Duty cycle shapes multi-mode transient responses in intermittent rotor–stator rub with no evidence of Sommerfeld capture

A multi-mode model is presented for the transient passage of a flexible rotor through its first critical speed with unilateral rotor–stator contact. The shaft is discretised with Euler–Bernoulli finite elements, with disks and elastic supports included before modal extraction and mass normalisation. Penetration is calculated from the physical displacement at the rub plane, and the contact forces are projected onto all retained modes. A torque-limited drive law is coupled to the lateral equations through the unbalance acceleration and friction torque. Contact near the first critical speed increases the displacement peak from 38.04 to 46.70 \(μ\) m over 0.110 s, with a maximum normal force of 4.67 N. No Sommerfeld capture is observed over the parameter ranges examined. The instantaneous friction torque reaches \(68%\) of the drive torque, but the revolution-averaged value that the drive must overcome stays below \(5%\) because contact occupies about one tenth of a revolution. A nonlinear induction-motor law of matched torque near resonance changes the peak by \(0.08%\) . Non-synchronous amplitudes remain below \(0.5%\) of the synchronous component, and a constant-speed scan over 51 operating points remains period one. Four published datasets are used only for contextual comparison, because their rigs and contact parameters differ from the model.