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

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.

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Fig. 1

Response Y direction with unit load = 34.5 bars

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Fig. 2

Exploded view of the four-bolt coupling

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Fig. 3

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

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Fig. 4

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

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Fig. 5

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

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Fig. 6

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

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Fig. 7

Response, four-bolt coupling under angular misalignment

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Fig. 8

Response, four-bolt coupling under parallel misalignment

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Fig. 9

Response, six-bolt coupling under angular misalignment

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Fig. 10

Response, six-bolt coupling under parallel misalignment

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Fig. 11

Response, eight-bolt coupling under parallel misalignment

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Fig. 12

Fixed displacement for parallel misalignment




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