Low order models for hybrid gas bearings

Abstract

A low order model was created to analyze a small scale gas bearing designed for the MIT microfabricated gas turbine engine. The journal has a diameter of 4.1 mm and is designed to spin at 2 million rpm. Due to microfabrication constraints, the bearing will have a very low length to diameter ratio (O(.1)) and a very large clearance to radius ratio (0(0.01)). As a result, the bearing lies outside the standard operating regime and stable operation is a challenge. The model presented in this paper is able to predict the bearing's behavior under hydrodynamic, hydrostatic and hybrid operation. The model is an application of Newton's second law of motion to the journal, after it has undergone a sudden perturbation from an assumed stable operating point. The equations include stiffness coefficients taken from a numerical simulation of the compressible Reynolds equation, and damping coefficients taken from a short width Full-Sommerfeld solution. The equations of motion are then modified, and rewritten in matrix form using variables relevant to the bearing literature. By studying the eigenvalues of the linear model, it is possible to determine at any operating point: 1) whether the journal can sustain stable operation, and 2) the whirling frequency of the journal. The model's results have been validated for hydrodynamic operation based on the Half-Sommerfeld and Full- Sommerfeld model coefficients. Analysis shows that the best way to operate the bearing is in a hybrid mode where the bearing relies on hydrostatics at low speeds and hydrodynamics at high speeds. However, in transitioning from hydrostatic to hydrodynamic operation, the model shows that the bearing is prone to instability problems and great care must be taken in the operating schedule.