Approach to rotor-shaft hysteretic whirl using Krylov-Bogoliubov techniques

The internal friction associated with the shaft hysteresis or with the possible release of some shrink fit coupling exerts a destabilizing effect on the over-critical rotor running, but may be efficiently counteracted by other external dissipative sources or by a proper anisotropic configuration of the support stiffness. The present analysis considers a symmetric rotor-shaft system on viscous-flexible supports with different stiffness on two orthogonal planes containing the bearing axis. The internal friction of the shaft is described either by a linear hysteretic model or by a non-linear Coulombian force contrasting the rotor motion relative to the shaft ends. The non-linear equations of motion are solved by an averaging approach of the Krylov-Bogoliubov type, which yields the steady orbit depending on the support dissipation applied to damp the whirl motion, for various working conditions. The beneficial influence of the support stiffness anisotropy is clearly identified.