3自由度气浮台力学性能研究——关于自重作用下不平衡力矩的分析

STUDY ON THE MECHANICS PROPERTY OF THREE DEGREES OF FREEDOM AIR-BEARING TESTBED- ANALYSIS ON UNBALANCE TORQUE ACTED ON GRAVITY

根据航天器姿态运动理论和弹性力学薄板弯曲理论,推导出重力作用下的有限元单元质心位移公式和结构整体质心弹性位移公式,计算了3自由度气浮台平台的自重变形引起的质心弹性位移和由此产生的不平衡力矩。对计算结果分析表明气浮台自重变形产生的不平衡力矩的原因是结构各方向的刚度不等,并给出了气浮台在任意欧拉角时的不平衡力矩公式。当气浮台绕水平轴旋转时,不平衡力矩呈正弦变化,俯仰或滚动角为45°时力矩达到最大值。

According to the theory on the spacecraft attitude kinetics and on the lamella bending of elastics mechanics, the formulary for the element mass-center displacement of the finite element and for the platform structure mass-center displacement are deduced. It is calculated that the mass-center elastics displacement resulted from deforming of the platform of air-bearing testbed acted on gravity and that the unbalance torque resulted from the displacement. The result shows that the unequal rigidity in different direction of the platform structure causes the unbalance torque when the platform acted on gravity. When rotating around horizontal axis, the change of platform＇s unbalance torqucis characterizec by sinusoid, and the torque reaches the top when roll angle or pitch angle and 45°.