Research On Dynamic Characteristics Of Rotating Blade-casing Rubbing Based On Semi-analytic Method

Rotating machinery has been widely used in aviation or aerospace fields.In the study of engine field,the clearance between blade tip of rotor machinery and inner casing is called blade tip-gap.In order to reduce weight,improve efficiency and pursue high thrust-weight ratio,the radial clearance between the blade tip and the casing should be as small as possible.The small blade-casing clearance can reduce the gas leakage,however,it will cause the increase of the possibility of blade-tip rubbing.The rubbing will lead to complicated vibration responses and short lives of blade and casing.The process of blade-casing rubbing is extremely complicated.Therefore the research on dynamic characteristics of rotating blade-casing is of great theoretical significance.In this paper,it mainly takes rotating blade-casing as research project.Based on Timoshenko beam and plate Theory,the dynamic model of rotating blade under multi-loads can be established using Hamilton’s principle and the Galerkin’s method.The blade-casing vibration characteristics with different external excitations are investigated.The effects of parameters of blade and casing on the rubbing-induced vibration responses during the run-up process,steady-state process and run-down process are also discussed.In this paper,the chief research contents are presented as follows:(1)Based on Timoshenko beam theory,a mathematical model of rotational twisted-shape cantilever beam is established using the Hamilton variation principle.The effects of the stagger and twist angles on the inherent characteristics of the twisted-shape cantilever blade are analyzed,and then compared with finite element results to verify the accuracy of the model.(2)On the basis of plate and shell vibration theory,the new model considered the influences of centrifugal stiffening,spin softening and Coriolis force,and the equations of motion of the rotational cantilever twisted-shape plate with the stagger angle are obtained using energy method.The cantilever twisted-shape plate model is also verified by comparing the natural characteristics with those acquired from finite element method.(3)Based on the rotational cantilever twisted-shape beam model and the rubbing force model of blade-casing,the rubbing model between blade and casing has been established.The rubbing responses have been acquired by numerical integration(Newmark-β)during the run-up process,steady-state process and run-down process.Through the analysis of the effects of rubbing excitation on resonance responses and the transient characters of rubbing during rotational process,the vibration laws have been summarized.(4)Based on the rotating twisted-shape plate model,considering the static angle-and radial-misalignments between the rotating axis of the blade and the casing center axis,a new rotating blade-casing rubbing model is presented.Point-and local-rubbings between the blade-tip and casing may occur under the action of the centrifugal force and aerodynamic force.In this paper,the vibration responses of the blade in the conditions of Point-and local-rubbings and lifting process are investigated.The vibration responses of blade under centrifugal force and aerodynamic load are analyzed.The effects of the stagger angle,twist angle,casing stiffness and some other parameters on the vibration responses of blade during the run-up process,steady-state process and run-down process are discussed.