Research On Vibration Characteristics Of The Rotor System Based On Approximate Analytic Method

The stability and reliability of aeroengines affect the safety performance of aircrafts directly.At present,the aircraft accident caused by the vibration failure of the aeroengine rotor system accounts for about 70%.As the main supporting structure of the aeroengine rotor system,the nonlinearity generated during rolling bearing operation has a negligible effect on the vibration characteristics of the rotor system.Therefore,in order to improve the safety performance and operation stability of the aeroengine rotor system,the vibration characteristics of the rolling bearing rotor system were studied in this paper.Throughout the study of the bearing rotor system,the research contents and theoretical models are quite abundant,however,most of them are based on numerical methods,which only get stable solutions of the rotor system models.The evolution rules of its motion state can’t be analyzed in depth.Based on approximate analytic method,the bifurcation characteristics and instability evolution rules of the rotor system were determined by judging the stability of periodic solutions under different speeds in this paper.The main contents of this paper are as follows:According to the analysis of nonlinear characteristics of the rolling bearing,three factors mainly considered,flexibility vibration,Hertz contact and bearing clearance.Through the rolling bearing kinematics model and Hertz theory,the nonlinear bearing force produced in the operation process was obtained,which was replaced by the rotor system to analyze the overall vibration characteristics.In this paper,two degrees of freedom model of the rolling bearing rotor system was established,which regarded the bearing inner ring,shaft and disc as one.Using the Runge-Kutta variable step numerical method to solve the dynamic differential equation model,the vibration characteristics of the rotor system of the global bifurcation diagram was analyzed.Because of the different system parameters has great influence on the vibration characteristics of the rotor system,the research on system parameters sensitivity of response of the rotor system has been studied in this paper.Through the derivation and calculation of the sensitivity formula of the rolling bearing rotor system response with the change of variables,the conclusion was obtained that the main factors which had great influence on the vibration characteristics of the rotor system were radial clearance of the bearing,the eccentricity of the disc and the mass of the rotor.Solving the dynamic model of the rolling bearing rigid rotor system with two degrees of freedom and the finite element model of the rolling bearing rotor system considering the flexibility of the rotor and the gyroscopic moment of the disc based on the approximate analytical method HB-AFT.By comparing the simulation results with the related literature,the correctness of the calculation method and results in this paper was verified.In view of the existing singular point problems in the process of tracking the periodic solutions of the rotor system,the arc length continuation method is adopted by introducing a new arc length parameter.Combining the arc length continuation method with the Floquet stability theory,the stability of periodic solutions of the rolling bearing rotor system at each speed was obtained.Finally the frequency response curve which can reflected the vibration stability of the rotor system was painted.Thereby the global bifurcation of the rotor system are analyzed,through which the instability evolution rules has been studied.