Vibration and Stability Analysis of a Bearing–Rotor System with Transverse Breathing Crack and Initial Bending

This paper focuses on the stability and nonlinear response of a bearing-rotor system affected by a transverse crack and initial bending which was thought to be part of an unbalance or had been neglected before. The differences of breathing functions for the transverse breathing crack caused by initial bending is presented here, and the calculation of time-varying finite elements stiffness matrix of the cracked shaft is improved by replacing traditional the approximate crack segment with an exact area. After establishing the dynamic model of the cracked rotor with initial bending, vibrational characteristics such as amplitude-speed diagram, frequency spectrogram and bifurcations are investigated in detail. The eigenvalues of the transition matrix are calculated and analyzed as an indicator of dynamic stability with the growths of crack depth and initial bending. Many differences are found between the two cases of dynamic response of rotor system by numerical simulation. The frequency change with the growth of initial bending is opposite to the change with the growth of crack depth, and the shapes of amplitude-speed also having great different features. Stable regions are reduced and extended laterally by initial bending. All these results obtained in this paper will contribute to identify the bending fault and assess the stability of the bearing-rotor systems.

On the Effects of a Shaft Crack Propagation on the Dynamic Behavior of a Steam Turbine

The symptoms of the propagation of shaft cracks in rotating machines, which can be brought out of the vibration data collected by condition monitoring systems, are often not very evident, especially when the crack depth is not very high. In fact, shaft cracks commonly propagate rather far from the cross-sections where the vibration probes have been mounted. At these measurement planes, the sensitivity of the machine dynamic behavior to the effects caused by a shaft crack can be fairly low. Therefore, it is very important to improve the capabilities of diagnostic techniques aimed at the early detection of shaft cracks. In this paper, the dynamic behavior of the cracked shaft of a HP-IP steam turbine is shown. The results of investigations on the influence of the periodic and non-periodic breathing of the crack on the rotor response, measured in different machine thermal states and at unusual cross-sections of the shaft, are shown and discussed.

The Vibration of a Transversely Cracked Rotor Supported by Anisotropic Journal Bearings with Speed-Dependent Characteristic

This paper presents the vibration of a transversely cracked rotor supported by anisotropic journal bearings, where the speed-dependent characteristic of bearing is considered. A 3D finite element model and the contact-based approach are employed for the shaft and crack. The governing differential equations of the whole cracked rotor-bearing system were obtained by synthesizing the equations of the cracked shaft, the breathing crack and the journal bearings. In order to solve the computational difficulties caused by the high dimensions of model, the free-interface complex component mode synthesis method (CMS) is employed to reduce the order of the model. On this basis, the eigenvalue and the steady-state forced response of the cracked rotor-bearing system are obtained by the Hill’s method. Finally, the effects of the anisotropic and speed-dependent characteristics of bearings on the vibration of the system are studied. Numerical results show that both the two characteristics can significantly affect the response of the system. The anisotropy in the bearing leads to the split of resonant peaks and influence the amplitudes of the peaks. The speed-dependent characteristic mainly affects the responses at the speeds close to the resonant regions, because the parametric excitation effect of the resonance region is greater than other speeds.

Elliptical Crack Identification in a Nonrotating Shaft

It is known that fatigue cracks are one of the most important problems of the mechanical components, since their propagation can cause severe loss, both personal and economic. So, it is essential to know deeply the behavior of the cracked element to have tools that allow predicting the breakage before it happens. The shafts are elements that are specially affected by the described problem, because they are subjected to alternative compression and tension stresses. This work presents, firstly, an analytical expression that allows determining the first four natural frequencies of bending vibration of a nonrotating cracked shaft, assumed as an Euler–Bernoulli beam, with circular cross section under pinned-pinned conditions, taking into account the elliptical shape of the crack. Second, once the direct problem is known, the inverse problem is approached. Genetic Algorithm technique has been used to estimate the crack parameters assuming known the natural frequencies of the cracked shaft.