Research Papers: Gas Turbines: Manufacturing, Materials, and Metallurgy

Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

[+] Author and Article Information
Philip Varney

e-mail: pvarney3@gatech.edu

Itzhak Green

e-mail: itzhak.green@me.gatech.edu
Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

1Corresponding author.

Contributed by the Manufacturing Materials and Metallurgy Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 5, 2013; final manuscript received July 8, 2013; published online September 17, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(11), 112101 (Sep 17, 2013) (8 pages) Paper No: GTP-13-1233; doi: 10.1115/1.4025039 History: Received July 05, 2013; Revised July 08, 2013

The goal of this work is to establish simple condition monitoring principles for diagnosing the depth and location of transverse fatigue cracks in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model, which should account for the crack's depth and location. Two gaping crack models are presented; the first emulates a finite-width notch typically manufactured for experimental purposes, while the second models a gaping fatigue crack. The rotordynamic model used herein is based upon an available overhung rotordynamic test rig that was originally constructed to monitor the dynamics of a mechanical face seal. Four degree-of-freedom, linear equations of motion for both crack models are presented and discussed. Free and forced response analyses are presented, emphasizing results applicable to condition monitoring and, particularly, to diagnosing the crack parameters. The results demonstrate that two identifiers are required to diagnose the crack parameters: the 2X resonance shaft speed and the magnitude of the angular 2X subharmonic resonance. First, a contour plot of the 2X resonance shaft speed versus crack depth and location is generated. The magnitude of the 2X resonance along the desired 2X frequency contour is then obtained, narrowing the possible pairs of crack location and depth to either one or two possibilities. Practical aspects of the suggested diagnostic procedure are discussed, as well as qualitative observations concerning crack detection.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Green, I., and Casey, C., 2005, “Crack Detection in a Rotor Dynamic System by Vibration Monitoring—Part I: Analysis,” ASME J. Eng. Gas Turb. Power, 127, pp. 425–436. [CrossRef]
Varney, P., and Green, I., 2012, “Crack Detection in a Rotordynamic System by Vibration Monitoring—Part II: Extended Analysis and Experimental Results,” ASME J. Eng. Gas Turb. Power, 134(11), p. 112501. [CrossRef]
Lee, A. S., and Green, I., 1994, “Higher Harmonic Oscillations in a Non-Contacting FMR Mechanical Face Seal Test Rig,” ASME J. Vib. Acoust., 116, pp. 161–167. [CrossRef]
Gasch, R., 2008, “Dynamic Behavior of the Laval Rotor With a Transverse Crack,” Mech. Syst. Signal Process., 22, pp. 790–804. [CrossRef]
Green, I., and Etsion, I., 1986, “A Kinematic Model for Mechanical Seals With Antirotation Locks or Positive Drive Devices,” ASME J. Tribol., 108, pp. 42–45. [CrossRef]
Green, I., 2008, “On the Kinematic and Kinetics of Mechanical Seals, Rotors, and Wobbling Body,” Mechanism Mach. Theory, 43, pp. 909–917. [CrossRef]
Lee, A. S., and Green, I., 1994, “Rotordynamics of a Mechanical Face Seal Riding on a Flexible Shaft,” ASME J. Tribol, 116, pp. 345–351. [CrossRef]
Lee, A. S., and Green, I., 1995, “Physical Modeling and Data Analysis of the Dynamic Response of a Flexibly Mounted Rotor Mechanical Seal,” ASME J. Tribol., 117, pp. 130–135. [CrossRef]
Darpe, A., Gupta, K., and Chawla, A., 2004, “Coupled Bending, Longitudinal, and Torsional Vibrations of a Cracked Rotor,” J. Sound Vib., 269(1), pp. 33–60. [CrossRef]
Darpe, A. K., Gupta, K., and Chawla, A., 2004, “Transient Response and Breathing Behavior of a Cracked Jeffcott Rotor,” J. Sound Vib., 272, pp. 207–242. [CrossRef]
Papadopoulos, C. A., 2008, “The Strain Energy Release Rate Approach for Modeling Cracks in Rotors: A State-of-the-Art Review,” Mech. Syst. Signal Process., 22(4), pp. 763–789. [CrossRef]
Dimarogonas, A., and Papadopoulos, C. A., 1983, “Vibration of Cracked Shafts in Bending,” J. Sound Vib., 91(4), pp. 583–593. [CrossRef]
Mayes, I. W., and Davies, W. G. R., 1976, “The Vibration Behaviour of a Rotating Shaft System Containing a Transverse Crack,” Vibrations in Rotating Machinery, IMechE, London, pp. 53–64.
Rao, J. S., 1996, Rotor Dynamics, 3rd ed., New Age International, New Delhi.
Silva, J., and Gomez, A., 1990, “Experimental Dynamic Analysis of Cracked Free-Free Beams,” Exp. Mech., 30(1), pp. 20–25. [CrossRef]
Grabowski, B., 1980, “The Vibration Behavior of a Turbine Rotor Containing a Transverse Shaft Crack,” ASME J. Mech. Design, 102, pp. 140–146. [CrossRef]
Gounaris, G. D., and Papadopoulos, C. A., 2002, “Crack Identification in Rotating Shafts by Coupled Response Measurements,” Eng. Fract. Mech., 69, pp. 339–352. [CrossRef]
Papadopoulos, C. A., and Dimarogonas, A. D., 1987, “Coupled Longitudinal and Bending Vibrations of a Rotating Shaft With an Open Crack,” J. Sound Vib., 117(1), pp. 81–93. [CrossRef]
Quinn, D., Mani, G., Kasarda, E., Bash, T., Inman, D. J., and Kirk, R. G., 2005, “Damage Detection of a Rotating Cracked Shaft Using an Active Magnetic Bearing as a Force Actuator—Analysis and Experimental Verification,” IEEE/ASME Trans. Mechatron., 10(6), pp. 640–647. [CrossRef]
Bucher, I., and Ewins, D. J., 2001, “Modal Analysis and Testing of Rotating Structures,” Philos. Transact. Ser. A Math. Phys. Eng. Sci., 359, pp. 61–96. [CrossRef]
Penny, J. E. T., and Friswell, M. I., 2007, “The Dynamics of Cracked Rotors,” IMAC-XXV: A Conference & Exposition on Structural Dynamics, Orlando, FL, February 19–22, Society for Experimental Mechanics, Bethel, CT.
Varney, P., 2013, “Transverse Fatigue Crack Diagnosis in a Rotordynamic System Using Vibration Monitoring,” Master's thesis, Georgia Institute of Technology, Atlanta, GA.
Casey, C., 2000, “Crack Detection in a Rotordynamic System by Vibration Monitoring,” Master's thesis, Georgia Institute of Technology, Atlanta, GA.
Budynas, R. G., and Nisbett, J. K., 2008, Shigley's Mechanical Engineering Design, 8th ed., McGraw-Hill, New York.
Dimarogonas, A. D., and Paipetis, S., 1983, Analytical Methods in Rotor Dynamics, Applied Science Publishers, London.
Varney, P., and Green, I., 2012, “Rotordynamic Analysis Using the Complex Transfer Matrix,” Proceedings of the ASME International Design Engineering and Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2012), Chicago, IL, August 12–15.
Patel, T. H., Zuo, M. J., and Darpe, A. K., 2011, “Vibration Response of Coupled Rotor Systems With Crack and Misalignment,” IMechE C: J. Mech. Eng. Sci., 225, pp. 700–713. [CrossRef]
Patel, T. H., and Darpe, A. K., 2008, “Vibration Response of a Cracked Rotor in Presence of Rotor-Stator Rub,” J. Sound Vib., 317(3), pp. 841–865. [CrossRef]


Grahic Jump Location
Fig. 1

Comparison of overhung rotordynamic systems: (a) undamaged overhung rotordynamic system; (b) overhung shaft with notch; (c) overhung shaft with gaping fatigue crack

Grahic Jump Location
Fig. 2

Rotor degrees of freedom

Grahic Jump Location
Fig. 3

Relationship between inertial and rotating reference frames

Grahic Jump Location
Fig. 5

Cross section of shaft containing transverse crack

Grahic Jump Location
Fig. 6

2X resonance shaft speed versus crack depth for a fixed-location crack

Grahic Jump Location
Fig. 7

Free response contour plot: 2X resonance shaft speeds: (a) notch; (b) gaping fatigue crack

Grahic Jump Location
Fig. 8

Forced response of a gaping fatigue crack: (a) forced response including imbalance and gravity, at n = 100 Hz; (b) forced response over a range of shaft speeds to demonstrate the 2X resonance shaft speed

Grahic Jump Location
Fig. 9

Magnitude contours of 2X angular resonance (in radians) versus crack location and depth

Grahic Jump Location
Fig. 10

Locus of 2X angular resonance magnitudes for a range of crack depth and location pairs: (a) 73 Hz 2X resonant contour; (b) 70 Hz 2X resonant contour

Grahic Jump Location
Fig. 11

Loci of 2X angular resonance magnitude for many 2X resonance shaft speeds



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In