Development and implementation of a differential elastic wheel-rail contact model for multibody applications

The wheel-rail contact analysis plays a fundamental role in the multibody modelling of railway vehicles. A good contact model must provide an accurate description of the global and local contact phenomena (contact forces, position and shape of the contact patch, stresses and displacements) and a general handling of the multiple contact. The model has also to assure high numerical efficiency (in order to be implemented directly online within multibody models) and a good compatibility with commercial multibody software (Simpack Rail, Adams Rail). In this work, an elastic wheel-rail contact model that satisfies the previous specifics is presented. The model considers the wheel and the rail as elastic deformable bodies and requires the numerical solution of Navier's elasticity equation. The contact between wheel and rail has been described by means of suitable analytical contact conditions. Subsequently, the contact model has been inserted within the multibody model of a benchmark railway vehicle (the Manchester Wagon) in order to obtain a complete model of the wagon. The model has been implemented in the Matlab/Simulink environment. Finally, numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performances of the model. The results obtained with the proposed method have been compared with those obtained by means of a standard commercial software. The main purpose is to achieve a better integration between the differential modelling and the multibody modelling. This kind of integration is almost absent in the literature (especially in the railway field) due to the computational cost and to the memory storage needs. However, it is very important because only the differential modelling allows an accurate analysis of the contact problem (in terms of contact forces, position and shape of the contact patch, stresses and displacements) while the multibody modelling is currently the standard in the study of the railway dynamics.