Abstract
Based on the energy flow theory of nonlinear dynamical system, the stabilities, bifurcations, possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper. It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-paramters. (a) Energy flow matrix has two negative and one positive energy flow factors, constructing an attractive local zero-energy flow surface, in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state, while forced vibrations by external forces show stable oscillations. (b) Energy flow matrix has one negative and two positive energy flow factors, spaning a divergence local zero-energy flow surface, so that the both free and forced vibrations are divergence oscillations with the system being unstable. (c) Energy flow matrix has a zero-energy flow factor and two opposite factors, which constructes a local zero-energy flow surface dividing the local phase space into stable, unstable and central subspace, and the simulation shows friction self-induced unstable vibrations for both free and forced cases. For a set of friction parameters, the system behaves a periodical oscillation, where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero. Numerical simulations have not found any possible chaotic motions of the system. It is discovered that the damping matrices of cases (a), (b) and (c) respectively have positive, negative and zero diagonal elements, resulting in the different dynamic behavour of system, which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.Graphic
Highlights
Water-lubricated bearings have been more and more used in the marine and pump industries to eliminate the pollution of metal bearings lubricated by oil and grease as well as to increase efficiency and reliability of marine propulsion systems
Graf and Ostermeyer [7] have shown how the stability of an oscillator sliding on a belt will change, if a dynamic friction law with inner variable is considered instead of a velocity-dependent coefficient of friction, which demonstrates the unstable vibration can even be found in the case of a positive velocity-dependency of friction coefficient
The energy flow of system is a function of time and the position of a point in phase space, which generates a scalar field called as the energy flow field of the nonlinear dynamical system
Summary
Water-lubricated bearings have been more and more used in the marine and pump industries to eliminate the pollution of metal bearings lubricated by oil and grease as well as to increase efficiency and reliability of marine propulsion systems. Ghorbel et al [10] proposed a minimal 2-DOF disk brake model to investigate the effects of different parameters on mode-coupling instability, which considers self-excited vibration, gyroscopic effect, friction-induced damping, and brake pad geometry. In designs of this type of berings, two research directions have been developing: one aims to obtain good friction characteristics using suitable geometric parameters with different facing layers and lubrications [11,12,13,14], and another is to create new bearing materials [15,16,17,18].
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