Theoretical analysis on conical whirl instability of unloaded submerged oil journal bearings

A nonlinear transient method is used to analyse the stability characteristics of an unloaded rigid rotor supported in submerged oil journal bearings undergoing conical whirl. The rotor has two degrees of freedom of motion in a self-excited conical whirl. The analysis considers cavitation effects, takes account of the oil film history and assumes that antisymmetry is maintained in the conical mode of vibration. The time-dependent form of the Reynolds equation (with the journal in the misaligned position) is solved by a finite-difference method with a successive over-relaxation scheme to obtain the moment components. Using these moment components, the equations of motion are solved by a fourth-order Runge-Kutta method, to predict the transient behaviour of the rotor. Journal centre trajectories in orthogonal coordinates are obtained for different operating conditions, using a high-speed digital computer and graphics.