Bifurcation and Chaos Analysis of Nonlinear Rotor System with Axial-grooved Gas-lubricated Journal Bearing Support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.

Numerical Analysis on the Static Performance of Gas Journal Bearing by Using Finite Element Method

In this paper,finite element method is used to calculate the static performance of gas journal bearing,in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed.The results indicate that the average gas film thicknesses corresponding to the maximum load capac-ity and stiffness,and the minimum attitude angle increase with the growth of orifice diameter.Load capacity and stiffness significantly improved with the increase of rotation speed,eccentricity ratio and supply pressure when the bearing has thin average gas film thickness.Attitude angle increases with the growth of rotation speed,while the growth rate slows down or even decreases at high speed.The most effective way of reducing attitude angle is to increase supply pressure.It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices,while other parameters have the same effect by changing gas pressure at orifice outlet.

New numerical solution for self-acting gas journal bearings

Taking a small pressure change in the gas film of self-acting gas-lubricated journal bearings into account, the corresponding nonlinear Reynolds equation is linearized through appropriate approximation and a modified Reynolds equation is derived and solved by means of the finite difference method (FDM). The gas film pressure distribution of a self-acting gas-lubricated journal bearing is attained and the load capacity is calculated. The numerical solution has a better agreement with experimental data than a direct numerical solution for different values of the bearing number. It is of interest to note that the eccentricity ratio, at which the new numerical solution is in better agreement with experimental data, is different when the bearing number is changing. The new numerical solution is slightly larger when the eccentricity ratio is smaller, and becomes slightly smaller when the eccentricity ratio is larger.