0
Research Papers: Gas Turbines: Structures and Dynamics

One Explanation for Two-Times Running Speed Response Due to Misalignment in Rotors Connected by Flexible Couplings

[+] Author and Article Information
Raul D. Avendano

Engineer
MPR Associates, Inc.,
Alexandria, VA 22314
e-mail: ravendano@mpr.com

Dara W. Childs

Leland T. Jordan Professor
Turbomachinery Laboratory,
Texas A&M University,
College Station, TX 77843
e-mail: dchilds@tamu.edu

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received June 29, 2012; final manuscript received November 14, 2012; published online May 20, 2013. Editor: Dilip R. Ballal.

J. Eng. Gas Turbines Power 135(6), 062501 (May 20, 2013) (10 pages) Paper No: GTP-12-1242; doi: 10.1115/1.4023232 History: Received June 29, 2012; Revised November 14, 2012

Misalignment in turbomachinery is commonly thought to produce two-times running-speed (2N) response. The source of 2N vibration response was investigated, starting with the development of finite-element models for three flexible disk-pack couplings (four-bolt, six-bolt, and eight-bolt couplings). Parallel and angular misalignments were analyzed. The resultant lateral stiffness terms had 1N, 2N, and 3N harmonic components versus the shaft rotation angle. The four-bolt coupling had large 1N stiffness components under angular and parallel misalignment. The six-bolt coupling had only a 1N reaction component under angular misalignment, while parallel misalignment showed a strong 2N reaction component, larger than either the 1N or 3N components. Under angular misalignment, the eight-bolt model produced large 1N reaction components. Under parallel misalignment, it produced 1N, 2N, and 3N components that were similar in magnitude. All the couplings behaved linearly in the range studied. Some experts attribute observed 2N response to nonlinear bearing forces produced by bearings at high unit loads. Static tests for a five-pad tilting-pad journal bearing with unit loads up to 34.5 bars produced small 2N motion components that did not grow with increasing unit load. A Jeffcott-rotor model with shaft stiffness orthotropy and a fixed-direction side load predicts that 2N response depends on three related factors: (1) the degree of orthotropy (the 1N stiffness variation magnitude), (2) the magnitude of the side load, and (3) the relative ratio of running speed to rotor first natural frequency, (ω/ωn). The 2N response magnitude is largest when ω is close to ωn/2. The side load is required to create 2N response due to shaft stiffness orthotropy. Misaligned couplings create precisely the same (very old) physical model as a two-pole turbogenerator rotor with a gravity side load (gravity critical speed). The response of a two-rotor/coupling system with parallel and angular misalignment was simulated using a time-transient code. When the frequency ratio was 0.5, the system response with the four-bolt and six-bolt coupling had a synchronous 1N component as well as a significant 2N component. Parallel misalignment at a coupling produces stiffness orthotropy and a fixed-direction side load. For ranges of running speed near ωn/2, these two elements can combine to produce 2N response.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Jackson, C., 1973, “Cold and Hot Alignment Techniques of Turbomachinery,” Proceedings of the 2nd Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX, October 22–25, pp. 1–7.
Mancuso, J., 1994, “General Purpose Vs Special Purpose Couplings,” Proceedings of the 23rd Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX, September 20–23, pp. 167–177.
Gibbons, C., 1976, “Coupling Misalignment Forces,” Proceedings of the 5th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX, October 12–14, pp. 111–116.
Redmond, I., 2007, “Shaft Misalignment and Vibration: A Model,” Saudi Aramco J. Technol., 4(2007), pp. 41–51.
Lees, A. W., 2007, “Misalignment in Rigidly Coupled Rotors,” J. Sound Vib., 305, pp. 261–271. [CrossRef]
Bahaloo, H., Ebrahimi, A., and Samadis, M., 2009, “Misalignment Modeling in Rotating Systems,” ASME Turbo Expo 2009: Power for Land, Sea, and Air, Orlando, FL, June 8–12, ASME Paper No. GT2009-60121. [CrossRef]
Sekhar, A., and Prabu, B., 1995, “Effects of Coupling Misalignment on Vibrations of Rotating Machinery,” J. Sound Vib., 185(4), pp. 655–671. [CrossRef]
Jackson, C., 1990, “Considerations in Hot and Cold Alignment and Couplings,” Proceedings of the 7th International Pump Users Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX, March, pp. 27–38.
Palazzolo, A., Locke, S., Calistrat, M., and Clark, R., Jr., 1992, “Gear Coupling Misalignment Induced Forces and Their Effects on Machinery Vibration,” Proceedings of the 21st Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX, September, pp. 83–96.
Pennachi, P., Vania, A., and Chatterton, S., 2011, “Analysis of the Effects of Parallel and Angular Misalignment in Hyperstatic Rotors Equipped With Oil-Film Bearings,” Proceedings of the ASME Turbo Expo, Vancouver, Canada, June 6–10, ASME Paper No. GT2011-45903. [CrossRef]
Carter, C., and Childs, D., 2009, “Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration,” ASME J. Eng. Gas Turbines Power, 131(1), p. 012507. [CrossRef]
Bloch, H., 1995, A Practical Guide to Steam Turbine Technology, McGraw-Hill, New York.
Bishop, R. E. D., and Parkinson, A., 1965, “Second Order Vibration of Flexible Shafts,” Philos. Trans. R. Soc. London, Ser. A, 259, pp. 1–31. [CrossRef]
Lorenc, J., 1991, “Changes in Pump Vibration Levels Caused by the Misalignment of Different Style Couplings,” Proceedings of the 8th International Pump Users Symposium, Texas A&M University, College Station, TX, pp. 63–70.

Figures

Grahic Jump Location
Fig. 1

Response Y direction with unit load = 34.5 bars

Grahic Jump Location
Fig. 2

Exploded view of the four-bolt coupling

Grahic Jump Location
Fig. 3

Eight θ rotation positions of the drive shaft for the four-bolt model

Grahic Jump Location
Fig. 4

Two-pole turbogenerator cross-section after Bishop and Parkinson [12]

Grahic Jump Location
Fig. 5

1N and 2N response components as a function of q for Eq. (20)

Grahic Jump Location
Fig. 6

1N and 2N response component amplitudes as a function of ω/ωn for q = 0.5, ζ = 0.1

Grahic Jump Location
Fig. 12

Fixed displacement for parallel misalignment

Grahic Jump Location
Fig. 11

Response, eight-bolt coupling under parallel misalignment

Grahic Jump Location
Fig. 10

Response, six-bolt coupling under parallel misalignment

Grahic Jump Location
Fig. 9

Response, six-bolt coupling under angular misalignment

Grahic Jump Location
Fig. 8

Response, four-bolt coupling under parallel misalignment

Grahic Jump Location
Fig. 7

Response, four-bolt coupling under angular misalignment

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In