An approximate solution of oil film forces of turbulent finite length journal bearing

•We propose a method to approximate oil film forces of journal bearings.•We employ the variational principle and separation of variables.•We use free boundary and Reynolds–Floberg–Jakobsson boundary conditions.•We analyze the influence of the parameters on the oil film forces.

An approximate analytical method is proposed for calculating oil film forces of turbulent finite length journal bearings. The dynamic ‘π’ oil film assumption is usually taken to determine oil film forces in the dynamic analysis of hydrodynamic journal bearing-rotor systems. However oil film field is not in the ‘π’ zone, i.e. the start position of the oil film is not 0, and the termination position of the oil film is not ‘π’. Based on the variational principle, separation of variables is employed to obtain the pressure distribution in this paper. The pressure distribution of the infinitely long journal bearing model is taken as a circumferential separable function of the pressure distribution. The start and termination positions of oil film in the circumferential direction are determined by using the continuity condition. The axial separable function of the pressure distribution is obtained by the variational principle and the circumferential separable function. The results calculated by the proposed method are in good agreement with the oil film forces by the finite element method, and the computing cost is reduced greatly. Meanwhile, the influence of the parameters on the oil film forces is analyzed.