The Dynamic Characteristic and Hysteresis Effect of an Air Spring

Abstract

In many applications of vibration technology, especially in chassis, air springs present a common alternative to steel spring concepts. A design-independent and therefore universal approach is presented to describe the dynamic characteristic of such springs. Differential and constitutive equations based on energy balances of the enclosed volume and the mountings are given to describe the nonlinear and dynamic characteristics. Therefore all parameters can be estimated directly from physical and geometrical properties, without parameter fitting. The numerically solved equations fit very well to measurements of a passenger car air spring. In a second step a simplification of this model leads to a pure mechanical equation. While in principle the same parameters are used, just an empirical correction of the effective heat transfer coefficient is needed to handle some simplification on this topic. Finally, a linearization of this equation leads to an analogous mechanical model that can be assembled from two common spring-and one dashpot elements in a specific arrangement. This transfer into "mechanical language" enables a system description with a simple force-displacement law and a consideration of the nonobvious hysteresis and stiffness increase of an air spring from a mechanical point of view.

Generalized Liquid-Based Damping Device for Passive Vibration Control

“…When comparing models (13) and (14), it can be seen that these models are identical if 11  . Therefore, the mass transferred between the working volumes of system (14) is not conserved.…”

“…Additionally, semi-active forms of these devices with adjustable properties were studied extensively in recent decades [8], [9], [10]. Another class of devices provides spring capabilities by exploiting fluid compressibility and other pressure-driven volumetric effects in loaded systems of varying complexity and composition [11], [12], [13]. The next class is represented by shock absorbers where stiffness and damping properties are integrated in one system to provide passive and often directionally asymmetric control of shock responses while, usually, offering a long stroke functionality in spatially constrained designs.…”

The Simulation of an Automotive Air Spring Suspension Using a Pseudo-Dynamic Procedure

“…Normally, the structural analysis and dynamic testing of bellows air springs are not presented with detail due to manufacturers' strategic restriction of technologic knowledge dissemination; alternatively, university institutions working in automotive engineering share valuable contributions. Examples can be assigned to Löcken and Welsch [4] (from Helmut Schmidt University, DE), who studied the dynamics of bellows air suspensions accounting for the coupled effect of air heating and spring stiffness increase by the coupled effect; the natural frequencies and damping methods were also studied. The shape of the elastic element considered by Löcken and Welsch [4] was not a toroidal shell like the one analyzed in the present work.…”

“…Examples can be assigned to Löcken and Welsch [4] (from Helmut Schmidt University, DE), who studied the dynamics of bellows air suspensions accounting for the coupled effect of air heating and spring stiffness increase by the coupled effect; the natural frequencies and damping methods were also studied. The shape of the elastic element considered by Löcken and Welsch [4] was not a toroidal shell like the one analyzed in the present work. Such a shape conditioned the spring geometry by the mutual surface contact of the elastomeric membrane and the internal rigid core, giving rise to the non-linear kinematics contact model in the numerical modeling.…”

Height Adjustment of Vehicles Based on a Static Equilibrium Position State Observation Algorithm

“…It has been widely used in commercial vehicles [8], railway vehicles [9], passenger vehicles [10] and agricultural machines [11,12] because of its advantages of adjustable stiffness and height. In the past few years, the research on air suspension systems has mainly focused on three aspects: air suspension analysis modeling [13][14][15][16][17], electronic control system [18][19][20][21][22] and vehicle height control algorithms [23][24][25][26][27][28][29][30].…”