Stability-optimized clearance configuration of fluid-film journal bearings

A clearance configuration of fluid-film journal bearings is optimized in a sense of enhancing the stability of a full circular bearing at high rotational speeds. A performance index is chosen as the sum of the squared whirl-frequency ratios over a wide range of eccentricity ratios, and a Fourier series is used to represent an arbitrary configuration of fluid-film bearings. An optimization problem is then formulated to find the Fourier coefficients to minimize the index. The whirl-frequency ratio is inversely proportional to the stability threshold speeds of a Jeffcott rotor. The short bearing approximation is used to simplify a mathematical model that describes a pressure distribution developed in a fluid-film bearing. The designed bearing cannot destabilize the Jeffcott rotor at any high rotating speed subject to the short-bearing assumption and significantly reduces the size of the unstable region for a finite-length bearing with a small length-to-diameter ratio.