Lund’s Elliptic Orbit Forced Response Analysis: The Keystone of Modern Rotating Machinery Analysis

[+] Author and Article Information
R. Gordon Kirk

Randolph Hall 0238, Virginia Tech, Blacksburg, VA 24061

J. Vib. Acoust 125(4), 455-461 (Oct 08, 2003) (7 pages) doi:10.1115/1.1605977 History: Received June 01, 2003; Online October 08, 2003
Copyright © 2003 by ASME
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Jeffcott,  H. H., 1919, “The Lateral Vibrations of Loaded Shafts in the Neighborhood of a Whirling Speed[[ellipsis]] The Effect of Want of Balance,” Philos. Mag., 37(6), pp. 304–314.
Prohl,  M. A., 1945, “A General Method for Calculating Critical Speeds of Flexible Rotors,” ASME J. Appl. Mech., 12(3), pp. 142–148.
Tang,  T. M., and Trumpler,  P. R., 1964, “Dynamics of Synchronous Precessing Turborotors With Particular Reference to Balancing; Part I, Theoretical Foundations,” ASME J. Appl. Mech., 31(1), March, pp. 115–122.
Kirk, R. G., 1972, “Nonlinear Transient Analysis of Multi-Mass Flexible Rotors,” Ph.D. Dissertation, University of Virginia, June.
Lund,  J. W., and Sternlicht,  B., 1962, “Rotor-Bearing Dynamics With Emphasis on Attenuation,” ASME J. Basic Eng., 84(4), pp. 491–502.
Rouch,  K. E., and Kao,  J. S., 1979, “A Tapered Beam Finite Element for Rotor Dynamics Analysis,” J. Sound Vib., 66, pp. 119–140.
Nelson,  H. D., 1980, “A Finite Rotating Shaft Element Using Timoshenko Beam Theory,” ASME J. Mech. Des., 102(10), pp. 793–803.
Nelson,  H. D., and McVaugh,  J. M., 1975, “The Dynamics of Rotor-Bearing Systems Using Finite Elements,” ASME J. Eng. Ind., 98(2), pp. 593–600.
Lund,  J. W., and Orcutt,  F. K., 1967, “Calculations and Experiments on the Unbalance Response of a Flexible Rotor,” ASME J. Eng. Ind., 89(4), pp. 785–796.
Lund, J. W., 1965, Rotor-Bearing Dynamics Technology, Part V, AFAPL-TR-65-45, Aero Propulsion Lab, Wright-Patterson Air Force Base, Dayton, Ohio, May.
Lund, J. W., 1988, “Keynote Paper: Topics in Rotor Dynamics,” The Second International Symposium on Transport Phenomena, Dynamics and Design of Rotating Machinery, Honolulu, Hawaii, pp. 205–211.
Kirk, R. G., and Gunter, E. J., 1973, “Nonlinear Transient Analysis of Multi-Mass Flexible Rotors-Theory and Applications,” NASA CR 2300.
Yamamoto, T., 1954, “On the Critical Speeds of a Shaft,” Memoirs of the Faculty of Engineering, Nagoya University, Japan.
Kirk,  R. G., Raju,  K. V. S., and Ramesh,  K., 1999, “PC-Based Analysis of Turbomachinery Vibration,” Shock Vib. Dig., 31(6), pp. 449–454.
Faulkner, H., Strong, W., and Kirk., R. G., 1997, “Thermally Induced Synchronous Instability of a Radial Inflow Overhung Turbine PART I,” Proceedings of ASME Design Technical Vibrations Conference, Sacramento, CA., Sept.
Faulkner, H., Strong, W., and Kirk., R. G., 1997, “Thermally Induced Synchronous Instability of a Radial Inflow Overhung Turbine PART II,” Proceedings of ASME Design Technical Vibrations Conference, Sacramento, CA, Sept.
Kirk,  R. G., and Gunter,  E. J., 1972, “The Effect of Support Flexibility and Damping on the Synchronous Response of a Single-Mass Flexible Rotor,” ASME J. Eng. Ind., 94(1), pp. 221–232.
Kirk, R. Gordon, 1998, “Observation of Disk Axial Face Instability,” Proceedings of 1998 IFTOMM Conference, Darmstadt Technical University Germany, Sept., pp. 595–604.


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The basic transfer elements and station nomenclature
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Lund presenting an invited Keynote Paper in 1988 explaining the dynamics of a lumped mass station including the support stiffness and gyroscopic terms
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Ellipse showing orientation angle, θ and semi-major, a semi-minor axis, b
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Graphical construction to find actual phase from an orbit with timing mark if the direction of whirl is known
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(a) Experimental results showing forward and backward whirl orbits; (b) Critical speed map for test rig showing predicted forward and backward modes
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Simulation of a turbocharger rotor to rotating imbalance excitation. The lower right hand corner shows orbits at the bearing locations plus a phase reference for the imbalance angular location.
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Major axis response to imbalance excitation versus rotor speed for a turbocharger




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