Dynamic response and stability of a rotor-support system with non-symmetric bearing clearances

Abstract

The non-linear vibrations of a rotordynamic system that is subjected to non-symmetric bearing clearance effects, are considered. Particular attention is paid to the system response near the primary resonance. Based on a Jeffcott rotor model, the steady-state oscillations and their stability are analysed employing the method of multiple scales. The “normal-loose” rotor stiffness condition, that occurs due to the bearing clearance effects is modelled through a discontinuous radial stiffness model. Expressions for the amplitude and phase modulating functions are obtained. Frequency-amplitude relationships that result from combined parametric and mass unbalance excitations are derived. Further, an associated stability analysis is performed by considering the singular points, based on the time evolution of the amplitude and phase of the steady-state rotor motions. The effects of “normal-loose” rotor stiffness condition on both the amplitude and phase of the near-resonance vibrations, as well as stability of the rotor system are systematically brought out. The effects of high speed acceleration during run-up of the rotor are both qualified and quantified. Similarly, the case of run-down of the rotor is analysed. A numerical study encompassing the effects of different system parameters is also presented, to demonstrate the severity of vibrations. The sensitivities of vibrational and stability characteristics to various rotordynamic system parameters and to the non-asymmetric bearing clearance effects, are also illustrated through this numerical investigation.