Alternative friction models for braking train dynamics

Abstract

Braking dynamics plays an essential role in ensuring the comfort and running safety of trains. Due to the complexity of the phenomena involved and the presence of dry friction, studies have been carried out by numerical methods using smoothening. Based on the non-smooth dynamics framework, in the present paper, an efficient and comprehensive alternative model is defined. Set-valued friction of Coulomb's law type is accounted for and motion equations are formulated as a differential inclusion. Some of the fundamental issues of contact dynamics are briefly reviewed. Static friction forces which arise in buffers are computed in a very intuitive and efficient manner, using an original method 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 vehicles on which tests have been carried out ranged from 5 to 50. Comparison with the smoothening method reveals significant differences. Computational efficiency is dramatically improved. Computation speed can rise by a few orders of magnitude. Specific phenomena such as stick–slip or persistent longitudinal forces can be evidenced. Computed values of the system states differ substantially. In addition to this, any wagon connection model can be embedded.