its complexity. Considering that the ignored model of the elastomeric diaphragm in pneumatic vibration isolators plays an important role in the discrepancy between the predicted and practical behavior, this paper develops an analytical model for the elastomeric diaphragm using the Mooney-Rivlin modeling method and elastomeric theory. Specifically, the elastomeric diaphragm consists of several segments in the axial section. After considering the structural restriction, each segment can be simplified as uniaxial stretching, and the force-strain equation can be established for each segment. By combining the equations of all segments, an analytical model of the elastomeric diaphragm can be built and solved via numerical methods. The developed model is added to the standard model of pneumatic cylinders to supply a complete analytical model for pneumatic vibration isolators. The experimental results demonstrate that the analytically predicted behavior is similar to the practical behavior. The proposed analytical model can be used as a guide for the parameter design of pneumatic isolators in practice.

As the damping ratio determines the response of a vibration isolation system at resonance, it is very necessary to estimate the damping ratio quickly and economically for an evaluation of the effectiveness to adjust the damping in practical engineering applications. An efficient method named the “ζ-Tr” method with the characteristics of simple operation and a high accuracy is introduced to estimate the damping ratio in this paper. According to the transmissibility curve, the specific mathematical relationship in which the value of the resonance peak corresponds to the value of the damping ratio is analysed theoretically. In this case, the recognition of the resonance peak can be used to directly estimate the damping ratio without an approximation or simplification. The “ζ-Tr” method is faster, more accurate and less costly than other estimation methods. Finally, the correctness of the “ζ-Tr” method is verified by a simulation and an experiment.