Nonlinear dynamic characteristics of marine rotor-bearing system under coupled heave and pitch ship motions

Abstract

The coupled heave and pitch motions of a ship sailing in head waves affect the stability of the marine rotor-bearing system. Based on the theory of analytical mechanics, this study establishes a dynamic model of the rotor-bearing system subjected to the coupled motions of heave and pitch, considering nonlinear oil film moments produced by the tilting of the rotor in the bearings. The nonlinear dynamic behaviours of the system are analysed using numerical methods to obtain Poincaré sections, bifurcation diagrams, and the largest Lyapunov exponents. The results show that dynamic bifurcation characteristics reveal complex quasi-periodic motion of upper and lower branches after the initial instability of the system, and the speed of second instability increase markedly. At high speeds, the amplitude of the rotor system increases sharply, which can cause the rotor to touch the inner wall of the bearings in the quasi-periodic state and a failure to transition to the chaotic state. Additionally, the effects of heave and pitch amplitude variations on the dynamic characteristics of the system are also discussed.

Nonlinear dynamics of the rotor system with a floating raft isolation structure under the coupled motion of ship heaving and rolling

“…According to literatures 5,26,[30][31][32] , the heaving displacement has the form x H = a max sin (ω H t), where a max is the maximum heaving amplitude and ω H is the heaving frequency; furthermore, the rolling angle can be represented as θ R = θ max sin (ω R t), where θ max is the maximum rolling amplitude, ω R is the rolling frequency. Therefore, the coupled motion of heaving and rolling of ship in the presence of different sea waves can be simulated by changing the above parameters.…”

“…A typical model of a journal bearing is shown in Figure 4, and based on the short bearing assumption and semi-Sommerfeld boundary condition, 22,23,30,31 the expressions of the nonlinear oil film reaction forces F r and F τ in the radial and tangential directions are as follows…”

“…A typical model of a journal bearing is shown in Figure 4, and based on the short bearing assumption and semi-Sommerfeld boundary condition, 22,23,30,31 the expressions of the nonlinear oil film reaction forces F r and F τ in the radial and tangential directions are as follows in which μ is the dynamic viscosity of the lubricating oil; R , L and c are the radius, axial length and radial clearance of the journal bearing, respectively; ω is the rotating speed; and ε and φ denote the eccentricity ratio and attitude angle, respectively. Moreover, ε ˙ = d ε / d t and φ ˙ = d φ / d t, and the equations of the Sommerfeld integrals G 1, G 2, G 3 and G 4 are where ε = x 3 2 + y 3 2 /…”

“…Very recently, Soni et al 28,29 proposed a dynamic model of a rotor-shaft-bearing system under the action of ship motion caused by water waves, and they performed a numerical simulation of the response of the system. Moreover, Han, Zhang, Du and Li 30–32 analysed the nonlinear dynamic characteristics of rotor-bearing systems in rotating machinery under ship motions by using the multiscale method and numerical methods. Refs 25–32 all considered the influence of base motions on the rotor-bearing system in moving carriers, and the vibration behaviours are investigated, but there is still a puzzle that how to reduce the vibration of the system.…”