An Approximate Solution Method for Nonlinear Oil Film Forces of Finite Length Journal Sliding Bearing

An approximate analytical method is proposed for calculating nonlinear oil film forces of finite length journal sliding bearing. The dynamic “π” oil film assumption is usually taken to determine nonlinear oil film forces in the dynamic analysis of hydrodynamic journal bearing-rotor system. In practice, oil film usually ruptures, and then cavitation arises, cavitaion of oil film results in Reynolds boundary conditions, i.e., oil film field is not “π” zone in the lubrication. In this paper, based on the variational principle, the method of separation of variables was employed to obtain the pressure distribution with Reynolds boundary conditions. The pressure distribution of infinite long journal bearing model was taken as a circumferential separable function of the pressure distribution. The termination positions of oil film in circumferential direction were determined by using the continuity condition. The axial separable function of the pressure distribution was obtained by the variational principle and the circumferential separable function. The results calculated by the proposed method were in good agreement with the oil film forces by the finite element method. Meanwhile, the influence of the bearing parameters on the pressure distribution was also analyzed.