Study On Vibration Suppression Of Large Aspect Ratio Flexible Rotors Using Ball Balancer

Some rotors such as spinning spindle and steam turbine sets have large aspect ratio and often work above their critical speed,thus can be treated as flexible rotors with large aspect ratio.At high speed,slight eccentricity will cause the rotor to vibrate violently.Therefore,the equipment often needs to go through strict dynamic balance before installing.However,in the long-term operation process,the load change,deformation,corrosion and other conditions of the equipment will cause new random unbalance of the rotor.In this paper,the ball dynamic balance technology of flexible rotor with large aspect ratio is studied,mainly includes rigid rotor with elastic bearing and flexible rotor.When the speed is higher than the critical speed of the rotor,the free-moving ball in the balancer will automatically move to the opposite side of rotor eccentricity under the action of centrifugal force,so as to greatly reduce or completely offset the influence of rotor imbalance.First of all,for the rigid rotor with elastic bearing,Lagrange equation is used to give the dynamic description of each component respectively,and the model of supporting force of rotor and damping force of the ball is established.Then the dynamic description of each component is assembled to get the system vibration model.Based on the balance relationship of spatial force system,the amplitude frequency and phase frequency curve equation of two-disk rotor are derived,its "self centering" phenomenon is pointed out,and the driving force source of its ball dynamic balance is analyzed.For one-disk rotor,the motion law of rotor axis is studied,and the vibration suppression mechanism of ball dynamic balance is analyzed.In addition,in order to discuss the stability and dynamic response of the rotor system,the above the rigid rotor with elastic bearing vibration model is transformed into an autonomous system by using the rotation coordinate transformation.The equilibrium solution constraint equation and its composition are discussed.According to the bifurcation theory,the stability of the rotor system is analyzed by using the bifurcation software AUTO,and the distribution of the stable interval is obtained.The bifurcation results are verified by numerical simulation.When the eccentric mass is in different phases of the rotor,the steady-state response and the transient response of the rotor system are studied under two conditions: with or without the ball balancer.The rolling resistance is introduced to discuss the influence of the rolling resistance on the dynamic response of the rotor system under different initial positions of the balance ball and different rotating speeds.After that,for the dynamic balance problem of the flexible rotor with ball balancer,based on the finite element method,the mass matrix,stiffness matrix,damping matrix and gyro matrix of the shaft element are established by using Timoshenko beam theory.Then,the rigid flexible coupling model of the flexible rotor with ball balancers is established by coupling with other rigid component models.? implicit iterative algorithm is introduced to solve the problem.The vibration suppression characteristics of the spherical balancer are studied by numerical simulation.Finally,in order to verify the theoretical results of the paper,a rigid rotor with elastic bearing and two ball balancers experiment platform was built.The movement track and steady position of the balance balls are studied under different rotating speeds and different eccentric mass phases by using high-speed camera.