Transient response and breathing behaviour of a cracked Jeffcott rotor

Abstract

In this paper, a cracked Jeffcott rotor is analyzed as it passes through its critical speed and subharmonic resonances. Three different crack models are studied, namely, a breathing crack model, a switching crack model and an open crack model. The breathing crack model which closely imitates the breathing behaviour of a real crack in a rotor is studied in detail as the rotor is accelerated or decelerated past the critical speed. It is shown that the breathing behaviour and the peak response are strongly influenced by the unbalance orientation angle relative to the crack direction. The effect of acceleration rate, crack depth and damping on the breathing behaviour is analysed in this study. The effects of these parameters on breathing behaviour have not been reported earlier. Due to the accurate breathing model considered in this study, the breathing behaviour obtained is closer to reality compared to that reported in previous studies. For most values of unbalance orientation angle the breathing crack model predicts a larger response compared to the switching crack model which was used earlier in literature. The presence of higher harmonics in the response causes subharmonic resonances during coasting-up of the accelerating rotor. At these subharmonic resonances, amplitudes of the higher harmonic components have been found to be stronger in the horizontal direction than in the vertical direction. It has also been observed that during passage through these subharmonic resonances the orientation of rotor orbit changes quite noticeably. Subsequently, the peak response variation as well as orbit orientation changes have been studied experimentally. The experimental findings validate most of the analytical results. It has been experimentally observed that for an unbalance phase in the range of 67.5–135°, decelerating slotted rotor gives higher response compared to accelerating rotor. The peak response variation is typical in case of slotted and cracked rotor that can be helpful in distinguishing asymmetric rotor from cracked rotor. The orbit orientation changes during passage through subharmonic resonances are also clearly seen in experimental investigation on cracked rotors, which can prove to be a convenient tool in crack diagnosis. The experimental observations also support the analytical results of stronger horizontal component of higher harmonics near the subharmonic resonances.