A seesaw-lever force-balancing suspension design for space and terrestrial gravity-gradient sensing

Abstract

We present the design, fabrication, and characterization of a seesaw-lever force-balancing suspension for a silicon gravity-gradient sensor, a gravity gradiometer, that is capable of operation over a range of gravity from 0 to 1 g. This allows for both air and space deployment after ground validation. An overall rationale for designing a microelectromechanical systems(MEMS) gravity gradiometer is developed, indicating that a gravity gradiometer based on a torsion-balance, rather than a differential-accelerometer, provides the best approach. The fundamental micromachined element, a seesaw-lever force-balancing suspension, is designed with a low fundamental frequency for in-plane rotation to response gravity gradient but with good rejection of all cross-axis modes. During operation under 1 g, a gravitational force is axially loaded on two straight-beams that perform as a stiff fulcrum for the mass-connection lever without affecting sensitive in-plane rotational sensing. The dynamics of this suspension are analysed by both closed-form and finite element analysis, with good agreement between the two. The suspension has been fabricated using through-wafer deep reactive-ion etching and the dynamics verified both in air and vacuum. The sensitivity of a gravity gradiometer built around this suspension will be dominated by thermal noise, contributing in this case a noise floor of around 10 E/Hz−−−√10 E/Hz (1 E = 10−9/s2) in vacuum. Compared with previous conventional gravity gradiometers, this suspension allows a gradiometer of performance within an order of magnitude but greatly reduced volume and weight. Compared with previous MEMS gravity gradiometers, our design has the advantage of functionality under Earth gravity.