Air springs with auxiliary chambers (ASAC) are widely used in automotive suspension systems. The introducing of the auxiliary chamber and the connecting flow passage makes the system more complex, especially in which case an additional resonance peak caused by the air inertia in a connecting pipe appears. To characterize the nonlinear dynamic characteristics, this paper proposes a novel physical-neural network hybrid modeling method for ASACs. Firstly, experiments are carried out to measure the dynamic characteristics of ASACs. Then, based on the thermodynamic principle, a nonlinear dynamic characteristic model for the ASAC is developed and a linearized process is performed to obtain a linearized physical model. Due to the amplitude dependence and frequency dependence in the dynamic characteristics of ASACs, the physical model cannot accurately characterize these nonlinearities. To compensate for the errors caused by the uncaptured frictional damping and nonlinear air resistance, a neural network model is developed. The proposed hybrid models are validated to be more accurate than a physical model. The proposed modeling method provides a guideline for the modeling of other nonlinear components in vehicles.
