Dynamic Study Of A High Speed Rotor Supported By Air Journal Bearings Based On Orbit Method

Compared to the traditional bearings,gas bearings have the advantages of low viscosity,high rotational speed,low noise and high precision,and have been widely used in precision lathe,spaceflight industry and other fields.However,when the rotational speed increases to be more than a certain value,the rotor will be unstable,the bearing and the journal contact each other,which seriously limits the further use of gas bearings.To improve the stability and safety of gas bearing-rotor system,this paper researched the dynamics of rotor.Because of higher speed and accuracy requirements from industries,small perturbation method has been inapplicable.Orbit method is used to research the stability in this paper.To research the dynamic behavior of the rotor,The time-dependent Reynolds equation is derived.The Galerkin’s weighted residual method is adopted to transform Reynolds equation from the second-order partial differential equation to the first-order one.The lubricant field is discretized using finite element method,and the equations including gas pressure at each node are obtained,the gas film forces and torques can be calculated through integration.Considering cylindrical and conical whirl,the coordinate systems are established.And expressions for calculating the gas film thickness are obtained.Considering unbalanced mass,the dynamic equations of the rotor are derived to describe the translational and rotational motion.The motion of rotor is solved through cross-interation between the Reynolds equation and dynamics equations,the time item in the Reynolds equation is discretized.Matlab code is written for numerical simulation.The stability of cylindrical whirl under initial eccentricity and conical whirl under initial tilting angle are investigated through orbit method.The influences of rotor mass,angular speed,bearing aspect ratio,supplied pressure,span between two bearings and rotor inertial tensor on stability are analyzed.Unlike small perturbation method,it is found that the stability of the rotor is related to the initial eccentricity or initial tilting angle,and there exists a stability boundary.When the initial perturbation is in the boundary,the rotor is stable;when the starting perturbation is out of the boundary,the rotor is unstable;the motion which initial perturbation is chosen on the boundary shows marginal stability.The stability boundary changes with the above structure parameters and operating parameters,and the threshold values of the above parameters for which the rotor is stable or unstable in the whole gas film gap are found.The motion of rotor with unbalanced mass is more complex,the rotor mass and rotational speed are chosen as research parameters.Through numerical simulation,the orbit diagrams,phase diagrams,spectrum diagrams,Poincaré maps and bifurcation diagram are made to research the nonlinear dynamic and bifurcation behavior,the result shows that with the increase of the rotor mass and rotational speed,the motion of the rotor changes from the T-periodic motion to quasi-periodic motion.