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Theoretical and nonlinear behavior analysis of a flexible rotor supported by a relative short Herringbone-Grooved gas journal-bearing system. (English) Zbl 1142.70328
Summary: This paper considers the bifurcation and nonlinear behavior of a flexible rotor supported by a relative short herringbone-grooved gas journal bearing system. A numerical method is employed to a time-dependent mathematical model. A finite difference method with successive over relation method is employed to solve the Reynolds’ equation. The system state trajectory, Poincaré maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and journal centers in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and quasi-periodic response of the rotor and journal centers. It further shown the dynamic behavior of this type of system varies with changes in bearing number and rotor mass. The results of this study contribute to a better understanding of the nonlinear dynamics of herringbone-grooved gas journal bearing systems.

70K50Transition to stochasticity (general mechanics)
70K55Transition to stochasticity (chaotic behavior)
Full Text: DOI
[1] J.H. Vohr, C.H.T. Pan, On the Spiral--Grooved, Self-Acting Gas Bearings, MTI Technical Report, MTI63TR52, 1963
[2] Vohr, J. H.; Chow, C. Y.: Characteristics of herringbone-grooved, gas-lubricated journal bearings. ASME J. Basic eng. 87, 568-578 (1965)
[3] B.J. Hamrock, D.P. Fleming, Optimization of self-acting herringbone grooved journal bearing for maximum radial load capacity, in: 5th Gas Bearing Symp, vol. 1 (13), 1971
[4] Bonneau, D.; Absi, J.: Analysis of aerodynamic journal bearing with small number of herringbone grooves by finite element method. ASME J. Tribology 116, 698-704 (1994)
[5] Zang, Y.; Hatch, M. R.: Analysis of coupled journal and thrust hydrodynamic bearing using finite volume method. ASME adv. Inform. storage process. Syst. 1, 71-79 (1995)
[6] Zirkelback, N.; Andres, L. San: Finite element analysis of herringbone groove journal bearings: A parametric study. ASME J. Tribology 120, 234-240 (1998)
[7] Jang, G. H.; Kim, Y. J.: Calculation of dynamic coefficients in a hydrodynamic bearing considering five degrees of freedom for a general rotor-bearing system. ASME J. Tribology 121, No. 3, 499-505 (1999)
[8] Castelli, V.; Elrod, H. G.: Solution of the stability problem for 360 degree self-acting, gas-lubricated bearing. ASME J. Basic eng. 87, 199-212 (1961)
[9] F.F. Ehrich, Subharmonic vibration of rotors in bearing clearance, ASME. 1966. Paper No. 66-MD-1
[10] Kim, Y. B.; Noah, S. T.: Bifurcation analysis of a modified jeffcot rotor with bearing clearances. Nonlinear dynam. 1, 221-241 (1990)
[11] Zhao, J. Y.; Linnett, I. W.; Mclean, L. J.: Subharmonic and quasi-periodic motion of an eccentric squeeze film damper-mounted rigid rotor. ASME J. Vibration acoustics 116, 357-363 (1994)
[12] Brown, R. D.; Addison, P.; Chan, A. H. C.: Chaos in the unbalance response of journal bearings. Nonlinear dynam. 5, 421-432 (1994)
[13] Adiletta, G.; Guido, A. R.; Rossi, C.: Chaotic motions of a rigid rotor in short journal bearings. Nonlinear dynam. 10, 251-269 (1996)
[14] Adiletta, G.; Guido, A. R.; Rossi, C.: Nonlinear dynamics of a rigid unbalanced rotor in short bearings. Part I: Theoretical analysis. Nonlinear dynam. 14, 57-87 (1997) · Zbl 0910.70008
[15] Adiletta, G.; Guido, A. R.; Rossi, C.: Nonlinear dynamics of a rigid unbalanced rotor in short bearings. Part II: Experimental analysis. Nonlinear dynam. 14, 157-189 (1997) · Zbl 0910.70008
[16] Sundararajan, P.; St, S. T. Noah: Dynamics of forced nonlinear systems using shooting/arc-length continuation method -- application to rotor systems. ASME J. Vibration acoustics 119, 9-20 (1997)
[17] Czolczynski, K.; Kapitaniak, T.: Hopf bifurcation in rotors supported in gas bearings. Chaos solitons fractals 4, 499-515 (1997) · Zbl 0963.70554
[18] Ji, J. C.; Leung, A. Y. T.: Non-linear oscillations of a rotor-magnetic bearing system under superharmonic resonance conditions. Internat. J. Non-linear mech. 38, 829-835 (2003) · Zbl 05138186
[19] Ji, J. C.: Dynamics of a jeffcott rotor-magnetic bearing system with time delays. Internat. J. Non-linear mech. 38, 1387-1401 (2003) · Zbl 05138229