Rubbing dynamic characteristics of the blisk-casing system with elastic supports

In order to simulate the rubbing dynamics of the multi-blades/flexible casing, the finite element model (FEM) of the blisk-oval casing system with elastic supports is established using the self-programmed beam-shell-spring hybrid elements in combination with two types of self-programmed interfacial coupling elements (ICEs). The rotating effects such as centrifugal stiffening, spin softening and Coriolis effects for the blade and gyroscopic effect for the disk are all included in the system. For improving the computational efficiency, a two-step hybrid Craig-Bampton method is utilized to build the reduced blisk model and one step reduction for the casing is sufficient. Corresponding accuracy is verified via the frequency convergence analysis. Then the central difference method in combination with the Lagrange multiplier method is applied to solve the rubbing dynamic responses of the reduced system under different rotating speeds and supporting stiffness. The results show that (1) the Craig-Bampton method is appropriate for reducing the number of dimensions and improving the computational efficiency under the premise of ensuring model accuracy; (2) the fundamental frequency in the vibration responses of the casing is the product of the rotating frequency of the blisk and the number of contact zone on the casing, and period-1 motion/chaotic motion indicates the equal/unequal and radially symmetric contact zones on the casing, respectively; (3) the effects of the casing supporting stiffness on the rubbing characteristics of the system are more significant than those of the blisk supporting stiffness, and the vibration responses of the casing relative to the blisk are more sensitive to the system state variations like the occurrence of the resonance.