Efficient decoupling technique applied to the numerical time integration of advanced interaction models for railway dynamics

[EN] Railway interaction is characterised by the coupling between the train and the track introduced through the wheel/rail contact. The introduction of the flexibility in the wheelset and the track through the finite element (FE) method in the last four decades has permitted to study high-frequency phenomena such as rolling noise and squeal, whose origin lies in the strongly non-steady state and non-linear behaviour of the contact forces that arise from the small contact area. In order to address models with a large number of degrees of freedom, innovative Eulerian-modal models for wheelsets with rotation and cyclic tracks have been developed in recent years. The aim of this paper is to extend the resulting formulation to an uncoupled linear matrix equation of motion that allows solving each equation independently for each time step, considerably reducing the associated computational cost. The decoupling integration method proposed is compared in terms of computational performance with Newmark and Runge-Kutta schemes, commonly used in vehicle dynamics, for simulations with the leading wheelset negotiating a tangent track and accounting the rail roughness. European Commission, Grant/Award Number: 777564; Generalitat Valenciana, Grant/Award Number: Prometeo/2016/007; Spanish Ministry of Economy, Industry, and Competitiveness and the European Regional Development Fund, Grant/Award Number: TRA2017¿84701¿R Giner Navarro, J.; Martínez Casas, J.; Denia, FD.; Baeza González, LM. (2020). Efficient decoupling technique applied to the numerical time integration of advanced interaction models for railway dynamics. Mathematical Methods in the Applied Sciences. 43(14):7915-7933. https://doi.org/10.1002/mma.5658 Nielsen, J. C. O., Lund n, R., Johansson, A., & Vernersson, T. (2003). Train-Track Interaction and Mechanisms of Irregular Wear on Wheel and Rail Surfaces. Vehicle System Dynamics, 40(1-3), 3-54. doi:10.1076/vesd.40.1.3.15874 Ekberg, A. (2009). Fatigue of railway wheels. Wheel–Rail Interface Handbook, 211-244. doi:10.1533/9781845696788.1.211 Grassie, S. L., Gregory, R. W., Harrison, D., & Johnson, K. L. (1982). The Dynamic Response of Railway Track to High Frequency Vertical Excitation. Journal of Mechanical Engineering Science, 24(2), 77-90. doi:10.1243/jmes_jour_1982_024_016_02 THOMPSON, D. J., & JONES, C. J. C. (2000). A REVIEW OF THE MODELLING OF WHEEL/RAIL NOISE GENERATION. Journal of Sound and Vibration, 231(3), 519-536. doi:10.1006/jsvi.1999.2542 Baeza, L