The Stability Of The Integrally Shrouded Blade With Contact-impact

For the turbine machinery system,friction and impact are the serious threats to the safe of blade system when the blade is failure.According to statistics,the vibration of the blade is one of the important factors that can threaten the safe operation of the rotating machines.Therefore,in order to ensure that large rotating machinery blade system can continuously work and operate in normal condition,how to improve the safety,running stability and reliability of the rotating machinery blades has become the focus of the researchers.As a novel design technique,while the machine rotates at a high-speed,the twist and torsion of Integrally Shrouded Blade(ISB)occurs and the shroud interfaces of adjacent blades get in touch with each other by the effect of centrifugal force.The advantages of ISB,such as consuming the vibration energy of blade,preventing the steam leakage and reducing the loss of the cross-flow at the top of leaf,is obvious.People are more interested in the influence of contact and collision to vibration characteristics and stability of blade,thus the structure of ISB has more and more attention of manufacturers and researchers.Many researchers and scholars have a thorough study on such vibration mechanism respectively in theory and experiment,the results provides an important theoretical guidance for the stable operation of the rotating machinery.So studying vibration mechanism of the blade caused by contact collision,optimizing the structure of the blade design and exploring the stability of the blade has very high research significance and engineering practical value.Therefore,it is necessary to understand the vibration characteristics of ISB.This work follows under:1.The contact-impact dynamic model of ISB is established.In this model,the ISB is modeled as cantilever beam,the Hertz contact force model is employed to describe the contact friction and impact between tips,and the effects of the mass inertial force and the gas excitation force are considered.2.The Galerkin method is employed to truncate the governing partial differential equations of ISB to ordinary differential equations.At the moment,the ordinary differential equations are reduced to the single degree of freedom system by taking the first-order model of cantilever beam.Modal equations were derived by the average method.In the process of the average calculation,the integrands of the integral without primitive function in the form of elementary function are expanded by 8 orders Taylor Formula,and the approximate expression of amplitude frequency relation of the blade vibration system is established.3.Finally by the average method we can get the approximate analytic solutions when 1/n sub-harmonic resonance and n super-harmonic resonance occur.By describing the amplitudefrequency curve,the nonlinear behavior of the sub-harmonic resonance and super-harmonic resonance is investigated by nonlinear dynamic theory.