| The blades of aero-engine always operate under the condition of high temperature,high pressure and high speed.In order to improve the engine performance and enhance the high thrust-weight ratio,the gap between the blade and the inner wall of the casing should be reduced as much as possible.However,too small clearance may causes the rubbing between the blade and the casing,which may generates excessive vibrations of the rotor or even results in the damage of the blade and the casing.It can bring about serious accidents.As two key parts of aero-engine,the performance of the blade and the casing is the significantly factor that affects the whole performance of aero-engine.Because of its simple structure and higher strength,cylindrical shell components are widely used in aero-engine casing as its main structural parts.The rotating blade-flexible casing is taken as the research object.Considering the influence of the stagger angle and the twisted angle,the rotating blade is simplified as cantilever pre-twisted beam model and cantilever pre-twisted plate model,respectively.The dynamic model of rotating blade is established based on Hamilton energy principle.Considering the influence of the flexibility of the casing during the rubbing process,the casing is simplified as a cylindrical shell model.Rayleigh-Ritz method is adopted based on Hamilton energy principle,and the dynamic model of the flexible casing is established through Scihmidt changes.Besides,the rubbing responses of the rotating blade-flexible casing are respectively analyzed based on the beam model and the plate model.The main research contents include as follows:(1)Based on Love shell theory,the cylindrical shell is modeled under the boundary conditions of simple-simple support.Then the cylindrical shell is modeled based on Sanders shell theory under the boundary conditions of the elastic support.And the accuracy of the analytical model is verified by comparison with the literature results and the finite element method.The natural characteristics of the cylindrical shell are analyzed under different boundary conditions,and the influences of boundary spring stiffness on the natural frequency of the cylindrical shells are discussed.(2)The static deformation characteristics of the cylindrical shells are studied under different supporting forms.The partition method is used to extend the response solving method of Sanders shells under the elastic constraint boundary.Then,the forced vibration responses of cylindrical shell are analyzed with proposed analytical method,and the results are verified by the finite element method.The influences among the frequency range selected by Rayleigh damping,the excitation frequency and the elastic supports on the response of the shell are analyzed,respectively.(3)Using the cylindrical shell model to simulate the casing,the rubbing dynamic model of the blade-flexible casing is established based on the cantilever pre-twisted beam model.The effects on the rubbing responses of the blade-casing are compared with the lumped mass point model and the analytical model of the cylindrical shell and the finite element model,respectively.Then the rubbing responses of the blade-casing are respectively analyzed under the fixed-free constraint and the elastic-elastic constraint.For the rubbing model with the elastic constraint,the influences of the blade speed,static misalignment,minimum clearance,casing thickness and spring stiffness on the rubbing responses are analyzed.(4)Based on the cantilever pre-twisted plate model,the rubbing dynamic model of the blade-flexible casing is established,comparing the blade-casing rubbing response by using the straight blade structure and the twisted shape blade structure with stagger angle.At the same time,a finite element model is established to verify the effectiveness of the established model.For the established model of cantilever plate blade and flexible casing with elastic constraint,the effects of the blade speed,blade thickness and support stiffness on the rubbing vibration response are discussed. |
