It has been known for many years that rotating machinery with hydrodynamic oil-film bearings can exhibit oil-whirl instability, where the unidirectional oil-film force acts on the rotor causing it to vibrate at a natural frequency. In this article, this phenomenon is investigated using two orthogonal coupled oscillators in which the bearing is modeled using short-bearing theory and an oscillating π oil-film to account for cavitation. It is found that at the point of instability, energy is extracted from the oil-film by one of the oscillators, and this energy is dissipated by the other one, such that there is no net energy gain or loss from the system. When the steady-state eccentricity ratio is such that the whirl frequency goes to zero, the oscillators effectively become undamped so that there is no energy exchange between them, and the system is stable.
Automotive turbochargers, which operate at very high speeds, exceeding 180,000 r/min, exhibit two strong subharmonic modes of vibrations due to oil-whirl instability. These are a conical mode and an in-phase whirl mode. The gyroscopic effects can be very important in such a rotor system. This article presents a theoretical investigation into these effects on the conical whirl instability of a turbocharger induced by the angular (tilting) motion of a rigid rotor. A simplified linear model is used to analyse the rotor-bearing system by investigating the effects of the gyroscopic moment on the internal moments. A gyroscopic coefficient, defined by the geometry of the rotor, is shown to govern the stability of the conical whirl motion. A threshold value of ½ is determined for this coefficient to suppress the conical whirl. This value remains unaffected if the rotor is asymmetric and is supported by floating ring bearings, which is the case in a practical turbocharger.
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