Increasing the driving amplitude could improve the sensitivity of silicon microgyroscope, which is the effective way to enhance the performance of gyroscope. However the large driving amplitude leads to the nonlinear effect. As a result, the resonance frequency is dependent with the driving amplitude, which influences the frequency stability of gyroscope. The equivalent model of driving beam is established, and the stiffness formulas of driving beam are derivated according to the large deflection theory. The linear stiffness of driving beam is 270.1N/m and the nonlinear stiffness is 3.237×108N/m3, which are 2.7% and 6.4% different from the simulative results. Harmonic balance method can be used to establish the relationship between driving amplitude and resonance frequency. The theoretical analysis results are carried out compared with the simulative analysis results. Also the impact of driving amplitude on resonance frequency is confirmed by experiment test. This paper is significant for improving the frequency stability, and provides a theoretical basis for optimizing the structure of gyroscope.
The proof mass of micromechanical silicon oscillating accelerometer is small in size and light in weight, which badly restricts the improvement of accelerometer sensitivity. So a method of using micro leverage mechanisms to amplify the inertia force is widely accepted. There are restraints existing in the input and output beam end of the leverage mechanism, and the whole structure is flexible body. Therefore the Card Theorem is adopted to deduce the theoretical formula of the leverage amplification factor. The finite element analysis (FEA) is conducted to verify the theoretical formula. Then optimize the leverage mechanics with the complex optimal method to get the reasonable design parameters of the leverage mechanism. Finally, another simulation is conducted to test the optimized result.
Nonlinearities of the resonator in silicon resonant accelerometer (SRA) limit the ultimate short term frequency stability. In SRA, this stability is a measure of the achievable resolution. This paper discusses the nonlinear vibration phenomenon of micro-resonator considering the impact of the entire structure of SRA and builds a model to calculate the micro-resonator nonlinear stiffness K3,eff of the SRA prototype. The dies of SRA were fabricated by Silicon on Insulator (SOI) process. The equivalent model of the micro-resonator is built and the analytical value of the elastic constraint stiffness Ka of micro-resonator is derived as 8.91×104 N/m. It is calculated that K3,eff is equal to 5×1011 N/m3,and as a comparison, the simulation result is 5.026×1011 N/m3. The error between them is 0.52%. The nonlinear vibration experiments show that the maximum error between the theoretical and experimental value of resonance frequency is 2.1%. The prediction for the nonlinear stiffness contributes to further research on nonlinear vibration of the resonant beam. The model in this paper could also provide guidance and reference for optimal design of SRA.
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