Properties of stability, bifurcation, and chaos of the tangential motion disk brake

This study proposes a new dynamic model of a brake system that combines pad tangential motion and disk torsional motion to reduce the vibration and noise of the brake system. The stability analysis of this system with a smoothed Stribeck friction model verified its instability, which is caused by Hopf bifurcation. Moreover, numerical simulation showed several phenomena of the system vibration changing with angular velocity: (1) the system vibration maintains in the stable limit cycle after Hopf bifurcation within a relatively wide range of low angular velocity and (2) period-doubling bifurcation and chaos will occur only by decreasing the angular velocity. This study further discusses the effects of friction parameter on stick–slip vibration within a common range of brake pressure under “low” and “lower” angular velocities; the result shows that a decrease of both μs−μkμs−μk and decay factor can effectively reduce the range of chaotic vibration region.