无驱动微机械陀螺敏感元件模态分析

Modal analysis on sensing element of no-driven micromechanical gyro

鉴于常规微机械陀螺的驱动结构和检测结构往往需要进行频率匹配,造成带宽较窄,工艺复杂的问题,设计了一种新的微机械陀螺,安装于旋转飞行器上,利用飞行器的旋转获得角动量,敏感飞行器的偏航和俯仰横向角速度。由于没有驱动结构,所以结构简单,带宽较宽。首先基于这种巧妙的结构建立了敏感元件的振动方程。根据振动方程,扭转梁是影响质量振动模态和模态频率的关键,同时考虑到应力、残余应力的释放以及工作能力,扭转梁设计成横截面积为矩形的弧形梁,并对其抗扭刚度进行了解析推导和计算,从而确定了敏感元件的固有频率。接着利用有限元分析的方法,对其振动模态进行了仿真,仿真结果表明,敏感元件的第一模态是扭转振动,固有频率相对于解析结果的误差为9.86%。为了进一步验证,设计了静电驱动电容检测的方法,实验测试得到的谐振频率和解析值的相对误差为5.21%。仿真和实验结果与理论计算一致,表明扭转梁的设计是合理的,模态分析是正确的,而且为动态性能评估和结构优化提供了理论依据。

The driving structure and detecting structure of traditional micromechanical gyroscope usually require frequency matching, causing narrow bandwidth and complex process. To solve this problem, a novel micromechanical gyroscope was designed, which is mounted on rotating aircraft, obtains angular momentum by using aircraft spin, and senses yawing and pitching angular velocity. Being without driven structure, the gyro's structure is simple and with large bandwidth. Based on this new structure, the motion equation was established. According to the vibration equation, the torsional beam is the key to vibrating modal and modal frequency of sensing element. Meanwhile, considering the stress, the residual stress's release and the working ability, the torsional beam was designed to be a circular beam with rectangular cross-section, and the torsional stiffness is analytically derived and calculated to determine the natural frequency. Then the vibrating modal is simulated by using finite element analysis (FEA) method. Simulation results show that the first mode is torsional vibrating, in which the relative error between natural frequency and analytical solution is 9.86%. In order to make further validation, an experimental method using the electrostatic driving and capacitance detection was designed, and the experimental results show that the relative error between natural frequency and analytical solution is 5.21%. Both simulation and experimental results demonstrate that the design is reasonable, and the modal analysis about torsional beam is correct. And it can be applied to the dynamic performance evaluation and the structure optimization.