Design and characterization of tunable stiffness flexural bearings

Abstract

Compressed flexures have a downwards-tunable stiffness in their compliant directions; their stiffness can theoretically be reduced by up to four orders of magnitude. The compression-stiffiness relation is linear for most of the loading, and this behavior can be taken advantage of to use the flexure as a tunable spring, opening up new design possibilities. Compressed flexures present the possibility of developing more sensitive flexure-based instruments such as accelerometers. The purpose of this research was to characterize the behavior of compressed flexures and develop guidelines for their design. Tradeoffs were assessed when substituting compressed flexures for conventional flexures and their suitability for use in a precision system. An experimental setup was designed and built to test a stage guided by four compressed flexure bearings. Compression was applied to the test flexures via a displacement input that was deamplified by a wedge pair to increase preload resolution. The motion in each of the stage's six degrees of freedom in response to flexure compression and in response to a voice coil actuator acting in the flexure's compliant direction was measured by seven capacitance probes arranged around the test stage, and a seventh capacitance probe measured the input displacement. With the experimental setup it was found that a stiffness reduction of a factor of 7 was possible. The magnitude of parasitic motions in the test stage were found to increase linearly with flexure compression. When being actuated in the compliant direction, parasitic motions were evident with magnitudes of the same order of magnitude as the sensor noise. Compressed flexures are highly sensitive to thermal variations; a 0.5 C temperature increase resulted in an 11% increase in stiffness. A model developed in this thesis predicts that deviations from column straightness of 2% of the flexure thickness limit the stiffness reduction to a factor of 1.2, while a deviation of 0.2% allows for a stiffness reduction of 10,000.