Making Precise Resonators for Mesoscale Vibratory Gyroscopes

NASA's Jet Propulsion Laboratory, Pasadena, California

An alternative approach to the design and fabrication of vibratory gyroscopes is founded on the use of fabrication techniques that yield best results in the mesoscopic size range, which is characterized by overall device dimensions of the order of a centimeter. This approach stands in contradistinction to prior approaches in (1) the macroscopic size range (the size range of conventional design and fabrication, characterized by overall device dimensions of many centimeters) and (2) the microscopic size range [the size range of microelectromechanical systems (MEMS), characterized by overall device dimensions of the order of a millimeter or less]. The mesoscale approach offers some of the advantage of the MEMS approach (sizes and power demands smaller than those of the macroscale approach) and some of the advantage of the macroscale approach (the possibility of achieving relative dimensional precision greater than that of the MEMS approach).

Relative dimensional precision is a major issue in the operation of a vibratory gyroscope. The heart of a vibratory gyroscope is a mechanical resonator that is required to have a specified symmetry in a plane orthogonal to the axis about which rotation is to be measured. If the resonator could be perfectly symmetrical, then in the absence of rotation, a free vibration of the resonator could remain fixed along any orientation relative to its housing; that is, the gyroscope could exhibit zero drift. In practice, manufacturing imprecision gives rise to some asymmetry in mass, flexural stiffness or dissipation, resulting in a slight drift or beating motion of an initial vibration pattern that cannot be distinguished from rotation.

In the mesoscale approach, one exploits the following concepts: For a given amount of dimensional error generated in manufacturing, the asymmetry and hence the rate-of-rotation drift of the gyroscope can be reduced by increasing the scale. The decrease in asymmetry also reduces coupling of vibrations to the external environment. Mechanical thermal noise and electronic measurement noise and drift can also be reduced by increasing the size of the resonator and its associated sensors. In the mesoscale approach, a resonator is fabricated from a silicon wafer. Central to the mesoscale approach is a combination of (1) precise polishing of both faces of the wafer to form parallel planar upper and lower resonator surfaces and (2) dry reactive- ion etching (DRIE) to remove material from the sides of the resonator perpendicular to the upper and lower surfaces.

An experimental resonator was designed and fabricated following the mesoscale approach. Its frequency split (the difference between the natural frequencies of its two nominal orthogonal vibration modes — a measure of its asymmetry) was so small as to be undetectable at a resonance quality factor (Q) of 105, as observed in operation in a nominal vacuum with residual pressure of 10–5 torr (1.3 × 10-3 Pa). Throughout intensive experimentation, it was observed that keeping the thickness of the wafer as nearly uniform as possible was the main requirement for keeping the frequency split small, whereas the frequency split was not much affected by the side-wall roughness resulting from DRIE.

This work was done by Eui-Hyeok Yang of Caltech for NASA's Jet Propulsion Laboratory. NPO-30431