| Silicon micromachined gyroscope (SMG) is a MEMS inertial device which senses angular rate of the object by the Coriolis effect. The sensitive structure and measurement circuit can be integrated into a single chip. It has an extensive application prospect in both military and civilian fileds for its advantages such as low cost, small size, light weight and low power consumption. Thus the SMG has been in rapid development since 1990s, and become increasingly attractive in national defense applications all over the world.Sensitive structure is the core component of SMG, which is directly related to the scale factor, zero bias and performance of vibration resistance. In this dissertation, the research is based on the dual-mass vibrating SMG which is designed by our research group. The theoretical model of stiffness matrix, multi-mode eigenfrequencies, quadrature error and damping characteristic of the sensitive structure are established, and the analytical results could provide practical guidance and theoretical basis for design and optimization of the high performance SMG.Firstly, the signal conversion mechanism of SMG and the basic theories of sensitive structure are studied. The relationship between output signal of SMG and key parameters of sensitive structure is set up, so the importance of theoretical research on sensitive structure is illustrated. The support system and low-frequency modes of sensitive structure is introduced, and the impact mechanism of parasitic modes on the performance of SMG is analyzed. The elastic theorem is used to establish the stiffness formulas of the drive beam. Then the formulas are validated by the Finite Element Method (FEM) simulations, and the stiffness matrix of sensitive structure is set up. The energy dissipation mechanism of sensitive structure is analyzed, and the vacuum packaging method is described, Then the experimental results of quality factor are given.Secondly, the dynamic eigenfrequencies of multi-mode are studied. The sensitive structure is seen as a multi-mode system, and the equivalent models of low-frequency modes are set up. The energy theorem is used to analyze the modal stiffness of the low-frequency modes. The model of dynamic eigenfrequencies of multi-mode is established. Then the analytical results are validated by the FEM simulations and the experiments. The largest analytical errors with respect to simulation and experiment are 8.63% and 10.56%, respectively. The mode design principles are presented, and the established model is used for the mode ordering.Thirdly, the quadrature error of sensitive structure is studied. The stiffness matrix with the machining error is set up. On this basis, the theoretical model of the quadrature error is established. The value range of the direct coupling coefficient is 4.74×10-5～2.33×10-4 and the value range of the second-order coupling coefficient is 8.44×10-7～2.03×10-5. Meanwhile, the analysis indicates the maximum value of the quadrature coupling coefficient is 9.35×10-4. And the accuracy of the calculating result is confirmed by the simulation. According to the theoretical model, a suppression method for the quadrature error based on the reasonable design of drive beam is proposed. The value range of quadrature error obtained by the experiment is 1.08×10-4～4.13×10-4.Fourthly, the damping characteristic of sensitive structure is studied. The thermoelastic coupling equations are solved, and the complex frequency model of thermoelastic damping (TED) is built. The theoretical result of TED is 9.19×10-6, and the analytical error with respect to simulation is 1.88%. According to the performance indicators of SMG, the design requirement of quality factor is proposed. And the design roadmap about the width of drive beam and the eigenfrequency of drive mode is presented. Then the temperature characteristic of TED is studied, and the temperature coefficient of TED is 9.76×10-3/℃ at normal temperature. The analytical errors with respect to simulation and experiment are 2.01% and 7.50%, respectively.Finally, the key parameters of the optimized sensitive structure are simulated and tested, and the validity and rationality of the optimization are verified. According to the IEEE testing standards for gyroscope, the performance of SMG is tested. The result shows that, the scale factor is 8193.77LSB/°/s, and the zero bias stability and repeatability are 4.54°/h and 6.14°/h respectively.
|
PDF Full Text Request