Oil whip induces self-excited vibration in fluid-handling machines, and what is worse, it can cause self-excited reverse precessional full annular rub, known as "dry whip", which is a secondary phenomenon resulting from a primary cause, and may lead to a catastrophic failure of machines; that is, "coincidence of oil whip and dry whip" that occurs repeatedly with constant frequency and amplitude in small clearance cases. This paper presents a technique using an electromagnetic exciter (EE), that can raise the threshold of stability of a rotary machine and then eliminate the coincidence of oil whip and dry whip in the normal operational range. In addition, an experimental rotor rig, a general model of a rotor/beating system with an EE and corresponding governing motion equations, computation of stiffness supplied by the EE, design example, stability judged by root locus plots, and criterion for eliminating the coincidence of the oil whip and dry whip are constructed, derived and established. Experimental results demonstrate that the coincidence of oil whip and dry whip of the rotary machine can be removed effectively. These results can be used to diagnose rub and fluid-induced instability in this kind of rotary machine.