刚度及静电力非线性对多自由度微陀螺静态特性影响

Effect of the non-linearity of stiffness and electrostatic force on static characteristics of MDOF micro gyroscope

为揭示静电力非线性及刚度非线性综合作用下多自由度微陀螺的静态特性,以一类四自由度静电驱动微机械陀螺为研究对象,用Hamilton原理分析了微陀螺在静电力及刚度非线性综合作用下的静态性.系统静态特性对偏置电压的敏感性随着刚度非线性的加强而增加,随着直流偏置电压的增大,非零非稳定平衡点逐渐向零稳定平衡点靠近,同速轨道消失异速轨道转化为同速轨道,当直流偏置电压超过某一临界值时整个相空间中均为不稳定流形,吸合行为发生.

In order to reveal the effect of the non-linearity of stiffness and electrostatic force on the multi-DOF micro-gyro′s static characteristics,the influence of the non-linearity of stiffness and electrostatic force on a class of 4-DOF micro-machined gyroscope is analyzed using Hamilton principle.The sensitivity of the system′s static characteristics to the bias voltage increases with the stiffness nonlinearity increases.The non-zero and non-stable equilibrium point is gradually approaching the zero-stable equilibrium point with the increase of the DC bias voltage,meanwhile,the homoclinic orbit disappears and the heteroclinic orbit changes into the homoclinic orbit.Unstable manifolds throughout the phase space when the DC bias voltage over a certain value,that means dynamic pull-in occurs.