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为研究三自由度比力作用下半球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。所提出的误差模型可预测300 m/s~2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。
In order to study the effect of the deformation of the air film on the platform inertial gyroscope output of three-floating gyroscope under the action of three degrees of freedom, a mathematical model for calculating the static error of the gyroscope by solving the Reynolds equation is proposed. Firstly, the corresponding Reynolds equation of lubrication is given for the hemispherical hydrodynamic bearing in the three-floating gyroscope under the condition of gas thinning effect. Then the pressure field of the gas film is solved by finite difference method, and the calculated load and rotor displacement are used to calculate Gyroscope error. Finally, by regression analysis, the static error model of the hemispherical hydrodynamic bearing air bearing is obtained. In order to simplify the process of regression analysis, the circumferential angle of disturbance torque and specific force and radial disturbance torque are introduced as intermediate parameters, and the problem of ternary regression analysis is transformed into the problem of binary regression analysis. The calculation results show that the radial interference torque increases with the increase of axial force and increases first and then decreases with the increase of radial force. The interference torque in the circumferential direction is 1.35- 1.55 rad. The proposed error model can predict the gyroscope static error caused by the rotor displacement under the specific force within 300 m / s ~ 2.