Bearing Performance Analysis And Error Model Research Of Gas-Dynamic Bearing Gyroscope

The accuracy of gyroscope is the bottleneck of the accuracy of inertial navigation system.In the gas-dynamic bearing gyroscope,gas-dynamic bearing is used as the support of the motor rotor with the advantage of low friction,high speed and smooth operation.However,the gas film has nonlinear elasticity,causing large drift error with the increasing carrier mobility,while the existing error model cannot describe the error precisely.At the same time,the development of inertial navigation and guidance technology puts forward higher requirements for the analysis and design of gas-dynamic bearing in the gyroscope.To improve the accuracy of inertial navigation system further,this dissertation carried out a thorough and systematic study on the error of gas-dynamic bearing gyroscope,which provides guidance for the design of gas-dynamic bearing,provides a novel idea for error modeling of the gas-dynamic bearing gyroscope,and provides comprehensive prediction information for the error of the gas-dynamic bearing gyroscope.The main research work of this dissertation has four aspects as follows:(1)The research on the error of gas-dynamic bearing gyroscope is based on the analysis of the static and dynamic characteristics of the gas-dynamic bearing.Based on the thin film lubrication theory,a lubrication calculation model of conical gas-dynamic bearing is established in this paper,considering the gas rarefaction effect and surface groove.The model includes transient Reynolds equation,steady-state Reynolds equation and perturbed Reynolds equation with five-degree-of-freedom(5-DOF)motion.Finite difference method is used to solve the Reynolds equation,and the results are compared with the existing research to validate the accuracy of the calculation model.On this basis,the gas film pressure distribution,bearing force and bearing torque of gas-dynamic bearing are calculated.Bearing clearance,groove depth and groove direction angle are designed to increase bearing force.In addition,the stiffness matrix and damping matrix of the bearing are calculated,and then the unbalanced response and stability of the rotor are analyzed.Results show that the amplitude of unbalanced response increases with the increase of motor speed,and the critical mass of stability decreases with the increase of motor speed.(2)To investigate the drift error caused by the non-linear deformation of the gas film in the gas-dynamic bearing gyroscope,the expression of the error is deduced according to the structure and working principle of the gyroscope.The drift error is calculated from the data of the rotor displacement and bearing force obtained from the analysis of the static characteristics of the bearing.Regression analysis is conducted with the 3-DOF specific force as independent variable,and the error model of gas-dynamic bearing gyroscope is obtained.In this process,considering the symmetry of the rotor-bearing system,the ternary regression analysis is transformed into two binary regression analysis,which reduces time of lubrication calculation.The error model of hemispherical gas-dynamic bearing gyroscope is also established and compared with the error model of the conical gas-dynamic bearing gyroscope.Results show that both gyroscopes produce drift errors when the specific force has both radial and axial components,while the drift errors of hemispherical gas-dynamic bearing gyroscope are smaller.In addition,the error model of conical gas-dynamic bearing gyroscope is deducted to be applicable with the change rate of specific force less than 8.4×103 m/s3,and the influence of angular velocity on the interference torque is also analyzed.(3)The transient changes of specific force and carrier angular velocity could cause complex vibration of the gas-floated rotor in the gyro motor,which is neglected in the error model based on the static characteristics of bearings.To compensate for the limitations of considering the system as steady state in the error model,a 5-DOF dynamic model of the rotor was established,and combined with the transient Reynolds equation of the gas-dynamic bearing,with the method to calculate transient interference torque proposed.In the case of sudden change of specific force and uniform change of specific force and carrier angular velocity,the response of rotor-bearing system is calculated,and the change law of transient interference torque is studied.Results show that the change law of transient interference torque is mainly determined by the direction of sudden change if the specific force changes suddenly,and the change law of interference torque mainly depends on the change of carrier angular velocity if the specific force and carrier angular velocity change uniformly.(4)Errors are unavoidable in the process of machining and assembling of gas-dynamic bearings.Because the dimensions of aerodynamic bearings are much larger than the film thickness,even a small manufacturing error will have a great impact on the film thickness.In this dissertation,the influence of several common manufacturing errors on the gas-dynamic bearing gyroscope is investigated,including taper error,oval error,three-lobing error,eccentric error of bearing installation axis and tilting error of bearing installation axis.The film thickness variation is used to describe manufacturing errors.Mathematical models are established and substituted into lubrication calculation model.The rotor displacement and additional interference torque under given specific force are solved by perturbation method and iteration method.With the standard of minimum gas film thickness as low as 1/10 of the bearing clearance,the ultimate overload is calculated under conditions of different manufacturing error.Results show that the increase of several manufacturing errors will lead to the increase of interference torque and the decrease of ultimate overload,among which the bearing taper has the greatest influence.In summary,to investigate the drift error caused by nonlinear deformation of gas film in the gas-dynamic bearing gyroscope,a method is proposed to establish error model and the error models of conical and hemispherical gas-dynamic bearing gyroscopes are established.The model overcomes the inconvenience that the rotor displacement must be taken as an independent variable in lubrication calculation.It can predict the error of measured angular velocity caused by the rotor displacement under any 3-DOF specific force directly.By combinig the Reynolds equation and the 5-DOF rotor dynamic equations,a method is promoted to calculate the transient interference torque of gas-dynamic bearing gyroscope,under the condition of sudden changed specific force and the condition of uniformly changed specific force and carrier angular velocity.In addition,several manufacturing errors of bearings are modeled,with their influences on the gyroscope performance analyzed from the aspects of interference torque and ultimate overload.The methods and results in this dissertation provide theoretical basis and technical support for further improving the accuracy of the gas-dynamic bearing gyroscope.