Research Papers: Gas Turbines: Manufacturing, Materials, and Metallurgy

Modeling of Abradable Coating Removal in Aircraft Engines Through Delay Differential Equations

[+] Author and Article Information
Nicolas Salvat

e-mail: nicolas.salvat@mail.mcgill.ca

Alain Batailly

e-mail: alain.batailly@mcgill.ca

Mathias Legrand

e-mail: mathias.legrand@mcgill.ca
Structural Dynamics and Vibration Laboratory,
Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West,
Montréal, QC H3A 2K6, Canada

The relative displacement between the tool and the workpiece usually makes it possible to assume that, at any time t, the cutter is in contact with the workpiece. Only a few studies consider cutter/workpiece detachment [12].

Note that the last n columns of B(t) are zeros; accordingly, the resulting DDE is of the retarded type.

The blade stiffness matrix is dependent on the rotational speed: K=K(Ω).

For conciseness, structural matrices, such as the mass and stiffness matrices M and K, are always the reduced version obtained with the aforementioned component mode synthesis method.

In addition to this assumption, unlike machining processes, the abradable coating removal in turbomachinery does not involve a feed.

Contributed by the Manufacturing Materials and Metallurgy 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), 102102 (Aug 30, 2013) (7 pages) Paper No: GTP-13-1205; doi: 10.1115/1.4024959 History: Received June 28, 2013; Revised July 02, 2013

In modern turbomachinery, abradable materials are implemented on casings to reduce operating tip clearances and mitigate direct unilateral contact occurrences between rotating and stationary components. However, both experimental and numerical investigations revealed that blade/abradable interactions may lead to blade failures. In order to comprehend the underlying mechanism, an accurate modeling of the abradable removal process is required. Time-marching strategies where the abradable removal is modeled through plasticity are available but another angle of attack is proposed in this work. It is assumed that the removal of abradable liners shares similarities with machine tool chatter encountered in manufacturing. Chatter is a self-excited vibration caused by the interaction between the machine and the workpiece through the cutting forces and the corresponding dynamics are efficiently captured by delay differential equations. These equations differ from ordinary differential equations in the sense that previous states of the system are involved in the formulation. This mathematical framework is employed here for the exploration of the blade stability during abradable removal. The proposed tool advantageously features a reduced computational cost and consistency with existing time-marching solution methods. Potentially dangerous interaction regimes are accurately predicted and instability lobes match both the flexural and torsional modal responses. Essentially, the regenerative nature of chatter in machining processes can also be attributed to abradable coating removal in turbomachinery.

Copyright © 2013 by ASME
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Erneux, T., 2009, Applied Delay Differential Equations (Surveys and Tutorials in the Applied Mathematical Sciences Series), Vol. 3, Springer-Verlag, New York.
Balachandran, B., Kalmar-Nagy, T., and Gilsinn, D., 2009, Delay Differential Equations: Recent Advances and New Directions, Springer-Verlag, New York.
Wang, W., and Chen, L., 1997, “A Predator-Prey System With Stage-Structure for Predator,” Comput. Math. Appl., 33(8), pp. 83–91. [CrossRef]
Roussel, M., 1996, “The Use of Delay Differential Equations in Chemical Kinetics,” J. Phys. Chem., 100(20), pp. 8323–8330. [CrossRef]
Cook, J. and Powell, B., 1988, “Modeling of an Internal Combustion Engine for Control Analysis,” IEEE Control Syst. Mag., 8(4), pp. 20–26. [CrossRef]
Stépán, G., Szalai, R., Mann, B., Bayly, P., Insperger, T., Gradisek, J., and Govekar, E., 2005, “Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments,” ASME J. Vibr. Acoust., 127(2), pp. 197–203. [CrossRef]
Insperger, T., Stépán, G., and Turi, J., 2007, “State-Dependent Delay in Regenerative Turning Processes,” Nonlinear Dyn., 47(1), pp. 275–283. [CrossRef]
Millecamps, A., Brunel, J.-F., Dufrénoy, P., Garcin, F., and Nucci, M., 2009, “Influence of Thermal Effects During Blade-Casing Contact Experiments,” ASME Conference Proceedings of the 22nd Biennial Conference on Mechanical Vibration and Noise, San Diego, CA, August 30–September 2, ASME Paper No. DETC2009-86842, pp. 855–862 [CrossRef].
Legrand, M., Batailly, A., and Pierre, C., 2012, “Numerical Investigation of Abradable Coating Removal Through Plastic Constitutive Law in Aircraft Engine,” ASME J. Comput. Nonlinear Dyn., 7, p. 011010. [CrossRef]
Batailly, A., Legrand, M., Millecamps, A., and Garcin, F., 2012, “Numerical-Experimental Comparison in the Simulation of Rotor/Stator Interaction Through Blade-Tip/Abradable Coating Contact,” ASME J. Eng. Gas Turbines Power, 134(8), p. 082504. [CrossRef]
Williams, R., 2011, “Simulation of Blade Casing Interaction Phenomena in Gas Turbines Resulting From Heavy Tip Rubs Using an Implicit Time Marching Method,” ASME Conference Proceedings of the Turbo Expo 2011, Vancouver, BC, Canada, June 6–10, ASME Paper No. GT2011-45495, pp. 1007–1016 [CrossRef].
Dombovari, Z., Barton, D., Wilson, R., and Stépán, G., 2011, “On the Global Dynamics of Chatter in the Orthogonal Cutting Model,” Int. J. Non-Linear Mech., 46(1), pp. 330–338. [CrossRef]
Jarlebring, E., 2008, “The Spectrum of Delay-Differential Equations: Numerical Methods, Stability and Perturbation,” Ph.D. thesis, Technische Universität Carolo-Wilhelmina zu Braunschweig, Vännäs, Germany.
Insperger, T., and Stépán, G., 2011, Semi-Discretization for Time-Delay Systems: Stability and Engineering Applications, Springer Science, New York.
Sternchüss, A., and Balmès, E., 2006, “On the Reduction of Quasi-Cyclic Disks With Variable Rotation Speeds,” Proceedings of the International Conference on Advanced Acoustics and Vibration Engineering (ISMA), Leuven, Belgium, September 18–20, pp. 3925–3939.
Tlusty, J., 2000, Manufacturing Processes and Equipment, Prentice-Hall, Englewood Cliffs, NJ.


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Fig. 1

Analogy between abradable removal and milling

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Fig. 2

Aircraft engine with the blade of interest: (1) fan, and (2) low pressure compressor

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Fig. 3

Schematic of milling with chatter

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Fig. 4

Schematic of abradable material removal

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Fig. 5

Test points: (blue dots) stable domain (Ke = 2 × 103 N/m), and (red dots) unstable domain (Ke = 2 × 104 N/m)

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Fig. 6

Tip radial displacement; Ke = 2 × 103 N/m (blue) and Ke = 2 × 104 N/m (red)

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Fig. 7

Time convergence: N = 40 (solid red line), N = 60 (dashed blue line), and N = 80 (dash-dotted black line)

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Fig. 8

Modal convergence: mode 1 (solid red line), modes 1 and 2 (dashed blue line), and modes 1 to 5 (dash-dotted black line)

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Fig. 9

Instability lobes with (dashed blue line), and without (solid red line) centrifugal effects

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Fig. 10

Instability lobes versus blade-tip contact location: trailing edge (solid red line), and leading edge (dashed blue line)

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Fig. 11

Abradable wear map: contact at the blade trailing edge

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Fig. 12

Abradable wear map: contact at the blade leading edge

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Fig. 13

Instability lobes: bending (dashed blue line), and torsion (solid red line) modes

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Fig. 14

Spectrum of the time-domain response: the first torsion mode (solid red line), and the first bending mode (dashed blue line); the instability lobes from Fig. 13 are superimposed



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