A Review about Crack Modelling
Cracked rotating shafts have been the object of studies and investigations since the 1970s, even if some failure cases are also reported during the 1950s (see section 1.2), therefore now we have a story lasting about 50 years. Important achievements have been made during these years, the knowledge of the dynamical behaviour of cracked rotors has allowed the presence of cracks to be recognized and cracked rotors to be stopped in time before catastrophic failures. Accurate inspections revealed that cracks had already propagated up to a depth of almost 50% of the diameter in many shafts (see for instance figure 2.15), which is obviously a very critical situation. Bearing in mind the fact that it is generally believed that propagating velocity increases exponentially, in many of these cases some further days of operation would have been sufficient to provoke a catastrophic failure, with the loss of the complete machine train and high risks for people and other equipment; also the loss of production of the unit, before the replacement with a new unit, is a comparable economic loss.
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References
Wauer, J.: On the dynamics of cracked rotors: a literature survey. Applied Mechanics Review 43(1), 13–17 (1990)
Gasch, R.: A survey of the dynamic behaviour of a simple rotating shaft with a transverse crack. Journal of Sound and Vibration 160(2), 313–332 (1993)
Dimarogonas, A.D.: Vibration of cracked structures: a state of the art review. Engineering Fracture Mechanics 55(5), 831–857 (1996)
Sabnavis, G., Kirk, R.G., Kasarda, M., Quinn, D.: Cracked shafts detection and diagnostics: a literature review. The Shock and Vibration Digest 36(4), 287–296 (2004)
Bachschmid, N., Pennacchi, P.: Special Issue: Crack effects in rotordynamics. Mechanical Systems and Signal Processing 22(4), 761–762 (2008)
Inglis, C.E.: Stresses in a plate due to the presence of cracks and sharp corners. Transactions of the Institution of Naval Architects 55, 219–230 (1913)
Griffith, A.A.: The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society A221, 163–198 (1920)
Irwin, G.R.: Fracture Dynamics. In: Fracturing of Metals, pp. 147–166. American Society for Metals, Cleveland (1948)
Irwin, G.R.: Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics 24, 361–364 (1957)
Williams, M.L.: On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics 24, 109–114 (1957)
Zienkiewicz: The finite element method, 4th edn. McGraw-Hill Co., New York (1987)
Barsoum, R.S.: On the Use of isoparametric finite elements in linear fracture mechanics. International Journal for Numeric Methods in Engineering 10, 25–37 (1976)
Henshell, R.D., Shaw, K.G.: Crack tip elements are unnecessary. International Journal for Numeric Methods in Engineering 9, 495–507 (1975)
Manu, C.: Quarter-point elements for curved cracks fronts. Computer & Structures 17, 227–231 (1983)
Pang, H.L.J.: Linear elastic fracture mechanics benchmarks: 2D finite element test cases. Engineering Fracture Mechanics 44(5), 741–751 (1993)
Broek, D.: The practical use of fracture mechanics, pp. 271–274. Kluwer Academic Publishers, Dordrecht (1989)
Hartranft, R.J., Sih, G.C.: Stress singularity for a crack with an arbitrarily curved front. Engineering Fracture Mechanics 9(3), 705–718 (1977)
Parks, D.M.: A stiffness derivative finite element technique for determination of elastic crack tip stress intensity factor. International Journal of Fracture 10, 487–502 (1974)
Suresh: Fatigue of materials. Cambridge University Press, Cambridge (1998)
Buch, A.: Fatigue data handbook. John Wiley and Sons, Chichester (1998)
Paris, P.C., Erdogan, F.: A critical analysis of crack propagation laws. Journal of Basic Engineering 85, 528–534 (1960)
Elber, W.: Fatigue crack closure under cyclic tension. Engineering Fracture Mechanics 2, 37–45 (1970)
Dentsoras, A.J., Dimarogonas, A.D.: Fatigue Crack Propagation in Resonating Structures. Engineering Fracture Mechanics 34(3), 721–728 (1989)
Shih, Y., Chen, J.: Analysis of Fatigue Crack Growth on a Cracked Shaft. International Journal of Fatigue 19(6), 477–485 (1997)
Gasch, R.: Dynamic behaviour of a simple rotor with a cross-sectional crack. In: IMechE Conf. Vibration in Rotating Machinery, paper C 178/76, Cambridge, UK, September 1976, pp. 123–128 (1976)
Mayes, I.W., Davies, W.G.R.: The vibrational behaviour of a rotating shaft system containing a transverse crack. In: IMechE Conf. Vibration in Rotating Machinery, paper C168/76, Cambridge, UK, September 1976, pp. 53–64 (1976)
Darpe, A.K., Gupta, K., Chawla, A.: Coupled bending longitudinal and torsional vibrations of a cracked rotor. Journal of Sound and Vibration 269(1-2), 33–60 (2004)
Papadopoulos, C.A.: Some comments on the calculation of the local flexibility of cracked shafts. Journal of Sound and Vibration 278(4-5), 1205–1211 (2004)
Wu, X., Friswell, M.I., Sawicki, J.T.: Finite element analysis of coupled lateral and torsional vibrations of a rotor with multiple cracks. Proceedings of ASME Turbo Expo 2005 Gas Turbine Technology: Focus for the Future 4, 841–850 (2005)
Varé, C., Andrieux, S.: Cracked beam section model applied to turbine rotors. In: ISCORMA Int. Symposium on Stability Control of Rotating Machinery, South Lake Tahoe, California, USA (August 2001)
Papadopoulos, C.A.: The strain energy release approach for modeling cracks in rotors: A state of the art review. Mechanical Systems and Signal Processing 22(4), 763–789 (2008)
Dimarogonas, A.D., Papadopoulos, C.A.: Vibration of cracked shafts in bending. Journal of Sound and Vibration 91(4), 583–593 (1983)
Chasalevris, A.C., Papadopoulos, C.A.: Identification of multiple cracks under bending Mechanical Systems and Signal Processing 20(7), 1631–1673 (2006)
Andrieux, S., Varé, C.: A 3D cracked beam model with unilateral contact. Application to rotors 21, 793–810 (2002)
Code_Aster@, Numerical simulation software for structural analysis (2006), http://www.code-aster.org
Yamamoto, T., Ishida, Y.: Linear and nonlinear rotordynamics. John Wiley & Sons, Inc., New York (2001)
Muszyńska, A.: Rotordynamics. CRC Press, Boca Raton (2005)
Theis, W.: Längs- und Torsionsschwingungen bei quer angerissenen Wellen (Longitudinal and torsional vibrations of rotating shafts with a transverse crack). VDI-Verlag series 11(131), Düsseldorf (1990)
Gasch, R., Person, M., Weitz, B.: Dynamic behaviour of the Laval rotor with a cracked hollow shaft – a comparison of crack models. In: IMechE Conf. Vibration in Rotating Machinery, paper C314/88, Edinburgh, UK (September 1988)
Schmalhorst, B.: Experimentelle und theoretische Untersuchung zum Schwingungsverhalten angerissener Rotoren (Experimental and theoretical approach to the vibrational behaviour of cracked rotors). VDI-Forschungs-berichte series 11(117), Düsseldorf
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 of Vibration, Acoustics, Stress and Reliability in Design 106, 139–145 (1984)
Friedmann, P.P.: Numerical methods for the treatment of periodic systems with applications to structural dynamics and helicopter rotor dynamics. Computer & Structures 35(4), 329–347 (1990)
Jordan, D.W., Smith, P.: Nonlinear Ordinary Equation- An Introduction to Dynamical System, 3rd edn. Oxford University Press, Oxford (1999)
Meng, G., Gasch, R.: Stability and stability degree of a cracked flexible rotor supported on journal bearings. ASME Journal of Vibration and Acoustics 122, 116–125 (2000)
Meng, G., Gasch, R.: Stabilität eines gleitgelagerten, einfachen Rotors mit Riß (Stability of a cracked rotor in fluidfilm bearings). SIRM-Tagung “Schwingungen in rotierenden Maschinen, Wien (February 1992)
Hiß, F.: Nichtlineare Dynamik und Zustandsbeobachtung gleitgelagerter elastischer Rotoren mit angerissenem Wellenquerschnitt (Nonlinear dynamics and monitoring of flexible rotors in fluidfilm bearings having a transverse crack). Dissertation TU Berlin (1996)
Sanderson, A.F.P.: The vibration behaviour of a large steam turbine generator during crack propagation through the generator rotor. In: IMechE Conf. Vibration in Rotating Machinery, paper C 432/102, Bath, UK (September 1992)
Allianz-Berichte: Schwingungsüberwachung von Turbosätzen – ein Weg zur Erkenntnis von Wellenrissen (Vibration monitoring in turbosets – A way to early crack detection). Bericht 24 (1987)
Lalanne, M., Ferraris, G.: Rotordynamics Prediction in Engineering. John Wiley & Sons Inc., Chichester (1998)
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Bachschmid, N., Pennacchi, P., Tanzi, E. (2010). Crack Modelling. In: Cracked Rotors. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01485-7_5
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