Dynamic modeling of rotary blade crack with regard to three-dimensional tip clearance

Abstract

To investigate the dynamic characteristics of the three-dimensional blade tip clearance (3D-BTC) of rotary blade cracks, a novel dynamic model of the rotary blade crack with regard to the 3D-BTC is derived based on the Timoshenko beam theory. In this model, the modal shape functions of the blade are derived based on the transfer matrix method, and the axial and circumferential aerodynamic loads are introduced to better obtain the dynamic responses of the blade vibration. Then, a breathing crack model of the blade trailing edge crack is established by considering the coupling effects of the centrifugal stress, axial bending stress, and circumferential bending stress. The crack opening width is introduced into the breathing crack model to comprehensively depict the crack together with the crack depth and crack location. Moreover, a numerical calculation method for the 3D-BTC is proposed for the rotary blade with cracks. The dynamic model is validated by comparing it with the finite element model and the experiment. Finally, the effects of the blade trailing edge crack on the 3D-BTC are analyzed. The results show that the cracked blade's first-order natural frequency decreases with the crack depth increase, and it increases first and then decreases slightly when the crack location moves away from the blade root. The effects of crack opening width on the first-order natural frequency are relatively small due to its small size. In the meantime, the nonlinear damage indicators (NDIs) of the 3D-BTC are calculated. The results show that the NDIs can reflect the severity of the blade crack, and the proposed model can comprehensively analyze the effects of rotary blade crack on the 3D-BTC, which is beneficial for the diagnosis method for blade cracks based on the 3D-BTC.