Analysis of stability and stick-slip motion of a friction-induced vibrating system with dwell-time effect

Abstract

In this paper, the authors investigate the stability and stick-slip motion of a friction-induced vibrating system placed on a belt moving at constant velocity using two-state model with consideration of dwell-time effect. The two-state model can be considered as an extension of the LuGre model because it can capture both Stribeck and dwell-time effects in the case of near-zero relative motion velocity between two surfaces. The previously known Stribeck effect is that the friction force decreases as the relative velocity increases in the near-zero range, while the dwell-time effect exhibits that the friction force increases as two surfaces are kept in contact for a certain time. With new effect of dwell-time, properties of stick-slip motion are explored in detail, including the equilibrium point position, the stability of the equilibrium point, Hopf bifurcation, characteristics of velocity and the change of friction force in different cases of belt velocity. The obtained result indicates that the influence of dwell-time on system responses is significant in the near-zero velocity range. Using the Routh-Hurwitz criterion, the authors show that there is a positive shift in the direction of increase of belt velocity for the stable zone of the equilibrium position compared with the stable zone obtained from the LuGre model. The formulations of the limit cycle and phases of motion in stick-slip vibration of the system are demonstrated by numerical simulations.