# Influence of Aging Time on Vertical Static Stiffness of Air Spring
## 1 Introduction  
Air springs are one of the most important components in the secondary suspension system of rail vehicles, and their performance directly affects the stability and safety of those vehicles. Exploring the application of a new prediction theory and method in predicting the performance decline of the train air spring can provide a theoretical basis and reference for detecting the performance of an air spring, so that it can be repaired or replaced. Research on, and applications of, air springs started earlier outside China [1,2]. The rubber spring was simplified and equivalent to parallel between the linear spring and linear viscoelastic damping, and the mechanical characteristics of the rubber spring were studied using a rubber spring experimental platform [3,4]. The air spring system has been studied for equivalent mechanical modeling, forming three air spring equivalent mechanical models: the Nishimura, VAMPIRE, and Berg models [5,6]. Considering the thermodynamic properties of the air spring pneumatic system, the effective friction of the connecting line, and the viscoelastic damping of the rubber airbag, the dynamic model of the air spring system was established. It can accurately predict the amplitude and frequency correlation characteristics and dynamic characteristics of the air spring [7].  
According to the traditional mechanical air spring model, the static and dynamic mathematical models of the air spring were established [8]. The nonlinear dynamic stiffness and static stiffness models of the cystic air spring were developed based on the thermal dynamics and by using an improved analytical calculation method. The finite element analysis of air springs is mainly based on Abaqus, MSC, Marc, ADAMS, and other software [9, 10, 11, 12]. [PERSON] et al. established the air spring model through the Abaqus analysis software. They used the fluid analysis software STAR-CCM to simulate the internal gas, exchanging data between the two through SIMULIA to calculate the dynamic stiffness of the air spring [13]. [PERSON] studied the relevant mechanical properties of air springs under low temperature, improving the air spring performance at low temperatures [14]. The servicelife of the air spring was investigated by an airbag rubber aging test, and the physical performance of the rubber was studied [15]. In order to accurately obtain the mechanical characteristics of air springs, it is necessary to select the finite element analysis software that can effectively deal with all kinds of nonlinear problems and various element types to simulate air springs. The Abaqus finite element simulation analysis software can simulate nonlinear problems well [16; 17; 18; 19; 20].  
Past research on the mechanical characteristics of air springs has considered the influence of aging less. In fact, some scholars have studied the effect of aging time on concrete [21]. However, because of the constant exposure of air springs to the atmosphere during service, the effect of sunlight on airbags, acid-alkali liquid corrosion, and other natural aging factors, the parameters of the air spring airbag cord and rubber change, affecting the mechanical characteristics of the air spring, and the comfort and safety of vehicle operation. In this study, the vertical stiffness of the air spring and the elastic moduli at different angles were investigated. A theoretical basis for air spring structure design and air spring maintenance in practical applications is provided.