Unified analysis model for railway train-track-substructure dynamic interaction Part I: the dynamics model construction and its solution

Railway train, track and substructure are the basic research objects of railway engineering systems. The unified description and analysis of the interaction between the three objects at the dynamics level is the main content and precondition of railway engineering dynamics research. By considering the train, track, and substructures as an integrated system, the coupled vehicle-track dynamics theory was taken as the core of the method, and the principle of total potential energy with a stationary value and the “set-in-right-position” rule for matrix formation were taken as the modeling methodology. The three sub-systems were coupled into a dynamic unified matrix equation, and a unified analysis model for the railway train-track-substructure dynamic interaction was established subsequently. In this model, the lateral wheel-rail creep adopted the wheel-rail space dynamic coupling model, and the wheel-rail vertical elastic contact adopted the Hertz nonlinear contact theory. The wheel and rail were treated as elastic beams, and their nonlinear time-dependent coupling was achieved. The track and substructures were simulated and assembled with different types of finite elements, and the position of the element was directly controlled by the element nodal coordinates with the sizes calculated. The point and surface coupling of the multi-scale finite elements between the track and the substructural layers were realized. The cyclic calculation method was used to solve time-varying dynamics problem of the train on the long-distance track-substructure systems. To realize the high-efficiency vibration analysis of the train-track-substructure system, the entire system was divided into the upper train-track system and the lower substructure system. The multi-timestep hybrid integration mode was used to solve the problem. The results show that the unified model can properly reflect the high-frequency vibration characteristics of the wheel and rail and thus can achieve the coupled dynamics analysis of the train-track-substructure system subject to multi-substructural forms. The research findings have engineering reliability and applicability. © 2023, Central South University Press. All rights reserved.