The Nonlinear Characteristic Research Of Rotor Systems With The Finite Element Incremental Transfer Matrix Method

The nonlinear dynamic characteristic of the rolling bearing,as the important supporting component in the aero-engine,exerts a strong influence on the stability and security of aircrafts,and can lead to complex dynamic responses,such as the hysteresis and jumps,super/sub-harmonic motions.In order to provide some reference for the optimization design of aero-engine as well as improve the stability performence,the mathematical model of the rolling bearing-complex rotor system,based on the high pressure rotor system of aero-enginges,is established in this article,and the nonlinear vibration characteristic is investugated.Among many techniques to obtain the vibration of nonlinear rotor systems,the efficient harmonic balance method(HBM)attracts attention of reseachers.However,the majority study focus on the low degree of freedom(DOF)systems,which are different from rotation machine used in engineering practice.Besides,existed HBM will cause considerable computational cost in the finite element model with a large of DOFs.Therefore,the finite element increment transfer matrix method(FE-ITM)is improved in this article,which is the combination of finite element metheod,transfer matrix method and the increment harmonic balance method.The periodic solution and stability,which is important in the analysis on nonlinear dynamics,of abundant DOFs systems can be obtained efficiently with this method.The main contents of this paper are as follows:(1)The FE-IHB method is improved,which can reduce the DOFs of systems and improve efficiency of calculation.The transfer matrix of beam,beam with disk,linear supporting and rolling bearing are established based on this method.In order to simplify the process in the analysis of complex systems and reduce the cumulative error in calculation,the global transfer matrix and Riccati matrix metheod are combined with the new transfer matrix.To obtain the complete solution branch,the incremental arc-length method is adopted,and the supplymentary equation is introduced.The method,with less calculation and simple process,of determining the periodic stability is provided.(2)The transfer matrix of the rolling bearing-rotor system with bifurcate structure is established based on the new method.The dynamic responses and solution branches at different bearing clearance,supporting stiffness,supporting damping are obtained,which reveal the relationship between vibration responses and parameters.The nonlinear behavior:quasi-periodic motion,contact resonance phenomen,bi-stability,hysteresis and jumps are observed and analyzed.(3)In order to solve the dynamic response of the rolling bearing-rotor system with unbalabnce fault.The multiple harmonic balance method is imbedded in FE-IHB,and the different types of transfer matrix are derived.The vibration responses of rotor system under multiple excitations,rotation frequency and time-varying compliance,are obtained,which are used to reveal the coupling relationship between two frequencies and the nature of nonlinear behavior.(4)The mathematical model of rolling bearing-rotor system with closed loop structure based on real rotor system test device is established,which takes the vibration of the base into consideration.The responses are solved with FE-IHB and verificated by test data.