T-FasTang: a transient hybrid BEM–FASTSIM solver for non-Hertzian wheel–rail rolling contact

In railway vehicle–track simulation the wheel–rail tangential contact problem must be solved at every time step, and when the contact conditions vary rapidly in time the stress history carried by the material through the contact patch cannot be neglected. Detailed solvers such as TangCG in the CONTACT software compute the traction and stick–slip fields accurately by accounting for the elastic interaction across the whole contact patch, but their cost is high when they are called repeatedly inside a dynamic simulation. FASTSIM is much faster, yet its simplified local-flexibility assumption reduces the accuracy of the local fields on realistic non-Hertzian geometries. This paper presents T-FasTang, a transient extension of the FasTang method. FasTang keeps the fast FASTSIM update in the slip zone and applies a boundary element solution only in the adhesion zone, but in its original form it treats each time step as an independent steady state. T-FasTang instead includes the time dependence explicitly, so that the stress history is transported through the moving contact patch. The method is examined on steady force–creepage curves, a transient wheel-flat simulation, and a case with varying spin on an asymmetric contact patch formed by actual wheel and rail profiles. Across these tests T-FasTang closely reproduces the forces, stick–slip boundaries, and local frictional power density obtained with TangCG, whereas FASTSIM shows clear errors in the local fields and, in the transient cases, also in the force histories. A performance test using successively refined grids confirms the expected computational scaling and shows that T-FasTang is about 1.3–1.5 times faster than a corresponding whole-domain TangCG solve. Because the local frictional power density governs wear and rolling-contact-fatigue estimates, resolving it at reduced cost while retaining fields of sufficient quality supports the use of the method within transient vehicle–track simulations.