An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring with an Elongated Circular Tube as the Orifice

Abstract

This paper proposes a simple expression for calculating the restoring and the damping forces of an air spring equipped with an elongated tube as the orifice. Air springs are commonly used in railway vehicles, automobiles, and various vibration isolators. The air spring used in this study consists of two tanks connected by a long tube. Using a tube 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. The oscillating system, which consists of a single mass supported by this type of air spring is a single-degree-of-freedom (SDOF) system. However, it has two resonance points for a reason that had been unknown for a long period of time. In this paper, we explain why the SDOF system has two resonance points. After that, assuming that the vibration is small and the flow through the tube is laminar, we derive the spring constant and the 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 value when the input amplitude approaches zero.