Interrogating the Lead-up to a Critical Speed in Rotordynamics

This paper presents a new approach to predicting an incipient critical speed in a rotating shaft. Based on the classical governing equations of motion for an eccentric mass on a flexible shaft (the Jeffcott rotor model), the approach is centered on examining the behavior of small perturbations or random disturbances to infer the approach of a critical speed (resonance). Such disturbances, that may be based on intentional probing, or simply the result of naturally occurring fluctuations, cause small transients. It is the changing nature of these transients (as characterized by their associated eigenvalues) that is used to assess the proximity to a critical speed. In this paper the material developed is based on analysis, but generating the data from simulations or experiments will be the next step. The approach is a kind of stress-test, conceptually not dissimilar to structural health monitoring and damage detection, but here directed toward the lead-up to resonance.