Analysis of vibration response during blade-casing rub events

Aiming at elastic blade-casing rub events, the motion differential equation of rotating blade, which is equivalent to a cantilever beam in the centrifugal load and the aerodynamic load, is established with Hamilton's principle. Moreover, the casing is equivalent to a mass-spring-damping model, considering its radial vibration. In some contact transient time, based on mechanical energy balance and the displacement relation between the blade and the casing, the representation model of the rub between the blade and the casing is deduced. The coupled vibration between them is discussed in the different working cases at this model. The results show that the vibration of casing can lead to unsteady motion of the blade and arouse the first order bending dynamic frequency. Improved stability can be obtained by increasing the mass of the casing, decreasing its stiffness, and increasing the rotating speed. Through analysis of the casing energy in the process of contact, more impact energy can be absorbed by decreasing the stiffness of the casing, which can lead to an increase of its vibration displacement.