A unified stiffness model of rolling lobe air spring with nonlinear structural parameters and air pressure dependence of rubber bellows

Abstract

The structural parameters of the rolling lobe air spring and the mechanical characteristic of rubber bellows are the key factors affecting the stiffness and mechanical characteristic of the rolling lobe air spring. Aiming at the prediction difficulties of structural parameters of the rolling lobe air spring with the composite curved contour piston and the modeling complexity of the hysteretic mechanical characteristic of rubber bellows under variable pressure conditions, the geometrical method is applied to derive the structural parameters models of the rolling lobe air spring with the composite curved contour piston. A new pressure factor is introduced and the Coulomb frictional pressure perturbation model and the fractional derivative Kelvin-Voigt pressure perturbation model are reconstructed to accurately describe the hysteretic mechanical characteristic of rubber bellows under variable pressure conditions. A unified pressure equation is constructed to characterize the evolution of model parameters under variable pressure conditions. Furthermore, a hysteretic mechanical characteristic pressure perturbation model (abbreviated as HMCPP model) of rubber bellows under variable pressure conditions is put forward. Finally, a unified stiffness model of the rolling lobe air spring including prediction models of nonlinear structural parameters and a HMCPP model of rubber bellows is built. Taking a certain type of rolling lobe air spring as the test sample A, the structural parameters tests and static/dynamic characteristic tests of sample A are carried out based on the MTS852.05 test bench, which verified the accuracy of the unified stiffness model of the rolling lobe air spring. The research results provide theoretical support for the mechanical characteristic matching and air pressure precise control of the rolling lobe air spring under variable pressure conditions.

Dynamic characteristic analysis and key parameter optimization of throttling orifice type air damping air spring

“…When conducting the static characteristic test, the hydraulic actuator applies a triangular wave excitation signal with a loading speed of 0.01 m min −1 to the test samples, and the static hysteretic loop of OADAS is obtained through the test. When conducting the dynamic characteristic test, apply a sine wave excitation signal with an excitation frequency range of 0.5-10 Hz and an interval of 0.5 Hz to the main air chamber [25]. The frequency versus equivalent stiffness and equivalent damping coefficient curves are obtained from the test.…”

“…The structure of the OADAS is shown in figure 1, the gas through the throttling orifice, and damping are generated, while the presence of an additional air chamber changes the effective volume of the main air chamber [19,20], widening the range of stiffness variation. The force-displacement relationship of the Coulomb friction pressure perturbation model is given as follows [23][24][25]: where, F fmax (p z ) is the maximum friction force; x 2 (p z ) is the displacement at half the maximum friction force; F f is the frictional force; x is the excitation displacement; x s is the reference state displacement; F fs is the reference state force; µ = F fs /F fmax (p z ), µ∈[−1 ,1].…”

“…The dynamic stiffness K f and hysteretic angle φ f of the Coulomb friction pressure perturbation model are expressed as [23][24][25]:…”

“…; b(p z ) is the damping coefficient; F v is the viscoelasticity force. The dynamic stiffness K v and hysteretic angle φ v of the fractional derivative Kelvin-Voigt pressure perturbation model can be written as [23][24][25]:…”