Research On Dynamic Characteristics Of Gas Bearing Rotor System For Gyroscope

To satisfy the higher precision,higher speed,smaller size,higher reliability,and longer lifespan requirements of gyroscopes,the spiral grooved gas bearings,which are widely used as supporting and lubricant components of inertial components,encounter great challenges in analysis,design and manufacture.And their application is limited because of their characteristics which are different from their conventional ones as follows: combined surface lubrication,ultra-thin film thickness,high operation speed,high stability,the inevitable manufacturing and assembly error.However,the effects of the above factors on the characteristics of the gas bearing for gyroscopes still have not been fully investigated.In this dissertation,the opposed-hemisphere gas bearing rotor system of a gyroscope,which is now developing actively in our country,is studied.The influences of the coupled effect of the combined surfaces,the gas rarefaction,the inertial effect and the manufacturing and assembly error on the capacity,stability and nonlinear dynamics of the spiral grooved opposed-hemisphere gas bearing system are investigated carefully.For the case that only the two hemisphere gas bearings are calculated in the classical gas bearing design,the lubrication models of the spiral grooved opposed-hemisphere gas bearing which consider the coupled effect of the combined surfaces are developed.To investigate the effect of the gas rarefaction,the ultra-thin lubrication equations are obtained by employing the first order slip model.The Reynolds equations considering the inertia effect are also derived from the gas equations of motion.And the Galerkin weighted residual method and finite element method are employed to solve the static lubrication equation.The effects of the journal coupling,the gas rarefaction,the inertia and the bearing parameters on the static characteristics of the bearing are comprehensively studied.For the case that only the cylindrical whirl motion is calculated in the classical perturbation method,a complete numerical procedure to calculate the stiffness and damping coefficients of the spiral-grooved opposed-hemisphere gas bearings considering five degrees freedom are presented,using the finite element method and first-order perturbation method.And the stability thresholds of the rotor-bearing are also determined,which consider the cylindrical whirl,axial whirl and axial whirl.The groove effects on the dynamic bearing performance are depicted.The effects of the journal coupling,the gas rarefaction,the inertia on the dynamic coefficients and stability of the bearing are illustrated for the first time.Moreover,the synchronous response and natural frequency are also investigated.Although the linear perturbation method has the advantages of simple analysis and fast calculation,the gas bearing is essentially a nonlinear system due to the compressibility and rarefaction of the gas.The mathematical model describing the nonlinear dynamic characteristics of the rotor-bearing system is established to obtain the complete dynamic maps of the rotor.The Galerkin weighted residual method and finite element method are employed to discretize the time dependent Reynolds equations.In order to calculate the transient item of the Reynolds equations,the finite difference method is used also.Three translational coordinates and two angular coordinates are considered in rotor d ynamics and solved coupling with Reynolds equations.The rotor responses to the initial disturbance,synchronous and nonsynchronous excitations are investigated.To analyze the complicated dynamic behavior of the rotor-bearing system,the trajectories of the rotor center or axes,time responses,phase portraits,power spectra,Poincaré maps and bifurcation diagrams are obtained from the numerical procedure.The results show that the conical whirl instability appears earlier than the cylindrical whirl instability with the increasing rotational speed for the rotor-bearing system with no unbalance mass.Moreover it reveals that the complex dynamic behavior of the system excited by unbalance mass varies with the rotational speed and the rotor mass.And the bifurcation diagrams employing the rotating speed and rotor mass as bifurcation parameters are obtained.The manufacturing and assembly error are inevitable in application.The models describing the out-of-sphericity and the assembly error are obtained.And the influences of these factors on the bearing performance,stability and friction torque are analyzed by numerical method.Based on the theoretical analysis and simulation results,the measure systems of the grooved hemisphere and sphere gas bearing are desi gned.The test beds are manufactured to measure the capacity of the two bearings.The variation of the capacity of the grooved hemisphere gas bearing with the rotating speed and the floating height is studied.And the relationships between the floating height and the rotating speed of the grooved spherical gas bearing with the gravity are obtained also.The theoretical model and research method are verified by comparing the test results,and the deviation between the theoretical and test results are analyzed.