Extended Windage Loss Models for Gas Bearing Supported Spindles Operated in Dense Gases

Generic models are proposed to evaluate the skin friction coefficient acting on enclosed rotating disks and cylinders under various flow regimes. In particular, a model taking into account the inner radius of the disk is developed. The models are compared with experimental data obtained from coast-down tests of a high-speed spindle supported on gas lubricated bearings, operated in air and in halocarbon R245fa at various pressures. The windage losses are first computed considering state-of-the-art laminar flow loss models in the gas bearings and an experimentally validated laminar-turbulent flow loss model in the air gap. This reference approach predicts the air data with a good accuracy (deviation less than 5%) but underestimates the organic fluid data by up to 36%. This deviation is considerably reduced (max 6.8%) when applying the proposed multiflow regime loss model for enclosed rotating disks to the thrust bearing. Finally, the proposed laminar-turbulent flow loss model for enclosed rotating cylinders is simultaneously applied to the journal bearings and the air gap. A peak deviation of 6.5% is maintained among all test cases when setting the critical Taylor number to an artificial value (67) instead of the theoretical value (41.1) characterizing the onset of growth of Taylor vortices. Taking into account the uncertainties on the bearing clearances, as well as on the operating pressure and temperature, a ±10% agreement with the experimental data is obtained.