A novel vibration modeling method for a rotating blade with breathing cracks

This paper proposes a vibration modeling method for a rotating blade with breathing cracks, considering the coupling of the centrifugal effects, the breathing effects and the crack effects. Firstly, considering the combined effects of the centrifugal stress and the bending stress, a crack breathing model for the rotating blade is proposed. Since the crack surface cannot provide the spanwise centrifugal tensile stress, an additional bending moment will be generated at the crack surface in the rotating state. Therefore, an additional bending moment caused by the centrifugal stress is then constructed. In addition, due to the discontinuity of the crack cross section, the additional stiffness caused by the centrifugal effects of the cracked blade will be smaller than that of the normal blade. Therefore, a correction coefficient of the centrifugal stiffness is built. Furthermore, based on the Lagrange equation and the assumed modal method, the vibration equation of the rotating blade with a breathing crack is established (RBC model), and a strategy is constructed for solving this vibration equation. Finally, taking the finite element model (FEM) as a reference, the vibration responses of the RBC model, the open crack model (OC) and the bilinear crack model (BC) are compared. The necessity of the RBC model is illustrated, and the accuracy of the RBC model is verified. The RBC model is a computationally efficient alternative to the finite element analysis for the rotating cracked blade. It can provide an important tool for the vibration modeling and the vibration analysis of the rotating shaft-disk-blade system with cracked blades.