Prediction of Dry-Friction Whirl and Whip Between a Rotor and a Stator

This paper addresses recent test results for dry-friction whip and whirl. Authors of these publications suggest that predictions from Black’s 1968 paper are deficient in predicting their observed transition speeds from whirl to whip and the associated precession frequencies of whirl and whip motion. Predictions from Black’s simple Jeffcott-rotor/point-mass stator are cited. This model is extended here to a multi-mode rotor and stator model with an arbitrary axial location for rotor-stator rubbing. Predictions obtained from this new model are quite close to experimental observations in terms of the transition from whip to whirl and observed precession frequencies. Paradoxically, nonlinear numerical simulations using Black’s model fail to produce the whirl and whip solutions. The Coulomb friction force in Black’s model has a fixed direction, and Bartha showed in 2000 that by making the friction-force direction depend on the relative sliding velocity, nonlinear simulations would produce the predicted whirl solutions. He also showed that Black’s proposed whip solution at the upper precession-frequency transition from whirl to whip was unstable. Results presented here show that Black’s whirl solutions are unstable for all whirl precession frequencies, not just the whirl-whip transition frequency. The multi-mode extension of Black’s model predicts a complicated range of whirl and whip possibilities; however, nonlinear time-transient simulations (including the sgn function definition for the Coulomb force) only produce the initial whirl precession range, the initial whirl-whip transition, and the initial whip frequency. Simulation results for these values agree well with predictions. However, none of the predicted higher-frequency whirl results are obtained. Also, the initial whip frequency persists to quite high running speeds and does not (as predicted) transition to higher frequencies. Hence, despite its deficiencies, correct and very useful predictions are obtained from a reasonable extension of Black’s model.