静电悬浮转子微陀螺高努森数下的空气阻尼力矩

针对工作于高真空密封腔中的静电悬浮MEMS陀螺微转子,为建立其旋转动力学模型,实现高精度恒速旋转控制,需要得到高努森数条件下的空气阻尼力矩特性。结合复杂结构的轮状扁平微转子,根据分子动理论和Christian模型,推导出压膜阻尼力矩特性;根据稀薄气体动力学,在考虑腔室内壁和转子表面具有不同切向动量适应系数的条件下,推导出滑膜阻尼力矩解析公式。以根据腔内空气流动特征进行的分区直接蒙特卡罗模拟(DSMC)结果为参考,总阻尼力矩系数的解析误差约为16%,表明解析模型具有较好的精度,对于高努森数条件下类似微器件的建模和系统设计具有较高的实用价值。

Air Damping Torques of Electrostatically Levitated Rotational Microgyro Under High Knudsen Number Condition

To achieve the constant spinning speed control with accurate spinning dynamics model for a micro rotor of an electrostatically levitated MEMS(MicroElectroMechanical Systems)gyro,which works in a high-vacuum cavity,the effects of air damping torques need to be taken into account.Based on a micro rotor of complex wheel-plate shape,the characteristic of squeeze damping torque was firstly analyzed using the molecule dynamic theory and the Christian model.And then,by the rarefied gas dynamics,the analytical formula for slide damping torque was presented,considering non-symmetrical TMAC(tangential momentum accommodation coefficient)of the surfaces of the rotor and the walls of the cavity.The accuracy and practical utility of the damping torque analysis models for modeling and design of similar micro devices were validated by segmented DSMC(direct simulation Monte Carlo)numerical simulations according to the characteristic of the ring flow in the cavity,with only 16% relative deviations.