Nonlinear Dynamics Of The Marine Rotor-bearing System Coupled With A Floating Raft Isolation Structure Under Heaving And Rolling Motion

In common sea conditions,a ship is often affected by wind and waves,which cause the hull to experience large-amplitude,low-frequency movements.Under the ship motion,a rotor-bearing system of marine rotating machinery will be affected by the transport inertial force,and its vibration will be unpredictable.Hence,it is of great theoretical importance and engineering value to study the vibration behaviors of the system under the above motion.In this study,two typical ship motion forms,heaving and rolling,which have a significant impact on the suitability and safety of ships,were taken into consideration.A mathematical model of the system under heaving and rolling was established based on Lagrange’s equation,and the steady-state responses were obtained by employing a numerical method.The results were qualitatively analyzed based on nonlinear dynamics theory,and the dynamic behaviors of the system were systematically studied.Here are the main research contents and results:(1)The dynamic model of the rotor-bearing system coupled with a floating raft isolation structure was established by the Newton Second Law,and the vibration responses of the system were presented by using a numerical method,The linearization expressions of oil film forces were deduced,and the reasons for the resonance peaks in the response of the system were analyzed.Moreover,the force transmission rate of the system was defined by the ratio of root mean square.The result shows that the responses of the system present the obvious nonlinear behaviors such as amplitude jumping,bifurcation and chaos;the resonance peaks of amplitude response of the system can be explained based on the linearization theory,on the one hand,which is caused by the rotor speed equal to the linear frequency of the system,on the other hand,which is due to the nonlinear factors of the oil film.Moreover,the floating raft isolation structure can efficiently reduce force transmission from the bearing to the hull,and there is an obvious jump phenomenon in the response of the force transmission rate.(2)After considering the effect of ship heaving motion,the dynamic model of the system under the motion was established,and the steady-state responses of the system were obtained by using a numerical method.The results show that,with the ship heaving motion,the amplitude of the system is larger than that without the above motion,and the responses of the system show obvious nonlinear behaviors such as amplitude jumping,bifurcation and chaos.With the increase of heaving amplitude or frequency,the amplitude of the raft increases until it collides with the displacement restrictor;and there are different ways to reduce the amplitude of the system effectively,for instance,increasing the mass ratio reasonably,increasing the linear frequency or the damping ratio.(3)The differential equations of motion of the system subject to ship rolling motion were derived based on Lagrange’s equation,and the vibration responses of the system were presented on numerical simulations.The results indicate that the amplitude of the system under rolling motion is larger than that without the above motion;as the rotating speed increases,there exist clear nonlinear characteristics in the responses of the system such as amplitude jumping,bifurcation and chaos;however,the vibration state of the system will not be affected by the changing of the rolling amplitude or frequency.As the rolling amplitude or frequency increases,the amplitude of the rotor and raft also increases.Moreover,the vibration amplitude can be reduced by increasing mass ratio,linear frequency or damping ratio.(4)Considering the effect of the coupled motion of heaving and rolling,a mathematical model of the system under the above motion was established based on Lagrange’s equation,and the dynamic responses of the system were simulated by the numerical solution.The results show that the amplitude of the system under the coupled motion of heaving and rolling is larger than that without the above motion;with the changing of the rotor speed,heaving amplitude or its frequency,the responses of the system show obvious nonlinear phenomena such as amplitude jump,bifurcation and chaos;while the rolling amplitude or its frequency generally do not change the motion state of the system.The amplitude of the rotor and the raft will also increase with the increase of heaving amplitude,heaving frequency,rolling amplitude or its frequency.Moreover,to reduce the vibration of the system,it is of great significance to reasonably increase the mass ratio,linear frequency or damping ratio.