Unsteady Flow and Dynamic Behavior of Ultrashort Lomakin Gas Bearings

Ultrashort microscale high-speed gas bearings exhibit a whirl instability limit and dynamic behavior much different from conventional hydrostatic gas bearings. In particular, the design space for a stable high-speed operation is confined to a narrow region and involves a singular behavior. The previously developed ultrashort gas bearing theory (Liu et al. (2005, “Hydrostatic Gas Journal Bearings for Micro-Turbomachinery,” ASME J. Vibr. Acoust., 127(2), pp. 157–164)) assumed fully developed flow in the journal bearing gap. There is experimental evidence that this assumption might not be fully applicable for the relatively short flow-through times in such bearings. This has an impact on the estimation of whirl instability onset, bearing operability and power requirements. In this paper, unsteady flow effects in the bearing gap are investigated with the goal to quantify their impact on the bearing dynamic behavior. It is shown that although three-dimensional flow calculations in the ultrashort journal bearing are necessary to quantify the onset of whirl instability, the underlying mechanisms can be qualitatively described by the impulsive starting of a Couette flow. Using this description, two time scales are identified that govern the journal bearing dynamic behavior: the viscous diffusion time and the axial flow-through time. Based on this, a reduced frequency parameter is introduced that determines the development of the flow field in the journal bearing and, together with bearing force models, yields a criterion for whirl instability onset. Detailed three-dimensional computational fluid dynamics calculations of the journal bearing flow have been conducted to assess the criterion. A singular behavior in whirl ratio as a function of the reduced frequency parameter is observed, verifying the refined stability criterion. Using high-fidelity flow calculations, the effects of unsteady journal bearing flow on whirl instability limit and bearing power loss are quantified, and design guidelines and implications on gas bearing modeling are discussed. The stability criterion is experimentally validated demonstrating repeatable, stable high-speed operation of a novel microbearing test device at whirl ratios of 35.