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.

References

References
1.
Newkirk
,
B.
, 1926, “
Shaft Rubbing
,”
Mech. Eng.
,
48
, pp.
830
832
.
2.
Black
,
H.
, 1967, “
Synchronous Whirling of a Shaft Within a Radially Flexible Annulus Having Small Radial Clearance
,”
Proc. Inst. Mech. Eng., Paper No.
4
(
181
), pp.
65
73
.
3.
Black
,
H.
, 1968, “
Interaction of a Whirling Rotor with a Vibrating Stator across a Clearance Annulus
,”
J. Mech. Eng. Sci.
,
10
(
1
), pp.
1
12
.
4.
Crandall
,
S.
, 1990, “
From Whirl to Whip in Rotordynamics
,”
IFToMM Third International Conference on Rotordynamics
,
Lyon
,
France
, pp.
19
26
.
5.
Lingener
,
A.
, 1990, “
Experimental Invesigation of Reverse Whirl of a Flexible Rotor
,”
IFToMM Third International Conference on Rotordynamics
,
Lyon
,
France
, pp.
13
18
.
6.
Choi
,
Y.-S.
, 2002, “
Investigation on the Whirling Motion of Full Annular Rub
,”
J. Sound Vib.
,
258
(
1
), pp.
191
198
.
7.
Bartha
,
A.
, 2000, “
Dry Friction Backward Whirl of Rotors
,”
dissertation ETH No. 13817
,
ETH
,
Zurich
.
8.
Yu
,
J. J.
,
Goldman
,
P.
,
Bently
,
D.
, 2000, “
Rotor/Seal Experimental and Analytical Study of Full Annular Rub
,”
Proceedings of ASME IGTI Turboexpo 2000
,
ASME
,
New York
, Vol.
2000-GT-389
, pp.
1
9
.
9.
Childs
,
D.
, and
Bhattacharya.
,
A.
, 2007, “
Prediction of Dry-Friction Whirl and Whip Between a Rotor and a Stator
,”
ASME J. Vib. Acoust.
,
129
, pp.
355
362
.
10.
Wilkes
,
J.
,
Dyck
,
B. J.
,
Childs
,
D.
, and
Phillips
,
S.
, 2009, “
The Numerical and Experimental Characteristics of Multi-Mode Dry-Friction Whip and Whirl,”
ASME J. Gas Turbines Power
,
132
(
5
), p.
0525031
.
11.
Hunt
,
K.
and
Crossley
,
F.
, 1975, “
Coefficient of Restitution Interpreted as Damping in Vibroimpact
,”
ASME J. Appl. Mech.
,
42
, pp.
440
.
12.
Clark
,
S.
,
Clay
,
H.
,
Goglia
,
J. A.
,
Hoopes
,
T. R.
,
Jacobs
,
L. T.
, and
Smith
,
R.
, 2009, “
Investigation of the NRG #40 Anemometer Slowdown
,”
Windpower 2009
,
American Wind Energy Association
,
Chicago, IL
, pp.
1
16
.
13.
Kärkkäinen
,
A.
,
Helfert
,
M.
,
Aeschlimann
,
B.
, and
Mikkola
,
A.
, 2008 “
Dynamic Analysis of Rotor System With Misaligned Retainer Bearings
,”
ASME J. Tribol.
,
130
,
02110
.
14.
Kumar
,
D.
, “
Backward Precessional Whip and Whirl for a Two-Point Rubbing Contact Model of a Rigid Rotor Supported by an Elastically Supported Rigid Stator
,” M. S. thesis, Department of Mechanical Engineering, Texas A&M University, College Station, TX.
15.
Childs
,
D.
, 1993,
Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis
,
John Wiley and Sons
,
New York
, pp.
395
431
.
16.
Wilkes
,
J.
, 2007, “
A Perspective on the Numerical and Experimental Characteristics of Multi-mode Dry-friction Whip and Whirl
,” M. S. thesis, Texas A&M, College Station, TX.
17.
Jiang
,
J.
,
Shang
,
Z.-Y.
, and
Hong
,
L.
, 2010, ”
Characteristics of Dry Friction Backward Whirl—A Self-Excited Oscillation in Rotor-to-Stator Contact Systems
,”
Sci. China, Ser E: Technol. Sci.
,
53
(
3
), pp.
674
683
.
You do not currently have access to this content.