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TECHNICAL PAPERS

Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method

[+] Author and Article Information
Siu-Tong Choi, Sheng-Yang Mau

Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, 70101, Taiwan, R.O.C

J. Mech. Des 123(4), 562-568 (Oct 01, 1999) (7 pages) doi:10.1115/1.1415739 History: Received October 01, 1999
Copyright © 2001 by ASME
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References

Mitchell, L. D., and Mellen, D. M., 1975, “Torsional-Lateral Coupling in a Geared High-Speed Rotor System,” ASME Paper No. 75-DET-75.
Lund,  J. W., 1978, “Critical Speeds, Stability and Response of a Geared Train of Rotors,” ASME J. Mech. Des., 100, No. 2, pp. 535–539.
David, J. W., and Park, N. G., 1987, “The Vibration Problem in Gear Coupled Rotor Systems,” ASME DE-Vol. 2, Rotating Machinery Dynamics, Volume One, Proceedings of The 11th Biennial Conference on Mechanical Vibration and Noise, Boston, U.S.A., pp. 297–303.
Ozguven,  H. N., and Houser,  D. R., 1988, “Mathematical Models Used in Gear Dynamics—a Review,” J. Sound Vib., 121, No. 3, pp. 383–411.
Kahraman,  A., Ozguven,  H. N., Houser,  D. R., and Zakrajsek,  J. J., 1992, “Dynamic Analysis of Geared Rotors by Finite Elements,” ASME J. Mech. Des., 114, No. 3, pp. 507–514.
Rao, J. S., 1991, Rotor Dynamics, 2nd edition, Wiley Eastern Ltd., New Delhi, India.
Nelson,  H. D., and McVaugh,  J. M., 1976, “The Dynamics of Rotor-Bearing Systems Using Finite Elements,” ASME J. Eng. Ind., 98, No. 2, pp. 593–600.
Iida,  H., Tamura,  A., Kikuch,  K., and Agata,  H., 1980, “Coupled Torsional-Flexural Vibration of Shaft in a Geared System of Rotors,” Bull. JSME, 23, No. 186, pp. 2111–2117.
Neriya,  S. V., Bhat,  R. B., and Sankar,  T. S., 1985, “Coupled Torsional-Flexible Vibration of a Geared Shaft System Using Finite Element Analysis,” The Shock and Vibration Bulletin,55, Part 3, pp. 13–25.
Shiau,  T. N., Rao,  J. S., Chang,  J. R., and Choi,  S.-T., 1999, “Dynamic Behavior of Geared Rotors,” ASME J. Eng. Gas Turbines Power, 121, pp. 494–503.
Lund,  J. W., 1974, “Stability and Damped Critical Speeds of Flexible Rotor in Fluid-Film Bearings,” ASME J. Eng. Ind., 96, No. 2, pp. 509–517.
Hibner,  D. H., 1975, “Dynamic Response of Viscous-Damped Multi-Shaft Jet Engines,” J. Aircr., 12, No. 4, pp. 305–312.
Lund,  J. W., and Orcutt,  F. K., 1967, “Calculations and Experiments on the Unbalance Response of a Flexible Rotor,” ASME J. Eng. Ind., 89, Series B, No. 4, pp. 785–796.
Gu,  J., 1986, “An Improved Transfer Matrix-Direct Integration Method for Rotor Dynamics,” ASME J. Vib., Acoust., Stress, Reliab. Des., 108, No. 2, pp. 182–188.
Lee,  A. C., Kang,  Y., and Liu,  S. L., 1991, “A Modified Transfer Matrix Method for Linear Rotor-Bearing Systems,” ASME J. Appl. Mech., 58, No. 3, pp. 776–783.
David,  J. W., Mitchell,  L. D., and Daws,  J. W., 1987, “Using Transfer Matrices for Parametric System Forced Response,” ASME J. Vib., Acoust., Stress, Reliab. Des., 109, No. 4, pp. 356–360.

Figures

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Coordinate system of a shaft element
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The discrete model of a geared rotor-bearing system
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Section view of a meshing pair of spur gears
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First four lateral-torsional coupled mode shapes of geared rotor system
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Campbell diagrams of two-shaft system with and without a gear mesh
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Responses of both gears with constant gear-mesh stiffness due to mass unbalance of the driving gear
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Responses of both gears with constant gear-mesh stiffness due to the geometric eccentricity situated on the driving gear
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Responses of both gears with constant gear-mesh stiffness due to the excitation of transmission error
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Responses of both gears with time-varying gear-mesh stiffness due to the excitation of transmission error

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