Theoretical modelling and experimental analysis of the vertical stiffness of a convoluted air spring including the effect of the stiffness of the bellows

A new refined model including a model of the bellows to describe the vertical stiffness of a convoluted air spring is developed. The new model of a convoluted air spring incorporates the structural parameters including the effective area, the rate of change in the effective area, the effective volume, the rate of change in the effective volume and the stiffness of the bellows. Analytical models of the structural parameters of a convoluted air spring are established using a geometrical analysis approach. Two convoluted air springs (type 1B5002 and type 2B5281) are designed and manufactured for testing purposes. An experimental set-up is designed in order to carry out identification of the structural parameters and to test the vertical static stiffness and the vertical dynamic stiffness. The analytical models of the structural parameters are validated by experiments, which provide good design guidance and improvement in the convoluted air spring at the design stage. Tests on the vertical static stiffness and the dynamic stiffness indicate that the stiffness of the bellows should be considered; furthermore, the stiffness of the bellows exhibits amplitude-dependent chacteristics and frequency-dependent characteristics. In a different approach from the previous studies, a model of the bellows is developed in this paper and is composed of a smooth friction model and a fractional derivative Zener model in parallel to represent the viscoelastic properties of the bellows. It is concluded that the simulation results of the proposed new model are in good agreement with the experimental data. The new refined model may be an effective tool for predicting the mechanical behaviours of a convoluted air spring before a prototype is constructed. The proposed refined model can also be practically utilized as a guide for designing the parameters and for matching the air suspension of the vehicle.