Stability analysis on gas-lubricated bearing for high speed cryogenic turbo-expander

Abstract

Here, instead of using static characteristics of gas journal bearing such as the damping coefficients and the misalignment angle for stability analysis, a linear method is presented for studying the whirl stability of a rigid rotor supported on both cylindrical bearing and externally pressurized bearing. First, by using linearization method, the gas film forces can be represented as 8-coefficents, and they are calculated through perturbation method, the static performance is validated by published literature. Then, based on the Routh-Hurwitz criterion, the stability threshold is determined and graphically presented regarding several non-dimensional system parameters, which reflects the effects of both the eccentricity and supply pressure on the system’s linear stability. This effective and computationally cheap method of stability analysis is helpful for the prior design of gas bearing.

Lumped parameters models for the stability analysis of rotors supported on gas bearings

“…In The stability threshold obtained from the models are compared in table 2. The cylindrical and the conical motions are uncoupled in case the Coriolis terms are neglected and the system's geometry satisfies condition (10) or condition (11). In the first case there is perfect symmetry: distances l1 and l2 must coincide and the journal bearings must have the same geometry and the same radial film thickness (same air film coefficients):…”

“…It is thus demonstrated in which cases the full rotor model can be reduced: in case of complete symmetry (condition 10) or more in general according to condition (11). Of course, in case the system does not exactly satisfy such conditions but the asymmetry is small or condition (11) is almost satisfied, the two modes can be still studied separately, being the out-of-diagonal elements negligible. In the other cases, the full model is to be preferred as it better estimates the stability threshold.…”

“…The classical perturbation method and an extended perturbation procedure incorporating the foil compliance explicitly were developed in [10]. The linearization method was used in [11] to compute the gas film coefficients for a high speed cryogenic turboexpander and in [12] for a heat pump turbocompressor. An interesting analysis of tilting pads is given in [13].…”