Analytical study of rotor-stator rubbing phenomenon

Rotor-stator rubbing is an intriguing dynamic phenomenon and can cause dangerous effects that may lead to machinery failure, hence, it is of fundamental and practical importance to investigate it. In this study, the established
approximate analytical solution to the problem of rotor-stator rubbing is extended to include the Coulomb friction between the rotor and stator. There are two sources of non-smoothness in the investigated problem, where the first is related to the switching between contact and non-contact regimes. The second non-smoothness relates to friction during contact and depends on the change in the direction of the relative velocity between the rotor and stator. The governing equations of motion are strongly nonlinear due to the nonlinear contact forces. The analytical solutions for the individual contact and noncontact regimes are obtained then both solutions are coupled together at the switching interface by precisely evaluating the switching instances. These instances represent the end time for the previous state and the initial time for the new state where switching occurs. Moreover, the relative velocity between the rotor and stator while in contact is monitored to adjust the direction of the tangential contact forces. The results of both the individual contact and noncontact models, and the complete analytical model are verified with the numerical methods based on direct integrations methods. The time response results show that both the numerical and analytical solutions are matched in case of periodic and quasi-periodic responses.