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Research Papers: Gas Turbines: Structures and Dynamics

Parametrically Induced Damping in a Cracked Rotor

[+] Author and Article Information
Zbigniew Kulesza

Faculty of Mechanical Engineering,
Bialystok University of Technology,
Bialystok 15-351, Poland
e-mail: z.kulesza@pb.edu.pl

Jerzy T. Sawicki

Fellow ASME
Center for Rotating Machinery Dynamics and
Control (RoMaDyC),
Washkewicz College of Engineering,
Cleveland State University,
Cleveland, OH 44115-2214
e-mail: j.sawicki@csuohio.edu

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 21, 2016; final manuscript received June 22, 2016; published online August 16, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(1), 012505 (Aug 16, 2016) (8 pages) Paper No: GTP-16-1262; doi: 10.1115/1.4034197 History: Received June 21, 2016; Revised June 22, 2016

A transverse shaft crack in a rotor is usually modeled as a local change in shaft stiffness. This local stiffness change is not constant and varies as a result of a so-called breathing mechanism, explained with periodical opening and closing of crack faces under the load of external forces applied to the rotor. The rotor with a periodically varied stiffness can be modeled as a parametrically excited linear system. In the presence of a parametric excitation, the vibrations of the system can be amplified or damped at specific excitation frequencies. Usually, the frequencies at which the vibrations are amplified are important, since they can affect stability of the system. However, the increased damping at specific frequencies is a significant feature of a parametrically excited system that can have some potentially useful applications. One of such applications can be an early detection of a shaft crack. This paper presents results of numerical analysis of the influence of Rayleigh's damping and gyroscopic effects on the increase in damping in a parametrically excited rotor with a cracked shaft. It is shown that the increase in damping in a parametrically excited system is rather a rare phenomenon that can be observed only at properly selected values of the excitation frequency and Rayleigh's damping. Furthermore, gyroscopic effects influence the exact values of antiresonance frequencies at which the phenomenon appears.

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References

Tondl, A. , 1975, “ Quenching of Self-Excited Vibrations: One- and Two-Frequency Vibrations,” J. Sound Vib., 42(2), pp. 261–271. [CrossRef]
Dohnal, F. , and Verhulst, F. , 2008, “ Averaging in Vibration Suppression by Parametric Stiffness Excitation,” Nonlinear Dyn., 54(3), pp. 231–248. [CrossRef]
Dohnal, F. , 2008, “ Damping by Parametric Stiffness Excitation: Resonance and Anti-Resonance,” J. Vib. Control, 14(5), pp. 669–688. [CrossRef]
Dohnal, F. , and Markert, R. , 2011, “ Enhancement of External Damping of a Flexible Rotor in Active Magnetic Bearings by Time-Periodic Stiffness Variation,” J. Syst. Des. Dyn., 5(5), pp. 856–865.
Dohnal, F. , 2012, “ Experimental Studies on Damping by Parametric Excitation Using Electromagnets,” Proc. Inst. Mech. Eng., Part C, 226(8), pp. 2015–2027. [CrossRef]
Ecker, H. , 2009, “ Parametric Excitation in Engineering Systems,” 20th International Congress of Mechanical Engineering, COBEM, Gramado, Brazil, Nov. 15–20, Paper No. COB09-2246.
Ecker, H. , 2011, “ Beneficial Effects of Parametric Excitation in Rotor Systems,” IUTAM Symposium on Emerging Trends in Rotor Dynamics (IUTAM Bookseries, Vol. 1011), Springer, Dordrecht, The Netherlands, pp. 361–371.
Ecker, H. , and Pumhössel, T. , 2011, “ Parametric Excitation of a Rotor System Due to a Periodic Axial Force,” 7th European Nonlinear Dynamics Conference, ENOC, Rome, Italy, July 24–29.
Kulesza, Z. , and Sawicki, J. T. , 2015, “ Damping by Parametric Excitation in a Set of Reduced-Order Cracked Rotor Systems,” J. Sound Vib., 354, pp. 167–179. [CrossRef]
Sawicki, J. T. , and Kulesza, Z. , 2014, “ Stability of a Cracked Rotor Subjected to Parametric Excitation,” ASME J. Eng. Gas Turbines Power, 137(5), p. 052508. [CrossRef]
Sawicki, J. T. , and Kulesza, Z. , 2015, “ Damping in a Parametrically Excited Cracked Rotor,” Proceedings of the 9th IFToMM International Conference on Rotor Dynamics (Mechanism and Machine Science, Vol. 21), Springer, Cham, Switzerland, pp. 335–345.
Kulesza, Z. , and Sawicki, J. T. , 2012, “ Rigid Finite Element Model of a Cracked Rotor,” J. Sound Vib., 331(18), pp. 4145–4169. [CrossRef]
Kulesza, Z. , and Sawicki, J. T. , 2013, “ New Finite Element Modeling Approach of a Propagating Shaft Crack,” ASME J. Appl. Mech., 80(2), p. 021025. [CrossRef]
Verhulst, F. , 1990, Nonlinear Differential Equations and Dynamical Systems, Springer-Verlag, Berlin, Germany.
Guo, C. , Al-Shudeifat, M. A. , Yan, J. , Bergman, L. A. , McFarland, D. M. , and Butcher, E. A. , 2013, “ Stability Analysis for Transverse Breathing Cracks in Rotor Systems,” Eur. J. Mech., A: Solids, 42, pp. 27–34. [CrossRef]
Han, Q. , and Chu, F. , 2012, “ Parametric Instability of a Rotor-Bearing System With Two Breathing Transverse Cracks,” Eur. J. Mech., A: Solids, 36, pp. 180–190. [CrossRef]
Huang, J. L. , Su, R. K. L. , and Chen, S. H. , 2009, “ Precise Hsu's Method for Analyzing the Stability of Periodic Solutions of Multi-Degrees-of-Freedom Systems With Cubic Nonlinearity,” Comput. Struct., 87(23–24), pp. 1624–1630. [CrossRef]
Turhan, Ö. , 1998, “ A Generalized Bolotin's Method for Stability Limit Determination of Parametrically Excited Systems,” J. Sound Vib., 216(5), pp. 851–863. [CrossRef]
Turhan, Ö. , and Koser, K. , 2004, “ Parametric Stability of Continuous Shafts, Connected to Mechanisms With Position-Dependent Inertia,” J. Sound Vib., 277(1–2), pp. 223–238. [CrossRef]
Al-Shudeifat, M. A. , and Butcher, E. A. , 2011, “ New Breathing Functions for the Transverse Breathing Crack of the Cracked Rotor System: Approach for Critical and Subcritical Harmonic Analysis,” J. Sound Vib., 330(3), pp. 526–544. [CrossRef]
Sawicki, J. T. , Friswell, M. I. , Kulesza, Z. , Wroblewski, A. , and Lekki, J. D. , 2011, “ Detecting Cracked Rotors Using Auxiliary Harmonic Excitation,” J. Sound Vib., 330(7), pp. 1365–1381. [CrossRef]
Al-Shudeifat, M. A. , 2015, “ Stability Analysis and Backward Whirl Investigation of Cracked Rotors With Time-Varying Stiffness,” J. Sound Vib., 348, pp. 365–380. [CrossRef]
Ricci, R. , and Pennacchi, P. , 2012, “ Discussion of the Dynamic Stability of a Multi-Degree-of-Freedom Rotor System Affected by a Transverse Crack,” Mech. Mach. Theory, 58, pp. 82–100. [CrossRef]
Han, Q. , and Chu, F. , 2013, “ Parametric Instability of a Jeffcott Rotor With Rotationally Asymmetric Inertia and Transverse Crack,” Nonlinear Dyn., 73(1), pp. 827–842. [CrossRef]
Sundermeyer, J. N. , and Weaver, R. L. , 1995, “ On Crack Identification and Characterization in a Beam by Non-Linear Vibration Analysis,” J. Sound Vib., 183(5), pp. 857–871. [CrossRef]
Pesch, A. H. , 2008, “ Damage Detection of Rotors Using Electromagnetic Force Actuator: Analysis and Experimental Verification,” M.Sc. thesis, Cleveland State University, Cleveland, OH.

Figures

Grahic Jump Location
Fig. 1

Tested rotor: (a) rigid finite element model and (b) shaft cross section at the crack location

Grahic Jump Location
Fig. 2

Stability surface of the cracked rotor; DG=0; βd=10−4 s

Grahic Jump Location
Fig. 3

Stability surface of the cracked rotor; DG=0; βd=10−5 s

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Fig. 4

Stability surface of the cracked rotor; DG=0; βd=10−6 s

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Fig. 5

Stability surface of the cracked rotor; DG=0; βd=10−7 s

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Fig. 6

Stability surface of the cracked rotor; DG≠0; βd=10−4 s

Grahic Jump Location
Fig. 7

Stability surface of the cracked rotor; DG≠0; βd=10−5 s

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Fig. 8

Stability surface of the cracked rotor; DG≠0; βd=10−6 s

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Fig. 9

Stability surface of the cracked rotor; DG≠0; βd=10−7 s

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Fig. 10

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG=0; βd=10−4 s

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Fig. 11

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG=0; βd=10−5 s

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Fig. 12

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG=0; βd=10−7 s

Grahic Jump Location
Fig. 13

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG≠0; βd=10−4 s

Grahic Jump Location
Fig. 14

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG≠0; βd=10−5 s

Grahic Jump Location
Fig. 15

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG≠0; βd=10−7 s

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