Controlling bifurcations in high-speed rotors utilizing active gas foil bearings

• Autorzy: Papadopoulos Anastasios , Gavalas Ioannis , Chasalevris Athanasios

Identyfikatory

DOI

10.24425/bpasts.2023.146796

• Języki publikacji: EN

Abstrakty

EN

High-speed rotors on gas foil bearings (GFBs) are applications of increasing interest due to their potential to increase the power-toweight ratio in machines and also formulate oil-free design solutions. The gas lubrication principles render lower (compared to oil) power loss and increase the threshold speed of instability in rotating systems. However, self-excited oscillations may still occur at circumferential speeds similar to those in oil-lubricated journal bearings. These oscillations are usually triggered through Hopf bifurcation of a fixed-point equilibrium (balanced rotor) or secondary Hopf bifurcation of periodic limit cycles (unbalanced rotor). In this work, an active gas foil bearing (AGFB) is presented as a novel configuration including several piezoelectric actuators that shape the foil through feedback control. A finite element model for the thin foil mounted in some piezoelectric actuators (PZTs), is developed. Second, the gas-structure interaction is modelled through the Reynolds equation for compressible flow. A simple physical model of a rotating system consisting of a rigid rotor and two identical gas foil bearings is then defined, and the dynamic system is composed with its unique source of nonlinearity to be the impedance forces from the gas to the rotor and the foil. The third milestone includes a linear feedback control scheme to stabilize (pole placement) the dynamic system, linearized around a speed-dependent equilibrium (balanced rotor). Further to that, linear feedback control is applied in the dynamic system utilizing polynomial feedback functions in order to overcome the problem of instability.

Słowa kluczowe

EN

bifurcation control; Hopf bifurcation; active gas foil bearings; nonlinear control; high speed rotor

PL

kontrola bifurkacji; bifurkacja Hopfa; sterowanie nieliniowe; łożysko foliowe gazowe aktywne; wirnik o dużej prędkości

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2023
• Tom: Vol. 71, nr 6
• Strony: art. no. e146796
• Opis fizyczny: Bibliogr. 28 poz., rys.

Twórcy

autor

Papadopoulos Anastasios

• National Technical University of Athens, Athens, Greece

autor

Gavalas Ioannis

• National Technical University of Athens, Athens, Greece

• https://orcid.org/0000-0001-5693-2382

autor

Chasalevris Athanasios

• National Technical University of Athens, Athens, Greece

• https://orcid.org/0000-0002-6891-439X

Bibliografia

• [1] T. Leister, C. Baum, and W. Seemann, “On the importance of frictional energy dissipation in the prevention of undesirable self-excited vibrations in gas foil bearing rotor systems,” Technische Mechanik, vol. 37, pp. 280–290, 2017, doi: 10.24352/UB.OVGU-2017-104.
• [2] H. Heshmat, J.A. Walowit, and O. Pinkus, “Analysis of Gas-Lubricated Foil Journal Bearings,” J.Lubr. Technol., vol. 105, no. 4, pp. 647–655, 1983, doi: 10.1115/1.3254697.
• [3] J.S. Larsen, I.F. Santos, and S. von Osmanski, “Stability of rigid rotors supported by air foil bearings: Comparison of two fundamental approaches,” J. Sound Vibr., vol. 381, pp. 179–191, 2016, doi: 10.1016/j.jsv.2016.06.022.
• [4] S.P. Bhore and A.K. Darpe, “Nonlinear dynamics of flexible rotor supported on the gas foil journal bearings,” J. Sound Vibr., vol. 332, no. 20, pp. 5135–5150, 2013, doi: 10.1016/j.jsv.2013.04.023.
• [5] D. Kim, “Parametric Studies on Static and Dynamic Performance of Air Foil Bearings with Different Top Foil Geometries and Bump Stiffness Distributions,” J. Tribol., vol. 129, no. 2, pp. 354–364, 2006, doi: 10.1115/1.2540065.
• [6] J.S. Larsen and I.F. Santos, “On the nonlinear steady-state response of rigid rotors supported by air foil bearings – theory and experiments,” J. Sound Vibr., vol. 346, pp. 284–297, 2015, doi: 10.1016/j.jsv.2015.02.017.
• [7] J.W. Lund, “Calculation of Stiffness and Damping Properties of Gas Bearings,” J. Lubr. Technol., vol. 90, no. 4, pp. 793–803, 1968, doi: 10.1115/1.3601723.
• [8] B.B. Nielsen and I.F. Santos, “Transient and steady state behaviour of elasto–aerodynamic air foil bearings, considering bump foil compliance and top foil inertia and flexibility: A numerical investigation,” Proc. Inst. Mech. Eng. Part J.-J. Eng. Tribol., vol. 231, no. 10, pp. 1235–1253, 2017, doi: 10.1177/1350650117689985.
• [9] H. Pham and P. Bonello, “Efficient techniques for the computation of the nonlinear dynamics of a foil-air bearing rotor system,” in Proc. ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. Volume 7B: Structures and Dynamics, USA, 2013, p. V07BT30A011, doi: 10.1115/GT2013-94389.
• [10] P. Bonello and H.M. Pham, “Nonlinear Dynamic Analysis of High Speed Oil-Free Turbomachinery With Focus on Stability and Self-Excited Vibration,” J. Tribol., vol. 136, no. 4, p. 041705, 2014, doi: 10.1115/1.4027859.
• [11] T. Pronobis and R. Liebich, “Comparison of stability limits obtained by time integration and perturbation approach for gas foil bearings,” J. Sound Vibr., vol. 458, pp. 497–509, 2019, doi: 10.1016/j.jsv.2019.06.034.
• [12] J. Park and K. Sim, “A Feasibility Study of Controllable Gas Foil Bearings With Piezoelectric Materials Via Rotordynamic Model Predictions,” J. Eng. Gas. Turbines Power-Trans. ASME, vol. 141, no. 2, p. 021027, 2018, doi: 10.1115/1.4041384.
• [13] L. Savin, D. Shutin, and A. Kuzavka, “Actuators of active tribotechnical systems of the rotor-bearing type,” in IOP Conference Series: Materials Science and Engineering, vol. 233, no. 1, p. 012043, 2017, doi: 10.1088/1757-899X/233/1/012043.
• [14] A. Chasalevris and F. Dohnal, “A journal bearing with variable geometry for the reduction of the maximum amplitude during passage through resonance,” J. Vib. Acoust., vol. 134, no. 6, p. 061005, 2012, doi: 10.1115/1.4007242.
• [15] A. Chasalevris and F. Dohnal, “A journal bearing with variable geometry for the suppression of vibrations in rotating shafts: Simulation, design, construction and experiment,” Mech. Syst. Signal Proc., vol. 52–53, no. 1, pp. 506–528, 2015, doi: 10.1016/j.ymssp.2014.07.002.
• [16] A. Chasalevris and G. Guignier, “Alignment and rotordynamic optimization of turbine shaft trains using adjustable bearings in real-time operation,” Proc. Inst. Mech. Eng. Part C-J. Eng. Mech. Eng. Sci., vol. 233, no. 7, pp. 2379–2399, 2019, doi: 10.1177/0954406218791636.
• [17] S. von Osmanski and I.F. Santos, “Gas foil bearings with radial injection: Multi-domain stability analysis and unbalance response,” J. Sound Vibr., vol. 508, p. 116177, 2021, doi: 10.1016/j.jsv.2021.116177.
• [18] S.-H. Chen and H.H. Pan, “Guyan reduction,” Commun. Appl. Num. Meth., vol. 4, no. 4, pp. 549–556, 1988, doi: 10.1002/cnm.1630040412.
• [19] P. Yu and G. Chen, “Hopf bifurcation control using nonlinear feedback with polynomial functions,” Int. J. Bifurcation Chaos, vol. 14, no. 05, pp. 1683–1704, 2004, doi: 10.1142/S0218127404010291.
• [20] M. Bonnet, A. Frangi, and C. Rey, The finite element method in solid mechanics. McGraw Hill Education, 2014. [Online]. Available: https://hal.science/hal-01083772.
• [21] E. Estupinan and I. Santos, “Controllable Lubrication for Main Engine Bearings Using Mechanical and Piezoelectric Actuators,” IEEE/ASME Trans. Mechatron., vol. 17, no. 2, pp. 279–287, 2012, doi: 10.1109/TMECH.2010.2099663.
• [22] E.A. Estupinan and I.F. Santos, “Controllable radial oil injection applied to main engine bearings-hybrid bearing configurations and control pressure rules,” Proc. STLE/ASME 2010 International Joint Tribology Conference. STLE/ASME 2010 International Joint Tribology Conference, USA, 2010, pp. 145–147, doi: 10.1115/IJTC2010-41170.
• [23] ANSI/IEEE, 1987. IEEE standard on piezoelectricity. Tech. Rep. Std 176-1987, IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society, New York.
• [24] A. Duvnjak and E. Marusic-Paloka, “Derivation of the reynolds equation for lubrication of a rotating shaft,” Arch. Math., vol. 036, no. 4, pp. 239253, 2000. [Online]. Available: http://eudml.org/doc/248566.
• [25] P. Papafragkos, I. Gavalas, I. Raptopoulos, and A. Chasalevris, “Optimizing energy dissipation in gas foil bearings to eliminate bifurcations of limit cycles in unbalanced rotor systems,” Nonlinear Dyn., vol. 111, no. 1, pp. 67–95, 2023, doi: 10.1007/s11071-022-07837-1.
• [26] C. Pukdeboon, “A review of fundamentals of Lyapunov theory,” J. Appl Sci., vol. 10, no. 01, pp. 55–61, 2011.
• [27] J. van der Woude, “A note on pole placement by static output feedback for single-input systems,” Syst. Control Lett., vol. 11, no. 4, pp. 285–287, 1988, doi: 10.1016/0167-6911(88)90072-2.
• [28] The MathWorks, Inc. (2022). Optimization Toolbox version: R2021b. [Online] Available: https://www.mathworks.com.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).