Investigation On Friction Characteristics Of The Water-Lubricated Rubber Bearings And The Induced Vibration Of The Propeller Shafting Systems

The propeller propulsion shafting system works as the important component of the power system of a submarine.The vibration of the propeller shafting system not only destroy the self performance but also can be transimitted to hull through bearing foundations or attachments then induce hull vibration and under water noise radiation,which discount the low-noise quality of the submarine.In which,the friction from the stern tube rubber bearing is one of the primary contributed sources exciting the shaft system.Especially,the water-lubricated rubber bearing often works at the mixed or boundary lubrication state,even contact directly with the rotor under the lowspeed,high-load,start-up and shut-down conditions.Greater bearing friction can induce abnormal vibration even squeal of the shaft system.In addition,bearing friction can couple with other factors,i.e.the cantilevered load of the propeller,bearing misalignment and the unbalanced load induced by mass eccentricity of the propeller.Accordingly,this study tries to further reveal the friction characteristics of water-lubricated rubber bearings and the coupled mechanisms of bearing friction,support vibration,bearing misalignment and unbalanced load,which can provide references for the vibration identification,diagnosis and performance improvement of the shaft system.Specifically,the main research contents can be presented as:(1)Model the quantitative dependences of friction coefficients of the water-lubricated rubber bearing on rotational velocities of the rotor and equivalent bearing pressures by means of experiments,into which the effect of the unbalanced load induced by the mass eccentricity is involved.To reveal the influence of the shape of inner surfaces of rubber busings of bearings on characteristics of bearing friction,friction coefficients associated with flat rubber bearings at different run states and concave rubber bearings are compared.The friction coefficients of rubber bearings being in the fully run play more sensitive to the variation of the rotor speed,as compared with friction coefficients of rubber bearings being in the early run.The friction coefficients of concave rubber bearings play more sensitive to the variation of the rotor speed,as compared with friction coefficients of flat rubber bearings.The rotor speed has much greater impact on friction coefficients of rubber bearings than bearing load.(2)Acoording to the presented model of friction coefficients of waterlubricated rubber bearings,analyze the coupled effect of water-lubricated rubber bearing friction and vibrations of flexible support on the characteristics of the self-excited vibration of a flexibly supported propeller shafting system placed in a gravity water tunnel.The coupled dynamic models associated with the lateral and longitudinal vibrations of the flexible support and the lateral and torsional vibrations of the rotor are built,into which the attachment effect of water on lateral vibrations of the flexible support and the rotor is involved.The mode truncation and the fourth Runge-Kutta methods are applied to solve governing equations and the influences of some physical paramters on chracteristics of the self-excited vibration of the inveatigted shafting system are analyzed,i.e.mode damping ratio,rotor speed and the slope of the friction coefficient on the relatively sliding velocity.The rotor speed are modulated and the dynamic forces transmitted from the flexible stern support to the frame are tested,which can demonstrate well the characteristics of the self-excited vibration.The instability mechanism of mode coupling through friction can be further understood by the summarization of numerical analysis and experiment results,sepecially,the mode shape and the related mode damping ratio are the determined factors on instability.(3)Acoording to the presented model of friction coefficients of waterlubricated rubber bearings,the coupled effect of the bearing friction and the bearing misalignment on lateral and torsional vibration characteristics of a propeller propulsion shafting system are analyzed.The Lagrange Equation and the finite element method are apllied to build the coupled dynamic models of lateral and torsional vibrations of the corresponding simplified system,into which the variation of rubber bearing stiffness resulted by bearing offset is introduced.The analysis associated with the influence of the bearing misalignment of stern and front bearings on natural characteristics of the system are conducted.The transient dynamics of the system induced by the stern rubber bearing friction coupling with the stern and front bearing misalignment are analyzed.Numerical results reveal that a small amount of bearing misalignment has little influence on the natural frequencies and mode shapes of the shafting system.However,bearing misalignment has great impact on the friction distribution of the stern bearing and further affects the vibration characteristic of the shafting system.Moreover,greater bearing friction can easily induce the self-excited vibration of the shafting system.Compared with the torsional modes of the shaft,the lateral modes are more prone to become unstable.(4)Acoording to the presented model of friction coefficients of waterlubricated rubber bearings,analyze the coupled effect of the bearing friction and the unbalanced load induced by the mass eccentricity of the propeller on vibration characteristics of a propeller shafting system,in which the influence of the unbalanced load on the friction of water-lubricated rubber bearings is considered.Some physical parameters of the system are ascertained by load calibration.The stiffness of the water film is tested and the corresponding results reveal that it is much greater than the stiffness of rubber bushing,which implies that the support stiffness of the rubber bearing is mainly determined by the rubber bushing.The dynamics on the coupled vibrations associated with the rotor and the support are modeled,and the steadily dynamic responses are analyzed.The static load resulting on the stern rubber bearing and the rotor speed are changed respectively,and the lateral and torsional vibrations of the rotor and the horizontal and vertical vibrations of the rubber bearing foundation are tested,respectively.Experimental results reveal that the bearing friction has less impact on rotor vibration,as compared with it on the vibration of the rubber bearing foundation.Numerical and experimental results demonstrate that the amplitudes associated with the horizontal and vertical vibrations of the rubber bearing foundation are amplified due to the greater rubber bearing firction induced by the greater load resulting on the rubber bearing.However,the influence intensity of the friction of the water-lubricated rubber bearing decreases as the rotor speed increases.In the investigated range of the rotor speed,the unbalanced load induced by the mass eccentricity has little effect on the rubber bearing friction.