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Research Papers

Active Subspace Development of Integrally Bladed Disk Dynamic Properties Due to Manufacturing Variations

[+] Author and Article Information
Joseph A. Beck

Perceptive Engineering Analytics, LLC,
Minneapolis, MN 55418
e-mail: Joseph.A.Beck@peanalyticsllc.com

Jeffrey M. Brown

AFRL/RQTI,
Wright-Patterson AFB, OH 45433
e-mail: Jeffrey.Brown.70@us.af.mil

Alex A. Kaszynski

Advanced Engineering Solutions,
Dayton, OH 45432
e-mail: akascap@gmail.com

Emily B. Carper

AFRL/RQTI,
Wright-Patterson AFB, OH 45433
e-mail: Emily.Carper@us.af.mil

1Corresponding author.

Manuscript received June 26, 2018; final manuscript received June 29, 2018; published online September 18, 2018. Editor: Jerzy T. Sawicki. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Eng. Gas Turbines Power 141(2), 021001 (Sep 18, 2018) (10 pages) Paper No: GTP-18-1374; doi: 10.1115/1.4040869 History: Received June 26, 2018; Revised June 29, 2018

The impact of geometry variations on integrally bladed disk eigenvalues is investigated. A large population of industrial bladed disks (blisks) are scanned via a structured light optical scanner to provide as-measured geometries in the form of point-cloud data. The point cloud data are transformed using principal component (PC) analysis that results in a Pareto of PCs. The PCs are used as inputs to predict the variation in a blisk's eigenvalues due to geometry variations from nominal when all blades have the same deviations. A large subset of the PCs is retained to represent the geometry variation, which proves challenging in probabilistic analyses because of the curse of dimensionality. To overcome this, the dimensionality of the problem is reduced by computing an active subspace that describes critical directions in the PC input space. Active variables in this subspace are then fit with a surrogate model of a blisk's eigenvalues. This surrogate can be sampled efficiently with the large subset of PCs retained in the active subspace formulation to yield a predicted distribution in eigenvalues. The ability of building an active subspace mapping PC coefficient to eigenvalues is demonstrated. Results indicate that exploitation of the active subspace is capable of capturing eigenvalue variation.

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References

Goodhand, M. N. , Miller, R. J. , and Lung, H. W. , 2014, “ The Impact of Geometric Variation on Compressor Two-Dimensional Incidence Range,” ASME J. Turbomach., 137(2), p. 021007. [CrossRef]
Saumweber, C. , and Schulz, A. , 2012, “ Effect of Geometry Variations on the Cooling Performance of Fan-Shaped Cooling Holes,” ASME J. Turbomach., 134(6), p. 061008. [CrossRef]
Bunker, R. S. , 2009, “ The Effects of Manufacturing Tolerances on Gas Turbine Cooling,” ASME J. Turbomach., 131(4), p. 041018. [CrossRef]
Schnell, R. , Lengyel-Kampmann, T. , and Nicke, E. , 2014, “ On the Impact of Geometric Variability on Fan Aerodynamic Performance, Unsteady Blade Row Interaction, and Its Mechanical Characteristics,” ASME J. Turbomach., 136(9), p. 091005. [CrossRef]
Goodhand, M. N. , and Miller, R. J. , 2011, “ The Impact of Real Geometries on Three-Dimensional Separations in Compressors,” ASME J. Turbomach., 134(2), p. 021007. [CrossRef]
Lange, A. , Voigt, M. , Vogeler, K. , Schrapp, H. , Johann, E. , and Gümmer, V. , 2012, “ Impact of Manufacturing Variability and Nonaxisymmetry on High-Pressure Compressor Stage Performance,” ASME J. Eng. Gas Turbines Power, 134(3), p. 032504. [CrossRef]
Lange, A. , Voigt, M. , Vogeler, K. , Schrapp, H. , Johann, E. , and Gümmer, V. , 2012, “ Impact of Manufacturing Variability on Multistage High-Pressure Compressor Performance,” ASME J. Eng. Gas Turbines Power, 134(11), p. 112601. [CrossRef]
Garzon, V. E. , and Darmofal, D. L. , 2003, “ Impact of Geometric Variability on Axial Compressor Performance,” ASME J. Turbomach., 125(4), pp. 692–703. [CrossRef]
Clark, J. P. , Beck, J. A. , Kaszynski, A. A. , Still, A. , and Ni, R.-H. , 2017, “ The Effect of Manufacturing Variations on Unsteady Interaction in a Transonic Turbine,” ASME Paper No. GT2017-64075.
Marcu, B. , Tran, K. , and Wright, B. , 2002, “ Prediction of Unsteady Loads and Analysis of Flow Changes Due to Turbine Blade Manufacturing Variations During the Development of Turbines for the MB-XX Advanced Upper Stage Engine,” AIAA Paper No. 2002-4162.
Bammert, K. , and Sandstede, H. , 1976, “ Influences of Manufacturing Tolerances and Surface Roughness of Blades on the Performance of Turbines,” ASME J. Eng. Power, 98(1), pp. 29–36. [CrossRef]
Andersson, S. , 2007, “ A Study of Tolerance Impact on Performance of a Supersonic Turbine,” AIAA Paper No. 2007-5513.
Kaszynski, A. A. , and Brown, J. M. , 2015, “ Accurate Blade Tip Timing Limits Through Geometry Mistuning Modeling,” ASME Paper No. GT2015-43192.
Beck, J. A. , Brown, J. M. , Slater, J. C. , and Cross, C. J. , 2013, “ Probabilistic Mistuning Assessment Using Nominal and Geometry Based Mistuning Methods,” ASME J. Turbomach., 135(5), p. 051004. [CrossRef]
Dow, E. A. , and Wang, Q. , 2015, “ The Implications of Tolerance Optimization on Compressor Blade Design,” ASME J. Turbomach., 137(10), p. 101008. [CrossRef]
Buske, C. , Krumme, A. , Schmidt, T. , Dresbach, C. , Zur, S. , and Tiefers, R. , 2016, “ Distributed Multidisciplinary Optimization of a Turbine Blade Regarding Performance, Reliability and Castability,” ASME Paper No. GT2016-56079.
Sampath, R. , Zhou, B. , Kulkarni, P. , Blair, A. , Griffiths, J. , Beley, J.-D. , and Perrin, S. , 2008, “ Sensitivity-Based Approach to Quantifying Uncertainty in Airfoil Modal Response,” AIAA Paper No. 2008-4741.
Kaszynski, A. A. , Beck, J. A. , and Brown, J. M. , 2013, “ Uncertainties of an Automated Optical 3D Geometry Measurement, Modeling, and Analysis Process for Mistuned Integrally Bladed Rotor Reverse Engineering,” ASME J. Eng. Gas Turbines Power, 135(10), p. 102504. [CrossRef]
Holtzhausen, S. , Schreiber, S. , Schöne, C. , Stelzer, R. , Heinze, K. , and Lange, A. , 2009, “ Highly Accurate Automated 3D Measuring and Data Conditioning for Turbine and Compressor Blades,” ASME Paper No. GT2009-59902.
Kaszynski, A. A. , Beck, J. A. , and Brown, J. M. , 2014, “ Automated Finite Element Model Mesh Updating Scheme Applicable to Mistuning Analysis,” ASME Paper No. GT2014-26925.
Kaszynski, A. A. , Beck, J. A. , and Brown, J. M. , 2015, “ Experimental Validation of a Mesh Quality Optimized Morphed Geometric Mistuning Model,” ASME Paper No. GT2015-43150.
Iooss, B. , and Lemaître, P. , 2015, “ A Review on Global Sensitivity Analysis Methods,” Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications, Springer, Boston, MA, pp. 101–122.
Constantine, P. , Dow, E. , and Wang, Q. , 2014, “ Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces,” SIAM J. Sci. Comput., 36(4), pp. A1500–A1524. [CrossRef]
Lukaczyk, T. W. , Constantine, P. , Palacios, F. , and Alonso, J. J. , 2014, “ Active Subspaces for Shape Optimization,” AIAA Paper No. 2014-1171.
del Rosario, Z. , Constantine, P. , and Iaccarino, G. , 2017, “ Developing Design Insight Through Active Subspaces,” AIAA Paper No. 2017-1090.
Seshadri, P. , Shahpar, S. , Constantine, P. , Parks, G. , and Adams, M. , 2017, “ Turbomachinery Active Subspace Performance Maps,” ASME Paper No. GT2017-64528.
Beck, J. , Brown, J. M. , Scott-Emuakpor, O. E. , Kaszynski, A. , and Henry, E. B. , 2018, “ Modal Expansion Method for Eigensensitivity Calculations of Cyclically Symmetric Bladed Disks,” AIAA Paper No. 2018-1951.
USAF, 2002, “ Engine Structural Integrity Program MIL HDBK-1783B,” Department of Defense Handbook: Engine Structural Integrity Program (ENSIP), No. MIL-HDBK-1783B. http://everyspec.com/MIL-HDBK/MIL-HDBK-1500-1799/MIL_HDBK_1783B_1924/
Lange, A. , Voigt, M. , Vogeler, K. , and Johann, E. , 2012, “ Principal Component Analysis on 3D Scanned Compressor Blades for Probabilistic CFD Simulation,” AIAA Paper No. 2012-1762.
Brown, J. M. , Slater, J. , and Grandhi, R. V. , 2003, “ Probabilistic Analysis of Geometric Uncertainty Effects on Blade Modal Response,” ASME Paper No. GT2003-38557.
Constantine, P. , and Gleich, D. , 2014, “ Computing Active Subspaces,” arXiv:1408.0545v1[math.NA]. https://arxiv.org/abs/1408.0545v1
Constantine, P. , and Gleich, D. , 2014, “ Computing Active Subspaces With Monte Carlo,” arXiv:1408.0545v2[math.NA]. https://arxiv.org/abs/1408.0545

Figures

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Fig. 1

Principal component variance (σ2) explained

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Fig. 2

Geometric surface deviations represented by PC1 on a blade (cropped)

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Fig. 3

Percent contribution of each blade to variation in PC1

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Fig. 4

Measured surface deviations of blade 4 (cropped) contributing the most to PC1 in Fig. 3

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Fig. 5

Empirical CDFs of the PC scores for the first ten PCs

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Fig. 6

First k eigenvalue estimates of Ĉ for λBlisk,1

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Fig. 7

First k subspace error for λBlisk,1

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Fig. 9

Active variable and h(Φ1Tx) for λBlisk,1

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Fig. 10

Cumulative distribution function of λBlisk,1

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Fig. 11

First k eigenvalue estimates of Ĉ for λBlisk,2–5

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Fig. 12

Φ1 for λBlisk,2–5: (a) frequency 2, (b) frequency 3, (c) frequency 4, and (d) frequency 5

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Fig. 13

First k eigenvalue estimates of Ĉ for λBlisk,1 with ρ = Gaussian plotted over data from Fig. 6

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Fig. 14

Φ1 for λBlisk,1 with ρ = Gaussian plotted over data from Fig. 8

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Fig. 15

Active variable and h(Φ1Tx) for λBlisk,1 with ρ = Gaussian (G) plotted over uniform (U) data from Fig. 9

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Fig. 16

Empirical CDF of λBlisk,1 with ρ = Gaussian (G) plotted over uniform (U) data from Fig. 10

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Fig. 17

Active variable and h(Φ1Tx) for λBlisk,1 with 99% confidence intervals on the mean for ρ = Gaussian

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Fig. 18

Empirical CDF of λBlisk,1 from fit in Fig. 17

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Fig. 19

Empirical CDF of λBlisk,2–5: (a) frequency 2, (b) frequency 3, (c) frequency 4, and (d) frequency 5

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Fig. 20

Φ1 for λBlisk,1 for all ρ

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Fig. 21

Empirical CDF of λBlisk,1 from m = 20 PCs

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Fig. 22

Industrial blisk 2

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Fig. 23

First four eigenvalue estimates of Ĉ for λBlisk,1 for blisk 2

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Fig. 24

Φ1 for λBlisk,1 for blisk 2

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Fig. 25

Active variable and h(Φ1Tx) for λBlisk,1 for blisk 2

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Fig. 26

Empirical CDF of λBlisk,1 for blisk 2

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