Representation of mechanic hysteresis in a railway track using the Preisach model

This paper presents an implementation of the classic scalar Preisach model to describe the hysteresis phenomenon created in a railway track subjected to lateral (in the horizontal plane) displacements. The principles of the Preisach theory and the scalar mathematical model of the mechanical hysteresis that is based on statistically distributed modified hysteresis operators are briefly presented. This article presents the characteristic states of the track displacements under lateral forces and their interpretation using the Preisach phase diagram. Formulas are presented that allow the calculation of the trajectory of the track displacements using the Preisach distribution function (PDF) and the Everett function (EF). Identification methods for the PDF and EF presented in the literature are discussed. A mathematical formula for the calculation of the EF on the basis of the major hysteresis loop is presented. The implemented hysteresis model is validated by comparing simulation results with experimental data. A good level of agreement between the two sets of results is observed which confirms the validity of the proposed model. The shape of the hysteresis loop created in the rail track depends on the stress state in the rails. It is suggested that this observation could be used to create an effective method to assess axial forces in continuous welded rail track.