Steady-state coupling vibration analysis of shaft–disk–blade system with blade crack

Rotating shaft–disk–blade (RSDB) system is one of the most important parts of turbomachinery, such as aero-engine, gas turbine and power plant. The coupling vibration of RSDB system with blade crack is vital for the blade health monitoring and crack detection of rotating blade. This study aims at addressing the dynamic modeling and steady-state coupling vibration mechanism of RSDB system with blade crack. First and foremost, on the basis of the stress state at crack section, an improved analytical breathing crack model (modified stress-based breathing crack model, MSBCM) for rotating blade is proposed. The validity of the proposed breathing crack model is verified by comparing the results obtained by MSBCM, finite element contact crack model and conventional analytical crack models. The comparative results suggest that MSBCM is of high fidelity and behaves best among the analytical crack models. Subsequently, a comprehensive dynamic model of the coupling vibration for RSDB system with blade crack is formulated on the basis of continuum beam theory and Lagrange equation. The shaft bending, shaft torsion, blade bending and blade radial deformation are comprehensively considered in this model. The validity of the proposed dynamic model is verified through comparison with finite element simulation and experimentation results. By introducing the proposed MSBCM, the dynamic coupling vibration model of the RSDB system with blade crack is formulated. At last, the steady-state coupling vibration mechanism of two typical structures for RSDB system is comprehensively investigated. It is suggested that the shaft torsional vibration is much more sensitive to blade crack than the shaft bending vibration be, which indicates that the vibration features of shaft torsional vibration may offer indicators for the presence of blade crack.