Summary
The dynamics of a linear oscillator undergoing high-frictional impact is investigated. The system is a core model of brake pads or rotor-stator in contact. First, a practical mathematical model for the impact is derived, exploiting Newton's coefficient of restitution, conservation of the angular momentum, and the Coulomb friction model. This leads to an apparent coefficient of restitution, which can be larger than one, implying that the impact can generate energy. This phenomenon can trigger self-excited oscillations. Then, a bifurcation analysis is performed, leading to the definition of a critical parameter value, separating global and local stability regions of non-impacting solutions. Finally, the effect of the addition of a harmonic excitation is analyzed, which leads to more involved dynamical phenomena.
