A nonlinear dynamic stiffness model of rolling-lobe air spring considering the Payne effect of the rubber diaphragm and the thermodynamic equivalent damping is proposed, with an aim to provide a theoretical basis for air spring structure design. A physical explanation and mathematical expression of each decoupled contribution term are given from the two dimensions of amplitude and frequency. An indicator test was designed to identify related parameters of the real and imaginary parts of dynamic stiffness. The results showed that the dynamic stiffness increases under a small excitation amplitude, verifying the correctness of the model considering the Payne effect. The influence of rubber diaphragm and gas terms is decoupled to separately illustrate the amplitude and frequency dependency of the real and imaginary parts of dynamic stiffness. A new evaluation index reflecting the contribution percentage of the rubber diaphragm is given, indicating that the stiffness of the rubber diaphragm at low amplitude cannot be ignored. In the end, the parameter influence and dynamic characteristics are provided so that the dynamic behavior of the rolling-lobe air spring can be predicted at the design stage. The proposed rolling-lobe air spring dynamic model considering the Payne effect of the rubber diaphragm provides guidance for the forward development and theoretical modeling of the air spring.

Experimentally and theoretically, this paper combines thermodynamics, aerodynamics and structural dynamics to give a universal dynamical model of dual-chamber air springs, with physical meanings of each stiffness and damping term. An indicator experiment was designed to verify the theory proposed in this paper. The experimental results show that the dynamic stiffness model can well reflect the hysteresis characteristics and the variable stiffness characteristics of the dual-chamber air spring. It can also clearly reveal the frequency dependence of the dynamic stiffness. Finally, based on the derived model, the influence regulation of each parameter term on the dynamic stiffness amplitude and hysteresis phase angle is given numerically. The results show that each term can influence different dynamic characteristic of the dual-chamber air springs. The conclusions of this article can provide positive guidance for the vehicle dynamics matching and design of air springs.