Dry-friction Whip Research Articles

Dry-Friction Whip and Whirl Predictions for a Rotor-Stator Model With Rubbing Contact at Two Locations

The present work investigates dry-friction whip and whirl phenomena for a rigid rotor contacting at two bearing locations. The idea originated with a paper by Clark et al. (2009, “Investigation of the NRG #40 Anemometer Slowdown,” American Wind Energy Association, Windpower 2009, Chicago, IL, pp. 1-16) on an anemometer undergoing dry-friction whip and whirl. The anemometer rotor was supported by two Teflon® bushings within an elastically supported housing. The dry-friction forces arose at the bushings. Prior models for dry friction whirl and whip have considered rub at one nonsupport location. The present analytical model consists of a rigid rotor connected to a rigid stator at two rubbing-contact locations. Analytical solutions are developed for the following normal reaction forces at the contact locations: (1) In phase, and (2) 180° out of phase. Analytical solutions are only possible for the same radius-to-clearance ratio (RCl) at the two rub locations and define regions where dry-friction whirl is possible in addition to indicating possible boundaries between whirl and whip. These solutions are similar to Black’s (1968, “Interaction of a Whirling Rotor with a Vibrating Stator Across a Clearance Annulus,” J. Mech. Eng. Sci., 10(1), pp. 1-12) and Crandall’s (1990, “From Whirl to Whip in Rotordynamics,” IFToMM Third Intl. Conf. on Rotordynamics, Lyon, France, pp. 19-26). A flexible-rotor/flexible-stator model with nonlinear connections at the bearings was developed to more correctly establish the range of possible solutions. The nonlinear connections at the rub surface are modeled using Hunt and Crossley’s 1975 contact model with Coulomb friction (Hunt and Crossley, F., 1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42, pp. 440). Dry friction simulations are performed for the following rotor center of gravity (C.G.) configurations with respect to the contact locations: (1) Centered, (2) [3/4]-span location, and (3) overhung, outside the contacts. Predictions from the in-phase analytical solutions and the nonlinear simulations agree to some extent when the rotor mass is centered and at the [3/4]-span location due to the fact that whirl-to-whip transitions occur near the pinned rotor-stator bounce frequency. For the overhung mass case, the nonlinear simulation predicts whip at different frequencies for the two contact locations. Neither analytical solution modes predicts this outcome. No 180 deg out-of-phase solutions could be obtained via time-transient simulations. Dry-friction whirling is normally characterized as supersynchronous precession with a precession frequency equal to the running speed ω times RCl. Simulation predictions for models with different RCl ratio mimic whirling. Specifically, with increasing rotor speed, the backward precessional (BP) frequency increases at each contact location. However, individual contact velocities show slipping at all conditions. Slipping is greater at one location than the other, netting a “whirl-like” motion. For the overhung model with different RCl ratios: in addition to whipping at different frequencies the two contacts also whirl at different frequencies corresponding to the separate RCl ratios at the respective contacts. Simulations predict a different running speed for the “jump up” in precession frequency associated with a transition from whirl-to-whip with increasing running speed than for the jump-down in precession frequency for whirl-to-whip in a speed-decreasing mode.

On Occurrence of Reverse Full Annular Rub

This paper discusses reverse full annular rub based on a two degree-of-freedom rotor/seal model where a rubbing location can be simulated away from the lumped rotor mass. The analytical model is much closer to the experimental setup for comparison of results, and real machines for analysis, than the previous one degree-of-freedom model. Its closed-form solution is given including reverse rub amplitudes and relative phases, as well as the normal contact force. The exact frequency equation in polynomial form yields reverse full annular rub frequencies without having to neglect any parameters. Many conclusions can be drawn directly from explicit expressions without numerical calculations. The solution with nonpositive normal contact force indicates a dry-friction whirl/whip-free region, usually accompanied by low friction and/or high damping. The analytical study covers both dry-friction whirl and dry-friction whip, and their relations with dry-friction factor, damping, and rotor speed. Range of reverse rub frequencies, their relation with rotor and rotor/seal coupled natural frequencies, and direction of frictional force, are also revealed. Destructive dry-friction whip experimental results are given, which have fully confirmed the analytical formulas.

Correction factors for NRG #40 anemometers potentially affected by dry friction whip: characterization, analysis, and validation

ABSTRACTOver 50,000 NRG Systems #40 anemometers manufactured between May 2006 and December 2008 are potentially affected by a self‐excited vibratory phenomenon termed dry friction whip (DFW). Affected anemometers can report wind speeds that are lower than true speeds by up to several percent. An analysis of post‐deployment wind tunnel calibration tests on 99 anemometers manufactured in this period found that about 85% were affected by the problem. The mean wind speed bias between 4 and 16 m s −1 for most of the anemometers compared with pre‐deployment tests ranged from −1.5% to −3.0%, and for some, the bias was as large as −6.5%. This finding was confirmed by field tests carried out for a mostly different sample of 53 potentially affected anemometers deployed in pairs with WindSensor P2546A or Vector A100LK anemometers. The field tests further indicated that the problem tends to worsen over time and varies with wind speed. However, the pattern of response varies greatly among anemometers. Based on this research, a method of adjusting data from NRG #40 anemometers manufactured in this period is proposed. The adjustments eliminate the mean bias in the field test data set, although significant scatter remains. Copyright © 2011 John Wiley & Sons, Ltd.

The Numerical and Experimental Characteristics of Multimode Dry-Friction Whip and Whirl

The nature of dry-friction whip and whirl is investigated through experimental and numerical methods. A test rig was designed and constructed to demonstrate and record the character of multimode dry-friction whip and whirl. These tests examined steady-state whip and whirl characteristics for a variety of rub materials and clearances. A simulation model was constructed using tapered Timoshenko beam finite elements to form multiple-degree-of-freedom rotor and stator models. These models were reduced by component mode synthesis to discard high-frequency modes while retaining physical coordinates at the rub location to model rotor-stator interaction using a nonlinear contact model with Coulomb friction. Simulations were performed for specific test cases, and compared against experimental data; these comparisons are favorable. Experimental data analysis showed multiple whirl and whip regions, despite claims of previous investigators that these regions are predicted analytically but not produced in simulations or experiments. Spectral analysis illustrates the presence of harmonic sidebands that accompany the fundamental whirl solution. These sidebands are more evident in whip, and can excite higher-frequency whirl solutions.

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 (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.

The Dynamic Stability of Rotor/Stator Radial Rubs in Rotating Machinery

The classic phenomenon of “dry friction whip,” generally associated with unlubricated journal bearings, is here reconsidered as playing an important role in the dynamic stability, and consequent integrity of radial rubs in all close clearance rotating machinery, particularly in turbomachinery elements such as labyrinth seals and blade tips. A simple analysis is completed for large (runaway) amplitudes of whipping on an analytic model which includes the stator as an independent dynamic system. Whirl frequencies are computed as a function of rotor and stator natural frequencies and damping. A stability criterion is developed as a function of these same variables. Testing on a simple experimental model gives general qualitative agreement to predicted trends, but is not conclusive quantitatively, probably because of the difficulty in simulating pure Coulomb friction at the rubbing interface. The simple generality that can be inferred from the set of derived stability criteria is that the broadest band of whip-free rubbing is achieved if rotor and stator dampings are made close to one another, and if the rotor and stator natural frequencies are kept dissimilar. Systems with identical rotor and stator natural frequencies are always unstable, and will whip at that same natural frequency. Systems with large stator damping will whip at rotor natural frequency. Systems with large rotor damping will whip at stator natural frequency.