Dynamic Modeling and Vibration Characterization of Cracked Rotor Based on Breathing Crack Function

The application of mathematical language to the periodic description of the change process of the breathing crack can more effectively restore the influence of the breathing crack on the vibration characteristics of the rotor. In this paper, the crack of the fixed structure rotor is parameterized, and a finite element mathematical model of the transverse breathing straight crack rotor is established based on the breathing crack function, and the finite element dynamics equations are deduced. The vibration characteristics of the rotor were analyzed by the harmonic balance method combined with specific boundary conditions, and the amplitude-frequency response characteristics of the rotor were extracted for different crack locations with different breathing crack depths. And through the cracked rotor dynamics test with known crack parameters, the frequency domain diagrams in transient state and the axial trajectory diagrams in steady state were obtained, which were compared with the theoretical calculation results in the previous paper to verify the validity of the constructed model. The results show that as the crack location approaches the rotor, the deeper the crack depth is, the more drastic is the decrease of the rotor first-order critical speed. The rotor system containing breathing cracks shows strong nonlinear characteristics, with more obvious displacement fluctuations at both 1/2 times the critical speed and 1/3 times the corresponding frequency of the critical speed.