Bladed Disks

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


Bladed-disk vibrations were well studied because of the critical fatigue problems. They are the most stressed systems in machines. Campbell [5], Stodola [52] and Sezawa [48] are amongst the first few who studied the bladed-disks. Kroon [25] applied difference calculus to the case of lashed blades to determine the blade stresses. Though no vibrations were considered, this paper is the first attempt to point out that the whole blade group should be considered. Smith [51] made a two-dimensional free vibrational analysis in the tangential direction using a dynamic stiffness matrix method on a six and twenty bladed group. His contribution was most significant since the group frequencies and mode shapes were determined for the first time as shown in Figure 17.1.


Mode Shape Strain Amplitude Steam Turbine Tapered Twist Blade Root 
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  1. 1.
    Armstrong, E.K., Christie, P.L., Hague, W.M.: Natural Frequencies of Bladed-Discs. In: Proc. I Mech E, vol. 180, part 31, p. 110 (1965)Google Scholar
  2. 2.
    Asai, K., Sakurai, S., Kudo, T., Ozawa, N.: Evaluation of Friction Damping in Dovetail Root Joints Based on Dissipation Energy on Contact Surfaces, ASME Turbo Expo., GT2009-59508 (2009)Google Scholar
  3. 3.
    Bishop, R.E.D., Johnson, D.C.: Mechanics of Vibration. Cambridge University Press, Cambridge (1960)zbMATHGoogle Scholar
  4. 4.
    Burdekin, N., Cowley, A., Back, N.: An Elastic Mechanism for the Micro-Sliding Characteristics between Contacting Machined Surfaces. Journal Mech. Engng. Sci. 20, 121 (1978)CrossRefGoogle Scholar
  5. 5.
    Campbell, W.: Prediction of Steam Turbine Disk Wheels from Axial Vibration. ASME 46(1920) (1924)Google Scholar
  6. 6.
    Cottney, D.J., Ewins, D.J.: Towards the Efficient Vibration Analysis of Shrouded Bladed Disk Assemblies. J. Engng Indus, Trans. ASME, 1054 (1974)Google Scholar
  7. 7.
    Courtney-Pratt, J.S., Eisner, E.: The Effect of a Tangential Force on the Contact of Metallic Bodies. In: Proc. Royal Soc., Series A, p. 529 (1957)Google Scholar
  8. 8.
    Deak, A.L., Baird, R.D.: A Procedure for Calculating the Frequencies of Steam Turbine Exhaust Blades. Trans. ASME 85, 324 (1963)Google Scholar
  9. 9.
    Deresiewicz, H.: Oblique Contact of Non-Spherical Elastic Bodies. Journal of Applied Mechanics 24, 623 (1957)Google Scholar
  10. 10.
    Dye, R.C.F., Henry, T.A.: Vibration Amplitudes of Compressor Blades Resulting from Scatter in Blade Natural Frequencies. Journal of Engineering for Power 91, 182 (1969)Google Scholar
  11. 11.
    Elchuri, V., Smith, G.C.C., Gallo, A.M.: NASTRAN Forced Vibration Analysis of Rotating Cyclic Structures. J. Vib. Acoust. Stress Rel. Des., ASME 1046, 224 (1984)Google Scholar
  12. 12.
    Ewins, D.J.: The Effects of Detuning upon Forced Vibrations of Bladed-Disks. Journal of Sound and Vibration 9, 66 (1969)CrossRefGoogle Scholar
  13. 13.
    Ewins, D.J.: Vibration Characteristics of Bladed-Disc Assemblies. J. Mech. Engng. Sci. 15(3), 165 (1973)CrossRefGoogle Scholar
  14. 14.
    Ewins, D.J., Rao, Y.V.K.S.: Effect of Blade Damping on the Forced Vibration Response of Bladed Discs, SRC Report No. 1, Imperial College, London (1975)Google Scholar
  15. 15.
    Feiner, D.M., Griffin, J.H.: Mistuning Identification of Bladed Disks Using a Fundamental Mistuning Model, Part I: Theory and Part II: Application. Journal of Turbomachinery 126, 150 (2004)CrossRefGoogle Scholar
  16. 16.
    Hagman, L.: Micro-slip and Surface Deformation, Licentiate Thesis, Royal Institute of Technology, Stockholm, Sweden, TRITA-MAE, 1993:5 (1993)Google Scholar
  17. 17.
    Hansen, M.P., et al.: A Method of Evaluating Loose-Blade Mounting as a Means of Suppressing Turbine and Compressor Blade Vibration. In: Proc. SESA, vol. 10, p. 103 (1953)Google Scholar
  18. 18.
    Irretier, H.: Coupled Vibration of Blades in Bending-Bending-Torsion and Discs in Out-of-Plane and In-Plane Motion, ASME 79-DET-90 (1979)Google Scholar
  19. 19.
    Irretier, H.: Spectral Analysis of Mistuned Bladed-Disc Assemblies by Component Mode Synthesis. In: Vibrations of Blades and Bladed-Disc Assemblies, ASME, p. 115 (1983)Google Scholar
  20. 20.
    Jarret, G.W., Warner, P.C.: Vibration of Rotating Tapered Twisted Beams. Journal of Applied Mechanics, ASME 20, 381 (1953)Google Scholar
  21. 21.
    Kenyon, J.A., Griffin, J.H.: Forced Response of Turbine Engine Bladed Disks and Sensitivity in Harmonic Mistuning. Journal of Engineering for Power 125, 352 (2003a)Google Scholar
  22. 22.
    Kenyon, J.A., Griffin, J.H.: Experimental Demonstration of Maximum Mistuned Bladed Disk Forced Response. Journal of Turbomachinery 125, 673 (2003b)CrossRefGoogle Scholar
  23. 23.
    Kenyon, J.A., Griffin, J.H., Feiner, D.M.: Maximum Bladed Disk Forced Response From Distortion of a Structural Mode. Journal of Turbomachinery 125, 673 (2003)CrossRefGoogle Scholar
  24. 24.
    Kirkhope, J., Wilson, G.J.: Analysis of Coupled Blade-Disk Vibration in Axial Flow Turbines and Fans. In: Proceedings 12th AIAA/ASME Conf. Struct. Dyn., Anaheim, CA (1971)Google Scholar
  25. 25.
    Kroon, R.P.: Influence of Lashing and Centrifugal Force on Turbine-Blade Stresses. Trans. ASME 56, 109 (1964)Google Scholar
  26. 26.
    Lazan, B.J.: Damping of Materials and Members in Structural Mechanics. Pergamon Press, Oxford (1968)Google Scholar
  27. 27.
    Marquina, F.J., Coro, A., Gutierrez, A., Alonso, R., Ewins, D.J., Girini, G.: Friction Damping Modeling in High Stress Contact Areas Using Microslip Friction Model. In: Proceedings of ASME Turbo Expo., GT2008-50359 (2008)Google Scholar
  28. 28.
    Mindlin, R.D., Deresiewicz, H.: Elastic Spheres in Contact under Varying Oblique Forces. Journal of Applied Mechanics 20, 327 (1953)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Muszynska, A., Jones, D.I.G.: On Tuned Bladed-Disc Dynamics – Some Aspects of Friction Related Mistuning. Journal of Sound and Vibration 86, 107 (1983)zbMATHCrossRefGoogle Scholar
  30. 30.
    Nashif, A.D., Jones, D.I.G., Henderson, J.P.: Vibration Damping. John Wiley & Sons, Chichester (1985)Google Scholar
  31. 31.
    Olofsson, U.: Cyclic Micro-Slip under Unlubricated Conditions. Tribology International 28, 207 (1995)CrossRefGoogle Scholar
  32. 32.
    Olofsson, U., Hagman, L.: A model for microslip between flat surfaces based on deformation of ellipsoidal elastic bodies. Tribology International 30(8), 599 (1997)CrossRefGoogle Scholar
  33. 33.
    Petrov, E.P., Ewins, D.J.: Analysis of the Worst Mistuning Parameters in Bladed-Disk Assemblies. Journal of Turbomachinery 125, 623 (2003)CrossRefGoogle Scholar
  34. 34.
    Prohl, M.A.: A Method for Calculating Vibration Frequency and Stress of a Banded Group of Turbine Buckets. ASME 80, 169 (1958)Google Scholar
  35. 35.
    Rao, J.S.: Turbomachine Blade Vibration. John Wiley & Sons, Chichester (1991)Google Scholar
  36. 36.
    Rao, J.S.: Mistuning Of Bladed Disk Assemblies to Mitigate Resonance. Advances in Vibration Engineering, Journal of Vibration Institute of India 5(1), 17 (2006)Google Scholar
  37. 37.
    Rao, J.S., Gupta, K., Vyas, N.S.: Blade Damping Measurement in a Spin Rig with Nozzle Passing Excitation Simulated by Electromagnets. Shock & Vib Bulletin 56, part 2, 109 (1986)Google Scholar
  38. 38.
    Rao, J.S., Narayan, R., Ranjith, M.C.: Lifing of Turbomachinery Blades – A Process Driven Approach. In: Proceedings ASME Turbo Expo., Berlin, Germany (2008) GT2008-50231Google Scholar
  39. 39.
    Rao, J.S., Narayan, R., Ranjith, M.C., Rejin, R.: Blade Lifing with Material and Friction Damping. In: Proceedings The Future of Gas Turbine Technology, 4th International Conference, Brussels, Belgium (2008)Google Scholar
  40. 40.
    Rao, J.S., Saldanha, A.: Turbomachine Blade Damping. Journal of Sound and Vibration 262(3), 731 (2003)CrossRefGoogle Scholar
  41. 41.
    Rao, J.S., Shah, C.B., Ganesh, C.L., Rao, Y.V.K.S.: Vibration Characteristics of Aircraft Engine Blade-Disk Assembly. Defence Science Journal 36, 9 (1986)Google Scholar
  42. 42.
    Rao, J.S., Usmani, M.A.W., Ramakrishnan, C.V.: Interface Damping in Blade Attach Damping in Blade Attachment Region. In: Proceedings 3rd International Conference Rotor Dynamics, Lyon, p. 185 (1990)Google Scholar
  43. 43.
    Reshetov, D.N., Levina, Z.M.: Machine Design for Contact Stiffness. Machines and Tooling 36, 15 (1965)Google Scholar
  44. 44.
    Rieger, N.F., Beck, C.M.: Damping Tests on Steam Turbine Blades, EPRI Project RP-1185 (1980)Google Scholar
  45. 45.
    Rowett, F.E.: Elastic Hysteresis in Steel. In: Proceedings Roy. Soc., vol. 89 (1914)Google Scholar
  46. 46.
    Rzadkowski, R.: Dynamics of Rotor, Steam Turbine Rotor Blading, Part Two, Bladed Discs, Maszyny Przepływowe Tom 22, Wrocław Ossolineum (1998)Google Scholar
  47. 47.
    Sanliturk, K.Y., Imregun, M., Ewins, D.J.: Statistical Analysis of Random Mistuning of Bladed Assemblies. Journal of Mechanical Engineering C432/110, 51 (1992)Google Scholar
  48. 48.
    Sezawa, K.: Vibration of Turbine Blades in Packets. Phil. Mag., 164 (1933)Google Scholar
  49. 49.
    Sinha, A.: Computation of the Maximum Amplitude of a Mistuned Bladed Disk Assembly via Infinity Norm. In: Proceedings ASME International Mechanical Engineering Congress and Exposition, vol. AD-55, p. 427 (1997)Google Scholar
  50. 50.
    Sinha, A., Griffin, J.: Effects of Static Friction on the Forced Response of Frictionally Damped Turbine Blades. J. Engng. Power and Gas Turbines, ASME 106, 65 (1984)CrossRefGoogle Scholar
  51. 51.
    Smith, D.M.: Vibrations of Turbine Blades in Packets. In: Proceedings 7th International Congress Applied Mechanics, London, p. 178 (1948)Google Scholar
  52. 52.
    Stodola, A.: Dampf- und Gasturbinen. Springer, Berlin (1910); Translation Steam and Gas Turbines. McGraw-Hill, New York (1927)Google Scholar
  53. 53.
    Swaminatham, M., et al.: On Modal Generation and Nodal Analysis of Flexible Bladed-Disc Assemblies. In: Proceedings ASME Vibrations Conference, vol. 6, p. 49. Bladed Disk-Assemblies, Cambridge, MA (1986)Google Scholar
  54. 54.
    Thomas, J., Subuncu, M.: Vibration Characteristics of Asymmetric Cross-section Bladed Discs under Rotation, ASME 79-DET-94 (1979)Google Scholar
  55. 55.
    Weaver, F.L., Prohl, M.A.: High Frequency Vibration of Steam Turbine Buckets. Trans. ASME 80, 181 (1958)Google Scholar
  56. 56.
    Whitehead, D.S.: Effect of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes. Journal of Mechanical Engineering Science 8(1), 15 (1966)CrossRefGoogle Scholar
  57. 57.
    Whitehead, D.S.: The maximum Factor by Which Forced Vibration of Blades Can Increase due to Mistuning. Journal of Engineering for Gas Turbines and Power 120, 115 (1998)CrossRefGoogle Scholar

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