Bladed discs; Damper model; Friction damping; Nonlinear dynamics; Passive control; Turbine blade vibrations; Turbine blade; Control and Systems Engineering; Signal Processing; Civil and Structural Engineering; Aerospace Engineering; Mechanical Engineering; Computer Science Applications
Abstract :
[en] Underplatform dampers (UPD) are commonly used in aircraft engines to mitigate the risk of high-cycle fatigue failure of turbine blades. The energy dissipated at the friction contact interface of the damper reduces the vibration amplitude significantly, and the couplings of the blades can also lead to significant shifts of the resonance frequencies of the bladed disk. The highly nonlinear behaviour of bladed discs constrained by UPDs requires an advanced modelling approach to ensure that the correct damper geometry is selected during the design of the turbine, and that no unexpected resonance frequencies and amplitudes will occur in operation. Approaches based on an explicit model of the damper in combination with multi-harmonic balance solvers have emerged as a promising way to predict the nonlinear behaviour of UPDs correctly, however rigorous experimental validations are required before approaches of this type can be used with confidence. In this study, a nonlinear analysis based on an updated explicit damper model having different levels of detail is performed, and the results are evaluated against a newly-developed UPD test rig. Detailed linear finite element models are used as input for the nonlinear analysis, allowing the inclusion of damper flexibility and inertia effects. The nonlinear friction interface between the blades and the damper is described with a dense grid of 3D friction contact elements which allow accurate capturing of the underlying nonlinear mechanism that drives the global nonlinear behaviour. The introduced explicit damper model showed a great dependence on the correct contact pressure distribution. The use of an accurate, measurement based, distribution, better matched the nonlinear dynamic behaviour of the test rig. Good agreement with the measured frequency response data could only be reached when the zero harmonic term (constant term) was included in the multi-harmonic expansion of the nonlinear problem, highlighting its importance when the contact interface experiences large normal load variation. The resulting numerical damper kinematics with strong translational and rotational motion, and the global blades frequency response were fully validated experimentally, showing the accuracy of the suggested high detailed explicit UPD modelling approach.
The authors are grateful to Innovate UK (Grant no. MEDY.P50254 ) and Rolls-Royce plc (Grant no. MEDY.P42978 ) for providing the financial support for this work and for giving permission to publish it. This work is part of a collaborative R&T project SILOET II P19.6 which is co-funded by Innovate UK and Rolls-Royce plc and carried out by Rolls-Royce plc and the Vibration UTC at Imperial College London.
[1] Petrov, E.P., Ewins, D.J., State-of-the-art dynamic analysis for non-linear gas turbine structures. Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 218:3 (2004), 199–211, 10.1243/0954410041872906.
[2] Cowles, B.A., High cycle fatigue in aircraft gas turbine – an industry prospective. Int. J. Fract. 80 (1996), 147–163, 10.1007/BF00012667.
[3] Gaul, L., Nitsche, R., The role of friction in mechanical joints. Appl. Mech. Rev. 54:2 (2001), 93–106, 10.1115/1.3097294.
[4] Feeny, B., Hinrichs, N., Popp, K., A historical review on dry friction and stick-slip phenomena. Appl. Mech. Rev. 51:5 (1998), 321–341.
[5] Griffin, J.H., A review of friction damping of turbine blade vibration. Int. J. Turbo Jet Engines 7 (1990), 297–307.
[6] Sanliturk, K.Y., Ewins, D.J., Stanbridge, A.B., Underplatform dampers for turbine blades: theoretical modeling, analysis, and comparison with experimental data. J. Eng. Gas Turbines Power, 123(4), 2001, 919, 10.1115/1.1385830.
[7] Sanliturk, K.Y., Ewins, D.J., Elliott, R., Green, J.S., Friction damper optimization: simulation of rainbow tests. J. Eng. Gas Turbines Power, 123(4), 2001, 930, 10.1115/1.1391278.
[8] Griffin, J.H., Friction damping of resonant stresses in gas turbine engine airfoils. J. Eng. Power 102 (1980), 329–333.
[9] Csaba, G., Forced response analysis in time and frequency domains of a tuned bladed disk with friction dampers. J. Sound Vib. 214:3 (1998), 395–412, 10.1006/jsvi.1997.1513.
[10] Yang, B.D., Menq, C.H., Characterization of contact kinematics and application to the design of wedge dampers in turbomachinery blading: Part 1 stick-slip contact kinematics. J. Eng. Gas. Turbines Power 120:1998 (1998), 410–417.
[11] L. Panning, W. Sextro, K. Popp, Optimization of interblade friction damper design, in: Proceedings of the ASME Turboexpo, 2000, pp. 1–8.
[12] J. Szwedowicz, C. Gibert, T.P. Sommer, R. Kellerer, Numerical and experimental damping assessment of a thin-walled friction damper in the rotating set-up with high pressure turbine blades, Journal of Engineering for Gas Turbines and Power 130, 1. http://dx.doi.org/10.1115/1.2771240.
[13] Griffin, J.H., An integrated approach for friction damper design. J. Vib. Acoust. 1:1990 (1990), 175–181.
[14] Yeh, G.C.K., Forced vibrations of a two degree of freedom system with combined coulomb and viscous damping. J. Acoust. Soc. Am. 39:1 (1966), 14–24, 10.1121/1.1909863.
[15] M.H. Jareland, A parametric study of a cottage-roof damper and comparison with experimental results, in: Proceedings of ASME TURBOEXPO, 2001, pp. 1–9.
[16] Panning, L., Sextro, W., Popp, K., Spatial dynamics of tuned and mistuned bladed disks with cylindrical and wedge-shaped friction dampers. Int. J. Rotat. Mach. 9 (2003), 219–228, 10.1155/S1023621×03000198.
[17] Cigeroglu, E., An, N., Menq, C.H., Forced response prediction of constrained and unconstrained structures coupled through frictional contacts. J. Eng. Gas. Turbines Power, 131(2), 2008, 919, 10.1115/1.2940356.
[18] Firrone, C.M., Zucca, S., Gola, M.M., The effect of underplatform dampers on the forced response of bladed disks by a coupled static/dynamic harmonic balance method. Int. J. Non-Linear Mech. 46:2 (2011), 363–375, 10.1016/j.ijnonlinmec.2010.10.001.
[19] Zucca, S., Firrone, C.M., Gola, M.M., Modeling underplatform dampers for turbine blades: a refined approach in the frequency domain. J. Vib. Control 19:7 (2013), 1087–1102, 10.1177/1077546312440809.
[20] Petrov, E.P., Ewins, D.J., Advanced modeling of underplatform friction dampers for analysis of bladed disk vibration. J. Turbomach., 129(1), 2007, 143, 10.1115/1.2372775.
[21] Petrov, E.P., Ewins, D.J., Analytical formulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed disks. J. Turbomach., 125(2), 2003, 364, 10.1115/1.1539868.
[22] Petrov, E.P., Explicit finite element models of friction dampers in forced response analysis of bladed disks. J. Eng. Gas Turbines Power, 130(2), 2008, 022502, 10.1115/1.2772633.
[23] Krack, M., von Scheidt, L.P., Wallaschek, J., A high-order harmonic balance method for systems with distinct states. J. Sound Vib. 332:21 (2013), 5476–5488, 10.1016/j.jsv.2013.04.048.
[24] Salles, L., Blanc, L., Thouverez, F., Gouskov, A., Jean, P., Dual time stepping algorithms with the high order harmonic balance method for contact interfaces with fretting-wear. J. Eng. Gas. Turbines Power, 134(3), 2012, 032503 (1–7).
[25] Grolet, A., Thouverez, F., On a new harmonic selection technique for harmonic balance method. Mech. Syst. Signal Process. 30 (2012), 43–60, 10.1016/j.ymssp.2012.01.024.
[26] Craig, R.R., Bampton, M.C.C., Coupling of substructures for dynamic analyses. AIAA J. 6:7 (1968), 1313–1319.
[27] Besselink, B., Tabak, U., Lutowska, A., van de Wouw, N., Nijmeijer, H., Rixen, D., Hochstenbach, M., Schilders, W., A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. J. Sound Vib. 332:19 (2013), 4403–4422, 10.1016/j.jsv.2013.03.025.
[28] Petrov, E.P., A high-accuracy model reduction for analysis of nonlinear vibrations in structures with contact interfaces. J. Eng. Gas Turbines Power, 133(10), 2011, 102503, 10.1115/1.4002810.
[29] J.S. Green, Controlling forced response of a high pressure turbine blade (Ph.D. thesis), KTH Royal Institute of Technology (2006). 〈 http://www.diva-portal.org/smash/get/diva2:10533/FULLTEXT01.pdf〉.
[30] Pfeiffer, F., Hajek, M., Stick-slip motion of turbine blade dampers. Philos. Trans. R. Soc. Lond. A 338 (1992), 503–517.
[31] Koh, K.-H., Griffin, J.H., Dynamic behavior of spherical friction dampers and its implication to damper contact stiffness. J. Eng. Gas Turbines Power, 129(2), 2007, 511, 10.1115/1.2436547.
[32] Firrone, C.M., Measurement of the kinematics of two underplatform dampers with different geometry and comparison with numerical simulation. J. Sound Vib. 323:1–2 (2009), 313–333, 10.1016/j.jsv.2008.12.019.
[33] Pesaresi, L., Salles, L., Elliot, R., Jones, A., Green, J.S., Schwingshackl, C.W., Numerical and experimental investigation of an underplatform damper test rig. Appl. Mech. Mater. 849 (2016), 1–12, 10.4028/www.scientific.net/AMM.849.1.
[34] Gola, M.M., Tong, L., A direct experimental, numerical method for investigations of a laboratory under-platform damper behavior. Int. J. Solids Struct. 51:25,26 (2014), 4245–4259, 10.1016/j.ijsolstr.2014.08.011.
[35] M.M. Gola, C. Gastaldi, Understanding complexities in underplatform damper mechanics, in: Proceedings of ASME TURBOEXPO, V07AT34A002, 2014. 〈 http://dx.doi.org/10.1115/GT2014-25240〉.
[36] Sever, I.a., Petrov, E.P., Ewins, D.J., Experimental and numerical investigation of rotating bladed disk forced response using underplatform friction dampers. J. Eng. Gas Turbines Power, 130(4), 2008, 042503, 10.1115/1.2903845.
[37] Berruti, T., Firrone, C.M., Gola, M.M., A test rig for noncontact traveling wave excitation of a bladed disk with underplatform dampers. J. Eng. Gas Turbines Power, 133(3), 2011, 032502, 10.1115/1.4002100.
[39] S. Smith, J. Bilbao-Ludena, S. Catalfamo, M. Brake, P. Reu, C.W. Schwingshackl, The effects of boundary conditions, measurement techniques, and excitation type on measurements of the properties of mechanical joints, in: Proceedings of the Society for Experimental Mechanics IMAC Conference, 2016.
[40] C.W. Schwingshackl, C. Joannin, L. Pesaresi, J.S. Green, N. Hoffmann, Test method development for nonlinear damping extraction of dovetail joints, in: Proceedings of the Society for Experimental Mechanics IMAC Conference, 2014.
[41] V. Ruffini, C. Schwingshackl, J. Green, Ldv measurement of local nonlinear contact conditions of flange joint, in: Topics in Nonlinear Dynamics, Volume 1: Proceedings of the 31st IMAC, A Conference on Structural Dynamics, 2013, Vol. 35, Springer Science & Business Media, 2013, p. 159.
[42] C.W. Schwingshackl, Measurement of friction contact parameters for nonlinear dynamic analysis, in: Proceedings of the Society for Experimental Mechanics IMAC Conference, 2012.
[43] Medina, S., Nowell, D., Dini, D., Analytical and numerical models for tangential stiffness of rough elastic contacts. Tribol. Lett. 49:1 (2013), 103–115, 10.1007/s11249-012-0049-y.
[44] Putignano, C., Ciavarella, M., Barber, J., Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads. J. Mech. Phys. Solids 59:12 (2011), 2442–2454, 10.1016/j.jmps.2011.09.005.
[45] Schwingshackl, C.W., Petrov, E.P., Ewins, D.J., Effects of contact interface parameters on vibration of turbine bladed disks with underplatform dampers. J. Eng. Gas Turbines Power, 134(3), 2012, 032507, 10.1115/1.4004721.
