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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.

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