非线性刚度对微机械陀螺动态性能的影响*

Effect of nonlinear stiffness on dynamic performance of the micromechanical gyroscope

摘要:

为了提高微机械陀螺的稳定性，研究自由振动状态下活动基座上 L-L 型双质量微机械陀螺的动态性能，建立微机械陀螺的数学模型，得到以幅值-相位为变量的运动微分方程的解，并给出这种解与轨道元素的联系。研究框架质量和弹性件非线性刚度对陀螺漂移量的影响，并给出数值例子。对所得到的解析关系式与曲线进行分析，作出关于系统性能的相应结论。

Abstract:

In order to improve the stability of the micromechanical gyroscope, the dynamic performance of the L-L type two-mass micromechanical gyroscope on the movable base in free vibration state is studied, and the mathematical model of the micromechanical gyroscope is established to obtain the solution of the motion differential equation with amplitude-phase as the variable, and the relation between the solution and the orbital elements is given. In addition, the effects of the frame mass and the nonlinear stiffness of elastic parts on the gyro drift are studied, and a numerical example is given. Finally, the obtained analytic relation and curve are analyzed, and the corresponding conclusions about the system performance are drawn.