Monolithic Cylindrical Fused Silica Resonators with High Q Factors

The cylindrical resonator gyroscope (CRG) is a typical Coriolis vibratory gyroscope whose performance is determined by the Q factor and frequency mismatch of the cylindrical resonator. Enhancing the Q factor is crucial for improving the rate sensitivity and noise performance of the CRG. In this paper, for the first time, a monolithic cylindrical fused silica resonator with a Q factor approaching 8 × 105 (ring-down time over 1 min) is reported. The resonator is made of fused silica with low internal friction and high isotropy, with a diameter of 25 mm and a center frequency of 3974.35 Hz. The structure of the resonator is first briefly introduced, and then the experimental non-contact characterization method is presented. In addition, the post-fabrication experimental procedure of Q factor improvement, including chemical and thermal treatment, is demonstrated. The Q factor improvement by both treatments is compared and the primary loss mechanism is analyzed. To the best of our knowledge, the work presented in this paper represents the highest reported Q factor for a cylindrical resonator. The proposed monolithic cylindrical fused silica resonator may enable high performance inertial sensing with standard manufacturing process and simple post-fabrication treatment

Design and Analysis of Extremely Low-Noise MEMS Gyroscopes for Navigation

Inertial measurement sensors that include three gyroscopes and three accelerometers are key elements of inertial navigation systems. Miniaturization of these sensors is desirable to achieve low manufacturing cost, high durability, low weight, small size, and low energy consumption. However, there is a tradeoff between miniaturization of inertial sensors and their performance. Developing all the necessary components for navigation using inertial sensors in a small volume requires major redesign and innovation in these sensors. The main goal of this research is to identify, analyze and optimize parameters that limit the performance of miniaturized inertial gyroscopes and provide comprehensive design guidelines for achieving multi-axis navigation-grade MEMS gyroscopes. It is shown that the fundamental performance limit of inertial gyroscopes is angle random walk (ARW) due to thermo-mechanical and electronic noises. Theoretical models show that resonant frequency, frequency mismatch between sensing and driving modes, effective mass, quality factor (Q), driving amplitude, sensing gap, sensing area and angular gain are the most important parameters that need to be optimized for best noise and most practical device design. In this research, two different structures are considered for low-noise MEMS gyroscopes: 1) shell gyroscopes in yaw direction, and 2) a novel super sensitive stacked (S3) gyroscope for pitch/roll directions. Extensive analytical and FEM numerical modeling was conducted throughout this research to investigate the mechanisms that affect Q and noise in shell resonators used in yaw-rate gyroscopes. These models provided insight into ways to significantly improve resonator design, structure, fabrication, and assembly and helped fabricate fused silica shells with Qs as high as 10 million (at least an order of magnitude larger than other similar shells). Noise performance of these fused silica shell gyroscopes with 5 mm dimeter improved by about two orders of magnitude (< 5×10-3 °/√hr), representing one of the best noise performances reported for a MEMS gyroscope. To build a high-performance MEMS-based planar vibratory pitch/roll gyroscope, it is critical to have a resonator with high Q in the out-of-plane resonant mode. Existing out-of-plane resonators suffer from low Q due to anchor loss or/and thermoelastic dissipation (TED). Increasing the thickness of the out-of-plane resonator reduces TED, but this increases the anchor loss. To reduce anchor loss significantly, a novel structure called S3 is designed. In this structure, two similar resonators are stacked on top of each other and move in opposite directions, thus providing a balanced stacked resonator with reduced anchor loss. The reduction of anchor loss allows larger thickness of silicon S3 gyroscopes, leading to a very low TED. A large-scale model of a stacked balanced resonator is fabricated and tested. The initial results show more than 50 times improvement in Q (measured in air) when resonators are stacked. It is expected that by testing this device in vacuum, Q would improve by more than three orders of magnitude. The S3 design also has an extremely large effective mass, a very large angular gain, a large driving amplitude, a very small sensing gap, and a large sensing area. It is estimated that a 500 µm thick silicon S3 gyroscope provides ARW of about 1.5×10-5 °/√hr (more than two orders of magnitude better performance than a navigation-grade gyroscope). This extraordinary small value can be improved for 1mm thick fused silica to 7.6×10-7 °/√hr if the technology for etching fused silica could be developed in the future.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147701/1/darvishi_1.pd