Study on numerical simulation methods of the railway vehicle-track dynamic interaction

A very efficient numerical simulation method of the railway vehicle–track dynamic interaction is described. When a vehicle runs at high speed on the railway track, contact forces between a wheel and a rail vary dynamically due to the profile irregularities existing on the surface of the rail. A large variation of contact forces causes undesired deteriorations of a track and its substructures. Therefore these dynamic contact forces are of main concern of the railway engineers. However it is very difficult to measure such dynamic contact forces directly. So it is important to develop an appropriate numerical simulation model and identify structural factors having a large influence on the variation of contact forces. When a contact force is expressed by the linearized Hertzian contact spring model, the equation of motions of the system is expressed as a second–order linear time–variant differential equation which has a time–dependent stiffness coefficient. Applying a well–known Newmark direct integration method, a numerical simulation is reduced to solving iteratively a time–variant, large–scale sparse, symmetric positive–definite linear system. In this study, by defining a special vector named a contact point one, it is shown that this time–variant stiffness coefficient can be expressed simply as a product of the contact point vector and its transpose and so the Sherman–Morrison–Woodbury formula applied for updating the inverse of the coefficient matrix. As a result, the execution of numerical simulation can be carried out very efficiently. A comparison of the computational time is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)