Vehicle–track interaction with consideration of rail irregularities at three-dimensional space

Modelling of vehicle–track interaction has long been a hot and interesting topic. In multibody dynamics based on force-equilibrium methods, Hertzian contact and creep theories have been applied in vehicle–track model constructions. In another aspect, the complementarity-based methods have also been widely used in establishing vehicle–track interaction, but still having drawbacks on characterization of wheel–rail contact geometry/creepage in three-dimensional space. In this study, we draw essences from methodologies of refined wheel–rail coupling models and energy-variational principle, and a model for vehicle–track three-dimensional interactions with inclusion of rail irregularity excitations is newly developed. This model possesses high accuracy compared with Hertzian contact, FastSim, and vehicle–track coupled model in the middle-low frequency domain, and also, the advantages in computational stability are possessed. In this model, the unevenness of rail irregularities at the three-dimensional space is preliminarily considered by taking a hypothesis of normal distribution and accordingly, the wheel–rail three-dimensional constraint equations are presented. Extensively, a series of numerical examples are shown to verify the effectiveness and engineering practicability of this model. Besides, the influence of rail three-dimensional irregularities on the dynamic performance of vehicle–track systems is further explored, which shows when the trochoid of the wheel–rail contact points changes rapidly, the additional inertial effects brought out by rail irregularities might exert great influence on wheel–rail forces.