Nonlinear Dynamics Of Marine Rotor-Bearing System Under Yawing And Swaying Motions

During the marine’s navigation,six types of transport motion such as swaying and yawing are generated due to the influences of uncontrollable factors like wind and waves.These large amplitudes and low-frequency rocking motions transfer energy to the roto r system through hull,thus exerting a great influence on the dynamics of the rotor-bearing system.In the thesis,the dynamic model of the marine rotor-bearing system under the combined actions of transport motion,yawing motion,swaying motion and coupled transport motion of yawing and swaying are established respectively based on the theory of short bearing.There are many kinds of additional forces in the differential equation of the system,such as the transport inertia force,the transport inertia moment,the oil film moment,the gyro moment and so on.The transport motion makes the system movement very sophisticated.Finally,the dynamic characteristics of the rotor-bearing system are studied by using nonlinear dynamics theories.The main contents and results are as follows:(1)Based on the short bearing theory,the differential equation of motion of the rotor-bearing system under yawing motion is deduced.The theoretical analysis shows that the differential equation of system motion shows strong geometric nonlinearity due to the existence of transport inertia moment,gyro moment and nonlinear oil film moment.Considering the same or similar speed,the influence of the presence or absence of yawing motion on the dynamic characteristics of the rotor system is compared and analyzed.On the whole,yawing can significantly increase the amplitude of the rotor in the horizontal direction.At lower speeds,the dynamic characteristics of the rotor system under yawing motion are quasi-period,while those without yawing motion are period 1.It can be seen that yawing motion can greatly advance the speed of the rotor into the state of the quasi-period.At hi gher speeds,yawing motion can make the rotor system dynamics behave as a more complex chaotic motion.The influence of the amplitude and frequency ratio of yawing motion on the dynamic characteristics of the rotor system is analyzed.The results show that the deflection of the rotor relative to the bearing pad increases due to the increase of yawing motion amplitude,and the j ournal trajectory will change greatly.When the frequency ratio is small,the rotor amplitude will fluctuate obviously due to various time-varying forces,and the influence of yaw on the rotor-bearing system tends to decrease with the increase of frequency ratio.(2)Considering the marine’s swaying motion,the motion differential equation of the rotor-bearing system is derived based on the short bearing oil film force model.The theoretical analysis illustrates that the differential equation of system motion shows strong geometric nonlinearity due to the influence of the transport inertial force and the nonlinear oil film force.The influence of swaying motion at different speeds on the nonlinear dynamic characteristics of the rotor-bearing system is discussed by using dynamic analysis methods.Similar to yawing motion,swaying motion can also advance the speed of the rotor into quasi-periodic motion,and the rotor will oscillate significantly in the horizontal direction in the whole range of speed variation.At the same dimensionless speed,the relative dynamic characteristics of the rotor-bearing system are compared under yawing and swaying motions.At low speeds,the yawing motion has a greater effect on the rotor amplitude than swaying motion.At high speeds,yawing motion makes the rotor dynamics manifested as complex chaotic.The parametric analysis of the rotor-bearing system under swaying motion indicates that as the swaying amplitude increases,the rotor’s transport inertial force also increases,and the rotor movement becomes more sophisticated.When the frequency ratio is small,the rotor moves very violently and even impacts the inner wall of the bearing bush,which is shown as complex a chaotic motion.When the frequency ratio is large,the influence of yawing motion on the rotor is weakened,which is shown as quasi-periodic motion.(3)Based on the short bearing theory,the differential equations of motion of the rotor-bearing system under coupled yawing and swaying motions are derived.The theoretical analysis reflects that the rotor is subjected to more complex forces under coupled transport motion,such as the swaying motion inertia force,the yawing motion inertia moment,nonlinear oil film moment,etc.,and the motion differential equation under coupled motion is more complex than that under single motion.The effects of coupled transport motion,yawing motion,and swaying motion on the dynamic characteristics of the system under the same parameters are compared and analyzed.The dynamic characteristics of the system under coupled transport motion are more complex due to the more complex forces.When the dimensionless speed is low,the rotor displacement and the amplitude is larger under the transport motions compared with a single implicated motion.When the dimensionless speed is high,the dynamic characteristics of the rotor system are chaotic due to the yaw,sway and coupled transport motion,but the motion of the rotor system is more intense and the trajectory is more complex,and it may even impact the inner wall of the bearing bush.The influence of yawing amplitude,swaying amplitude and frequency ratio on the dynamic characteristics of the rotor-bearing system is discussed.The analysis proclaims that although the dynamic characteristics of the system under coupled transport motion are similar to the characteristics under yawing motion,the amplitude of the rotor is larger than that under single transport motion due to the presence of swaying motion.It is evident that coupled transport motion makes the dynamic characteristics of the rotor-bearing system more complex than the single transport motion.