Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro Gas Journal Bearing Dynamic Behavior

The high-speed micro hydrostatic gas journal bearings used in the high-power density MIT micro-engines are of very low aspect ratio with an L/D of less than 0.1 and are running at surface speeds of order 500 m/s. These ultra-short high-speed bearings exhibit whirl instability limits and a dynamic behavior much different from conventional hydrostatic gas bearings. The design space for stable high-speed operation is confined to a narrow region and involves singular behavior (Spakovszky and Liu (2003)). This together with the limits on achievable fabrication tolerance that can be achieved in the silicon chip manufacturing technology severely affects bearing operability and limits the maximum achievable speeds of the micro turbomachinery. This paper introduces a novel variation of the axial-flow hydrostatic micro-gas journal bearing concept which yields anisotropy in bearing stiffness. By departing from axial symmetry and introducing biaxial symmetry in hydrostatic stiffness, the bearing’s top speed is increased and fabrication tolerance requirements are substantially relieved making more feasible extended stable high-speed bearing operation. The objectives of this work are: (1) to characterize the underlying physical mechanisms and the dynamic behavior of this novel bearing concept, and (2) to report on the design, implementation and test of this new micro-bearing technology. The technical approach involves the combination of numerical simulations, experiment, and simple, first principles based modeling of the gas bearing flow field and the rotordynamics. A simple description of the whirl instability threshold with stiffness anisotropy is derived explaining the instability mechanisms and linking the governing parameters to the whirl ratio and stability limit. An existing analytical hydrostatic gas bearing model is extended and modified to guide the bearing design with stiffness anisotropy. Numerical simulations of the full non-linear governing equations are conducted to validate the theory and the novel bearing concept. Experimental results obtained from a micro-bearing test device are presented and show good agreement between the theory and the measurements. The theoretical increase in achievable bearing top speed and the relief in fabrication tolerance requirements due to stiffness anisotropy are quantified and important design implications and guidelines for micro gas journal bearings are discussed.