Controlling the Nature of Bifurcation in Friction-Induced Vibrations with a Dynamic (Lugre) Friction Model by Delayed Position Feedback (original) (raw)

We analyse the effect of time-delayed position feedback in controlling frictioninduced vibrations of a single degree-of-freedom spring-mass-damper system on a moving belt. The friction force is modeled by a dynamic (LuGre) friction model. The control force is applied in a direction normal to the friction force. Linear stability analysis shows that the stability of the steady-state changes via a Hopf bifurcation. Numerical analysis of the full nonlinear equations reveals the possibility of changing the nature of the bifurcation from subcritical to supercritical using the linear control force employed in our study. Detailed numerical studies using a continuation scheme shows an interesting range of control parameters for which the steady-state is stable for low and high belt velocities and unstable for the intermediate ones. Interestingly, this phenomena is observed only for those control parameters for which the bifurcation is supercritical in nature. In particular, there are combina...