频率型微陀螺谐振子振动非线性特性的理论与实验研究

This project aims at optimizing the structure and the parameters of the resonator in the direct frequency output micro gyroscope. To this end, the nonlinear characteristics under different vibrating amplitudes, including small amplitude, the steady and transient time-varying parametrical excitement behavior, and the influencing rule of the coupling between the nonlinear vibration and the time-varying parametrical excitement of the resonator in the direct frequency output micro gyroscope will be investigated. Grasping the strating point of the thorough investigation of the resonator sensing mechanism of the micro gyroscope, and by a combined method of the analytical calculation based on weighted residual method and small parameter perturbation method, numerical simulation considering the practical working conditions and the experimental validation based on the synthetical testing analyzer, several investigations will be thoroughly performed. These investigations include the effect of the alternating loads, the environmental temperature, driving and detecting methods and the vibrating amplitudes on the nonlinear vibration of the resonator in the micro gyroscope, the critical vibrating amplitude guaranteeing the normal operation of the gyroscope, the stable areas under parametrical excitement, the measurement error of the gyroscope rising from the nonlinear vibration, the approximate solution of Mathieu-like function for engineering application, and the modelling of the nonlinear vibration with the consideration of the practical application of the micro gyroscope. These efforts of this project will provide the optimizing methods to decrease the measurement error of the direct frequency output micro gyroscope rising from the nonlinear vibration and to improve the dynamic response in the measuremment. These investigations will provide solid theoretical and experimental foundations for developing high performance direct frequency output micro gyroscope.

以频率型微陀螺谐振子结构和参数的优化设计为目标，研究频率型微陀螺谐振子在不同振幅（包括小振幅）下的非线性特性、在稳态及瞬态下的时变参数激励特性，以及振动非线性与时变参数激励的耦合影响规律。以对微陀螺谐振子敏感机理的系统深入研究为切入点，通过基于加权残值和小参数摄动法的解析分析、针对微陀螺实际工况下的数值仿真计算，以及基于综合测试分析仪器的模拟实验验证相结合的方式，深入研究交变载荷、环境温度、激励检测方式、振动幅度等对微陀螺谐振子的振动非线性特性的影响，以及保证陀螺正常工作的振幅阈值、参数激励的稳定性区域、振动非线性引起的陀螺测量误差、类Mathieu方程的工程应用近似解等关键问题，建立符合微陀螺实际应用特点的非线性振动模型。通过本项目的研究将给出减小频率型微陀螺振动非线性引起的测量误差，以及改善其实际测量过程动态响应的优化设方法，为研制高性能频率型微陀螺奠定坚实的理论与实验基础。

课题针对谐振式硅微机械陀螺非线性问题进行了研究，主要完成的研究工作如下：.（1）基于Euler-Bernoulli梁理论，建立了用于微陀螺的梁谐振子的振动方程，并归一化为Mathieu方程。在此基础上，以梁谐振子为研究对象，建立了谐振式微陀螺振非线性振动模型，并对被测角速率、以及谐振梁几何参数对非线性的影响进行了探讨。.（2）针对直接输出频率的谐振式微陀螺几何结构参数变化对其输出非线性的影响，创新性地采用等效模拟电路方法进行研究，分别采用龙格-库塔法和小参数摄动法验证模拟电路输出波形和频率变化的正确性，并对其解算误差进行了评估。.（3）针对频率型微陀螺实际应用情况，率先定量研究了微陀螺考虑阻尼情况下的动态响应，分析了阻尼对梁谐振子振动特性的影响，提出了补偿阻尼振动的方案。.（4）基于频率型微陀螺谐振子模拟电路模型，制作了基于FPGA的频率型微陀螺谐振子参数激励特性实验装置，可用于研究陀螺的非线性振动特性。.（5）设计了一种基于希尔伯特变换的陀螺信号解算方法，对其性能进行了仿真测试与分析。结果表明，该算法对于静态或缓变信号具有很好的解调精度。.（6）实现了基于模拟解析解的谐振式微陀螺信号解算，为传感器的理论设计提供了重要的理论基础与技术支持。