Friction-induced planar vibration of two rigid plates

The dynamical model for friction-induced vibration of two rigid circular plates in point contact is studied in this paper. Besides the rotational motion in the circumferential direction that is normally regarded as the principal direction of relative motion, the twodimensional translational motion is also considered for both rigid plates. The coupling of the translational motion and the rotational motion causes the direction of relative motion and friction force to shift from the circumferential direction and vary during vibration (in relation to the situation in which translational motion is absent), thereby greatly increasing the complexity of the dynamics of the friction-excited system. The system dynamics comprises two distinct states of motion, i.e., slip and stick, and the friction force during sticking is a reaction force enforcing the constraint of zero relative velocity, which cannot be explicitly expressed as a function of state variables, therefore the values of state variables and friction force in the state of stick cannot be directly obtained from the integration of equations of motion. To address this problem, two different methods are proposed and the accuracy and efficiency of the two numerical methods are subsequently examined. Both the linear stability and the nonlinear steady-state responses of the system are investigated. The numerical study demonstrates that the coupling of the translational motion and the rotational motion of the two rigid plates greatly expands the ranges of operating parameters for dynamic instability compared with those of the situation where the two rigid plates undergo only rotational motion, and results in rich bifurcation behaviours. Therefore this study underlies the necessity to take into account the oscillations of components that seem not to be in the principal direction of relative motion in the research of friction-induced vibration of mechanical systems. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper studies the dynamical model for friction-induced vibration of two rigid circular plates in point contact. The coupling of translational and rotational motion increases the complexity of the dynamics of the friction-excited system. The study shows that the coupling greatly expands the range of operating parameters for dynamic instability and leads to rich bifurcation behaviors.