Nonlinearity measurement for low-pressure encapsulated MEMS gyroscopes by transient response

To measure the nonlinear dynamic features of micromechanical gyroscopes, a non-parametric method based on Hilbert transform is proposed. Using a sequence of frequency stepping sinusoidal pulses as the excitation signal, a set of transient responses in the vicinity of the resonant frequency are obtained. The envelopes of the time-domain response signals are calculated by Hilbert transform. The location of the resonant frequency, as well as whether the gyroscope is working in linear or nonlinear region, can be approximately assessed from the waveform of the envelopes. In order to obtain the dynamic parameters of the gyroscope, a modified FREEVIB algorithm is designed for analyzing the free damped oscillation signals. The instantaneous amplitudes and instantaneous frequencies that extracted by Hilbert transform are further processed by singular spectrum analysis (SSA). Numerical simulation results indicate that the algorithm behaves better anti-noise performance and can be practically used for processing the experimentally sampled transient signals. Vibrating ring microgyroscopes are experimentally tested under different air pressure (10-100 Pa). From the largest response segment of the response sequences, qualification of the operation state, i.e. whether the gyroscope is working in the nonlinear region, is obtained from the envelope of the forced transient signal. Other parameters, including the Backbone, frequency response function (FRF) and Q-value curves, are calculated from the free damped oscillation signals. The results are in good agreement with those obtained by traditional frequency sweeping method.