Forced vibrations of a spring–dashpot mechanism with dry friction and backlash

Abstract

Mechanical systems like the Centre Buffer Couplers, which connect railway coaches, are spring–dashpot mechanisms characterized by presence of dry friction and backlash and are subjected to large dynamic forces. While systems with individual characteristics mentioned above, have been studied by earlier researchers, a system where all of the above physical features are present simultaneously, is analysed in this study. A single degree of freedom system with dry friction, backlash and spring–dashpot element is considered and subjected to harmonic excitation. The response is analysed through displacement, phase-space plots, orbit diagrams and Poincare maps using numerical simulations. Occurrence of bifurcations and chaos for different system parameters is numerically evaluated. The qualitative behaviour of systems with deteriorated conditions of low viscous damping, higher backlash and increased dry friction is established through numerical simulations and comparisons are made with that of a normal system. A transitional value of deteriorated condition is illustrated in terms of the ratio of viscous damping to dry friction, beyond which the response does not remain periodic. Additional verification is done through the Filippov method. Since, two discontinuities, i.e. the dry friction and backlash are simultaneously present in the system, the vector space gets divided into nine subspaces. Various possible transitions of state space trajectory between two adjacent subspaces have been analysed. To the knowledge of authors, such complex planar system with presence of more than one mutually perpendicular line discontinuities which intersect each other, has been analysed in various subspaces for the first time.