基于参数激励的两自由度耦合MEMS谐振式陀螺

A 2-DOF Coupled MEMS Resonant Gyroscope Driven by Parametric Excitation

模态耦合是微机电系统(Micro-Electro-Mechanical System,MEMS)陀螺仪的主要误差来源,针对这个问题,首先从建立陀螺的两自由度动力学模型入手,研究非理想模态耦合条件下的参数激励方法。然后,将多尺度法、龙格-库塔法(Runge-Kutta methods)和牛顿迭代法(Newton-Raphson method)等综合分析方法应用于该模型,表征模态耦合对参数驱动的影响。最终的仿真结果表明,通过适当调节参数激励的强度可以有效地放大两个模态的振动振幅,特别是当参数激励进入不稳定区域时效果更明显。而耦合项会引起微陀螺模态之间的能量传递,产生的影响是响应振幅会被修正,并且刚度耦合可以提升不稳定区的阈值,改变共振频率。这些结论有助于设计者改进和提高MEMS陀螺仪的设计及性能。

The mode coupling terms are the major error sources of MEMS gyroscopes.Aiming at this problem,this paper investigates the parametric drive method for a 2-DOF resonant gyroscope.First of all,a 2-DOF dynamic model of the gyroscope is established,and the parameter excitation method under the non-ideal mode coupling constraints is studied.Then,a comprehensive analysis including multi-scale method,Runge-Kutta method and Newton-Raphson method are applied to this model to characterize the influences of the mode coupling terms on the parametric drive.The simulation results indicate that the parametric drive with proper tuning procedures can effectively amplify the vibration amplitude of the modes.This effect is even more obvious if the parametric drive transits into the unstable region.The mode coupling terms can cause the energy transfer between the modes of the gyroscope which will lead to the modification of the amplitude of the response.The stiffness coupling will increase the threshold of the unstable region and change the resonant frequency.These conclusions are helpful for improvement and design of MEMS gyroscopes.