Mathematical modelling of the secondary airspring suspension in railway vehicles and its effect on safety and ride comfort

The mathematical model of suspension components in a railway vehicle may have an important effect on the results of vehicle dynamics simulations and their accuracy in reproducing the actual vehicle behaviour. This paper aims to define and compare alternative mathematical modelling approaches for the secondary airspring suspension and to assess their effect on the accuracy of rail vehicle dynamics multibody simulation. To derive reliable models of the suspension, a quasi-static and dynamic characterisation of the suspension was performed by means of a full-scale laboratory experiment. Based on this, two different modelling approaches were developed for the airspring suspension: a quasi-static one, in which the frequency-dependent behaviour of the suspension is neglected, but the coupling between shear and roll stiffness is included, and a dynamic one in which additionally the frequency-dependent behaviour of the suspension in vertical direction is represented using a thermodynamic model, and additionally the dependency of lateral/roll stiffness parameters on the load is incorporated. The results of vehicle dynamics simulations in curved track and/or in the presence of crosswinds and the results of ride comfort calculations are presented, to assess the effect of the models developed, in comparison with a simpler model only reproducing the vertical and lateral stiffness of the suspension. It is demonstrated that the quasi-static coupling effect between shear and roll deformation in the airsprings can have a large effect on the simulation of load transfer effects in curved track and in the presence of crosswinds, and hence remarkably affect the assessment of ride safety and track loading, whereas the dynamic model of the airspring suspension appears to be required when wheel unloading under the action of crosswind is evaluated. Finally, it is shown that a dynamic model of the airspring is required to assess ride comfort correctly, especially when the pneumatic layout of the suspension includes a long pipe between the airspring and the reservoir.