The self-excited vibration induced by friction of the shaft-hull coupled system with the water-lubricated rubber bearing and its stick-slip phenomenon

To the underwater vehicle, its self-excited vibration induced by friction in the stern bearing is the non-ignorable component of the propeller vibration and noise. This paper describes how to solve the self-excited vibration, and discuss the effects on the self-excited vibration and its stick-slip phenomenon. After making the analysis about the supporting characteristics between shaft and hull substructures, this paper takes the shaft-hull coupled system as the analysis object, and constructs the FEM (Finite Element Method) model of the system. Based on the FEM model validated by the experiment, the required modal frequencies and the shapes of the shaft and the hull are calculated. Then, the friction force between shaft and water-lubricated rubber bearing is calculated, according to the Stribeck friction curve. Hereafter, through the friction force, the modal shapes of the shaft and the hull are combined to establish the nonlinear differential governing equations of the shaft-hull coupled system, by employing the modal synthesis method of substructures. Subsequently, the self-excited vibration responses induced by the friction can be obtained by solving the nonlinear differential governing equations, by Runge-Kutta method. On this basis, the discussions about the effects of friction coefficient, damping ratio, rotation speed and support stiffness on the self-excited vibration of the shaft-hull coupled system are conducted. The results show that the larger the damping is, or the faster the rotation of shaft is, or the stronger the supporting stiffness is, the more difficultly the shaft-hull coupled system's self-excited vibration will happen. The works on how to solve the self-excited vibration induced by friction in the stern bearing will be of great significance to accurately predict the propeller vibration and noise and optimize the acoustic design of the underwater vehicle.