The nonlinear and transient vibration of a rotor,which dropped onto back-up bearings when its active magnetic bearings were out of order,was investigated.After strictly deriving its equations of motion and performing numerical simulations,the time-histories of rotating speed of the dropping rotor,and normal force at the rubbing contact point as well as the frequency spectrum of the vibration displacement of back-up bearings are fully analyzed.It is found that the strong and unsteady forced bending vibration of the unbalancced and damped rotor decelerating through its first bending vibtation of the unbalaned and damped rotor decelerating through its first critical speed as well as chattering at high frequencies caused by the non-linearity at the rubbing contact point between the journal and back-up bearings may lead to the catastrophic damage of the system.
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