Analytical prediction on stick-slip whirling oscillations induced by dry friction between a rotating imbalanced rotor and a flexibly supported stator

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Non-smooth dry friction between the contact surfaces of rotor/stator rubbing systems can induce self-excited dry friction backward whirl, which may exhibit various discontinuity-induced sliding bifurcations corresponding to stick-slip whirling oscillations with different local dynamical characteristics around the switching manifold. The analytical method proposed in this paper aims to predict the self-excited stick-slip whirling oscillations in a general rotor/stator rubbing system, wherein both the dynamics of a rotor and a stator as well as deformation and friction at contact surfaces are taken into full consideration. The solution of the dry friction backward whirl for the four-degree-of-freedom non-smooth model with a switching manifold of a curved hypersurface is analytically derived under the hypothesis of pure rolling, which consists of a self-excited backward whirl part and a forced forward whirl part. For the validation with numerical simulation, it is found, as expected, that the analytical solution achieves high precision prediction on the response magnitudes and frequencies of the dry friction backward whirl in case of pure rolling at various rotating speeds. The analytical solution can also provide an eligible approximation on the stick-slip whirling oscillations with a relatively short slip phase in one period of stick-slip oscillation due to the negligible damping produced by slipping, such as in the case of a grazing-sliding motion, by which both the rotor and the stator undergo very large harmful amplitudes of vibration.