Abstract
This paper investigates oscillations in a flexible rotor system with radial clearance between an outer ring of the bearing and a casing by experiments and numerical simulations. The mathematical model considers the collisions of the bearing with the casing. The following phenomena are found: (1) Nonlinear resonances of subharmonic, super-subharmonic and combination oscillation occur. (2) Self-excited oscillation of a forward whirling mode occurs in a wide range above the major critical speed. (3) Entrainment phenomena from self-excited oscillation to nonlinear forced oscillation occur at these nonlinear resonance ranges. Moreover, this study analyzes periodic solutions of the mathematical model by the Harmonic Balance Method (HBM). As the results, the nonlinear resonances of subharmonic oscillation and its entrainment phenomenon can be explained theoretically by investigating the stability of the periodic solutions. The influence of the static force and the bearing damping on these oscillation are also clarified.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Den Hartog, J.P.: Mechanical Vibrations, 4th edn. McGraw–Hill, New York (1956)
Black, H.F.: Interaction of a whirling rotor with a vibrating stator across a clearance annulus. J. Mech. Eng. Sci. 10(1), 1–12 (1968)
Ehehalt, U.: Stability of synchronous forward whirl at rotor–stator contact. ASME DETC2005-84440 (2002)
Ehehalt, U., Hahn, E., Markert, R.: Motion patterns at rotor–stator contact. In: The 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (2005)
Muszynska, A.: Rotor-to-stationary part full annular contact modeling. In: The 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (2002)
Li, G.X., Ppaidoussis, M.P.: Impact phenomena of rotor–casing dynamical systems. Nonlinear Dyn. 5, 53–70 (1994)
Choi, Y.S., Noah, S.T.: Nonlinear steady-state response of a rotor–support system. ASME J. Vib. Acoust. Stress. Reliab. 109(7), 255–261 (1987)
Kim, Y.B., Noah, S.T.: Bifurcation analysis for a modified Jeffcott rotor with bearing clearance. Nonlinear Dyn. 1, 221–241 (1990)
Fumagalli, M., Schweitzer, G.: Measurement on a rotor contacting its housing. IMechE C500/085/96 (1996)
Swanson, E.E., Raju, K.V.S., Kirk, R.G.: Test results and numerical simulation of AMB rotor drop. IMechE C500/074/96 (1996)
Ehrich, F.F.: Stator whirl with rotors in bearing clearance. ASME J. Eng. Ind., 381–390 (1967)
Ehrich, F.F.: High order subharmonic response of high speed rotors in bearing clearance. ASME J. Vib. Acoust. Stress. Reliab. 110(1), 9–15 (1988)
Ehrich, F.F.: Nonlinear phenomena in dynamic response of rotors in anisotropic mounting systems. ASME Spec. 50th Anniv. Des. Issue 117(6), 154–161 (1995)
Childs, D.W.: Fractional-frequency rotor motion due to nonsymmetric clearance effects. ASME J. Eng. Power 104, 533–541 (1982)
Yamamoto, T., Ishida, Y.: Linear and Nonlinear Rotor Dynamics. Wiley Series in Nonlinear Science, pp. 21–31 (2001)
Johnson, K.L.: Contact Mechanics, pp. 129–134. Cambridge University Press, Cambridge (1985)
Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics, pp. 158–172. Wiley–Interscience, New York (1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ishida, Y., Inagaki, M., Ejima, R. et al. Nonlinear resonances and self-excited oscillations of a rotor caused by radial clearance and collision. Nonlinear Dyn 57, 593–605 (2009). https://doi.org/10.1007/s11071-009-9482-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-009-9482-3