Thermodynamic models of the air spring on the high-speed pantograph

The modelling method of the air spring and its additional pneumatic system has been studied more frequently in recent years. As for the railway field, the study of the secondary suspension system of the bogie is the most popular, while little focus is on the air spring of the pantograph. In this paper, the modelling method of the air spring on the pantograph is investigated and developed. Four thermodynamic models are derived step by step, which can roughly be separated into two types. The first two models are established to express the relationship between the inner pressure and the vertical displacement of the air spring, and the effect of a regulator is illustrated and discussed. The latter two models that are developed from the first two models are set up to express the relationship between the vertical force and the vertical displacement of the air spring, where the effect of air spring material is illustrated and discussed. All four models are validated by comparing the simulation results with experimental results for frequency characteristics. Finally, the characteristics of the four proposed models are illustrated and discussed.