Bellows stiffness characteristics of cord-reinforced air spring with winding formation under preload conditions

The bellows structure in an air spring can be constantly reinforced to cope with the complicated work environment, but it exerts a stronger and stronger effect on the stiffness characteristics of the air spring. However, there is not any effective way for the parameterized solution of the bellows stiffness of the air spring. With the precise transfer matrix method, the bellows stiffness characteristics of a cord-reinforced air spring with winding formation under preload conditions were analyzed in this paper. The thin-shell theory was used to solve the bellows pre-stress of the air spring under preload conditions. The pre-stress was introduced into the equilibrium equation for the bellows. Based on the geometrical and physical equations for the bellows with the complex cord winding characteristics, the precise integration method was borrowed to construct a transfer matrix for the bellows of the air spring under preload conditions. The state vector of the bellows in the air spring was solved through boundary conditions. The iteration method was adopted to develop the expression for the bellows stiffness characteristics, and combined with the theoretical model of pneumatic stiffness to solve the stiffness characteristics of the air spring. The comparison with the prototype test results verified the validity and correctness of the theoretical model. On this basis, we explored the influence of preload conditions, geometrical structure, and material characteristics on the stiffness characteristics of the air spring. The research findings will provide significant guidance for the structural design and material selection of cord-reinforced air springs with winding formation.