Frequency entrainment and suppression of stick–slip vibrations in a 3 DoF discontinuous disc brake model

Friction-induced stick–slip vibration has been identified as the main reason for various types of disc brake noises like creep groan, squeak and creak. In this work, we investigate the suppression of stick–slip vibrations in disc brakes due to the application of a small-amplitude normal harmonic force on the brake pad. The discontinuity induced bifurcations that lead to such suppression are studied in detail. The frequency range of the normal force in which suppression of stick–slip vibration occur is identified. A 3 DoF discontinuous model of the disc brake is considered. The discontinuous oscillator is modelled as a Filippov system with smooth vector fields separated by a discontinuity surface. It is shown that the normal harmonic force entrains the non-smooth limit cycle even for very small forcing amplitudes. Different frequency intervals exhibiting harmonic, super-harmonic, and sub-harmonic entrainments are identified. It is demonstrated that the initiation and termination of these entrainment intervals are associated with Neimark–Sacker bifurcations. It is also shown that discontinuity induced grazing-sliding mechanism brings about these bifurcations. Switching-sliding bifurcations happening in the entrainment region give rise to a sub-interval which is associated with suppression of stick–slip vibrations. We also report interesting discontinuity induced bifurcation scenarios in higher order entrainment regimes like grazing-sliding involving different orbit loops at lower and upper limits of the interval and splitting–merging of the sliding surface.