Research On Oblique Collision Vibration Of Turbine Blades

The structure of integral shroud blade(ISB)is developed form blade with bulges on the tip.It is good for a smooth flow passage and less leaking airflow,so that a machine can own high efficiency.It has been used on many turbines for about 20 years.The collision vibration between ISBs is very complex,and the study of nonlinear dynamic behaviors,damping mechanism and damping effect about it are still unclear.So,it is meaningful to make a study on them.The conclusion is not only helpful in the designing of steam turbine with ISB,but also can be used for other turbo-machineries.It can provide a way to solving the key problem on independent design of ISB.The paper presents researching works and achievements form the follow pars:1.The paper made an introduction of mapping method,which applied to the oblique collision system.Various classic and non-classic bifurcation types,judge basis,differences were presented.The applicable range of hypothesis of instantaneous collision,direct impact and oblique impact were also discussed.2.Simplifying the ISB for spring-mass system,which has slope as collision surface,using the Coulomb friction model and selecting collision surface for the Poincare section,the paper studied the cyclical conditions of the mapping process and discussed the existence conditions of single collision for cycle n movement.One obtained the variation of eigenvalue,which acquired from the Jacobi matrix of mapping P at the fixed point,using the semi-analytical method.Research shows that the steady-state response of the oblique collision system appears a variety of classic bifurcation,such as period-doubling bifurcation,N-S bifurcation,static bifurcation and so on.3.The paper verified the stability of the single collision by numerical analysis,One did the calculation to get the bifurcation diagram,Poincare maps and phase portraits,Accordingly,revealed the pattern of influence of the different control parameters on the steady-state collision response.Period-doubling bifurcation makes the steady periodic collision vibration producing transformation between various types,Hopf bifurcation makes the periodic collision vibration entering chaos through almost periodic vibration,meanwhile,there still exist the non-classical bifurcations,such as jumping,collision suddenly disappeared,boundary crisis which the boundary crisis makes system directly into chaos.4.Basing on the Hamilton’s principle,the partial differential equations of the ISB which can be simplify as cantilever beam cantilever beam with concentrated mass at the free end were obtained.Taking Galerkin truncation and then selecting the two order formation for dimension reduction,the partial differential dynamic equations are changed to ordinary differential equations.Basing on the dynamics equation,one deduced the generalized impulse and momentum equations,and combining recovery coefficient equations,collision response were obtained.The bifurcation diagrams,Poincaré maps and Phase portraits are obtained by numerical analysis.Those diagrams reveal the pattern of influence of the external excitation frequency on the steady-state collision vibration response.In the same range of ω,the beams 1-2 and the beams 2-3 have the same stable responses.And the phase portraits show that the colliding times of middle beam is the sum of colliding times on both sides.5.In the process of contact,the normal contact forces are obtained by using linear spring and nonlinear damping models and tangential friction are described by using Coulomb frictions and tangential contact stiffness.The time histories of friction diagram reveals the begin-end moment and time of viscous movement;The root-mean-square and the mean square of amplitude for a given location of the middle beams are solved,the δ histories of are got and the of the best vibration attenuation is found.