Research On Nonlinear Vibration Characteristics Of Rotating Shrouded Blades

As an important part of the aero-engine,the blade is subjected to high-speed impact from high-temperature gas during rotation,so the high-cycle fatigue often occurs.In order to make the rotating blade have higher reliability,engineering practice often uses the method of adding shroud to the blade.The contact vibration process of the shrouded blade is very complicated,and has typical nonlinear characteristics.Therefore,it is necessary to analyze the vibration damping mechanism of the single blade and the shrouded blade group,as well as to investigate the vibration response of the integrally shrouded circle blades.In this paper,the shrouded blades are taken as the research object.Based on EulerBernoulli beam theory and Timoshenko beam theory,the frequency equation and mode shape function of the elastic support beam whose root is constrained by spring and torsion spring are derived.The semi-analytical method is used to establish the dynamic model of single-blade,shrouded blade group and integrally shrouded circle blades.The shroud structure is equivalent to a nonlinear spring,and considering the damping effect and the shroud mass and a stick-slip friction model considering the variable normal load is introduced.The nonlinear vibration differential equations of the blades are established by using the Lagrangian equation and the Galerkin discrete method.Finally,from the perspective of vibration damping mechanism,the damping characteristics of the shroud and the vibration characteristics of the integrally shrouded circle blades are analyzed.This article mainly focuses on the following aspects:(1)Firstly,the semi-analytical method and the Euler-Bernoulli beam theory are used to establish the dynamic model of single shrouded blade with the boundary of fixed blade root.Based on the contact mechanics theory,the nonlinear contact force model and the stick-slip friction model considering the variable normal load are established,and the influence of the shroud mass is considered.Then,taking the rotational speed,contact angle,shroud clearance,friction coefficient and shroud position as the research parameters,the damping mechanism of the shroud is investigated from the perspective of amplitude frequency response,energy and force.(2)Secondly,the semi-analytical method and Euler-Bernoulli beam theory are used to establish the dynamic model of shrouded blade group with elastic support.The correctness of the elastic support beam model is verified.Based on the contact mechanics theory,the nonlinear contact force model and the stick-slip friction model considering the variable normal load are established,and the effects of installation angle and shroud mass are considered.Then,taking the rotating speed,contact angle,shroud clearance,shroud position and contact stiffness as the research parameters,the damping mechanism of the shroud is investigated from the perspective of amplitude frequency response,energy and force.(3)Finally,the semi-analytical method and Timoshenko beam theory are used to establish the dynamic model of the integrally shrouded circle blades with elastic support,and the correctness of the elastic beam model is verified.Based on the contact mechanics theory,the nonlinear contact force model considering the damping effect and the stick-slip friction model considering the variable normal load are established,and the effects of installation angle and shroud mass are considered.Then,taking the rotating speed,contact angle,contact stiffness,friction coefficient and shroud clearance as the research parameters,the the vibration response of the integrally shrouded circle blades are investigated under the aerodynamic excitation.