Stability Analysis Of Cantilever-Type Foil Aerodynamic Journal Bearings

The cantilever-type foil aerodynamic journal bearing supported by cantilevered elastic components is one of the self-acting gas journal bearing. The special structure of the foil bearing has many outstanding advantages such as self-adaptive ability, lower friction loss, high speed, and good rotating stability, and so on. The cantilever-type foil aerodynamic journal bearing has important valuable application and vast potential for future development in many fields. With the rapid development of science and technology, the rotor needs to work on higher rotating speed. The high speed stability of bearing is the key to solve the problem. A more systematic theory research method for this problem is present in this study.The primary content of this paper can be listed as follows:(1) The fundamental equations are derived. First, the calculation model of the foil elastic deformation by the non-linear shell theory for the cantilever-type foils aerodynamic journal bearings is established. A system of partial differential equations is obtained by the combination of geometric equations, physical equations and balanced differential equations. Second, The basic form of gas-lubricated Reynolds equation under isothermal conditions is obtained.(2) The gas film thickness model influenced by compressibility of gas and elastic foil deformation is established. Based on this model, Finite Deference Method (FDM) and Newton-Raphson iterative Method are both applied to solve the coupled air film thickness and the Reynolds pressure governing equation. And more, the static characteristics are discussed including the influence of bearing number, eccentricity and W/D on static performance.(3) Based on small perturbation method and static analysis, ten equations which are related to differential pressure and film thickness are built. The eight stiffness and damping coefficients can be solved by coupling above 10 equations. The influence factors on dynamical coefficient parameters include eccentricity, disturbance frequency, bearing number, length-diameter ratio and foil elasticity coefficient is discussed.(4) Two methods of judging the stability are established. Based on eight dynamic characteristic coefficients and dynamics motion equations, a rotor system is preliminary calculated and validated by Routh-Hurwitz standards.This studies can provide systematic theory methods to study the stability of cantilever-type foil aerodynamic journal bearings, and the theoretical references to the dynamic design.