An Improved Analytical Model Of Air Spring With Effect Of The Elastomeric Diaphragm

The working accuracy of the precision instruments can be seriously influenced by external vibration. Therefore, vibration isolators have become important means to ensure the accuracy of the precision instruments. In which, the air spring is widely used because of its high cost-effective. However, previous studies on stiffness of air spring usually neglected the rubber diaphragm, which causes the result of stiffness or frequency of analysis models have large errors comparing with the measured numerical models. To compensate for these errors, some studies modified the analysis models through "reverse" methods, which obtained the stiffness of rubber diaphragm through experimental tests, then obtained total stiffness of air spring by superposing with fitting stiffness of air. This way is very inconvenient for the initial design, and optimization needs high experience, time and cost. Therefore, this paper will research the air spring by mechanical modeling to make up for the missing rubber diaphragm of dynamic model of air spring in the previous studies, to form a more complete model of the air spring and provide a more forward and accurate analysis & design tool to designers. Then further study on properties of air spring will carry out through parameter optimization and experiments.Firstly, for the air spring of vibration isolation, the total vertical stiffness will be divided as gas chamber stiffness and rubber diaphragm stiffness. Where, the gas chamber stiffness based on the linear model established by C.Erin. The rubber diaphragm stiffness will be obtained by direct dynamic modeling, and the rubber diaphragm is divided into several segments. This paper considers that the rubber diaphragm is in restricted condition, then the rubber diaphragm can be pulled only in two directions and each segmented rubber diaphragm can be simplified as uniaxial stretching. It’s possible to establish analytical model or numerical analysis model of rubber diaphragm according to classical theory of rubber. This paper adopts the Mooney-Rivlin model to establish the analytical expression of the vertical stiffness of each segment of rubber diaphragm, then solves each segment of rubber diaphragm independently, according to connection method of each segment of rubber diaphragm, then obtains the total stiffness by linear superposition of each segment. Then a more accurate total stiffness of air spring will be obtained by adding the rubber diaphragm stiffness to the previous studies.Secondly, based on the more accurate stiffness of air spring to optimize the parameters of the air springs and to explore ways to get the best performance. The analysis model indicates that increasing height of inner and outer rubber as well as reducing the thickness and hardness of rubber diaphragm have a greater impact to reduce the stiffness of air spring. Increasing the volume of the top chamber and the bottom chamber have a smaller impact to reduce the stiffness of air spring. These conclusions give a clear direction to design air spring. In order to obtain an optimal vibration isolation performance, the air spring parameters optimization becomes a single objective function optimization problem with nonlinear constrained, then optimizing computation is conducted by MATLAB genetic algorithm optimization tool, stiffness of the optimized of the design parameters of the air spring is reduced 70% to 80%.Finally, the above studies are verified by experiments, and the final results showed that the error of the stiffness obtained by the mechanical model considering rubber diaphragm combine comparing with the experiments can be reduced from about 90% to about 5%, the error of natural frequency reduced from about 65% to about 3%.