关键词: 极坐标圆, 裂纹转子, 亚临界共振

Abstract: Based on the simple hinge crack model, the dynamic equation of a cracked rotor with initial deflection is modelled, in which the external excitations are derived from the crack, mass eccentricity and initial deflection. Transformed into dimensionless form, it can be applied to the vibration characteristic analysis of cracked rotor with different parameters at stationary, transient or nonlinear state. With Euler equation in analytical solution, the frequency components of the cracked rotor with initial deflection are compared with those without initial deflection, and the subcritical resonance is investigated. The polar circle diagram that is suitable for the vibration analysis of cracked rotor is defined, which can thoroughly demonstrate the amplitude change of vibration responses. By numerical simulation, the polar circles of different parameters are obtained, and the influence of the stiffness variation, mass eccentricity and eccentric angle, the initial deflection and orientation of initial deflection is investigated, which can provide the basis for the system optimization or vibration suppression. The analysis of corresponding axis orbit and spectrum verifies the validity and feasibility of the polar circle diagram.

Key words: Cracked rotor, Polar circle, Subcritical resonance