Modal Analysis And Nonlinear Coupled Vibration Dynamics Of A Rotating Blisk

In order to lighten the aircraft engine and improve its propulsion efficiency,many aero engines adopt the blisk structure comprising both the rotor disk and blades.Since the disk becomes thinner,the stiffness of the structure decreased apparently,which causes the occurrence of large amplitude vibration in the blisk.These nonlinear vibrations are harmful to the operation of aero engines.This paper focuses on the nonlinear coupled oscillations of a compressor blisk with the varying rotating speed under the supersonic gas flow.At first,the coupled vibration characteristics of the blisk with realistic geometric data is investigated utilizing the CFD and FEM softwares,in which the effects of the aerodynamic load and the centrifugal load are considered.According to the Campbell diagram,the most critical mode is attained.It is found that the mode shape of the fourth order in the blisk is the coupling of the disk torsional and blades first bending vibration.It is easy to lead to the vibration failure when large amplitude vibration of the fourth mode occur in the blisk.Thus,based on the critical mode,a lumped mass-spring blisk mechanical model is built.The accuracy of the model is verified by comparing its natural frequency and the resonant frequency in the modal analysis.The elastic nonlinearity,the aerodynamic wake excitation,the centrifugal force,and the perturbed angular speed due to the periodically varying air velocity are considered.Afterwards,the Hamiltonian principle and the discretization method are applied to obtain the nonlinear differential governing equations for the blisk.The case of 1:1 internal resonance and primary resonance in vibration of the fourth mode for the blisk is only analyzed.The nonlinear ordinary equations in the polar form is obtained by the method of multiple scales in order to study the frequency-response of the system.Numerical simulations are performed to study the nonlinear dynamic response of the blisk.Based on the frequency response curves,we give a detailed discussion on the contribution of factors including nonlinear elasticity and rotating speed to the steady-state nonlinear responses of the rotating blisk.Then the continual parameter model of the blisk is built and the nonlineardynamical equations are derived according to Hamilton principle,and the frequency-response characteristics of the system are studied through numerical approach.