Influence of Electrostatic Force Nonlinearity on the Sensitivity Performance of a Tapered Beam Micro-Gyroscope Based on Frequency Modulation

Electrostatic force nonlinearity is widely present in MEMS systems, which could impact the system sensitivity performance. The Frequency modulation (FM) method is proposed as an ideal solution to solve the problem of environmental fluctuation stability. The effect of electrostatic force nonlinearity on the sensitivity performance of a class of FM micro-gyroscope is investigated. The micro-gyroscope consists of a tapered cantilever beam with a tip mass attached to the end. Considering the case of unequal width and thickness, the motion equations of the system are derived by applying Hamilton’s principle. The differential quadrature method (DQM) was used to analyze the micro-gyroscope’s static deflection, pull-in voltage, and natural frequency characteristics. We observed that from the onset of rotation, the natural frequencies of the drive and sense modes gradually split into a pair of natural frequencies that were far from each other. The FM method directly measures the angular velocity by tracking the frequency of the drive and sense modes. Then, based on the linear system, the reduced-order model was used to analyze the influence of the shape factor and DC voltage on the sensitivity performance. Most importantly, the nonlinear frequency of system was obtained using the invariant manifold method (IMM). The influence of electrostatic force nonlinearity on the performance of the FM micro-gyroscope was investigated. The results show that the different shape factors of width and thickness, as well as the different DC voltages along the drive and sense directions, break the symmetry of the micro-gyroscope and reduce the sensitivity of the system. The sensitivity has a non-linear trend with the rotation speed. The DC voltage is proportional to the electrostatic force nonlinearity coefficient. As the DC voltage gradually increases, the nonlinearity is enhanced, resulting in a significant decrease in the sensitivity of the micro-gyroscope. It is found that the negative shape factor (width and thickness gradually increase along the beam) can effectively restrain the influence of electrostatic force nonlinearity, and a larger dynamic detection range can be obtained.