Investigations of Cylindrical and Conical Whirl Instabilities on Hydrodynamic Journal Bearings

Hydrodynamic journal bearings induced serious shaft vibrations called oil whirl. Since they often give severe damages to the mechanical systems, it is important to fully understand the phenomenon to avoid the occurrence by the proper bearing design. This study theoretically and experimentally investigated both cylindrical and conical whirl instabilities, which can be appeared in journal bearings, and their relation was discussed. As the result, the span length of the bearings had a significant effect on the vibration mode. The transitional state in which the cylindrical and conical whirl instabilities alternately appeared was observed.

On the stabilising effect of gyroscopic moments in an automotive turbocharger

Automotive turbochargers, which operate at very high speeds, exceeding 180,000 r/min, exhibit two strong sub-harmonic 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.

A Semi-Analytical Solution to the Dynamic Tracking of Non-contacting Gas Face Seals

The gas film stiffness and damping coefficients for a non-contacting gas face seal are obtained from the unsteady nonlinear Reynolds equation using the perturbation method. The seal assembly is converted to an equivalent spring-damper-mass system. The stator tracking motion is treated as a forced vibration caused by the rotor motion due to its runout and misalignment. The seal steady-state dynamic responses are solved semianalytically. Results for a typical spiral groove gas face seal agree well with that from a full numerical simulation. Stability of the seal axial pulsating and conical whirl are examined using the frequency dependent dynamic force and moment coefficients.

Forces and Moments Due to Combined Motion of Conical and Cylindrical Whirls for a Long Seal

The mutual interaction effects of cylindrical and conical whirl on the dynamic fluid forces and moments, which act on a long annular seal, were studied experimentally. A whirling motion composed of cylindrical and conical whirls is actuated by intentionally giving the phase difference between the seal exit and inlet whirling movements. This whirling motion is believed to generate during actual pump running. The experiment was conducted by changing the phase difference, at various rotor speeds and with a pressure difference between the seal inlet and exit. The result of this study revealed that fluid forces and moments are greatly dependent on the phase difference of the whirl, namely the long seal has a significant coupling between displacements and rotations. Furthermore, dynamic fluid forces and moments were derived theoretically, assuming that total fluid force acting on the rotor could be determined by superposing fluid forces due to conical and cylindrical whirling movements. It was confirmed that the experimental results moderately agree with the theoretical values, if the rotor and seal are set in concentric alignment, the principle of superposition becomes applicable.

Interrelated Rotordynamic Effects of Cylindrical and Conical Whirl of Annular Seal Rotors

A comprehensive approach for computing the dynamic coefficients of an annular seal is presented. The coefficients are partly those associated with a uniform lateral eccentricity mode of the rotor (known as the cylindrical whirl mode) and with an angular eccentricity (which gives rise to a conical whirl type). The rotor excitation effects in both cases are treated as interrelated by recognizing the fluid-exerted moments resulting from the lateral eccentricity and the net fluid force resulting from the angular eccentricity. In all cases, the rotor is assumed to undergo a whirling motion around the housing centerline. The computational procedure is a finite-element perturbation model in which the zeroth-order undisplaced-rotor flow solution in the clearance gap is obtained through a Petrov-Galerkin approach. Next, the rotor translational and angular eccentricities, considered to be infinitesimally small, are perceived to cause virtual distortions of varied magnitudes in the finite element assembly which occupies the clearance gap. Perturbations in the flow variables including, in particular, the rotor surface pressure, are then obtained by expanding the finite-element equations in terms of the rotor eccentricity components. The fluid-exerted forces and moments are in this case computed by integration over the rotor surface, and the full matrix of rotordynamic coefficients, in the end, obtained. The computational model is verified against a bulk-flow model for a sample case involving a straight annular seal. Choice of this sample model for validation was made on the basis that no other existing model has yet been expanded to account for the mutual interaction between the cylindrical and conical rotor whirl, which is under focus in this study.