An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe

This paper proposes a simple expression for calculating the restoring and damping forces of an air spring equipped with a small pipe. Air springs are commonly used in railway vehicles, automobiles, and various vibration isolators. The air spring discussed in this study consists of two tanks connected by a long pipe. Using a pipe instead of an orifice enables flexibility in the arrangement of the two tanks. In addition, this makes it possible to manufacture a thin air spring. A vertical translational oscillating system, which consists of a single mass supported by this type of air spring, looks like a single-degree-of-freedom (SDOF) system. However, it may have two resonance points. In this paper, we propose a vibratory model of a system supported by the air spring. With the proposed model it is possible to correctly reproduce the two resonance points of a system consisting of a single mass supported by this type of air spring. In our analysis, assuming that the vibration amplitude is small and the flow through the pipe is laminar, we derive the spring constant and damping coefficient of an air spring subjected to a simple harmonic motion. Then, we calculate the frequency response curves for the system and compare the calculated results with the experimental values. According to the experiment, there is a remarkable amplitude dependency in this type of air spring, so the frequency response curves for the system change with the magnitude of the input amplitude. It becomes clear that the calculation results are in agreement with the limit case when the input amplitude approaches zero. We use a commercially available air spring in this experiment. Our study is useful in the design of thin air spring vibration isolators for isolating small vibrations.