Theoretical Prediction of Journal Center Motion Trajectory in Two-Lobe Hydrodynamic Journal Bearings

Abstract

In this study, the theoretical prediction of a journal center motion trajectory for high-speed rotors supported by two-lobe hydrodynamic oil film journal bearings is presented for three different values of the noncircular ratios, γ=0, 0.5 and 1.0. In order to obtain values for the oil film forces used in the equations of motion for rotor-bearing systems, the Reynolds equation governing the oil film pressure generated in the bearing gap was solved using the semianalytical finite-element method for each time step. Furthermore, for each time step, the nonlinear equations of motion for a rigid rotor supported by two identical aligned bearings were solved using the improved Euler integration method. From the numerical results, the relations between the journal center motion trajectory and the corresponding pressure distribution were examined theoretically, and the effect of the noncircular ratio on the stability of rotor bearing systems was clarified for the cases of both balanced and unbalanced rotors.