Nonlinear analysis of cylindrical and conical hysteretic whirl motions in rotor-dynamics

The internal friction of a rotor-shaft-support system is mainly due to the shaft structural hysteresis and to some possible shrink-fit release of the assembly. The experimentation points out the destabilizing effect of the internal friction in the over-critical rotor running. Nevertheless, this detrimental influence may be efficiently counterbalanced by other external dissipative sources located in the supports or by a proper anisotropic configuration of the support stiffness. The present analysis considers a rotor-shaft system which is symmetric with respect to the mid span and is constrained by viscous-flexible supports with different stiffness on two orthogonal planes. The cylindrical and conical whirling modes are easily uncoupled and separately analyzed. The internal dissipation is modelled by nonlinear Coulombian forces and moments, which counteract the translational and rotational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are solved by averaging approaches of the Krylov-Bogoliubov type. In both the over-critical whirling motions, cylindrical and conical, stable limit cycles may be attained whose amplitude is as large as the external dissipation applied by the supports is low. The stiffness anisotropy of the supports may be recognized as quite beneficial for the cylindrical whirl.