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Research Papers: Gas Turbines: Structures and Dynamics

Implementation of Speed Variation in the Structural Dynamic Assessment of Turbomachinery Flow Path Components

[+] Author and Article Information
Andrew M. Brown

Aerospace Engineer
e-mail: andy.brown@nasa.gov

R. Benjamin Davis

Aerospace Engineer
e-mail: robert.b.davis@nasa.gov

Michael K. DeHaye

Aerospace Engineer
e-mail: michael.k.dehaye@nasa.gov
Propulsion Structural Dynamic Analysis,
Mail Code ER41,
NASA Marshall Space Flight Center,
Huntsville, AL 35812

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 28, 2013; final manuscript received July 2, 2013; published online August 30, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(10), 102503 (Aug 30, 2013) (6 pages) Paper No: GTP-13-1206; doi: 10.1115/1.4024960 History: Received June 28, 2013; Revised July 02, 2013

During the design of turbomachinery flow path components, the assessment of possible structural resonant conditions is critical. Higher frequency modes of these structures are frequently found to be subject to resonance and, in these cases, design criteria require a forced response analysis of the structure with the assumption that the excitation speed exactly equals the resonant frequency. The design becomes problematic if the response analysis shows a violation of the high cycle fatigue (HCF) criteria. One possible solution is to perform a “finite-life” analysis, where Miner's rule is used to calculate the actual life in seconds in comparison to the required life. In this situation, it is beneficial to incorporate the fact that, for a variety of turbomachinery control reasons, the speed of the rotor does not actually dwell at a single value but instead dithers about a nominal mean speed and during the time that the excitation frequency is not equal to the resonant frequency, the damage accumulated by the structure is significantly diminished. Building on previous investigations into this process, we show that a steady-state assumption of the response is extremely accurate for this typical case, resulting in the ability to quickly account for speed variation in the finite-life analysis of a component which has previously had its peak dynamic stress at resonance calculated. A technique using a Monte Carlo simulation is also presented which can be used when specific speed time histories are not available. The implementation of these techniques can prove critical for successful turbopump design, since the improvement in life when speed variation is considered is shown to be greater than a factor of two.

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References

Lewis, F. M., 1932, “Vibration During Acceleration Through a Critical Speed,” Trans. ASME, 54(1), pp. 253–261.
Cronin, D. L., 1965, “Response of Linear, Viscous Damped Sytems to Excitations Having Time-Varying Frequency,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
Lollack, J. A., 2002, “The Effect of Swept Sinusoidal Excitation on the Response of a Single Degree-of-Freedom Oscillator,” Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, April 22–25, AIAA Paper No. 2002-1230. [CrossRef]
Henson, G. M., 2008, “Response of an Oscillating System to Harmonic Forces of Time-Varying Frequency,” AIAA J., 46(8), pp. 2033–22041. [CrossRef]
Seuaciuc-Osorio, T., and Daqaq, M. F., 2010, “Energy Harvesting Under Excitations of Time-Varying Frequency,” J. Sound Vib., 329(13), pp. 2497–22515. [CrossRef]
Davis, R. B., Durham, R. C., and Brown, A. M., 2010, “The Response of a Mechanical Oscillator to Swept and Dithered Excitation,” Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL, April 12–15, AIAA Paper No. 2010-2891. [CrossRef]
Cash, J. R., and Karp, A. H., 1990, “A Variable Order Runge-Kutta Method for Initial Value Problems With Rapidly Varying Right-Hand Sides,” ACM Trans. Math.Softw., 16(3), pp. 201–2222. [CrossRef]

Figures

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Fig. 1

A representative 10 s time history of the excitation frequency (as measured during a recent J2-X powerpack II secondary mode test)

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Fig. 2

Histograms of the J2-X and Space Shuttle main engine rotor speed data

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Fig. 3

Time history of the stress response using different time steps

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Fig. 4

Damage accumulation using a numerical transient solution with three different time steps

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Fig. 5

Representative 0.25 s time history of the stress response as calculated using numerical integration (solid line) and the analytical steady-state formula (dashed line)

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Fig. 6

Damage accumulation using the numerical transient solution (solid line) and the analytical steady state solution (dashed line)

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Fig. 7

FFTs of the J2-X and Space Shuttle main engine rotor speed data

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Fig. 8

Accumulation of damage including frequency dither (dashed line) and not including dither (solid line)

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Fig. 9

Damage fraction using Monte Carlo statistics of the excitation frequencies (solid line) and using the analytical steady-state solution and the measured time history of the excitation frequency from powerpack testing (dashed line)

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Fig. 10

Dither life ratio as a function of the standard deviation of the rotor speed for various damping ratios. Calculated data is represented by points and second-order polynomial curve fits are shown as solid lines.

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