Axial-bending coupling vibration characteristics of a rotating blade with breathing crack

Blade crack is one of the most common blade failures of rotating machines which may lead to catastrophic accidents. Although many nonlinear vibrations of breathing crack have been investigated, there are few reports on the axial-bending coupling vibration caused by crack. With the aim of providing physical insight into the mechanisms of axis-bending coupling due to crack, a novel axial-bending coupled breathing crack model (ABCBCM) for the rotating blade is proposed in this study. The proposed ABCBCM is analytically formulated based on the Timoshenko beam theory and Castigliano's principle, and validated by comparing the natural and dynamic characteristics with the finite element model (FEM) and experimental tests. In addition, the effects of boundary conditions (rotational speed), crack parameters (crack depth and crack location) and loading conditions (excitation load) on the vibration characteristics of the cracked blade are investigated. The results indicate that the blade axial response is more sensitive to the nonlinearity caused by the breathing crack than the bending response; the axial-bending coupling caused by the crack changes the equilibrium position of the axial and bending displacement; the phase portrait of axial response and the orbit of axial-bending displacement are effective methods to detect breathing crack; and the axial displacement amplitude ratio and the axial acceleration amplitude ratio also are valuable indicators to estimate the severity of the blade crack. The proposed model can provide valuable insights for fault diagnosis and safety monitoring of cracked blade.