Control of Friction-Induced Instability in Simultaneous Time-Frequency Domain

A flexible cantilever beam pressed against a rigid rotating disk is explored for studying self-excited friction-induced vibrations that are inherently unstable due to alternating friction conditions and decreasing dynamic friction characteristics. Because no linearization or approximation scheme is followed, the genuine characteristics of the system including stick-slip and inherent discontinuities are fully disclosed without any distortion. It is shown that the system dynamics is stable only within certain ranges of the relative velocity. With increasing relative velocity, the response loses its stability with diverging amplitude and broadening spectrum. A novel time-frequency controller is subsequently applied to negate the chaotic vibrations at high relative velocity by adjusting the applied normal force. The controller design requires no closed-form solution or transfer function, hence allowing the underlying features of the discontinuous system to be fully established and properly controlled. The inception of chaotic response at high relative velocity is effectively denied to result in a restoration of the system back to a relatively stable state of limit-cycle.