This paper presents a novel finite element elastohydrodynamic lubrication analysis appropriate for gas journal bearings under dynamic conditions. The method employs gas pressure as a state variable, and structural sleeve deformation is represented by a linear combination of pre-selected mode shapes obtained from a related eigenvalue problem. The method takes into account temporal variation of journal position and velocity, and second-order slip flow boundary effects are included at no additional computational cost. The formulation is subsequently applied to a particular example (flexible large-aspect ratio, high-speed, MEMS-scale journal microbearing), where it is shown that a judicious choice of structural sleeve elasticity can significantly improve bearing performance (as measured by pressure distribution and load capacity) when compared with results obtained using rigid bearing surfaces.

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