Unified model of vertical mechanical characteristics of rolling lobe air springs under variable angle conditions

The installation angle of the rolling lobe air spring and the mechanical characteristics of the rubber bellows are key factors affecting its mechanical characteristics. However, accurately characterizing the mechanical properties of rolling lobe air springs remains challenging due to the variability of structural parameters under different installation angles and the pronounced nonlinear characteristics of the rubber bellows. To address this issue, an angle parameter is introduced, and an angular unification equation is constructed. Furthermore, the Coulomb friction angular perturbation model (CFAPM) and the quadratic parabola fractional derivative Kelvin-Voigt angular perturbation model (QKAPM) are developed to describe the amplitude-frequency response and the large-amplitude bending behavior of the rubber bellows. By incorporating the compressed air angular perturbation model (CAAPM), a unified vertical mechanical characteristic model of diaphragm-type air springs under variable-angle operating conditions is ultimately established, along with a key parameter identification method for the model. Both numerical calculations and test results demonstrate that the maximum relative error of static stiffness hysteresis return is less than 1.9%, and the maximum relative error of dynamic stiffness at the static equilibrium position is less than 7.9%, which verifies the accuracy and universality of the unified model. Moreover, the influence of the angle parameter on the parameters of the unified model is elucidated, providing a theoretical basis for determining the installation angle and designing the vertical stiffness of rolling lobe air springs in the chassis of vehicles.