Nonlinear Aeroelastic Stability Analysis Of Rotating Shrouded Blades

The harsh working environment of blades in high-speed rotating machineries such as aero-engines and gas turbines,coupled with the nonlinear factors in structure and gas,lead to the outstanding nonlinear aeroelasticity of the blades.The blade flutter instability will occur under the aerodynamic force,and the centrifugal force and collision force on the rotating shrouded blade have an important influence on the flutter of the blade.At present,the research on the aerodynamic elasticity under the combined action of centrifugal force and aerodynamic force is not sufficient.Therefore,the study of nonlinear aeroelastic stability of rotating shrouded blades has become the key problems in this thesis.In this paper,based on the previous scholars' researches,the nonlinear aeroelastic characteristics of rotating shrouded blades are studied,and the stability of the system is studied from the theoretical and numerical simulation.The main contents can be divided into the following aspects:1.The shrouded blade of high speed rotating is simplified as an Euler-Bernoulli thin-walled beam model with the end mass attached to the rigid rotating hub.Considering the variable speed and the geometric nonlinear factors of large deformation,the aerodynamic force and aerodynamic torque of the blade are obtained by using the first order piston theory,and the blade is subjected to bending and twisting deformation.The nonlinear dynamic equations of the two degree of freedom coupling of a high speed rotating blade with two degrees of freedom is established by using the Hamilton principle.2.The four order Runge-Kutta method is used to calculate the nonlinear dynamic equation of the shrouded blades.By means of the eigenvalue theory,the rotational angular velocity of the flutter of the shrouded blades is calculated,and the corresponding time history and phase diagrams are obtained.At the same time,the influence of the related structural parameters of the blade on the flutter speed is analyzed.It is found that the mass and its position have a certain influence on the flutter speed of the shrouded blades.3.The limit cycle response of a shrouded blades is analyzed by the harmonic balance method.The analytic solution corresponding to the equation is obtained by the harmonic balance method.The results show that the Hopf bifurcation will occur with the change of the speed.At the same time,the results are compared with the numerical results,and the results are consistent with the results of the two methods.The effect of mass on the response of the limit cycle of the blade is discussed.4.Through Solidworks,a cantilever beam model with mass is established,which is imported into ANSYS Workbench for modal analysis to get the natural frequencies and mode shapes at different rotational speeds.From the Campbell diagram,it is found that the natural frequency is changed as the speed increases.At the same time,the modal under the rotating prestress and the unidirectional fluid structure coupling are analyzed,and the natural frequency is larger than that under the static state.5.Considering the collision between the shrouded blades,the collision force model is established,and the dynamic equation of the collision with shrouded blades is introduced.The analytical solution of the equation is obtained by the harmonic balance method,and the response characteristics of the shrouded blades under different parameters are analyzed.In this paper,the nonlinear aeroelastic response characteristics of shrouded blades considering bending-torsional coupling motion are analyzed comprehensively,which is of guiding significance for the design and optimization of shrouded blades.