Optimal design of piezoelectric micromachined modal gyroscope (PMMG) with modes matched: modal analysis

Piezoelectric micromachined modal gyroscope is a solid state inertial sensor, which uses a special mode of PZT block as the reference mode of the gyroscope conventionally. In the paper, another special mode is found, which can be used as the sensing mode, and modes matched concept for this piezoelectric modal gyroscope is firstly proposed. Through finite element modal analysis, the frequencies of reference mode and sensing mode are obtained as the length and width of PZT block is varied. Using fitting method, the empirical formulae of resonant frequencies with high goodness fit are induced. Based on the empirical formulae of resonant frequencies, the modes matched equations are induced. The resonance frequencies, kinetic energy ratios, original scale factors of gyroscope are compared to evaluate the mode quality. The results show that thicker is the PZT block, larger is the original scale factor of the gyroscope. When the thickness of PZT block is same, larger length will decrease the original scale factor. The original scale factor of the modes matched gyroscope has improved nearly 20 times better than that without modes matched. Given the thickness of PZT block, the length and width can be determined through modes matched condition. The analysis showed that the thicker of the PZT block is, the higher precision will be obtained. The modes matched condition also indicates that the thicker of the PZT block is, the condition of modes matched is more sensitive with the width. This makes the fabrication more difficult.