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1. Introduction
Many engineering structures contain one or more cavities inflated with gas. Such engineering structure is defined as a “pneumatic structure”. The air spring depicted in Figure 1 is one of the typical pneumatic structures, which is widely used in secondary suspension systems of high-speed trains, metropolitan and mainline railway vehicles. As the top plate and bottom support moves relatively up and down, the internal volume expands or contracts. As a result, the pressure of the inner compressed air decreases or increases, which provides a resistance force against the vibration. The characterization of this process is usually measured by a parameter of stiffness, which is one of the most important features of an air spring.
More and more vehicles are equipped with air suspensions, which provide more excellent ride comfort and lower noise than other suspensions. In many case, the mechanical behavior of an air spring needs to be predicted using the finite element method (FEM) by the designer or the researcher. The ability to precisely predict the stiffness of an air spring in the design phase is very important, which would allow the air spring designer to analyze and improve air spring behavior with less prototype testing or even none. Many published work has focused on this field. Berry (1994) developed a pneumatic element which was implemented in the nonlinear finite element program ABAQUS to solve pneumatic structures, and applied his method to calculate the vertical stiffness of a double-bellow air spring in both isothermal and adiabatic cases. The simulated results agreed with the experimentation. In order to research the fatigue property of an air spring, Oman and Nagode (2013) carried out an FEM simulation by employing pneumatic elements to obtain the stress of the diaphragm in the adiabatic case. Sun (2011) and Liu et al. (2006) studied the static vertical stiffness of an unrestricted and rolling lobe air spring by FEM in the isothermal case. Wei et al. (2013) used the isothermal process to simulate the vertical stiffness of an unrestricted air spring. The simulated results are about 20 percent lower than those of the experiments.
Except for using FEM to predict the stiffness of air springs, some other methods were also reported. A formula for the calculation of vertical stiffness of...