A discontinuous model simulation for train start-up dynamics

Start-up dynamics plays an essential role in ensuring the comfort and running safety and structural integrity of trains. Based on the discontinuous dynamics framework, in the present work, an efficient innovative model is proposed. The model is derived from previous train braking studies and in order to highlight the possibility of a non-smooth approach to train start longitudinal dynamics. Set-valued friction of Coulomb's law type is accounted for and motion equations are formulated as a differential inclusion. Static friction forces which arise in buffers are computed in a very intuitive and efficient manner, using involving generalised inverses of matrices. The corresponding algorithm is described. Numerical integration is done by an event-driven algorithm. Indeterminate system configurations can be appropriately handled. The number of train vehicles may be easily adjusted, and any wagon connection model can be embedded. Specific phenomena like stick-slip or persistent longitudinal forces can be evidenced. Any feature or situation regarding train collisions may be modelled. A demonstrative application is presented.