Simulation procedure for vehicle–substructure dynamic interactions and wheel movements using linearized wheel–rail interfaces

A simulation procedure for vehicle–substructure dynamic interactions and wheel movements is presented. The vehicles and substructure systems interact though wheel–rail interfaces satisfying two compatibilities, i.e., the equilibrium of contact forces including a lateral creep damping force and the geometry relating wheel and rail movements, rail irregularities and local contact deformations. Each vehicle is modeled as a multi-axle two layer of mass-spring-damper system having 27 degrees of freedom. The bridge modeling is made adaptive to various finite elements; the element forces and responses at wheel positions are related to the nodal ones by consistent shape functions. The proposed solution algorithm consists of separate integrations for the vehicles and substructures and an iterative scheme for wheel–rail contact forces and geometry. The vehicle and substructure coefficient matrices are time-independent, symmetric, and performed in one-dimensional bases. The updating and re-decomposing time is excluded; thus the procedure is versatile and applicable for various types of vehicle configuration, large number of vehicles, and complex substructures. The simulation is validated by an analytical sprung-mass bridge model and good agreement is obtained. A real train of fifteen vehicles over a rough slab-track railway having a simply supported bridge is investigated. The vehicle accelerations and wheel relative displacements increase largely when they are crossing the bridge.