Vibration behavior of a two-crack shaft in a rotor disc-bearing system

The vibration response characteristics of a rotor disc-bearing system with one and two cracks are analytically investigated using a modified harmonic balance method. The analytical model is formulated considering rigid-short bearing supports to study the effects of cracks' characteristics such as depth, location and relative angular position on selected vibrational properties, namely, critical speeds, harmonic and super-harmonic components of the unbalance lateral response and the shaft center orbit. Each crack is initially described by a breathing function proposed by Mayes and Davies, which is subsequently modified as a softly-clipped cosine function to accurately describe saturation in breathing phenomenon. The response characteristics of the cracked shaft are also compared with those of the system with an intact shaft in order to identify potential measures for detecting cracks. The results show that the presence of a second crack emphasizes changes in the critical speeds of the rotor disc-bearing system, while relative angular position of the cracks influences the shaft center orbit. The validity of the proposed analytical model and the solution method is also investigated through simulations of a finite element model of the system.