Periodic stresses are always imposed on a rotor, and thus, a crack due to fatigue is unavoidable. Machinery must be properly diagnosed to avoid tragic accidents. Vibration detection is the most important tool for such a diagnosis system. It is important to know the vibration characteristics of a cracked rotor in order to develop a monitoring system which can detect a crack in an early stage of propagation. In this study, to explore the crack breathing mechanism, a three-dimensional finite element model is simulated by using a commercial analysis solver-Abaqus/Standard. A two-disc rotor system with a slant crack is used under the coupling effect of rotor weight and unbalance force. Unlike crack breathing under rotor weight-only, a crack opens and closes differently under the effects of unbalance forces. Crack breathing depends on its location along the length of the shaft and individual parameters of the rotor system. A few crack locations are recognised along shaft length where the crack may stay fully closed or open during shaft rotation under certain loading circumstances. These locations also split the shaft into different areas based on the orientation of the unbalance force, crack size and location, where shaft stiffness may be higher or lower. Presented findings indicate that predicting the dynamic response of cracked rotors can be anticipated much accurately. Therefore, the impacts of unbalance forces and individual rotor physical characteristics on crack breathing must be taking into consideration.
The dependence of crack breathing behaviors on the crack location was investigated under the effect of unbalanced force. A parameter known as the effectual bending angle is introduced to describe the nonlinear relationship between crack direction and bending direction for balanced and unbalanced shafts along the shaft length. The breathing behavior of cracks was visualized by examining the duration of each crack status (open, closed, and partially open/closed) during a full shaft rotation. It is shown that a crack in an unbalanced shaft has more breathing patterns than a crack in a balanced shaft, including a single status (fully open/never closed or fully closed/never open) and dual statuses. Two pairs of interesting locations along the shaft length were identified, where the crack shows specific breathing behaviors. Further, the angular range, during which a crack remains fully closed, partially open/closed, or fully open, changes significantly with the crack location. The analytical model developed in this work can be further utilized to obtain the time-varying stiffness matrix of the cracked shaft element under the influence of unbalanced force.
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