Probability analysis of train-track-bridge interactions using a random wheel/rail contact model

Based on the random theory of the probability density evolution method (PDEM), a refined random wheel/rail contact model for train-track-bridge systems is proposed. The trace line method with the law of equal slopes is developed to determine the wheel/rail contact locations, which are described by probability density functions on the wheel/rail surface. The number theoretic method (NTM) and stochastic harmonic functions (SHFs) are employed to generate the representative random track irregularities. Considering the excitation of random track irregularities and the wheel/rail contact geometry, the wheel/rail normal contact force and the tangential creep force are accurately calculated and analyzed using the proposed wheel/rail contact model. A high-speed railway case study is presented to reveal the random dynamic characteristics of a train-track-bridge system and the wheel/rail interaction. The results show that the time-varying probability density evolution functions of the wheel/rail contact points can effectively indicate both the phenomenon of wear on the rail surface and its distribution characteristics. Additionally, some significant conclusions are obtained.