Influence of crack nonlinear breathing behavior on critical speed of rotor

The general motion equations of a Jeffcott rotor with a transverse crack were developed for studying the influence of crack nonlinear breathing behavior due to whirling with the critical speed of the rotor, in which the complicated manner of the rotor's whirl was considered. With the new equations, the numerical results and analysis for the steady vibration response of the cracked rotor near the critical speed showed that the nonlinear breathing behavior not only can strengthen the stability of the rotor (compared with the opening cracked rotor), but also can reduce the vibration response in certain conditions (compared with the un-cracked rotor); the stable cracked rotor is similar to the un-cracked rotor, when the rotating speed coincides with the critical speed, the vibration response is the maximum and the center of gravity rotates about 90°; the critical speed is a function of the imbalance orientation angle, it varys between the natural frequencies of the rotor with crack opening and those with crack closing; the passage through critical speed experiment observations of a cracked rotor on a rotor test rig support the theoretical study results.