半球型动压气浮轴承陀螺仪的静态误差模型

为研究三自由度比力作用下半球型动压气浮轴承气膜变形对平台惯导中三浮陀螺仪输出的影响，提出了一种通过求解Reynolds方程来计算陀螺仪静态误差的数学模型。首先，在考虑气体稀薄效应条件下，针对三浮陀螺仪中的半球型动压气浮轴承给出对应的Reynolds润滑方程；然后，用有限差分法求解气膜压力场，并利用得到的载荷与转子位移计算陀螺仪静态误差；最终，通过回归分析，得到半球型动压气浮轴承陀螺仪的静态误差模型。为简化回归分析的过程，引入干扰力矩与比力的周向夹角和径向干扰力矩作为中间参数，将三元回归分析问题转化为二元回归分析问题。计算结果表明:径向干扰力矩随着轴向比力的增大而增大，随着径向比力的增大呈现先增大后减小的趋势；干扰力矩在周向上超前比力1.35~1.55 rad。本文静态误差模型可预测300 m/s2以内任意方向比力作用下由转子位移所引起的陀螺仪静态误差。 

Static error model of a gyroscope with gas-dynamic hemispherical bearings

In order to investigate the influence of deformation of gas film in gas-dynamic hemispherical bearings on the output of three-floated gyroscopes in the platform initial navigation system subject to 3-DOF specific forces, a mathematical model is established to calculate the static error by solving Reynolds equation. Firstl, Reynolds equation is modified to describe gas flow in hemispherical bearings considering the effect of gas rarefaction. Secondl, it is solved by finite difference method to obtain the pressure distribution, and the relationship between load and rotor displacement is used to calculate the gyroscope error. Finally, by regression analysis, a static error model of the gyroscope with gas-dynamic hemispherical bearings is obtained. To simplify the ternary regression analysis to binary regression analysis, the circumferential angle between interference torque and specific force, and the radial interference torque are introduced as intermediate parameters. Numerical results show that the radial interference torque increases with the increase of axial specific force. With the increase of radial specific force, the radial interference torque increases when the radial specific force is small, and decreases when the interference torque is large. Interference torque is 1.35-1.55 rad ahead of specific force in radial direction. The proposed static error model can predict the gyroscope static error caused by rotor displacement with any specific force below 300 m/s².