Abstract
Bearings are key elements for a detailed dynamical analysis of rotating machines. In this way, a rotating component sustained by flexible supports and transmitting power creates typical problems that are found in several machines, being that small or large turbines, turbo generators, motors, compressors or pumps. Therefore, representative mathematical models, such as the use of bearings nonlinear forces modeling, have been developed in order to simulate specific systems working conditions. The numerical solution of the equation of motion, when considering nonlinear complete solution of finite hydrodynamic bearings, is highly expensive in terms of computational processing time. A solution to overcome this problem without losing the nonlinear characteristics of the component is use a high order Taylor series expansion to characterize the hydrodynamic forces obtained by the Reynolds equation. This procedure accelerates the nominal behavior predictions, facilitating fault models insertion and making feasible actions in control systems design. So, this papers aims to analyze the use of nonlinear coefficients, generated by the high order Taylor series expansion, to simulate the rotor dynamics under strong nonlinear bearing behavior. The results obtained were compared with Reynolds and linear simulations, and demonstrated that the nonlinear coefficients can be successful to represent bearing behavior even in extreme situations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Lund, J.W., Thomsen, K.K.: A calculation method and data for the dynamic coefficients of oil-lubricated journal bearings. In: Topics in Fluid Bearing and Rotor Bearing System Design and Optimization ASME, pp. 11–28 (1978)
Lund, J.W.: Review of the concept of dynamic coefficients for fluid film journal bearings. ASME J. Tribol. 109, 37–41 (1987)
Hattori, H.: Dynamic analysis of a rotor-journal bearing system with large dynamic loads (stiffness and damping coefficients variation in bearing oil films). JSME Int. J. Ser. C 36(2), 251–257 (1993)
Khonsari, M.M., Chang, Y.J.: Stability boundary of non-linear orbits within clearance circle of journal bearings. J. Vib. Acoust. 115, 303–307 (1993)
Zhao, S.X., Zhou, H., Meng, G., Zhu, J.: Experimental identification of linear oil-film coefficients using least-mean-square method in time domain. J. Sound Vib. 287, 809–825 (2005)
Dakel, M., Baguet, S., Dufour, R.: Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings. J. Sound Vib. 333, 2774–2799 (2014)
Brancati, R., Rocca, E., Russo, M., Russo, R.: Journal orbits and their stability for rigid unbalanced rotors. J. Tribol. 117(4), 709–716 (1995)
Castro, H.F., Cavalca, K.L., Nordmann, R.: Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model. J. Sound Vib. 317, 273–293 (2008)
Ma, H., Li, H., Niu, H., Song, R., Wen, B.: Nonlinear dynamic analysis of a rotor bearing seal system under two loading conditions. J. Sound Vib. 332, 6128–6154 (2013)
Capone, G.: Orbital motions of rigid symmetric rotor supported on journal bearings. La Mecc. Italiana 199, 37–46 (1986)
Capone, G.: Analytical description of fluid—dynamic force field in cylindrical journal bearing. L’ Energia Elettrica 3, 105–110 (1991)
Zhao, S.X., Dai, X.D., Meng, G., Zhu, J.: An experimental study of nonlinear oil-film forces of a journal bearing. J. Sound Vib. 287, 827–843 (2005)
Asgharifard-Sharabiani, P., Ahmadian, H.: Nonlinear model identification of oil-lubricated tilting pad bearings. Tribol. Int. 92, 533–543 (2015)
Nelson, H.D., McVaugh, J.M.: The dynamics of rotor-bearing systems using finite elements. ASME J. Eng. Ind. 98(2), 593–600 (1976)
Nelson, H.D.: A finite rotating shaft element using timoshenko beam theory. ASME J. Mech. Des. 102(4), 793–803 (1980)
Genta, G.: Dynamics of Rotating Systems, 1st edn. Springer Science + Business Media, New York (2005)
Pinkus, O., Sternlicht, S.A.: Theory of Hydrodynamic Lubrication. McGraw-Hill, New York (1961)
Stewart, J.: Calculus: Early Transcendentals, 7th edn. Brooks/Cole Cengage Learning, Belmont (2012)
Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning: Data Mining, Inference and Prediction, 2nd edn. Springer, Berlin (2009)
Patankar, S.V.: Numerical Heat Transfer and Fluid Flow, 1st edn. Hemisphere Publishing Corporation, New York (1980)
Bathe, K.: Finite Element Procedures in Engineering Analysis, 1st edn. Prentice-Hall, New Jersey (1982)
International Organization for Standardization: Mechanical Vibration – Balance Quality Requirements for Rotors in a Constant (Rigid) State – Part1: Specification and Verification of Balance Tolerances (ISO 1940-1:2003), 2nd edn. ISO Copyright Office, Geneva (2003)
Acknowledgements
The authors would like to thank CNPq and grant #2015/20363-6 from the São Paulo Research Foundation (FAPESP) for the financial support to this research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Alves, D.S., Cavalca, K.L. (2019). Numerical Identification of Nonlinear Hydrodynamic Forces. In: Cavalca, K., Weber, H. (eds) Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM. IFToMM 2018. Mechanisms and Machine Science, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-319-99262-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-99262-4_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99261-7
Online ISBN: 978-3-319-99262-4
eBook Packages: EngineeringEngineering (R0)