Parametric instability of anisotropic rotor-bearing systems with a transverse crack

Abstract

The parametric excitations caused by the time-varying stiffness characteristics of breathing cracks are important sources of instability in cracked rotor systems. The anisotropy property of journal bearings may also affect the stability of rotor systems. These two factors were, however, seldom addressed simultaneously in available investigations. In this paper, the stability of an anisotropic rotor-bearing system with a transverse crack is discussed. The breathing crack is modeled as the time-varying area moments of inertia at the cracked element. The finite element model and the eight-coefficient model are employed for modeling the shaft and the journal bearings, respectively. An efficient method based on the Hill’s method is developed to compute the complex eigenvalues of the periodically time-varying system. On this basis, the stability of the system can be assessed by checking the real parts of eigenvalues. Finally, the dynamic stability of a cracked rotor-bearing system due to the anisotropy and the speed-dependent characteristics of bearings are discussed. Numerical results show that the stability of the rotor-bearing system can be significantly influenced by the two factors, and the different anisotropic patterns play different roles on the system’s stability. Besides, the speed-dependent characteristic can make the instability regions be narrowed due to the variation of the stiffness coefficients with the rotating speed.