Most literatures in rotor dynamic analysis of instability caused by rubbing or contact between rotor and stator have used a simple Jeffcott rotor and studied the instability when a stationary vibration amplitude is greater than a clearance.However in many practical machines, a sudden unbalance, such as blade loss in turbine and discharge of sludge in a high speed centrifugal separator, may occur.It is well known that the transient vibration amplitudes will always be greater than stationary vibration amplitudes.This paper investigates the instability of a flexible rotor only as transient vibration amplitudes are greater than a clearance and stationary vibration amplitudes are less than the clearance.The studied rotor is an overhang rotor with an extremely large disc at the end and the rotor runs far above the rotors first critical speed.This is a typical case for a high speed centrifugal separator.