Investigation of the Nonlinear Dynamic Stiffness of Rolling-Lobe Air Springs Considering Rubber Payne Effect

Abstract

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.

A theoretical model of amplitude-dependent dynamical stiffness for cord-rubber air springs

“…Zhang et al 38 modeled the dynamic amplitude- and frequency dependency of the air spring using the friction model and fractal viscoelasticity model, which is the typical phenomenological model, and the physical mechanism hasn’t been discussed. Wu et al 4 investigated the nonlinear dynamic stiffness of rolling lobe air springs, gave a phenomenal model considering the rubber Payne effect, and experimentally revealed the real and imaginary part of the dynamic stiffness for air springs (as shown in Figure 2). However, they failed to give the relationship between rubber diaphragm stiffness and its material, structure, and size.…”

“…Equivalent mechanical models of air springs have been described in many studies. [3][4][5][6][7][8] For large amplitude excitation, the models proposed are accurate enough to simulate the dynamic behavior of the air spring. However, under ordinary circumstances, air springs undergo excitation with a small amplitude, so it is necessary to analyze the dynamic behavior of this situation.…”