Lateral coordinate of the wheel surface xL Length of the strip x,y,z Cartesian coordinates y0 One dimension of the SDEC α Direction of the linear creepage γ Tangent angle of the cross-section γ Right-hand side of the acceleration constraint equations vector δ Penetration magnitude max  Maximum penetration velocity ΔFx Deviation of the longitudinal creep force ΔFy Deviation of the lateral creep force ΔMz Deviation of the spin creep moment Δr Step size for the radial coordinate Δs Width of the strip Δθ Step size for the angular coordinate ε Parameter that takes into account the existing deformation η Normalized lateral creepage θ Angular coordinate κ Curvature λ Lagrange multipliers vector μ Friction coefficient ν Magnitude of the linear creepages ξ Normalized longitudinal creepage σ Poisson ratio υx Longitudinal creepage υy Lateral creepage φ Spin creepage Φq Jacobian matrix of the constraint equations χ Normalized spin creepage ψ Shape factor of SDEC ω Angular velocity vector

The standard approach to railway vehicle dynamic analysis includes running the vehicle multibody models in rigid railway tracks. The wheel-rail contact, independently of the rolling contact model used, is either handled online or via lookup tables. This traditional approach disregards the coupling effects between the railway vehicle dynamics and the railway track flexibility. In this work the assumption of rigidity of the railway track is released and a finite element model of the complete track, i.e., rails, pads, sleepers, ballast and infrastructure, is used to represent the track geometry and flexibility. A rail-wheel contact model that evaluates the contact conditions and forces is used online. The dynamics of the railway vehicle is described using a multibody methodology while the track structure is described using a finite element approach. Due to the fact that not only the multibody and the finite element dynamic analysis use different integration algorithms but also because the vehicle and track models are simulated in different codes a co-simulation procedure is proposed and demonstrated to address the coupled dynamics of the system. This approach allows to analyse the vehicle dynamics in a flexible track with a general geometry modelled with finite elements, i.e., including curvature, cant, vertical slopes and irregularities, which is another novel contribution. The methodology proposed in this work is demonstrated in an application in which the railway vehicle-track interaction shows the influence of the vehicle dynamics on the track dynamics and vice-versa.

In railway dynamics, the interpolation of lookup tables (LUTs) is a procedure to reduce the computational effort when computing the wheel-rail interaction forces. However, the generation of LUTs with multiple inputs and multiple outputs is a challenging task for which issues such as their minimal size and uniform accuracy over the LUT domain have not been systematically addressed before. This work presents a comprehensive methodology for a detailed analysis of general LUTs, identifying ways to improve them. First, an analysis of the variation of the input parameters is made and the interpolation error is assessed on the cells and edges of the original table. From this analysis, two enhanced LUTs are proposed. One is approximately 5 times smaller than the original but holds similar accuracy. The other table exhibits half of the maximum interpolation error of the original LUT but holds an identical size. This methodology is demonstrated here using the recently published Kalker Book of Tables for Non-Hertzian contact (KBTNH) but it can be used by any other LUT approach in order to improve accuracy and/or to reduce size.