Vibration and stability of a rotating shaft containing a transverse crack

The dynamic response of a rotating shaft containing a transverse crack is investigated. The local flexibility due to the crack is first evaluated from the theory of fracture mechanics. The energy principle in conjunction with the assumed mode method yields the discretized equations of motion; these are time-varying with periodic coefficients due to the breathing effect. The steady state responses and the stability criteria are then obtained, and the effects of crack depth, crack location and rotational speed are discussed. The results show that an increase of crack depth magnifies the response amplitude as expected. It is discovered that the crack affects the dynamic response more significantly when it occurs near a place where the bending moment exhibits a larger value. From the FFT analysis of the displacement responses, it is seen that the 1Ω and 2Ω components are excited prominently due to crack. Hence they provide possibly good indices for an on-line crack monitoring system. The stability of a cracked shaft is examined via the Floquet theory, and the results show that, for an undamped shaft, instability occurs as rotation is close to an integer fraction or an integer multiple of the shaft bending frequency when the crack depth reaches half of the radius. However, a small amount of damping is found to raise effectively the unstable region.