Abstract
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.
Highlights
Pneumatic vibration isolators are widely applied in optics, semiconductors, and other fields [1, 2]
This work developed an analytical model of the elastomeric diaphragm using the Mooney-Rivlin modeling method and elastomeric theory
The stiffness of the elastomeric diaphragm was ignored in the previous model of pneumatic vibration isolators
Summary
Pneumatic vibration isolators are widely applied in optics, semiconductors, and other fields [1, 2]. The discrepancies between the model-predicted behavior and the practically observed behavior of pneumatic vibration isolators exceeded 50% because the effect of the elastomeric diaphragm was ignored. To obtain a more accurate model of the pneumatic isolator, Erin and Wilson proposed an improved model for pneumatic isolators by incorporating the stiffness and damping effect of the elastomeric diaphragm based on experimental investigation. A direct theoretical derivation method must be established for the development of an analytical model for a pneumatic vibration isolator. Experimental tests were conducted, and the results demonstrate that the analytically predicted behavior is similar to the practically observed behavior The error in this method can be reduced to less than 10% after the elastomeric diaphragm model is added to the standard pneumatic cylinder model. The proposed analytical model facilitates the practical parameter optimization design of pneumatic isolators
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