Design and analysis of a low-power, low-frequency flexure pivot resonator using rotary comb drives

Abstract

This work presents the first electrical flexure pivot resonator that is driven and sensed by rotary comb drives. It was determined that the mechanical power consumption of a resonator scales with frequency to the power of three. Flexure pivot resonators are able to achieve good frequency stability and decent Q-factors at very low operating frequencies. As a result, an electrical variant of such a flexure pivot resonator could rival the power consumption of Quartz and MEMS resonators. An analytical model was derived for predicting the performance of such a resonator. The analytical model covers driving torque, motional resistance, mechanical power consumption, gravity-induced frequency errors, sensing signal, four damping mechanisms, and pull-in stability. Individual parts of the model were validated through simulations performed in COMSOL Multiphysics. A 64 Hz, rotary comb-driven design nicknamed Swallow is created, which is based on the already existing mechanical flexure pivot resonator designed by the company Flexous Mechanisms. Swallow is predicted to have a mechanical power consumption of 408.96 nW at atmospheric pressure with a Q factor of 28.64. Such a power consumption could already rival that of MEMS and quartz. Air damping is found to be the dominant loss mechanism. A supported assumption was therefore made that Swallow could reach a Q factor of at least 1000 in a vacuum, which would drop the mechanical power consumption to 11.77 nW, well below the power consumption of quartz and MEMS resonators. Gravimetric error results show the design having a frequency error of 152.39 parts per million (ppm) for gravity acting along the Y direction, exceeding the 100 ppm criterion set for this work. In other orientations, the error stays around 3.5 ppm. \\

Two scaled variants of Swallow operating at 183 and 237 Hz were designed and fabricated through a SOIMUMPs process. After analyzing the production results, it was discovered that the dies had collapsed onto the handle layer upon release, causing them to get stuck. Experimental testing was then performed on the resonator designed by Flexous Mechanisms, where the Q factor of the resonator was tested at varying air pressure levels. Results showed the quality factor constantly increasing as air pressure decreased. These results confirm that air damping is dominant. In the end, the report shows that the rotary comb-driven flexure pivot resonators are promising in terms of power consumption due to their low frequency. This work, however, fails to produce a working device onto which the lower power consumption claim can be experimentally validated.