Stiffness Tuning of Hemispherical Shell Resonator Based on Electrostatic Force Applied to Discrete Electrodes

This article describes a method for stiffness tuning (ST) of a hemispherical shell resonator (HSR) based on the electrostatic forces applied to discrete electrodes. The frequency splitting information generated by stiffness anisotropy in the HSR is identified, while the standing wave is functioning in the self-procession state. Following that, a tuning strategy based on the frequency splitting information is created to eliminate the frequency difference and quadrature component caused by frequency splitting. The nonlinearity of the electrodes influences the tuning process. The nonlinearity of the driving electrodes introduces errors at the eighth harmonic of the circumferential frequency, which has a major impact on tuning performance. The causes and effects of frequency splitting are examined. The tuning mechanism of electrostatic stiffness on frequency splitting is deduced, and the influence of electrode nonlinearity on ST is investigated. A method for tuning the stiffness of discrete electrodes is proposed. To validate the proposed method, simulations and tests are carried out. This method can generate the optimum ST scheme based on the frequency splitting parameters and finish the frequency tuning (FT) at the mHz level while maintaining high efficiency and precision. The frequency difference is lowered from 8.22 to 0.97 mHz after tuning, and quadrature component is reduced to 22.9% of its initial magnitude.