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

Abstract

This paper addresses recent test results for dry-friction whip and whirl. Authors of these publications suggest that predictions from Black’s 1968 paper (J. Mech. Eng. Sci., 10(1), pp. 1–12) 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 multimode 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 (“Dry Friction Backward Whirl of Rotors,” Dissertation, THE No. 13817, ETH Zurich) 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. The multimode 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, initial whirl-whip transition, and 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.

An Improved Catcher Bearing Model and an Explanation of the Forward Whirl/Whip Phenomenon Observed in Active Magnetic Bearing Transient Drop Experiments

“…The lateral interaction between the journal O, and CB inner race O^, will be defined by a Hunt-Crossley nonlinear contact model [12], This approach has been used previously by Bartha [13,14], Wilkes [15] and Wilkes et al, [9], and Childs and Bhattacharya [16], who all obtained As usual, it is good practice to begin with a formal definition of the coordinates used in the analysis. Figure 4 shows the rotor/journal contacting the CB inner race (CBIR), In this case, the displacement of Oj and 0¿,, is…”

“…(16) and (17) can be integrated for a range of inner-race speed ratios to determine the lateral forces (Fcai) and torques (Tcai) on the rotor as the inner race speeds up after contact with the thrust bearing occurs. Figure 7 shows the normalized radial and tangential forces and torques versus inner-race speed ratio for the example scenario.…”

Chaotic vibration analysis of rotating, flexible, continuous shaft-disk system with a rub-impact between the disk and the stator

“…Shen et al [21] reported that, under the influence of the initial permanent bow, there are different routes to chaos that could greatly affect the rub-impact. Childs and Bhattacharya [22] presented a new model for predicting the dry frictions whirl and whip between a rotor and a stator. The effect of the centering springs on the bifurcation of a flexible rotor response supported by squeeze film dampers is presented in [23,24].…”

Rotor-Stator Contact – Overview of Current Research

“…Some papers like e.g. Black [5] and Childs [6] use an identical model only investigating continuous contact (δ = 0) and therefore using the contact condition (4). This simplification gives rise to analytical solutions for continuous contact (see 4.1 and 4.2).…”