1. BACKWARD PRECESSIONAL WHIP AND WHIRL FOR A TWO-POINT RUBBING CONTACT MODEL OF A RIGID ROTOR SUPPORTED BY AN ELASTICALLY SUPPORTED RIGID STATOR
Masters Thesis
By
Dhruv D. Kumar

2. SINGLE POINT AND TWO POINT CONTACT
ANALYTIC SINGLE CONTACT MODEL
ANALYTIC TWO-CONTACT MODEL
Flexible rotor
Elastically supported stator
One point of contact between rotor-stator.
Rigid rotor
Elastically supported rigid stator
Two points of contact between rotor-stator.
Figure cited from-Childs, D. W., and Bhattacharya, A., 2007, Prediction of Dry-Friction whirl and
whip between a Rotor and a Stator, ASME J. Vib. Acoust., 129, pp. 355362.
3. EVENTS LEADING TO 2 POINT DRY FRICTION INVESTIGATION

NRG systems #40 anemometer sensors were exhibiting post calibration slowdown

4. Faulty sensors had a dominant vibration frequency separate from the rotating speed. 5. Effected sensors exhibited spiral sort of motion, NRG systems perceived it as self excited vibratory phenomena. 6. Dr Childs confirmed NRGs suspicion that the observed phenomenon was dry-friction whip. 7. Low RCl and friction was the reason of occurrence of dry friction whip. 8. Anemometer has a rigid shaft with a mass disk at roughly its center, this rotor is supported on 2 Teflon bearings, the rubbing contact. Radius to clearance ratio is of the order of 30Solidworks model NRG#40 anemometerby `NRG systems
Solidworks model NRG#40 anemometerby `NRG systems
9.

Childs two contact model was extended to incorporate pitch and yaw motion.

10. Assuming:(i) Contact always occurs at both locations,and (ii) The same radius-to-clearance (RCl) ratio holds at both contact locations Mode1 and Mode 2 solutions were developed.Figure cited from-Krkkinen, A., Helfert, M., Aeschlimann, B., Mikkola A., Dynamic Analysis of Rotor System With Misaligned Retainer Bearings, ASMEJ. Tribol. 130, 021102 (2008)

Non-Linear simulation model was developed with similar properties to validate the mathematical model

Method of Research
11.

Rotor equation of motion derived.

12. The equations were derived using Lagranges Equation 13. The above equation is in complex form where ROTOR DIAGRAM
Analytical model
14.

Stator equation of motion derived

15. The equation is in complex form, whereSTATOR DIAGRAM

Relations between the rotor and stator displacement vectors at either contact location form geometric constraints.

CLEARANCE DIAGRAM
Analytical model
16.

Mode 1 solution developed- Assumed planar precessing mode with the normal reaction contact forces in phase at the two contact points.

17. Mode 2 solution developed- Assumed planar precessing mode with the normal reaction contact forces out of phase at the two contact points. 18. These solutions were evaluated for three different configurations Disk at center
Disk at location
Disk at overhang location
Analytical solution
19. Model Definition

The model defined is a purely made up model and is not

connected to any piece of Turbomachinery.

Friction is required to produce a solution against the BP frequency