In this article, the parametric model for the stiffness characteristic and burst pressure of cord-reinforced air spring with winding formation is developed. Based on the non-geostrophic winding model and the assumption of cord cross-stability, the cord winding trajectory model of the capsule is established. Then, the anisotropic and nonlinear mechanics model of the capsule with complex cord winding trajectory variation characteristics is constructed by the classical thin-shell theory. The capsule state vector is solved by the extended homogeneous capacity precision integration method. Due to the complex coupling relationship between the capsule state vector and the internal air pressure, the stiffness characteristic is solved by the iterative integration method. The burst pressure of the air spring is solved by the Tsai–Hill strength theory. Eventually, the accuracy and reliability of the proposed method are verified by the experimental results. The effects of the material properties, winding parameters, and geometric structure parameters on stiffness characteristics and burst pressure are discussed. The results of this article provide an important theoretical basis for the performance design of cord-reinforced air springs with winding formation.

No abstract

A precise transfer matrix was employed to analyze the free vibration characteristics of a cord-reinforced air spring with winding formation under preload conditions. The air spring was abstracted as a rotary combined shell structure with variable winding trajectory characteristics. The rotary structure, which consisted of cylindrical and toroidal shells, was analyzed for its shell pre-stress under preload conditions. The shell pre-stress was combined with the theory of thin shells to create the rotary shell vibration control equations under preload effect. The Helmholtz equation was used to analyze the influence of sound pressure inside shells under the fluid–structure coupling boundary conditions. The rotary shell transfer matrix was derived from the variable winding trajectory equation, geometrical equation, and physical equation of shells. Under the continuous conditions of state vector between the cylindrical and toroidal shells, the shells were combined into a rotary combined shell structure to obtain its total free vibration equation. The shell boundary conditions were considered to solve the natural frequency of the air spring. The calculation results were compared with the prototype test and simulation results to verify the effectiveness and accuracy of the theoretical model. On this basis, we explored the influence of axial half wave number, circumferential wave number, geometrical structure, and material characteristics on the free vibration characteristics of the air spring. The research findings would provide important and significant guidance for the structural design of cord-reinforced air springs with winding formation.