On the stability of periodic motions of an unbalanced rigid rotor on lubricated journal bearings

A theoretical investigation is carried out on the orbital motions of a symmetrical, unbalanced, rigid rotor subjected to a constant vertical load and supported on two lubricated journal bearings. In order to determine the fluid film forces, the short bearing theory is adopted. A method is illustrated that makes it possible to determine the analytical equation of the orbit as an approximated solution of the system of non-linear differential equations of motion of the journal axis. A procedure is also described for evaluating the stability of the solution found. Diagrams of the curves delimiting, in the working plane of the rotor sigma-m sigma, the areas of stability of the various periodic solutions determined are provided. Finally, the results obtained are compared and combined with those provided by a direct integration of the motion equation made using the Runge-Kutta method.