Semi-analytical model for rub dynamics to investigate whirling

Rotor–stator rub interactions are a significant area of interest in rotordynamics because they can generate backward whirling, often causing malfunctions. This paper extends the analytical solution for rotor–stator rub dynamics to include friction at the rotor–stator contact. A simple two-degrees-of-freedom Jeffcott rotor model is used, and the contact mechanics follows a piecewise-smooth model with Coulomb friction. The rotor can be in the contact or non-contact regime, introducing motion-dependent discontinuities and strong nonlinear behaviour due to contact forces. To obtain an analytical solution, these nonlinear forces are approximated using the first-order Taylor expansion. Eigenvalue and nonlinear dynamics analyses of the model are also undertaken. The analytical solution is validated against fourth/fifth order Runge-Kutta integration. Effects of varying friction, rotor damping, and stator stiffness are investigated. The main contribution is an analytical solution applicable to wide range of problems from rotordynamics including drill-string whirling, offering faster computation while maintaining accuracy, and contributing to improved rotor dynamics modelling.