Design Optimization of Linear-Arm Flexure Bearings

Abstract

Flexure bearings have been used in linear-resonant compressors to maintain a non-contacting clearance seal between the piston and cylinder. This paper examines the linear-arm flexure bearing which was recently introduced. Linear-arm flexures have a higher radial stiffness and a higher radial-to-axial stiffness ratio than the spiral-arm flexures which are commonly used. Finite element analysis was used to study a wide range of linear-arm flexure sizes and materials. From this modeling, design graphs have been developed to assist in early compressor design stages and to provide the initial geometry for a more detailed finite element analysis. For a given stroke, diameter, stress, and Young’s modulus, the optimized material thickness and flexure arm geometry can be determined to maximize the radial stiffness. The radial stiffness, radial-to-axial stiffness ratio, and axial rotation can then be closely approximated from the design graphs presented here. A range of stroke-to-diameter ratios up to 0.2 was analyzed. A linear-arm flexure bearing was fabricated, and the measured stiffness agreed with that calculated by the finite element model to within 12%.