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Rotor Dynamics Methods

  • J. S. Rao
Part of the History of Mechanism and Machine Science book series (HMMS, volume 20)

Abstract

The industrial revolution began with reciprocating steam engines as devised by James Watt in 1780, and the 19th century witnessed a rapid expansion in various industrial sectors. Unfortunately, the reciprocating steam engine had several problems because of external combustion and excessive alternating load due to reciprocating masses that limited speeds and capacities. The industry was looking for non-reciprocating systems, purely rotating systems that could usher in an era of socalled “Vibration Free” engines. The dynamics of rotating structures are different from those of stationary structures. Basically, all the vibration phenomena will be valid, however, there are several differences and we have to set up new procedures for handling rotors and their vibratory phenomena.

Keywords

Critical Speed Gyroscopic Effect Flexible Rotor Hydrodynamic Bearing Unbalance Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alford, J.: Protecting Turbomachinery from Self Excited Rotor Whirl. J. Engng. Power 87(4), 333 (1965)Google Scholar
  2. 2.
    Archer, S.: Some Factors influencing the Life of Marine Crankshafts. Trans. Instn. Marine Engineers (1964)Google Scholar
  3. 3.
    Bhat, R.B., Rao, J.S., Sankar, T.S.: Optimum Journal Bearing Parameters for Minimum Unbalance Response in Synchronous Whirl. J. Mech. Des., ASME 104, 339 (1982)CrossRefGoogle Scholar
  4. 4.
    Black, H.F.: The Effect of Inlet Flow Swirl on the Dynamic Coefficients of High Pressure Annular Clearance Seals. Univ. of Virginia, Charlottesville (1977)Google Scholar
  5. 5.
    Brown, R.D.: Dynamic Characteristics of Long Annular Seals in Centrifugal Pumps. In: Proceedings 5th International I Mech E Conf. on Vibrations in Rotating Machinery, p. 467 (1992)Google Scholar
  6. 6.
    Carnegie, W.: Rotary Inertia and Gyroscopic Effects in Overhung Shaft Systems. Bull. Mech. Engng. Educ. 3, 191 (1964)Google Scholar
  7. 7.
    Carnegie, W., Rao, J.S., Pasricha, M.S.: A Theoretical Study of the Effects of Variable Inertia on the Torsional Vibrations of a Single Cylinder Engine System. In: Presented at Vibration Section of Institution of Marine Engineers, (November 17, 1971)Google Scholar
  8. 8.
    Childs, D.W.: Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis. Inter Science. Wiley, Chichester (1993)Google Scholar
  9. 9.
    Childs, D.W., Dressman, J.B.: Testing of Turbulent Seals for Rotordynamic Coefficients. NASA CP, vol. 2250, p. 157 (1982)Google Scholar
  10. 10.
    Childs, D.W., Wade, J.: Rotordynamic-Coefficient and Leakage Characteristics for Hole-Pattern-Stator Annular Gas Seals – Measurements Versus Predictions. Journal of Tribology, Transactions of the ASME 126, 326 (2004)CrossRefGoogle Scholar
  11. 11.
    Den Hartog, J.P.: Mechanical Vibration. McGraw-Hill Book Co, New York (1940/1956)Google Scholar
  12. 12.
    Dimarogonas, A.D., Papadopoulos, C.A.: Vibration of Cracked Shafts in Bending. Journal of Sound and Vibration 91(4), 583 (1983)zbMATHCrossRefGoogle Scholar
  13. 13.
    Draminsky, P.: Secondary Resonance and Subharmonics in Torsional Vibration. In: Acta Polytechnica, Scandinavia, Copenhagen, vol. 10 (1961)Google Scholar
  14. 14.
    Dunkerley, S.: On the Whirling of Vibration of Shafts, Philos. In: Philos. Trans. Roy. Soc., Series A, vol. 185, p. 279.(1894)Google Scholar
  15. 15.
    Ehrich, F.F.: Shaft Whirl Induced by Rotor Internal Damping. Journal of Applied Mechanics 23(1), 109 (1964)Google Scholar
  16. 16.
    Ehrich, F.F.: Self Excited Vibration, Shock and Vibration Handbook. McGraw-Hill, New York (1987)Google Scholar
  17. 17.
    Ehrich, F.F.: Handbook of Rotor Dynamics. McGraw-Hill, New York (1992)Google Scholar
  18. 18.
    Ehrich, F.F.: Nonlinear Phenomena in Dynamic Response of Rotors in Anisotropic Mounting Systems. ASME Special 50th Anniversary Design Issue 117, 154 (1995)Google Scholar
  19. 19.
    Floquet, G.: Sur les équations différentielles linéaires à coefficients périodiques. Ann. École Norm. Sup. 12, 47 (1883)MathSciNetGoogle Scholar
  20. 20.
    Föppl, O.: Das Problem der Lavalschen Turbinenwelle. Der Civilingenieur 4, 335 (1895)Google Scholar
  21. 21.
    Föppl, O.: Z. f. gesamte Turb. Wesen 19–18Google Scholar
  22. 22.
    Föppl, O.: Zeitschrift der VDI, p. 866 (1919)Google Scholar
  23. 23.
    Gasch, R.: Dynamic Behavior of a Simple Rotor with a Cross-Sectional Crack. In: Proc. I Mech. E Conf. Vibrations in Rotating Machinery, p. 123. Cambridge (1976) C178/76Google Scholar
  24. 24.
    Gasch, R., Pfutzner, H.: Rotordynamik, Springer Verlag (1975)Google Scholar
  25. 25.
    Gibbons, C.B.: Coupling Misalignment Forces. In: Proceedings Fifth Turbomachinery Symposium, pp. 111–116. Texas A&M University, Gas Turbine Laboratories (1976)Google Scholar
  26. 26.
    Goldsborough, G.R.: Torsional Vibration in Reciprocating Engine Shafts. Proc. Roy. Soc. 109, 99 (1925)CrossRefGoogle Scholar
  27. 27.
    Goldsborough, G.R.: The Properties of Torsional Vibration in Reciprocating Engine Shafts. Proc. Roy. Soc. 113, 259 (1926)CrossRefGoogle Scholar
  28. 28.
    Green, R.: Gyroscopic Effects of the Critical Speeds of Flexible Rotors. Journal Applied Mechanics 15, 369 (1948)Google Scholar
  29. 29.
    Gümbel, Dinglers Polytechnic Journal, p. 235 (1917)Google Scholar
  30. 30.
    Gümbel, Dinglers Polytechnic Journal, p. 71 (1918)Google Scholar
  31. 31.
    Gunter, E.J.: Dynamic Stability of Rotor Bearing System. NASA report SP 113 (1966)Google Scholar
  32. 32.
    Harris, C.M., Crede, C.E.: Shock and Vibration Handbook. McGraw-Hill, New York (1981)Google Scholar
  33. 33.
    Holzer, H.: Die Berechnung der Drehschwingungen. Springer, Heidelberg (1921)zbMATHGoogle Scholar
  34. 34.
    Holzer, H.: Tabular Method for Torsional Vibration Analysis of Multiple-Rotor ShSft systems. Machine Design, 141 (1922)Google Scholar
  35. 35.
    Iwatsubo, T.: Vibration of Asymmetric Shaft. JSME 37, 1503 (1971)Google Scholar
  36. 36.
    Iwatsubo, T., Sheng, B.C., Matsumoto, T.: An Experimental Study on the Static and Dynamic Characteristics of Pump Annular Seals. NASA CP 3026, 229 (1988)Google Scholar
  37. 37.
    Jeffcott, H.H.: The Lateral Vibration of Loaded Shafts in the Neighborhood of a Whirling Speed – The Effect of Want of Balance. In: Philos. Mag.. 6, vol. 37, p. 304 (1919)Google Scholar
  38. 38.
    Kimball, A.L.: Internal Friction Theory of Shaft Whipping. General Electric Review 27, 244 (1924)Google Scholar
  39. 39.
    Klompas, N.: Nature of Vibratory Waves in Bladed Disks. 2001-GT 0291 (2001)Google Scholar
  40. 40.
    Krämer, E.: Dynamics of Rotors and Foundations. Springer, Berlin (1993)Google Scholar
  41. 41.
    Kutta, W.: Beiträge zur näherungsweisen Integration totaler Differentialgleichungen, Ph. D. Thesis, University of Munich (1900)Google Scholar
  42. 42.
    Lee, Y.S.: Modeling and Vibration Analysis of Misaligned Rotor-Ball Bearing Systems, Ph.D. Thesis, KAIST, Korea (1998)Google Scholar
  43. 43.
    Lomakin, A.A.: Feed Pumps of the SWP-220-280 Type with Ultra-High Operating Data. Energomashinotroenie 2 (1955)Google Scholar
  44. 44.
    Lomakin, A.A.: Calculation of Critical Speeds and Securing of the Dynamic Stability of Hydraulic High-Pressure Machines with Reference of the Forces Arising in the Gap Seals. Energomashinotroenie 4(1) (1958)Google Scholar
  45. 45.
    Lund, J.W.: Rotor Bearing Dynamic Design Technology, Part III: Design Handbook for Fluid Film Bearings. In: Part V: Computer Program for Unbalance Response and Stability, vol. 45, Mechanical Technology Inc (1965) AFAPL-Tr-65-45.Google Scholar
  46. 46.
    Lund, J.W.: Stability and Damped Critical Speeds of a Flexible Rotor in Fluid Film Bearings. Journal of Engineering for Industry, Trans. ASME 92, 509 (1974)CrossRefGoogle Scholar
  47. 47.
    Mathieu, E.: Mémoire sur le Mouvement Vibratoire d’une Membrane de forme Elliptique. In: Journal des Mathématique Pures et Appliquées, p. 137 (1868)Google Scholar
  48. 48.
    Mayes, I.W., Davies, W.G.R.: The Vibrational Behavior of A Rotating Shaft System Containing A Transverse Crack. In: Proceedings I Mech. E Conf. Vibrations in Rotating Machinery, vol. C168/76, p. 53. Cambridge (1976)Google Scholar
  49. 49.
    Mayes, I.W., Davies, W.G.R.: A Method of Calculating Vibrational Behavior of Coupled Rotating Shafts Containing a Transverse Crack. Proceedings I Mech. E Conf. Vibrations in Rotating Machinery C254/80, 18 (1980)Google Scholar
  50. 50.
    Mayes, I.W., Davies, W.G.R.: Analysis of the Response of a Multi-Rotor-Bearing System Containing a Transverse Crack in a Rotor. Journal Vib. Acoust. Stress and Rel. in Des. 106, 139 (1984)Google Scholar
  51. 51.
    McLachlan, N.W.: Theory and Application of Mathieu Functions, Dover (1962)Google Scholar
  52. 52.
    Morrison, D., Peterson, A.N.: Criteria for Unstable Oil Whirl of Flexible Rotor. In: Proc. I Mech E, vol. 179(3J), p. 45 (1964)Google Scholar
  53. 53.
    Morton, P.G.: Influence of Coupled Asymmetric Bearings on the Motion of a Massive Flexible Rotor. Proc. Inst. Mech. Engrs. 182(13), 255 (1967)CrossRefGoogle Scholar
  54. 54.
    Nataraj, C., Nelson, H.D.: The Dynamics of a Rotor System with a Cracked Shaft. Journal Vib. Acoustic. Stress and Rel. in Des. 108, 189 (1986)Google Scholar
  55. 55.
    Newkirk, B.L.: Shaft Whipping. General Electric Review 27, 169 (1924)Google Scholar
  56. 56.
    Newkirk, B.L., Taylor, H.D.: Oil Film Whirl – An Investigation of Disturbances on Oil Film in Journal Bearings. General Electric Review 28, 559 (1925)Google Scholar
  57. 57.
    Nordmann, R., Dietzen, F.J.: Finite-Difference Analysis of Rotor dynamic Seal Coefficients for An Eccentric Shaft Position. In: Proceedings Vibrations in Rotating Machinery Conf. I. Mech. E., p. 379 (1988)Google Scholar
  58. 58.
    Nordmann, R., Massman, H.: Identification of Dynamic Coefficients of Annular Turbulent Seals. NASA, 295 (1984)Google Scholar
  59. 59.
    Ocvirk, F.W.: Short Bearing Approximation for Full Journal Bearings. NASA TN 2808 (1952)Google Scholar
  60. 60.
    Oravsky, V., Rao, J.S.: Dynamic Characteristics of Two Different Systems with Variable Inertia controlled by Same Equations. In: Proceedings I Mech. E Conference Transactions, Sixth Intl. Conf. on Vibrations in Rotating Machinery, p. 609. Oxford (1996)Google Scholar
  61. 61.
    Petroff, N.: Reibung in Maschinen und Wirkung des Schmiermittels. Original Russisch, Neue Theorie der Reibung, Leipzig 1887 (1883)Google Scholar
  62. 62.
    Pinkus, O., Sternlicht, B.: Theory of Hydrodynamic Lubrication. McGraw-Hill, New York (1961)zbMATHGoogle Scholar
  63. 63.
    Prandtl, L.: Beitrage zur Frage der Kritischen Drehzahlen. In: Dinglers Polytechnic Journal, p. 179 (1918)Google Scholar
  64. 64.
    Rankine, W.J.M.: On the Centrifugal Force of Rotating Shafts. Engineer 27, 249 (1869)Google Scholar
  65. 65.
    Rao, J.S.: Synchronous Whirl of a Flexible Rotor in Hydrodynamic Bearings. Mechanism and Machine Theory 17(2), 143 (1982)CrossRefGoogle Scholar
  66. 66.
    Rao, J.S.: Rotor Dynamics. John Wiley & Sons, New Age International, Chichester (1983)Google Scholar
  67. 67.
    Rao, J.S.: Instability of Rotors in Fluid Film Bearings. ASME J. Vib. Acoustic. Stress Rel. Des. 105, 274 (1983)Google Scholar
  68. 68.
    Rao, J.S.: Instability of Rotors Mounted on Fluid Film Bearings with a Negative Cross-Coupled Stiffness Coefficient. Mechanism and Machine Theory 20(3), 181 (1985)CrossRefGoogle Scholar
  69. 69.
    Rao, J.S.: Advanced Theory of Vibration. John Wiley & Sons, Chichester (1992)Google Scholar
  70. 70.
    Rao, J.S.: A Note on Quality Factor of Rotor with Hydrodynamic Bearings. Journal of Engineering for Gas Turbines and Power, Trans. ASME 115, 261 (1993)CrossRefGoogle Scholar
  71. 71.
    Rao, J.S., Raju, R.J., Reddy, K.B.V.: Experimental Investigation on Oil Whip of Flexible Rotors. Tribology, 100 (1970)Google Scholar
  72. 72.
    Rao, J.S., Saravana, M.: Numerical Simulation of Seal Flow and Determination of Stiffness and Damping Coefficients. In: Proceedings 7th IFToMM-Conference on Rotor Dynamics, Vienna, Austria, pp. 25–28 (2006)Google Scholar
  73. 73.
    Rao, J.S., Sharma, M.: Dynamic Analysis of Bowed Rotors, Advances in Vibration Engineering. Journal of Vibration Institute of India 2(2), 128 (2003)Google Scholar
  74. 74.
    Rao, J.S., Sreenivas, R.: Dynamic Analysis of Misaligned Rotor Systems, Advances in Vibration Engineering. Journal of Vib Institute of India 2(1), 1 (2003)Google Scholar
  75. 75.
    Rao, J.S., Sreenivas, R., George, P.: Dynamics of High Speed Cryo Pump Rotors. Proceedings 8th International I Mech E Conference on Vibrations in Rotating Machinery,C623/103 467 (2004)Google Scholar
  76. 76.
    Rayleigh, J.W.S.: Theory of Sound. Macmillan, London (1877)Google Scholar
  77. 77.
    Reynolds, O.: On the Theory of Lubrication and its Application to Mr. Beauchamp Tower’s Experiments. Philos. Trans. Royal Society 1, 177 (1886)Google Scholar
  78. 78.
    Robertson, D.: Whirling of Journal in Sleeve Bearings. Philos. Mag. 15, 113 (1933)Google Scholar
  79. 79.
    Scarborough, J.B.: Numerical Mathematical Analysis. Johns Hopkins Press (1950)Google Scholar
  80. 80.
    Schmied, J., Krämer, E.: Vibrational Behavior of a Rotor with a Cross-sectional Crack. In: Proc. I Mech. E Conf. Vibrations in Rotating Machinery, Edinburgh, vol. 84, p. 183 (1984) C279/84Google Scholar
  81. 81.
    Sommerfeld, O.Z.: Math. Phys., vol. 50, p. 97 (1904)Google Scholar
  82. 82.
    Stodola, A.: Dampf- und Gasturbinen, Springer, Berlin. Translation, Steam and Gas Turbines, McGraw-Hill (1910)Google Scholar
  83. 83.
    Stodola, A.: Schweiz Bauztg., 69th edn., pp. 93–229 (1917)Google Scholar
  84. 84.
    Stodola, A.: Dinglers Polytechnic Journal, pp. 1, 17, 117 and 135 (1918a)Google Scholar
  85. 85.
    Stodola, A.: Dinglers Polytechnic Journal, p. 182 (1918b)Google Scholar
  86. 86.
    Subbaiah, R., Bhat, R.B., Sankar, T.S., Rao, J.S.: Backward Whirl in a Simple Rotor Supported on Hydrodynamic Bearings, NASA Conf. Publication 2409, p. 145 (1985)Google Scholar
  87. 87.
    Taylor, H.D.: Critical Speed Behavior of Unsymmetrical Shafts. ASME Journal of Applied Mechanics 84, 77 (1945)Google Scholar
  88. 88.
    Thomas, H.: Instabile Eigenschwingungen von Turbinenläufern angefacht durch die Spaltströmungen Stopfbuschen und Beschauflungen. Bulletin de l’AIM 71, 1039 (1958)Google Scholar
  89. 89.
    Thomson, W.T.: Matrix Solution of Vibration of Non-Uniform Beams. ASME Paper 49A-11 (1949)Google Scholar
  90. 90.
    Timoshenko, S.P.: Vibration Problems in Engineering. D. Van Nostrand Co. Inc. D. Van Nostrand Co. Inc (1955)Google Scholar
  91. 91.
    Tondl, A.: Some Problems of Rotordynamics, Chapman and Hall (1965)Google Scholar
  92. 92.
    Tower, B.: First Report on Friction Experiments (Friction of Lubricated Bearings). In: Proc. Instn. of Mech. Engrs, p. 632 (1883)Google Scholar
  93. 93.
    Urlichs, K.: Leakage Flow in Thermal Turbomachines as the Origin of Vibration Exciting Lateral Forces. NASA TT F 17409 (1976)Google Scholar
  94. 94.
    Vanderplaats, G.N.: Structural Optimization by Methods of Feasible Directions, Computers and Structures, vol. Computers and Structures 3, 739 (1973)CrossRefGoogle Scholar
  95. 95.
    Whittaker, E.T.: On the General Solution of Mathieu’s Equation. Proc. Edinburgh Math. Soc. 32, 75 (1914)CrossRefGoogle Scholar
  96. 96.
    Wohlrab, R.: Experimentelle Ermittlung Spaltsströmungsbedingter Kräfte an Turbinenstufen und Deren Einfluss auf die Laufstabilität Einfacher Rotoren, Doctoral Thesis. In: Technical University, Munich. (1975)Google Scholar

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