Analysis and modelling of the dynamic stiffness up to 400 Hz of an air spring with a pipeline connected to a reservoir

The present research addresses the dynamic behaviour of an air spring with a pipeline connected to a reservoir in a frequency range up to 400 Hz, in which structure-borne vibration transmission may occur due to both the structural behaviour of the bellows and fluid dynamics in the pneumatic circuit of the suspension. Based on experimental results, three frequency ranges are distinguished where different resonances of the suspension appear: low (up to 30 Hz) due to the air flow between the bellows and the surge reservoir, intermediate (30–150 Hz) due to the formation of standing waves in the pipeline and high (beyond 150 Hz) due to the structural dynamics of the bellows. A novel modelling technique to predict the dynamic behaviour of the pneumatic system in all these frequency ranges is presented and validated: this consists of an enhanced Finite Element Model (FEM) considering the structural properties of the bellows and the effect of pressurised air in the bellows and in the reservoir, coupled to a model of fluid exchange between the two main air volumes which is defined using a VUFLUIDECH user subroutine developed in ABAQUS. The study focusses on the axial dynamic stiffness of the pneumatic suspension, which plays a key role in determining the transmissibility of the suspension. However, the mathematical model introduced in the paper is capable of predicting also the vibration modes of the suspension in shear and rotation, which may be relevant in some applications, e.g. when air springs are used in vehicle suspensions.