Abstract
With industry diverging away from the use of oil in the hopes of a more environmentally friendly production, the use of Gas Foil Bearings (GFBs) can facilitate an oil-free alternative for high-speed rotating light machinery. Currently, their application is, however, limited by their low load-bearing capability and low vibration damping. Hybridization has the possibility to mitigate these limitations. The system presented in this paper demonstrates the increased system capabilities through passive and active Hybrid Gas Foil Bearings (HGFB) with radial gas injection. The non-linear differential equations comprising the system, pressure states, foil deflections, rotor movements, and actuator position, are solved simultaneously with and without control feedback. The presented results comprise unbalance response waterfall diagrams.
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References
Oh, K.P., Rohde, S.M.: A theoretical investigation of the multileaf journal bearing. J. Appl. Mech. 43, 237–242 (1976)
Heshmat, H., Walowit, J.A., Pinkus, O.: Analysis of gas-lubricated foil journal bearings. J. Lubr. Technol. 105, 647–655 (1983)
Peng, J., Carpino, M.: Calculation of stiffness and damping coefficients for elastically supported gas foil bearings. J. Tribol. 115, 20–27 (1993)
Schiffmann, J., Spakovszky, Z.S.: Foil bearing design guidelines for improved stability. J. Tribol. 135, 12 (2012)
Pattnayak, M., Ganai, P., Pandey, R., Dutt, J., Fillon, M.: An overview and assessment on aerodynamic journal bearings with important findings and scope for explorations. Tribol. Int. 174, 107778 (2022)
Adolfo, D., Ertas, B.: Dynamic characterization of a novel externally pressurized compliantly damped gas-lubricated bearing with hermetically sealed squeeze film damper modules. In: ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, p. V07BT34A050 (2018)
Ertas, B., Adolfo, D.: Compliant hybrid gas bearing using modular hermetically sealed squeeze film dampers. J. Eng. Gas Turbines Power 141, 08 (2018)
Feng, K., Cao, Y., Yu, K., Hanqing, G., Wu, Y., Guo, Z.: Characterization of a controllable stiffness foil bearing with shape memory alloy springs. Tribol. Int. 136, 03 (2019)
Yazdi, B.Z., Kim, D.: Rotordynamic performance of hybrid air foil bearings with regulated hydrostatic injection. In: Journal of Engineering for Gas Turbines and Power-transactions of the ASME, p. V07AT34A012 (2017)
Hanqing, G., Feng, K., Cao, Y.-L., Huang, M., Wu, Y.-H., Guo, Z.: Experimental and theoretical investigation of rotordynamic characteristics of a rigid rotor supported by an active bump-type foil bearing. J. Sound Vib. 466, 115049 (2019)
Ha, D., Stolarski, T., Yoshimoto, S.: An aerodynamic bearing with adjustable geometry and self-lifting capacity. part 1: self-lift capacity by squeeze film. In: Proceedings of the Institution of Mechanical Engineers Part J-Journal of Engineering Tribology - PROC INST MECH ENG J-J ENG TR, vol. 219, pp. 33–39 (2005)
Belforte, G., Raparelli, T., Viktorov, V., Trivella, A.: Discharge coefficients of orifice-type restrictor for aerostatic bearings. Tribol. Int. 40, 512–521 (2007)
Chang, S., Chan, C., Jeng, Y.: Numerical analysis of discharge coefficients in aerostatic bearings with orifice-type restrictors. Tribol. Int. 90, 157–163 (2015)
Gao, S., Cheng, K., Chen, S., Ding, H., Fu, H.: CFD based investigation on influence of orifice chamber shapes for the design of aerostatic thrust bearings at ultra-high speed spindles. Tribol. Int. 92, 12 (2015)
Renn, J.-C., Hsiao, C.-H.: Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings. Tribol. Int. 37, 309–315 (2004)
Rowe, W.B.: Basic Flow Theory 1st(ed.), p. 25-48. Elsevier (2012)
Zhou, Y., Chen, X., Chen, H.: A hybrid approach to the numerical solution of air flow field in aerostatic thrust bearings. Tribol. Int. 102, 04 (2016)
Larsen, J., Varela, A.C., Santos, I.: Numerical and experimental investigation of bump foil mechanical behaviour. Tribol. Int. 74, 46–56 (2014)
Larsen, J., Santos, I., Hansen, A.: Experimental and theoretical analysis of a rigid rotor supported by air foil bearings. Mech. Ind. 09 (2014)
Larsen, J., Santos, I., von Osmanski, S.: Stability of rigid rotors supported by air foil bearings: comparison of two fundamental approaches. J. Sound Vib. 381, 07 (2016)
Larsen, J., Nielsen, B., Santos, I.: On the numerical simulation of nonlinear transient behavior of compliant air foil bearings. In: Proceedings of the 11th International Conference on Schwingungen Rotierenden Maschinen, pp. 1–13 (2015)
Larsen, J., Santos, I.: On the nonlinear steady-state response of rigid rotors supported by air foil bearings - theory and experiments. J. Sound Vib. 346, 03 (2015)
von Osmanski, S., Larsen, J., Santos, I.: A fully coupled air foil bearing model considering friction - theory & experiment. J. Sound Vib. 400, 660–679 (2017)
Heinemann, S.T., Jensen, J.W., von Osmanski, S., Santos, I.F.: Numerical modelling of compliant foil structure in gas foil bearings: comparison of four top foil models with and without radial injection. J. Sound Vib. 117513 (2022)
von Osmanski, S., Santos, I.: Gas foil bearings with radial injection: multi-domain stability analysis and unbalance response. J. Sound Vib. 508, 116177 (2021)
Heinemann, S.: Design of controllable segmented foil bearings based on multi-physics modelling techniques, Master’s Thesis (2020)
Larsen, J., Santos, I.: Efficient solution of the non-linear reynolds equation for compressible fluid using the finite element method. J. Braz. Soc. Mech. Sci. Eng. 37, 07 (2014)
von Osmanski, S., Larsen, J., Santos, I.: Modelling of compliant-type gas bearings: a numerical recipe. In: 13th International Conference on Dynamics of Rotating Machinery (SIRM 2019), pp. 13–27 (2019)
Hestmat, H., Walowit, J.A.: Analysis of gas lubricated compliant trust bearings. J. Lubr. Technol. 105(4), 638–646 (1983)
Hestmat, H., Walowit, J.A.: Analysis of gas lubricated foil bearings. J. Lubr. Technol. 105(4), 647–655 (1983)
Inman, D.J.: Engineering Vibration, 4th edn. Pearson, London (2014)
Pierart, F., Santos, I.: Active lubrication applied to radial gas journal bearings. part 2: modelling improvement and experimental validation. Tribol. Int. 96, 12 (2015)
Annon. IEEE standard on piezoelectricity. ANSI/IEEE Std 176-19871 (1988)
Christensen, R., Santos, I.: Design of active controlled rotor-blade systems based on time-variant modal analysis. J. Sound Vib. 280(3), 863–882 (2005)
Christensen, R., Santos, I.: Modal controllability and observability of bladed disks and their dependency on the angular velocity. J. Vib. Control 11(6), 801–828 (2005)
Hendricks, E., Jannerup, O., Sørensen, P.H.: Linear Systems control, Deterministic and Stochastic Methods. Springer-Verlag, Berlin (2008)
Cook, R.D., Malkus, D.S., Plesha, M.E., Witt, R.J.: Concepts and Applications of Finite Element Analysis, 4th edn. Wiley, Hoboken (2001)
Dennis, J.J.E., Schnabel, R.B.: Numerical methods for unconstrained optimization and nonlinear equations. Society for Industrial and Applied Mathematics, SIAM (1983)
Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical solution of initial-value problems in differential-algebraic equations. Society for Industrial and Applied Mathematics, SIAM (1996)
Morosi, S., Santos, I.: On the modelling of hybrid aerostatic-gas journal bearings. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 225, pp. 641–653 (2011)
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Jensen, J.W., Santos, I.F. (2023). A Presentation of Control Theory Applied to the Design of Controllable Segmented Gas Foil Bearings. In: Chasalevris, A., Proppe, C. (eds) Advances in Active Bearings in Rotating Machinery. ABROM 2022. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-32394-2_3
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DOI: https://doi.org/10.1007/978-3-031-32394-2_3
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