Stability Analysis of a Linear Friction-Induced Vibration Model and Its Prevention Using Active Force Control

Abstract

This paper presents friction-induced vibration (FIV) caused by combined mode-coupling and negative damping effects in a simple FIV model. In doing so, a new four-degree-of-freedom linear model which consists of a slider and a block is proposed and then simulated using MATLAB/Simulink. Stability or instability of the FIV model is defined by the convergence or divergence of time domain responses of the slider and the block. Having found critical slope of friction-velocity characteristics that generate instabilities in the model, a conventional closed loop proportional-integral-derivative (PID) controller is first introduced into the main model in order to attenuate the vibration level and subsequently to suppress it. Later, the model is integrated with the active force control (AFC) element to effectively reject the disturbance and reduce the vibrations. It is found that the integrated PID-AFC scheme is effective in reducing vibration compared to the pure PID controller alone. Thus, the proposed control scheme can be one of the potential solutions to suppress vibration in a friction-induced vibration system.