Analytical expressions of friction-induced self-excited vibration amplitudes of the marine rubber bearing-shaft system

Abstract

By the analytical method, this paper investigates the mode-coupling friction-induced instability and the resulting stick-slip self-excited vibration of the marine stern water-lubricated rubber bearing-shaft system. The 2-DOF simplified theoretical model is reasonably developed to characterize stern water-lubricated rubber bearing-shaft system. The complex eigenvalue analysis is conducted to analyze the instability behaviors of the model. Results show the normal force and nonlinear stiffness often deteriorate the stability of the model. Subsequently, two types of analytical expressions for stick-slip vibration amplitude of the model are by the Krylov-Bogoliubbov-Mitropolsky method, which match well with the results from numerical integration. Then, parameter discussion about the influences of friction coefficient, damping, normal force and nonlinear contact stiffness on self-excited vibration amplitudes are performed. The results indicate that the bearing-shaft system can keep the steady-state static equilibrium or the oscillations with small amplitude if the proper parameter values of the variables are chosen, which will benefits controlling the friction-induced vibration of the water-lubricated rubber bearing-shaft system. The novelty of this work is to give analytical expressions for stick-slip self-excited vibration amplitude of the simplified model.