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Abstract
Ever since Sir Frank Whittle built the first jet engine for aircraft propulsion, rotor dynamics became the key issue in design and continues to be most vexing problem for the designers. The rotors are gradually replaced by drum construction and the bearing supports have become very flexible owing to thin engine casings mounted on the wings. The compressor and turbine rotors are no more coupled serially through couplings as in steam turbines but are mounted one over other as spools. Now, there are several critical speeds of multi spools excited by unbalances and misalignment. The disks mounted on the rotors carrying the blades have also become very flexible with several critical speeds excited by different per rev excitations from flow path and subjected to severe resonances during start up and shut down operations. Besides, these mounted parts have become globally elastic but locally plastic structures and their lifing has become an important design problem. This paper traces the developments taken place leading to optimum designs and life estimation of gas turbine rotating parts.
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References
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- Kearton, W. J., "Steam Turbine Theory and Practice", The English Language Book Society and Pitman Publishing, 7th edition, 1973.
- Jeffcott, H. H., "The Lateral Vibration of Loaded Shafts in the Neighborhood of a Whirling Speed The Effect of Want of Balance", Phi. Mag., Series 6, Vol. 37, 1919, p. 304.
- Rao, J. S., "Rotor Dynamics", 3rd edition, New Age International, New Delhi, 1996.
- Rao, J. S., Sreenivas, R. and Chawla, A., "Analytical and Experimental Investigations on Misaligned Rotors", DD-ABS-025, ISROMAC-9, 2002.
- Holzer, H., Die Berechnung der Drehschwingungen, Springer Verlag OHG, Berlin, 1921.
- Myklestad, N. O., "Vibration Analysis", McGraw Hill, New York, 1944.
- Prohl, M. A., "A General Method of Calculating Critical speeds of Flexible Rotors", J. Applied Mech., Trans. ASME, Series E, Vol. 67, 1945, p. 142.
- Lund, J. W., "Stability and Damped Critical Speeds of a Flexible Rotor in Fluid Film Bearings", Journal of Engineering for Industry, Trans. ASME, Vol. 92, 1974, p. 509.
- Pestel, E. C. and Leckie, F. A., "Matrix Methods in Elastomechanics", McGraw Hill, New York, 1963.
- Eshleman, R. L., "Torsional Response of Internal Combustion Engines", Journal of Engineering for Industry, Trans. ASME, 1976, p. 441.
- Rao, J. S., Rao, D. K. and Bhaskara Sarma, K. V., "The Transient Response of Turbo-Alternator Rotor Systems under Short Circuiting Conditions", Vibrations in Rotating Machinery, Instn. of Mechanical Engrs, Cambridge, England, 1980, p. 271.13. Rayleigh, J. W. S., "Theory of Sound", Macmillan, London, 1877.
- Den Hartog, J. P., "Mechanical Vibration", McGraw Hill, New York, 1956.
- Gupta, K. D., Gupta, K., Rao, J. S. and Bhaskara Sarma, K. V., "Dynamic Response of a Dual Rotor System by Extended Transfer Matrix Method", Proc. Intl. Conf. Vibrations in Rotating Machinery, Instn.
- Mech. Engrs., 1988, p. 599.
- Courant, R., "Variational Methods for the Solution of Problems of Equilibrium and Vibrations", Bull Amer Math Soc., Vol. 49, 1943, p.1.
- Turner, M. J., Clough, R. C., Martin, H. C. and Topp, L. J., "Stiffness and Deflection Analysis of Complex Structures", J. Aero Sci., Vol. 23, 1956, p. 805.
- Ruhl, R. L. and Booker, J. F., "A Finite Element Model for Distributed Parameter Turborotor Systems", Journal of Engineering for Industry, Trans. ASME, Vol. 94, 1972, p.126.
- Nelson, H. D. and McVaugh, J. M., "The Dynamics of Rotor Bearing Systems using Finite Elements", J.
- of Engineering for Industry, Trans. ASME, Vol. 98, May 1976, p. 593.
- Timoshenko, S. P., "On the Transverse Vibrations of Bars of Uniform Cross-section", Phil. Mag., Series 6, Vol. 43, 1922, p. 125.
- Lalanne, M. and Ferraris, G., "Rotordynamics Prediction in Engineering", John Wiley, 2nd edition, 1998.
- Rao, J. S., Shiau, T. N., Chang, J. R. and Siu-Tong Choi., "Dynamic Behavior of Geared Rotors", Journal of Engineering for Gas Turbines and Power, Trans ASME, July 1999,Vol.121, No.3 p.494.
- Rajan, M., Nelson, H. D. and Chen, W. J., "Parameters Sensitivity in the Dynamics of Rotor-Bearing Systems", J Vib. Acoust. Stress and Rel. Des., Trans.ASME, Vol. 108, 1986, p. 197.
- Rao, J. S., Singh, A. K. and Narayana Sharma., "Dynamic Analysis of Combined Rotor-BearingFoundation System", ASME IGTI PWP, Amsterdam, June 2002.
- Shiau, T. N., Rao, J. S. and Chang, J. R., "Dynamic Coupling in Simple Geared Rotor Bearing System", Vibrations in Rotating Machinery, Instn. of Mech.Engrs., C500/127/96, 1996, p. 599.
- Shiau, T. N., Rao, J. S., Chang, J. R. and Siu-Tong Choi., "Dynamic Behavior of Geared Rotors", Journal of Engineering for Gas Turbines and Power, Trans ASME, Vol.121, No.3, 1999, p.494.
- Rao, J. S., Sreenivas, R. and Veeresh, C. V., "Solid Rotor Dynamics", Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Blacksburg, VA, 23-28 June 2002.
- Rao, J. S., "Rotor Dynamics Comes of Age", Keynote Address, Sixth IFToMM International Conference Rotor Dynamics, Sydney, September 30-October 3, 2002, Vol. I, p. 15.
- Rao, J. S., "Aerospace Applications of Solid Model Rotor Dynamics", IPROMM 2005, Indian Institute of Technology Kharagpur, February 24-25, 2005.
- Rao, J. S., Sreenivas, R. and George, P. P., "Dynamics of High Speed Cryo Pump Rotors", 8th International I Mech E Conference on Vibrations in Rotating Machinery, September 7-9, 2004, C623/103/2004, p.467.
- Rao, J. S., "Application of Fracture Mechanics in the Failure Analysis of a Last Stage Steam Turbine Blade", Mechanism and Machine Theory, Vol. 33, No. 5, 1998, p. 599.
- Ludwik, P., Elemente der Technologischen Mechanik, Springer Publication, 1909.
- Hollomon, J. H., "Tensile Deformation", Trans. American Inst. Mining and Metallurgical Engrs., Vol. 162, 1945, p. 268.
- Hertzberg, R. W., "Deformation and Fracture Mechanics of Engineering Materials", John Wiley, 1976.
- Martin, J. F., Topper, T. H. and Sinclair, G. M., "Computer Based Simulation of Cyclic Stress StrainBehavior", T and A.M. Report No. 326, University of Illinois, Urbana, July 1969.
- Neuber, H., "Theory of Stress Concentration for Shear-Strained Prismatical Bodies with Arbitrary Nonlinear Stress-Strain Law", Trans. ASME, J Applied Mechanics, Vol. 8, 1961, p. 544.
- Basquin, O. H., "The Experimental Law of Endurance Tests", Proc. ASTM, Vol. 10, 1910, p. 625.
- Manson, S. S., "Behavior of Materials under Constant Thermal Stress", Heat Transfer Symposium, University of Michigan, Engg. Research Institute, 1953, p. 9.
- Coffin, L. F. Jr., "A Study of the effects of Cyclic Thermal Stresses on A Ductile Material", Trans
- ASME, Vol. 76, 1954, p. 931.
- Rao, J. S. and Saldanha, A., "Turbomachine Blade Damping", Journal of Sound and Vibration, Vol. 262,
- Issue 3, May 2003, pp.731-738.
- Rao, J. S., Vyas, N. S. and Gupta, K., "Blade Damping Measurement in a Spin Rig with Nozzle Passing
- Excitation Simulated by Electromagnets", Shock and Vib Bull, 56, Part 2, 1986, p.109.
- Lazan, B. J., "Damping of Materials and Members in Structural Mechanics", Pergammon Press, New
- York, 1968.
- Rao, J. S. and Vyas, N. S., "Determination of Blade Stresses Under Constant Speed and Transient Conditions with Nonlinear Damping", J of Engg for Gas Turbines and Power, Trans ASME, Vol. 118, No. 2,
- , p. 424.
- Rao, J. S., "Turbine Blade Life Estimation", Narosa Publication, New Delhi and Alpha Science, UK,
- Rao, J. S. and Saravana Kumar, M., "Numerical Simulation of the Flow in a Two Stage Turbine
- driving a Liquid Oxygen Pump", 12th International Symposium on Transport Phenomena and Dynamics
- of Rotating Machinery, Honolulu, Hawaii, February 17-22, 2008, ISROMAC12-2008-20111.
- Rao, J. S. and Vyas, N. S., "Equations of Motion of a Blade Rotating with Variable Angular Velocity",
- Journal of Sound and Vibration, Vol. 155, No. 2, June 1992, p. 327.
- Rao, J. S., Narayan, R. and Ranjith, M. C., "Lifing of Turbomachinery Blades - A Process Driven Approach", GT2008-50231, ASME Turbo Expo 2008,June 9-13, 2008, Berlin, Germany.
- Rao, J. S., Narayan, R. and Ranjith, M. C., "Blade Lifing - A Comprehensive and Process Driven Approach", 4th India/ASEAN HyperWorks Technology Conference 2008, 31st July - 2nd August 2008, Bangalore.
- Rao, J. S. and Suresh, S., "Blade Root Shape Optimization", The Future of Gas Turbine Technology, 3rd
- International Conference, October 11-12, 2006, Brussels, Belgium.
- Rao, J. S., Bhaskar Kishore, Ch. and Vasanthakumar Mahadevappa., "Weight Optimization of Turbine
- Blades", 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery,
- Honolulu, Hawaii, February 17-22, 2008, ISROMAC12-2008-20020.
References
Rankine, W. J., "On the Centrifugal Force of Rotating Shafts", Engineer, Vol. 27, 1869, p.249.
Kearton, W. J., "Steam Turbine Theory and Practice", The English Language Book Society and Pitman Publishing, 7th edition, 1973.
Jeffcott, H. H., "The Lateral Vibration of Loaded Shafts in the Neighborhood of a Whirling Speed The Effect of Want of Balance", Phi. Mag., Series 6, Vol. 37, 1919, p. 304.
Rao, J. S., "Rotor Dynamics", 3rd edition, New Age International, New Delhi, 1996.
Rao, J. S., Sreenivas, R. and Chawla, A., "Analytical and Experimental Investigations on Misaligned Rotors", DD-ABS-025, ISROMAC-9, 2002.
Holzer, H., Die Berechnung der Drehschwingungen, Springer Verlag OHG, Berlin, 1921.
Myklestad, N. O., "Vibration Analysis", McGraw Hill, New York, 1944.
Prohl, M. A., "A General Method of Calculating Critical speeds of Flexible Rotors", J. Applied Mech., Trans. ASME, Series E, Vol. 67, 1945, p. 142.
Lund, J. W., "Stability and Damped Critical Speeds of a Flexible Rotor in Fluid Film Bearings", Journal of Engineering for Industry, Trans. ASME, Vol. 92, 1974, p. 509.
Pestel, E. C. and Leckie, F. A., "Matrix Methods in Elastomechanics", McGraw Hill, New York, 1963.
Eshleman, R. L., "Torsional Response of Internal Combustion Engines", Journal of Engineering for Industry, Trans. ASME, 1976, p. 441.
Rao, J. S., Rao, D. K. and Bhaskara Sarma, K. V., "The Transient Response of Turbo-Alternator Rotor Systems under Short Circuiting Conditions", Vibrations in Rotating Machinery, Instn. of Mechanical Engrs, Cambridge, England, 1980, p. 271.13. Rayleigh, J. W. S., "Theory of Sound", Macmillan, London, 1877.
Den Hartog, J. P., "Mechanical Vibration", McGraw Hill, New York, 1956.
Gupta, K. D., Gupta, K., Rao, J. S. and Bhaskara Sarma, K. V., "Dynamic Response of a Dual Rotor System by Extended Transfer Matrix Method", Proc. Intl. Conf. Vibrations in Rotating Machinery, Instn.
Mech. Engrs., 1988, p. 599.
Courant, R., "Variational Methods for the Solution of Problems of Equilibrium and Vibrations", Bull Amer Math Soc., Vol. 49, 1943, p.1.
Turner, M. J., Clough, R. C., Martin, H. C. and Topp, L. J., "Stiffness and Deflection Analysis of Complex Structures", J. Aero Sci., Vol. 23, 1956, p. 805.
Ruhl, R. L. and Booker, J. F., "A Finite Element Model for Distributed Parameter Turborotor Systems", Journal of Engineering for Industry, Trans. ASME, Vol. 94, 1972, p.126.
Nelson, H. D. and McVaugh, J. M., "The Dynamics of Rotor Bearing Systems using Finite Elements", J.
of Engineering for Industry, Trans. ASME, Vol. 98, May 1976, p. 593.
Timoshenko, S. P., "On the Transverse Vibrations of Bars of Uniform Cross-section", Phil. Mag., Series 6, Vol. 43, 1922, p. 125.
Lalanne, M. and Ferraris, G., "Rotordynamics Prediction in Engineering", John Wiley, 2nd edition, 1998.
Rao, J. S., Shiau, T. N., Chang, J. R. and Siu-Tong Choi., "Dynamic Behavior of Geared Rotors", Journal of Engineering for Gas Turbines and Power, Trans ASME, July 1999,Vol.121, No.3 p.494.
Rajan, M., Nelson, H. D. and Chen, W. J., "Parameters Sensitivity in the Dynamics of Rotor-Bearing Systems", J Vib. Acoust. Stress and Rel. Des., Trans.ASME, Vol. 108, 1986, p. 197.
Rao, J. S., Singh, A. K. and Narayana Sharma., "Dynamic Analysis of Combined Rotor-BearingFoundation System", ASME IGTI PWP, Amsterdam, June 2002.
Shiau, T. N., Rao, J. S. and Chang, J. R., "Dynamic Coupling in Simple Geared Rotor Bearing System", Vibrations in Rotating Machinery, Instn. of Mech.Engrs., C500/127/96, 1996, p. 599.
Shiau, T. N., Rao, J. S., Chang, J. R. and Siu-Tong Choi., "Dynamic Behavior of Geared Rotors", Journal of Engineering for Gas Turbines and Power, Trans ASME, Vol.121, No.3, 1999, p.494.
Rao, J. S., Sreenivas, R. and Veeresh, C. V., "Solid Rotor Dynamics", Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Blacksburg, VA, 23-28 June 2002.
Rao, J. S., "Rotor Dynamics Comes of Age", Keynote Address, Sixth IFToMM International Conference Rotor Dynamics, Sydney, September 30-October 3, 2002, Vol. I, p. 15.
Rao, J. S., "Aerospace Applications of Solid Model Rotor Dynamics", IPROMM 2005, Indian Institute of Technology Kharagpur, February 24-25, 2005.
Rao, J. S., Sreenivas, R. and George, P. P., "Dynamics of High Speed Cryo Pump Rotors", 8th International I Mech E Conference on Vibrations in Rotating Machinery, September 7-9, 2004, C623/103/2004, p.467.
Rao, J. S., "Application of Fracture Mechanics in the Failure Analysis of a Last Stage Steam Turbine Blade", Mechanism and Machine Theory, Vol. 33, No. 5, 1998, p. 599.
Ludwik, P., Elemente der Technologischen Mechanik, Springer Publication, 1909.
Hollomon, J. H., "Tensile Deformation", Trans. American Inst. Mining and Metallurgical Engrs., Vol. 162, 1945, p. 268.
Hertzberg, R. W., "Deformation and Fracture Mechanics of Engineering Materials", John Wiley, 1976.
Martin, J. F., Topper, T. H. and Sinclair, G. M., "Computer Based Simulation of Cyclic Stress StrainBehavior", T and A.M. Report No. 326, University of Illinois, Urbana, July 1969.
Neuber, H., "Theory of Stress Concentration for Shear-Strained Prismatical Bodies with Arbitrary Nonlinear Stress-Strain Law", Trans. ASME, J Applied Mechanics, Vol. 8, 1961, p. 544.
Basquin, O. H., "The Experimental Law of Endurance Tests", Proc. ASTM, Vol. 10, 1910, p. 625.
Manson, S. S., "Behavior of Materials under Constant Thermal Stress", Heat Transfer Symposium, University of Michigan, Engg. Research Institute, 1953, p. 9.
Coffin, L. F. Jr., "A Study of the effects of Cyclic Thermal Stresses on A Ductile Material", Trans
ASME, Vol. 76, 1954, p. 931.
Rao, J. S. and Saldanha, A., "Turbomachine Blade Damping", Journal of Sound and Vibration, Vol. 262,
Issue 3, May 2003, pp.731-738.
Rao, J. S., Vyas, N. S. and Gupta, K., "Blade Damping Measurement in a Spin Rig with Nozzle Passing
Excitation Simulated by Electromagnets", Shock and Vib Bull, 56, Part 2, 1986, p.109.
Lazan, B. J., "Damping of Materials and Members in Structural Mechanics", Pergammon Press, New
York, 1968.
Rao, J. S. and Vyas, N. S., "Determination of Blade Stresses Under Constant Speed and Transient Conditions with Nonlinear Damping", J of Engg for Gas Turbines and Power, Trans ASME, Vol. 118, No. 2,
, p. 424.
Rao, J. S., "Turbine Blade Life Estimation", Narosa Publication, New Delhi and Alpha Science, UK,
Rao, J. S. and Saravana Kumar, M., "Numerical Simulation of the Flow in a Two Stage Turbine
driving a Liquid Oxygen Pump", 12th International Symposium on Transport Phenomena and Dynamics
of Rotating Machinery, Honolulu, Hawaii, February 17-22, 2008, ISROMAC12-2008-20111.
Rao, J. S. and Vyas, N. S., "Equations of Motion of a Blade Rotating with Variable Angular Velocity",
Journal of Sound and Vibration, Vol. 155, No. 2, June 1992, p. 327.
Rao, J. S., Narayan, R. and Ranjith, M. C., "Lifing of Turbomachinery Blades - A Process Driven Approach", GT2008-50231, ASME Turbo Expo 2008,June 9-13, 2008, Berlin, Germany.
Rao, J. S., Narayan, R. and Ranjith, M. C., "Blade Lifing - A Comprehensive and Process Driven Approach", 4th India/ASEAN HyperWorks Technology Conference 2008, 31st July - 2nd August 2008, Bangalore.
Rao, J. S. and Suresh, S., "Blade Root Shape Optimization", The Future of Gas Turbine Technology, 3rd
International Conference, October 11-12, 2006, Brussels, Belgium.
Rao, J. S., Bhaskar Kishore, Ch. and Vasanthakumar Mahadevappa., "Weight Optimization of Turbine
Blades", 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery,
Honolulu, Hawaii, February 17-22, 2008, ISROMAC12-2008-20020.