磁悬浮陀螺转子转动惯量数学模型的分析

Analysis of Mathematical Model of Rotational Inertia of Magnetic Suspending Gyroscope Rotor

这种磁悬浮陀螺仪是建立在经典理论基础上 ,将惯性刚体转子与超导电子学相结合而发展起来的陀螺仪 ,它的随机漂移率减少到空前的高度。本文通过对新型陀螺转子的结构分析 ,建立了该陀螺转子的转动惯量的数学模型 ,并且分析了转子转动惯量的一些特性 ,给出了转子的惯量椭球与惯性主轴 ,建立了转子的惯性张量 ;通过分析转子的本体极迹 (极点在惯量椭球上所画出来的轨迹 )发现Z轴上是一对孤立的点 ,其余部分全是环绕Z轴的同心圆。在Z轴的附近区域来说 ,属于封闭型本体极迹 ,但在赤道面上对于过原点的一切轴线 ,它们的本体极迹是被赤道极迹连接起来的 ,所以属于分离型本体极迹。

Magnetic suspending gyroscope is developed based on the classical theory and by integrating inertial rigid body with superconducting electronics. Its random drift can be reduced to a unprecedented minimum. Depending on structure analysis of magnetic suspending gyroscope rotor, the authors of this paper have developed a math model of rotational inertia of the rotor, analyzed some characteristics of its rotational inertia, given an inertia ellipse and principal axis, and established the rotor′s inertia tensor. By analyzing noumenon pole tracks, the authors find that there is a pair of isolated points on Z axis while others are the concentric circles around Z axis. The area nearby Z axis is closed-type noumenon pole tracks, but all the other axes on the plane through the equator have a separate-type noumenon pole tracks linked by the pole track on the equator. At last, the authors analyzed the rotor′s random drift and stability.