A mathematical model is developed for a real rotor/stator system with high degrees-of-freedoms, multiple disks, flexible bearing supports and couplings. The safe clearance level for coasting up of the rotor is calculated for a general high degree-of-freedom rotor/stator system. The harmful phenomena of dry friction whip, which is generally observable for simple 2 degree-of-freedom Jeffcott rotors in the absence of gravity only, can be proved to exist (in real rotor/stator systems) even in the presence of gravity for a wide range of clearance levels. In case of Jeffcott rotors, by fixing the clearance and increasing the rotor spin frequency, the response of the system follows the pattern: No rub - Forward Annular Rub (FAR) - Partial Forward Whirl (PFW) - Partial Backward Whirl (PBW) - dry whip (WHIP). In case of a real rotor/stator system, at certain frequencies, the system directly jumps to dry whip. The simulated results show a rich variety of system dynamics including FAR, PFW and WHIP in case of vertical rotors where the effect of gravity is neglected. For horizontal rotors, under the effect of gravity, the system response contains multi-harmonics, chaotic responses and multi-period vibrations. Based on these responses, a robust fault diagnosis strategy can be designed to identify the rubbing action in rotating machinery.